Subgroups — #72338648

Order 4096.

At least 15337 conjugacy classes of subgroups; only the 771 normal subgroups are shown.

The subgroup lattice has 467 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338647	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338646	C₂	1	1	yes	maximal, characteristic, complemented
3	#72338645	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338642	C₂	1	1	yes	maximal, characteristic, complemented
5	#72338639	C₂	1	1	yes	maximal, characteristic, complemented
6	#72338638	C₂²	1	1	yes	characteristic, complemented
7	#72338637	C₂	1	1	yes	maximal, characteristic, complemented
8	#72338631	C₂²	1	1	yes	characteristic
9	#72338510	C₂	1	2	yes	maximal, complemented
10	#72338509	C₂	1	2	yes	maximal, complemented
11	#72338508	C₂²	1	1	yes	characteristic, complemented
12	#72338507	C₂²	1	1	yes	characteristic, complemented
13	#72338471	C₂	1	2	yes	maximal, complemented
14	#72338470	C₂	1	2	yes	maximal, complemented
15	#72338469	C₂²	1	2	yes	complemented
16	#72338469	C₂²	1	2	yes	complemented
17	#72338468	C₂²	1	1	yes	characteristic, complemented
18	#72338467	C₂	1	1	yes	maximal, characteristic, complemented
19	#72338466	C₂²	1	1	yes	characteristic, complemented
20	#72338464	C₂²	1	1	yes	characteristic
21	#72338463	C₂²	1	1	yes	characteristic, complemented
22	#72319146	C₂	1	2	yes	maximal, complemented
23	#72319143	C₂²	1	1	yes	characteristic, complemented
24	#72319135	C₂²	1	2	yes	complemented
25	#72319109	C₂	1	2	yes	maximal, complemented
26	#72319107	C₂²	1	2	yes	complemented
27	#72319099	C₂²	1	1	yes	characteristic, complemented
28	#72319089	C₂²	1	2	yes	complemented
29	#72319089	C₂²	1	2	yes	complemented
30	#72318312	C₂²	1	2	yes	complemented
31	#72318082	C₂	1	2	yes	maximal, complemented
32	#72318075	C₂²	1	2	yes	complemented
33	#72318050	C₂	1	2	yes	maximal, complemented
34	#72318044	C₂²	1	2	yes	complemented
35	#72318041	C₂²	1	2	yes	complemented
36	#72318041	C₂²	1	2	yes	complemented
37	#72318036	C₂²	1	2	yes	complemented
38	#72318036	C₂²	1	2	yes	complemented
39	C₂×#8195808	C₂²	1	1	yes	characteristic, complemented
40	#72285817	C₂²	1	2	yes	complemented
41	#72285817	C₂²	1	2	yes	complemented
42	#72285797	C₂²	1	2	yes	—
43	#72285797	C₂²	1	2	yes	—
44	#72285589	C₂²	1	2	yes	complemented
45	#72285589	C₂²	1	2	yes	complemented
46	#72278621	C₂²	1	1	yes	characteristic, complemented
47	#72278601	C₂²	1	1	yes	characteristic
48	#72251822	C₂	1	2	yes	maximal, complemented
49	#72251812	C₂²	1	4	yes	complemented
50	#72251808	C₂²	1	4	yes	complemented
51	#72251760	C₂	1	2	yes	maximal, complemented
52	#72251759	C₂²	1	2	yes	complemented
53	#72251755	C₂²	1	4	yes	complemented
54	#72251750	C₂²	1	4	yes	complemented
55	#72251681	C₂²	1	2	yes	complemented
56	#72241310	C₂²	1	4	yes	complemented
57	#72241309	C₂²	1	4	yes	complemented
58	#72237054	C₂²	1	1	yes	characteristic, complemented
59	#72237047	C₂²	1	1	yes	characteristic, complemented
60	#72236974	C₂²	1	2	yes	—
61	#72236974	C₂²	1	2	yes	—
62	#72236669	C₂²	1	2	yes	—
63	#72236596	C₂²	1	2	yes	—
64	#72236596	C₂²	1	2	yes	complemented
65	#72219690	C₂²	1	1	yes	characteristic, complemented
66	#72216867	C₂	1	2	yes	maximal, complemented
67	#72216847	C₂²	1	4	yes	complemented
68	#72216843	C₂²	1	4	yes	complemented
69	#72216832	C₂²	1	4	yes	complemented
70	#72216611	C₂	1	2	yes	maximal, complemented
71	#72216589	C₂²	1	4	yes	complemented
72	#72216584	C₂²	1	4	yes	complemented
73	#72216577	C₂²	1	4	yes	complemented
74	#72216567	C₂²	1	2	yes	complemented
75	#72216144	C₂²	1	1	yes	characteristic, complemented
76	#72215721	C₂²	1	1	yes	characteristic, complemented
77	#72215568	C₂²	1	2	yes	—
78	#72215568	C₂²	1	2	yes	complemented
79	#72213704	C₂²	1	4	yes	complemented
80	#72213695	C₂²	1	4	yes	complemented
81	#72213685	C₂²	1	2	yes	—
82	#72213678	C₂²	1	4	yes	complemented
83	#72213671	C₂²	1	4	yes	complemented
84	#72213534	C₂²	1	2	yes	complemented
85	#72213519	C₂²	1	2	yes	complemented
86	#72213514	C₂²	1	1	yes	characteristic, complemented
87	#72213436	C₂²	1	2	yes	complemented
88	#72213428	C₂²	1	2	yes	complemented
89	#72210575	C₂²	1	2	yes	—
90	#72210566	C₂²	1	2	yes	complemented
91	#10585995	D₄	1	1	yes	characteristic, complemented
92	#10576178	C₂³	1	1	yes	characteristic, complemented
93	#10575547	C₂³	1	1	yes	characteristic
94	#8195808	C₂³	1	2	yes	—
95	#8195808	C₂³	1	2	yes	—
96	C₂×#52004	C₂³	1	2	yes	—
97	C₂×#35272	C₂³	1	1	yes	characteristic
98	#7504294	C₂³	1	1	yes	characteristic, complemented
99	#7504292	C₂³	1	1	yes	characteristic, complemented
100	#6628970	D₄	1	1	yes	characteristic, complemented
101	#6628970	D₄	1	1	yes	characteristic, complemented
102	#6628970	C₂³	1	1	yes	characteristic
103	#6628970	C₂³	1	1	yes	characteristic
104	#6452932	D₄	1	1	yes	characteristic, complemented
105	#6451876	D₄	1	1	yes	characteristic, complemented
106	#6447741	D₄	1	1	yes	characteristic, complemented
107	#6447741	C₂³	1	1	yes	characteristic
108	#6443331	D₄	1	1	yes	characteristic, complemented
109	#6443331	C₂³	1	1	yes	characteristic
110	#6437449	D₄	1	1	yes	characteristic, complemented
111	#6437449	D₄	1	1	yes	characteristic, complemented
112	#6437449	C₂³	1	1	yes	characteristic
113	#6437449	C₂³	1	1	yes	characteristic
114	#6437445	C₂³	1	1	yes	characteristic
115	C₂×#23906	D₄	1	1	yes	characteristic, complemented
116	#6407636	C₂³	1	1	yes	characteristic, complemented
117	#6374211	D₄	1	1	yes	characteristic, complemented
118	#6370950	D₄	1	1	yes	characteristic, complemented
119	#512119	D₄	1	4	yes	complemented
120	#511771	D₄	1	4	yes	complemented
121	#501096	D₄	1	8	yes	complemented
122	#500179	C₂³	1	4	yes	—
123	#500179	C₂³	1	4	yes	—
124	#500177	C₂³	1	4	yes	—
125	#499832	C₂³	1	4	yes	—
126	#499831	C₂³	1	4	yes	—
127	#499831	C₂³	1	4	yes	—
128	#496311	C₂³	1	2	yes	—
129	#496311	C₂³	1	2	yes	—
130	#493372	C₂³	1	2	yes	—
131	#493370	C₂³	1	2	yes	—
132	#451783	C₂³	1	1	yes	characteristic, complemented
133	#451037	D₄	1	1	yes	characteristic, complemented
134	#451037	D₄	1	1	yes	characteristic, complemented
135	#451037	C₂³	1	1	yes	characteristic
136	#451037	C₂³	1	1	yes	characteristic
137	#449491	C₂³	1	1	yes	characteristic, complemented
138	#444622	C₂³	1	1	yes	characteristic, complemented
139	#441113	D₄	1	1	yes	characteristic, complemented
140	#441113	D₄	1	1	yes	characteristic, complemented
141	#441113	C₂³	1	1	yes	characteristic
142	#441113	C₂³	1	1	yes	characteristic
143	#423223	C₂³	1	1	yes	characteristic, complemented
144	#422772	D₄	1	1	yes	characteristic, complemented
145	#422772	D₄	1	1	yes	characteristic, complemented
146	#422772	C₂³	1	1	yes	characteristic
147	#422772	C₂³	1	1	yes	characteristic
148	#418772	C₂³	1	1	yes	characteristic, complemented
149	#418770	C₂³	1	1	yes	characteristic, complemented
150	#417907	C₂³	1	1	yes	characteristic, complemented
151	#417805	C₂³	1	1	yes	characteristic, complemented
152	#417566	D₄	1	1	yes	characteristic, complemented
153	#417566	D₄	1	1	yes	characteristic, complemented
154	#417566	C₂³	1	1	yes	characteristic
155	#417566	C₂³	1	1	yes	characteristic
156	#391962	C₂³	1	1	yes	characteristic, complemented
157	#388126	C₂³	1	1	yes	characteristic, complemented
158	#383186	C₂³	1	1	yes	characteristic, complemented
159	#382709	D₄	1	1	yes	characteristic, complemented
160	#382414	C₂³	1	1	yes	characteristic
161	#374020	C₂³	1	1	yes	characteristic, complemented
162	#359941	D₄	1	1	yes	characteristic, complemented
163	#359707	D₄	1	1	yes	characteristic, complemented
164	#359509	C₂³	1	1	yes	characteristic
165	#359458	D₄	1	1	yes	characteristic, complemented
166	#246930	C₂³	1	4	yes	—
167	#246927	C₂³	1	4	yes	—
168	#187811	C₂³	1	2	yes	—
169	#152323	C₂³	1	4	yes	complemented
170	#152322	C₂³	1	4	yes	complemented
171	#152319	C₂³	1	4	yes	complemented
172	#152069	C₂³	1	4	yes	complemented
173	#152049	C₂³	1	4	yes	complemented
174	#152021	C₂³	1	4	yes	complemented
175	#152018	C₂³	1	4	yes	complemented
176	#152017	C₂³	1	4	yes	complemented
177	#134094	C₂³	1	2	yes	—
178	#134094	C₂³	1	2	yes	—
179	#133905	C₂³	1	2	yes	—
180	#133905	C₂³	1	2	yes	—
181	#133356	C₂³	1	4	yes	—
182	#133356	C₂³	1	4	yes	—
183	#131979	C₂³	1	4	yes	—
184	#131979	C₂³	1	4	yes	—
185	#94441	C₂³	1	4	yes	complemented
186	#94441	C₂³	1	4	yes	complemented
187	#94423	C₂³	1	4	yes	complemented
188	#94423	C₂³	1	4	yes	complemented
189	#62814	C₂×D₄	1	1	yes	characteristic
190	#62813	C₂×D₄	1	1	yes	characteristic
191	#62812	C₂×D₄	1	1	yes	characteristic
192	#62811	C₂×D₄	1	1	yes	characteristic
193	#62811	C₂×D₄	1	1	yes	characteristic
194	C₂×#3484	C₂×D₄	1	1	yes	characteristic
195	C₂²×D₄²	C₂×D₄	1	2	yes	—
196	C₂²×#535	C₂×D₄	1	1	yes	characteristic
197	C₂²×#535	C₂⁴	1	1	yes	characteristic
198	C₂³×#127	C₂×D₄	1	1	yes	characteristic
199	C₄×#585	C₂×D₄	1	1	yes	characteristic
200	C₄×#585	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×#41	C₂×D₄	1	1	yes	characteristic
202	#60644	C₂×D₄	1	1	yes	characteristic
203	#60644	C₂⁴	1	1	yes	characteristic
204	#60619	C₂×D₄	1	1	yes	characteristic
205	#60619	C₂⁴	1	1	yes	characteristic
206	C₂×#3021	C₂×D₄	1	1	yes	characteristic
207	C₂×#3021	C₂×D₄	1	1	yes	characteristic
208	C₂×#3021	C₂×D₄	1	1	yes	characteristic
209	C₂×#3021	C₂×D₄	1	1	yes	characteristic
210	C₂×#3021	C₂×D₄	1	1	yes	characteristic
211	C₂×#3021	C₂×D₄	1	1	yes	characteristic
212	C₂×#3021	C₂⁴	1	1	yes	characteristic
213	C₂×#3021	C₂⁴	1	1	yes	characteristic
214	C₂×#3019	C₂×D₄	1	1	yes	characteristic
215	C₂×#3019	C₂⁴	1	1	yes	characteristic
216	C₂²×#453	C₂×D₄	1	1	yes	characteristic
217	C₂²×#453	C₂×D₄	1	1	yes	characteristic
218	#60124	C₂×D₄	1	1	yes	characteristic
219	#52004	C₂×D₄	1	4	yes	—
220	#52004	C₂⁴	1	4	yes	—
221	#35272	C₂×D₄	1	1	yes	characteristic
222	#35272	C₂×D₄	1	1	yes	characteristic
223	#35272	C₂×D₄	1	1	yes	characteristic
224	#35272	C₂×D₄	1	1	yes	characteristic
225	#35272	C₂×D₄	1	1	yes	characteristic
226	#35272	C₂×D₄	1	1	yes	characteristic
227	#35272	C₂⁴	1	1	yes	characteristic
228	#35272	C₂⁴	1	1	yes	characteristic
229	C₂×#2380	C₂×D₄	1	2	yes	—
230	#34171	C₂×D₄	1	1	yes	characteristic
231	C₂×#2309	C₂×D₄	1	1	yes	characteristic
232	C₂×#2309	C₂×D₄	1	1	yes	characteristic
233	C₂×#2285	C₂×D₄	1	1	yes	characteristic
234	C₂×#2196	C₂×D₄	1	8	yes	—
235	C₂×#2128	C₂×D₄	1	4	yes	—
236	#23913	C₂×D₄	1	4	yes	—
237	#23906	C₂×D₄	1	4	yes	—
238	#23560	C₂×D₄	1	1	yes	characteristic
239	#23560	C₂×D₄	1	1	yes	characteristic
240	#23498	C₂×D₄	1	1	yes	characteristic
241	#23498	C₂×D₄	1	1	yes	characteristic
242	#23469	C₂×D₄	1	1	yes	characteristic
243	#23469	C₂×D₄	1	1	yes	characteristic
244	#23445	C₂×D₄	1	1	yes	characteristic
245	#23445	C₂×D₄	1	1	yes	characteristic
246	#20956	C₂×D₄	1	1	yes	characteristic
247	#20956	C₂×D₄	1	1	yes	characteristic
248	#20956	C₂×D₄	1	1	yes	characteristic
249	#20956	C₂×D₄	1	1	yes	characteristic
250	#20956	C₂×D₄	1	1	yes	characteristic
251	#20956	C₂×D₄	1	1	yes	characteristic
252	#20956	C₂⁴	1	1	yes	characteristic
253	#20956	C₂⁴	1	1	yes	characteristic
254	#20953	C₂×D₄	1	1	yes	characteristic
255	#20953	C₂⁴	1	1	yes	characteristic
256	C₂×#1887	C₂×D₄	1	1	yes	characteristic
257	C₂×#1887	C₂×D₄	1	1	yes	characteristic
258	#20694	C₂×D₄	1	1	yes	characteristic
259	#20690	C₂×D₄	1	1	yes	characteristic
260	#20690	C₂×D₄	1	1	yes	characteristic
261	#20688	C₂×D₄	1	1	yes	characteristic
262	#20637	C₂×D₄	1	1	yes	characteristic
263	#20637	C₂×D₄	1	1	yes	characteristic
264	#20591	C₂×D₄	1	1	yes	characteristic
265	#20591	C₂×D₄	1	1	yes	characteristic
266	C₂×#1783	C₂×D₄	1	1	yes	characteristic
267	C₂×#1783	C₂×D₄	1	1	yes	characteristic
268	#20586	C₂×D₄	1	1	yes	characteristic
269	#20586	C₂×D₄	1	1	yes	characteristic
270	C₄×#413	C₂×D₄	1	1	yes	characteristic
271	C₄×#413	C₂×D₄	1	1	yes	characteristic
272	#13049	C₂×D₄	1	8	yes	—
273	#12966	C₂×D₄	1	8	yes	—
274	#12759	C₂×D₄	1	8	yes	—
275	#12697	C₂⁴	1	4	yes	—
276	#12696	C₂⁴	1	4	yes	—
277	#12693	C₂×D₄	1	4	yes	—
278	#11167	C₂×D₄	1	1	yes	characteristic
279	#11167	C₂×D₄	1	1	yes	characteristic
280	#11167	C₂×D₄	1	1	yes	characteristic
281	#11167	C₂×D₄	1	1	yes	characteristic
282	#11006	C₂×D₄	1	1	yes	characteristic
283	#11006	C₂×D₄	1	1	yes	characteristic
284	#11006	C₂⁴	1	1	yes	characteristic
285	#11006	C₂⁴	1	1	yes	characteristic
286	#10989	C₂×D₄	1	1	yes	characteristic
287	#10989	C₂×D₄	1	1	yes	characteristic
288	#10989	C₂⁴	1	1	yes	characteristic
289	#10989	C₂⁴	1	1	yes	characteristic
290	#10975	C₂×D₄	1	1	yes	characteristic
291	#10975	C₂×D₄	1	1	yes	characteristic
292	#10975	C₂×D₄	1	1	yes	characteristic
293	#10975	C₂×D₄	1	1	yes	characteristic
294	#10939	C₂×D₄	1	1	yes	characteristic
295	#10939	C₂×D₄	1	1	yes	characteristic
296	#10939	C₂×D₄	1	1	yes	characteristic
297	#10939	C₂×D₄	1	1	yes	characteristic
298	#10893	C₂×D₄	1	1	yes	characteristic
299	#10893	C₂×D₄	1	1	yes	characteristic
300	#10893	C₂×D₄	1	1	yes	characteristic
301	#10893	C₂×D₄	1	1	yes	characteristic
302	#8522	C₂⁴	1	4	yes	—
303	C₂×#585	C₂²×D₄	1	1	yes	characteristic
304	C₂×#585	C₂²×D₄	1	1	yes	characteristic
305	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
306	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
307	C₂⁴×D₄	#120	1	1	yes	characteristic
308	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
309	#3485	#120	1	2	yes	—
310	#3484	#120	1	2	yes	—
311	C₂×D₄²	C₂²×D₄	1	4	yes	—
312	#3458	C₂²×D₄	1	1	yes	characteristic
313	#3449	C₂²×D₄	1	1	yes	characteristic
314	C₂×#535	#120	1	1	yes	characteristic
315	C₂×#535	#120	1	1	yes	characteristic
316	C₂×#535	C₂²×D₄	1	1	yes	characteristic
317	C₂×#535	C₂²×D₄	1	1	yes	characteristic
318	C₂×#535	C₂²×D₄	1	1	yes	characteristic
319	C₂×#535	C₂²×D₄	1	1	yes	characteristic
320	C₂×#535	C₂²×D₄	1	2	yes	—
321	C₂×#535	C₂²×D₄	1	1	yes	characteristic
322	C₂×#535	H(5,𝔽₂)	1	2	yes	—
323	C₂×#535	C₂⁵	1	1	yes	characteristic
324	C₂²×#127	#120	1	1	yes	characteristic
325	C₂²×#127	#120	1	1	yes	characteristic
326	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
327	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
328	C₂²×#127	C₂²×D₄	1	2	yes	—
329	C₂²×#124	H(5,𝔽₂)	1	2	yes	—
330	#3428	C₂²×D₄	1	1	yes	characteristic
331	#3428	C₂²×D₄	1	1	yes	characteristic
332	C₂×#518	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×#41	#120	1	1	yes	characteristic
334	C₂×C₄×#41	#120	1	1	yes	characteristic
335	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
337	C₂²×#117	#120	1	1	yes	characteristic
338	C₂²×#117	#120	1	1	yes	characteristic
339	C₂²×#117	C₂²×D₄	1	1	yes	characteristic
340	C₂³×C₄²	#120	1	1	yes	characteristic
341	C₂×#453	#120	1	4	yes	—
342	C₂×#453	C₂²×D₄	1	4	yes	—
343	C₂×#413	C₂²×D₄	1	1	yes	characteristic
344	C₂×#413	C₂²×D₄	1	1	yes	characteristic
345	C₂×#413	C₂²×D₄	1	1	yes	characteristic
346	C₂×#413	C₂²×D₄	1	1	yes	characteristic
347	C₂²×#100	C₂²×D₄	1	1	yes	characteristic
348	C₂²×#100	C₂²×D₄	1	1	yes	characteristic
349	C₂²×#100	C₂²×D₄	1	1	yes	characteristic
350	C₂²×#100	C₂²×D₄	1	1	yes	characteristic
351	#2873	C₂²×D₄	1	1	yes	characteristic
352	#2873	C₂²×D₄	1	1	yes	characteristic
353	#2380	C₂²×D₄	1	4	yes	—
354	#2309	#120	1	1	yes	characteristic
355	#2309	#120	1	1	yes	characteristic
356	#2309	#120	1	1	yes	characteristic
357	#2309	#120	1	1	yes	characteristic
358	#2309	C₂²×D₄	1	1	yes	characteristic
359	#2309	C₂²×D₄	1	1	yes	characteristic
360	#2309	C₂²×D₄	1	1	yes	characteristic
361	#2309	C₂²×D₄	1	1	yes	characteristic
362	#2309	C₂²×D₄	1	1	yes	characteristic
363	#2309	C₂²×D₄	1	1	yes	characteristic
364	#2285	#120	1	1	yes	characteristic
365	#2285	#120	1	1	yes	characteristic
366	#2285	C₂²×D₄	1	1	yes	characteristic
367	#2285	C₂²×D₄	1	1	yes	characteristic
368	C₂×#353	C₂²×D₄	1	8	yes	—
369	#1887	#120	1	4	yes	—
370	#1887	C₂²×D₄	1	4	yes	—
371	#1785	#120	1	2	yes	—
372	#1783	#120	1	2	yes	—
373	#1742	C₂²×D₄	1	1	yes	characteristic
374	#1742	C₂²×D₄	1	1	yes	characteristic
375	#1740	C₂²×D₄	1	1	yes	characteristic
376	#1740	C₂²×D₄	1	1	yes	characteristic
377	C₂×H(5,𝔽₂)	C₂×#120	1	2	yes	—
378	C₂²×#41	C₂×#120	1	1	yes	characteristic
379	C₂²×#41	C₂×#120	1	1	yes	characteristic
380	C₂²×#41	#534	1	1	yes	characteristic
381	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
382	C₂³×Q₈	#534	1	1	yes	characteristic
383	C₂³×D₄	C₂×#120	1	1	yes	characteristic
384	C₂³×D₄	C₂×#120	1	1	yes	characteristic
385	C₂³×D₄	C₂×#120	1	1	yes	characteristic
386	C₂³×D₄	C₂×#120	1	1	yes	characteristic
387	C₂³×D₄	D₄²	1	2	yes	—
388	C₂³×D₄	D₄²	1	2	yes	—
389	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
390	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
391	C₂×#127	C₂×#120	1	2	yes	—
392	C₂×#127	D₄²	1	2	yes	—
393	C₂×#127	D₄²	1	2	yes	—
394	C₂×#127	C₂³×D₄	1	2	yes	—
395	C₂×#124	#534	1	2	yes	—
396	C₂×#124	D₄²	1	2	yes	—
397	C₂×#124	D₄²	1	2	yes	—
398	C₂×#124	C₂×H(5,𝔽₂)	1	2	yes	—
399	#518	C₂×#120	1	2	yes	—
400	C₂×#117	B(4,𝔽₂)	1	1	yes	characteristic
401	C₂×#117	B(4,𝔽₂)	1	1	yes	characteristic
402	C₂×#117	C₂×#120	1	1	yes	characteristic
403	C₂×#117	C₂×#120	1	1	yes	characteristic
404	C₂×#117	C₂×#120	1	1	yes	characteristic
405	C₂×#117	C₂×#120	1	1	yes	characteristic
406	C₂×#117	C₂×#120	1	1	yes	characteristic
407	C₂×#117	D₄²	1	2	yes	—
408	C₂×#117	C₂³×D₄	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic
411	C₂²×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
412	C₂²×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
413	C₂²×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
414	C₂²×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
415	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
416	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
417	C₂²×C₄²	D₄²	1	2	yes	—
418	C₂×#100	C₂×#120	1	2	yes	—
419	C₂×#100	C₂×#120	1	2	yes	—
420	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
421	C₂²×Q₈	#2403	1	1	yes	characteristic
422	C₂²×Q₈	C₂×#534	1	1	yes	characteristic
423	C₂²×D₄	#2403	1	1	yes	characteristic
424	C₂²×D₄	#2403	1	2	yes	—
425	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
426	C₂²×D₄	C₂×D₄²	1	2	yes	—
427	C₂³×C₄	#2403	1	1	yes	characteristic
428	C₂³×C₄	#2403	1	1	yes	characteristic
429	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
430	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
431	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
432	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
437	C₂×C₄²	#2403	1	2	yes	—
438	C₂×C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
439	C₂×C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
440	C₂×C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
441	C₂×C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
442	C₂×C₄²	C₂×D₄²	1	2	yes	—
443	C₂⁴	#23900	1	1	yes	characteristic
444	C₂⁴	#23900	1	1	yes	characteristic
445	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
446	C₂×D₄	#60399	1	2	yes	—
447	C₂²×C₄	#23900	1	1	yes	characteristic
448	C₂²×C₄	#23900	1	1	yes	characteristic
449	C₂²×C₄	C₂×#2403	1	1	yes	characteristic
450	C₂²×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
451	C₄²	#33551	1	1	yes	characteristic
452	C₄²	#33551	1	1	yes	characteristic
453	C₄²	#33551	1	1	yes	characteristic
454	C₄²	#33551	1	1	yes	characteristic
455	C₂³	C₂×#23900	1	1	yes	characteristic
456	C₂³	#7622868	1	1	yes	characteristic
457	C₂³	#7622876	1	1	yes	characteristic
458	C₂×C₄	#6437629	1	1	yes	characteristic
459	C₂×C₄	#6437632	1	1	yes	characteristic
460	C₂×C₄	C₂×#33551	1	1	yes	characteristic
461	C₂×C₄	C₂×#33551	1	1	yes	characteristic
462	C₂²	#72218077	1	1	yes	characteristic
463	C₂²	#72261209	1	1	yes	characteristic
464	C₂²	#72317615	1	1	yes	characteristic
465	C₂	#72317812	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72317812
commutator, Frattini, cosocle	C₂×#535	C₂⁵
LCS	G ▷ C₂×#535 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×#35272 ◁ G
LECS	G ▷ C₂×#535 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72338647	C₂	semidirect
2. #72338646	C₂	semidirect
3. #72338645	C₂	semidirect
4. #72338642	C₂	semidirect
5. #72338639	C₂	semidirect
6. #72338638	C₂²	semidirect
7. #72338637	C₂	semidirect
9. #72338510	C₂	semidirect
10. #72338509	C₂	semidirect
11. #72338508	C₂²	semidirect
12. #72338507	C₂²	semidirect
13. #72338471	C₂	semidirect
14. #72338470	C₂	semidirect
15. #72338469	C₂²	semidirect
16. #72338469	C₂²	semidirect
17. #72338468	C₂²	semidirect
18. #72338467	C₂	semidirect
19. #72338466	C₂²	semidirect
21. #72338463	C₂²	semidirect
22. #72319146	C₂	semidirect
23. #72319143	C₂²	semidirect
24. #72319135	C₂²	semidirect
25. #72319109	C₂	semidirect
26. #72319107	C₂²	semidirect
27. #72319099	C₂²	semidirect
28. #72319089	C₂²	semidirect
29. #72319089	C₂²	semidirect
30. #72318312	C₂²	semidirect
31. #72318082	C₂	semidirect
32. #72318075	C₂²	semidirect
33. #72318050	C₂	semidirect
34. #72318044	C₂²	semidirect
35. #72318041	C₂²	semidirect
36. #72318041	C₂²	semidirect
37. #72318036	C₂²	semidirect
38. #72318036	C₂²	semidirect
39. C₂×#8195808	C₂²	semidirect
40. #72285817	C₂²	semidirect
41. #72285817	C₂²	semidirect
44. #72285589	C₂²	semidirect
45. #72285589	C₂²	semidirect
46. #72278621	C₂²	semidirect
48. #72251822	C₂	semidirect
49. #72251812	C₂²	semidirect
50. #72251808	C₂²	semidirect
51. #72251760	C₂	semidirect
52. #72251759	C₂²	semidirect
53. #72251755	C₂²	semidirect
54. #72251750	C₂²	semidirect
55. #72251681	C₂²	semidirect
56. #72241310	C₂²	semidirect
57. #72241309	C₂²	semidirect
58. #72237054	C₂²	semidirect
59. #72237047	C₂²	semidirect
64. #72236596	C₂²	semidirect
65. #72219690	C₂²	semidirect
66. #72216867	C₂	semidirect
67. #72216847	C₂²	semidirect
68. #72216843	C₂²	semidirect
69. #72216832	C₂²	semidirect
70. #72216611	C₂	semidirect
71. #72216589	C₂²	semidirect
72. #72216584	C₂²	semidirect
73. #72216577	C₂²	semidirect
74. #72216567	C₂²	semidirect
75. #72216144	C₂²	semidirect
76. #72215721	C₂²	semidirect
78. #72215568	C₂²	semidirect
79. #72213704	C₂²	semidirect
80. #72213695	C₂²	semidirect
82. #72213678	C₂²	semidirect
83. #72213671	C₂²	semidirect
84. #72213534	C₂²	semidirect
85. #72213519	C₂²	semidirect
86. #72213514	C₂²	semidirect
87. #72213436	C₂²	semidirect
88. #72213428	C₂²	semidirect
90. #72210566	C₂²	semidirect
91. #10585995	D₄	semidirect
92. #10576178	C₂³	semidirect
98. #7504294	C₂³	semidirect
99. #7504292	C₂³	semidirect
100. #6628970	D₄	semidirect
101. #6628970	D₄	semidirect
104. #6452932	D₄	semidirect
105. #6451876	D₄	semidirect
106. #6447741	D₄	semidirect
108. #6443331	D₄	semidirect
110. #6437449	D₄	semidirect
111. #6437449	D₄	semidirect
115. C₂×#23906	D₄	semidirect
116. #6407636	C₂³	semidirect
117. #6374211	D₄	semidirect
118. #6370950	D₄	semidirect
119. #512119	D₄	semidirect
120. #511771	D₄	semidirect
121. #501096	D₄	semidirect
132. #451783	C₂³	semidirect
133. #451037	D₄	semidirect
134. #451037	D₄	semidirect
137. #449491	C₂³	semidirect
138. #444622	C₂³	semidirect
139. #441113	D₄	semidirect
140. #441113	D₄	semidirect
143. #423223	C₂³	semidirect
144. #422772	D₄	semidirect
145. #422772	D₄	semidirect
148. #418772	C₂³	semidirect
149. #418770	C₂³	semidirect
150. #417907	C₂³	semidirect
151. #417805	C₂³	semidirect
152. #417566	D₄	semidirect
153. #417566	D₄	semidirect
156. #391962	C₂³	semidirect
157. #388126	C₂³	semidirect
158. #383186	C₂³	semidirect
159. #382709	D₄	semidirect
161. #374020	C₂³	semidirect
162. #359941	D₄	semidirect
163. #359707	D₄	semidirect
165. #359458	D₄	semidirect
169. #152323	C₂³	semidirect
170. #152322	C₂³	semidirect
171. #152319	C₂³	semidirect
172. #152069	C₂³	semidirect
173. #152049	C₂³	semidirect
174. #152021	C₂³	semidirect
175. #152018	C₂³	semidirect
176. #152017	C₂³	semidirect
185. #94441	C₂³	semidirect
186. #94441	C₂³	semidirect
187. #94423	C₂³	semidirect
188. #94423	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72338647	2
#72338646	2
#72338645	2
#72338642	2
#72338639	2
#72338637	2
#72338510	2
#72338509	2
#72338471	2
#72338470	2
#72338467	2
#72319146	2
#72319109	2
#72318082	2
#72318050	2
#72251822	2
#72251760	2
#72216867	2
#72216611	2