Subgroups — #72266108

Order 4096.

At least 22295 conjugacy classes of subgroups; only the 1489 normal subgroups are shown.

The subgroup lattice has 669 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266107	C₂	1	2	yes	maximal, complemented
2	#72266106	C₂	1	2	yes	maximal, complemented
3	#72266105	C₂	1	2	yes	maximal, complemented
4	#72266104	C₂	1	2	yes	maximal, complemented
5	#72266103	C₂	1	1	yes	maximal, characteristic, complemented
6	#72266102	C₂	1	2	yes	maximal, complemented
7	#72266101	C₂²	1	2	yes	complemented
8	#72266100	C₂²	1	2	yes	complemented
9	#72266097	C₂	1	1	yes	maximal, characteristic, complemented
10	#72266096	C₂	1	2	yes	maximal, complemented
11	#72266095	C₂²	1	2	yes	complemented
12	#72266095	C₂²	1	2	yes	complemented
13	#72266091	C₂	1	2	yes	maximal, complemented
14	#72266086	C₂	1	1	yes	maximal, characteristic, complemented
15	#72266084	C₂	1	2	yes	maximal, complemented
16	#72266083	C₂²	1	2	yes	complemented
17	#72266082	C₂²	1	2	yes	complemented
18	#72266082	C₂²	1	2	yes	complemented
19	#72266081	C₂²	1	2	yes	complemented
20	#72266079	C₂²	1	2	yes	complemented
21	#72266076	C₂²	1	2	yes	complemented
22	#72266075	C₂²	1	2	yes	complemented
23	#72266073	C₂²	1	2	yes	complemented
24	#72266042	C₂	1	2	yes	maximal, complemented
25	#72266041	C₂²	1	2	yes	complemented
26	#72266036	C₂	1	2	yes	maximal, complemented
27	#72266035	C₂²	1	2	yes	complemented
28	#72266035	C₂²	1	2	yes	complemented
29	#72266032	C₂²	1	2	yes	complemented
30	#72266032	C₂²	1	2	yes	complemented
31	#72266029	C₂²	1	2	yes	complemented
32	#72266028	C₂²	1	2	yes	complemented
33	#72266023	C₂	1	1	yes	maximal, characteristic, complemented
34	#72266021	C₂²	1	1	yes	characteristic, complemented
35	#72266021	C₂²	1	1	yes	characteristic, complemented
36	#72266016	C₂	1	2	yes	maximal, complemented
37	#72266014	C₂²	1	2	yes	complemented
38	#72266014	C₂²	1	2	yes	complemented
39	#72266012	C₂²	1	2	yes	complemented
40	#72266010	C₂²	1	1	yes	characteristic, complemented
41	#72266009	C₂	1	2	yes	maximal, complemented
42	#72266008	C₂²	1	2	yes	complemented
43	#72266007	C₂²	1	2	yes	complemented
44	#72266007	C₂²	1	2	yes	complemented
45	C₂×#201687	C₂²	1	2	yes	complemented
46	C₂×#201687	C₂²	1	2	yes	complemented
47	#72262701	C₂²	1	2	yes	complemented
48	#72261893	C₂²	1	2	yes	complemented
49	#72261893	C₂²	1	2	yes	complemented
50	#72259008	C₂²	1	2	yes	complemented
51	#72258626	C₂²	1	2	yes	complemented
52	#72258626	C₂²	1	2	yes	complemented
53	#72258626	C₂²	1	2	yes	complemented
54	#72258626	C₂²	1	2	yes	complemented
55	#72258613	C₂²	1	2	yes	complemented
56	C₂²×#9495	C₂²	1	2	yes	complemented
57	C₂²×#9495	C₂²	1	2	yes	complemented
58	#72241123	C₂²	1	2	yes	complemented
59	#72240620	C₂	1	1	yes	maximal, characteristic, complemented
60	#72240619	C₂²	1	1	yes	characteristic, complemented
61	#72240619	C₂²	1	1	yes	characteristic, complemented
62	#72240617	C₂²	1	2	yes	complemented
63	#72240568	C₂²	1	2	yes	complemented
64	#72238531	C₂²	1	2	yes	complemented
65	#72238531	C₂²	1	2	yes	complemented
66	#72238049	C₂²	1	2	yes	complemented
67	#72238049	C₂²	1	2	yes	complemented
68	#72238031	C₂²	1	2	yes	complemented
69	C₂×#233541	C₂²	1	2	yes	complemented
70	#72235847	C₂²	1	2	yes	complemented
71	#72234749	C₂	1	1	yes	maximal, characteristic, complemented
72	#72234749	C₂	1	1	yes	maximal, characteristic, complemented
73	#72234689	C₂²	1	2	yes	complemented
74	#72234689	C₂²	1	2	yes	complemented
75	#72234675	C₂²	1	1	yes	characteristic
76	#72234668	C₂²	1	1	yes	characteristic, complemented
77	#72234668	C₂²	1	2	yes	complemented
78	#72234668	C₂²	1	1	yes	characteristic, complemented
79	#72234629	C₂²	1	2	yes	—
80	#72234629	C₂²	1	2	yes	—
81	#72234629	C₂²	1	2	yes	—
82	#72234629	C₂²	1	2	yes	—
83	#72234629	C₂²	1	2	yes	—
84	#72234629	C₂²	1	2	yes	—
85	#72234629	C₂²	1	2	yes	complemented
86	#72234629	C₂²	1	2	yes	complemented
87	#72234625	C₂²	1	2	yes	complemented
88	#72234625	C₂²	1	1	yes	characteristic, complemented
89	#72234625	C₂²	1	1	yes	characteristic, complemented
90	C₂×#6628892	C₂²	1	2	yes	complemented
91	C₂×#6628892	C₂²	1	2	yes	complemented
92	#72233780	C₂²	1	1	yes	characteristic, complemented
93	#72233780	C₂²	1	1	yes	characteristic, complemented
94	#72225801	C₂²	1	2	yes	complemented
95	#72225801	C₂²	1	2	yes	complemented
96	#72225796	C₂²	1	2	yes	complemented
97	#72225796	C₂²	1	2	yes	complemented
98	#72225796	C₂²	1	2	yes	complemented
99	#72225783	C₂²	1	1	yes	characteristic, complemented
100	#72219307	C₂²	1	1	yes	characteristic
101	#72219307	C₂²	1	1	yes	characteristic
102	#72219307	C₂²	1	1	yes	characteristic
103	#72219307	C₂²	1	1	yes	characteristic
104	C₂×#7631286	C₂²	1	1	yes	characteristic
105	C₂×#7631286	C₂²	1	1	yes	characteristic
106	C₂²×#32898	C₂²	1	2	yes	complemented
107	C₂⁴×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
108	C₂⁴×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
109	C₂×#62817	C₂³	1	1	yes	characteristic
110	C₂²×#3484	D₄	1	2	yes	complemented
111	C₂³×D₄²	C₂³	1	1	yes	characteristic
112	C₂×#35347	D₄	1	2	yes	complemented
113	C₂×#35346	D₄	1	2	yes	complemented
114	C₂×#34980	C₂³	1	1	yes	characteristic
115	C₂×#34980	C₂³	1	2	yes	—
116	C₂×#34980	C₂³	1	1	yes	characteristic
117	C₂×#34980	C₂³	1	2	yes	—
118	C₂×#34980	C₂³	1	2	yes	—
119	C₂×#34980	C₂³	1	2	yes	—
120	C₂×#34980	C₂³	1	2	yes	—
121	C₂×#34980	C₂³	1	2	yes	—
122	C₂×#34980	C₂³	1	2	yes	—
123	C₂²×#2403	C₂³	1	1	yes	characteristic
124	C₂²×#2403	C₂³	1	2	yes	—
125	C₂²×#2403	C₂³	1	2	yes	—
126	C₂²×#2403	C₂³	1	1	yes	characteristic
127	C₂²×#2403	C₂³	1	2	yes	—
128	#7626202	C₂³	1	1	yes	characteristic
129	C₂×#34256	D₄	1	2	yes	complemented
130	C₂×#34171	C₂³	1	1	yes	characteristic
131	C₂×#34171	C₂³	1	1	yes	characteristic
132	C₂²×#2308	C₂³	1	2	yes	—
133	C₂×#21746	C₂³	1	1	yes	characteristic
134	C₂×#21746	C₂³	1	2	yes	—
135	C₂×#21746	C₂³	1	2	yes	—
136	C₂×#21746	C₂³	1	1	yes	characteristic
137	C₂×#21746	C₂³	1	2	yes	—
138	C₂×#21746	C₂³	1	2	yes	—
139	C₂×#21746	C₂³	1	2	yes	—
140	C₂×#21746	C₂³	1	2	yes	—
141	C₂×#21746	C₂³	1	2	yes	—
142	C₂×#21746	C₂³	1	2	yes	—
143	C₂×#21746	C₂³	1	2	yes	—
144	C₂×#21746	C₂³	1	2	yes	—
145	C₂²×#1781	C₂³	1	2	yes	—
146	C₂²×#1781	C₂³	1	2	yes	—
147	C₂²×#1781	C₂³	1	2	yes	—
148	C₂²×#1781	C₂³	1	2	yes	—
149	C₂²×#1781	C₂³	1	2	yes	—
150	C₂²×#1781	C₂³	1	2	yes	—
151	C₂²×#1781	C₂³	1	2	yes	—
152	C₂²×#1781	C₂³	1	2	yes	—
153	C₂²×#1781	C₂³	1	2	yes	—
154	C₂²×#1781	C₂³	1	2	yes	—
155	C₂²×#1781	C₂³	1	2	yes	—
156	C₂²×#1781	C₂³	1	2	yes	—
157	C₂²×#1781	C₂³	1	2	yes	—
158	C₂²×#1781	C₂³	1	2	yes	—
159	#556820	C₂³	1	2	yes	—
160	#556752	C₂³	1	2	yes	—
161	#517411	C₂³	1	1	yes	characteristic
162	#517411	C₂³	1	1	yes	characteristic
163	#517411	C₂³	1	1	yes	characteristic
164	#517411	C₂³	1	2	yes	—
165	#517411	C₂³	1	2	yes	—
166	#517411	C₂³	1	2	yes	—
167	#517411	C₂³	1	1	yes	characteristic
168	#517411	C₂³	1	1	yes	characteristic
169	#517411	C₂³	1	2	yes	—
170	#517411	C₂³	1	2	yes	—
171	#517411	C₂³	1	2	yes	—
172	#517411	C₂³	1	1	yes	characteristic
173	#405104	D₄	1	8	yes	complemented
174	#405104	D₄	1	8	yes	complemented
175	#405090	D₄	1	8	yes	complemented
176	#394058	D₄	1	8	yes	complemented
177	#393929	D₄	1	8	yes	complemented
178	#393929	D₄	1	8	yes	complemented
179	#392245	D₄	1	2	yes	complemented
180	#392109	D₄	1	2	yes	complemented
181	#382422	D₄	1	2	yes	complemented
182	#382390	D₄	1	2	yes	complemented
183	#355913	C₂³	1	2	yes	—
184	#355913	C₂³	1	2	yes	—
185	#355913	C₂³	1	2	yes	—
186	#355913	C₂³	1	2	yes	—
187	#355913	C₂³	1	2	yes	—
188	#355913	C₂³	1	2	yes	—
189	#355913	C₂³	1	2	yes	—
190	#355913	C₂³	1	2	yes	—
191	#355913	C₂³	1	2	yes	—
192	#355913	C₂³	1	2	yes	—
193	#355913	C₂³	1	2	yes	—
194	#355913	C₂³	1	2	yes	—
195	#355913	C₂³	1	2	yes	—
196	C₂×#8101	C₂³	1	2	yes	—
197	C₂×#8101	C₂³	1	2	yes	—
198	C₂×#8101	C₂³	1	2	yes	—
199	C₂×#8101	C₂³	1	2	yes	—
200	C₂×#8101	C₂³	1	2	yes	—
201	C₂×#8101	C₂³	1	2	yes	—
202	C₂×#8101	C₂³	1	2	yes	—
203	C₂×#8101	C₂³	1	2	yes	—
204	C₂²×#1304	C₂³	1	2	yes	—
205	C₂²×#1304	C₂³	1	2	yes	—
206	C₂²×#1304	C₂³	1	2	yes	—
207	C₂²×#1304	C₂³	1	2	yes	—
208	C₂³×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
209	C₂³×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
210	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
211	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
212	C₂⁵×D₄	C₂⁴	1	2	yes	—
213	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
214	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
215	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
216	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
217	C₂²×#534	C₂×D₄	1	2	yes	—
218	C₂²×#534	C₂×D₄	1	2	yes	—
219	C₂²×#534	C₂×D₄	1	4	yes	complemented
220	C₂²×#534	C₂×D₄	1	4	yes	complemented
221	C₂³×#127	#41	1	1	yes	characteristic
222	C₂³×#121	C₂×D₄	1	1	yes	characteristic
223	C₂³×#121	C₂×D₄	1	1	yes	characteristic
224	C₂³×#121	#41	1	1	yes	characteristic
225	C₂³×#121	#41	1	1	yes	characteristic
226	C₂³×#120	C₂×D₄	1	2	yes	—
227	C₂³×#120	C₂×D₄	1	2	yes	—
228	C₂³×#120	C₂×D₄	1	1	yes	characteristic
229	C₂³×#120	C₂×D₄	1	1	yes	characteristic
230	C₂³×#120	C₂×D₄	1	4	yes	complemented
231	C₂³×#120	#41	1	1	yes	characteristic
232	C₂³×#120	C₂⁴	1	1	yes	characteristic
233	C₂³×#120	C₂⁴	1	2	yes	—
234	C₂²×#518	C₂×D₄	1	2	yes	—
235	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
236	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
237	C₂×#2849	C₂×D₄	1	4	yes	—
238	C₂×#2846	C₂×D₄	1	4	yes	—
239	#34980	C₂×D₄	1	8	yes	—
240	C₂×#2405	C₂×D₄	1	4	yes	—
241	C₂×#2405	C₂×D₄	1	4	yes	—
242	C₂×#2403	C₂×D₄	1	8	yes	—
243	C₂×#2403	C₂×D₄	1	8	yes	—
244	C₂×#2403	C₂×D₄	1	4	yes	—
245	C₂×#2403	C₂×D₄	1	4	yes	—
246	C₂×#2308	C₂×D₄	1	2	yes	—
247	C₂×#2308	C₂×D₄	1	2	yes	—
248	C₂×#2308	C₂×D₄	1	2	yes	—
249	C₂×#2308	C₂×D₄	1	4	yes	complemented
250	C₂×#2308	C₂×D₄	1	4	yes	complemented
251	C₂²×#386	C₂×D₄	1	2	yes	—
252	C₂²×#386	C₂×D₄	1	2	yes	—
253	C₂²×#386	C₂×D₄	1	4	yes	complemented
254	C₂²×#379	C₂⁴	1	2	yes	—
255	C₂²×#379	C₂⁴	1	2	yes	—
256	C₂²×#379	C₂⁴	1	2	yes	—
257	C₂²×#379	C₂⁴	1	2	yes	—
258	C₂²×#379	C₂⁴	1	2	yes	—
259	C₂²×#379	C₂⁴	1	2	yes	—
260	C₂²×#379	C₂⁴	1	2	yes	—
261	C₂²×#379	C₂⁴	1	2	yes	—
262	C₂²×#379	C₂⁴	1	2	yes	—
263	C₂²×#379	C₂⁴	1	1	yes	characteristic
264	C₂²×#379	C₂⁴	1	1	yes	characteristic
265	C₂²×#379	C₂⁴	1	2	yes	—
266	C₂×#1898	C₂×D₄	1	8	yes	—
267	C₂×#1819	C₂×D₄	1	4	yes	—
268	C₂×#1819	C₂×D₄	1	4	yes	complemented
269	C₂×#1819	C₂×D₄	1	4	yes	complemented
270	C₂×#1781	C₂×D₄	1	4	yes	—
271	C₂×#1781	C₂×D₄	1	4	yes	—
272	C₂×#1781	C₂×D₄	1	4	yes	—
273	C₂×#1781	C₂×D₄	1	4	yes	complemented
274	C₂×#1781	C₂×D₄	1	8	yes	complemented
275	C₂×#1781	C₂×D₄	1	8	yes	complemented
276	C₂×#1781	C₂×D₄	1	8	yes	complemented
277	C₂×#1781	C₂×D₄	1	4	yes	complemented
278	#14681	C₂×D₄	1	2	yes	—
279	#14681	C₂×D₄	1	2	yes	—
280	#14681	C₂×D₄	1	4	yes	complemented
281	#14679	C₂×D₄	1	2	yes	—
282	#14679	C₂×D₄	1	2	yes	—
283	#14679	C₂×D₄	1	4	yes	complemented
284	#13867	C₂×D₄	1	8	yes	—
285	#13867	C₂×D₄	1	8	yes	—
286	#10735	C₂×D₄	1	8	yes	complemented
287	#10725	C₂×D₄	1	8	yes	complemented
288	#10725	C₂×D₄	1	8	yes	complemented
289	C₂⁷	#121	1	1	yes	characteristic, complemented
290	C₂⁷	C₂²×D₄	1	2	yes	—
291	C₂⁷	C₂²×D₄	1	1	yes	characteristic
292	C₂⁷	C₂²×D₄	1	1	yes	characteristic
293	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
295	C₂⁷	C₂⁵	1	1	yes	characteristic
296	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
297	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
298	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
299	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
300	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
301	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
302	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
303	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
304	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
305	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
306	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
307	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
308	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
309	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
310	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
311	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
312	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
313	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
314	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
315	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
316	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
317	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
318	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
319	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
320	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
321	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
322	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
323	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
324	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
325	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
326	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
327	C₂⁵×C₄	#121	1	1	yes	characteristic, complemented
328	C₂⁵×C₄	#121	1	1	yes	characteristic, complemented
329	C₂⁵×C₄	C₂²×D₄	1	2	yes	—
330	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×#534	#120	1	8	yes	—
335	C₂²×#120	#120	1	8	yes	—
336	C₂²×#120	C₂²×D₄	1	4	yes	—
337	C₂²×#120	H(5,𝔽₂)	1	4	yes	—
338	C₂³×C₄⋊C₄	#121	1	1	yes	characteristic, complemented
339	C₂³×C₄⋊C₄	#121	1	1	yes	characteristic, complemented
340	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
341	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
342	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
343	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
344	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
345	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
346	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
347	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
348	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
349	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
350	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
351	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
352	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
353	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
354	C₂³×C₂²⋊C₄	C₂×#41	1	1	yes	characteristic
355	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
356	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
357	C₂³×C₄²	#121	1	1	yes	characteristic, complemented
358	#2308	#120	1	8	yes	—
359	C₂×#386	#120	1	8	yes	—
360	C₂×#379	#120	1	8	yes	complemented
361	C₂×#379	C₂²×D₄	1	4	yes	—
362	C₂×#379	C₂²×D₄	1	4	yes	—
363	C₂×#379	C₂²×D₄	1	4	yes	—
364	C₂×#379	C₂²×D₄	1	4	yes	—
365	C₂×#379	C₂²×D₄	1	4	yes	—
366	C₂×#379	C₂²×D₄	1	4	yes	—
367	C₂×#379	C₂²×D₄	1	4	yes	—
368	C₂×#379	C₂²×D₄	1	4	yes	—
369	C₂×#379	C₂²×D₄	1	4	yes	—
370	C₂×#379	C₂²×D₄	1	4	yes	—
371	C₂×#379	C₂²×D₄	1	4	yes	—
372	C₂×#379	H(5,𝔽₂)	1	4	yes	—
373	C₂×#379	H(5,𝔽₂)	1	4	yes	—
374	C₂²⋊#95	#120	1	8	yes	complemented
375	C₂⁶	C₂×#120	1	2	yes	—
376	C₂⁶	C₂×#120	1	2	yes	—
377	C₂⁶	C₂×#121	1	1	yes	characteristic
378	C₂⁶	C₂×#121	1	1	yes	characteristic
379	C₂⁶	C₂×#121	1	1	yes	characteristic
380	C₂⁶	C₂×#121	1	1	yes	characteristic
381	C₂⁶	C₂×#121	1	1	yes	characteristic
382	C₂⁶	#534	1	2	yes	—
383	C₂⁶	#534	1	2	yes	—
384	C₂⁶	#534	1	2	yes	—
385	C₂⁶	#535	1	2	yes	—
386	C₂⁶	D₄²	1	4	yes	—
387	C₂⁶	D₄²	1	4	yes	—
388	C₂⁶	D₄²	1	2	yes	—
389	C₂⁶	C₂³×D₄	1	1	yes	characteristic
390	C₂⁶	C₂³×D₄	1	1	yes	characteristic
391	C₂⁶	C₂³×D₄	1	2	yes	—
392	C₂⁶	C₂³×D₄	1	2	yes	—
393	C₂⁶	C₂³×D₄	1	2	yes	—
394	C₂⁶	C₂²×#41	1	1	yes	characteristic
395	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
399	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
400	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
401	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
403	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
404	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
406	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
407	C₂⁶	#585	1	2	yes	—
408	C₂³×D₄	C₂×#120	1	4	yes	—
409	C₂³×D₄	C₂×#120	1	4	yes	—
410	C₂³×D₄	C₂×#120	1	2	yes	—
411	C₂³×D₄	#534	1	2	yes	—
412	C₂³×D₄	D₄²	1	8	yes	—
413	C₂³×D₄	D₄²	1	4	yes	—
414	C₂³×D₄	D₄²	1	4	yes	—
415	C₂³×D₄	D₄²	1	4	yes	—
416	C₂³×D₄	D₄²	1	4	yes	—
417	C₂³×D₄	D₄²	1	4	yes	—
418	C₂³×D₄	#546	1	4	yes	—
419	C₂³×D₄	#546	1	4	yes	—
420	C₂³×D₄	#546	1	4	yes	—
421	C₂³×D₄	#546	1	4	yes	—
422	C₂³×D₄	#546	1	4	yes	—
423	C₂⁴×C₄	C₂×#120	1	2	yes	—
424	C₂⁴×C₄	C₂×#120	1	2	yes	—
425	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
426	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
427	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
428	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
429	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
430	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
431	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
432	C₂⁴×C₄	#534	1	2	yes	—
433	C₂⁴×C₄	#534	1	2	yes	—
434	C₂⁴×C₄	#534	1	2	yes	—
435	C₂⁴×C₄	#535	1	2	yes	—
436	C₂⁴×C₄	D₄²	1	4	yes	—
437	C₂⁴×C₄	D₄²	1	2	yes	—
438	C₂⁴×C₄	D₄²	1	2	yes	—
439	C₂⁴×C₄	D₄²	1	2	yes	—
440	C₂⁴×C₄	D₄²	1	4	yes	—
441	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
442	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
443	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
444	C₂²×C₂²⋊C₄	C₂×#120	1	8	yes	—
445	C₂²×C₂²⋊C₄	#534	1	2	yes	—
446	C₂²×C₂²⋊C₄	D₄²	1	4	yes	—
447	C₂²×C₂²⋊C₄	#546	1	4	yes	—
448	#379	D₄²	1	8	yes	—
449	#379	D₄²	1	8	yes	—
450	C₂⁵	#2403	1	4	yes	—
451	C₂⁵	#2408	1	2	yes	—
452	C₂⁵	#2408	1	2	yes	—
453	C₂⁵	#2410	1	2	yes	—
454	C₂⁵	#2410	1	2	yes	—
455	C₂⁵	#2410	1	2	yes	—
456	C₂⁵	C₂²×#120	1	1	yes	characteristic
457	C₂⁵	C₂²×#120	1	1	yes	characteristic
458	C₂⁵	C₂²×#120	1	1	yes	characteristic
459	C₂⁵	C₂²×#121	1	1	yes	characteristic
460	C₂⁵	C₂×#534	1	1	yes	characteristic
461	C₂⁵	C₂×#534	1	1	yes	characteristic
462	C₂⁵	C₂×#534	1	1	yes	characteristic
463	C₂⁵	C₂×#534	1	1	yes	characteristic
464	C₂⁵	C₂×#535	1	1	yes	characteristic
465	C₂⁵	#3459	1	2	yes	—
466	C₂⁵	C₂×D₄²	1	2	yes	—
467	C₂⁵	C₂×D₄²	1	2	yes	—
468	C₂⁵	C₂×D₄²	1	2	yes	—
469	C₂⁵	C₂×D₄²	1	2	yes	—
470	C₂⁵	C₂×D₄²	1	2	yes	—
471	C₂⁵	C₂×D₄²	1	2	yes	—
472	C₂⁵	C₂×D₄²	1	2	yes	—
473	C₂⁵	C₂×D₄²	1	2	yes	—
474	C₂⁵	C₂×D₄²	1	2	yes	—
475	C₂⁵	C₂×#546	1	2	yes	—
476	C₂⁵	C₂×#546	1	2	yes	—
477	C₂⁵	C₂×#546	1	2	yes	—
478	C₂⁵	#3484	1	2	yes	—
479	C₂⁵	#3484	1	1	yes	characteristic
480	C₂⁵	#3484	1	2	yes	—
481	C₂⁵	#3484	1	1	yes	characteristic
482	C₂⁵	#3484	1	2	yes	—
483	C₂⁵	#3484	1	2	yes	—
484	C₂⁵	#3484	1	2	yes	—
485	C₂⁵	#3484	1	2	yes	—
486	C₂⁵	#3484	1	1	yes	characteristic
487	C₂⁵	#3484	1	2	yes	—
488	C₂⁵	#3484	1	2	yes	—
489	C₂⁵	#3484	1	2	yes	—
490	C₂⁵	#3484	1	2	yes	—
491	C₂⁵	#3484	1	2	yes	—
492	C₂⁵	#3484	1	2	yes	—
493	C₂⁵	#3484	1	2	yes	—
494	C₂⁵	#3484	1	2	yes	—
495	C₂⁵	#3484	1	2	yes	—
496	C₂⁵	#3484	1	2	yes	—
497	C₂⁵	#3484	1	2	yes	—
498	C₂⁵	#3484	1	2	yes	—
499	C₂⁵	#3484	1	2	yes	—
500	C₂⁵	#3484	1	2	yes	—
501	C₂⁵	#3485	1	1	yes	characteristic
502	C₂⁵	#3488	1	2	yes	—
503	C₂⁵	#3488	1	2	yes	—
504	C₂⁵	#3488	1	2	yes	—
505	C₂⁵	#3488	1	2	yes	—
506	C₂⁵	#3490	1	1	yes	characteristic
507	C₂⁵	#3490	1	1	yes	characteristic
508	C₂⁵	#3490	1	1	yes	characteristic
509	C₂⁵	#3490	1	1	yes	characteristic
510	C₂⁵	#3490	1	1	yes	characteristic
511	C₂⁵	#3490	1	1	yes	characteristic
512	C₂⁵	#3496	1	2	yes	—
513	C₂⁵	#3496	1	2	yes	—
514	C₂⁵	#3496	1	2	yes	—
515	C₂⁵	#3498	1	2	yes	—
516	C₂⁵	#3498	1	2	yes	—
517	C₂⁵	#3532	1	2	yes	—
518	C₂⁵	#3532	1	2	yes	—
519	C₂⁵	#3532	1	2	yes	—
520	C₂⁵	#3532	1	2	yes	—
521	C₂⁵	#3532	1	2	yes	—
522	C₂⁵	#3532	1	2	yes	—
523	C₂⁵	#3532	1	2	yes	—
524	C₂⁵	#3532	1	2	yes	—
525	C₂⁵	#3534	1	2	yes	—
526	C₂⁵	#3534	1	2	yes	—
527	C₂⁵	#3534	1	2	yes	—
528	C₂⁵	#3534	1	2	yes	—
529	C₂⁵	#3537	1	2	yes	—
530	C₂⁵	#3537	1	2	yes	—
531	C₂⁵	#3537	1	2	yes	—
532	C₂⁵	#3537	1	2	yes	—
533	C₂⁵	#3537	1	2	yes	—
534	C₂⁵	#3537	1	2	yes	—
535	C₂⁵	#3537	1	2	yes	—
536	C₂⁵	#3537	1	2	yes	—
537	C₂⁵	#3537	1	2	yes	—
538	C₂⁵	#3537	1	2	yes	—
539	C₂⁵	#3543	1	2	yes	—
540	C₂⁵	#3543	1	2	yes	—
541	C₂⁵	#3558	1	2	yes	—
542	C₂⁵	#3558	1	2	yes	—
543	C₂³×C₄	#2403	1	4	yes	—
544	C₂³×C₄	#2408	1	2	yes	—
545	C₂³×C₄	#2408	1	2	yes	—
546	C₂³×C₄	#2410	1	2	yes	—
547	C₂³×C₄	#2410	1	2	yes	—
548	C₂³×C₄	#2410	1	2	yes	—
549	C₂³×C₄	#2410	1	2	yes	—
550	C₂³×C₄	#2410	1	2	yes	—
551	C₂⁴	#23895	1	8	yes	complemented
552	C₂⁴	C₂×#2403	1	1	yes	characteristic
553	C₂⁴	C₂×#2410	1	1	yes	characteristic
554	C₂⁴	C₂×#2410	1	1	yes	characteristic
555	C₂⁴	C₂×#2408	1	1	yes	characteristic
556	C₂⁴	#34980	1	1	yes	characteristic
557	C₂⁴	#34980	1	1	yes	characteristic
558	C₂⁴	#34981	1	1	yes	characteristic
559	C₂⁴	#34984	1	1	yes	characteristic
560	C₂⁴	#35346	1	1	yes	characteristic
561	C₂⁴	#35348	1	1	yes	characteristic
562	C₂⁴	#35348	1	1	yes	characteristic
563	C₂⁴	#35512	1	1	yes	characteristic
564	C₂⁴	#35680	1	2	yes	—
565	C₂⁴	#35680	1	2	yes	—
566	C₂⁴	D₄×#120	1	2	yes	—
567	C₂⁴	D₄×#120	1	2	yes	—
568	C₂⁴	D₄×#120	1	2	yes	—
569	C₂⁴	D₄×#120	1	2	yes	—
570	C₂⁴	#36717	1	1	yes	characteristic
571	C₂⁴	#36721	1	1	yes	characteristic
572	C₂⁴	#37436	1	1	yes	characteristic
573	C₂⁴	#37644	1	2	yes	—
574	C₂⁴	#37644	1	2	yes	—
575	C₂⁴	#37645	1	2	yes	—
576	C₂⁴	#37645	1	2	yes	—
577	C₂⁴	#37672	1	2	yes	—
578	C₂⁴	#37672	1	2	yes	—
579	C₂⁴	#37744	1	2	yes	—
580	C₂⁴	#37744	1	2	yes	—
581	C₂⁴	#37744	1	2	yes	—
582	C₂⁴	#37744	1	2	yes	—
583	C₂⁴	#39412	1	2	yes	—
584	C₂⁴	#39412	1	2	yes	—
585	C₂⁴	#40486	1	2	yes	—
586	C₂⁴	#40486	1	2	yes	—
587	C₂⁴	#40584	1	2	yes	—
588	C₂⁴	#40584	1	2	yes	—
589	C₂⁴	#42996	1	2	yes	—
590	C₂⁴	#43001	1	2	yes	—
591	C₂⁴	#43001	1	2	yes	—
592	C₂⁴	#43001	1	2	yes	—
593	C₂⁴	#43001	1	2	yes	—
594	C₂⁴	#43001	1	2	yes	—
595	C₂⁴	#43001	1	2	yes	—
596	C₂⁴	#43023	1	2	yes	—
597	C₂⁴	#43023	1	2	yes	—
598	C₂⁴	#43098	1	2	yes	—
599	C₂⁴	#43098	1	2	yes	—
600	C₂⁴	#43098	1	2	yes	—
601	C₂⁴	#44877	1	2	yes	—
602	C₂⁴	#44877	1	2	yes	—
603	C₂⁴	#45355	1	2	yes	—
604	C₂⁴	#45355	1	2	yes	—
605	C₂⁴	#46384	1	1	yes	characteristic
606	C₂⁴	#46384	1	1	yes	characteristic
607	C₂⁴	#46387	1	1	yes	characteristic
608	C₂⁴	#46996	1	1	yes	characteristic
609	C₂⁴	#47827	1	2	yes	—
610	C₂⁴	#47827	1	2	yes	—
611	C₂⁴	#47827	1	2	yes	—
612	C₂⁴	#47838	1	2	yes	—
613	C₂⁴	#47838	1	2	yes	—
614	C₂⁴	#47838	1	2	yes	—
615	C₂⁴	#47838	1	2	yes	—
616	C₂⁴	#47942	1	2	yes	—
617	C₂⁴	#47942	1	2	yes	—
618	C₂⁴	#52004	1	2	yes	—
619	C₂⁴	#52004	1	2	yes	—
620	C₂⁴	#52004	1	2	yes	—
621	C₂⁴	#52031	1	2	yes	—
622	C₂⁴	#52031	1	2	yes	—
623	C₂⁴	#56344	1	2	yes	—
624	C₂⁴	#56346	1	2	yes	—
625	C₂⁴	#56346	1	2	yes	—
626	C₂⁴	#56413	1	2	yes	—
627	C₂⁴	#58990	1	2	yes	—
628	C₂⁴	#58990	1	2	yes	—
629	C₂⁴	#58990	1	2	yes	—
630	C₂⁴	#58991	1	2	yes	—
631	C₂⁴	#58991	1	2	yes	—
632	C₂⁴	#58991	1	2	yes	—
633	C₂⁴	#58991	1	2	yes	—
634	C₂⁴	#58991	1	2	yes	—
635	C₂⁴	#58991	1	2	yes	—
636	C₂⁴	#58997	1	2	yes	—
637	C₂⁴	#58997	1	2	yes	—
638	C₂⁴	#59126	1	2	yes	—
639	C₂³	#625760	1	1	yes	characteristic
640	C₂³	#647670	1	1	yes	characteristic
641	C₂³	#647670	1	1	yes	characteristic
642	C₂³	#688032	1	1	yes	characteristic
643	C₂³	#688032	1	1	yes	characteristic
644	C₂³	#759288	1	1	yes	characteristic
645	C₂³	#772778	1	2	yes	—
646	C₂³	#1259281	1	2	yes	—
647	C₂³	#1259281	1	2	yes	—
648	C₂³	#1418385	1	2	yes	—
649	C₂³	#1418393	1	2	yes	—
650	C₂³	#2601293	1	2	yes	—
651	C₂³	#2805709	1	2	yes	—
652	C₂³	#2805719	1	2	yes	—
653	C₂³	#4029237	1	2	yes	—
654	C₂³	#4029237	1	2	yes	—
655	C₂³	#4029441	1	2	yes	—
656	C₂³	#4029469	1	2	yes	—
657	C₂³	#4387614	1	1	yes	characteristic
658	C₂³	C₂×#23895	1	4	yes	—
659	C₂³	#6499874	1	4	yes	—
660	C₂²	#72225619	1	2	yes	—
661	C₂²	#72225625	1	4	yes	—
662	C₂²	#72225634	1	4	yes	—
663	C₂²	#72225647	1	2	yes	—
664	C₂²	#72264992	1	1	yes	characteristic
665	C₂	#72265721	1	1	yes	characteristic
666	C₂	#72265823	1	1	yes	characteristic
667	C₂	#72265868	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72264992
commutator, Frattini, cosocle	C₂⁷	C₂⁵
LCS	G ▷ C₂⁷ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁷ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266107	C₂	semidirect
2. #72266106	C₂	semidirect
3. #72266105	C₂	semidirect
4. #72266104	C₂	semidirect
5. #72266103	C₂	semidirect
6. #72266102	C₂	semidirect
7. #72266101	C₂²	semidirect
8. #72266100	C₂²	semidirect
9. #72266097	C₂	semidirect
10. #72266096	C₂	semidirect
11. #72266095	C₂²	semidirect
12. #72266095	C₂²	semidirect
13. #72266091	C₂	semidirect
14. #72266086	C₂	semidirect
15. #72266084	C₂	semidirect
16. #72266083	C₂²	semidirect
17. #72266082	C₂²	semidirect
18. #72266082	C₂²	semidirect
19. #72266081	C₂²	semidirect
20. #72266079	C₂²	semidirect
21. #72266076	C₂²	semidirect
22. #72266075	C₂²	semidirect
23. #72266073	C₂²	semidirect
24. #72266042	C₂	semidirect
25. #72266041	C₂²	semidirect
26. #72266036	C₂	semidirect
27. #72266035	C₂²	semidirect
28. #72266035	C₂²	semidirect
29. #72266032	C₂²	semidirect
30. #72266032	C₂²	semidirect
31. #72266029	C₂²	semidirect
32. #72266028	C₂²	semidirect
33. #72266023	C₂	semidirect
34. #72266021	C₂²	semidirect
35. #72266021	C₂²	semidirect
36. #72266016	C₂	semidirect
37. #72266014	C₂²	semidirect
38. #72266014	C₂²	semidirect
39. #72266012	C₂²	semidirect
40. #72266010	C₂²	semidirect
41. #72266009	C₂	semidirect
42. #72266008	C₂²	semidirect
43. #72266007	C₂²	semidirect
44. #72266007	C₂²	semidirect
45. C₂×#201687	C₂²	semidirect
46. C₂×#201687	C₂²	semidirect
47. #72262701	C₂²	semidirect
48. #72261893	C₂²	semidirect
49. #72261893	C₂²	semidirect
50. #72259008	C₂²	semidirect
51. #72258626	C₂²	semidirect
52. #72258626	C₂²	semidirect
53. #72258626	C₂²	semidirect
54. #72258626	C₂²	semidirect
55. #72258613	C₂²	semidirect
56. C₂²×#9495	C₂²	semidirect
57. C₂²×#9495	C₂²	semidirect
58. #72241123	C₂²	semidirect
59. #72240620	C₂	semidirect
60. #72240619	C₂²	semidirect
61. #72240619	C₂²	semidirect
62. #72240617	C₂²	semidirect
63. #72240568	C₂²	semidirect
64. #72238531	C₂²	semidirect
65. #72238531	C₂²	semidirect
66. #72238049	C₂²	semidirect
67. #72238049	C₂²	semidirect
68. #72238031	C₂²	semidirect
69. C₂×#233541	C₂²	semidirect
70. #72235847	C₂²	semidirect
71. #72234749	C₂	semidirect
72. #72234749	C₂	semidirect
73. #72234689	C₂²	semidirect
74. #72234689	C₂²	semidirect
76. #72234668	C₂²	semidirect
77. #72234668	C₂²	semidirect
78. #72234668	C₂²	semidirect
85. #72234629	C₂²	semidirect
86. #72234629	C₂²	semidirect
87. #72234625	C₂²	semidirect
88. #72234625	C₂²	semidirect
89. #72234625	C₂²	semidirect
90. C₂×#6628892	C₂²	semidirect
91. C₂×#6628892	C₂²	semidirect
92. #72233780	C₂²	semidirect
93. #72233780	C₂²	semidirect
94. #72225801	C₂²	semidirect
95. #72225801	C₂²	semidirect
96. #72225796	C₂²	semidirect
97. #72225796	C₂²	semidirect
98. #72225796	C₂²	semidirect
99. #72225783	C₂²	semidirect
106. C₂²×#32898	C₂²	semidirect
110. C₂²×#3484	D₄	semidirect
112. C₂×#35347	D₄	semidirect
113. C₂×#35346	D₄	semidirect
129. C₂×#34256	D₄	semidirect
173. #405104	D₄	semidirect
174. #405104	D₄	semidirect
175. #405090	D₄	semidirect
176. #394058	D₄	semidirect
177. #393929	D₄	semidirect
178. #393929	D₄	semidirect
179. #392245	D₄	semidirect
180. #392109	D₄	semidirect
181. #382422	D₄	semidirect
182. #382390	D₄	semidirect
219. C₂²×#534	C₂×D₄	semidirect
220. C₂²×#534	C₂×D₄	semidirect
230. C₂³×#120	C₂×D₄	semidirect
249. C₂×#2308	C₂×D₄	semidirect
250. C₂×#2308	C₂×D₄	semidirect
253. C₂²×#386	C₂×D₄	semidirect
268. C₂×#1819	C₂×D₄	semidirect
269. C₂×#1819	C₂×D₄	semidirect
273. C₂×#1781	C₂×D₄	semidirect
274. C₂×#1781	C₂×D₄	semidirect
275. C₂×#1781	C₂×D₄	semidirect
276. C₂×#1781	C₂×D₄	semidirect
277. C₂×#1781	C₂×D₄	semidirect
280. #14681	C₂×D₄	semidirect
283. #14679	C₂×D₄	semidirect
286. #10735	C₂×D₄	semidirect
287. #10725	C₂×D₄	semidirect
288. #10725	C₂×D₄	semidirect
289. C₂⁷	#121	semidirect
296. C₂⁴×D₄	#121	semidirect
297. C₂⁴×D₄	#121	semidirect
298. C₂⁴×D₄	#121	semidirect
299. C₂⁴×D₄	#121	semidirect
300. C₂⁴×D₄	#121	semidirect
327. C₂⁵×C₄	#121	semidirect
328. C₂⁵×C₄	#121	semidirect
338. C₂³×C₄⋊C₄	#121	semidirect
339. C₂³×C₄⋊C₄	#121	semidirect
340. C₂³×C₂²⋊C₄	#121	semidirect
341. C₂³×C₂²⋊C₄	#121	semidirect
342. C₂³×C₂²⋊C₄	#121	semidirect
343. C₂³×C₂²⋊C₄	#121	semidirect
344. C₂³×C₂²⋊C₄	#121	semidirect
357. C₂³×C₄²	#121	semidirect
360. C₂×#379	#120	semidirect
374. C₂²⋊#95	#120	semidirect
551. C₂⁴	#23895	semidirect

Maximal subgroups

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

subgroup	index
#72266107	2
#72266106	2
#72266105	2
#72266104	2
#72266103	2
#72266102	2
#72266097	2
#72266096	2
#72266091	2
#72266086	2
#72266084	2
#72266042	2
#72266036	2
#72266023	2
#72266016	2
#72266009	2
#72240620	2
#72234749	2