Subgroups — AGL(1,ℤ/8)×#360 #72342533

Order 2048.

At least 6667 conjugacy classes of subgroups; only the 1562 normal subgroups are shown.

The subgroup lattice has 1059 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72342532	C₂	1	1	yes	maximal, characteristic, complemented
2	#72342531	C₂	1	1	yes	maximal, characteristic, complemented
3	#72342530	C₂	1	1	yes	maximal, characteristic, complemented
4	#72342529	C₂	1	1	yes	maximal, characteristic, complemented
5	#72342528	C₂	1	1	yes	maximal, characteristic, complemented
6	M₁₆×#360	C₂	1	1	yes	maximal, characteristic, complemented
7	#41×#360	C₂	1	1	yes	maximal, characteristic, complemented
8	#72342525	C₂	1	1	yes	maximal, characteristic, complemented
9	#72342524	C₂	1	1	yes	maximal, characteristic, complemented
10	#72342523	C₂	1	1	yes	maximal, characteristic, complemented
11	#72342486	C₂	1	2	yes	maximal, complemented
12	#72342475	C₂	1	2	yes	maximal, complemented
13	#72342452	C₂	1	2	yes	maximal, complemented
14	SD₁₆×#360	C₂	1	2	yes	maximal, complemented
15	#135×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
16	M₃₂×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
17	D₈×#360	C₂	1	2	yes	maximal, complemented
18	#72309855	C₂	1	2	yes	maximal, complemented
19	#72309556	C₂	1	2	yes	maximal, complemented
20	C₂×D₄×#360	C₂	1	1	yes	maximal, characteristic, complemented
21	#106×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
22	#72265070	C₂	1	1	yes	maximal, characteristic, complemented
23	#72227032	C₂	1	2	yes	maximal, complemented
24	#41×#135	C₂²	1	1	yes	characteristic
25	C₂×D₄×#135	C₂²	1	1	yes	characteristic
26	#41×M₃₂	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×M₃₂	C₂²	1	1	yes	characteristic, complemented
28	#41×#106	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×#106	C₂²	1	1	yes	characteristic, complemented
30	#6358832	C₄	1	2	yes	complemented
31	#6358830	C₄	1	2	yes	complemented
32	#6358820	C₄	1	2	yes	complemented
33	#6358818	C₄	1	2	yes	complemented
34	#6358796	C₄	1	1	yes	characteristic, complemented
35	#6358790	C₄	1	1	yes	characteristic, complemented
36	#6358777	C₄	1	1	yes	characteristic, complemented
37	#6358770	C₄	1	1	yes	characteristic, complemented
38	Q₁₆×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic, complemented
39	#6358743	C₄	1	1	yes	characteristic, complemented
40	#6358736	C₄	1	1	yes	characteristic, complemented
41	D₈×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic, complemented
42	SD₁₆×#135	C₂²	1	2	yes	—
43	D₈×#135	C₂²	1	2	yes	—
44	#6358344	C₂²	1	2	yes	—
45	#6358342	C₂²	1	2	yes	—
46	#6357137	C₂²	1	1	yes	characteristic
47	#6353901	C₂²	1	1	yes	characteristic
48	#6353889	C₂²	1	1	yes	characteristic
49	M₁₆×#135	C₂²	1	1	yes	characteristic
50	C₂×C₈×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
51	#497676	C₂²	1	1	yes	characteristic, complemented
52	#497676	C₂²	1	1	yes	characteristic, complemented
53	Q₈×#360	C₂²	1	1	yes	characteristic, complemented
54	Q₈×#360	C₂²	1	1	yes	characteristic, complemented
55	#497552	C₂²	1	1	yes	characteristic, complemented
56	#497552	C₂²	1	1	yes	characteristic, complemented
57	D₄×#360	C₂²	1	2	yes	—
58	D₄×#360	C₂²	1	2	yes	—
59	D₄×#360	C₂²	1	2	yes	complemented
60	D₄×#360	C₂²	1	2	yes	complemented
61	D₄×#360	C₂²	1	1	yes	characteristic, complemented
62	D₄×#360	C₂²	1	1	yes	characteristic, complemented
63	#496497	C₂²	1	1	yes	characteristic, complemented
64	#496363	C₂²	1	1	yes	characteristic, complemented
65	#495564	C₂²	1	1	yes	characteristic, complemented
66	#495527	C₂²	1	1	yes	characteristic, complemented
67	C₂×#13255	C₂²	1	1	yes	characteristic, complemented
68	C₂×#13210	C₂²	1	1	yes	characteristic, complemented
69	#494041	C₂²	1	1	yes	characteristic
70	C₂×#12816	C₂²	1	1	yes	characteristic
71	C₂×C₄×#360	C₂²	1	1	yes	characteristic
72	#483603	C₂²	1	2	yes	complemented
73	#483567	C₂²	1	2	yes	complemented
74	SD₁₆×M₃₂	C₂²	1	2	yes	complemented
75	D₈×M₃₂	C₂²	1	2	yes	complemented
76	#483356	C₂²	1	1	yes	characteristic, complemented
77	#483162	C₂²	1	1	yes	characteristic, complemented
78	#483111	C₂²	1	1	yes	characteristic, complemented
79	#481282	C₂²	1	1	yes	characteristic
80	#481160	C₂²	1	1	yes	characteristic, complemented
81	#481116	C₂²	1	1	yes	characteristic, complemented
82	M₁₆×M₃₂	C₂²	1	1	yes	characteristic, complemented
83	SD₁₆×#106	C₂²	1	2	yes	complemented
84	D₈×#106	C₂²	1	2	yes	complemented
85	#225517	C₂²	1	2	yes	complemented
86	#225516	C₂²	1	2	yes	complemented
87	#191432	C₂²	1	1	yes	characteristic, complemented
88	#189102	C₂²	1	1	yes	characteristic, complemented
89	#189094	C₂²	1	1	yes	characteristic, complemented
90	M₁₆×#106	C₂²	1	1	yes	characteristic, complemented
91	#141779	C₂²	1	2	yes	complemented
92	#141751	C₂²	1	2	yes	complemented
93	#141673	C₂²	1	2	yes	complemented
94	#141643	C₂²	1	2	yes	complemented
95	#141307	C₂²	1	2	yes	complemented
96	#141294	C₂²	1	2	yes	complemented
97	#141250	C₂²	1	2	yes	complemented
98	#141233	C₂²	1	2	yes	complemented
99	#138680	C₂²	1	2	yes	complemented
100	#138680	C₂²	1	2	yes	complemented
101	#138653	C₂²	1	2	yes	complemented
102	#138653	C₂²	1	2	yes	complemented
103	#138653	C₂²	1	2	yes	complemented
104	#138653	C₂²	1	2	yes	complemented
105	#138587	C₂²	1	2	yes	complemented
106	#138587	C₂²	1	2	yes	complemented
107	#136987	C₂²	1	2	yes	complemented
108	#136987	C₂²	1	2	yes	complemented
109	#136918	C₂²	1	2	yes	complemented
110	#136918	C₂²	1	2	yes	complemented
111	#136885	C₂²	1	2	yes	complemented
112	#136885	C₂²	1	2	yes	complemented
113	#136885	C₂²	1	2	yes	complemented
114	#136885	C₂²	1	2	yes	complemented
115	#135033	C₂²	1	2	yes	complemented
116	#135024	C₂²	1	2	yes	complemented
117	#134955	C₂²	1	2	yes	complemented
118	#134940	C₂²	1	2	yes	complemented
119	#131962	C₂²	1	2	yes	complemented
120	#131932	C₂²	1	2	yes	complemented
121	#131902	C₂²	1	2	yes	complemented
122	#131865	C₂²	1	2	yes	—
123	#131865	C₂²	1	2	yes	—
124	#131865	C₂²	1	2	yes	complemented
125	#131865	C₂²	1	2	yes	complemented
126	#131865	C₂²	1	2	yes	complemented
127	#128750	C₂²	1	2	yes	complemented
128	#128735	C₂²	1	2	yes	complemented
129	#128710	C₂²	1	2	yes	complemented
130	C₈×#360	C₂²	1	2	yes	complemented
131	#127784	C₂²	1	1	yes	characteristic, complemented
132	#127759	C₂²	1	1	yes	characteristic, complemented
133	#126884	C₂²	1	1	yes	characteristic, complemented
134	#126695	C₂²	1	1	yes	characteristic, complemented
135	#61436	C₂×C₄	1	1	yes	characteristic, complemented
136	#61435	C₂×C₄	1	1	yes	characteristic, complemented
137	#61433	C₂×C₄	1	1	yes	characteristic, complemented
138	#61431	C₂×C₄	1	1	yes	characteristic, complemented
139	#61430	C₂×C₄	1	1	yes	characteristic, complemented
140	Q₁₆×#41	C₂×C₄	1	1	yes	characteristic, complemented
141	#61427	C₂×C₄	1	1	yes	characteristic, complemented
142	D₈×#41	C₂×C₄	1	1	yes	characteristic, complemented
143	#61393	C₂³	1	1	yes	characteristic
144	Q₈×#135	C₂³	1	1	yes	characteristic
145	#61234	C₂³	1	1	yes	characteristic
146	D₄×#135	C₂×C₄	1	2	yes	complemented
147	D₄×#135	C₂×C₄	1	2	yes	complemented
148	D₄×#135	C₂³	1	2	yes	—
149	D₄×#135	C₂³	1	2	yes	—
150	D₄×#135	C₂³	1	1	yes	characteristic
151	C₂×#3287	C₂×C₄	1	1	yes	characteristic, complemented
152	C₂×D₄×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
153	C₂×#3283	C₂×C₄	1	1	yes	characteristic, complemented
154	C₂×D₄×D₈	C₂×C₄	1	1	yes	characteristic, complemented
155	#60673	C₂³	1	1	yes	characteristic
156	C₂×#3147	C₂³	1	1	yes	characteristic
157	C₂×C₈×#41	C₂³	1	1	yes	characteristic
158	C₂×C₄×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
159	C₂×C₄×#135	C₂³	1	1	yes	characteristic
160	C₂²×C₈×D₄	C₂³	1	1	yes	characteristic
161	Q₈×M₃₂	C₂³	1	1	yes	characteristic, complemented
162	Q₈×M₃₂	C₂³	1	1	yes	characteristic, complemented
163	D₄×M₃₂	C₂³	1	2	yes	—
164	D₄×M₃₂	C₂³	1	2	yes	—
165	D₄×M₃₂	C₂³	1	1	yes	characteristic, complemented
166	D₄×M₃₂	C₂³	1	1	yes	characteristic, complemented
167	#33418	C₂³	1	1	yes	characteristic
168	#33418	C₂³	1	1	yes	characteristic
169	C₂×#2150	C₂³	1	1	yes	characteristic
170	C₂²×#360	D₄	1	1	yes	characteristic
171	C₂²×#360	D₄	1	1	yes	characteristic
172	C₂×C₄×M₃₂	C₂³	1	1	yes	characteristic
173	Q₈×#106	C₂³	1	1	yes	characteristic, complemented
174	Q₈×#106	C₂³	1	1	yes	characteristic, complemented
175	D₄×#106	C₂³	1	2	yes	—
176	D₄×#106	C₂³	1	2	yes	—
177	D₄×#106	C₂³	1	1	yes	characteristic, complemented
178	D₄×#106	C₂³	1	1	yes	characteristic, complemented
179	#20816	C₂³	1	1	yes	characteristic
180	C₂×#1844	C₂³	1	1	yes	characteristic
181	C₂×C₄×#106	C₂³	1	1	yes	characteristic
182	#19986	C₂×C₄	1	2	yes	complemented
183	#19985	C₂×C₄	1	2	yes	complemented
184	SD₁₆×Q₁₆	C₂×C₄	1	2	yes	complemented
185	#19983	C₂×C₄	1	2	yes	complemented
186	#19980	C₂×C₄	1	2	yes	complemented
187	#19979	C₂×C₄	1	2	yes	complemented
188	#19976	C₂×C₄	1	2	yes	complemented
189	#19975	C₂×C₄	1	2	yes	complemented
190	D₈×Q₁₆	C₂×C₄	1	2	yes	complemented
191	#19973	C₂×C₄	1	2	yes	complemented
192	#19973	C₂×C₄	1	2	yes	complemented
193	#19971	C₂×C₄	1	2	yes	complemented
194	D₈×SD₁₆	C₂×C₄	1	2	yes	complemented
195	#19968	C₂×C₄	1	2	yes	complemented
196	#19968	C₂×C₄	1	2	yes	complemented
197	D₈²	C₂×C₄	1	2	yes	complemented
198	#19962	C₂×C₄	1	2	yes	complemented
199	#19960	C₂×C₄	1	2	yes	complemented
200	#19955	C₂×C₄	1	2	yes	complemented
201	#19953	C₂×C₄	1	2	yes	complemented
202	#19943	C₂×C₄	1	2	yes	complemented
203	#19937	C₂×C₄	1	2	yes	complemented
204	#19935	C₂×C₄	1	2	yes	complemented
205	#19933	C₂×C₄	1	2	yes	complemented
206	#19928	C₂×C₄	1	2	yes	complemented
207	#19926	C₂×C₄	1	2	yes	complemented
208	#19908	C₂×C₄	1	2	yes	complemented
209	#19902	C₂×C₄	1	2	yes	complemented
210	#19900	C₂×C₄	1	2	yes	complemented
211	#19898	C₂×C₄	1	2	yes	complemented
212	#19885	C₂×C₄	1	2	yes	complemented
213	#19883	C₂×C₄	1	2	yes	complemented
214	#19647	C₂×C₄	1	2	yes	complemented
215	#19645	C₂×C₄	1	2	yes	complemented
216	#19639	C₂×C₄	1	1	yes	characteristic, complemented
217	#19635	C₂×C₄	1	1	yes	characteristic, complemented
218	#19632	C₂×C₄	1	1	yes	characteristic, complemented
219	#19629	C₂×C₄	1	1	yes	characteristic, complemented
220	#19603	C₂³	1	2	yes	—
221	#19596	C₂³	1	2	yes	—
222	#19269	C₂×C₄	1	2	yes	complemented
223	#19269	C₂×C₄	1	2	yes	complemented
224	#19268	C₂×C₄	1	1	yes	characteristic, complemented
225	#19268	C₂×C₄	1	1	yes	characteristic, complemented
226	#19267	C₂×C₄	1	1	yes	characteristic, complemented
227	#19267	C₂×C₄	1	1	yes	characteristic, complemented
228	#19259	C₂×C₄	1	2	yes	complemented
229	#19258	C₂×C₄	1	2	yes	complemented
230	#19256	C₂×C₄	1	1	yes	characteristic, complemented
231	#19256	C₂×C₄	1	1	yes	characteristic, complemented
232	#19255	C₂×C₄	1	1	yes	characteristic, complemented
233	#19255	C₂×C₄	1	1	yes	characteristic, complemented
234	#19114	C₂³	1	2	yes	—
235	#19105	C₂³	1	2	yes	—
236	#19101	C₂³	1	2	yes	—
237	#19101	C₂³	1	2	yes	—
238	#18039	C₂×C₄	1	2	yes	complemented
239	M₁₆×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
240	M₁₆×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
241	#18035	C₂×C₄	1	2	yes	complemented
242	M₁₆×D₈	C₂×C₄	1	1	yes	characteristic, complemented
243	M₁₆×D₈	C₂×C₄	1	1	yes	characteristic, complemented
244	#17886	C₂³	1	2	yes	—
245	C₈×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
246	C₈×AGL(1,ℤ/8)	C₂×C₄	1	2	yes	—
247	C₈×AGL(1,ℤ/8)	C₂×C₄	1	2	yes	—
248	C₈×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
249	C₈×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
250	C₈×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
251	C₈×AGL(1,ℤ/8)	D₄	1	2	yes	—
252	C₈×AGL(1,ℤ/8)	D₄	1	2	yes	—
253	C₈×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
254	C₈×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
255	C₈×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
256	C₈×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
257	C₂×#1580	D₄	1	2	yes	—
258	C₂×SD₁₆⋊C₈	D₄	1	2	yes	—
259	C₈×#135	C₂³	1	2	yes	—
260	C₂×C₈×SD₁₆	C₂³	1	2	yes	—
261	C₂×C₈×D₈	C₂³	1	2	yes	—
262	#17793	C₂³	1	1	yes	characteristic
263	C₂×#1566	C₂³	1	1	yes	characteristic
264	C₂×#1565	D₄	1	1	yes	characteristic
265	C₂×#1477	D₄	1	1	yes	characteristic
266	C₂×#1478	D₄	1	1	yes	characteristic
267	C₂×C₈×M₁₆	C₂³	1	1	yes	characteristic
268	#13287	C₂³	1	1	yes	characteristic, complemented
269	#13287	C₂³	1	1	yes	characteristic, complemented
270	#13287	C₂³	1	2	yes	complemented
271	#13278	C₂³	1	1	yes	characteristic, complemented
272	#13278	C₂³	1	1	yes	characteristic, complemented
273	#13255	C₂³	1	2	yes	—
274	#13255	C₂³	1	2	yes	—
275	#13255	C₂³	1	1	yes	characteristic, complemented
276	#13255	C₂³	1	1	yes	characteristic, complemented
277	#13210	C₂³	1	2	yes	—
278	#13210	C₂³	1	2	yes	—
279	#13210	C₂³	1	2	yes	—
280	#13210	C₂³	1	2	yes	—
281	#13210	C₂³	1	1	yes	characteristic, complemented
282	#13210	C₂³	1	1	yes	characteristic, complemented
283	#13210	C₂³	1	2	yes	complemented
284	#12816	C₂³	1	1	yes	characteristic
285	#12816	C₂³	1	1	yes	characteristic
286	#12816	C₂³	1	1	yes	characteristic
287	#12816	C₂³	1	1	yes	characteristic
288	#12816	C₂³	1	2	yes	—
289	#12816	C₂³	1	2	yes	—
290	C₄×#360	D₄	1	1	yes	characteristic
291	C₄×#360	D₄	1	1	yes	characteristic
292	C₄×#360	D₄	1	1	yes	characteristic
293	C₄×#360	D₄	1	1	yes	characteristic
294	C₄×#360	C₂³	1	1	yes	characteristic
295	C₄×#360	C₂³	1	1	yes	characteristic
296	C₄×#360	C₂³	1	1	yes	characteristic
297	C₄×#360	C₂³	1	1	yes	characteristic
298	C₂×#1386	D₄	1	1	yes	characteristic
299	C₂×#1386	D₄	1	1	yes	characteristic
300	#12004	C₂³	1	2	yes	complemented
301	#11996	C₂³	1	2	yes	complemented
302	#11936	C₂³	1	2	yes	complemented
303	#11925	C₂³	1	2	yes	—
304	#11925	C₂³	1	2	yes	—
305	#11925	C₂³	1	2	yes	complemented
306	#11607	C₂³	1	2	yes	complemented
307	#11598	C₂³	1	2	yes	—
308	#11598	C₂³	1	2	yes	—
309	#11583	C₂³	1	2	yes	—
310	#11583	C₂³	1	2	yes	—
311	#11583	C₂³	1	2	yes	complemented
312	#11402	C₂³	1	2	yes	complemented
313	C₈×M₃₂	C₂³	1	2	yes	complemented
314	#8814	C₂³	1	2	yes	complemented
315	#8813	C₂³	1	2	yes	complemented
316	#8643	C₂³	1	2	yes	complemented
317	#8642	C₂³	1	2	yes	—
318	#8642	C₂³	1	2	yes	—
319	#8642	C₂³	1	2	yes	complemented
320	#8283	C₂³	1	2	yes	complemented
321	C₈×#106	C₂³	1	2	yes	complemented
322	#7278	C₂³	1	2	yes	complemented
323	#7278	C₂³	1	2	yes	complemented
324	#7278	C₂³	1	2	yes	complemented
325	#7278	C₂³	1	2	yes	complemented
326	#7175	C₂³	1	2	yes	complemented
327	#7175	C₂³	1	2	yes	complemented
328	#7158	C₂³	1	2	yes	complemented
329	#7158	C₂³	1	2	yes	complemented
330	C₂²×AGL(1,ℤ/8)	D₈	1	1	yes	characteristic
331	C₂²×#135	C₂×D₄	1	1	yes	characteristic
332	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
334	C₂²×M₃₂	C₂×D₄	1	1	yes	characteristic
335	C₂²×M₃₂	C₂×D₄	1	1	yes	characteristic
336	#3396	C₂²×C₄	1	1	yes	characteristic, complemented
337	#3395	C₂²×C₄	1	1	yes	characteristic, complemented
338	#3393	C₂²×C₄	1	1	yes	characteristic, complemented
339	#3391	C₂²×C₄	1	1	yes	characteristic, complemented
340	#3383	C₂²×C₄	1	1	yes	characteristic, complemented
341	Q₈×Q₁₆	C₂²×C₄	1	1	yes	characteristic, complemented
342	#3380	C₂²×C₄	1	1	yes	characteristic, complemented
343	Q₈×D₈	C₂²×C₄	1	1	yes	characteristic, complemented
344	#3342	C₂²×C₄	1	1	yes	characteristic, complemented
345	#3341	C₂²×C₄	1	1	yes	characteristic, complemented
346	#3338	C₂²×C₄	1	1	yes	characteristic, complemented
347	#3334	C₂²×C₄	1	1	yes	characteristic, complemented
348	#3287	C₂²×C₄	1	2	yes	—
349	#3287	C₂²×C₄	1	2	yes	—
350	#3287	C₂²×C₄	1	1	yes	characteristic, complemented
351	D₄×Q₁₆	C₂²×C₄	1	2	yes	—
352	D₄×Q₁₆	C₂²×C₄	1	2	yes	—
353	D₄×Q₁₆	C₂²×C₄	1	1	yes	characteristic, complemented
354	#3283	C₂²×C₄	1	2	yes	—
355	#3283	C₂²×C₄	1	2	yes	—
356	#3283	C₂²×C₄	1	1	yes	characteristic, complemented
357	D₄×D₈	C₂²×C₄	1	2	yes	—
358	D₄×D₈	C₂²×C₄	1	2	yes	—
359	D₄×D₈	C₂²×C₄	1	1	yes	characteristic, complemented
360	#3170	C₂²×C₄	1	1	yes	characteristic
361	#3170	C₂²×C₄	1	1	yes	characteristic
362	#3169	C₂²×C₄	1	1	yes	characteristic
363	#3169	C₂²×C₄	1	1	yes	characteristic
364	#3160	C₂⁴	1	1	yes	characteristic
365	#3147	C₂²×C₄	1	2	yes	—
366	#3147	C₂⁴	1	1	yes	characteristic
367	#3147	C₂⁴	1	2	yes	—
368	C₂×#494	C₂²×C₄	1	1	yes	characteristic
369	C₂×#493	C₂²×C₄	1	1	yes	characteristic
370	C₈×#41	C₂²×C₄	1	1	yes	characteristic
371	C₈×#41	C₂²×C₄	1	1	yes	characteristic
372	C₈×#41	C₂²×C₄	1	1	yes	characteristic
373	C₈×#41	C₂²×C₄	1	1	yes	characteristic
374	C₈×#41	C₂×D₄	1	1	yes	characteristic
375	C₈×#41	C₂×D₄	1	1	yes	characteristic
376	C₈×#41	C₂×D₄	1	1	yes	characteristic
377	C₈×#41	C₂×D₄	1	1	yes	characteristic
378	C₂×C₈×Q₈	C₂×D₄	1	1	yes	characteristic
379	C₂×C₈×Q₈	C₂⁴	1	1	yes	characteristic
380	C₄×AGL(1,ℤ/8)	C₂²⋊C₄	1	2	yes	—
381	C₄×AGL(1,ℤ/8)	C₂²⋊C₄	1	2	yes	—
382	C₄×AGL(1,ℤ/8)	C₂²⋊C₄	1	1	yes	characteristic
383	C₄×AGL(1,ℤ/8)	C₂²⋊C₄	1	1	yes	characteristic
384	C₄×AGL(1,ℤ/8)	C₂²⋊C₄	1	1	yes	characteristic
385	C₄×AGL(1,ℤ/8)	C₂²⋊C₄	1	1	yes	characteristic
386	C₄×AGL(1,ℤ/8)	SD₁₆	1	1	yes	characteristic
387	C₄×AGL(1,ℤ/8)	SD₁₆	1	1	yes	characteristic
388	C₄×AGL(1,ℤ/8)	SD₁₆	1	1	yes	characteristic
389	C₄×AGL(1,ℤ/8)	SD₁₆	1	1	yes	characteristic
390	C₄×AGL(1,ℤ/8)	SD₁₆	1	2	yes	—
391	C₄×AGL(1,ℤ/8)	SD₁₆	1	2	yes	—
392	C₂×#442	D₈	1	2	yes	—
393	C₂×#440	D₈	1	2	yes	—
394	C₄×#135	C₂²×C₄	1	1	yes	characteristic
395	C₄×#135	C₂²×C₄	1	1	yes	characteristic
396	C₄×#135	C₂×D₄	1	1	yes	characteristic
397	C₄×#135	C₂×D₄	1	1	yes	characteristic
398	C₄×#135	#41	1	1	yes	characteristic
399	C₄×#135	#41	1	1	yes	characteristic
400	C₄×#135	C₂⁴	1	1	yes	characteristic
401	C₄×#135	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×Q₁₆	C₂²×C₄	1	1	yes	characteristic
403	C₂×C₄×Q₁₆	#41	1	1	yes	characteristic
404	C₂×C₄×SD₁₆	C₂×D₄	1	2	yes	—
405	C₂×C₄×D₈	C₂²×C₄	1	1	yes	characteristic
406	C₂×C₄×D₈	C₂×D₄	1	2	yes	—
407	C₂×C₄×D₈	#41	1	1	yes	characteristic
408	C₂×C₈×D₄	C₂²×C₄	1	1	yes	characteristic
409	C₂×C₈×D₄	C₂²×C₄	1	1	yes	characteristic
410	C₂×C₈×D₄	C₂²×C₄	1	2	yes	—
411	C₂×C₈×D₄	C₂×D₄	1	1	yes	characteristic
412	C₂×C₈×D₄	C₂×D₄	1	1	yes	characteristic
413	C₂×C₈×D₄	C₂×D₄	1	2	yes	—
414	C₂×C₈×D₄	C₂×D₄	1	1	yes	characteristic
415	C₂×C₈×D₄	C₂×D₄	1	2	yes	—
416	C₂×C₈×D₄	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×D₄	C₂⁴	1	2	yes	—
418	C₂×#431	C₂×D₄	1	1	yes	characteristic
419	C₂×#431	C₂×D₄	1	1	yes	characteristic
420	C₂×#428	D₈	1	1	yes	characteristic
421	C₂×#427	C₂×D₄	1	1	yes	characteristic
422	C₂²×#106	C₂×D₄	1	1	yes	characteristic
423	C₂²×#106	C₂×D₄	1	1	yes	characteristic
424	C₂²×C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
425	C₂×#417	D₈	1	1	yes	characteristic
426	C₂×#418	D₈	1	1	yes	characteristic
427	C₂×C₄×M₁₆	C₂×D₄	1	1	yes	characteristic
428	C₂²×C₄×C₈	C₂⁴	1	1	yes	characteristic
429	#2150	C₂⁴	1	1	yes	characteristic
430	#2150	C₂⁴	1	1	yes	characteristic
431	#2150	C₂⁴	1	2	yes	—
432	C₂×#360	C₂×D₄	1	1	yes	characteristic
433	C₂×#360	C₂×D₄	1	1	yes	characteristic
434	C₂×#360	C₂×D₄	1	1	yes	characteristic
435	C₂×#360	C₂×D₄	1	1	yes	characteristic
436	C₂×#360	C₂×D₄	1	1	yes	characteristic
437	C₂×#360	C₂×D₄	1	1	yes	characteristic
438	C₂×#360	C₂×D₄	1	1	yes	characteristic
439	C₂×#360	C₂×D₄	1	1	yes	characteristic
440	C₄×M₃₂	C₂×D₄	1	1	yes	characteristic
441	C₄×M₃₂	C₂×D₄	1	1	yes	characteristic
442	C₄×M₃₂	C₂⁴	1	2	yes	—
443	C₄×M₃₂	C₂⁴	1	1	yes	characteristic
444	C₄×M₃₂	C₂⁴	1	1	yes	characteristic
445	#1844	C₂⁴	1	2	yes	—
446	#1844	C₂⁴	1	1	yes	characteristic
447	#1844	C₂⁴	1	1	yes	characteristic
448	C₄×#106	C₂×D₄	1	1	yes	characteristic
449	C₄×#106	C₂×D₄	1	1	yes	characteristic
450	C₄×#106	C₂⁴	1	1	yes	characteristic
451	C₄×#106	C₂⁴	1	1	yes	characteristic
452	#1713	C₂²×C₄	1	2	yes	complemented
453	#1712	C₂²×C₄	1	2	yes	complemented
454	#1709	C₂²×C₄	1	2	yes	complemented
455	#1709	C₂²×C₄	1	2	yes	complemented
456	#1707	C₂²×C₄	1	2	yes	complemented
457	#1707	C₂²×C₄	1	2	yes	complemented
458	#1706	C₂²×C₄	1	2	yes	complemented
459	#1706	C₂²×C₄	1	2	yes	complemented
460	#1675	C₂²×C₄	1	2	yes	—
461	#1675	C₂²×C₄	1	2	yes	—
462	#1673	C₂²×C₄	1	2	yes	—
463	#1673	C₂²×C₄	1	2	yes	—
464	#1670	C₂²×C₄	1	2	yes	complemented
465	#1670	C₂²×C₄	1	2	yes	complemented
466	#1669	C₂²×C₄	1	2	yes	—
467	#1669	C₂²×C₄	1	2	yes	—
468	#1669	C₂²×C₄	1	2	yes	complemented
469	#1669	C₂²×C₄	1	2	yes	complemented
470	#1668	C₂²×C₄	1	2	yes	complemented
471	#1668	C₂²×C₄	1	2	yes	complemented
472	#1667	C₂²×C₄	1	2	yes	—
473	#1667	C₂²×C₄	1	2	yes	—
474	#1667	C₂²×C₄	1	2	yes	complemented
475	#1667	C₂²×C₄	1	2	yes	complemented
476	#1591	C₂²×C₄	1	2	yes	complemented
477	#1591	C₂²×C₄	1	2	yes	complemented
478	#1589	C₂²×C₄	1	2	yes	complemented
479	#1589	C₂²×C₄	1	2	yes	complemented
480	#1580	C₂²⋊C₄	1	2	yes	—
481	#1580	C₂²⋊C₄	1	2	yes	—
482	#1580	C₂²⋊C₄	1	2	yes	—
483	#1580	C₂²⋊C₄	1	2	yes	—
484	#1580	C₂²⋊C₄	1	2	yes	—
485	#1580	C₂²⋊C₄	1	2	yes	—
486	#1580	C₂²⋊C₄	1	2	yes	—
487	#1580	C₂²⋊C₄	1	2	yes	—
488	SD₁₆⋊C₈	C₂²⋊C₄	1	2	yes	—
489	SD₁₆⋊C₈	C₂²⋊C₄	1	2	yes	—
490	SD₁₆⋊C₈	C₂²⋊C₄	1	2	yes	—
491	SD₁₆⋊C₈	C₂²⋊C₄	1	2	yes	—
492	SD₁₆⋊C₈	C₂²⋊C₄	1	2	yes	—
493	SD₁₆⋊C₈	C₂²⋊C₄	1	2	yes	—
494	SD₁₆⋊C₈	C₂²⋊C₄	1	2	yes	—
495	SD₁₆⋊C₈	C₂²⋊C₄	1	2	yes	—
496	C₈×Q₁₆	C₂²×C₄	1	2	yes	complemented
497	C₈×Q₁₆	C₂²×C₄	1	2	yes	complemented
498	C₈×SD₁₆	C₂²×C₄	1	2	yes	—
499	C₈×SD₁₆	C₂²×C₄	1	2	yes	—
500	C₈×SD₁₆	C₂²×C₄	1	2	yes	—
501	C₈×SD₁₆	C₂²×C₄	1	2	yes	—
502	C₈×SD₁₆	C₂×D₄	1	2	yes	—
503	C₈×SD₁₆	C₂×D₄	1	2	yes	—
504	C₈×SD₁₆	C₂×D₄	1	2	yes	—
505	C₈×SD₁₆	C₂×D₄	1	2	yes	—
506	C₈×D₈	C₂²×C₄	1	2	yes	—
507	C₈×D₈	C₂²×C₄	1	2	yes	—
508	C₈×D₈	C₂²×C₄	1	2	yes	—
509	C₈×D₈	C₂²×C₄	1	2	yes	—
510	C₈×D₈	C₂²×C₄	1	2	yes	complemented
511	C₈×D₈	C₂²×C₄	1	2	yes	complemented
512	C₈×D₈	C₂×D₄	1	2	yes	—
513	C₈×D₈	C₂×D₄	1	2	yes	—
514	C₈×D₈	C₂×D₄	1	2	yes	—
515	C₈×D₈	C₂×D₄	1	2	yes	—
516	#1568	C₂²×C₄	1	2	yes	—
517	#1567	C₂²×C₄	1	1	yes	characteristic
518	#1567	C₂²×C₄	1	1	yes	characteristic
519	#1565	C₂²⋊C₄	1	1	yes	characteristic
520	#1565	C₂²⋊C₄	1	1	yes	characteristic
521	#1565	C₂²⋊C₄	1	1	yes	characteristic
522	#1565	C₂²⋊C₄	1	1	yes	characteristic
523	#1565	C₂²⋊C₄	1	2	yes	—
524	#1565	C₂²⋊C₄	1	2	yes	—
525	#1564	C₂⁴	1	2	yes	—
526	C₂×#335	C₂×D₄	1	2	yes	—
527	C₂×#334	C₂×D₄	1	2	yes	—
528	C₂×#334	C₂⁴	1	2	yes	—
529	#1478	C₂²⋊C₄	1	1	yes	characteristic
530	#1478	C₂²⋊C₄	1	1	yes	characteristic
531	#1478	C₂²⋊C₄	1	1	yes	characteristic
532	#1478	C₂²⋊C₄	1	1	yes	characteristic
533	#1478	C₂²⋊C₄	1	2	yes	—
534	#1478	C₂²⋊C₄	1	2	yes	—
535	#1477	C₂²⋊C₄	1	2	yes	—
536	#1477	C₂²⋊C₄	1	2	yes	—
537	#1477	C₂²⋊C₄	1	1	yes	characteristic
538	#1477	C₂²⋊C₄	1	1	yes	characteristic
539	#1477	C₂²⋊C₄	1	1	yes	characteristic
540	#1477	C₂²⋊C₄	1	1	yes	characteristic
541	C₂×Q₈⋊C₈	C₂×D₄	1	2	yes	—
542	C₂×D₄⋊C₈	C₂×D₄	1	2	yes	—
543	C₂×D₄⋊C₈	C₂×D₄	1	2	yes	—
544	C₂×D₄⋊C₈	C₂×D₄	1	2	yes	—
545	C₈×M₁₆	C₂²×C₄	1	1	yes	characteristic
546	C₈×M₁₆	C₂²×C₄	1	1	yes	characteristic
547	C₈×M₁₆	C₂²×C₄	1	2	yes	—
548	C₈×M₁₆	C₂×D₄	1	1	yes	characteristic
549	C₈×M₁₆	C₂×D₄	1	1	yes	characteristic
550	C₈×M₁₆	C₂×D₄	1	2	yes	—
551	C₂×#322	C₂×D₄	1	2	yes	—
552	C₂×C₈²	C₂⁴	1	2	yes	—
553	#1386	C₂×D₄	1	1	yes	characteristic
554	#1386	C₂×D₄	1	1	yes	characteristic
555	#1386	C₂×D₄	1	1	yes	characteristic
556	#1386	C₂×D₄	1	1	yes	characteristic
557	#1386	C₂×D₄	1	1	yes	characteristic
558	#1386	C₂×D₄	1	1	yes	characteristic
559	#1386	C₂×D₄	1	1	yes	characteristic
560	#1386	C₂×D₄	1	1	yes	characteristic
561	C₂²×#41	C₂×D₈	1	1	yes	characteristic
562	C₂³×D₄	C₂×D₈	1	1	yes	characteristic
563	C₂×AGL(1,ℤ/8)	#102	1	1	yes	characteristic
564	C₂×AGL(1,ℤ/8)	#102	1	1	yes	characteristic
565	C₂×AGL(1,ℤ/8)	#102	1	1	yes	characteristic
566	C₂×AGL(1,ℤ/8)	#102	1	2	yes	—
567	C₂×AGL(1,ℤ/8)	#102	1	2	yes	—
568	C₂×AGL(1,ℤ/8)	#102	1	1	yes	characteristic
569	C₂×#135	C₄×D₄	1	1	yes	characteristic
570	C₂×#135	C₄×D₄	1	1	yes	characteristic
571	C₂×#135	C₂²×D₄	1	1	yes	characteristic
572	C₂×#135	C₂²×D₄	1	1	yes	characteristic
573	C₂²×Q₁₆	C₄×D₄	1	1	yes	characteristic
574	C₂²×SD₁₆	C₂×D₈	1	2	yes	—
575	C₂²×D₈	C₄×D₄	1	1	yes	characteristic
576	C₂²×D₈	C₂×D₈	1	2	yes	—
577	C₂²×M₁₆	C₂×D₈	1	1	yes	characteristic
578	C₂²×M₁₆	C₂×D₈	1	1	yes	characteristic
579	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
580	C₂³×C₈	H(5,𝔽₂)	1	1	yes	characteristic
581	C₄×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
582	C₄×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
583	C₄×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
584	C₄×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
585	C₄×#41	C₂×SD₁₆	1	1	yes	characteristic
586	C₄×#41	C₂×SD₁₆	1	1	yes	characteristic
587	C₄×#41	C₂×SD₁₆	1	1	yes	characteristic
588	C₄×#41	C₂×SD₁₆	1	1	yes	characteristic
589	C₂×C₄×Q₈	C₂×D₈	1	1	yes	characteristic
590	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
591	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
592	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
593	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
594	C₂×C₄×D₄	C₂×D₈	1	1	yes	characteristic
595	C₂×C₄×D₄	C₂×D₈	1	2	yes	—
596	C₂×C₄×D₄	C₂×SD₁₆	1	2	yes	—
597	C₂×C₄×D₄	C₂×SD₁₆	1	1	yes	characteristic
598	C₂×C₄×D₄	C₂×SD₁₆	1	1	yes	characteristic
599	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
600	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
601	C₂×#117	C₂×D₈	1	1	yes	characteristic
602	C₂²×C₄⋊C₄	C₂×D₈	1	1	yes	characteristic
603	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
604	C₂×M₃₂	C₂²×D₄	1	1	yes	characteristic
605	C₂×M₃₂	C₂²×D₄	1	1	yes	characteristic
606	C₂×M₃₂	C₂²×D₄	1	1	yes	characteristic
607	C₂×M₃₂	C₂²×D₄	1	1	yes	characteristic
608	#500	C₂³×C₄	1	1	yes	characteristic
609	#500	C₂³×C₄	1	1	yes	characteristic
610	#494	C₂³×C₄	1	1	yes	characteristic
611	#494	C₂³×C₄	1	2	yes	—
612	#493	C₂³×C₄	1	1	yes	characteristic
613	#493	C₂³×C₄	1	2	yes	—
614	C₈×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
615	C₈×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
616	C₈×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
617	C₈×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
618	C₈×Q₈	C₂³×C₄	1	1	yes	characteristic
619	C₈×Q₈	C₂³×C₄	1	1	yes	characteristic
620	C₈×Q₈	C₂²×D₄	1	1	yes	characteristic
621	C₈×Q₈	C₂²×D₄	1	1	yes	characteristic
622	#442	#102	1	2	yes	—
623	#442	#102	1	2	yes	—
624	#442	#102	1	2	yes	—
625	#442	#102	1	2	yes	—
626	#442	#102	1	2	yes	—
627	#442	#102	1	2	yes	—
628	#442	#102	1	2	yes	—
629	#442	#102	1	2	yes	—
630	#440	#102	1	2	yes	—
631	#440	#102	1	2	yes	—
632	#440	#102	1	2	yes	—
633	#440	#102	1	2	yes	—
634	#440	#102	1	2	yes	—
635	#440	#102	1	2	yes	—
636	#440	#102	1	2	yes	—
637	#440	#102	1	2	yes	—
638	C₄×Q₁₆	C₄×D₄	1	1	yes	characteristic
639	C₄×Q₁₆	C₄×D₄	1	1	yes	characteristic
640	C₄×Q₁₆	C₄×D₄	1	1	yes	characteristic
641	C₄×Q₁₆	C₄×D₄	1	1	yes	characteristic
642	C₄×Q₁₆	C₂³×C₄	1	1	yes	characteristic
643	C₄×Q₁₆	C₂³×C₄	1	1	yes	characteristic
644	C₄×Q₁₆	C₂×#41	1	1	yes	characteristic
645	C₄×Q₁₆	C₂×#41	1	1	yes	characteristic
646	C₄×SD₁₆	C₂×C₂²⋊C₄	1	2	yes	—
647	C₄×SD₁₆	C₂×C₂²⋊C₄	1	2	yes	—
648	C₄×SD₁₆	C₂×C₂²⋊C₄	1	2	yes	—
649	C₄×SD₁₆	C₂×C₂²⋊C₄	1	2	yes	—
650	C₄×SD₁₆	C₂×SD₁₆	1	2	yes	—
651	C₄×SD₁₆	C₂×SD₁₆	1	2	yes	—
652	C₄×SD₁₆	C₂×SD₁₆	1	2	yes	—
653	C₄×SD₁₆	C₂×SD₁₆	1	2	yes	—
654	C₄×D₈	C₂×C₂²⋊C₄	1	2	yes	—
655	C₄×D₈	C₂×C₂²⋊C₄	1	2	yes	—
656	C₄×D₈	C₂×C₂²⋊C₄	1	2	yes	—
657	C₄×D₈	C₂×C₂²⋊C₄	1	2	yes	—
658	C₄×D₈	C₄×D₄	1	1	yes	characteristic
659	C₄×D₈	C₄×D₄	1	1	yes	characteristic
660	C₄×D₈	C₄×D₄	1	1	yes	characteristic
661	C₄×D₈	C₄×D₄	1	1	yes	characteristic
662	C₄×D₈	C₂×SD₁₆	1	2	yes	—
663	C₄×D₈	C₂×SD₁₆	1	2	yes	—
664	C₄×D₈	C₂×SD₁₆	1	2	yes	—
665	C₄×D₈	C₂×SD₁₆	1	2	yes	—
666	C₄×D₈	C₂³×C₄	1	1	yes	characteristic
667	C₄×D₈	C₂³×C₄	1	1	yes	characteristic
668	C₄×D₈	C₂×#41	1	1	yes	characteristic
669	C₄×D₈	C₂×#41	1	1	yes	characteristic
670	C₈×D₄	C₂×C₂²⋊C₄	1	2	yes	—
671	C₈×D₄	C₂×C₂²⋊C₄	1	2	yes	—
672	C₈×D₄	C₂×C₂²⋊C₄	1	2	yes	—
673	C₈×D₄	C₂×C₂²⋊C₄	1	2	yes	—
674	C₈×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
675	C₈×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
676	C₈×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
677	C₈×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
678	C₈×D₄	C₂³×C₄	1	1	yes	characteristic
679	C₈×D₄	C₂³×C₄	1	1	yes	characteristic
680	C₈×D₄	C₂³×C₄	1	2	yes	—
681	C₈×D₄	C₂³×C₄	1	2	yes	—
682	C₈×D₄	C₂²×D₄	1	1	yes	characteristic
683	C₈×D₄	C₂²×D₄	1	1	yes	characteristic
684	C₈×D₄	C₂²×D₄	1	2	yes	—
685	C₈×D₄	C₂²×D₄	1	2	yes	—
686	#431	C₂×C₂²⋊C₄	1	1	yes	characteristic
687	#431	C₂×C₂²⋊C₄	1	1	yes	characteristic
688	#431	C₂×C₂²⋊C₄	1	1	yes	characteristic
689	#431	C₂×C₂²⋊C₄	1	1	yes	characteristic
690	#431	C₂×C₂²⋊C₄	1	1	yes	characteristic
691	#431	C₂×C₂²⋊C₄	1	2	yes	—
692	#431	C₂×C₂²⋊C₄	1	1	yes	characteristic
693	#428	#102	1	1	yes	characteristic
694	#428	#102	1	1	yes	characteristic
695	#428	#102	1	2	yes	—
696	#428	#102	1	2	yes	—
697	#428	#102	1	1	yes	characteristic
698	#428	#102	1	1	yes	characteristic
699	#427	C₄×D₄	1	1	yes	characteristic
700	#427	C₄×D₄	1	1	yes	characteristic
701	#427	C₂²×D₄	1	1	yes	characteristic
702	#427	C₂²×D₄	1	1	yes	characteristic
703	C₂×#107	C₄×D₄	1	1	yes	characteristic
704	C₂×#107	C₄×D₄	1	1	yes	characteristic
705	C₂×#107	C₂×D₈	1	2	yes	—
706	C₂×#106	C₂×D₈	1	2	yes	—
707	C₂×#106	C₂²×D₄	1	1	yes	characteristic
708	C₂×#106	C₂²×D₄	1	1	yes	characteristic
709	C₂×#106	C₂²×D₄	1	1	yes	characteristic
710	C₂×#106	C₂²×D₄	1	1	yes	characteristic
711	C₂×C₄⋊C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
712	C₂×C₄⋊C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
713	C₂×C₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
714	C₂×C₄⋊C₈	C₂²×D₄	1	1	yes	characteristic
715	C₂×C₄⋊C₈	C₂²×D₄	1	1	yes	characteristic
716	C₂×C₄⋊C₈	C₂²×D₄	1	2	yes	—
717	#418	#102	1	1	yes	characteristic
718	#418	#102	1	1	yes	characteristic
719	#418	#102	1	1	yes	characteristic
720	#418	#102	1	1	yes	characteristic
721	#418	#102	1	2	yes	—
722	#418	#102	1	2	yes	—
723	#417	#102	1	2	yes	—
724	#417	#102	1	2	yes	—
725	#417	#102	1	1	yes	characteristic
726	#417	#102	1	1	yes	characteristic
727	#417	#102	1	1	yes	characteristic
728	#417	#102	1	1	yes	characteristic
729	C₂×#103	C₂×D₈	1	2	yes	—
730	C₂×#102	C₂×D₈	1	2	yes	—
731	C₂×#102	C₂×D₈	1	2	yes	—
732	C₂×#102	C₂×D₈	1	2	yes	—
733	C₄×M₁₆	C₂×C₂²⋊C₄	1	1	yes	characteristic
734	C₄×M₁₆	C₂×C₂²⋊C₄	1	1	yes	characteristic
735	C₄×M₁₆	C₂×C₂²⋊C₄	1	2	yes	—
736	C₄×M₁₆	C₂×SD₁₆	1	1	yes	characteristic
737	C₄×M₁₆	C₂×SD₁₆	1	2	yes	—
738	C₄×M₁₆	C₂×SD₁₆	1	1	yes	characteristic
739	C₂×#97	C₂×D₈	1	2	yes	—
740	C₂×C₄×C₈	C₂³×C₄	1	1	yes	characteristic
741	C₂×C₄×C₈	C₂³×C₄	1	1	yes	characteristic
742	C₂×C₄×C₈	C₂²×D₄	1	2	yes	—
743	C₂×C₄×C₈	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₄×C₈	C₂²×D₄	1	2	yes	—
745	C₂×C₄×C₈	C₂²×D₄	1	1	yes	characteristic
746	C₂×C₄×C₈	C₂²×D₄	1	1	yes	characteristic
747	C₂×C₄×C₈	C₂²×D₄	1	1	yes	characteristic
748	C₂×C₄×C₈	C₂×#41	1	1	yes	characteristic
749	C₂×C₄×C₈	C₂×#41	1	1	yes	characteristic
750	C₂×C₄×C₈	H(5,𝔽₂)	1	1	yes	characteristic
751	C₂×C₄×C₈	H(5,𝔽₂)	1	1	yes	characteristic
752	C₂×C₄×C₈	H(5,𝔽₂)	1	1	yes	characteristic
753	C₂×C₄×C₈	C₂⁵	1	1	yes	characteristic
754	#360	AGL(1,ℤ/8)	1	4	yes	direct product factor
755	#335	C₂×C₂²⋊C₄	1	2	yes	—
756	#335	C₂×C₂²⋊C₄	1	2	yes	—
757	#335	C₂×C₂²⋊C₄	1	2	yes	—
758	#335	C₂×C₂²⋊C₄	1	2	yes	—
759	#335	C₂³×C₄	1	2	yes	—
760	#335	C₂³×C₄	1	2	yes	—
761	#334	C₂×C₂²⋊C₄	1	2	yes	—
762	#334	C₂×C₂²⋊C₄	1	2	yes	—
763	#334	C₂×C₂²⋊C₄	1	2	yes	—
764	#334	C₂×C₂²⋊C₄	1	2	yes	—
765	Q₈⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
766	Q₈⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
767	Q₈⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
768	Q₈⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
769	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
770	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
771	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
772	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
773	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
774	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
775	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
776	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
777	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
778	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
779	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
780	D₄⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
781	#322	C₂×C₂²⋊C₄	1	2	yes	—
782	#322	C₂×C₂²⋊C₄	1	2	yes	—
783	#322	C₂×C₂²⋊C₄	1	2	yes	—
784	#322	C₂×C₂²⋊C₄	1	2	yes	—
785	C₈²	C₂³×C₄	1	2	yes	—
786	C₈²	C₂³×C₄	1	2	yes	—
787	C₈²	C₂²×D₄	1	2	yes	—
788	C₈²	C₂²×D₄	1	2	yes	—
789	C₂×#41	C₂×#102	1	1	yes	characteristic
790	C₂×#41	C₂×#102	1	1	yes	characteristic
791	C₂×#41	C₂×#102	1	1	yes	characteristic
792	C₂×#41	C₂×#102	1	1	yes	characteristic
793	C₂²×Q₈	C₂²×D₈	1	1	yes	characteristic
794	C₂²×D₄	C₂×#102	1	1	yes	characteristic
795	C₂²×D₄	C₂×#102	1	2	yes	—
796	C₂²×D₄	C₂×#102	1	1	yes	characteristic
797	C₂²×D₄	C₂²×D₈	1	2	yes	—
798	C₂²×D₄	C₂²×D₈	1	1	yes	characteristic
799	C₂³×C₄	D₄²	1	1	yes	characteristic
800	C₂³×C₄	C₂²×D₈	1	1	yes	characteristic
801	C₂³×C₄	#576	1	1	yes	characteristic
802	AGL(1,ℤ/8)	#360	1	8	yes	direct product factor
803	#135	C₂×AGL(1,ℤ/8)	1	2	yes	—
804	#135	#575	1	2	yes	—
805	C₂×Q₁₆	C₂×C₄×D₄	1	1	yes	characteristic
806	C₂×Q₁₆	C₂×C₄×D₄	1	1	yes	characteristic
807	C₂×SD₁₆	C₂×#102	1	2	yes	—
808	C₂×SD₁₆	C₂×#102	1	2	yes	—
809	C₂×SD₁₆	C₂×#102	1	2	yes	—
810	C₂×SD₁₆	C₂×#102	1	2	yes	—
811	C₂×D₈	C₂×#102	1	2	yes	—
812	C₂×D₈	C₂×#102	1	2	yes	—
813	C₂×D₈	C₂×#102	1	2	yes	—
814	C₂×D₈	C₂×#102	1	2	yes	—
815	C₂×D₈	C₂×C₄×D₄	1	1	yes	characteristic
816	C₂×D₈	C₂×C₄×D₄	1	1	yes	characteristic
817	C₂×M₁₆	C₂×#102	1	1	yes	characteristic
818	C₂×M₁₆	C₂×#102	1	1	yes	characteristic
819	C₂×M₁₆	C₂×#102	1	1	yes	characteristic
820	C₂×M₁₆	C₂×#102	1	2	yes	—
821	C₂×M₁₆	C₂×#102	1	2	yes	—
822	C₂×M₁₆	C₂×#102	1	1	yes	characteristic
823	C₂²×C₈	C₂×C₄×D₄	1	1	yes	characteristic
824	C₂²×C₈	C₂×C₄×D₄	1	1	yes	characteristic
825	C₂²×C₈	#518	1	1	yes	characteristic
826	C₂²×C₈	#518	1	1	yes	characteristic
827	C₂²×C₈	D₄²	1	1	yes	characteristic
828	C₂²×C₈	D₄²	1	1	yes	characteristic
829	C₂²×C₈	D₄²	1	1	yes	characteristic
830	C₂²×C₈	D₄²	1	1	yes	characteristic
831	C₂²×C₈	#546	1	1	yes	characteristic
832	C₂²×C₈	#546	1	1	yes	characteristic
833	C₂²×C₈	C₂²×D₈	1	2	yes	—
834	C₂²×C₈	C₂²×D₈	1	2	yes	—
835	C₂²×C₈	C₂³×D₄	1	1	yes	characteristic
836	C₂²×C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
837	C₄×Q₈	C₂×#102	1	1	yes	characteristic
838	C₄×Q₈	C₂×#102	1	1	yes	characteristic
839	C₄×Q₈	C₂×#102	1	1	yes	characteristic
840	C₄×Q₈	C₂×#102	1	1	yes	characteristic
841	C₄×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
842	C₄×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
843	C₄×Q₈	C₂²×SD₁₆	1	1	yes	characteristic
844	C₄×Q₈	C₂²×SD₁₆	1	1	yes	characteristic
845	C₄×D₄	C₂×#102	1	2	yes	—
846	C₄×D₄	C₂×#102	1	1	yes	characteristic
847	C₄×D₄	C₂×#102	1	2	yes	—
848	C₄×D₄	C₂×#102	1	2	yes	—
849	C₄×D₄	C₂×#102	1	2	yes	—
850	C₄×D₄	C₂×#102	1	1	yes	characteristic
851	C₄×D₄	C₂×#102	1	1	yes	characteristic
852	C₄×D₄	C₂×#102	1	1	yes	characteristic
853	C₄×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
854	C₄×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
855	C₄×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
856	C₄×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
857	C₄×D₄	C₂²×SD₁₆	1	2	yes	—
858	C₄×D₄	C₂²×SD₁₆	1	1	yes	characteristic
859	C₄×D₄	C₂²×SD₁₆	1	2	yes	—
860	C₄×D₄	C₂²×SD₁₆	1	1	yes	characteristic
861	#117	C₂×#102	1	1	yes	characteristic
862	#117	C₂×#102	1	1	yes	characteristic
863	#117	C₂×#102	1	1	yes	characteristic
864	#117	C₂×#102	1	1	yes	characteristic
865	C₂×C₄⋊C₄	C₂×#102	1	1	yes	characteristic
866	C₂×C₄⋊C₄	C₂×#102	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂×#102	1	2	yes	—
868	C₂×C₄⋊C₄	C₂²×D₈	1	2	yes	—
869	C₂×C₄⋊C₄	C₂²×D₈	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂²×D₈	1	1	yes	characteristic
871	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
872	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
873	C₂×C₄²	D₄²	1	1	yes	characteristic
874	C₂×C₄²	#546	1	1	yes	characteristic
875	C₂×C₄²	#546	1	1	yes	characteristic
876	C₂×C₄²	C₂²×D₈	1	1	yes	characteristic
877	C₂×C₄²	C₂²×SD₁₆	1	1	yes	characteristic
878	C₂×C₄²	C₂²×SD₁₆	1	1	yes	characteristic
879	C₂×C₄²	#576	1	1	yes	characteristic
880	C₂×C₄²	#577	1	1	yes	characteristic
881	C₂×C₄²	#577	1	1	yes	characteristic
882	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
883	M₃₂	C₂×AGL(1,ℤ/8)	1	2	yes	complemented
884	#107	C₂×#102	1	2	yes	—
885	#107	C₂×#102	1	2	yes	—
886	#107	C₂×#102	1	2	yes	—
887	#107	C₂×#102	1	2	yes	—
888	#107	C₂×C₄×D₄	1	1	yes	characteristic
889	#107	C₂×C₄×D₄	1	1	yes	characteristic
890	#107	C₂×C₄×D₄	1	1	yes	characteristic
891	#107	C₂×C₄×D₄	1	1	yes	characteristic
892	#106	C₂×#102	1	2	yes	—
893	#106	C₂×#102	1	2	yes	—
894	#106	C₂×#102	1	2	yes	—
895	#106	C₂×#102	1	2	yes	—
896	#106	C₂×AGL(1,ℤ/8)	1	2	yes	complemented
897	C₄⋊C₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
898	C₄⋊C₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
899	C₄⋊C₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
900	C₄⋊C₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
901	C₄⋊C₈	C₂²×C₂²⋊C₄	1	2	yes	—
902	C₄⋊C₈	C₂²×C₂²⋊C₄	1	2	yes	—
903	#103	C₂×#102	1	2	yes	—
904	#103	C₂×#102	1	2	yes	—
905	#103	C₂×#102	1	2	yes	—
906	#103	C₂×#102	1	2	yes	—
907	#102	C₂×#102	1	2	yes	—
908	#102	C₂×#102	1	2	yes	—
909	#102	C₂×#102	1	2	yes	—
910	#102	C₂×#102	1	2	yes	—
911	#102	C₂×#102	1	2	yes	—
912	#102	C₂×#102	1	2	yes	—
913	#102	C₂×#102	1	2	yes	—
914	#102	C₂×#102	1	2	yes	—
915	#102	C₂×#102	1	2	yes	—
916	#102	C₂×#102	1	2	yes	—
917	#102	C₂×#102	1	2	yes	—
918	#102	C₂×#102	1	2	yes	—
919	#97	C₂×#102	1	2	yes	—
920	#97	C₂×#102	1	2	yes	—
921	#97	C₂×#102	1	2	yes	—
922	#97	C₂×#102	1	2	yes	—
923	C₄×C₈	C₂²×C₂²⋊C₄	1	2	yes	—
924	C₄×C₈	C₂²×C₂²⋊C₄	1	2	yes	—
925	C₄×C₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
926	C₄×C₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
927	C₄×C₈	C₂²×C₂²⋊C₄	1	2	yes	—
928	C₄×C₈	C₂²×C₂²⋊C₄	1	2	yes	—
929	C₄×C₈	C₂×C₄×D₄	1	1	yes	characteristic
930	C₄×C₈	C₂×C₄×D₄	1	1	yes	characteristic
931	C₄×C₈	#518	1	1	yes	characteristic
932	C₄×C₈	#518	1	1	yes	characteristic
933	C₄×C₈	D₄²	1	1	yes	characteristic
934	C₄×C₈	D₄²	1	1	yes	characteristic
935	C₄×C₈	#546	1	1	yes	characteristic
936	C₄×C₈	#546	1	1	yes	characteristic
937	C₄×C₈	#546	1	1	yes	characteristic
938	C₄×C₈	#546	1	1	yes	characteristic
939	C₄×C₈	C₂²×SD₁₆	1	2	yes	—
940	C₄×C₈	C₂²×SD₁₆	1	2	yes	—
941	C₄×C₈	C₂⁴×C₄	1	1	yes	characteristic
942	C₄×C₈	C₂³×D₄	1	1	yes	characteristic
943	C₄×C₈	C₂²×#41	1	1	yes	characteristic
944	C₄×C₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
945	C₂⁴	D₄×D₈	1	1	yes	characteristic
946	#41	C₂×#360	1	4	yes	complemented
947	C₂×Q₈	C₂²×#102	1	1	yes	characteristic
948	C₂×Q₈	C₂²×#102	1	1	yes	characteristic
949	C₂×D₄	C₂×#360	1	4	yes	complemented
950	C₂×D₄	C₂²×#102	1	1	yes	characteristic
951	C₂×D₄	C₂²×#102	1	2	yes	—
952	C₂×D₄	C₂²×#102	1	2	yes	—
953	C₂×D₄	C₂²×#102	1	1	yes	characteristic
954	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
955	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
956	C₂²×C₄	C₂²×#102	1	1	yes	characteristic
957	C₂²×C₄	C₂²×#102	1	1	yes	characteristic
958	C₂²×C₄	#2897	1	1	yes	characteristic
959	C₂²×C₄	#2897	1	1	yes	characteristic
960	C₂²×C₄	D₄×D₈	1	1	yes	characteristic
961	C₂²×C₄	D₄×D₈	1	1	yes	characteristic
962	C₂²×C₄	D₄×D₈	1	1	yes	characteristic
963	C₂²×C₄	D₄×SD₁₆	1	1	yes	characteristic
964	C₂²×C₄	D₄×SD₁₆	1	1	yes	characteristic
965	C₂²×C₄	#3294	1	1	yes	characteristic
966	C₂²×C₄	#3294	1	1	yes	characteristic
967	C₂²×C₄	#3295	1	1	yes	characteristic
968	C₂²×C₄	#3295	1	1	yes	characteristic
969	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
970	C₂²×C₄	C₂³×D₈	1	1	yes	characteristic
971	C₂²×C₄	C₂×#576	1	1	yes	characteristic
972	Q₁₆	C₄×AGL(1,ℤ/8)	1	2	yes	complemented
973	SD₁₆	C₂×#360	1	8	yes	complemented
974	D₈	C₂×#360	1	8	yes	complemented
975	D₈	C₄×AGL(1,ℤ/8)	1	2	yes	complemented
976	M₁₆	C₂×#360	1	4	yes	complemented
977	C₂×C₈	D₄×C₂²⋊C₄	1	1	yes	characteristic
978	C₂×C₈	D₄×C₂²⋊C₄	1	1	yes	characteristic
979	C₂×C₈	D₄×C₂²⋊C₄	1	1	yes	characteristic
980	C₂×C₈	D₄×C₂²⋊C₄	1	1	yes	characteristic
981	C₂×C₈	C₂²×#102	1	2	yes	—
982	C₂×C₈	C₂²×#102	1	2	yes	—
983	C₂×C₈	C₂²×#102	1	2	yes	—
984	C₂×C₈	C₂²×#102	1	2	yes	—
985	C₂×C₈	C₂²×C₄×D₄	1	1	yes	characteristic
986	C₂×C₈	C₂×#518	1	1	yes	characteristic
987	C₂×C₈	C₂×D₄²	1	1	yes	characteristic
988	C₂×C₈	C₂×#546	1	1	yes	characteristic
989	C₂×C₈	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
990	C₂×C₈	C₂×#575	1	1	yes	characteristic
991	C₂×C₈	#3585	1	1	yes	characteristic
992	C₂×C₈	#3585	1	1	yes	characteristic
993	C₄⋊C₄	C₂²×#102	1	1	yes	characteristic
994	C₄⋊C₄	C₂²×#102	1	1	yes	characteristic
995	C₄⋊C₄	C₂²×#102	1	1	yes	characteristic
996	C₄⋊C₄	C₂²×#102	1	1	yes	characteristic
997	C₄⋊C₄	C₂²×#102	1	2	yes	—
998	C₄⋊C₄	C₂²×#102	1	2	yes	—
999	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
1000	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
1001	C₄²	C₂²×#102	1	1	yes	characteristic
1002	C₄²	C₂²×#102	1	1	yes	characteristic
1003	C₄²	#2897	1	1	yes	characteristic
1004	C₄²	#2897	1	1	yes	characteristic
1005	C₄²	D₄×SD₁₆	1	1	yes	characteristic
1006	C₄²	D₄×SD₁₆	1	1	yes	characteristic
1007	C₄²	#3294	1	1	yes	characteristic
1008	C₄²	#3294	1	1	yes	characteristic
1009	C₄²	#3295	1	1	yes	characteristic
1010	C₄²	#3295	1	1	yes	characteristic
1011	C₄²	C₂³×C₂²⋊C₄	1	1	yes	characteristic
1012	C₄²	C₂×#546	1	1	yes	characteristic
1013	C₄²	C₂³×SD₁₆	1	1	yes	characteristic
1014	C₄²	C₂×#577	1	1	yes	characteristic
1015	C₂³	D₄×#102	1	1	yes	characteristic
1016	C₂³	D₄×#102	1	1	yes	characteristic
1017	C₂³	C₂×D₄×D₈	1	1	yes	characteristic
1018	Q₈	C₂²×#360	1	2	yes	complemented
1019	D₄	C₂²×#360	1	4	yes	—
1020	D₄	C₂²×#360	1	2	yes	complemented
1021	C₂×C₄	D₄×#102	1	1	yes	characteristic
1022	C₂×C₄	D₄×#102	1	1	yes	characteristic
1023	C₂×C₄	D₄×#102	1	1	yes	characteristic
1024	C₂×C₄	D₄×#102	1	1	yes	characteristic
1025	C₂×C₄	D₄×#102	1	1	yes	characteristic
1026	C₂×C₄	D₄×#102	1	1	yes	characteristic
1027	C₂×C₄	C₂²×#360	1	2	yes	—
1028	C₂×C₄	#33388	1	2	yes	—
1029	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	1	yes	characteristic
1030	C₂×C₄	C₂³×#102	1	1	yes	characteristic
1031	C₂×C₄	C₂×#2897	1	1	yes	characteristic
1032	C₂×C₄	C₂×D₄×SD₁₆	1	1	yes	characteristic
1033	C₂×C₄	D₄×AGL(1,ℤ/8)	1	1	yes	characteristic
1034	C₂×C₄	#61066	1	1	yes	characteristic
1035	C₂×C₄	#61106	1	1	yes	characteristic
1036	C₂×C₄	#61107	1	1	yes	characteristic
1037	C₂×C₄	C₂×#3294	1	1	yes	characteristic
1038	C₂×C₄	C₂×#3295	1	1	yes	characteristic
1039	C₈	C₂²×#360	1	4	yes	complemented
1040	C₈	C₂×C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
1041	C₈	#60168	1	1	yes	characteristic
1042	C₈	D₄×AGL(1,ℤ/8)	1	1	yes	characteristic
1043	C₈	#61066	1	1	yes	characteristic
1044	C₂²	D₄×#360	1	2	yes	—
1045	C₂²	D₈×AGL(1,ℤ/8)	1	1	yes	characteristic
1046	C₂²	#6358723	1	1	yes	characteristic
1047	C₂²	C₂×D₄×#102	1	1	yes	characteristic
1048	C₄	D₄×#360	1	2	yes	—
1049	C₄	SD₁₆×AGL(1,ℤ/8)	1	1	yes	characteristic
1050	C₄	#6358729	1	1	yes	characteristic
1051	C₄	C₂²⋊C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
1052	C₄	#6379211	1	1	yes	characteristic
1053	C₄	C₂³×#360	1	1	yes	characteristic
1054	C₄	C₂×#33388	1	1	yes	characteristic
1055	C₂	#102×AGL(1,ℤ/8)	1	1	yes	characteristic
1056	C₂	C₂×D₄×#360	1	1	yes	characteristic
1057	C₂	#72285581	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×D₄×#102
commutator	C₄×C₈	C₂⁴×C₄
Frattini, cosocle	C₂×C₄×C₈	C₂⁵
prime radical	#135×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×C₈×AGL(1,ℤ/8) ◁ G
LECS	G ▷ C₂×C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #72342532	C₂	semidirect
2. #72342531	C₂	semidirect
3. #72342530	C₂	semidirect
4. #72342529	C₂	semidirect
5. #72342528	C₂	semidirect
6. M₁₆×#360	C₂	semidirect
7. #41×#360	C₂	semidirect
8. #72342525	C₂	semidirect
9. #72342524	C₂	semidirect
10. #72342523	C₂	semidirect
11. #72342486	C₂	semidirect
12. #72342475	C₂	semidirect
13. #72342452	C₂	semidirect
14. SD₁₆×#360	C₂	semidirect
16. M₃₂×AGL(1,ℤ/8)	C₂	semidirect
17. D₈×#360	C₂	semidirect
18. #72309855	C₂	semidirect
19. #72309556	C₂	semidirect
20. C₂×D₄×#360	C₂	semidirect
21. #106×AGL(1,ℤ/8)	C₂	semidirect
22. #72265070	C₂	semidirect
23. #72227032	C₂	semidirect
26. #41×M₃₂	C₂²	semidirect
27. C₂×D₄×M₃₂	C₂²	semidirect
28. #41×#106	C₂²	semidirect
29. C₂×D₄×#106	C₂²	semidirect
30. #6358832	C₄	semidirect
31. #6358830	C₄	semidirect
32. #6358820	C₄	semidirect
33. #6358818	C₄	semidirect
34. #6358796	C₄	semidirect
35. #6358790	C₄	semidirect
36. #6358777	C₄	semidirect
37. #6358770	C₄	semidirect
38. Q₁₆×AGL(1,ℤ/8)	C₄	semidirect
39. #6358743	C₄	semidirect
40. #6358736	C₄	semidirect
41. D₈×AGL(1,ℤ/8)	C₄	semidirect
51. #497676	C₂²	semidirect
52. #497676	C₂²	semidirect
53. Q₈×#360	C₂²	semidirect
54. Q₈×#360	C₂²	semidirect
55. #497552	C₂²	semidirect
56. #497552	C₂²	semidirect
59. D₄×#360	C₂²	semidirect
60. D₄×#360	C₂²	semidirect
61. D₄×#360	C₂²	semidirect
62. D₄×#360	C₂²	semidirect
63. #496497	C₂²	semidirect
64. #496363	C₂²	semidirect
65. #495564	C₂²	semidirect
66. #495527	C₂²	semidirect
67. C₂×#13255	C₂²	semidirect
68. C₂×#13210	C₂²	semidirect
72. #483603	C₂²	semidirect
73. #483567	C₂²	semidirect
74. SD₁₆×M₃₂	C₂²	semidirect
75. D₈×M₃₂	C₂²	semidirect
76. #483356	C₂²	semidirect
77. #483162	C₂²	semidirect
78. #483111	C₂²	semidirect
80. #481160	C₂²	semidirect
81. #481116	C₂²	semidirect
82. M₁₆×M₃₂	C₂²	semidirect
83. SD₁₆×#106	C₂²	semidirect
84. D₈×#106	C₂²	semidirect
85. #225517	C₂²	semidirect
86. #225516	C₂²	semidirect
87. #191432	C₂²	semidirect
88. #189102	C₂²	semidirect
89. #189094	C₂²	semidirect
90. M₁₆×#106	C₂²	semidirect
91. #141779	C₂²	semidirect
92. #141751	C₂²	semidirect
93. #141673	C₂²	semidirect
94. #141643	C₂²	semidirect
95. #141307	C₂²	semidirect
96. #141294	C₂²	semidirect
97. #141250	C₂²	semidirect
98. #141233	C₂²	semidirect
99. #138680	C₂²	semidirect
100. #138680	C₂²	semidirect
101. #138653	C₂²	semidirect
102. #138653	C₂²	semidirect
103. #138653	C₂²	semidirect
104. #138653	C₂²	semidirect
105. #138587	C₂²	semidirect
106. #138587	C₂²	semidirect
107. #136987	C₂²	semidirect
108. #136987	C₂²	semidirect
109. #136918	C₂²	semidirect
110. #136918	C₂²	semidirect
111. #136885	C₂²	semidirect
112. #136885	C₂²	semidirect
113. #136885	C₂²	semidirect
114. #136885	C₂²	semidirect
115. #135033	C₂²	semidirect
116. #135024	C₂²	semidirect
117. #134955	C₂²	semidirect
118. #134940	C₂²	semidirect
119. #131962	C₂²	semidirect
120. #131932	C₂²	semidirect
121. #131902	C₂²	semidirect
124. #131865	C₂²	semidirect
125. #131865	C₂²	semidirect
126. #131865	C₂²	semidirect
127. #128750	C₂²	semidirect
128. #128735	C₂²	semidirect
129. #128710	C₂²	semidirect
130. C₈×#360	C₂²	semidirect
131. #127784	C₂²	semidirect
132. #127759	C₂²	semidirect
133. #126884	C₂²	semidirect
134. #126695	C₂²	semidirect
135. #61436	C₂×C₄	semidirect
136. #61435	C₂×C₄	semidirect
137. #61433	C₂×C₄	semidirect
138. #61431	C₂×C₄	semidirect
139. #61430	C₂×C₄	semidirect
140. Q₁₆×#41	C₂×C₄	semidirect
141. #61427	C₂×C₄	semidirect
142. D₈×#41	C₂×C₄	semidirect
146. D₄×#135	C₂×C₄	semidirect
147. D₄×#135	C₂×C₄	semidirect
151. C₂×#3287	C₂×C₄	semidirect
152. C₂×D₄×Q₁₆	C₂×C₄	semidirect
153. C₂×#3283	C₂×C₄	semidirect
154. C₂×D₄×D₈	C₂×C₄	semidirect
161. Q₈×M₃₂	C₂³	semidirect
162. Q₈×M₃₂	C₂³	semidirect
165. D₄×M₃₂	C₂³	semidirect
166. D₄×M₃₂	C₂³	semidirect
173. Q₈×#106	C₂³	semidirect
174. Q₈×#106	C₂³	semidirect
177. D₄×#106	C₂³	semidirect
178. D₄×#106	C₂³	semidirect
182. #19986	C₂×C₄	semidirect
183. #19985	C₂×C₄	semidirect
184. SD₁₆×Q₁₆	C₂×C₄	semidirect
185. #19983	C₂×C₄	semidirect
186. #19980	C₂×C₄	semidirect
187. #19979	C₂×C₄	semidirect
188. #19976	C₂×C₄	semidirect
189. #19975	C₂×C₄	semidirect
190. D₈×Q₁₆	C₂×C₄	semidirect
191. #19973	C₂×C₄	semidirect
192. #19973	C₂×C₄	semidirect
193. #19971	C₂×C₄	semidirect
194. D₈×SD₁₆	C₂×C₄	semidirect
195. #19968	C₂×C₄	semidirect
196. #19968	C₂×C₄	semidirect
197. D₈²	C₂×C₄	semidirect
198. #19962	C₂×C₄	semidirect
199. #19960	C₂×C₄	semidirect
200. #19955	C₂×C₄	semidirect
201. #19953	C₂×C₄	semidirect
202. #19943	C₂×C₄	semidirect
203. #19937	C₂×C₄	semidirect
204. #19935	C₂×C₄	semidirect
205. #19933	C₂×C₄	semidirect
206. #19928	C₂×C₄	semidirect
207. #19926	C₂×C₄	semidirect
208. #19908	C₂×C₄	semidirect
209. #19902	C₂×C₄	semidirect
210. #19900	C₂×C₄	semidirect
211. #19898	C₂×C₄	semidirect
212. #19885	C₂×C₄	semidirect
213. #19883	C₂×C₄	semidirect
214. #19647	C₂×C₄	semidirect
215. #19645	C₂×C₄	semidirect
216. #19639	C₂×C₄	semidirect
217. #19635	C₂×C₄	semidirect
218. #19632	C₂×C₄	semidirect
219. #19629	C₂×C₄	semidirect
222. #19269	C₂×C₄	semidirect
223. #19269	C₂×C₄	semidirect
224. #19268	C₂×C₄	semidirect
225. #19268	C₂×C₄	semidirect
226. #19267	C₂×C₄	semidirect
227. #19267	C₂×C₄	semidirect
228. #19259	C₂×C₄	semidirect
229. #19258	C₂×C₄	semidirect
230. #19256	C₂×C₄	semidirect
231. #19256	C₂×C₄	semidirect
232. #19255	C₂×C₄	semidirect
233. #19255	C₂×C₄	semidirect
238. #18039	C₂×C₄	semidirect
239. M₁₆×Q₁₆	C₂×C₄	semidirect
240. M₁₆×Q₁₆	C₂×C₄	semidirect
241. #18035	C₂×C₄	semidirect
242. M₁₆×D₈	C₂×C₄	semidirect
243. M₁₆×D₈	C₂×C₄	semidirect
268. #13287	C₂³	semidirect
269. #13287	C₂³	semidirect
270. #13287	C₂³	semidirect
271. #13278	C₂³	semidirect
272. #13278	C₂³	semidirect
275. #13255	C₂³	semidirect
276. #13255	C₂³	semidirect
281. #13210	C₂³	semidirect
282. #13210	C₂³	semidirect
283. #13210	C₂³	semidirect
300. #12004	C₂³	semidirect
301. #11996	C₂³	semidirect
302. #11936	C₂³	semidirect
305. #11925	C₂³	semidirect
306. #11607	C₂³	semidirect
311. #11583	C₂³	semidirect
312. #11402	C₂³	semidirect
313. C₈×M₃₂	C₂³	semidirect
314. #8814	C₂³	semidirect
315. #8813	C₂³	semidirect
316. #8643	C₂³	semidirect
319. #8642	C₂³	semidirect
320. #8283	C₂³	semidirect
321. C₈×#106	C₂³	semidirect
322. #7278	C₂³	semidirect
323. #7278	C₂³	semidirect
324. #7278	C₂³	semidirect
325. #7278	C₂³	semidirect
326. #7175	C₂³	semidirect
327. #7175	C₂³	semidirect
328. #7158	C₂³	semidirect
329. #7158	C₂³	semidirect
336. #3396	C₂²×C₄	semidirect
337. #3395	C₂²×C₄	semidirect
338. #3393	C₂²×C₄	semidirect
339. #3391	C₂²×C₄	semidirect
340. #3383	C₂²×C₄	semidirect
341. Q₈×Q₁₆	C₂²×C₄	semidirect
342. #3380	C₂²×C₄	semidirect
343. Q₈×D₈	C₂²×C₄	semidirect
344. #3342	C₂²×C₄	semidirect
345. #3341	C₂²×C₄	semidirect
346. #3338	C₂²×C₄	semidirect
347. #3334	C₂²×C₄	semidirect
350. #3287	C₂²×C₄	semidirect
353. D₄×Q₁₆	C₂²×C₄	semidirect
356. #3283	C₂²×C₄	semidirect
359. D₄×D₈	C₂²×C₄	semidirect
452. #1713	C₂²×C₄	semidirect
453. #1712	C₂²×C₄	semidirect
454. #1709	C₂²×C₄	semidirect
455. #1709	C₂²×C₄	semidirect
456. #1707	C₂²×C₄	semidirect
457. #1707	C₂²×C₄	semidirect
458. #1706	C₂²×C₄	semidirect
459. #1706	C₂²×C₄	semidirect
464. #1670	C₂²×C₄	semidirect
465. #1670	C₂²×C₄	semidirect
468. #1669	C₂²×C₄	semidirect
469. #1669	C₂²×C₄	semidirect
470. #1668	C₂²×C₄	semidirect
471. #1668	C₂²×C₄	semidirect
474. #1667	C₂²×C₄	semidirect
475. #1667	C₂²×C₄	semidirect
476. #1591	C₂²×C₄	semidirect
477. #1591	C₂²×C₄	semidirect
478. #1589	C₂²×C₄	semidirect
479. #1589	C₂²×C₄	semidirect
496. C₈×Q₁₆	C₂²×C₄	semidirect
497. C₈×Q₁₆	C₂²×C₄	semidirect
510. C₈×D₈	C₂²×C₄	semidirect
511. C₈×D₈	C₂²×C₄	semidirect
754. #360	AGL(1,ℤ/8)	direct (N × H)
802. AGL(1,ℤ/8)	#360	direct (N × H)
883. M₃₂	C₂×AGL(1,ℤ/8)	semidirect
896. #106	C₂×AGL(1,ℤ/8)	semidirect
946. #41	C₂×#360	semidirect
949. C₂×D₄	C₂×#360	semidirect
972. Q₁₆	C₄×AGL(1,ℤ/8)	semidirect
973. SD₁₆	C₂×#360	semidirect
974. D₈	C₂×#360	semidirect
975. D₈	C₄×AGL(1,ℤ/8)	semidirect
976. M₁₆	C₂×#360	semidirect
1018. Q₈	C₂²×#360	semidirect
1020. D₄	C₂²×#360	semidirect
1039. C₈	C₂²×#360	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#72342532	2
#72342531	2
#72342530	2
#72342529	2
#72342528	2
M₁₆×#360	2
#41×#360	2
#72342525	2
#72342524	2
#72342523	2
#72342486	2
#72342475	2
#72342452	2
SD₁₆×#360	2
#135×AGL(1,ℤ/8)	2
M₃₂×AGL(1,ℤ/8)	2
D₈×#360	2
#72309855	2
#72309556	2
C₂×D₄×#360	2
#106×AGL(1,ℤ/8)	2
#72265070	2
#72227032	2