Subgroups — #72310871

Order 2048.

At least 8808 conjugacy classes of subgroups; only the 1534 normal subgroups are shown.

The subgroup lattice has 737 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72310866	C₂	1	1	yes	maximal, characteristic, complemented
2	#72310855	C₂	1	4	yes	maximal, complemented
3	#72310854	C₂	1	4	yes	maximal, complemented
4	#72310819	C₂	1	1	yes	maximal, characteristic, complemented
5	#72310758	C₂	1	4	yes	maximal, complemented
6	#72310731	C₂	1	1	yes	maximal, characteristic, complemented
7	#72302947	C₂	1	1	yes	maximal, characteristic, complemented
8	#72302942	C₂	1	1	yes	maximal, characteristic, complemented
9	#72302941	C₂	1	1	yes	maximal, characteristic
10	#72302908	C₂	1	1	yes	maximal, characteristic, complemented
11	#72266931	C₂	1	4	yes	maximal, complemented
12	#72265901	C₂	1	4	yes	maximal, complemented
13	#72233461	C₂	1	4	yes	maximal, complemented
14	#10586020	C₂²	1	1	yes	characteristic
15	#7634872	C₄	1	2	yes	complemented
16	#7629120	C₂²	1	1	yes	characteristic
17	#6470235	C₄	1	2	yes	complemented
18	#6470235	C₂²	1	2	yes	—
19	#6470234	C₄	1	2	yes	complemented
20	#6470234	C₂²	1	2	yes	—
21	#6470232	C₄	1	2	yes	complemented
22	#6470232	C₂²	1	2	yes	—
23	#6470231	C₄	1	2	yes	complemented
24	#6470231	C₂²	1	2	yes	—
25	#6440459	C₄	1	2	yes	complemented
26	#6440459	C₂²	1	2	yes	—
27	#6437616	C₄	1	2	yes	complemented
28	#6437616	C₂²	1	2	yes	—
29	#6374188	C₂²	1	4	yes	—
30	#6374187	C₂²	1	4	yes	—
31	#6374186	C₂²	1	4	yes	—
32	#6374127	C₄	1	2	yes	complemented
33	#6370703	C₂²	1	1	yes	characteristic
34	#6370692	C₂²	1	1	yes	characteristic
35	#6370692	C₂²	1	1	yes	characteristic
36	#6370692	C₂²	1	1	yes	characteristic
37	#6370692	C₂²	1	1	yes	characteristic
38	#496241	C₂²	1	2	yes	complemented
39	#496240	C₂²	1	2	yes	complemented
40	#496238	C₂²	1	2	yes	complemented
41	#496237	C₂²	1	2	yes	complemented
42	#493857	C₂²	1	2	yes	complemented
43	#493392	C₂²	1	4	yes	—
44	#493391	C₂²	1	4	yes	—
45	#493390	C₂²	1	4	yes	—
46	#493352	C₂²	1	2	yes	complemented
47	#213831	C₂²	1	2	yes	complemented
48	#213830	C₂²	1	2	yes	complemented
49	#213829	C₂²	1	2	yes	complemented
50	#213828	C₂²	1	2	yes	complemented
51	#190099	C₂²	1	2	yes	complemented
52	#188029	C₂²	1	2	yes	complemented
53	#139843	C₂²	1	16	yes	complemented
54	#139843	C₂²	1	16	yes	complemented
55	#139750	C₂²	1	16	yes	complemented
56	#139749	C₂²	1	16	yes	complemented
57	#128067	C₂²	1	4	yes	complemented
58	#128067	C₂²	1	4	yes	complemented
59	#128062	C₂²	1	4	yes	complemented
60	#128061	C₂²	1	4	yes	complemented
61	#128024	C₂²	1	4	yes	complemented
62	#128016	C₂²	1	4	yes	complemented
63	C₂²×#585	D₄	1	1	yes	characteristic
64	C₂²×#585	C₂³	1	1	yes	characteristic
65	#62859	D₄	1	2	yes	—
66	#62859	D₄	1	2	yes	—
67	#62852	C₂×C₄	1	2	yes	—
68	#62852	C₂³	1	2	yes	—
69	#62842	C₂×C₄	1	2	yes	—
70	#62842	D₄	1	2	yes	—
71	#62842	D₄	1	2	yes	—
72	#62842	C₂³	1	2	yes	—
73	#62811	C₂×C₄	1	2	yes	—
74	#62811	D₄	1	2	yes	—
75	#62811	D₄	1	2	yes	—
76	#62811	C₂³	1	2	yes	—
77	C₂×#3449	C₂×C₄	1	2	yes	—
78	C₂×#3449	D₄	1	2	yes	—
79	C₂²×#525	C₂×C₄	1	1	yes	characteristic, complemented
80	C₂²×#525	C₂×C₄	1	1	yes	characteristic, complemented
81	C₂²×#525	C₂³	1	1	yes	characteristic
82	C₂×#3428	D₄	1	1	yes	characteristic
83	C₂²×#410	D₄	1	2	yes	complemented
84	#36965	C₂×C₄	1	4	yes	complemented
85	#36955	C₂×C₄	1	4	yes	complemented
86	#36714	C₂×C₄	1	4	yes	complemented
87	#36702	C₂×C₄	1	4	yes	complemented
88	#36614	C₂×C₄	1	4	yes	complemented
89	#35446	C₂×C₄	1	1	yes	characteristic, complemented
90	#35446	C₂×C₄	1	1	yes	characteristic, complemented
91	#35446	C₂³	1	1	yes	characteristic
92	#35446	C₂³	1	1	yes	characteristic
93	#35346	C₂×C₄	1	1	yes	characteristic, complemented
94	#35346	C₂×C₄	1	1	yes	characteristic, complemented
95	#35346	C₂³	1	1	yes	characteristic
96	#35346	C₂³	1	1	yes	characteristic
97	#34635	C₂×C₄	1	4	yes	complemented
98	#34044	C₂×C₄	1	2	yes	complemented
99	#34044	C₂×C₄	1	1	yes	characteristic, complemented
100	#34044	C₂×C₄	1	1	yes	characteristic, complemented
101	#34044	D₄	1	2	yes	complemented
102	#34044	C₂³	1	1	yes	characteristic
103	#24058	C₂×C₄	1	4	yes	complemented
104	#24058	C₂×C₄	1	4	yes	complemented
105	#24058	C₂×C₄	1	4	yes	complemented
106	#24058	C₂×C₄	1	4	yes	complemented
107	#24058	C₂×C₄	1	4	yes	complemented
108	#24058	C₂×C₄	1	4	yes	complemented
109	#24058	C₂³	1	4	yes	—
110	#24058	C₂³	1	4	yes	—
111	#23901	C₂×C₄	1	4	yes	complemented
112	#23901	C₂×C₄	1	4	yes	complemented
113	#23901	C₂×C₄	1	4	yes	complemented
114	#23901	C₂³	1	4	yes	—
115	#23900	C₂×C₄	1	4	yes	complemented
116	#23900	C₂×C₄	1	4	yes	complemented
117	#23900	C₂×C₄	1	4	yes	complemented
118	#23900	C₂³	1	4	yes	—
119	#21776	C₂³	1	16	yes	—
120	#21750	C₂×C₄	1	4	yes	complemented
121	#21750	C₂×C₄	1	4	yes	complemented
122	#21749	C₂×C₄	1	4	yes	complemented
123	#21749	C₂×C₄	1	4	yes	complemented
124	#20983	C₂×C₄	1	4	yes	complemented
125	#20983	C₂×C₄	1	4	yes	complemented
126	#20592	C₂³	1	2	yes	—
127	#20592	C₂³	1	2	yes	—
128	#20591	C₂³	1	2	yes	—
129	#20587	D₄	1	2	yes	complemented
130	#20586	C₂×C₄	1	2	yes	complemented
131	#20586	D₄	1	2	yes	complemented
132	#20586	C₂³	1	2	yes	—
133	#20586	C₂³	1	2	yes	—
134	#20586	C₂³	1	2	yes	—
135	#20586	C₂³	1	2	yes	—
136	#20585	C₂×C₄	1	2	yes	complemented
137	#20585	D₄	1	2	yes	complemented
138	#20585	D₄	1	2	yes	complemented
139	#20585	C₂³	1	2	yes	—
140	#20585	C₂³	1	2	yes	—
141	#20585	C₂³	1	2	yes	—
142	#20585	C₂³	1	2	yes	—
143	#20584	C₂×C₄	1	2	yes	complemented
144	#20584	D₄	1	2	yes	complemented
145	#20584	D₄	1	2	yes	complemented
146	#20584	C₂³	1	2	yes	—
147	#20584	C₂³	1	2	yes	—
148	#20584	C₂³	1	2	yes	—
149	#20584	C₂³	1	2	yes	—
150	#12854	C₂³	1	4	yes	complemented
151	#12854	C₂³	1	4	yes	complemented
152	#12705	C₂³	1	16	yes	—
153	#12688	C₂³	1	4	yes	complemented
154	#12687	C₂³	1	4	yes	complemented
155	#8746	C₂³	1	4	yes	complemented
156	#8746	C₂³	1	4	yes	complemented
157	#8543	C₂³	1	4	yes	complemented
158	#8541	C₂³	1	4	yes	complemented
159	#7316	C₂³	1	16	yes	complemented
160	#7310	C₂³	1	16	yes	complemented
161	C₂×#585	C₂²⋊C₄	1	2	yes	—
162	C₂×#585	C₂²⋊C₄	1	2	yes	—
163	C₂×#585	C₂×D₄	1	2	yes	—
164	C₂×#585	C₂×D₄	1	2	yes	—
165	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
166	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
167	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
168	C₂²×2₋¹⁺⁴	#41	1	1	yes	characteristic
169	C₂²×2₋¹⁺⁴	#41	1	1	yes	characteristic
170	C₂²×2₋¹⁺⁴	#41	1	1	yes	characteristic
171	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	2	yes	—
172	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
173	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
174	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
175	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
176	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
177	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
178	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
179	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
180	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
181	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
182	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
183	C₂³×#41	C₂²⋊C₄	1	2	yes	—
184	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
185	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
186	C₂³×#41	C₂×D₄	1	1	yes	characteristic
187	C₂³×#41	C₂×D₄	1	1	yes	characteristic
188	C₂³×#41	C₂×D₄	1	1	yes	characteristic
189	C₂³×#41	C₂×D₄	1	1	yes	characteristic
190	C₂³×#41	C₂×D₄	1	1	yes	characteristic
191	C₂³×#41	C₂×D₄	1	1	yes	characteristic
192	C₂³×#41	C₂×D₄	1	1	yes	characteristic
193	C₂³×#41	C₂×D₄	1	1	yes	characteristic
194	C₂³×#41	#41	1	1	yes	characteristic
195	C₂³×#41	#41	1	1	yes	characteristic
196	C₂³×#41	#41	1	1	yes	characteristic
197	C₂³×#41	#41	1	1	yes	characteristic
198	C₂³×#41	C₂⁴	1	1	yes	characteristic
199	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic, complemented
200	#3485	C₂²⋊C₄	1	4	yes	—
201	#3485	C₂²⋊C₄	1	4	yes	—
202	#3485	C₂²⋊C₄	1	4	yes	—
203	#3485	C₂²⋊C₄	1	4	yes	—
204	#3485	C₂×D₄	1	4	yes	—
205	#3485	C₂×D₄	1	4	yes	—
206	#3485	C₂×D₄	1	4	yes	—
207	#3485	C₂×D₄	1	4	yes	—
208	#3484	C₂²⋊C₄	1	4	yes	—
209	#3484	C₂²⋊C₄	1	4	yes	—
210	#3484	C₂²×C₄	1	4	yes	—
211	#3484	C₂²×C₄	1	4	yes	—
212	#3484	C₂²×C₄	1	4	yes	—
213	#3484	C₂×D₄	1	4	yes	—
214	#3484	C₂×D₄	1	4	yes	—
215	#3484	C₂⁴	1	4	yes	—
216	#3449	C₂²⋊C₄	1	4	yes	—
217	#3449	C₂²⋊C₄	1	4	yes	—
218	#3449	C₂×D₄	1	4	yes	—
219	#3449	C₂×D₄	1	4	yes	—
220	C₂×#536	C₂²⋊C₄	1	4	yes	—
221	C₂×#535	C₂²×C₄	1	4	yes	—
222	C₂×#534	C₂²⋊C₄	1	4	yes	—
223	C₂×#534	C₂²⋊C₄	1	4	yes	—
224	C₂×#534	C₂²×C₄	1	4	yes	—
225	C₂×#534	C₂×D₄	1	4	yes	—
226	C₂×#525	C₂²⋊C₄	1	4	yes	—
227	C₂×#525	C₂²×C₄	1	4	yes	—
228	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
229	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
230	C₂²×#123	C₂²×C₄	1	1	yes	characteristic, complemented
231	C₂²×#123	C₂²×C₄	1	1	yes	characteristic, complemented
232	C₂²×#123	C₂²×C₄	1	1	yes	characteristic, complemented
233	C₂²×#123	C₂⁴	1	1	yes	characteristic
234	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
235	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
236	C₂²×#120	C₂²×C₄	1	1	yes	characteristic, complemented
237	C₂²×#120	C₂²×C₄	1	1	yes	characteristic, complemented
238	C₂²×#120	C₂²×C₄	1	1	yes	characteristic, complemented
239	C₂²×#120	C₂⁴	1	1	yes	characteristic
240	#3428	C₂²⋊C₄	1	2	yes	—
241	#3428	C₂²⋊C₄	1	2	yes	—
242	#3428	C₂×D₄	1	2	yes	—
243	#3428	C₂×D₄	1	2	yes	—
244	C₂×#518	C₂²⋊C₄	1	2	yes	—
245	C₂×#518	C₂×D₄	1	2	yes	—
246	C₂²×#117	C₂²⋊C₄	1	2	yes	—
247	C₂²×#117	C₂²×C₄	1	1	yes	characteristic, complemented
248	C₂²×#117	C₂²×C₄	1	1	yes	characteristic, complemented
249	C₂²×#117	C₂²×C₄	1	1	yes	characteristic, complemented
250	C₂×#410	C₂×D₄	1	4	yes	—
251	C₂×#410	C₂×D₄	1	4	yes	—
252	C₂²×#99	C₂×D₄	1	4	yes	—
253	#2849	C₂²×C₄	1	8	yes	complemented
254	#2846	C₂²×C₄	1	8	yes	complemented
255	#2622	C₂²×C₄	1	8	yes	complemented
256	#2622	C₂²×C₄	1	8	yes	complemented
257	#2309	C₂²×C₄	1	4	yes	—
258	#2309	C₂×D₄	1	4	yes	—
259	#2308	C₂²×C₄	1	1	yes	characteristic
260	#2308	C₂²×C₄	1	1	yes	characteristic
261	#2308	C₂²×C₄	1	1	yes	characteristic
262	#2308	C₂²×C₄	1	1	yes	characteristic
263	#2308	C₂²×C₄	1	4	yes	complemented
264	#2308	C₂²×C₄	1	1	yes	characteristic, complemented
265	#2308	C₂²×C₄	1	1	yes	characteristic, complemented
266	#2308	C₂²×C₄	1	1	yes	characteristic, complemented
267	#2308	C₂²×C₄	1	1	yes	characteristic, complemented
268	#2308	C₂²×C₄	1	1	yes	characteristic, complemented
269	#2308	C₂²×C₄	1	1	yes	characteristic, complemented
270	#2308	C₂×D₄	1	4	yes	—
271	#2308	C₂⁴	1	1	yes	characteristic
272	#2308	C₂⁴	1	1	yes	characteristic
273	#2280	C₂²×C₄	1	4	yes	complemented
274	#2280	C₂×D₄	1	4	yes	—
275	#1898	C₂²×C₄	1	8	yes	complemented
276	#1898	C₂²×C₄	1	8	yes	complemented
277	#1898	C₂²×C₄	1	8	yes	complemented
278	#1898	C₂²×C₄	1	8	yes	complemented
279	#1783	C₂⁴	1	4	yes	—
280	#1782	C₂×D₄	1	4	yes	—
281	#1782	C₂×D₄	1	4	yes	—
282	#1781	C₂²×C₄	1	4	yes	—
283	#1781	C₂²×C₄	1	4	yes	complemented
284	#1781	C₂²×C₄	1	4	yes	complemented
285	#1781	C₂×D₄	1	4	yes	—
286	#1781	C₂×D₄	1	4	yes	—
287	#1781	C₂×D₄	1	4	yes	—
288	#1781	C₂×D₄	1	4	yes	—
289	#1781	C₂⁴	1	4	yes	—
290	#1781	C₂⁴	1	4	yes	—
291	#1781	C₂⁴	1	4	yes	—
292	#1781	C₂⁴	1	4	yes	—
293	C₂⁶	C₂³×C₄	1	1	yes	characteristic
294	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	4	yes	—
295	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	4	yes	—
296	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	4	yes	—
297	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
298	C₂²×#41	#99	1	4	yes	complemented
299	C₂²×#41	#99	1	4	yes	complemented
300	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	—
309	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	—
310	C₂²×#41	C₄×D₄	1	1	yes	characteristic
311	C₂²×#41	C₄×D₄	1	1	yes	characteristic
312	C₂²×#41	C₄×D₄	1	1	yes	characteristic
313	C₂²×#41	C₄×D₄	1	1	yes	characteristic
314	C₂²×#41	C₄×D₄	1	1	yes	characteristic
315	C₂²×#41	C₄×D₄	1	1	yes	characteristic
316	C₂²×#41	C₄×D₄	1	1	yes	characteristic
317	C₂²×#41	C₄×D₄	1	1	yes	characteristic
318	C₂²×#41	C₄×D₄	1	1	yes	characteristic
319	C₂²×#41	C₄×D₄	1	1	yes	characteristic
320	C₂²×#41	C₄×D₄	1	1	yes	characteristic
321	C₂²×#41	C₄×D₄	1	1	yes	characteristic
322	C₂²×#41	C₄×D₄	1	1	yes	characteristic
323	C₂²×#41	C₄×D₄	1	1	yes	characteristic
324	C₂²×#41	C₄×D₄	1	1	yes	characteristic
325	C₂²×#41	C₄×D₄	1	1	yes	characteristic
326	C₂²×#41	C₄×D₄	1	1	yes	characteristic
327	C₂²×#41	C₄×D₄	1	1	yes	characteristic
328	C₂²×#41	C₄×D₄	1	1	yes	characteristic
329	C₂²×#41	C₄×D₄	1	1	yes	characteristic
330	C₂²×#41	#120	1	1	yes	characteristic
331	C₂²×#41	#120	1	1	yes	characteristic
332	C₂²×#41	#120	1	1	yes	characteristic
333	C₂²×#41	#120	1	1	yes	characteristic
334	C₂²×#41	#120	1	1	yes	characteristic
335	C₂²×#41	#120	1	1	yes	characteristic
336	C₂²×#41	#120	1	1	yes	characteristic
337	C₂²×#41	#120	1	1	yes	characteristic
338	C₂²×#41	#121	1	1	yes	characteristic
339	C₂²×#41	#121	1	1	yes	characteristic
340	C₂²×#41	#121	1	1	yes	characteristic
341	C₂²×#41	#121	1	1	yes	characteristic
342	C₂²×#41	#121	1	1	yes	characteristic
343	C₂²×#41	#121	1	1	yes	characteristic
344	C₂²×#41	#121	1	1	yes	characteristic
345	C₂²×#41	#121	1	1	yes	characteristic
346	C₂²×#41	#121	1	1	yes	characteristic
347	C₂²×#41	#121	1	1	yes	characteristic
348	C₂²×#41	#121	1	1	yes	characteristic
349	C₂²×#41	#121	1	1	yes	characteristic
350	C₂²×#41	#121	1	1	yes	characteristic
351	C₂²×#41	#121	1	1	yes	characteristic
352	C₂²×#41	#121	1	1	yes	characteristic
353	C₂²×#41	#121	1	1	yes	characteristic
354	C₂²×#41	#123	1	1	yes	characteristic
355	C₂²×#41	#123	1	1	yes	characteristic
356	C₂²×#41	#123	1	1	yes	characteristic
357	C₂²×#41	#123	1	1	yes	characteristic
358	C₂²×#41	#123	1	1	yes	characteristic
359	C₂²×#41	#123	1	1	yes	characteristic
360	C₂²×#41	#123	1	1	yes	characteristic
361	C₂²×#41	#123	1	1	yes	characteristic
362	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
363	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
364	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
365	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
366	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
367	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
368	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
369	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
370	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
371	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
372	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
373	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
374	C₂²×#41	C₂×#41	1	1	yes	characteristic
375	C₂²×#41	C₂×#41	1	1	yes	characteristic
376	C₂²×#41	C₂×#41	1	1	yes	characteristic
377	C₂²×#41	C₂×#41	1	1	yes	characteristic
378	C₂²×#41	C₂×#41	1	1	yes	characteristic
379	C₂²×#41	C₂×#41	1	1	yes	characteristic
380	C₂²×#41	C₂×#41	1	1	yes	characteristic
381	C₂²×#41	C₂×#41	1	1	yes	characteristic
382	C₂³×Q₈	#99	1	2	yes	complemented
383	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
384	C₂³×Q₈	C₄×D₄	1	1	yes	characteristic
385	C₂³×Q₈	#120	1	1	yes	characteristic
386	C₂³×Q₈	#121	1	1	yes	characteristic
387	C₂³×Q₈	#121	1	1	yes	characteristic
388	C₂³×Q₈	#121	1	1	yes	characteristic
389	C₂³×Q₈	#121	1	1	yes	characteristic
390	C₂³×Q₈	#121	1	1	yes	characteristic
391	C₂³×Q₈	#121	1	1	yes	characteristic
392	C₂³×Q₈	#123	1	1	yes	characteristic
393	C₂³×Q₈	#123	1	1	yes	characteristic
394	C₂³×Q₈	#123	1	1	yes	characteristic
395	C₂³×Q₈	#123	1	1	yes	characteristic
396	C₂³×Q₈	#123	1	1	yes	characteristic
397	C₂³×Q₈	C₂×#41	1	1	yes	characteristic
398	C₂³×D₄	#99	1	2	yes	complemented
399	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
402	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
403	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
405	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
406	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
407	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
408	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
409	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
410	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
411	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
412	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
413	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
414	C₂³×D₄	#120	1	1	yes	characteristic
415	C₂³×D₄	#120	1	1	yes	characteristic
416	C₂³×D₄	#120	1	1	yes	characteristic
417	C₂³×D₄	#120	1	1	yes	characteristic
418	C₂³×D₄	#120	1	1	yes	characteristic
419	C₂³×D₄	#121	1	1	yes	characteristic
420	C₂³×D₄	#121	1	1	yes	characteristic
421	C₂³×D₄	#121	1	1	yes	characteristic
422	C₂³×D₄	#121	1	1	yes	characteristic
423	C₂³×D₄	#121	1	1	yes	characteristic
424	C₂³×D₄	#121	1	1	yes	characteristic
425	C₂³×D₄	#123	1	1	yes	characteristic
426	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
427	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
428	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
429	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
430	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
431	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
432	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
433	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
434	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
435	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
436	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
437	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
438	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
439	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
440	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
441	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
442	C₂³×D₄	C₂×#41	1	1	yes	characteristic
443	C₂³×D₄	C₂×#41	1	1	yes	characteristic
444	C₂³×D₄	C₂⁵	1	1	yes	characteristic
445	C₂⁴×C₄	#99	1	4	yes	complemented
446	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
447	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
448	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
449	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
450	C₂⁴×C₄	#120	1	1	yes	characteristic
451	C₂⁴×C₄	#120	1	1	yes	characteristic
452	C₂⁴×C₄	#121	1	1	yes	characteristic
453	C₂⁴×C₄	#121	1	1	yes	characteristic
454	C₂⁴×C₄	#121	1	1	yes	characteristic
455	C₂⁴×C₄	#121	1	1	yes	characteristic
456	C₂⁴×C₄	#123	1	1	yes	characteristic
457	C₂⁴×C₄	#123	1	1	yes	characteristic
458	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
459	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
460	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
461	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
462	#534	C₂×C₂²⋊C₄	1	8	yes	—
463	#534	C₂×C₂²⋊C₄	1	8	yes	—
464	#534	C₂×C₂²⋊C₄	1	8	yes	—
465	#534	C₂²×D₄	1	8	yes	—
466	C₂×#123	C₂×C₂²⋊C₄	1	8	yes	—
467	C₂×#123	C₂×C₂²⋊C₄	1	8	yes	—
468	C₂×#120	C₂×C₂²⋊C₄	1	8	yes	—
469	C₂×#120	C₂³×C₄	1	8	yes	—
470	#518	C₂×C₂²⋊C₄	1	4	yes	—
471	#518	C₂×C₂²⋊C₄	1	4	yes	—
472	#518	C₂×C₂²⋊C₄	1	4	yes	—
473	#518	C₂²×D₄	1	4	yes	—
474	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
475	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	—
476	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
477	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
478	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
479	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
480	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
481	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
482	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
483	C₂×#99	C₂²×D₄	1	8	yes	—
484	#379	C₂³×C₄	1	8	yes	—
485	#379	C₂²×D₄	1	8	yes	—
486	C₂⁵	#386	1	1	yes	characteristic
487	C₂⁵	#386	1	1	yes	characteristic
488	C₂⁵	#386	1	1	yes	characteristic
489	C₂⁵	#386	1	1	yes	characteristic
490	C₂⁵	C₂×#99	1	4	yes	—
491	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
492	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
493	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
494	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
495	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
496	C₂⁵	C₂×#120	1	1	yes	characteristic
497	C₂⁵	C₂×#120	1	1	yes	characteristic
498	C₂⁵	C₂×#121	1	1	yes	characteristic
499	C₂⁵	C₂×#121	1	1	yes	characteristic
500	C₂⁵	C₂⁴×C₄	1	1	yes	characteristic
501	C₂⁵	C₂³×D₄	1	1	yes	characteristic
502	C₂²×Q₈	#386	1	1	yes	characteristic
503	C₂²×Q₈	#386	1	1	yes	characteristic
504	C₂²×Q₈	#386	1	1	yes	characteristic
505	C₂²×Q₈	#386	1	1	yes	characteristic
506	C₂²×Q₈	#386	1	1	yes	characteristic
507	C₂²×Q₈	#386	1	1	yes	characteristic
508	C₂²×Q₈	#386	1	1	yes	characteristic
509	C₂²×Q₈	#386	1	1	yes	characteristic
510	C₂²×Q₈	#386	1	1	yes	characteristic
511	C₂²×Q₈	#386	1	1	yes	characteristic
512	C₂²×Q₈	#386	1	1	yes	characteristic
513	C₂²×Q₈	#386	1	1	yes	characteristic
514	C₂²×Q₈	C₂×#99	1	4	yes	—
515	C₂²×Q₈	C₂×#99	1	4	yes	—
516	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
517	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
518	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
519	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
520	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
521	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
522	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
523	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
524	C₂²×D₄	#386	1	1	yes	characteristic
525	C₂²×D₄	#386	1	1	yes	characteristic
526	C₂²×D₄	#386	1	1	yes	characteristic
527	C₂²×D₄	#386	1	1	yes	characteristic
528	C₂²×D₄	#386	1	1	yes	characteristic
529	C₂²×D₄	#386	1	1	yes	characteristic
530	C₂²×D₄	#386	1	1	yes	characteristic
531	C₂²×D₄	#386	1	1	yes	characteristic
532	C₂²×D₄	#386	1	1	yes	characteristic
533	C₂²×D₄	#386	1	1	yes	characteristic
534	C₂²×D₄	#386	1	1	yes	characteristic
535	C₂²×D₄	#386	1	1	yes	characteristic
536	C₂²×D₄	#386	1	1	yes	characteristic
537	C₂²×D₄	#386	1	1	yes	characteristic
538	C₂²×D₄	#386	1	1	yes	characteristic
539	C₂²×D₄	#386	1	1	yes	characteristic
540	C₂²×D₄	#386	1	1	yes	characteristic
541	C₂²×D₄	#386	1	1	yes	characteristic
542	C₂²×D₄	#386	1	1	yes	characteristic
543	C₂²×D₄	#386	1	1	yes	characteristic
544	C₂²×D₄	C₂×#99	1	4	yes	—
545	C₂²×D₄	C₂×#99	1	8	yes	—
546	C₂²×D₄	C₂×#99	1	4	yes	—
547	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
548	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
549	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
550	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
551	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
552	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
553	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
554	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
555	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
556	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
557	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
558	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
559	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
560	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
561	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
562	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
563	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
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×C₄×D₄	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×#120	1	1	yes	characteristic
571	C₂²×D₄	C₂×#120	1	1	yes	characteristic
572	C₂²×D₄	C₂×#120	1	1	yes	characteristic
573	C₂²×D₄	C₂×#120	1	1	yes	characteristic
574	C₂²×D₄	C₂×#121	1	1	yes	characteristic
575	C₂²×D₄	C₂×#121	1	1	yes	characteristic
576	C₂²×D₄	C₂×#121	1	1	yes	characteristic
577	C₂²×D₄	C₂×#121	1	1	yes	characteristic
578	C₂²×D₄	C₂×#121	1	1	yes	characteristic
579	C₂²×D₄	C₂×#121	1	1	yes	characteristic
580	C₂²×D₄	C₂×#121	1	1	yes	characteristic
581	C₂²×D₄	C₂×#121	1	1	yes	characteristic
582	C₂²×D₄	C₂×#123	1	1	yes	characteristic
583	C₂²×D₄	C₂×#123	1	1	yes	characteristic
584	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
585	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
586	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
587	C₂²×D₄	C₂²×#41	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	#386	1	1	yes	characteristic
594	C₂³×C₄	#386	1	1	yes	characteristic
595	C₂³×C₄	#386	1	1	yes	characteristic
596	C₂³×C₄	#386	1	1	yes	characteristic
597	C₂³×C₄	#386	1	1	yes	characteristic
598	C₂³×C₄	#386	1	1	yes	characteristic
599	C₂³×C₄	#386	1	1	yes	characteristic
600	C₂³×C₄	#386	1	1	yes	characteristic
601	C₂³×C₄	#386	1	1	yes	characteristic
602	C₂³×C₄	#386	1	1	yes	characteristic
603	C₂³×C₄	#386	1	1	yes	characteristic
604	C₂³×C₄	#386	1	1	yes	characteristic
605	C₂³×C₄	#386	1	1	yes	characteristic
606	C₂³×C₄	#386	1	1	yes	characteristic
607	C₂³×C₄	#386	1	1	yes	characteristic
608	C₂³×C₄	#386	1	1	yes	characteristic
609	C₂³×C₄	#386	1	1	yes	characteristic
610	C₂³×C₄	#386	1	1	yes	characteristic
611	C₂³×C₄	#386	1	1	yes	characteristic
612	C₂³×C₄	#386	1	1	yes	characteristic
613	C₂³×C₄	#386	1	1	yes	characteristic
614	C₂³×C₄	#386	1	1	yes	characteristic
615	C₂³×C₄	#386	1	1	yes	characteristic
616	C₂³×C₄	C₂×#99	1	8	yes	—
617	C₂³×C₄	C₂×#99	1	8	yes	—
618	C₂³×C₄	C₂×#99	1	4	yes	—
619	C₂³×C₄	C₂×#99	1	2	yes	—
620	C₂³×C₄	C₂×#99	1	2	yes	—
621	C₂³×C₄	C₂×#99	1	2	yes	—
622	C₂³×C₄	C₂×#99	1	2	yes	—
623	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
624	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
625	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
626	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
627	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
628	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
629	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
630	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
631	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
632	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
633	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
634	C₂³×C₄	C₂×#120	1	1	yes	characteristic
635	C₂³×C₄	C₂×#120	1	1	yes	characteristic
636	C₂³×C₄	C₂×#120	1	1	yes	characteristic
637	C₂³×C₄	C₂×#120	1	1	yes	characteristic
638	C₂³×C₄	C₂×#121	1	1	yes	characteristic
639	C₂³×C₄	C₂×#121	1	1	yes	characteristic
640	C₂³×C₄	C₂×#121	1	1	yes	characteristic
641	C₂³×C₄	C₂×#121	1	1	yes	characteristic
642	C₂³×C₄	C₂×#121	1	1	yes	characteristic
643	C₂³×C₄	C₂×#121	1	1	yes	characteristic
644	C₂³×C₄	C₂×#121	1	1	yes	characteristic
645	C₂³×C₄	C₂×#121	1	1	yes	characteristic
646	C₂³×C₄	C₂×#121	1	1	yes	characteristic
647	C₂³×C₄	C₂×#121	1	1	yes	characteristic
648	C₂³×C₄	C₂×#123	1	1	yes	characteristic
649	C₂³×C₄	C₂×#123	1	1	yes	characteristic
650	C₂³×C₄	C₂×#123	1	1	yes	characteristic
651	C₂³×C₄	C₂×#123	1	1	yes	characteristic
652	C₂³×C₄	C₂×#123	1	1	yes	characteristic
653	C₂³×C₄	C₂×#123	1	1	yes	characteristic
654	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	—
656	C₂⁴	C₂×#386	1	1	yes	characteristic
657	C₂⁴	C₂×#386	1	1	yes	characteristic
658	C₂⁴	C₂×#386	1	1	yes	characteristic
659	C₂⁴	C₂×#386	1	1	yes	characteristic
660	C₂⁴	C₂×#386	1	1	yes	characteristic
661	C₂⁴	C₂×#386	1	1	yes	characteristic
662	C₂⁴	C₂×#386	1	1	yes	characteristic
663	C₂⁴	C₂×#386	1	1	yes	characteristic
664	C₂⁴	C₂×#386	1	1	yes	characteristic
665	C₂⁴	C₂×#386	1	1	yes	characteristic
666	C₂⁴	C₂²×#99	1	8	yes	—
667	C₂⁴	C₂²×#99	1	2	yes	—
668	C₂⁴	C₂²×#99	1	2	yes	—
669	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
670	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
671	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
672	C₂⁴	C₂²×#120	1	1	yes	characteristic
673	C₂⁴	C₂²×#121	1	1	yes	characteristic
674	C₂²×C₄	#1898	1	1	yes	characteristic
675	C₂²×C₄	#1898	1	2	yes	—
676	C₂²×C₄	#1898	1	1	yes	characteristic
677	C₂²×C₄	#1898	1	2	yes	—
678	C₂²×C₄	#1898	1	1	yes	characteristic
679	C₂²×C₄	#1898	1	1	yes	characteristic
680	C₂²×C₄	#1898	1	2	yes	—
681	C₂²×C₄	#1898	1	2	yes	—
682	C₂²×C₄	#1898	1	2	yes	—
683	C₂²×C₄	#1898	1	2	yes	—
684	C₂²×C₄	#1913	1	2	yes	—
685	C₂²×C₄	#1913	1	2	yes	—
686	C₂²×C₄	C₂×#386	1	1	yes	characteristic
687	C₂²×C₄	C₂×#386	1	1	yes	characteristic
688	C₂²×C₄	C₂×#386	1	1	yes	characteristic
689	C₂²×C₄	C₂×#386	1	1	yes	characteristic
690	C₂²×C₄	C₂×#386	1	1	yes	characteristic
691	C₂²×C₄	C₂×#386	1	1	yes	characteristic
692	C₂²×C₄	C₂×#386	1	1	yes	characteristic
693	C₂²×C₄	C₂×#386	1	1	yes	characteristic
694	C₂²×C₄	C₂×#386	1	1	yes	characteristic
695	C₂²×C₄	C₂×#386	1	1	yes	characteristic
696	C₂²×C₄	C₂×#386	1	1	yes	characteristic
697	C₂²×C₄	C₂×#386	1	1	yes	characteristic
698	C₂²×C₄	C₂×#386	1	1	yes	characteristic
699	C₂²×C₄	C₂×#386	1	1	yes	characteristic
700	C₂²×C₄	C₂²×#99	1	2	yes	—
701	C₂²×C₄	C₂²×#99	1	2	yes	—
702	C₂²×C₄	C₂²×#99	1	8	yes	—
703	C₂²×C₄	C₂²×#99	1	2	yes	—
704	C₂²×C₄	C₂²×#99	1	2	yes	—
705	C₂²×C₄	#3026	1	2	yes	—
706	C₂²×C₄	#3026	1	2	yes	—
707	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
708	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
709	C₂³	C₂×#1898	1	1	yes	characteristic
710	C₂³	C₂×#1898	1	2	yes	—
711	C₂³	C₂×#1898	1	1	yes	characteristic
712	C₂³	C₂×#1913	1	2	yes	—
713	C₂³	C₂²×#386	1	1	yes	characteristic
714	C₂³	C₂³×#99	1	2	yes	—
715	C₂³	C₂×#3026	1	2	yes	—
716	C₂×C₄	#20960	1	2	yes	—
717	C₂×C₄	#20960	1	1	yes	characteristic
718	C₂×C₄	#20960	1	1	yes	characteristic
719	C₂×C₄	C₂×#1898	1	1	yes	characteristic
720	C₂×C₄	C₂×#1898	1	2	yes	—
721	C₂×C₄	C₂×#1898	1	2	yes	—
722	C₂×C₄	C₂×#1898	1	1	yes	characteristic
723	C₂×C₄	C₂×#1898	1	1	yes	characteristic
724	C₂×C₄	C₂×#1898	1	1	yes	characteristic
725	C₂×C₄	C₂×#1913	1	2	yes	—
726	C₂×C₄	C₂×#1913	1	1	yes	characteristic
727	C₂×C₄	C₂×#1913	1	1	yes	characteristic
728	C₂²	C₂×#20960	1	1	yes	characteristic
729	C₂²	C₂²×#1898	1	1	yes	characteristic
730	C₂²	C₂²×#1913	1	1	yes	characteristic
731	C₄	#201687	1	1	yes	characteristic
732	C₄	#201687	1	1	yes	characteristic
733	C₄	#201687	1	1	yes	characteristic
734	C₄	#201687	1	1	yes	characteristic
735	C₂	C₂×#201687	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#201687
commutator	C₂⁵	C₂⁴×C₄
Frattini, cosocle	C₂³×D₄	C₂⁵
socle	C₂	C₂×#201687
prime radical	#72302941	C₂
LCS	G ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×#585 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72310866	C₂	semidirect
2. #72310855	C₂	semidirect
3. #72310854	C₂	semidirect
4. #72310819	C₂	semidirect
5. #72310758	C₂	semidirect
6. #72310731	C₂	semidirect
7. #72302947	C₂	semidirect
8. #72302942	C₂	semidirect
10. #72302908	C₂	semidirect
11. #72266931	C₂	semidirect
12. #72265901	C₂	semidirect
13. #72233461	C₂	semidirect
15. #7634872	C₄	semidirect
17. #6470235	C₄	semidirect
19. #6470234	C₄	semidirect
21. #6470232	C₄	semidirect
23. #6470231	C₄	semidirect
25. #6440459	C₄	semidirect
27. #6437616	C₄	semidirect
32. #6374127	C₄	semidirect
38. #496241	C₂²	semidirect
39. #496240	C₂²	semidirect
40. #496238	C₂²	semidirect
41. #496237	C₂²	semidirect
42. #493857	C₂²	semidirect
46. #493352	C₂²	semidirect
47. #213831	C₂²	semidirect
48. #213830	C₂²	semidirect
49. #213829	C₂²	semidirect
50. #213828	C₂²	semidirect
51. #190099	C₂²	semidirect
52. #188029	C₂²	semidirect
53. #139843	C₂²	semidirect
54. #139843	C₂²	semidirect
55. #139750	C₂²	semidirect
56. #139749	C₂²	semidirect
57. #128067	C₂²	semidirect
58. #128067	C₂²	semidirect
59. #128062	C₂²	semidirect
60. #128061	C₂²	semidirect
61. #128024	C₂²	semidirect
62. #128016	C₂²	semidirect
79. C₂²×#525	C₂×C₄	semidirect
80. C₂²×#525	C₂×C₄	semidirect
83. C₂²×#410	D₄	semidirect
84. #36965	C₂×C₄	semidirect
85. #36955	C₂×C₄	semidirect
86. #36714	C₂×C₄	semidirect
87. #36702	C₂×C₄	semidirect
88. #36614	C₂×C₄	semidirect
89. #35446	C₂×C₄	semidirect
90. #35446	C₂×C₄	semidirect
93. #35346	C₂×C₄	semidirect
94. #35346	C₂×C₄	semidirect
97. #34635	C₂×C₄	semidirect
98. #34044	C₂×C₄	semidirect
99. #34044	C₂×C₄	semidirect
100. #34044	C₂×C₄	semidirect
101. #34044	D₄	semidirect
103. #24058	C₂×C₄	semidirect
104. #24058	C₂×C₄	semidirect
105. #24058	C₂×C₄	semidirect
106. #24058	C₂×C₄	semidirect
107. #24058	C₂×C₄	semidirect
108. #24058	C₂×C₄	semidirect
111. #23901	C₂×C₄	semidirect
112. #23901	C₂×C₄	semidirect
113. #23901	C₂×C₄	semidirect
115. #23900	C₂×C₄	semidirect
116. #23900	C₂×C₄	semidirect
117. #23900	C₂×C₄	semidirect
120. #21750	C₂×C₄	semidirect
121. #21750	C₂×C₄	semidirect
122. #21749	C₂×C₄	semidirect
123. #21749	C₂×C₄	semidirect
124. #20983	C₂×C₄	semidirect
125. #20983	C₂×C₄	semidirect
129. #20587	D₄	semidirect
130. #20586	C₂×C₄	semidirect
131. #20586	D₄	semidirect
136. #20585	C₂×C₄	semidirect
137. #20585	D₄	semidirect
138. #20585	D₄	semidirect
143. #20584	C₂×C₄	semidirect
144. #20584	D₄	semidirect
145. #20584	D₄	semidirect
150. #12854	C₂³	semidirect
151. #12854	C₂³	semidirect
153. #12688	C₂³	semidirect
154. #12687	C₂³	semidirect
155. #8746	C₂³	semidirect
156. #8746	C₂³	semidirect
157. #8543	C₂³	semidirect
158. #8541	C₂³	semidirect
159. #7316	C₂³	semidirect
160. #7310	C₂³	semidirect
199. C₂⁵×C₄	C₂²×C₄	semidirect
230. C₂²×#123	C₂²×C₄	semidirect
231. C₂²×#123	C₂²×C₄	semidirect
232. C₂²×#123	C₂²×C₄	semidirect
236. C₂²×#120	C₂²×C₄	semidirect
237. C₂²×#120	C₂²×C₄	semidirect
238. C₂²×#120	C₂²×C₄	semidirect
247. C₂²×#117	C₂²×C₄	semidirect
248. C₂²×#117	C₂²×C₄	semidirect
249. C₂²×#117	C₂²×C₄	semidirect
253. #2849	C₂²×C₄	semidirect
254. #2846	C₂²×C₄	semidirect
255. #2622	C₂²×C₄	semidirect
256. #2622	C₂²×C₄	semidirect
263. #2308	C₂²×C₄	semidirect
264. #2308	C₂²×C₄	semidirect
265. #2308	C₂²×C₄	semidirect
266. #2308	C₂²×C₄	semidirect
267. #2308	C₂²×C₄	semidirect
268. #2308	C₂²×C₄	semidirect
269. #2308	C₂²×C₄	semidirect
273. #2280	C₂²×C₄	semidirect
275. #1898	C₂²×C₄	semidirect
276. #1898	C₂²×C₄	semidirect
277. #1898	C₂²×C₄	semidirect
278. #1898	C₂²×C₄	semidirect
283. #1781	C₂²×C₄	semidirect
284. #1781	C₂²×C₄	semidirect
298. C₂²×#41	#99	semidirect
299. C₂²×#41	#99	semidirect
382. C₂³×Q₈	#99	semidirect
398. C₂³×D₄	#99	semidirect
445. C₂⁴×C₄	#99	semidirect

Maximal subgroups

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

subgroup	index
#72310866	2
#72310855	2
#72310854	2
#72310819	2
#72310758	2
#72310731	2
#72302947	2
#72302942	2
#72302941	2
#72302908	2
#72266931	2
#72265901	2
#72233461	2