Subgroups — #72316844

Order 2048.

At least 7558 conjugacy classes of subgroups; only the 1544 normal subgroups are shown.

The subgroup lattice has 823 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72316839	C₂	1	1	yes	maximal, characteristic, complemented
2	#72316827	C₂	1	1	yes	maximal, characteristic, complemented
3	#72316775	C₂	1	1	yes	maximal, characteristic, complemented
4	#72316751	C₂	1	4	yes	maximal, complemented
5	#72316728	C₂	1	4	yes	maximal, complemented
6	#72316715	C₂	1	4	yes	maximal, complemented
7	#72316694	C₂	1	4	yes	maximal, complemented
8	#72312648	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#6385980	C₂	1	1	yes	maximal, characteristic, complemented
10	#72285551	C₂	1	1	yes	maximal, characteristic, complemented
11	#72282464	C₂	1	4	yes	maximal, complemented
12	#72282248	C₂	1	4	yes	maximal, complemented
13	#72279493	C₂	1	1	yes	maximal, characteristic
14	C₂²×#3498	C₂²	1	1	yes	characteristic
15	C₂×#60561	C₄	1	1	yes	characteristic, complemented
16	C₂²×#3038	C₄	1	1	yes	characteristic, complemented
17	#7628157	C₂²	1	1	yes	characteristic
18	#6512762	C₄	1	2	yes	complemented
19	#6512762	C₂²	1	2	yes	—
20	#6512761	C₄	1	2	yes	complemented
21	#6512761	C₂²	1	2	yes	—
22	#6512748	C₄	1	2	yes	complemented
23	#6512748	C₂²	1	2	yes	—
24	#6512747	C₄	1	2	yes	complemented
25	#6512747	C₂²	1	2	yes	—
26	#6440417	C₄	1	2	yes	complemented
27	#6440417	C₂²	1	2	yes	—
28	#6437510	C₄	1	2	yes	complemented
29	#6437510	C₂²	1	2	yes	—
30	#6385980	C₂²	1	4	yes	—
31	#6385980	C₂²	1	4	yes	—
32	C₂×D₄×#99	C₂²	1	4	yes	—
33	#6374554	C₄	1	1	yes	characteristic, complemented
34	#6374537	C₂²	1	1	yes	characteristic
35	#6374304	C₄	1	1	yes	characteristic, complemented
36	#6370950	C₂²	1	1	yes	characteristic
37	C₂×#20723	C₂²	1	1	yes	characteristic
38	C₂×#20723	C₂²	1	1	yes	characteristic
39	#6342561	C₂²	1	1	yes	characteristic
40	#496509	C₂²	1	2	yes	complemented
41	#496508	C₂²	1	2	yes	complemented
42	#496417	C₂²	1	2	yes	complemented
43	#496334	C₂²	1	2	yes	complemented
44	#495588	C₂²	1	2	yes	complemented
45	#495587	C₂²	1	2	yes	complemented
46	#482630	C₂²	1	2	yes	complemented
47	#482629	C₂²	1	2	yes	complemented
48	#482427	C₂²	1	2	yes	complemented
49	#482361	C₂²	1	2	yes	complemented
50	#482236	C₂²	1	2	yes	complemented
51	#482234	C₂²	1	2	yes	complemented
52	#185785	C₂²	1	4	yes	—
53	#185755	C₂²	1	4	yes	—
54	#185733	C₂²	1	4	yes	—
55	#138962	C₂²	1	16	yes	complemented
56	#138960	C₂²	1	16	yes	complemented
57	#138886	C₂²	1	16	yes	complemented
58	#138884	C₂²	1	16	yes	complemented
59	#127399	C₂²	1	4	yes	complemented
60	#127389	C₂²	1	4	yes	complemented
61	#127388	C₂²	1	4	yes	complemented
62	#127141	C₂²	1	4	yes	complemented
63	#127124	C₂²	1	4	yes	complemented
64	#127106	C₂²	1	4	yes	complemented
65	C₂³×AGL(1,ℤ/8)	C₂×C₄	1	2	yes	complemented
66	C₂×#3498	C₂×C₄	1	2	yes	—
67	C₂×#3498	C₂×C₄	1	2	yes	—
68	C₂×#3498	D₄	1	2	yes	—
69	C₂×#3498	D₄	1	2	yes	—
70	C₂×#3498	D₄	1	2	yes	—
71	C₂×#3498	D₄	1	2	yes	—
72	C₂×#3498	C₂³	1	2	yes	—
73	C₂×#3498	C₂³	1	2	yes	—
74	C₂²×#550	D₄	1	2	yes	—
75	C₂²×D₄²	C₂×C₄	1	2	yes	—
76	C₂²×D₄²	D₄	1	2	yes	—
77	C₂²×D₄²	C₂³	1	2	yes	—
78	C₂²×#532	C₂×C₄	1	1	yes	characteristic
79	C₂²×#532	D₄	1	1	yes	characteristic
80	C₂²×#532	D₄	1	1	yes	characteristic
81	C₂³×#127	C₂×C₄	1	1	yes	characteristic
82	C₂³×#127	D₄	1	1	yes	characteristic
83	C₂³×#127	D₄	1	1	yes	characteristic
84	C₂²×C₄×#41	C₂×C₄	1	1	yes	characteristic, complemented
85	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
86	C₂×#3112	C₂×C₄	1	2	yes	complemented
87	C₂×#3109	C₂×C₄	1	2	yes	complemented
88	C₂×#3103	C₂×C₄	1	2	yes	complemented
89	C₂×#3100	C₂×C₄	1	2	yes	complemented
90	C₂×#3094	C₂×C₄	1	2	yes	complemented
91	C₂²×#460	C₂×C₄	1	2	yes	complemented
92	C₂²×#460	C₂×C₄	1	2	yes	complemented
93	C₂²×#459	C₂×C₄	1	2	yes	complemented
94	C₂²×#459	C₂×C₄	1	2	yes	complemented
95	C₂×#3006	C₂×C₄	1	2	yes	complemented
96	C₂×#2920	C₂×C₄	1	1	yes	characteristic, complemented
97	C₂²×#423	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂²×#418	C₂×C₄	1	2	yes	complemented
99	#34971	C₂×C₄	1	1	yes	characteristic, complemented
100	#34971	C₂³	1	1	yes	characteristic
101	#34963	C₂×C₄	1	1	yes	characteristic, complemented
102	#34963	C₂³	1	1	yes	characteristic
103	#34952	C₂×C₄	1	1	yes	characteristic, complemented
104	#34952	C₂³	1	1	yes	characteristic
105	#34935	C₂×C₄	1	1	yes	characteristic, complemented
106	#34935	C₂³	1	1	yes	characteristic
107	#34809	C₂×C₄	1	1	yes	characteristic, complemented
108	#34809	C₂³	1	1	yes	characteristic
109	#34736	C₂×C₄	1	1	yes	characteristic, complemented
110	#34736	C₂³	1	1	yes	characteristic
111	#34012	C₂×C₄	1	1	yes	characteristic, complemented
112	#24033	C₂×C₄	1	4	yes	complemented
113	#24033	C₂×C₄	1	4	yes	complemented
114	#24033	C₂×C₄	1	4	yes	complemented
115	#24033	C₂³	1	4	yes	—
116	#24032	C₂×C₄	1	4	yes	complemented
117	#24032	C₂×C₄	1	4	yes	complemented
118	#24032	C₂×C₄	1	4	yes	complemented
119	#24032	C₂³	1	4	yes	—
120	#23849	C₂×C₄	1	4	yes	complemented
121	#23849	C₂×C₄	1	4	yes	complemented
122	#23849	C₂×C₄	1	4	yes	complemented
123	#23849	C₂³	1	4	yes	—
124	#23848	C₂×C₄	1	4	yes	complemented
125	#23848	C₂×C₄	1	4	yes	complemented
126	#23848	C₂×C₄	1	4	yes	complemented
127	#23848	C₂³	1	4	yes	—
128	D₄×#99	C₂³	1	16	yes	—
129	#21888	C₂×C₄	1	2	yes	complemented
130	#21888	C₂×C₄	1	2	yes	complemented
131	#21884	C₂×C₄	1	2	yes	complemented
132	#21884	C₂×C₄	1	2	yes	complemented
133	#21851	C₂×C₄	1	2	yes	complemented
134	#21851	C₂³	1	2	yes	—
135	#21847	C₂×C₄	1	2	yes	complemented
136	#21847	C₂³	1	2	yes	—
137	#21810	C₂×C₄	1	2	yes	complemented
138	#21810	C₂×C₄	1	2	yes	complemented
139	#21803	C₂×C₄	1	2	yes	complemented
140	#21803	C₂×C₄	1	2	yes	complemented
141	#20973	C₂×C₄	1	2	yes	complemented
142	#20973	C₂×C₄	1	2	yes	complemented
143	#20898	C₂×C₄	1	2	yes	complemented
144	#20898	C₂³	1	2	yes	—
145	#20728	C₂³	1	2	yes	—
146	#20726	C₂³	1	2	yes	—
147	#20723	D₄	1	2	yes	—
148	#20723	D₄	1	2	yes	—
149	#20723	D₄	1	2	yes	—
150	#20723	D₄	1	2	yes	—
151	#20723	C₂³	1	2	yes	—
152	#20723	C₂³	1	2	yes	—
153	#20723	C₂³	1	2	yes	—
154	#20723	C₂³	1	2	yes	—
155	C₂×#1820	D₄	1	2	yes	—
156	#20637	C₂³	1	2	yes	—
157	C₂×#1799	D₄	1	2	yes	—
158	C₂×#1799	C₂³	1	2	yes	—
159	#20598	C₂×C₄	1	2	yes	complemented
160	#20598	C₂×C₄	1	2	yes	complemented
161	C₂×#1782	D₄	1	2	yes	—
162	C₂×C₄×#99	D₄	1	2	yes	—
163	C₂×C₄×#99	C₂³	1	2	yes	—
164	#17366	C₂³	1	2	yes	—
165	#17364	C₂³	1	2	yes	—
166	#17349	C₂³	1	2	yes	—
167	#13296	C₂³	1	4	yes	complemented
168	#13295	C₂³	1	4	yes	complemented
169	#13221	C₂³	1	4	yes	complemented
170	#13220	C₂³	1	4	yes	complemented
171	#11899	C₂³	1	4	yes	complemented
172	#11898	C₂³	1	4	yes	complemented
173	#11874	C₂³	1	4	yes	complemented
174	#11873	C₂³	1	4	yes	complemented
175	#8383	C₂³	1	16	yes	—
176	#7236	C₂³	1	16	yes	complemented
177	#7204	C₂³	1	16	yes	complemented
178	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
179	C₂³×#41	C₂×D₄	1	1	yes	characteristic
180	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
181	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
182	C₂⁴×D₄	C₂×D₄	1	2	yes	—
183	C₂³×SD₁₆	C₂²×C₄	1	4	yes	complemented
184	C₂³×D₈	C₂²×C₄	1	4	yes	complemented
185	C₂³×M₁₆	C₂²×C₄	1	2	yes	—
186	C₂×#550	C₂²⋊C₄	1	4	yes	—
187	C₂×#550	C₂²⋊C₄	1	4	yes	—
188	C₂×#550	C₂×D₄	1	4	yes	—
189	C₂×#550	C₂×D₄	1	4	yes	—
190	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
191	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
192	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
193	C₂×D₄²	C₂²⋊C₄	1	4	yes	—
194	C₂×D₄²	C₂²×C₄	1	4	yes	—
195	C₂×D₄²	C₂²×C₄	1	4	yes	—
196	C₂×D₄²	C₂²×C₄	1	4	yes	—
197	C₂×D₄²	C₂×D₄	1	4	yes	—
198	C₂×D₄²	C₂×D₄	1	4	yes	—
199	C₂×D₄²	C₂×D₄	1	4	yes	—
200	C₂×D₄²	C₂×D₄	1	4	yes	—
201	C₂×D₄²	C₂⁴	1	4	yes	—
202	C₂×#532	C₂²⋊C₄	1	2	yes	—
203	C₂×#532	C₂²⋊C₄	1	2	yes	—
204	C₂×#532	C₂²⋊C₄	1	2	yes	—
205	C₂×#532	C₂²⋊C₄	1	2	yes	—
206	C₂×#532	C₂²⋊C₄	1	2	yes	—
207	C₂×#532	C₂²⋊C₄	1	2	yes	—
208	C₂×#532	C₂²×C₄	1	2	yes	—
209	C₂×#532	C₂²×C₄	1	2	yes	—
210	C₂×#532	C₂×D₄	1	2	yes	—
211	C₂×#532	C₂×D₄	1	2	yes	—
212	C₂×#532	C₂×D₄	1	2	yes	—
213	C₂×#532	C₂×D₄	1	2	yes	—
214	C₂²×C₄⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×#127	C₂²⋊C₄	1	2	yes	—
216	C₂²×#127	C₂²⋊C₄	1	2	yes	—
217	C₂²×#127	C₂²⋊C₄	1	2	yes	—
218	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
219	C₂²×#127	C₂²⋊C₄	1	2	yes	—
220	C₂²×#127	C₂²⋊C₄	1	2	yes	—
221	C₂²×#127	C₂²⋊C₄	1	2	yes	—
222	C₂²×#127	C₂²⋊C₄	1	2	yes	—
223	C₂²×#127	C₂²⋊C₄	1	2	yes	—
224	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
225	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
226	C₂²×#127	C₂²×C₄	1	2	yes	—
227	C₂²×#127	C₂²×C₄	1	2	yes	—
228	C₂²×#127	C₂×D₄	1	2	yes	—
229	C₂²×#127	C₂×D₄	1	2	yes	—
230	C₂²×#127	C₂×D₄	1	2	yes	—
231	C₂²×#127	C₂×D₄	1	2	yes	—
232	C₂²×#127	C₂×D₄	1	2	yes	—
233	C₂²×#121	C₂²⋊C₄	1	2	yes	—
234	C₂²×#121	C₂²×C₄	1	2	yes	—
235	C₂²×#121	C₂×D₄	1	2	yes	—
236	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
239	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
240	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
241	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
242	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
243	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
244	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
245	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
246	C₂×C₄×#41	#41	1	1	yes	characteristic
247	C₂×C₄×#41	#41	1	1	yes	characteristic
248	C₂×C₄×#41	#41	1	1	yes	characteristic
249	C₂×C₄×#41	#41	1	1	yes	characteristic
250	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×Q₈	C₂²×C₄	1	1	yes	characteristic, complemented
253	C₂²×C₄×Q₈	C₂²×C₄	1	1	yes	characteristic, complemented
254	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×Q₈	#41	1	1	yes	characteristic
256	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
257	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
258	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
259	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
260	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic, complemented
261	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
262	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×D₄	#41	1	1	yes	characteristic
266	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
267	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
268	C₂²×#117	C₂×D₄	1	1	yes	characteristic
269	C₂²×#117	#41	1	1	yes	characteristic
270	C₂²×#117	#41	1	1	yes	characteristic
271	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
272	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
273	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
274	C₂×#481	C₂²×C₄	1	4	yes	complemented
275	C₂×#480	C₂²×C₄	1	4	yes	complemented
276	C₂×#448	C₂²×C₄	1	4	yes	complemented
277	C₂×#447	C₂²×C₄	1	4	yes	complemented
278	C₂×#432	C₂²×C₄	1	2	yes	complemented
279	C₂×#431	C₂²×C₄	1	2	yes	complemented
280	C₂²×C₄⋊C₈	C₂²×C₄	1	2	yes	complemented
281	C₂²×C₄⋊C₈	C₂²×C₄	1	2	yes	complemented
282	C₂²×#102	C₂²×C₄	1	4	yes	complemented
283	C₂²×#102	C₂²×C₄	1	4	yes	complemented
284	C₂²×#99	C₂×D₄	1	4	yes	—
285	C₂×#407	C₂²×C₄	1	2	yes	—
286	#2487	C₂²×C₄	1	1	yes	characteristic
287	#2487	C₂²×C₄	1	1	yes	characteristic, complemented
288	#2487	C₂²×C₄	1	1	yes	characteristic, complemented
289	#2487	C₂⁴	1	1	yes	characteristic
290	#2486	C₂²×C₄	1	1	yes	characteristic
291	#2486	C₂²×C₄	1	1	yes	characteristic, complemented
292	#2486	C₂²×C₄	1	1	yes	characteristic, complemented
293	#2486	C₂⁴	1	1	yes	characteristic
294	#2409	C₂²×C₄	1	1	yes	characteristic
295	#2409	C₂²×C₄	1	1	yes	characteristic, complemented
296	#2409	C₂²×C₄	1	1	yes	characteristic, complemented
297	#2409	C₂⁴	1	1	yes	characteristic
298	#2408	C₂²×C₄	1	1	yes	characteristic
299	#2408	C₂²×C₄	1	1	yes	characteristic, complemented
300	#2408	C₂²×C₄	1	1	yes	characteristic, complemented
301	#2408	C₂⁴	1	1	yes	characteristic
302	#2285	C₂²×C₄	1	1	yes	characteristic, complemented
303	#2285	C₂²×C₄	1	1	yes	characteristic, complemented
304	#2283	C₂²×C₄	1	1	yes	characteristic, complemented
305	#2283	C₂²×C₄	1	1	yes	characteristic, complemented
306	#2280	C₂²×C₄	1	1	yes	characteristic
307	#2280	C₂²×C₄	1	1	yes	characteristic
308	#1893	C₂²×C₄	1	4	yes	complemented
309	#1893	C₂²×C₄	1	4	yes	complemented
310	#1893	C₂²×C₄	1	4	yes	complemented
311	#1893	C₂²×C₄	1	4	yes	complemented
312	#1869	C₂²×C₄	1	4	yes	—
313	#1869	C₂²×C₄	1	4	yes	complemented
314	#1869	C₂²×C₄	1	4	yes	complemented
315	#1869	C₂⁴	1	4	yes	—
316	#1820	C₂×D₄	1	4	yes	—
317	#1820	C₂×D₄	1	4	yes	—
318	#1800	C₂⁴	1	4	yes	—
319	#1799	C₂×D₄	1	4	yes	—
320	#1799	C₂×D₄	1	4	yes	—
321	#1799	C₂×D₄	1	4	yes	—
322	#1799	C₂⁴	1	4	yes	—
323	#1786	C₂²×C₄	1	4	yes	complemented
324	#1786	C₂²×C₄	1	4	yes	complemented
325	#1786	C₂²×C₄	1	4	yes	complemented
326	#1786	C₂²×C₄	1	4	yes	complemented
327	#1782	C₂×D₄	1	4	yes	—
328	#1782	C₂×D₄	1	4	yes	—
329	C₄×#99	C₂×D₄	1	4	yes	—
330	C₄×#99	C₂×D₄	1	4	yes	—
331	C₄×#99	C₂×D₄	1	4	yes	—
332	C₄×#99	C₂⁴	1	4	yes	—
333	C₂×#342	C₂×D₄	1	4	yes	—
334	#1460	C₂⁴	1	4	yes	—
335	C₂²×#41	C₄×D₄	1	1	yes	characteristic
336	C₂²×#41	C₄×D₄	1	1	yes	characteristic
337	C₂²×#41	#120	1	1	yes	characteristic
338	C₂²×#41	#120	1	1	yes	characteristic
339	C₂²×#41	#121	1	1	yes	characteristic
340	C₂²×#41	#121	1	1	yes	characteristic
341	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
342	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
343	C₂³×Q₈	#121	1	1	yes	characteristic
344	C₂³×Q₈	C₂³×C₄	1	1	yes	characteristic
345	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
346	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
347	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
348	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
349	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
350	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
351	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
352	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
353	C₂³×D₄	#120	1	1	yes	characteristic
354	C₂³×D₄	C₂³×C₄	1	4	yes	—
355	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
356	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
357	C₂³×D₄	C₂²×D₄	1	4	yes	—
358	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
359	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
360	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
361	C₂⁴×C₄	#120	1	1	yes	characteristic
362	C₂⁴×C₄	#120	1	1	yes	characteristic
363	C₂⁴×C₄	#121	1	1	yes	characteristic
364	C₂⁴×C₄	#121	1	1	yes	characteristic
365	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
366	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
367	C₂³×C₈	C₂³×C₄	1	4	yes	—
368	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
369	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
370	C₂×#127	#99	1	2	yes	—
371	C₂×#127	#99	1	2	yes	—
372	C₂×#127	#99	1	2	yes	—
373	C₂×#127	#99	1	2	yes	—
374	C₂×#127	#99	1	2	yes	—
375	C₂×#127	#99	1	2	yes	—
376	C₂×#127	#99	1	2	yes	—
377	C₂×#127	#99	1	2	yes	—
378	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
379	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
380	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
381	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
382	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
383	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
384	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
385	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
386	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
387	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
388	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
389	C₂×#127	C₂²×D₄	1	4	yes	—
390	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
391	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
392	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
393	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
394	C₂×#121	C₂³×C₄	1	4	yes	—
395	C₂×#121	C₂²×D₄	1	4	yes	—
396	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
399	C₂×C₄×Q₈	C₄×D₄	1	1	yes	characteristic
400	C₂×C₄×Q₈	#121	1	1	yes	characteristic
401	C₂×C₄×Q₈	#121	1	1	yes	characteristic
402	C₂×C₄×Q₈	#121	1	1	yes	characteristic
403	C₂×C₄×Q₈	#121	1	1	yes	characteristic
404	C₂×C₄×Q₈	#121	1	1	yes	characteristic
405	C₂×C₄×Q₈	#121	1	1	yes	characteristic
406	C₂×C₄×Q₈	#123	1	1	yes	characteristic
407	C₂×C₄×Q₈	#123	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×Q₈	C₂×#41	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂×#41	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
413	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
414	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
415	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
416	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
417	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
421	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
422	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
423	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
424	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
425	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
426	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
427	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
428	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
429	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
430	C₂×C₄×D₄	C₄×D₄	1	1	yes	characteristic
431	C₂×C₄×D₄	#120	1	1	yes	characteristic
432	C₂×C₄×D₄	#120	1	1	yes	characteristic
433	C₂×C₄×D₄	#120	1	1	yes	characteristic
434	C₂×C₄×D₄	#120	1	1	yes	characteristic
435	C₂×C₄×D₄	#120	1	1	yes	characteristic
436	C₂×C₄×D₄	#120	1	1	yes	characteristic
437	C₂×C₄×D₄	#121	1	1	yes	characteristic
438	C₂×C₄×D₄	#121	1	1	yes	characteristic
439	C₂×C₄×D₄	#121	1	1	yes	characteristic
440	C₂×C₄×D₄	#121	1	1	yes	characteristic
441	C₂×C₄×D₄	#121	1	1	yes	characteristic
442	C₂×C₄×D₄	#121	1	1	yes	characteristic
443	C₂×C₄×D₄	#123	1	1	yes	characteristic
444	C₂×C₄×D₄	#123	1	1	yes	characteristic
445	C₂×C₄×D₄	#123	1	1	yes	characteristic
446	C₂×C₄×D₄	#123	1	1	yes	characteristic
447	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
448	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
450	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
460	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
462	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
463	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
464	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
465	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
466	C₂×#117	C₄×D₄	1	1	yes	characteristic
467	C₂×#117	C₄×D₄	1	1	yes	characteristic
468	C₂×#117	C₄×D₄	1	1	yes	characteristic
469	C₂×#117	C₄×D₄	1	1	yes	characteristic
470	C₂×#117	C₄×D₄	1	1	yes	characteristic
471	C₂×#117	C₄×D₄	1	1	yes	characteristic
472	C₂×#117	#120	1	1	yes	characteristic
473	C₂×#117	#120	1	1	yes	characteristic
474	C₂×#117	#121	1	1	yes	characteristic
475	C₂×#117	#121	1	1	yes	characteristic
476	C₂×#117	#121	1	1	yes	characteristic
477	C₂×#117	#121	1	1	yes	characteristic
478	C₂×#117	#121	1	1	yes	characteristic
479	C₂×#117	#121	1	1	yes	characteristic
480	C₂×#117	#123	1	1	yes	characteristic
481	C₂×#117	#123	1	1	yes	characteristic
482	C₂×#117	#123	1	1	yes	characteristic
483	C₂×#117	#123	1	1	yes	characteristic
484	C₂×#117	C₂²×D₄	1	1	yes	characteristic
485	C₂×#117	C₂²×D₄	1	1	yes	characteristic
486	C₂×#117	C₂×#41	1	1	yes	characteristic
487	C₂×#117	C₂×#41	1	1	yes	characteristic
488	C₂×#117	C₂×#41	1	1	yes	characteristic
489	C₂×#117	C₂×#41	1	1	yes	characteristic
490	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
491	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
492	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
493	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
494	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
495	C₂²×C₄⋊C₄	#123	1	1	yes	characteristic
496	C₂²×C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
497	C₂²×C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
498	C₂²×C₄⋊C₄	C₂×#41	1	1	yes	characteristic
499	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
500	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
501	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
502	C₂²×C₂²⋊C₄	#123	1	1	yes	characteristic
503	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
504	C₂²×C₂²⋊C₄	C₂×#41	1	1	yes	characteristic
505	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
506	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
507	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
508	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
509	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
510	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
511	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
512	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
513	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
514	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
515	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
516	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
517	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
518	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
519	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
520	C₂²×C₄²	#120	1	1	yes	characteristic
521	C₂²×C₄²	#120	1	1	yes	characteristic
522	C₂²×C₄²	#121	1	1	yes	characteristic
523	C₂²×C₄²	#121	1	1	yes	characteristic
524	C₂²×C₄²	#121	1	1	yes	characteristic
525	C₂²×C₄²	#121	1	1	yes	characteristic
526	C₂²×C₄²	#121	1	1	yes	characteristic
527	C₂²×C₄²	#121	1	1	yes	characteristic
528	C₂²×C₄²	#123	1	1	yes	characteristic
529	C₂²×C₄²	#123	1	1	yes	characteristic
530	C₂²×C₄²	#123	1	1	yes	characteristic
531	C₂²×C₄²	#123	1	1	yes	characteristic
532	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
533	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
534	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
535	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
536	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
537	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
538	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
539	C₂×#99	C₂²×D₄	1	8	yes	—
540	C₂×C₂²⋊C₈	C₂³×C₄	1	4	yes	—
541	#380	C₂³×C₄	1	1	yes	characteristic
542	#380	C₂³×C₄	1	1	yes	characteristic
543	#380	C₂³×C₄	1	1	yes	characteristic
544	#380	C₂³×C₄	1	1	yes	characteristic
545	#342	C₂²×D₄	1	8	yes	—
546	C₂⁵	#386	1	1	yes	characteristic
547	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
548	C₂⁵	C₂×#120	1	1	yes	characteristic
549	C₂²×Q₈	#386	1	1	yes	characteristic
550	C₂²×Q₈	#386	1	1	yes	characteristic
551	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
552	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
553	C₂²×D₄	#386	1	1	yes	characteristic
554	C₂²×D₄	#386	1	1	yes	characteristic
555	C₂²×D₄	#386	1	1	yes	characteristic
556	C₂²×D₄	#386	1	1	yes	characteristic
557	C₂²×D₄	C₂×#99	1	4	yes	—
558	C₂²×D₄	C₂×#99	1	4	yes	—
559	C₂²×D₄	C₂×#99	1	4	yes	—
560	C₂²×D₄	C₂×#99	1	4	yes	—
561	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
562	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
563	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
564	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
565	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
566	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
567	C₂²×D₄	C₂×#120	1	1	yes	characteristic
568	C₂²×D₄	C₂×#120	1	1	yes	characteristic
569	C₂²×D₄	C₂×#120	1	1	yes	characteristic
570	C₂²×D₄	C₂×#121	1	1	yes	characteristic
571	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
572	C₂³×C₄	#386	1	1	yes	characteristic
573	C₂³×C₄	#386	1	1	yes	characteristic
574	C₂³×C₄	#386	1	1	yes	characteristic
575	C₂³×C₄	#386	1	1	yes	characteristic
576	C₂³×C₄	#386	1	1	yes	characteristic
577	C₂³×C₄	#386	1	1	yes	characteristic
578	C₂³×C₄	#386	1	1	yes	characteristic
579	C₂³×C₄	#386	1	1	yes	characteristic
580	C₂³×C₄	#386	1	1	yes	characteristic
581	C₂³×C₄	#386	1	1	yes	characteristic
582	C₂³×C₄	#386	1	1	yes	characteristic
583	C₂³×C₄	#386	1	1	yes	characteristic
584	C₂³×C₄	#386	1	1	yes	characteristic
585	C₂³×C₄	#386	1	1	yes	characteristic
586	C₂³×C₄	#386	1	1	yes	characteristic
587	C₂³×C₄	#386	1	1	yes	characteristic
588	C₂³×C₄	#386	1	1	yes	characteristic
589	C₂³×C₄	#386	1	1	yes	characteristic
590	C₂³×C₄	#386	1	1	yes	characteristic
591	C₂³×C₄	#386	1	1	yes	characteristic
592	C₂³×C₄	#386	1	1	yes	characteristic
593	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
594	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
595	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
596	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
597	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
598	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
599	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
600	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
601	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
602	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
603	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
604	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
605	C₂³×C₄	C₂×#120	1	1	yes	characteristic
606	C₂³×C₄	C₂×#120	1	1	yes	characteristic
607	C₂³×C₄	C₂×#120	1	1	yes	characteristic
608	C₂³×C₄	C₂×#120	1	1	yes	characteristic
609	C₂³×C₄	C₂×#120	1	1	yes	characteristic
610	C₂³×C₄	C₂×#121	1	1	yes	characteristic
611	C₂³×C₄	C₂×#121	1	1	yes	characteristic
612	C₂³×C₄	C₂×#121	1	1	yes	characteristic
613	C₂³×C₄	C₂×#121	1	1	yes	characteristic
614	C₂³×C₄	C₂×#121	1	1	yes	characteristic
615	C₂³×C₄	C₂×#121	1	1	yes	characteristic
616	C₂³×C₄	C₂×#123	1	1	yes	characteristic
617	C₂³×C₄	C₂×#123	1	1	yes	characteristic
618	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
619	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
620	#127	C₂×#99	1	4	yes	—
621	#127	C₂×#99	1	4	yes	—
622	#127	C₂×#99	1	4	yes	—
623	#127	C₂×#99	1	4	yes	—
624	#127	C₂×#99	1	4	yes	—
625	#127	C₂×#99	1	4	yes	—
626	#127	C₂×#99	1	4	yes	—
627	#127	C₂×#99	1	4	yes	—
628	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
629	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
630	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
631	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
632	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
633	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
634	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
635	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
636	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
637	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	4	yes	—
639	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂²×#41	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
662	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂²×#41	1	1	yes	characteristic
677	C₂×C₄²	#386	1	1	yes	characteristic
678	C₂×C₄²	#386	1	1	yes	characteristic
679	C₂×C₄²	#386	1	1	yes	characteristic
680	C₂×C₄²	#386	1	1	yes	characteristic
681	C₂×C₄²	#386	1	1	yes	characteristic
682	C₂×C₄²	#386	1	1	yes	characteristic
683	C₂×C₄²	#386	1	1	yes	characteristic
684	C₂×C₄²	#386	1	1	yes	characteristic
685	C₂×C₄²	#386	1	1	yes	characteristic
686	C₂×C₄²	#386	1	1	yes	characteristic
687	C₂×C₄²	#386	1	1	yes	characteristic
688	C₂×C₄²	#386	1	1	yes	characteristic
689	C₂×C₄²	#386	1	1	yes	characteristic
690	C₂×C₄²	#386	1	1	yes	characteristic
691	C₂×C₄²	#386	1	1	yes	characteristic
692	C₂×C₄²	#386	1	1	yes	characteristic
693	C₂×C₄²	#386	1	1	yes	characteristic
694	C₂×C₄²	#386	1	1	yes	characteristic
695	C₂×C₄²	C₂×#99	1	1	yes	characteristic
696	C₂×C₄²	C₂×#99	1	1	yes	characteristic
697	C₂×C₄²	C₂×#99	1	1	yes	characteristic
698	C₂×C₄²	C₂×#99	1	1	yes	characteristic
699	C₂×C₄²	C₂×#99	1	1	yes	characteristic
700	C₂×C₄²	C₂×#99	1	1	yes	characteristic
701	C₂×C₄²	C₂×#99	1	1	yes	characteristic
702	C₂×C₄²	C₂×#99	1	1	yes	characteristic
703	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
704	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
705	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
706	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
707	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
708	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
709	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
710	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
711	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
712	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
713	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
714	C₂×C₄²	C₂×#121	1	1	yes	characteristic
715	C₂×C₄²	C₂×#121	1	1	yes	characteristic
716	C₂×C₄²	C₂×#121	1	1	yes	characteristic
717	C₂×C₄²	C₂×#121	1	1	yes	characteristic
718	C₂×C₄²	C₂×#121	1	1	yes	characteristic
719	C₂×C₄²	C₂×#121	1	1	yes	characteristic
720	C₂×C₄²	C₂×#123	1	1	yes	characteristic
721	C₂×C₄²	C₂×#123	1	1	yes	characteristic
722	C₂×C₄²	C₂×#123	1	1	yes	characteristic
723	C₂×C₄²	C₂×#123	1	1	yes	characteristic
724	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
725	C₂⁴	C₂×#386	1	1	yes	characteristic
726	C₂⁴	C₂×#386	1	1	yes	characteristic
727	C₂⁴	C₂×#386	1	1	yes	characteristic
728	C₂⁴	C₂×#386	1	1	yes	characteristic
729	C₂⁴	C₂×#386	1	1	yes	characteristic
730	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
731	C₂⁴	C₂²×#120	1	1	yes	characteristic
732	C₂×D₄	#1904	1	4	yes	—
733	C₂×D₄	C₂²×#99	1	8	yes	—
734	C₂×D₄	C₂²×#99	1	8	yes	—
735	C₂×D₄	#3585	1	4	yes	—
736	C₂²×C₄	#1898	1	1	yes	characteristic
737	C₂²×C₄	#1898	1	1	yes	characteristic
738	C₂²×C₄	#1898	1	1	yes	characteristic
739	C₂²×C₄	#1898	1	1	yes	characteristic
740	C₂²×C₄	#1898	1	1	yes	characteristic
741	C₂²×C₄	#1898	1	1	yes	characteristic
742	C₂²×C₄	#1898	1	1	yes	characteristic
743	C₂²×C₄	#1898	1	1	yes	characteristic
744	C₂²×C₄	C₂×#386	1	1	yes	characteristic
745	C₂²×C₄	C₂×#386	1	1	yes	characteristic
746	C₂²×C₄	C₂×#386	1	1	yes	characteristic
747	C₂²×C₄	C₂×#386	1	1	yes	characteristic
748	C₂²×C₄	C₂×#386	1	1	yes	characteristic
749	C₂²×C₄	C₂×#386	1	1	yes	characteristic
750	C₂²×C₄	C₂×#386	1	1	yes	characteristic
751	C₂²×C₄	C₂×#386	1	1	yes	characteristic
752	C₂²×C₄	C₂×#386	1	1	yes	characteristic
753	C₂²×C₄	C₂×#386	1	1	yes	characteristic
754	C₂²×C₄	C₂×#386	1	1	yes	characteristic
755	C₂²×C₄	C₂×#386	1	1	yes	characteristic
756	C₂²×C₄	C₂×#386	1	1	yes	characteristic
757	C₂²×C₄	C₂×#386	1	1	yes	characteristic
758	C₂²×C₄	C₂×#386	1	1	yes	characteristic
759	C₂²×C₄	C₂×#386	1	1	yes	characteristic
760	C₂²×C₄	C₂×#386	1	1	yes	characteristic
761	C₂²×C₄	C₂×#386	1	1	yes	characteristic
762	C₂²×C₄	C₂×#386	1	1	yes	characteristic
763	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
764	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
765	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
766	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
767	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
768	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
769	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
770	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
771	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
772	C₄²	#1898	1	1	yes	characteristic
773	C₄²	#1898	1	1	yes	characteristic
774	C₄²	#1898	1	1	yes	characteristic
775	C₄²	#1898	1	1	yes	characteristic
776	C₄²	#1898	1	1	yes	characteristic
777	C₄²	#1898	1	1	yes	characteristic
778	C₄²	#1898	1	1	yes	characteristic
779	C₄²	#1898	1	1	yes	characteristic
780	C₄²	C₂²×#99	1	1	yes	characteristic
781	C₄²	C₂²×#99	1	1	yes	characteristic
782	C₄²	C₂²×#99	1	1	yes	characteristic
783	C₄²	C₂²×#99	1	1	yes	characteristic
784	C₄²	C₂²×#99	1	1	yes	characteristic
785	C₄²	C₂²×#99	1	1	yes	characteristic
786	C₄²	C₂²×#99	1	1	yes	characteristic
787	C₄²	C₂²×#99	1	1	yes	characteristic
788	C₂³	C₂×#1898	1	1	yes	characteristic
789	C₂³	C₂×#1898	1	1	yes	characteristic
790	C₂³	C₂×#1904	1	2	yes	—
791	C₂³	C₂×#1904	1	2	yes	—
792	C₂³	C₂²×#386	1	1	yes	characteristic
793	C₂³	#60168	1	2	yes	—
794	C₂³	#60367	1	2	yes	—
795	C₂×C₄	C₂×#1898	1	1	yes	characteristic
796	C₂×C₄	C₂×#1898	1	1	yes	characteristic
797	C₂×C₄	C₂×#1898	1	1	yes	characteristic
798	C₂×C₄	C₂×#1898	1	1	yes	characteristic
799	C₂×C₄	C₂×#1898	1	1	yes	characteristic
800	C₂×C₄	C₂×#1898	1	1	yes	characteristic
801	C₂×C₄	C₂×#1898	1	1	yes	characteristic
802	C₂×C₄	C₂×#1898	1	1	yes	characteristic
803	C₂×C₄	C₂×#1898	1	1	yes	characteristic
804	C₂×C₄	C₂×#1898	1	1	yes	characteristic
805	C₂×C₄	C₂×#1904	1	2	yes	—
806	C₂×C₄	#33348	1	2	yes	—
807	C₂×C₄	#33350	1	2	yes	—
808	C₂×C₄	C₂³×#99	1	1	yes	characteristic
809	C₂×C₄	C₂³×#99	1	1	yes	characteristic
810	C₂×C₄	#60423	1	2	yes	—
811	C₂²	#494701	1	2	yes	—
812	C₂²	#6371420	1	1	yes	characteristic
813	C₂²	C₂²×#1898	1	1	yes	characteristic
814	C₂²	C₂²×#1904	1	1	yes	characteristic
815	C₄	#494701	1	2	yes	—
816	C₄	#494758	1	2	yes	—
817	C₄	C₂×#33348	1	1	yes	characteristic
818	C₄	C₂×#33350	1	1	yes	characteristic
819	C₂	#72235984	1	1	yes	characteristic
820	C₂	C₂×#494758	1	1	yes	characteristic
821	C₂	C₂×#494701	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1898
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂×C₄×D₄	C₂⁵
prime radical	#72279493	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂²×#3498 ◁ G
LECS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72316839	C₂	semidirect
2. #72316827	C₂	semidirect
3. #72316775	C₂	semidirect
4. #72316751	C₂	semidirect
5. #72316728	C₂	semidirect
6. #72316715	C₂	semidirect
7. #72316694	C₂	semidirect
8. #72312648	C₂	semidirect
9. C₂×#6385980	C₂	semidirect
10. #72285551	C₂	semidirect
11. #72282464	C₂	semidirect
12. #72282248	C₂	semidirect
15. C₂×#60561	C₄	semidirect
16. C₂²×#3038	C₄	semidirect
18. #6512762	C₄	semidirect
20. #6512761	C₄	semidirect
22. #6512748	C₄	semidirect
24. #6512747	C₄	semidirect
26. #6440417	C₄	semidirect
28. #6437510	C₄	semidirect
33. #6374554	C₄	semidirect
35. #6374304	C₄	semidirect
40. #496509	C₂²	semidirect
41. #496508	C₂²	semidirect
42. #496417	C₂²	semidirect
43. #496334	C₂²	semidirect
44. #495588	C₂²	semidirect
45. #495587	C₂²	semidirect
46. #482630	C₂²	semidirect
47. #482629	C₂²	semidirect
48. #482427	C₂²	semidirect
49. #482361	C₂²	semidirect
50. #482236	C₂²	semidirect
51. #482234	C₂²	semidirect
55. #138962	C₂²	semidirect
56. #138960	C₂²	semidirect
57. #138886	C₂²	semidirect
58. #138884	C₂²	semidirect
59. #127399	C₂²	semidirect
60. #127389	C₂²	semidirect
61. #127388	C₂²	semidirect
62. #127141	C₂²	semidirect
63. #127124	C₂²	semidirect
64. #127106	C₂²	semidirect
65. C₂³×AGL(1,ℤ/8)	C₂×C₄	semidirect
84. C₂²×C₄×#41	C₂×C₄	semidirect
86. C₂×#3112	C₂×C₄	semidirect
87. C₂×#3109	C₂×C₄	semidirect
88. C₂×#3103	C₂×C₄	semidirect
89. C₂×#3100	C₂×C₄	semidirect
90. C₂×#3094	C₂×C₄	semidirect
91. C₂²×#460	C₂×C₄	semidirect
92. C₂²×#460	C₂×C₄	semidirect
93. C₂²×#459	C₂×C₄	semidirect
94. C₂²×#459	C₂×C₄	semidirect
95. C₂×#3006	C₂×C₄	semidirect
96. C₂×#2920	C₂×C₄	semidirect
97. C₂²×#423	C₂×C₄	semidirect
98. C₂²×#418	C₂×C₄	semidirect
99. #34971	C₂×C₄	semidirect
101. #34963	C₂×C₄	semidirect
103. #34952	C₂×C₄	semidirect
105. #34935	C₂×C₄	semidirect
107. #34809	C₂×C₄	semidirect
109. #34736	C₂×C₄	semidirect
111. #34012	C₂×C₄	semidirect
112. #24033	C₂×C₄	semidirect
113. #24033	C₂×C₄	semidirect
114. #24033	C₂×C₄	semidirect
116. #24032	C₂×C₄	semidirect
117. #24032	C₂×C₄	semidirect
118. #24032	C₂×C₄	semidirect
120. #23849	C₂×C₄	semidirect
121. #23849	C₂×C₄	semidirect
122. #23849	C₂×C₄	semidirect
124. #23848	C₂×C₄	semidirect
125. #23848	C₂×C₄	semidirect
126. #23848	C₂×C₄	semidirect
129. #21888	C₂×C₄	semidirect
130. #21888	C₂×C₄	semidirect
131. #21884	C₂×C₄	semidirect
132. #21884	C₂×C₄	semidirect
133. #21851	C₂×C₄	semidirect
135. #21847	C₂×C₄	semidirect
137. #21810	C₂×C₄	semidirect
138. #21810	C₂×C₄	semidirect
139. #21803	C₂×C₄	semidirect
140. #21803	C₂×C₄	semidirect
141. #20973	C₂×C₄	semidirect
142. #20973	C₂×C₄	semidirect
143. #20898	C₂×C₄	semidirect
159. #20598	C₂×C₄	semidirect
160. #20598	C₂×C₄	semidirect
167. #13296	C₂³	semidirect
168. #13295	C₂³	semidirect
169. #13221	C₂³	semidirect
170. #13220	C₂³	semidirect
171. #11899	C₂³	semidirect
172. #11898	C₂³	semidirect
173. #11874	C₂³	semidirect
174. #11873	C₂³	semidirect
176. #7236	C₂³	semidirect
177. #7204	C₂³	semidirect
183. C₂³×SD₁₆	C₂²×C₄	semidirect
184. C₂³×D₈	C₂²×C₄	semidirect
252. C₂²×C₄×Q₈	C₂²×C₄	semidirect
253. C₂²×C₄×Q₈	C₂²×C₄	semidirect
259. C₂²×C₄×D₄	C₂²×C₄	semidirect
260. C₂²×C₄×D₄	C₂²×C₄	semidirect
274. C₂×#481	C₂²×C₄	semidirect
275. C₂×#480	C₂²×C₄	semidirect
276. C₂×#448	C₂²×C₄	semidirect
277. C₂×#447	C₂²×C₄	semidirect
278. C₂×#432	C₂²×C₄	semidirect
279. C₂×#431	C₂²×C₄	semidirect
280. C₂²×C₄⋊C₈	C₂²×C₄	semidirect
281. C₂²×C₄⋊C₈	C₂²×C₄	semidirect
282. C₂²×#102	C₂²×C₄	semidirect
283. C₂²×#102	C₂²×C₄	semidirect
287. #2487	C₂²×C₄	semidirect
288. #2487	C₂²×C₄	semidirect
291. #2486	C₂²×C₄	semidirect
292. #2486	C₂²×C₄	semidirect
295. #2409	C₂²×C₄	semidirect
296. #2409	C₂²×C₄	semidirect
299. #2408	C₂²×C₄	semidirect
300. #2408	C₂²×C₄	semidirect
302. #2285	C₂²×C₄	semidirect
303. #2285	C₂²×C₄	semidirect
304. #2283	C₂²×C₄	semidirect
305. #2283	C₂²×C₄	semidirect
308. #1893	C₂²×C₄	semidirect
309. #1893	C₂²×C₄	semidirect
310. #1893	C₂²×C₄	semidirect
311. #1893	C₂²×C₄	semidirect
313. #1869	C₂²×C₄	semidirect
314. #1869	C₂²×C₄	semidirect
323. #1786	C₂²×C₄	semidirect
324. #1786	C₂²×C₄	semidirect
325. #1786	C₂²×C₄	semidirect
326. #1786	C₂²×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72316839	2
#72316827	2
#72316775	2
#72316751	2
#72316728	2
#72316715	2
#72316694	2
#72312648	2
C₂×#6385980	2
#72285551	2
#72282464	2
#72282248	2
#72279493	2