Subgroups — #72251829

Order 4096.

At least 22998 conjugacy classes of subgroups; only the 773 normal subgroups are shown.

The subgroup lattice has 573 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72251826	C₂	1	2	yes	maximal, complemented
2	#72251825	C₂	1	2	yes	maximal, complemented
3	#72251824	C₂	1	2	yes	maximal, complemented
4	#72251823	C₂	1	2	yes	maximal, complemented
5	#72251822	C₂	1	1	yes	maximal, characteristic, complemented
6	#72251821	C₂	1	1	yes	maximal, characteristic, complemented
7	#72251820	C₂	1	1	yes	maximal, characteristic, complemented
8	#72251819	C₂	1	2	yes	maximal, complemented
9	#72251818	C₂²	1	2	yes	complemented
10	#72251817	C₂²	1	2	yes	complemented
11	#72251816	C₂	1	2	yes	maximal, complemented
12	#72251815	C₂²	1	2	yes	complemented
13	#72251814	C₂²	1	2	yes	complemented
14	#72251813	C₂	1	2	yes	maximal, complemented
15	#72251812	C₂²	1	2	yes	complemented
16	#72251811	C₂²	1	2	yes	complemented
17	#72251810	C₂²	1	2	yes	complemented
18	#72251809	C₂	1	2	yes	maximal, complemented
19	#72251808	C₂²	1	2	yes	complemented
20	#72251807	C₂²	1	2	yes	complemented
21	#72251806	C₂²	1	2	yes	complemented
22	#72251804	C₂	1	1	yes	maximal, characteristic, complemented
23	#72251803	C₂²	1	1	yes	characteristic, complemented
24	#72251802	C₂²	1	1	yes	characteristic, complemented
25	#72251798	C₂²	1	1	yes	characteristic, complemented
26	#72251796	C₂²	1	1	yes	characteristic, complemented
27	#72251788	C₂²	1	1	yes	characteristic, complemented
28	#72251787	C₂²	1	1	yes	characteristic, complemented
29	#72251785	C₂²	1	1	yes	characteristic, complemented
30	#72251777	C₂²	1	1	yes	characteristic, complemented
31	#72251774	C₂	1	1	yes	maximal, characteristic, complemented
32	#72251772	C₂	1	1	yes	maximal, characteristic, complemented
33	#72251759	C₂²	1	1	yes	characteristic, complemented
34	#72251753	C₂²	1	2	yes	complemented
35	#72251753	C₂²	1	2	yes	complemented
36	#72251747	C₂²	1	2	yes	complemented
37	#72251747	C₂²	1	2	yes	complemented
38	#72251743	C₂²	1	2	yes	—
39	#72251743	C₂²	1	2	yes	complemented
40	#72251742	C₂²	1	2	yes	—
41	#72251742	C₂²	1	2	yes	complemented
42	#72251736	C₂	1	1	yes	maximal, characteristic, complemented
43	#72251735	C₂²	1	2	yes	complemented
44	#72251735	C₂²	1	2	yes	complemented
45	#72251734	C₂²	1	2	yes	complemented
46	#72251734	C₂²	1	2	yes	complemented
47	#72251733	C₂	1	1	yes	maximal, characteristic, complemented
48	#72251732	C₂²	1	2	yes	complemented
49	#72251732	C₂²	1	2	yes	complemented
50	#72251730	C₂²	1	2	yes	complemented
51	#72251730	C₂²	1	2	yes	complemented
52	#72251681	C₂²	1	1	yes	characteristic, complemented
53	#72241309	C₂²	1	2	yes	complemented
54	#72237541	C₂	1	1	yes	maximal, characteristic, complemented
55	#72237539	C₂²	1	2	yes	complemented
56	#72237539	C₂²	1	2	yes	complemented
57	#72237538	C₂²	1	2	yes	complemented
58	#72237537	C₂²	1	2	yes	complemented
59	#72237534	C₂²	1	1	yes	characteristic, complemented
60	#72237533	C₂²	1	1	yes	characteristic, complemented
61	#72237056	C₂	1	1	yes	maximal, characteristic, complemented
62	#72237055	C₂²	1	1	yes	characteristic, complemented
63	#72237054	C₂²	1	1	yes	characteristic, complemented
64	#72237053	C₂²	1	2	yes	complemented
65	#72237052	C₂²	1	2	yes	complemented
66	#72237051	C₂²	1	2	yes	complemented
67	#72237049	C₂²	1	1	yes	characteristic, complemented
68	#72236784	C₂	1	1	yes	maximal, characteristic, complemented
69	#72236775	C₂²	1	2	yes	—
70	#72236775	C₂²	1	2	yes	complemented
71	#72236769	C₂²	1	2	yes	complemented
72	#72236704	C₂²	1	1	yes	characteristic, complemented
73	#72236701	C₂²	1	1	yes	characteristic
74	#72235102	C₂²	1	1	yes	characteristic
75	#72235082	C₂²	1	1	yes	characteristic
76	#72233499	C₂²	1	2	yes	—
77	C₂×#8181078	C₂²	1	1	yes	characteristic, complemented
78	#72219546	C₂	1	1	yes	maximal, characteristic, complemented
79	#72219545	C₂²	1	2	yes	complemented
80	#72219543	C₂²	1	2	yes	complemented
81	#72219542	C₂²	1	2	yes	complemented
82	#72219541	C₂²	1	2	yes	complemented
83	#72219531	C₂	1	1	yes	maximal, characteristic, complemented
84	#72219525	C₂²	1	2	yes	complemented
85	#72219523	C₂²	1	2	yes	complemented
86	#72219521	C₂²	1	2	yes	complemented
87	#72219496	C₂²	1	1	yes	characteristic, complemented
88	#72219495	C₂²	1	1	yes	characteristic, complemented
89	#72216977	C₂	1	1	yes	maximal, characteristic, complemented
90	#72216958	C₂²	1	2	yes	complemented
91	#72216948	C₂²	1	2	yes	complemented
92	#72216942	C₂²	1	2	yes	complemented
93	#72216935	C₂²	1	2	yes	complemented
94	#72216611	C₂	1	1	yes	maximal, characteristic, complemented
95	#72216589	C₂²	1	2	yes	complemented
96	#72216584	C₂²	1	2	yes	complemented
97	#72216577	C₂²	1	2	yes	complemented
98	#72216567	C₂²	1	1	yes	characteristic, complemented
99	#72216567	C₂²	1	1	yes	characteristic, complemented
100	#72216112	C₂²	1	1	yes	characteristic, complemented
101	#72215912	C₂²	1	1	yes	characteristic, complemented
102	#72215737	C₂²	1	1	yes	characteristic, complemented
103	#72215737	C₂²	1	1	yes	characteristic, complemented
104	#72215721	C₂²	1	1	yes	characteristic, complemented
105	#72215568	C₂²	1	1	yes	characteristic, complemented
106	#72215536	C₂²	1	1	yes	characteristic, complemented
107	#72213697	C₂²	1	2	yes	complemented
108	#72213695	C₂²	1	2	yes	complemented
109	#72213691	C₂²	1	1	yes	characteristic, complemented
110	#72213685	C₂²	1	1	yes	characteristic, complemented
111	#72213674	C₂²	1	2	yes	complemented
112	#72213671	C₂²	1	2	yes	complemented
113	#72213534	C₂²	1	1	yes	characteristic, complemented
114	#72213519	C₂²	1	1	yes	characteristic, complemented
115	#72213452	C₂²	1	1	yes	characteristic, complemented
116	#72213445	C₂²	1	1	yes	characteristic, complemented
117	#72213429	C₂²	1	1	yes	characteristic, complemented
118	#72213428	C₂²	1	1	yes	characteristic, complemented
119	#72213238	C₂²	1	1	yes	characteristic
120	#72213238	C₂²	1	1	yes	characteristic, complemented
121	#72210575	C₂²	1	1	yes	characteristic
122	#72210575	C₂²	1	1	yes	characteristic, complemented
123	C₂²×#3484	D₄	1	1	yes	characteristic, complemented
124	#10576178	C₂³	1	1	yes	characteristic, complemented
125	#10575547	C₂³	1	1	yes	characteristic
126	#10575442	D₄	1	1	yes	characteristic, complemented
127	#8181078	C₂³	1	2	yes	—
128	#8181078	C₂³	1	2	yes	—
129	C₂×#52004	C₂³	1	1	yes	characteristic
130	C₂×#51902	C₂³	1	1	yes	characteristic
131	C₂×#35222	C₂³	1	1	yes	characteristic
132	#7504294	C₂³	1	1	yes	characteristic, complemented
133	#7504292	C₂³	1	1	yes	characteristic, complemented
134	#6629171	D₄	1	1	yes	characteristic, complemented
135	#6629171	C₂³	1	1	yes	characteristic
136	#6628867	D₄	1	1	yes	characteristic, complemented
137	#6628867	C₂³	1	1	yes	characteristic
138	#6451869	D₄	1	1	yes	characteristic, complemented
139	#6451748	D₄	1	1	yes	characteristic, complemented
140	#6440354	D₄	1	1	yes	characteristic, complemented
141	#6440354	D₄	1	1	yes	characteristic, complemented
142	#6437963	D₄	1	1	yes	characteristic, complemented
143	#6437963	D₄	1	1	yes	characteristic, complemented
144	#6437963	C₂³	1	1	yes	characteristic
145	#6437963	C₂³	1	1	yes	characteristic
146	#6437616	D₄	1	1	yes	characteristic, complemented
147	#6437449	C₂³	1	1	yes	characteristic
148	#6437445	C₂³	1	1	yes	characteristic
149	#6437445	C₂³	1	1	yes	characteristic
150	#6407636	C₂³	1	1	yes	characteristic, complemented
151	C₂²×#1783	D₄	1	1	yes	characteristic, complemented
152	#512119	D₄	1	2	yes	complemented
153	#512117	D₄	1	2	yes	complemented
154	#511775	D₄	1	2	yes	complemented
155	#511771	D₄	1	2	yes	complemented
156	#501104	D₄	1	4	yes	complemented
157	#501097	D₄	1	4	yes	complemented
158	#500203	C₂³	1	2	yes	—
159	#500188	C₂³	1	2	yes	—
160	#500188	C₂³	1	2	yes	—
161	#500179	C₂³	1	2	yes	—
162	#500177	C₂³	1	2	yes	—
163	#500177	C₂³	1	2	yes	—
164	#499855	C₂³	1	2	yes	—
165	#499839	C₂³	1	2	yes	—
166	#499839	C₂³	1	2	yes	—
167	#499832	C₂³	1	2	yes	—
168	#499832	C₂³	1	2	yes	—
169	#499831	C₂³	1	2	yes	—
170	#496194	C₂³	1	2	yes	—
171	#496194	C₂³	1	2	yes	—
172	#493385	C₂³	1	1	yes	characteristic
173	#493372	C₂³	1	1	yes	characteristic
174	#493370	C₂³	1	1	yes	characteristic
175	#493370	C₂³	1	1	yes	characteristic
176	#451783	C₂³	1	1	yes	characteristic, complemented
177	#449562	D₄	1	1	yes	characteristic, complemented
178	#449562	D₄	1	1	yes	characteristic, complemented
179	#449562	C₂³	1	1	yes	characteristic
180	#449562	C₂³	1	1	yes	characteristic
181	#449496	D₄	1	1	yes	characteristic, complemented
182	#449496	D₄	1	1	yes	characteristic, complemented
183	#449496	C₂³	1	1	yes	characteristic
184	#449496	C₂³	1	1	yes	characteristic
185	#449491	C₂³	1	1	yes	characteristic, complemented
186	#444620	C₂³	1	1	yes	characteristic, complemented
187	#423218	C₂³	1	1	yes	characteristic, complemented
188	#418772	C₂³	1	1	yes	characteristic, complemented
189	#418770	C₂³	1	1	yes	characteristic, complemented
190	#417954	D₄	1	1	yes	characteristic, complemented
191	#417954	D₄	1	1	yes	characteristic, complemented
192	#417954	C₂³	1	1	yes	characteristic
193	#417954	C₂³	1	1	yes	characteristic
194	#417909	C₂³	1	1	yes	characteristic, complemented
195	#417790	C₂³	1	1	yes	characteristic, complemented
196	#417774	D₄	1	1	yes	characteristic, complemented
197	#417774	D₄	1	1	yes	characteristic, complemented
198	#417774	C₂³	1	1	yes	characteristic
199	#417774	C₂³	1	1	yes	characteristic
200	#391960	C₂³	1	1	yes	characteristic, complemented
201	#388123	C₂³	1	1	yes	characteristic, complemented
202	#383184	C₂³	1	1	yes	characteristic, complemented
203	#382419	D₄	1	1	yes	characteristic, complemented
204	#382414	C₂³	1	1	yes	characteristic
205	#374018	C₂³	1	1	yes	characteristic, complemented
206	#359766	D₄	1	1	yes	characteristic, complemented
207	#359762	D₄	1	1	yes	characteristic, complemented
208	#359513	C₂³	1	1	yes	characteristic
209	#359507	D₄	1	1	yes	characteristic, complemented
210	#246993	C₂³	1	2	yes	—
211	#246987	C₂³	1	2	yes	—
212	#246930	C₂³	1	2	yes	—
213	#246927	C₂³	1	2	yes	—
214	#187811	C₂³	1	1	yes	characteristic
215	#187811	C₂³	1	1	yes	characteristic
216	#152324	C₂³	1	2	yes	complemented
217	#152324	C₂³	1	2	yes	complemented
218	#152323	C₂³	1	2	yes	complemented
219	#152322	C₂³	1	2	yes	complemented
220	#152322	C₂³	1	2	yes	complemented
221	#152319	C₂³	1	2	yes	complemented
222	#152071	C₂³	1	2	yes	complemented
223	#152069	C₂³	1	2	yes	complemented
224	#152049	C₂³	1	2	yes	complemented
225	#152047	C₂³	1	2	yes	complemented
226	#152021	C₂³	1	2	yes	complemented
227	#152020	C₂³	1	2	yes	complemented
228	#152020	C₂³	1	2	yes	complemented
229	#152018	C₂³	1	2	yes	complemented
230	#152018	C₂³	1	2	yes	complemented
231	#152017	C₂³	1	2	yes	complemented
232	#134049	C₂³	1	2	yes	—
233	#134049	C₂³	1	2	yes	—
234	#133843	C₂³	1	2	yes	—
235	#133843	C₂³	1	2	yes	—
236	#133362	C₂³	1	2	yes	—
237	#133362	C₂³	1	2	yes	—
238	#133350	C₂³	1	2	yes	—
239	#133350	C₂³	1	2	yes	—
240	#132001	C₂³	1	2	yes	—
241	#132001	C₂³	1	2	yes	—
242	#131979	C₂³	1	2	yes	—
243	#131979	C₂³	1	2	yes	—
244	#94442	C₂³	1	2	yes	complemented
245	#94442	C₂³	1	2	yes	complemented
246	#94441	C₂³	1	2	yes	complemented
247	#94441	C₂³	1	2	yes	complemented
248	#94424	C₂³	1	2	yes	complemented
249	#94424	C₂³	1	2	yes	complemented
250	#94420	C₂³	1	2	yes	complemented
251	#94420	C₂³	1	2	yes	complemented
252	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
253	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
254	#62814	C₂×D₄	1	1	yes	characteristic, complemented
255	#62811	C₂×D₄	1	1	yes	characteristic, complemented
256	C₂×#3484	C₂×D₄	1	1	yes	characteristic
257	C₂×#3484	C₂×D₄	1	1	yes	characteristic
258	C₂×#3484	C₂×D₄	1	1	yes	characteristic
259	C₂×#3484	C₂×D₄	1	1	yes	characteristic
260	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic, complemented
261	C₂²×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic, complemented
262	C₂²×#535	C₂×D₄	1	1	yes	characteristic
263	C₂²×#535	C₂⁴	1	1	yes	characteristic
264	C₂²×#525	C₂×D₄	1	1	yes	characteristic
265	C₂²×#518	C₂×D₄	1	1	yes	characteristic
266	#60644	C₂×D₄	1	1	yes	characteristic, complemented
267	#60644	C₂⁴	1	1	yes	characteristic
268	#60619	C₂×D₄	1	1	yes	characteristic, complemented
269	#60619	C₂⁴	1	1	yes	characteristic
270	#60518	C₂×D₄	1	1	yes	characteristic
271	#60518	C₂×D₄	1	1	yes	characteristic, complemented
272	C₂×#3025	C₂×D₄	1	1	yes	characteristic
273	C₂×#3025	C₂×D₄	1	1	yes	characteristic, complemented
274	C₂×#3021	C₂×D₄	1	1	yes	characteristic, complemented
275	C₂×#3021	C₂⁴	1	1	yes	characteristic
276	C₂×#3019	C₂×D₄	1	1	yes	characteristic
277	C₂×#3019	C₂×D₄	1	1	yes	characteristic
278	C₂×#3019	C₂⁴	1	1	yes	characteristic
279	C₂×#3019	C₂⁴	1	1	yes	characteristic
280	#60369	C₂×D₄	1	1	yes	characteristic
281	#60369	C₂×D₄	1	1	yes	characteristic, complemented
282	#60124	C₂×D₄	1	1	yes	characteristic, complemented
283	C₂³×#100	C₂×D₄	1	1	yes	characteristic
284	C₂³×#100	C₂×D₄	1	1	yes	characteristic
285	#60064	C₂×D₄	1	1	yes	characteristic, complemented
286	#52004	C₂×D₄	1	2	yes	complemented
287	#52004	C₂⁴	1	2	yes	—
288	#51902	C₂×D₄	1	2	yes	complemented
289	#51902	C₂⁴	1	2	yes	—
290	#35222	C₂×D₄	1	1	yes	characteristic
291	#35222	C₂×D₄	1	1	yes	characteristic
292	#35222	C₂×D₄	1	1	yes	characteristic
293	#35222	C₂×D₄	1	1	yes	characteristic
294	#35222	C₂×D₄	1	1	yes	characteristic
295	#35222	C₂×D₄	1	1	yes	characteristic
296	#35222	C₂⁴	1	1	yes	characteristic
297	#35222	C₂⁴	1	1	yes	characteristic
298	C₂×#2380	C₂×D₄	1	1	yes	characteristic, complemented
299	C₂×#2372	C₂×D₄	1	1	yes	characteristic, complemented
300	C₂×#2309	C₂×D₄	1	1	yes	characteristic
301	C₂×#2309	C₂×D₄	1	1	yes	characteristic
302	C₂×#2280	C₂×D₄	1	1	yes	characteristic
303	C₂×#2199	C₂×D₄	1	4	yes	—
304	C₂×#2196	C₂×D₄	1	4	yes	—
305	C₂×#2127	C₂×D₄	1	2	yes	complemented
306	C₂×#2127	C₂×D₄	1	2	yes	complemented
307	#23912	C₂×D₄	1	2	yes	—
308	#23912	C₂×D₄	1	2	yes	—
309	#23907	C₂×D₄	1	2	yes	—
310	#23906	C₂×D₄	1	2	yes	—
311	#23467	C₂×D₄	1	1	yes	characteristic
312	#23467	C₂×D₄	1	1	yes	characteristic, complemented
313	#23463	C₂×D₄	1	1	yes	characteristic
314	#23463	C₂×D₄	1	1	yes	characteristic, complemented
315	#23443	C₂×D₄	1	1	yes	characteristic
316	#23443	C₂×D₄	1	1	yes	characteristic, complemented
317	#23407	C₂×D₄	1	1	yes	characteristic
318	#23407	C₂×D₄	1	1	yes	characteristic, complemented
319	#20959	C₂×D₄	1	1	yes	characteristic
320	#20959	C₂×D₄	1	1	yes	characteristic, complemented
321	#20956	C₂×D₄	1	1	yes	characteristic, complemented
322	#20956	C₂⁴	1	1	yes	characteristic
323	#20953	C₂×D₄	1	1	yes	characteristic
324	#20953	C₂×D₄	1	1	yes	characteristic
325	#20953	C₂⁴	1	1	yes	characteristic
326	#20953	C₂⁴	1	1	yes	characteristic
327	#20856	C₂×D₄	1	1	yes	characteristic
328	#20856	C₂×D₄	1	1	yes	characteristic
329	#20856	C₂×D₄	1	1	yes	characteristic
330	#20856	C₂×D₄	1	1	yes	characteristic
331	#20694	C₂×D₄	1	1	yes	characteristic, complemented
332	#20688	C₂×D₄	1	1	yes	characteristic, complemented
333	#20616	C₂×D₄	1	1	yes	characteristic
334	#20616	C₂×D₄	1	1	yes	characteristic
335	#20616	C₂×D₄	1	1	yes	characteristic
336	#20616	C₂×D₄	1	1	yes	characteristic
337	#20591	C₂×D₄	1	1	yes	characteristic, complemented
338	C₂×#1783	C₂×D₄	1	1	yes	characteristic
339	C₂×#1783	C₂×D₄	1	1	yes	characteristic
340	C₂×#1783	C₂×D₄	1	1	yes	characteristic
341	C₂×#1783	C₂×D₄	1	1	yes	characteristic
342	#20584	C₂×D₄	1	1	yes	characteristic, complemented
343	#13049	C₂×D₄	1	4	yes	—
344	#13048	C₂×D₄	1	4	yes	—
345	#12966	C₂×D₄	1	4	yes	complemented
346	#12965	C₂×D₄	1	4	yes	complemented
347	#12763	C₂×D₄	1	4	yes	complemented
348	#12759	C₂×D₄	1	4	yes	complemented
349	#12703	C₂⁴	1	2	yes	—
350	#12697	C₂⁴	1	2	yes	—
351	#12696	C₂⁴	1	2	yes	—
352	#12696	C₂⁴	1	2	yes	—
353	#12694	C₂×D₄	1	2	yes	complemented
354	#12693	C₂×D₄	1	2	yes	complemented
355	#11006	C₂×D₄	1	1	yes	characteristic, complemented
356	#11006	C₂×D₄	1	1	yes	characteristic, complemented
357	#11006	C₂⁴	1	1	yes	characteristic
358	#11006	C₂⁴	1	1	yes	characteristic
359	#10993	C₂×D₄	1	1	yes	characteristic
360	#10993	C₂×D₄	1	1	yes	characteristic
361	#10993	C₂×D₄	1	1	yes	characteristic, complemented
362	#10993	C₂×D₄	1	1	yes	characteristic, complemented
363	#10987	C₂×D₄	1	1	yes	characteristic, complemented
364	#10987	C₂×D₄	1	1	yes	characteristic, complemented
365	#10987	C₂⁴	1	1	yes	characteristic
366	#10987	C₂⁴	1	1	yes	characteristic
367	#10984	C₂×D₄	1	1	yes	characteristic
368	#10984	C₂×D₄	1	1	yes	characteristic
369	#10984	C₂×D₄	1	1	yes	characteristic, complemented
370	#10984	C₂×D₄	1	1	yes	characteristic, complemented
371	#10948	C₂×D₄	1	1	yes	characteristic
372	#10948	C₂×D₄	1	1	yes	characteristic
373	#10948	C₂×D₄	1	1	yes	characteristic, complemented
374	#10948	C₂×D₄	1	1	yes	characteristic, complemented
375	#10937	C₂×D₄	1	1	yes	characteristic
376	#10937	C₂×D₄	1	1	yes	characteristic
377	#10937	C₂×D₄	1	1	yes	characteristic, complemented
378	#10937	C₂×D₄	1	1	yes	characteristic, complemented
379	#8522	C₂⁴	1	2	yes	—
380	#8522	C₂⁴	1	2	yes	—
381	C₂×#585	C₂²×D₄	1	1	yes	characteristic
382	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
383	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
384	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
385	C₂⁴×D₄	#120	1	1	yes	characteristic
386	C₂⁴×D₄	#120	1	1	yes	characteristic
387	C₂⁴×D₄	#120	1	1	yes	characteristic
388	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
389	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
390	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
391	C₂⁵×C₄	#120	1	1	yes	characteristic
392	C₂×H(3,𝔽₄)	C₂²×D₄	1	2	yes	—
393	#3484	#120	1	2	yes	—
394	#3484	#120	1	2	yes	—
395	C₂×D₄²	C₂²×D₄	1	2	yes	—
396	#3458	C₂²×D₄	1	1	yes	characteristic
397	#3449	C₂²×D₄	1	1	yes	characteristic
398	C₂×#535	#120	1	1	yes	characteristic
399	C₂×#535	#120	1	1	yes	characteristic
400	C₂×#535	C₂²×D₄	1	1	yes	characteristic
401	C₂×#535	C₂²×D₄	1	1	yes	characteristic
402	C₂×#535	C₂²×D₄	1	1	yes	characteristic
403	C₂×#535	C₂²×D₄	1	1	yes	characteristic
404	C₂×#535	C₂²×D₄	1	1	yes	characteristic
405	C₂×#535	C₂²×D₄	1	1	yes	characteristic
406	C₂×#535	C₂²×D₄	1	1	yes	characteristic
407	C₂×#535	H(5,𝔽₂)	1	1	yes	characteristic
408	C₂×#535	H(5,𝔽₂)	1	1	yes	characteristic
409	C₂×#535	C₂⁵	1	1	yes	characteristic
410	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
411	C₂²×#127	H(5,𝔽₂)	1	1	yes	characteristic
412	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
413	C₂²×#124	H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×#525	#120	1	1	yes	characteristic
415	C₂×#525	#120	1	1	yes	characteristic
416	C₂×#525	C₂²×D₄	1	1	yes	characteristic
417	C₂×#525	C₂²×D₄	1	1	yes	characteristic
418	#3428	C₂²×D₄	1	1	yes	characteristic
419	C₂×#518	C₂²×D₄	1	1	yes	characteristic
420	C₂×#518	C₂²×D₄	1	1	yes	characteristic
421	C₂²×#117	#120	1	1	yes	characteristic
422	C₂²×#117	#120	1	1	yes	characteristic
423	C₂²×#117	C₂²×D₄	1	1	yes	characteristic
424	C₂×#455	#120	1	2	yes	—
425	C₂×#455	C₂²×D₄	1	2	yes	—
426	C₂×#453	#120	1	2	yes	—
427	C₂×#453	C₂²×D₄	1	2	yes	—
428	C₂×#413	C₂²×D₄	1	1	yes	characteristic
429	C₂×#413	C₂²×D₄	1	1	yes	characteristic
430	C₂²×#100	C₂²×D₄	1	1	yes	characteristic
431	C₂²×#100	C₂²×D₄	1	1	yes	characteristic
432	C₂²×#100	C₂²×D₄	1	1	yes	characteristic
433	C₂²×#100	C₂²×D₄	1	1	yes	characteristic
434	C₂×#410	C₂²×D₄	1	1	yes	characteristic
435	C₂×#410	C₂²×D₄	1	1	yes	characteristic
436	#2879	C₂²×D₄	1	1	yes	characteristic
437	#2879	C₂²×D₄	1	1	yes	characteristic
438	#2873	C₂²×D₄	1	1	yes	characteristic
439	#2873	C₂²×D₄	1	1	yes	characteristic
440	#2380	C₂²×D₄	1	2	yes	—
441	#2372	C₂²×D₄	1	2	yes	—
442	#2309	#120	1	1	yes	characteristic
443	#2309	#120	1	1	yes	characteristic
444	#2309	#120	1	1	yes	characteristic
445	#2309	#120	1	1	yes	characteristic
446	#2309	C₂²×D₄	1	1	yes	characteristic
447	#2309	C₂²×D₄	1	1	yes	characteristic
448	#2309	C₂²×D₄	1	1	yes	characteristic
449	#2309	C₂²×D₄	1	1	yes	characteristic
450	#2280	#120	1	1	yes	characteristic
451	#2280	#120	1	1	yes	characteristic
452	#2280	C₂²×D₄	1	1	yes	characteristic
453	#2280	C₂²×D₄	1	1	yes	characteristic
454	C₂×#354	C₂²×D₄	1	4	yes	—
455	C₂×#353	C₂²×D₄	1	4	yes	—
456	#1887	#120	1	2	yes	—
457	#1887	C₂²×D₄	1	2	yes	—
458	#1885	#120	1	2	yes	—
459	#1885	C₂²×D₄	1	2	yes	—
460	#1783	#120	1	2	yes	—
461	#1783	#120	1	2	yes	—
462	#1742	C₂²×D₄	1	1	yes	characteristic
463	#1742	C₂²×D₄	1	1	yes	characteristic
464	#1740	C₂²×D₄	1	1	yes	characteristic
465	#1740	C₂²×D₄	1	1	yes	characteristic
466	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
467	C₂×H(5,𝔽₂)	C₂×#120	1	2	yes	—
468	C₂²×#41	C₂×#120	1	1	yes	characteristic
469	C₂²×#41	D₄²	1	1	yes	characteristic
470	C₂²×#41	D₄²	1	1	yes	characteristic
471	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
472	C₂³×Q₈	D₄²	1	1	yes	characteristic
473	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
474	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
475	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
476	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
477	C₂³×D₄	C₂×#120	1	1	yes	characteristic
478	C₂³×D₄	C₂×#120	1	1	yes	characteristic
479	C₂³×D₄	C₂×#120	1	1	yes	characteristic
480	C₂³×D₄	C₂×#120	1	1	yes	characteristic
481	C₂³×D₄	C₂×#120	1	1	yes	characteristic
482	C₂³×D₄	#534	1	1	yes	characteristic
483	C₂³×D₄	#534	1	1	yes	characteristic
484	C₂³×D₄	D₄²	1	1	yes	characteristic
485	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
486	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
487	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
488	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
489	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
490	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
491	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
492	C₂×#127	C₂×#120	1	1	yes	characteristic
493	C₂×#127	#534	1	1	yes	characteristic
494	C₂×#127	D₄²	1	1	yes	characteristic
495	C₂×#127	D₄²	1	1	yes	characteristic
496	C₂×#127	D₄²	1	1	yes	characteristic
497	C₂×#127	D₄²	1	1	yes	characteristic
498	C₂×#127	C₂³×D₄	1	1	yes	characteristic
499	C₂×#127	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂×#124	C₂×#120	1	1	yes	characteristic
501	C₂×#124	#534	1	1	yes	characteristic
502	C₂×#124	D₄²	1	1	yes	characteristic
503	C₂×#124	D₄²	1	1	yes	characteristic
504	C₂×#124	D₄²	1	1	yes	characteristic
505	C₂×#124	D₄²	1	1	yes	characteristic
506	C₂×#124	C₂³×D₄	1	1	yes	characteristic
507	C₂×#124	C₂×H(5,𝔽₂)	1	1	yes	characteristic
508	#518	C₂×#120	1	2	yes	—
509	C₂×#117	C₂×#120	1	1	yes	characteristic
510	C₂×#117	C₂×#120	1	1	yes	characteristic
511	C₂×#117	C₂×#120	1	1	yes	characteristic
512	C₂×#117	C₂×#120	1	1	yes	characteristic
513	C₂×#117	C₂×#120	1	1	yes	characteristic
514	C₂×#117	D₄²	1	1	yes	characteristic
515	C₂×#117	D₄²	1	1	yes	characteristic
516	C₂×#117	C₂³×D₄	1	1	yes	characteristic
517	C₂²×C₄²	D₄²	1	1	yes	characteristic
518	C₂²×C₄²	D₄²	1	1	yes	characteristic
519	C₂×#100	C₂×#120	1	2	yes	—
520	C₂×#100	C₂×#120	1	2	yes	—
521	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
522	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
523	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
524	C₂²×Q₈	#2403	1	1	yes	characteristic
525	C₂²×Q₈	C₂×D₄²	1	1	yes	characteristic
526	C₂²×D₄	#2403	1	1	yes	characteristic
527	C₂²×D₄	#2403	1	1	yes	characteristic
528	C₂²×D₄	#2403	1	1	yes	characteristic
529	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
530	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
531	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
532	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
533	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
534	C₂²×D₄	C₂×#534	1	1	yes	characteristic
535	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
536	C₂³×C₄	#2403	1	1	yes	characteristic
537	C₂³×C₄	#2403	1	1	yes	characteristic
538	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
539	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
540	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
541	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
542	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
543	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
544	C₂×C₄²	#2403	1	1	yes	characteristic
545	C₂×C₄²	#2403	1	1	yes	characteristic
546	C₂×C₄²	C₂×D₄²	1	1	yes	characteristic
547	C₂×C₄²	C₂×D₄²	1	1	yes	characteristic
548	C₂⁴	#23900	1	1	yes	characteristic
549	C₂⁴	#23900	1	1	yes	characteristic
550	C₂⁴	#33551	1	1	yes	characteristic
551	C₂⁴	#33551	1	1	yes	characteristic
552	C₂⁴	#33551	1	1	yes	characteristic
553	C₂⁴	#33551	1	1	yes	characteristic
554	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
555	C₂×D₄	#33551	1	2	yes	—
556	C₂×D₄	#60399	1	2	yes	—
557	C₂²×C₄	#23900	1	1	yes	characteristic
558	C₂²×C₄	#23900	1	1	yes	characteristic
559	C₂²×C₄	C₂×#2403	1	1	yes	characteristic
560	C₂²×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
561	C₂³	C₂×#23900	1	1	yes	characteristic
562	C₂³	C₂×#33551	1	1	yes	characteristic
563	C₂³	C₂×#33551	1	1	yes	characteristic
564	C₂×C₄	#6437629	1	1	yes	characteristic
565	C₂×C₄	#6437632	1	1	yes	characteristic
566	C₂×C₄	C₂×#33551	1	1	yes	characteristic
567	C₂×C₄	#7622875	1	1	yes	characteristic
568	C₂²	#72218077	1	1	yes	characteristic
569	C₂²	#72233116	1	1	yes	characteristic
570	C₂²	#72237496	1	1	yes	characteristic
571	C₂	#72240176	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72240176
commutator, Frattini, cosocle	C₂×#535	C₂⁵
LCS	G ▷ C₂×#535 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×#35222 ◁ 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. #72251826	C₂	semidirect
2. #72251825	C₂	semidirect
3. #72251824	C₂	semidirect
4. #72251823	C₂	semidirect
5. #72251822	C₂	semidirect
6. #72251821	C₂	semidirect
7. #72251820	C₂	semidirect
8. #72251819	C₂	semidirect
9. #72251818	C₂²	semidirect
10. #72251817	C₂²	semidirect
11. #72251816	C₂	semidirect
12. #72251815	C₂²	semidirect
13. #72251814	C₂²	semidirect
14. #72251813	C₂	semidirect
15. #72251812	C₂²	semidirect
16. #72251811	C₂²	semidirect
17. #72251810	C₂²	semidirect
18. #72251809	C₂	semidirect
19. #72251808	C₂²	semidirect
20. #72251807	C₂²	semidirect
21. #72251806	C₂²	semidirect
22. #72251804	C₂	semidirect
23. #72251803	C₂²	semidirect
24. #72251802	C₂²	semidirect
25. #72251798	C₂²	semidirect
26. #72251796	C₂²	semidirect
27. #72251788	C₂²	semidirect
28. #72251787	C₂²	semidirect
29. #72251785	C₂²	semidirect
30. #72251777	C₂²	semidirect
31. #72251774	C₂	semidirect
32. #72251772	C₂	semidirect
33. #72251759	C₂²	semidirect
34. #72251753	C₂²	semidirect
35. #72251753	C₂²	semidirect
36. #72251747	C₂²	semidirect
37. #72251747	C₂²	semidirect
39. #72251743	C₂²	semidirect
41. #72251742	C₂²	semidirect
42. #72251736	C₂	semidirect
43. #72251735	C₂²	semidirect
44. #72251735	C₂²	semidirect
45. #72251734	C₂²	semidirect
46. #72251734	C₂²	semidirect
47. #72251733	C₂	semidirect
48. #72251732	C₂²	semidirect
49. #72251732	C₂²	semidirect
50. #72251730	C₂²	semidirect
51. #72251730	C₂²	semidirect
52. #72251681	C₂²	semidirect
53. #72241309	C₂²	semidirect
54. #72237541	C₂	semidirect
55. #72237539	C₂²	semidirect
56. #72237539	C₂²	semidirect
57. #72237538	C₂²	semidirect
58. #72237537	C₂²	semidirect
59. #72237534	C₂²	semidirect
60. #72237533	C₂²	semidirect
61. #72237056	C₂	semidirect
62. #72237055	C₂²	semidirect
63. #72237054	C₂²	semidirect
64. #72237053	C₂²	semidirect
65. #72237052	C₂²	semidirect
66. #72237051	C₂²	semidirect
67. #72237049	C₂²	semidirect
68. #72236784	C₂	semidirect
70. #72236775	C₂²	semidirect
71. #72236769	C₂²	semidirect
72. #72236704	C₂²	semidirect
77. C₂×#8181078	C₂²	semidirect
78. #72219546	C₂	semidirect
79. #72219545	C₂²	semidirect
80. #72219543	C₂²	semidirect
81. #72219542	C₂²	semidirect
82. #72219541	C₂²	semidirect
83. #72219531	C₂	semidirect
84. #72219525	C₂²	semidirect
85. #72219523	C₂²	semidirect
86. #72219521	C₂²	semidirect
87. #72219496	C₂²	semidirect
88. #72219495	C₂²	semidirect
89. #72216977	C₂	semidirect
90. #72216958	C₂²	semidirect
91. #72216948	C₂²	semidirect
92. #72216942	C₂²	semidirect
93. #72216935	C₂²	semidirect
94. #72216611	C₂	semidirect
95. #72216589	C₂²	semidirect
96. #72216584	C₂²	semidirect
97. #72216577	C₂²	semidirect
98. #72216567	C₂²	semidirect
99. #72216567	C₂²	semidirect
100. #72216112	C₂²	semidirect
101. #72215912	C₂²	semidirect
102. #72215737	C₂²	semidirect
103. #72215737	C₂²	semidirect
104. #72215721	C₂²	semidirect
105. #72215568	C₂²	semidirect
106. #72215536	C₂²	semidirect
107. #72213697	C₂²	semidirect
108. #72213695	C₂²	semidirect
109. #72213691	C₂²	semidirect
110. #72213685	C₂²	semidirect
111. #72213674	C₂²	semidirect
112. #72213671	C₂²	semidirect
113. #72213534	C₂²	semidirect
114. #72213519	C₂²	semidirect
115. #72213452	C₂²	semidirect
116. #72213445	C₂²	semidirect
117. #72213429	C₂²	semidirect
118. #72213428	C₂²	semidirect
120. #72213238	C₂²	semidirect
122. #72210575	C₂²	semidirect
123. C₂²×#3484	D₄	semidirect
124. #10576178	C₂³	semidirect
126. #10575442	D₄	semidirect
132. #7504294	C₂³	semidirect
133. #7504292	C₂³	semidirect
134. #6629171	D₄	semidirect
136. #6628867	D₄	semidirect
138. #6451869	D₄	semidirect
139. #6451748	D₄	semidirect
140. #6440354	D₄	semidirect
141. #6440354	D₄	semidirect
142. #6437963	D₄	semidirect
143. #6437963	D₄	semidirect
146. #6437616	D₄	semidirect
150. #6407636	C₂³	semidirect
151. C₂²×#1783	D₄	semidirect
152. #512119	D₄	semidirect
153. #512117	D₄	semidirect
154. #511775	D₄	semidirect
155. #511771	D₄	semidirect
156. #501104	D₄	semidirect
157. #501097	D₄	semidirect
176. #451783	C₂³	semidirect
177. #449562	D₄	semidirect
178. #449562	D₄	semidirect
181. #449496	D₄	semidirect
182. #449496	D₄	semidirect
185. #449491	C₂³	semidirect
186. #444620	C₂³	semidirect
187. #423218	C₂³	semidirect
188. #418772	C₂³	semidirect
189. #418770	C₂³	semidirect
190. #417954	D₄	semidirect
191. #417954	D₄	semidirect
194. #417909	C₂³	semidirect
195. #417790	C₂³	semidirect
196. #417774	D₄	semidirect
197. #417774	D₄	semidirect
200. #391960	C₂³	semidirect
201. #388123	C₂³	semidirect
202. #383184	C₂³	semidirect
203. #382419	D₄	semidirect
205. #374018	C₂³	semidirect
206. #359766	D₄	semidirect
207. #359762	D₄	semidirect
209. #359507	D₄	semidirect
216. #152324	C₂³	semidirect
217. #152324	C₂³	semidirect
218. #152323	C₂³	semidirect
219. #152322	C₂³	semidirect
220. #152322	C₂³	semidirect
221. #152319	C₂³	semidirect
222. #152071	C₂³	semidirect
223. #152069	C₂³	semidirect
224. #152049	C₂³	semidirect
225. #152047	C₂³	semidirect
226. #152021	C₂³	semidirect
227. #152020	C₂³	semidirect
228. #152020	C₂³	semidirect
229. #152018	C₂³	semidirect
230. #152018	C₂³	semidirect
231. #152017	C₂³	semidirect
244. #94442	C₂³	semidirect
245. #94442	C₂³	semidirect
246. #94441	C₂³	semidirect
247. #94441	C₂³	semidirect
248. #94424	C₂³	semidirect
249. #94424	C₂³	semidirect
250. #94420	C₂³	semidirect
251. #94420	C₂³	semidirect
254. #62814	C₂×D₄	semidirect
255. #62811	C₂×D₄	semidirect
260. C₂²×D₄²	C₂×D₄	semidirect
261. C₂²×H(3,𝔽₄)	C₂×D₄	semidirect
266. #60644	C₂×D₄	semidirect
268. #60619	C₂×D₄	semidirect
271. #60518	C₂×D₄	semidirect
273. C₂×#3025	C₂×D₄	semidirect
274. C₂×#3021	C₂×D₄	semidirect
281. #60369	C₂×D₄	semidirect
282. #60124	C₂×D₄	semidirect
285. #60064	C₂×D₄	semidirect
286. #52004	C₂×D₄	semidirect
288. #51902	C₂×D₄	semidirect
298. C₂×#2380	C₂×D₄	semidirect
299. C₂×#2372	C₂×D₄	semidirect
305. C₂×#2127	C₂×D₄	semidirect
306. C₂×#2127	C₂×D₄	semidirect
312. #23467	C₂×D₄	semidirect
314. #23463	C₂×D₄	semidirect
316. #23443	C₂×D₄	semidirect
318. #23407	C₂×D₄	semidirect
320. #20959	C₂×D₄	semidirect
321. #20956	C₂×D₄	semidirect
331. #20694	C₂×D₄	semidirect
332. #20688	C₂×D₄	semidirect
337. #20591	C₂×D₄	semidirect
342. #20584	C₂×D₄	semidirect
345. #12966	C₂×D₄	semidirect
346. #12965	C₂×D₄	semidirect
347. #12763	C₂×D₄	semidirect
348. #12759	C₂×D₄	semidirect
353. #12694	C₂×D₄	semidirect
354. #12693	C₂×D₄	semidirect
355. #11006	C₂×D₄	semidirect
356. #11006	C₂×D₄	semidirect
361. #10993	C₂×D₄	semidirect
362. #10993	C₂×D₄	semidirect
363. #10987	C₂×D₄	semidirect
364. #10987	C₂×D₄	semidirect
369. #10984	C₂×D₄	semidirect
370. #10984	C₂×D₄	semidirect
373. #10948	C₂×D₄	semidirect
374. #10948	C₂×D₄	semidirect
377. #10937	C₂×D₄	semidirect
378. #10937	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72251826	2
#72251825	2
#72251824	2
#72251823	2
#72251822	2
#72251821	2
#72251820	2
#72251819	2
#72251816	2
#72251813	2
#72251809	2
#72251804	2
#72251774	2
#72251772	2
#72251736	2
#72251733	2
#72237541	2
#72237056	2
#72236784	2
#72219546	2
#72219531	2
#72216977	2
#72216611	2