Subgroups — #72266127

Order 4096.

At least 21338 conjugacy classes of subgroups; only the 1403 normal subgroups are shown.

The subgroup lattice has 644 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266121	C₂	1	2	yes	maximal, complemented
2	#72266116	C₂	1	2	yes	maximal, complemented
3	#72266115	C₂	1	2	yes	maximal, complemented
4	#72266114	C₂	1	2	yes	maximal, complemented
5	#72266105	C₂	1	2	yes	maximal, complemented
6	#72266104	C₂	1	2	yes	maximal, complemented
7	#72266101	C₂²	1	2	yes	complemented
8	#72266101	C₂²	1	2	yes	complemented
9	#72266097	C₂	1	1	yes	maximal, characteristic, complemented
10	#72266095	C₂²	1	2	yes	complemented
11	#72266090	C₂	1	2	yes	maximal, complemented
12	#72266087	C₂	1	2	yes	maximal, complemented
13	#72266086	C₂	1	1	yes	maximal, characteristic, complemented
14	#72266083	C₂²	1	2	yes	complemented
15	#72266082	C₂²	1	2	yes	complemented
16	#72266080	C₂	1	2	yes	maximal, complemented
17	#72266079	C₂²	1	2	yes	complemented
18	#72266079	C₂²	1	2	yes	complemented
19	#72266077	C₂²	1	2	yes	complemented
20	#72266075	C₂²	1	2	yes	complemented
21	#72266073	C₂²	1	2	yes	complemented
22	#72266068	C₂	1	1	yes	maximal, characteristic, complemented
23	#72266066	C₂²	1	2	yes	complemented
24	#72266045	C₂	1	2	yes	maximal, complemented
25	#72266044	C₂	1	1	yes	maximal, characteristic, complemented
26	#72266041	C₂²	1	1	yes	characteristic, complemented
27	#72266041	C₂²	1	1	yes	characteristic, complemented
28	#72266035	C₂²	1	2	yes	complemented
29	#72266035	C₂²	1	2	yes	complemented
30	#72266035	C₂²	1	2	yes	complemented
31	#72266035	C₂²	1	2	yes	complemented
32	#72266033	C₂²	1	2	yes	complemented
33	#72266032	C₂²	1	2	yes	complemented
34	#72266029	C₂²	1	2	yes	complemented
35	#72266029	C₂²	1	2	yes	complemented
36	#72266029	C₂²	1	2	yes	complemented
37	#72266028	C₂²	1	2	yes	complemented
38	#72266028	C₂²	1	2	yes	complemented
39	#72266026	C₂	1	2	yes	maximal, complemented
40	#72266021	C₂²	1	2	yes	complemented
41	#72266015	C₂	1	2	yes	maximal, complemented
42	#72266014	C₂²	1	2	yes	complemented
43	#72266014	C₂²	1	2	yes	complemented
44	#72266008	C₂²	1	2	yes	complemented
45	#72266007	C₂²	1	2	yes	complemented
46	#72266007	C₂²	1	2	yes	complemented
47	#72262603	C₂²	1	2	yes	complemented
48	#72259008	C₂²	1	1	yes	characteristic, complemented
49	#72258662	C₂	1	1	yes	maximal, characteristic, complemented
50	#72258662	C₂	1	1	yes	maximal, characteristic, complemented
51	#72258649	C₂²	1	1	yes	characteristic, complemented
52	#72258649	C₂²	1	1	yes	characteristic, complemented
53	#72258626	C₂²	1	2	yes	complemented
54	#72258626	C₂²	1	2	yes	complemented
55	#72258613	C₂²	1	2	yes	complemented
56	C₂²×#10336	C₂²	1	2	yes	—
57	C₂²×#10336	C₂²	1	2	yes	—
58	C₂²×#10336	C₂²	1	2	yes	complemented
59	#72241122	C₂²	1	2	yes	complemented
60	#72240620	C₂	1	1	yes	maximal, characteristic, complemented
61	#72240619	C₂²	1	2	yes	—
62	#72240619	C₂²	1	2	yes	complemented
63	#72240619	C₂²	1	2	yes	complemented
64	#72240619	C₂²	1	1	yes	characteristic, complemented
65	#72240619	C₂²	1	1	yes	characteristic, complemented
66	#72240617	C₂²	1	2	yes	—
67	#72240617	C₂²	1	2	yes	—
68	#72240617	C₂²	1	2	yes	—
69	#72240617	C₂²	1	2	yes	complemented
70	#72240568	C₂²	1	2	yes	complemented
71	C₂×#6370693	C₂²	1	2	yes	complemented
72	#72238531	C₂²	1	2	yes	complemented
73	#72238531	C₂²	1	2	yes	complemented
74	#72238049	C₂²	1	2	yes	complemented
75	#72238031	C₂²	1	2	yes	complemented
76	#72238031	C₂²	1	2	yes	complemented
77	C₂×#233541	C₂²	1	2	yes	complemented
78	C₂×#233541	C₂²	1	2	yes	complemented
79	C₂×#201664	C₂²	1	2	yes	complemented
80	#72235847	C₂²	1	1	yes	characteristic, complemented
81	#72234689	C₂²	1	2	yes	complemented
82	#72234689	C₂²	1	2	yes	complemented
83	#72234629	C₂²	1	2	yes	—
84	#72234629	C₂²	1	2	yes	—
85	#72233780	C₂²	1	2	yes	—
86	#72233780	C₂²	1	1	yes	characteristic, complemented
87	#72233780	C₂²	1	1	yes	characteristic, complemented
88	#72225796	C₂²	1	2	yes	—
89	#72225796	C₂²	1	2	yes	—
90	#72225796	C₂²	1	2	yes	—
91	#72225796	C₂²	1	2	yes	—
92	#72225796	C₂²	1	2	yes	complemented
93	#72225796	C₂²	1	2	yes	complemented
94	#72225796	C₂²	1	2	yes	complemented
95	#72225796	C₂²	1	2	yes	complemented
96	#72225796	C₂²	1	2	yes	complemented
97	#72225783	C₂²	1	1	yes	characteristic, complemented
98	#72225783	C₂²	1	1	yes	characteristic, complemented
99	#72225665	C₂²	1	1	yes	characteristic
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	—
107	C₂⁴×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
108	C₂⁴×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
109	C₂³×D₄²	C₂³	1	1	yes	characteristic
110	C₂×#35250	D₄	1	2	yes	complemented
111	C₂×#34980	D₄	1	2	yes	complemented
112	C₂×#34980	C₂³	1	2	yes	—
113	C₂×#34980	C₂³	1	1	yes	characteristic
114	C₂×#34980	C₂³	1	2	yes	—
115	C₂×#34736	D₄	1	2	yes	complemented
116	C₂²×#2403	D₄	1	2	yes	complemented
117	C₂²×#2403	C₂³	1	2	yes	—
118	C₂²×#2403	C₂³	1	1	yes	characteristic
119	C₂²×#2403	C₂³	1	1	yes	characteristic
120	C₂²×#2403	C₂³	1	2	yes	—
121	C₂²×#2403	C₂³	1	2	yes	—
122	C₂²×#2403	C₂³	1	2	yes	—
123	C₂²×#2403	C₂³	1	2	yes	—
124	C₂²×#2403	C₂³	1	2	yes	—
125	C₂×#34171	C₂³	1	1	yes	characteristic
126	C₂×#34171	C₂³	1	1	yes	characteristic
127	C₂×#34171	C₂³	1	2	yes	—
128	C₂×#34171	C₂³	1	2	yes	—
129	C₂×#21746	C₂³	1	1	yes	characteristic
130	C₂×#21746	C₂³	1	1	yes	characteristic
131	C₂×#21746	C₂³	1	1	yes	characteristic
132	C₂×#21746	C₂³	1	1	yes	characteristic
133	C₂×#21746	C₂³	1	2	yes	—
134	C₂×#21746	C₂³	1	2	yes	—
135	C₂²×#1781	C₂³	1	2	yes	—
136	C₂²×#1781	C₂³	1	2	yes	—
137	C₂²×#1781	C₂³	1	2	yes	—
138	C₂²×#1781	C₂³	1	2	yes	—
139	C₂²×#1781	C₂³	1	2	yes	—
140	C₂²×#1781	C₂³	1	2	yes	—
141	C₂²×#1781	C₂³	1	2	yes	—
142	C₂²×#1781	C₂³	1	2	yes	—
143	C₂²×#1781	C₂³	1	2	yes	—
144	C₂²×#1781	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	#613188	D₄	1	8	yes	complemented
153	#612424	D₄	1	8	yes	complemented
154	#556820	C₂³	1	2	yes	—
155	#556752	C₂³	1	1	yes	characteristic
156	#517411	C₂³	1	1	yes	characteristic
157	#517411	C₂³	1	2	yes	—
158	#517411	C₂³	1	2	yes	—
159	#517411	C₂³	1	2	yes	—
160	#517411	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	1	yes	characteristic
166	#517411	C₂³	1	2	yes	—
167	#517411	C₂³	1	2	yes	—
168	#517411	C₂³	1	2	yes	—
169	#517411	C₂³	1	2	yes	—
170	#517411	C₂³	1	1	yes	characteristic
171	#392658	D₄	1	8	yes	complemented
172	#392245	D₄	1	2	yes	complemented
173	#392109	D₄	1	2	yes	complemented
174	#382422	D₄	1	2	yes	complemented
175	#382390	D₄	1	2	yes	complemented
176	#379754	D₄	1	8	yes	complemented
177	#355913	C₂³	1	2	yes	—
178	#355913	C₂³	1	2	yes	—
179	#355913	C₂³	1	2	yes	—
180	#355913	C₂³	1	2	yes	—
181	#355913	C₂³	1	2	yes	—
182	#355913	C₂³	1	2	yes	—
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	C₂×#8101	C₂³	1	2	yes	—
193	C₂×#8101	C₂³	1	2	yes	—
194	C₂×#8101	C₂³	1	2	yes	—
195	C₂×#8101	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	C₂²×#1304	C₂³	1	2	yes	—
204	C₂²×#1304	C₂³	1	2	yes	—
205	C₂²×#1304	C₂³	1	2	yes	—
206	C₂⁴×#41	C₂×D₄	1	4	yes	—
207	C₂⁴×#41	C₂×D₄	1	2	yes	—
208	C₂⁵×D₄	C₂×D₄	1	2	yes	—
209	C₂⁵×D₄	C₂×D₄	1	4	yes	—
210	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
211	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
212	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
213	C₂⁵×D₄	C₂⁴	1	2	yes	—
214	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
215	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
216	C₂⁵×D₄	C₂⁴	1	2	yes	—
217	C₂³×#127	#41	1	1	yes	characteristic
218	C₂³×#121	C₂×D₄	1	1	yes	characteristic
219	C₂³×#121	C₂×D₄	1	1	yes	characteristic
220	C₂³×#121	#41	1	1	yes	characteristic
221	C₂³×#121	#41	1	1	yes	characteristic
222	C₂³×#120	C₂×D₄	1	4	yes	—
223	C₂³×#120	C₂×D₄	1	1	yes	characteristic
224	C₂³×#120	C₂×D₄	1	1	yes	characteristic
225	C₂³×#120	#41	1	1	yes	characteristic
226	C₂³×#120	C₂⁴	1	1	yes	characteristic
227	C₂²×#518	C₂×D₄	1	4	yes	complemented
228	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
229	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
230	C₂×#2405	C₂×D₄	1	4	yes	—
231	C₂×#2403	C₂×D₄	1	8	yes	—
232	C₂×#2403	C₂×D₄	1	4	yes	—
233	C₂×#2403	C₂×D₄	1	8	yes	—
234	C₂×#2403	C₂×D₄	1	4	yes	—
235	C₂×#2403	C₂×D₄	1	4	yes	—
236	C₂×#2403	C₂×D₄	1	4	yes	—
237	C₂×#2403	C₂×D₄	1	4	yes	—
238	C₂×#2403	#41	1	8	yes	—
239	C₂×#2308	C₂×D₄	1	4	yes	complemented
240	C₂²×#386	C₂×D₄	1	4	yes	—
241	C₂×#2280	C₂×D₄	1	2	yes	—
242	C₂²×#379	C₂×D₄	1	2	yes	—
243	C₂²×#379	C₂⁴	1	2	yes	—
244	C₂²×#379	C₂⁴	1	2	yes	—
245	C₂²×#379	C₂⁴	1	2	yes	—
246	C₂²×#379	C₂⁴	1	2	yes	—
247	C₂²×#379	C₂⁴	1	1	yes	characteristic
248	C₂²×#379	C₂⁴	1	2	yes	—
249	C₂²×#379	C₂⁴	1	2	yes	—
250	C₂²×#379	C₂⁴	1	2	yes	—
251	C₂²×#379	C₂⁴	1	2	yes	—
252	C₂²×#379	C₂⁴	1	2	yes	—
253	C₂²×#379	C₂⁴	1	1	yes	characteristic
254	C₂²×#379	C₂⁴	1	1	yes	characteristic
255	C₂²×#379	C₂⁴	1	2	yes	—
256	C₂×#1819	C₂×D₄	1	4	yes	—
257	C₂×#1781	C₂×D₄	1	4	yes	—
258	C₂×#1781	C₂×D₄	1	4	yes	—
259	C₂×#1781	C₂×D₄	1	4	yes	—
260	C₂×#1781	C₂×D₄	1	4	yes	complemented
261	C₂×#1781	C₂×D₄	1	4	yes	complemented
262	#14681	C₂×D₄	1	4	yes	—
263	#14681	C₂×D₄	1	2	yes	—
264	#14681	C₂×D₄	1	2	yes	—
265	#14679	C₂×D₄	1	4	yes	—
266	#14679	C₂×D₄	1	2	yes	—
267	#14679	C₂×D₄	1	2	yes	—
268	#13867	C₂×D₄	1	8	yes	—
269	#13867	C₂×D₄	1	8	yes	—
270	#13867	C₂×D₄	1	8	yes	—
271	#13867	C₂×D₄	1	8	yes	—
272	#10725	C₂×D₄	1	8	yes	complemented
273	#10725	C₂×D₄	1	8	yes	complemented
274	C₂⁷	#120	1	2	yes	complemented
275	C₂⁷	#121	1	1	yes	characteristic, complemented
276	C₂⁷	C₂²×D₄	1	1	yes	characteristic
277	C₂⁷	C₂²×D₄	1	1	yes	characteristic
278	C₂⁷	C₂²×D₄	1	2	yes	—
279	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂⁷	H(5,𝔽₂)	1	2	yes	—
281	C₂⁷	C₂⁵	1	1	yes	characteristic
282	C₂⁴×Q₈	#120	1	2	yes	complemented
283	C₂⁴×D₄	#120	1	4	yes	complemented
284	C₂⁴×D₄	#120	1	2	yes	complemented
285	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
286	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
287	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
288	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
289	C₂⁴×D₄	#121	1	1	yes	characteristic, complemented
290	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
291	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
292	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
293	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
294	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
295	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
296	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
297	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
298	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
299	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
300	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
301	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
302	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
303	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
304	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
305	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
306	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
307	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
308	C₂⁴×D₄	C₂×#41	1	4	yes	—
309	C₂⁴×D₄	C₂×#41	1	4	yes	—
310	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
311	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
312	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
313	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
314	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
315	C₂⁵×C₄	#120	1	4	yes	complemented
316	C₂⁵×C₄	#120	1	2	yes	complemented
317	C₂⁵×C₄	#121	1	1	yes	characteristic, complemented
318	C₂⁵×C₄	#121	1	1	yes	characteristic, complemented
319	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
320	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
321	C₂⁵×C₄	C₂²×D₄	1	2	yes	—
322	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂⁵×C₄	H(5,𝔽₂)	1	2	yes	—
324	C₂³×C₄⋊C₄	#121	1	1	yes	characteristic, complemented
325	C₂³×C₄⋊C₄	#121	1	1	yes	characteristic, complemented
326	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
327	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
328	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
329	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
330	C₂³×C₂²⋊C₄	#121	1	1	yes	characteristic, complemented
331	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
334	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
335	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
336	C₂³×C₂²⋊C₄	C₂×#41	1	1	yes	characteristic
337	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
338	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
339	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
340	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
341	C₂³×C₄²	#121	1	1	yes	characteristic, complemented
342	#2403	#121	1	8	yes	complemented
343	#2403	#121	1	8	yes	complemented
344	#2403	#121	1	8	yes	complemented
345	#2403	#121	1	8	yes	complemented
346	C₂×#379	#120	1	8	yes	complemented
347	C₂×#379	C₂²×D₄	1	4	yes	—
348	C₂×#379	C₂²×D₄	1	4	yes	—
349	C₂×#379	C₂²×D₄	1	4	yes	—
350	C₂×#379	C₂²×D₄	1	4	yes	—
351	C₂×#379	C₂²×D₄	1	4	yes	—
352	C₂×#379	C₂²×D₄	1	4	yes	—
353	C₂×#379	C₂²×D₄	1	4	yes	—
354	C₂×#379	C₂²×D₄	1	4	yes	—
355	C₂×#379	C₂×#41	1	4	yes	—
356	C₂×#379	H(5,𝔽₂)	1	2	yes	—
357	C₂×#379	H(5,𝔽₂)	1	4	yes	—
358	C₂²⋊#95	#120	1	8	yes	complemented
359	C₂⁶	C₂×#120	1	2	yes	—
360	C₂⁶	C₂×#120	1	4	yes	—
361	C₂⁶	C₂×#120	1	2	yes	—
362	C₂⁶	C₂×#121	1	1	yes	characteristic
363	C₂⁶	C₂×#121	1	1	yes	characteristic
364	C₂⁶	C₂×#121	1	1	yes	characteristic
365	C₂⁶	C₂×#121	1	1	yes	characteristic
366	C₂⁶	C₂×#121	1	1	yes	characteristic
367	C₂⁶	#525	1	2	yes	—
368	C₂⁶	#534	1	4	yes	—
369	C₂⁶	#534	1	2	yes	—
370	C₂⁶	D₄²	1	2	yes	—
371	C₂⁶	D₄²	1	2	yes	—
372	C₂⁶	#546	1	4	yes	—
373	C₂⁶	C₂³×D₄	1	1	yes	characteristic
374	C₂⁶	C₂³×D₄	1	1	yes	characteristic
375	C₂⁶	C₂³×D₄	1	2	yes	—
376	C₂⁶	C₂³×D₄	1	2	yes	—
377	C₂⁶	C₂²×#41	1	1	yes	characteristic
378	C₂⁶	C₂²×#41	1	2	yes	—
379	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
381	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
384	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
385	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
386	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
387	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
388	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
389	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
390	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂⁶	#585	1	2	yes	—
392	C₂³×D₄	C₂×#121	1	4	yes	—
393	C₂³×D₄	C₂×#121	1	4	yes	—
394	C₂³×D₄	C₂×#121	1	4	yes	—
395	C₂³×D₄	C₂×#121	1	4	yes	—
396	C₂³×D₄	#525	1	4	yes	—
397	C₂³×D₄	#525	1	4	yes	—
398	C₂³×D₄	#534	1	4	yes	—
399	C₂³×D₄	#534	1	4	yes	—
400	C₂³×D₄	D₄²	1	4	yes	—
401	C₂³×D₄	D₄²	1	4	yes	—
402	C₂³×D₄	D₄²	1	4	yes	—
403	C₂³×D₄	D₄²	1	4	yes	—
404	C₂³×D₄	#546	1	4	yes	—
405	C₂³×D₄	#546	1	4	yes	—
406	C₂³×D₄	#546	1	4	yes	—
407	C₂³×D₄	#546	1	4	yes	—
408	C₂⁴×C₄	C₂×#120	1	2	yes	—
409	C₂⁴×C₄	C₂×#120	1	2	yes	—
410	C₂⁴×C₄	C₂×#120	1	4	yes	—
411	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
412	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
413	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
414	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
415	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
416	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
417	C₂⁴×C₄	C₂×#121	1	1	yes	characteristic
418	C₂⁴×C₄	#525	1	2	yes	—
419	C₂⁴×C₄	#534	1	4	yes	—
420	C₂⁴×C₄	#534	1	2	yes	—
421	C₂⁴×C₄	D₄²	1	2	yes	—
422	C₂⁴×C₄	D₄²	1	2	yes	—
423	C₂⁴×C₄	#546	1	4	yes	—
424	C₂²×C₂²⋊C₄	C₂×#120	1	8	yes	—
425	C₂²×C₂²⋊C₄	#534	1	8	yes	—
426	#379	C₂×#121	1	8	yes	—
427	C₂⁵	#2410	1	2	yes	—
428	C₂⁵	#2410	1	2	yes	—
429	C₂⁵	#2410	1	4	yes	—
430	C₂⁵	#2410	1	4	yes	—
431	C₂⁵	#2847	1	2	yes	—
432	C₂⁵	#2847	1	2	yes	—
433	C₂⁵	C₂²×#120	1	1	yes	characteristic
434	C₂⁵	C₂²×#120	1	1	yes	characteristic
435	C₂⁵	C₂²×#121	1	1	yes	characteristic
436	C₂⁵	C₂²×#121	1	2	yes	—
437	C₂⁵	C₂×#525	1	2	yes	—
438	C₂⁵	C₂×#525	1	1	yes	characteristic
439	C₂⁵	C₂×#534	1	2	yes	—
440	C₂⁵	C₂×#534	1	2	yes	—
441	C₂⁵	C₂×#534	1	1	yes	characteristic
442	C₂⁵	C₂×#534	1	2	yes	—
443	C₂⁵	C₂×D₄²	1	2	yes	—
444	C₂⁵	C₂×D₄²	1	2	yes	—
445	C₂⁵	C₂×D₄²	1	2	yes	—
446	C₂⁵	C₂×#546	1	2	yes	—
447	C₂⁵	C₂×#546	1	2	yes	—
448	C₂⁵	C₂×#546	1	2	yes	—
449	C₂⁵	#3484	1	1	yes	characteristic
450	C₂⁵	#3484	1	2	yes	—
451	C₂⁵	#3484	1	2	yes	—
452	C₂⁵	#3484	1	1	yes	characteristic
453	C₂⁵	#3484	1	1	yes	characteristic
454	C₂⁵	#3484	1	2	yes	—
455	C₂⁵	#3484	1	1	yes	characteristic
456	C₂⁵	#3484	1	2	yes	—
457	C₂⁵	#3484	1	2	yes	—
458	C₂⁵	#3484	1	2	yes	—
459	C₂⁵	#3484	1	1	yes	characteristic
460	C₂⁵	#3484	1	2	yes	—
461	C₂⁵	#3484	1	2	yes	—
462	C₂⁵	#3484	1	2	yes	—
463	C₂⁵	#3484	1	1	yes	characteristic
464	C₂⁵	#3484	1	1	yes	characteristic
465	C₂⁵	#3484	1	2	yes	—
466	C₂⁵	#3484	1	2	yes	—
467	C₂⁵	#3484	1	2	yes	—
468	C₂⁵	#3484	1	2	yes	—
469	C₂⁵	#3485	1	1	yes	characteristic
470	C₂⁵	#3488	1	2	yes	—
471	C₂⁵	#3490	1	2	yes	—
472	C₂⁵	#3490	1	1	yes	characteristic
473	C₂⁵	#3490	1	1	yes	characteristic
474	C₂⁵	#3490	1	1	yes	characteristic
475	C₂⁵	#3490	1	1	yes	characteristic
476	C₂⁵	#3490	1	1	yes	characteristic
477	C₂⁵	#3490	1	1	yes	characteristic
478	C₂⁵	#3490	1	2	yes	—
479	C₂⁵	#3490	1	2	yes	—
480	C₂⁵	#3496	1	2	yes	—
481	C₂⁵	#3496	1	2	yes	—
482	C₂⁵	#3496	1	2	yes	—
483	C₂⁵	#3496	1	2	yes	—
484	C₂⁵	#3498	1	2	yes	—
485	C₂⁵	#3498	1	2	yes	—
486	C₂⁵	#3498	1	2	yes	—
487	C₂⁵	#3505	1	2	yes	—
488	C₂⁵	#3513	1	2	yes	—
489	C₂⁵	#3514	1	2	yes	—
490	C₂⁵	#3519	1	2	yes	—
491	C₂⁵	#3519	1	2	yes	—
492	C₂⁵	#3519	1	2	yes	—
493	C₂⁵	#3519	1	2	yes	—
494	C₂⁵	#3519	1	2	yes	—
495	C₂⁵	#3519	1	2	yes	—
496	C₂⁵	#3532	1	2	yes	—
497	C₂⁵	#3532	1	2	yes	—
498	C₂⁵	#3532	1	2	yes	—
499	C₂⁵	#3532	1	2	yes	—
500	C₂⁵	#3532	1	2	yes	—
501	C₂⁵	#3532	1	2	yes	—
502	C₂⁵	#3532	1	2	yes	—
503	C₂⁵	#3534	1	2	yes	—
504	C₂⁵	#3534	1	2	yes	—
505	C₂⁵	#3534	1	2	yes	—
506	C₂⁵	#3534	1	2	yes	—
507	C₂⁵	#3537	1	2	yes	—
508	C₂⁵	#3537	1	2	yes	—
509	C₂⁵	#3537	1	2	yes	—
510	C₂⁵	#3537	1	2	yes	—
511	C₂⁵	#3537	1	2	yes	—
512	C₂⁵	#3537	1	2	yes	—
513	C₂⁵	#3542	1	2	yes	—
514	C₂⁵	#3543	1	2	yes	—
515	C₂⁵	#3543	1	2	yes	—
516	C₂⁵	#3543	1	2	yes	—
517	C₂⁵	#3543	1	2	yes	—
518	C₂⁵	#3543	1	2	yes	—
519	C₂⁵	#3558	1	2	yes	—
520	C₂³×C₄	#2410	1	2	yes	—
521	C₂³×C₄	#2410	1	4	yes	—
522	C₂³×C₄	#2410	1	2	yes	—
523	C₂³×C₄	#2410	1	4	yes	—
524	C₂³×C₄	#2847	1	2	yes	—
525	C₂³×C₄	#2847	1	2	yes	—
526	C₂⁴	C₂×#2410	1	1	yes	characteristic
527	C₂⁴	C₂×#2410	1	2	yes	—
528	C₂⁴	#34980	1	2	yes	—
529	C₂⁴	#34981	1	1	yes	characteristic
530	C₂⁴	#34981	1	2	yes	—
531	C₂⁴	#35346	1	1	yes	characteristic
532	C₂⁴	#35346	1	1	yes	characteristic
533	C₂⁴	#35347	1	1	yes	characteristic
534	C₂⁴	#35348	1	1	yes	characteristic
535	C₂⁴	#35348	1	1	yes	characteristic
536	C₂⁴	#35348	1	1	yes	characteristic
537	C₂⁴	#35352	1	2	yes	—
538	C₂⁴	#35355	1	1	yes	characteristic
539	C₂⁴	#35355	1	1	yes	characteristic
540	C₂⁴	#35358	1	1	yes	characteristic
541	C₂⁴	#35361	1	2	yes	—
542	C₂⁴	#35527	1	1	yes	characteristic
543	C₂⁴	#35680	1	2	yes	—
544	C₂⁴	#35691	1	2	yes	—
545	C₂⁴	#35691	1	2	yes	—
546	C₂⁴	#35691	1	2	yes	—
547	C₂⁴	#35692	1	2	yes	—
548	C₂⁴	#35692	1	2	yes	—
549	C₂⁴	#35714	1	2	yes	—
550	C₂⁴	#35761	1	2	yes	—
551	C₂⁴	D₄×#120	1	2	yes	—
552	C₂⁴	#36098	1	2	yes	—
553	C₂⁴	#36098	1	2	yes	—
554	C₂⁴	#36098	1	2	yes	—
555	C₂⁴	C₂×#2847	1	1	yes	characteristic
556	C₂⁴	#36702	1	2	yes	—
557	C₂⁴	#37117	1	1	yes	characteristic
558	C₂⁴	#37232	1	1	yes	characteristic
559	C₂⁴	#37644	1	2	yes	—
560	C₂⁴	#37644	1	2	yes	—
561	C₂⁴	#37644	1	2	yes	—
562	C₂⁴	#37672	1	2	yes	—
563	C₂⁴	#37832	1	2	yes	—
564	C₂⁴	#37832	1	2	yes	—
565	C₂⁴	#38020	1	2	yes	—
566	C₂⁴	#38076	1	2	yes	—
567	C₂⁴	#38904	1	2	yes	—
568	C₂⁴	#38949	1	2	yes	—
569	C₂⁴	#39336	1	2	yes	—
570	C₂⁴	#39358	1	2	yes	—
571	C₂⁴	#40584	1	2	yes	—
572	C₂⁴	#40584	1	2	yes	—
573	C₂⁴	#40584	1	2	yes	—
574	C₂⁴	#40585	1	2	yes	—
575	C₂⁴	#42996	1	2	yes	—
576	C₂⁴	#42996	1	2	yes	—
577	C₂⁴	#42996	1	2	yes	—
578	C₂⁴	#42997	1	2	yes	—
579	C₂⁴	#42997	1	2	yes	—
580	C₂⁴	#42998	1	2	yes	—
581	C₂⁴	#43001	1	2	yes	—
582	C₂⁴	#43001	1	2	yes	—
583	C₂⁴	#43019	1	2	yes	—
584	C₂⁴	#43095	1	2	yes	—
585	C₂⁴	#43095	1	2	yes	—
586	C₂⁴	#43886	1	2	yes	—
587	C₂⁴	#46350	1	2	yes	—
588	C₂⁴	#46350	1	2	yes	—
589	C₂⁴	#46351	1	2	yes	—
590	C₂⁴	#46355	1	2	yes	—
591	C₂⁴	#46355	1	2	yes	—
592	C₂⁴	#46364	1	2	yes	—
593	C₂⁴	#46384	1	1	yes	characteristic
594	C₂⁴	#46384	1	1	yes	characteristic
595	C₂⁴	#46387	1	1	yes	characteristic
596	C₂⁴	#46504	1	2	yes	—
597	C₂⁴	#46504	1	2	yes	—
598	C₂⁴	#46512	1	2	yes	—
599	C₂⁴	#46996	1	1	yes	characteristic
600	C₂⁴	#47042	1	2	yes	—
601	C₂⁴	#47827	1	2	yes	—
602	C₂⁴	#47827	1	2	yes	—
603	C₂⁴	#47827	1	2	yes	—
604	C₂⁴	#47830	1	2	yes	—
605	C₂⁴	#47853	1	2	yes	—
606	C₂⁴	#47877	1	2	yes	—
607	C₂⁴	#47878	1	2	yes	—
608	C₂⁴	#48082	1	2	yes	—
609	C₂⁴	#48088	1	2	yes	—
610	C₂⁴	#48143	1	2	yes	—
611	C₂⁴	#48149	1	2	yes	—
612	C₂⁴	#50646	1	2	yes	—
613	C₂³	#612459	1	1	yes	characteristic
614	C₂³	#616969	1	1	yes	characteristic
615	C₂³	#686258	1	2	yes	—
616	C₂³	#687655	1	2	yes	—
617	C₂³	#763341	1	1	yes	characteristic
618	C₂³	#1082707	1	2	yes	—
619	C₂³	#1082737	1	2	yes	—
620	C₂³	#1082757	1	2	yes	—
621	C₂³	#1082791	1	2	yes	—
622	C₂³	#1082853	1	2	yes	—
623	C₂³	#1084821	1	2	yes	—
624	C₂³	#1099105	1	2	yes	—
625	C₂³	#1100993	1	2	yes	—
626	C₂³	#4312050	1	2	yes	—
627	C₂³	#4312899	1	2	yes	—
628	C₂³	#4379766	1	1	yes	characteristic
629	C₂³	#4387614	1	1	yes	characteristic
630	C₂³	#4928940	1	1	yes	characteristic
631	C₂³	#4929118	1	1	yes	characteristic
632	C₂³	#6499874	1	4	yes	—
633	C₂³	#6499874	1	4	yes	—
634	C₂²	#72225633	1	4	yes	—
635	C₂²	#72225635	1	2	yes	—
636	C₂²	#72225638	1	4	yes	—
637	C₂²	#72225646	1	2	yes	—
638	C₂²	#72237761	1	2	yes	—
639	C₂²	#72264985	1	1	yes	characteristic
640	C₂	#72265801	1	1	yes	characteristic
641	C₂	#72265815	1	1	yes	characteristic
642	C₂	#72265889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72264985
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. #72266121	C₂	semidirect
2. #72266116	C₂	semidirect
3. #72266115	C₂	semidirect
4. #72266114	C₂	semidirect
5. #72266105	C₂	semidirect
6. #72266104	C₂	semidirect
7. #72266101	C₂²	semidirect
8. #72266101	C₂²	semidirect
9. #72266097	C₂	semidirect
10. #72266095	C₂²	semidirect
11. #72266090	C₂	semidirect
12. #72266087	C₂	semidirect
13. #72266086	C₂	semidirect
14. #72266083	C₂²	semidirect
15. #72266082	C₂²	semidirect
16. #72266080	C₂	semidirect
17. #72266079	C₂²	semidirect
18. #72266079	C₂²	semidirect
19. #72266077	C₂²	semidirect
20. #72266075	C₂²	semidirect
21. #72266073	C₂²	semidirect
22. #72266068	C₂	semidirect
23. #72266066	C₂²	semidirect
24. #72266045	C₂	semidirect
25. #72266044	C₂	semidirect
26. #72266041	C₂²	semidirect
27. #72266041	C₂²	semidirect
28. #72266035	C₂²	semidirect
29. #72266035	C₂²	semidirect
30. #72266035	C₂²	semidirect
31. #72266035	C₂²	semidirect
32. #72266033	C₂²	semidirect
33. #72266032	C₂²	semidirect
34. #72266029	C₂²	semidirect
35. #72266029	C₂²	semidirect
36. #72266029	C₂²	semidirect
37. #72266028	C₂²	semidirect
38. #72266028	C₂²	semidirect
39. #72266026	C₂	semidirect
40. #72266021	C₂²	semidirect
41. #72266015	C₂	semidirect
42. #72266014	C₂²	semidirect
43. #72266014	C₂²	semidirect
44. #72266008	C₂²	semidirect
45. #72266007	C₂²	semidirect
46. #72266007	C₂²	semidirect
47. #72262603	C₂²	semidirect
48. #72259008	C₂²	semidirect
49. #72258662	C₂	semidirect
50. #72258662	C₂	semidirect
51. #72258649	C₂²	semidirect
52. #72258649	C₂²	semidirect
53. #72258626	C₂²	semidirect
54. #72258626	C₂²	semidirect
55. #72258613	C₂²	semidirect
58. C₂²×#10336	C₂²	semidirect
59. #72241122	C₂²	semidirect
60. #72240620	C₂	semidirect
62. #72240619	C₂²	semidirect
63. #72240619	C₂²	semidirect
64. #72240619	C₂²	semidirect
65. #72240619	C₂²	semidirect
69. #72240617	C₂²	semidirect
70. #72240568	C₂²	semidirect
71. C₂×#6370693	C₂²	semidirect
72. #72238531	C₂²	semidirect
73. #72238531	C₂²	semidirect
74. #72238049	C₂²	semidirect
75. #72238031	C₂²	semidirect
76. #72238031	C₂²	semidirect
77. C₂×#233541	C₂²	semidirect
78. C₂×#233541	C₂²	semidirect
79. C₂×#201664	C₂²	semidirect
80. #72235847	C₂²	semidirect
81. #72234689	C₂²	semidirect
82. #72234689	C₂²	semidirect
86. #72233780	C₂²	semidirect
87. #72233780	C₂²	semidirect
92. #72225796	C₂²	semidirect
93. #72225796	C₂²	semidirect
94. #72225796	C₂²	semidirect
95. #72225796	C₂²	semidirect
96. #72225796	C₂²	semidirect
97. #72225783	C₂²	semidirect
98. #72225783	C₂²	semidirect
110. C₂×#35250	D₄	semidirect
111. C₂×#34980	D₄	semidirect
115. C₂×#34736	D₄	semidirect
116. C₂²×#2403	D₄	semidirect
152. #613188	D₄	semidirect
153. #612424	D₄	semidirect
171. #392658	D₄	semidirect
172. #392245	D₄	semidirect
173. #392109	D₄	semidirect
174. #382422	D₄	semidirect
175. #382390	D₄	semidirect
176. #379754	D₄	semidirect
227. C₂²×#518	C₂×D₄	semidirect
239. C₂×#2308	C₂×D₄	semidirect
260. C₂×#1781	C₂×D₄	semidirect
261. C₂×#1781	C₂×D₄	semidirect
272. #10725	C₂×D₄	semidirect
273. #10725	C₂×D₄	semidirect
274. C₂⁷	#120	semidirect
275. C₂⁷	#121	semidirect
282. C₂⁴×Q₈	#120	semidirect
283. C₂⁴×D₄	#120	semidirect
284. C₂⁴×D₄	#120	semidirect
285. C₂⁴×D₄	#121	semidirect
286. C₂⁴×D₄	#121	semidirect
287. C₂⁴×D₄	#121	semidirect
288. C₂⁴×D₄	#121	semidirect
289. C₂⁴×D₄	#121	semidirect
315. C₂⁵×C₄	#120	semidirect
316. C₂⁵×C₄	#120	semidirect
317. C₂⁵×C₄	#121	semidirect
318. C₂⁵×C₄	#121	semidirect
324. C₂³×C₄⋊C₄	#121	semidirect
325. C₂³×C₄⋊C₄	#121	semidirect
326. C₂³×C₂²⋊C₄	#121	semidirect
327. C₂³×C₂²⋊C₄	#121	semidirect
328. C₂³×C₂²⋊C₄	#121	semidirect
329. C₂³×C₂²⋊C₄	#121	semidirect
330. C₂³×C₂²⋊C₄	#121	semidirect
341. C₂³×C₄²	#121	semidirect
342. #2403	#121	semidirect
343. #2403	#121	semidirect
344. #2403	#121	semidirect
345. #2403	#121	semidirect
346. C₂×#379	#120	semidirect
358. C₂²⋊#95	#120	semidirect

Maximal subgroups

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

subgroup	index
#72266121	2
#72266116	2
#72266115	2
#72266114	2
#72266105	2
#72266104	2
#72266097	2
#72266090	2
#72266087	2
#72266086	2
#72266080	2
#72266068	2
#72266045	2
#72266044	2
#72266026	2
#72266015	2
#72258662	2
#72240620	2