Subgroups — #72266119

Order 4096.

At least 16823 conjugacy classes of subgroups; only the 1445 normal subgroups are shown.

The subgroup lattice has 582 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266118	C₂	1	1	yes	maximal, characteristic, complemented
2	#72266117	C₂	1	1	yes	maximal, characteristic, complemented
3	#72266116	C₂	1	2	yes	maximal, complemented
4	#72266115	C₂	1	1	yes	maximal, characteristic, complemented
5	#72266114	C₂	1	2	yes	maximal, complemented
6	#72266113	C₂	1	1	yes	maximal, characteristic, complemented
7	#72266112	C₂	1	2	yes	maximal, complemented
8	#72266111	C₂²	1	1	yes	characteristic, complemented
9	#72266110	C₂	1	1	yes	maximal, characteristic, complemented
10	#72266109	C₂²	1	1	yes	characteristic, complemented
11	#72266102	C₂	1	2	yes	maximal, complemented
12	#72266101	C₂²	1	2	yes	complemented
13	#72266100	C₂²	1	1	yes	characteristic, complemented
14	#72266096	C₂	1	2	yes	maximal, complemented
15	#72266095	C₂²	1	2	yes	complemented
16	#72266094	C₂	1	2	yes	maximal, complemented
17	#72266084	C₂	1	2	yes	maximal, complemented
18	#72266083	C₂²	1	2	yes	complemented
19	#72266082	C₂²	1	2	yes	complemented
20	#72266081	C₂²	1	1	yes	characteristic, complemented
21	#72266080	C₂	1	2	yes	maximal, complemented
22	#72266079	C₂²	1	2	yes	complemented
23	#72266079	C₂²	1	2	yes	complemented
24	#72266079	C₂²	1	2	yes	complemented
25	#72266079	C₂²	1	1	yes	characteristic, complemented
26	#72266078	C₂	1	2	yes	maximal, complemented
27	#72266077	C₂²	1	2	yes	complemented
28	#72266076	C₂²	1	2	yes	complemented
29	#72266075	C₂²	1	2	yes	complemented
30	#72266074	C₂²	1	1	yes	characteristic, complemented
31	#72266073	C₂²	1	2	yes	complemented
32	#72266073	C₂²	1	2	yes	complemented
33	#72266073	C₂²	1	2	yes	complemented
34	#72266073	C₂²	1	2	yes	complemented
35	#72266067	C₂	1	2	yes	maximal, complemented
36	#72266066	C₂²	1	2	yes	complemented
37	#72266065	C₂²	1	2	yes	complemented
38	#72266065	C₂²	1	2	yes	complemented
39	#72266039	C₂	1	1	yes	maximal, characteristic, complemented
40	#72266035	C₂²	1	2	yes	complemented
41	#72266035	C₂²	1	2	yes	complemented
42	#72266035	C₂²	1	2	yes	complemented
43	#72266029	C₂²	1	2	yes	complemented
44	#72266028	C₂²	1	2	yes	complemented
45	#72266028	C₂²	1	2	yes	complemented
46	#72266028	C₂²	1	1	yes	characteristic, complemented
47	#72266028	C₂²	1	1	yes	characteristic, complemented
48	#72266028	C₂²	1	2	yes	complemented
49	#72266020	C₂	1	2	yes	maximal, complemented
50	#72266012	C₂²	1	2	yes	complemented
51	#72266012	C₂²	1	2	yes	complemented
52	#72266006	C₂	1	2	yes	maximal, complemented
53	#72266005	C₂²	1	2	yes	complemented
54	C₂×#201687	C₂²	1	2	yes	complemented
55	#72259008	C₂²	1	2	yes	complemented
56	#72259008	C₂²	1	1	yes	characteristic, complemented
57	#72258613	C₂²	1	2	yes	—
58	#72258613	C₂²	1	2	yes	—
59	#72258613	C₂²	1	2	yes	complemented
60	#72258613	C₂²	1	2	yes	complemented
61	#72258613	C₂²	1	1	yes	characteristic, complemented
62	C₂²×#245225	C₂	1	1	yes	maximal, characteristic, complemented
63	C₂²×#9495	C₂²	1	2	yes	—
64	C₂²×#9495	C₂²	1	2	yes	—
65	C₂²×#10336	C₂²	1	2	yes	—
66	C₂²×#10336	C₂²	1	1	yes	characteristic
67	C₂²×#10336	C₂²	1	1	yes	characteristic
68	#72241143	C₂²	1	1	yes	characteristic, complemented
69	#72240619	C₂²	1	2	yes	—
70	#72240619	C₂²	1	2	yes	—
71	#72240619	C₂²	1	2	yes	complemented
72	#72240619	C₂²	1	2	yes	complemented
73	#72240619	C₂²	1	2	yes	complemented
74	#72240617	C₂²	1	2	yes	complemented
75	#72240568	C₂²	1	2	yes	complemented
76	C₂×#6370693	C₂²	1	2	yes	complemented
77	#72238531	C₂²	1	2	yes	—
78	#72238531	C₂²	1	2	yes	—
79	#72238531	C₂²	1	2	yes	complemented
80	#72238031	C₂²	1	2	yes	complemented
81	C₂×#233541	C₂²	1	2	yes	complemented
82	C₂×#233541	C₂²	1	2	yes	complemented
83	C₂×#233541	C₂²	1	1	yes	characteristic, complemented
84	C₂×#201664	C₂²	1	2	yes	complemented
85	#72234689	C₂²	1	2	yes	complemented
86	#72234668	C₂²	1	2	yes	complemented
87	#72234668	C₂²	1	2	yes	complemented
88	#72234668	C₂²	1	1	yes	characteristic, complemented
89	#72234629	C₂²	1	2	yes	—
90	#72234629	C₂²	1	2	yes	—
91	#72234629	C₂²	1	2	yes	complemented
92	C₂×#6628892	C₂²	1	2	yes	complemented
93	C₂²×#35346	C₂²	1	2	yes	—
94	#72225801	C₂²	1	2	yes	complemented
95	#72225796	C₂²	1	2	yes	complemented
96	#72225796	C₂²	1	2	yes	complemented
97	#72225796	C₂²	1	1	yes	characteristic, complemented
98	#72225796	C₂²	1	2	yes	complemented
99	#72225791	C₂²	1	2	yes	complemented
100	#72225783	C₂²	1	2	yes	complemented
101	#72219254	C₂²	1	1	yes	characteristic
102	C₂²×#32898	C₂²	1	2	yes	—
103	C₂²×#32898	C₂²	1	2	yes	—
104	C₂²×#8541	C₂²	1	1	yes	characteristic
105	C₂²×#8541	C₂²	1	2	yes	—
106	C₂²×#8541	C₂²	1	1	yes	characteristic
107	C₂⁴×H(5,𝔽₂)	C₂³	1	2	yes	—
108	C₂⁴×#120	C₂³	1	1	yes	characteristic
109	#7641846	C₂³	1	1	yes	characteristic
110	C₂×#34980	C₂³	1	2	yes	—
111	C₂×#34980	C₂³	1	2	yes	—
112	C₂×#34980	C₂³	1	1	yes	characteristic
113	C₂×#34980	C₂³	1	2	yes	—
114	C₂²×#2403	C₂³	1	2	yes	—
115	C₂²×#2403	C₂³	1	2	yes	—
116	C₂²×#2403	C₂³	1	2	yes	—
117	C₂²×#2403	C₂³	1	2	yes	—
118	C₂²×#2403	C₂³	1	2	yes	—
119	C₂²×#2403	C₂³	1	1	yes	characteristic
120	C₂²×#2403	C₂³	1	1	yes	characteristic
121	#7626202	C₂³	1	1	yes	characteristic
122	C₂×#34171	C₂³	1	2	yes	—
123	C₂×#34171	C₂³	1	2	yes	—
124	C₂²×#2308	C₂³	1	2	yes	—
125	C₂×#32898	D₄	1	8	yes	complemented
126	C₂×#32898	D₄	1	8	yes	complemented
127	C₂×#21746	C₂³	1	2	yes	—
128	C₂×#21746	C₂³	1	2	yes	—
129	C₂×#21746	C₂³	1	1	yes	characteristic
130	C₂×#21746	C₂³	1	2	yes	—
131	C₂²×#1781	C₂³	1	2	yes	—
132	C₂²×#1781	C₂³	1	2	yes	—
133	C₂²×#1781	C₂³	1	2	yes	—
134	C₂²×#1781	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	1	yes	characteristic
143	C₂²×#1781	C₂³	1	2	yes	—
144	C₂²×#1781	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
154	C₂²×#1781	C₂³	1	2	yes	—
155	C₂²×#1781	C₂³	1	2	yes	—
156	C₂²×#1781	C₂³	1	1	yes	characteristic
157	#517411	C₂³	1	2	yes	—
158	#517411	C₂³	1	1	yes	characteristic
159	#517411	C₂³	1	2	yes	—
160	#517411	C₂³	1	2	yes	—
161	#517411	C₂³	1	2	yes	—
162	#517411	C₂³	1	2	yes	—
163	#405104	D₄	1	8	yes	complemented
164	#393929	D₄	1	8	yes	complemented
165	#359695	D₄	1	8	yes	complemented
166	#359428	D₄	1	8	yes	complemented
167	#355913	C₂³	1	2	yes	—
168	#355913	C₂³	1	2	yes	—
169	#355913	C₂³	1	2	yes	—
170	#355913	C₂³	1	2	yes	—
171	#355913	C₂³	1	2	yes	—
172	#355913	C₂³	1	2	yes	—
173	#355913	C₂³	1	2	yes	—
174	#355913	C₂³	1	2	yes	—
175	#355913	C₂³	1	2	yes	—
176	#355913	C₂³	1	2	yes	—
177	#355913	C₂³	1	1	yes	characteristic
178	#355913	C₂³	1	1	yes	characteristic
179	#355913	C₂³	1	2	yes	—
180	#355913	C₂³	1	2	yes	—
181	#355913	C₂³	1	2	yes	—
182	#355913	C₂³	1	1	yes	characteristic
183	#355913	C₂³	1	2	yes	—
184	#355913	C₂³	1	2	yes	—
185	#355913	C₂³	1	2	yes	—
186	C₂×#10336	D₄	1	8	yes	complemented
187	C₂×#8101	C₂³	1	2	yes	—
188	C₂×#8101	C₂³	1	2	yes	—
189	C₂×#8101	C₂³	1	2	yes	—
190	C₂×#8101	C₂³	1	2	yes	—
191	C₂×#8101	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
198	C₂²×#1304	C₂³	1	1	yes	characteristic
199	C₂²×#1304	C₂³	1	2	yes	—
200	C₂²×#1304	C₂³	1	1	yes	characteristic
201	C₂⁸	#41	1	1	yes	characteristic, complemented
202	C₂³×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
203	C₂³×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
204	C₂⁵×D₄	C₂⁴	1	2	yes	—
205	C₂⁵×D₄	C₂⁴	1	2	yes	—
206	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
207	C₂⁵×D₄	C₂⁴	1	2	yes	—
208	C₂²×#534	C₂×D₄	1	4	yes	—
209	C₂³×#120	C₂×D₄	1	4	yes	—
210	C₂³×#120	#41	1	4	yes	complemented
211	C₂³×#120	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₂²⋊C₄	#41	1	2	yes	complemented
213	C₂⁴×C₂²⋊C₄	#41	1	1	yes	characteristic, complemented
214	C₂×#2405	C₂×D₄	1	4	yes	complemented
215	C₂×#2403	C₂×D₄	1	8	yes	—
216	C₂×#2403	C₂×D₄	1	8	yes	—
217	C₂×#2403	C₂×D₄	1	8	yes	—
218	C₂×#2403	C₂×D₄	1	8	yes	—
219	C₂×#2403	C₂×D₄	1	4	yes	—
220	C₂×#2403	C₂×D₄	1	4	yes	—
221	C₂×#2403	C₂×D₄	1	4	yes	—
222	C₂×#2403	C₂×D₄	1	4	yes	complemented
223	C₂×#2308	C₂×D₄	1	4	yes	—
224	C₂²×#386	C₂×D₄	1	4	yes	—
225	C₂²×#386	#41	1	4	yes	complemented
226	C₂×#2280	C₂×D₄	1	4	yes	complemented
227	C₂²×#379	C₂×D₄	1	4	yes	complemented
228	C₂²×#379	C₂⁴	1	1	yes	characteristic
229	C₂²×#379	C₂⁴	1	2	yes	—
230	C₂²×#379	C₂⁴	1	2	yes	—
231	C₂²×#379	C₂⁴	1	1	yes	characteristic
232	C₂²×#379	C₂⁴	1	2	yes	—
233	C₂²×#379	C₂⁴	1	2	yes	—
234	C₂²×#379	C₂⁴	1	2	yes	—
235	C₂²×#379	C₂⁴	1	1	yes	characteristic
236	C₂²×#379	C₂⁴	1	1	yes	characteristic
237	C₂²×#379	C₂⁴	1	1	yes	characteristic
238	C₂²×#379	C₂⁴	1	2	yes	—
239	C₂²×#379	C₂⁴	1	2	yes	—
240	C₂²×#379	C₂⁴	1	2	yes	—
241	C₂²×#379	C₂⁴	1	2	yes	—
242	C₂×#1819	C₂×D₄	1	4	yes	complemented
243	C₂×#1781	C₂×D₄	1	8	yes	—
244	C₂×#1781	C₂×D₄	1	8	yes	—
245	C₂×#1781	C₂×D₄	1	8	yes	—
246	C₂×#1781	C₂×D₄	1	4	yes	—
247	C₂×#1781	C₂×D₄	1	4	yes	—
248	C₂×#1781	C₂×D₄	1	8	yes	—
249	C₂×#1781	C₂×D₄	1	8	yes	—
250	C₂×#1781	C₂×D₄	1	8	yes	—
251	C₂×#1781	C₂×D₄	1	4	yes	—
252	C₂×#1781	C₂×D₄	1	4	yes	complemented
253	#14681	C₂×D₄	1	4	yes	complemented
254	#14679	C₂×D₄	1	4	yes	complemented
255	#13867	C₂×D₄	1	8	yes	complemented
256	#10725	C₂×D₄	1	8	yes	complemented
257	#10725	C₂×D₄	1	8	yes	complemented
258	#10725	C₂×D₄	1	8	yes	complemented
259	C₂×#1304	C₂×D₄	1	4	yes	—
260	C₂⁷	C₂²×D₄	1	2	yes	—
261	C₂⁷	C₂×#41	1	1	yes	characteristic
262	C₂⁷	C₂×#41	1	2	yes	—
263	C₂⁷	C₂×#41	1	2	yes	—
264	C₂⁷	C₂⁵	1	1	yes	characteristic
265	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
266	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
267	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
268	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
269	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
270	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
271	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
272	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
273	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
274	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
275	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
276	C₂⁴×D₄	C₂×#41	1	4	yes	—
277	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
278	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
279	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
280	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
281	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
282	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
283	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
284	C₂⁴×D₄	H(5,𝔽₂)	1	4	yes	—
285	C₂⁵×C₄	C₂²×D₄	1	2	yes	—
286	C₂⁵×C₄	C₂×#41	1	2	yes	—
287	C₂⁵×C₄	C₂×#41	1	1	yes	characteristic
288	C₂⁵×C₄	C₂×#41	1	2	yes	—
289	C₂²×#120	#120	1	16	yes	—
290	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
291	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
292	C₂³×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
293	C₂³×C₂²⋊C₄	C₂×#41	1	4	yes	—
294	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
295	#2403	#120	1	4	yes	complemented
296	#2403	#120	1	4	yes	complemented
297	#2403	#120	1	8	yes	complemented
298	C₂×#386	#120	1	16	yes	—
299	C₂×#379	C₂²×D₄	1	4	yes	—
300	C₂×#379	C₂²×D₄	1	2	yes	—
301	C₂×#379	C₂²×D₄	1	4	yes	—
302	C₂×#379	C₂²×D₄	1	4	yes	—
303	C₂×#379	C₂²×D₄	1	4	yes	—
304	C₂×#379	C₂²×D₄	1	2	yes	—
305	C₂×#379	C₂²×D₄	1	4	yes	—
306	C₂×#379	C₂²×D₄	1	4	yes	—
307	C₂×#379	C₂²×D₄	1	4	yes	—
308	C₂×#379	C₂²×D₄	1	4	yes	—
309	C₂×#379	C₂²×D₄	1	4	yes	—
310	C₂×#379	C₂²×D₄	1	4	yes	—
311	C₂×#379	C₂²×D₄	1	4	yes	—
312	C₂×#379	H(5,𝔽₂)	1	2	yes	—
313	C₂×#379	H(5,𝔽₂)	1	4	yes	—
314	C₂×#379	H(5,𝔽₂)	1	2	yes	—
315	C₂×#379	H(5,𝔽₂)	1	4	yes	—
316	C₂⁶	C₂×#120	1	4	yes	—
317	C₂⁶	#525	1	4	yes	—
318	C₂⁶	D₄²	1	1	yes	characteristic
319	C₂⁶	D₄²	1	2	yes	—
320	C₂⁶	D₄²	1	4	yes	—
321	C₂⁶	D₄²	1	2	yes	—
322	C₂⁶	#546	1	4	yes	—
323	C₂⁶	#546	1	4	yes	—
324	C₂⁶	#546	1	2	yes	—
325	C₂⁶	#546	1	4	yes	—
326	C₂⁶	C₂³×D₄	1	2	yes	—
327	C₂⁶	C₂³×D₄	1	2	yes	—
328	C₂⁶	C₂³×D₄	1	2	yes	—
329	C₂⁶	C₂³×D₄	1	1	yes	characteristic
330	C₂⁶	C₂²×#41	1	1	yes	characteristic
331	C₂⁶	C₂²×#41	1	2	yes	—
332	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
333	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
334	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
335	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
336	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
339	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
340	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
341	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
342	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
343	C₂⁶	#585	1	1	yes	characteristic
344	C₂⁶	#585	1	2	yes	—
345	C₂³×D₄	C₂×#120	1	4	yes	—
346	C₂³×D₄	C₂×#120	1	4	yes	—
347	C₂³×D₄	C₂×#120	1	8	yes	—
348	C₂³×D₄	#534	1	4	yes	—
349	C₂³×D₄	#534	1	4	yes	—
350	C₂³×D₄	#535	1	8	yes	—
351	C₂³×D₄	D₄²	1	4	yes	—
352	C₂³×D₄	D₄²	1	4	yes	—
353	C₂³×D₄	D₄²	1	4	yes	—
354	C₂³×D₄	D₄²	1	4	yes	—
355	C₂³×D₄	#546	1	8	yes	—
356	C₂³×D₄	#546	1	8	yes	—
357	C₂⁴×C₄	C₂×#120	1	4	yes	—
358	C₂⁴×C₄	#525	1	4	yes	—
359	C₂⁴×C₄	D₄²	1	2	yes	—
360	C₂⁴×C₄	D₄²	1	1	yes	characteristic
361	C₂⁴×C₄	D₄²	1	2	yes	—
362	C₂⁴×C₄	D₄²	1	2	yes	—
363	C₂⁴×C₄	D₄²	1	4	yes	—
364	C₂⁴×C₄	#546	1	4	yes	—
365	C₂⁴×C₄	#546	1	2	yes	—
366	C₂⁴×C₄	#546	1	4	yes	—
367	C₂⁴×C₄	#546	1	4	yes	—
368	C₂²×C₂²⋊C₄	C₂×#120	1	8	yes	—
369	C₂²×C₂²⋊C₄	#546	1	8	yes	—
370	#379	C₂×#120	1	4	yes	—
371	#379	D₄²	1	8	yes	—
372	#379	D₄²	1	4	yes	—
373	C₂⁵	#2403	1	4	yes	—
374	C₂⁵	#2403	1	4	yes	—
375	C₂⁵	#2404	1	8	yes	—
376	C₂⁵	C₂²×#120	1	2	yes	—
377	C₂⁵	C₂²×#120	1	1	yes	characteristic
378	C₂⁵	C₂×#525	1	2	yes	—
379	C₂⁵	C₂×#534	1	2	yes	—
380	C₂⁵	C₂×#535	1	2	yes	—
381	C₂⁵	#3459	1	1	yes	characteristic
382	C₂⁵	C₂×D₄²	1	1	yes	characteristic
383	C₂⁵	C₂×D₄²	1	2	yes	—
384	C₂⁵	C₂×D₄²	1	2	yes	—
385	C₂⁵	C₂×D₄²	1	2	yes	—
386	C₂⁵	C₂×D₄²	1	2	yes	—
387	C₂⁵	C₂×D₄²	1	1	yes	characteristic
388	C₂⁵	C₂×D₄²	1	2	yes	—
389	C₂⁵	C₂×#546	1	2	yes	—
390	C₂⁵	C₂×#546	1	2	yes	—
391	C₂⁵	C₂×#546	1	2	yes	—
392	C₂⁵	C₂×#546	1	2	yes	—
393	C₂⁵	C₂×#546	1	1	yes	characteristic
394	C₂⁵	C₂×#546	1	2	yes	—
395	C₂⁵	C₂×#546	1	2	yes	—
396	C₂⁵	D₄×#41	1	2	yes	—
397	C₂⁵	D₄×#41	1	2	yes	—
398	C₂⁵	#3481	1	1	yes	characteristic
399	C₂⁵	#3484	1	2	yes	—
400	C₂⁵	#3484	1	2	yes	—
401	C₂⁵	#3484	1	2	yes	—
402	C₂⁵	#3484	1	1	yes	characteristic
403	C₂⁵	#3484	1	2	yes	—
404	C₂⁵	#3484	1	2	yes	—
405	C₂⁵	#3484	1	2	yes	—
406	C₂⁵	#3484	1	2	yes	—
407	C₂⁵	#3484	1	2	yes	—
408	C₂⁵	#3484	1	2	yes	—
409	C₂⁵	#3484	1	2	yes	—
410	C₂⁵	#3484	1	2	yes	—
411	C₂⁵	#3484	1	2	yes	—
412	C₂⁵	#3484	1	2	yes	—
413	C₂⁵	#3484	1	2	yes	—
414	C₂⁵	#3484	1	1	yes	characteristic
415	C₂⁵	#3484	1	2	yes	—
416	C₂⁵	#3484	1	1	yes	characteristic
417	C₂⁵	#3485	1	2	yes	—
418	C₂⁵	#3488	1	2	yes	—
419	C₂⁵	#3488	1	2	yes	—
420	C₂⁵	#3488	1	2	yes	—
421	C₂⁵	#3488	1	1	yes	characteristic
422	C₂⁵	#3490	1	2	yes	—
423	C₂⁵	#3490	1	1	yes	characteristic
424	C₂⁵	#3490	1	2	yes	—
425	C₂⁵	#3490	1	2	yes	—
426	C₂⁵	#3490	1	2	yes	—
427	C₂⁵	#3496	1	2	yes	—
428	C₂⁵	#3496	1	2	yes	—
429	C₂⁵	#3498	1	2	yes	—
430	C₂⁵	#3500	1	1	yes	characteristic
431	C₂⁵	#3505	1	2	yes	—
432	C₂⁵	#3513	1	2	yes	—
433	C₂⁵	#3519	1	2	yes	—
434	C₂⁵	#3519	1	2	yes	—
435	C₂⁵	#3519	1	2	yes	—
436	C₂⁵	#3519	1	2	yes	—
437	C₂⁵	#3532	1	2	yes	—
438	C₂⁵	#3532	1	1	yes	characteristic
439	C₂⁵	#3532	1	1	yes	characteristic
440	C₂⁵	#3532	1	2	yes	—
441	C₂⁵	#3532	1	2	yes	—
442	C₂⁵	#3532	1	2	yes	—
443	C₂⁵	#3532	1	2	yes	—
444	C₂⁵	#3532	1	1	yes	characteristic
445	C₂⁵	#3532	1	2	yes	—
446	C₂⁵	#3532	1	1	yes	characteristic
447	C₂⁵	#3534	1	2	yes	—
448	C₂⁵	#3534	1	1	yes	characteristic
449	C₂⁵	#3534	1	2	yes	—
450	C₂⁵	#3534	1	2	yes	—
451	C₂⁵	#3534	1	2	yes	—
452	C₂⁵	#3537	1	1	yes	characteristic
453	C₂⁵	#3537	1	2	yes	—
454	C₂⁵	#3542	1	2	yes	—
455	C₂⁵	#3542	1	2	yes	—
456	C₂⁵	#3542	1	2	yes	—
457	C₂⁵	#3543	1	2	yes	—
458	C₂⁵	#3543	1	2	yes	—
459	C₂⁵	#3543	1	2	yes	—
460	C₂⁵	#3549	1	1	yes	characteristic
461	C₂⁵	#3558	1	2	yes	—
462	C₂⁵	#3558	1	2	yes	—
463	C₂³×C₄	#2403	1	4	yes	—
464	C₂³×C₄	#2403	1	4	yes	—
465	C₂³×C₄	#2404	1	8	yes	—
466	C₂⁴	#23996	1	16	yes	complemented
467	C₂⁴	C₂×#2403	1	2	yes	—
468	C₂⁴	#34655	1	1	yes	characteristic
469	C₂⁴	C₂×#2404	1	2	yes	—
470	C₂⁴	#35346	1	2	yes	—
471	C₂⁴	#35346	1	1	yes	characteristic
472	C₂⁴	#35352	1	2	yes	—
473	C₂⁴	#35680	1	2	yes	—
474	C₂⁴	#35692	1	2	yes	—
475	C₂⁴	#35750	1	1	yes	characteristic
476	C₂⁴	D₄×#120	1	2	yes	—
477	C₂⁴	D₄×#120	1	2	yes	—
478	C₂⁴	#36096	1	2	yes	—
479	C₂⁴	#36098	1	2	yes	—
480	C₂⁴	#36098	1	2	yes	—
481	C₂⁴	#36152	1	1	yes	characteristic
482	C₂⁴	#36152	1	2	yes	—
483	C₂⁴	#36212	1	2	yes	—
484	C₂⁴	#37644	1	2	yes	—
485	C₂⁴	#37644	1	2	yes	—
486	C₂⁴	#37645	1	2	yes	—
487	C₂⁴	#37645	1	2	yes	—
488	C₂⁴	#37650	1	2	yes	—
489	C₂⁴	#37674	1	2	yes	—
490	C₂⁴	#37744	1	2	yes	—
491	C₂⁴	#37744	1	1	yes	characteristic
492	C₂⁴	#37776	1	2	yes	—
493	C₂⁴	#37832	1	2	yes	—
494	C₂⁴	#37832	1	2	yes	—
495	C₂⁴	#38076	1	2	yes	—
496	C₂⁴	#38358	1	2	yes	—
497	C₂⁴	#40585	1	2	yes	—
498	C₂⁴	#40588	1	2	yes	—
499	C₂⁴	#40912	1	1	yes	characteristic
500	C₂⁴	#42997	1	2	yes	—
501	C₂⁴	#42997	1	2	yes	—
502	C₂⁴	#43000	1	1	yes	characteristic
503	C₂⁴	#43023	1	2	yes	—
504	C₂⁴	#43095	1	2	yes	—
505	C₂⁴	#43095	1	2	yes	—
506	C₂⁴	#43095	1	2	yes	—
507	C₂⁴	#43098	1	1	yes	characteristic
508	C₂⁴	#43098	1	2	yes	—
509	C₂⁴	#43118	1	2	yes	—
510	C₂⁴	#43118	1	2	yes	—
511	C₂⁴	#43886	1	2	yes	—
512	C₂⁴	#43889	1	2	yes	—
513	C₂⁴	#44241	1	1	yes	characteristic
514	C₂⁴	#44870	1	1	yes	characteristic
515	C₂⁴	#44877	1	2	yes	—
516	C₂⁴	#44936	1	2	yes	—
517	C₂⁴	#46351	1	2	yes	—
518	C₂⁴	#46354	1	1	yes	characteristic
519	C₂⁴	#46355	1	2	yes	—
520	C₂⁴	#46996	1	1	yes	characteristic
521	C₂⁴	#47042	1	2	yes	—
522	C₂⁴	#47794	1	2	yes	—
523	C₂⁴	#47826	1	2	yes	—
524	C₂⁴	#47830	1	2	yes	—
525	C₂⁴	#47831	1	1	yes	characteristic
526	C₂⁴	#47878	1	2	yes	—
527	C₂⁴	#48088	1	2	yes	—
528	C₂⁴	#48555	1	2	yes	—
529	C₂⁴	#49545	1	2	yes	—
530	C₂⁴	#51889	1	2	yes	—
531	C₂⁴	#51889	1	2	yes	—
532	C₂⁴	#52004	1	1	yes	characteristic
533	C₂⁴	#52004	1	2	yes	—
534	C₂⁴	#56344	1	1	yes	characteristic
535	C₂⁴	#57958	1	2	yes	—
536	C₂⁴	#57974	1	2	yes	—
537	C₂⁴	#58990	1	1	yes	characteristic
538	C₂⁴	#58990	1	2	yes	—
539	C₂⁴	#58990	1	1	yes	characteristic
540	C₂⁴	#58991	1	1	yes	characteristic
541	C₂⁴	#58991	1	2	yes	—
542	C₂⁴	#58991	1	2	yes	—
543	C₂⁴	#58991	1	2	yes	—
544	C₂⁴	#58991	1	2	yes	—
545	C₂⁴	#58994	1	2	yes	—
546	C₂⁴	#59004	1	2	yes	—
547	C₂⁴	#59029	1	2	yes	—
548	C₂⁴	#59041	1	1	yes	characteristic
549	C₂⁴	#59089	1	2	yes	—
550	C₂⁴	#59095	1	2	yes	—
551	C₂⁴	#59123	1	2	yes	—
552	C₂⁴	#59123	1	2	yes	—
553	C₂⁴	#59808	1	2	yes	—
554	C₂³	#647656	1	1	yes	characteristic
555	C₂³	#647657	1	2	yes	—
556	C₂³	#647938	1	2	yes	—
557	C₂³	#772779	1	2	yes	—
558	C₂³	#773018	1	1	yes	characteristic
559	C₂³	#777314	1	2	yes	—
560	C₂³	#1082743	1	2	yes	—
561	C₂³	#1082853	1	2	yes	—
562	C₂³	#1083750	1	1	yes	characteristic
563	C₂³	#1418391	1	2	yes	—
564	C₂³	#1418501	1	2	yes	—
565	C₂³	#1419371	1	1	yes	characteristic
566	C₂³	#2108778	1	2	yes	—
567	C₂³	#2109240	1	1	yes	characteristic
568	C₂³	#2109298	1	2	yes	—
569	C₂³	#3860058	1	2	yes	—
570	C₂³	#3860124	1	2	yes	—
571	C₂³	#4029469	1	1	yes	characteristic
572	C₂³	#4122215	1	1	yes	characteristic
573	C₂³	C₂×#23996	1	8	yes	—
574	C₂²	#72225620	1	4	yes	—
575	C₂²	#72225630	1	4	yes	—
576	C₂²	#72225632	1	4	yes	—
577	C₂²	#72237791	1	2	yes	—
578	C₂²	#72264978	1	1	yes	characteristic
579	C₂	#72265830	1	2	yes	—
580	C₂	#72265893	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72264978
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. #72266118	C₂	semidirect
2. #72266117	C₂	semidirect
3. #72266116	C₂	semidirect
4. #72266115	C₂	semidirect
5. #72266114	C₂	semidirect
6. #72266113	C₂	semidirect
7. #72266112	C₂	semidirect
8. #72266111	C₂²	semidirect
9. #72266110	C₂	semidirect
10. #72266109	C₂²	semidirect
11. #72266102	C₂	semidirect
12. #72266101	C₂²	semidirect
13. #72266100	C₂²	semidirect
14. #72266096	C₂	semidirect
15. #72266095	C₂²	semidirect
16. #72266094	C₂	semidirect
17. #72266084	C₂	semidirect
18. #72266083	C₂²	semidirect
19. #72266082	C₂²	semidirect
20. #72266081	C₂²	semidirect
21. #72266080	C₂	semidirect
22. #72266079	C₂²	semidirect
23. #72266079	C₂²	semidirect
24. #72266079	C₂²	semidirect
25. #72266079	C₂²	semidirect
26. #72266078	C₂	semidirect
27. #72266077	C₂²	semidirect
28. #72266076	C₂²	semidirect
29. #72266075	C₂²	semidirect
30. #72266074	C₂²	semidirect
31. #72266073	C₂²	semidirect
32. #72266073	C₂²	semidirect
33. #72266073	C₂²	semidirect
34. #72266073	C₂²	semidirect
35. #72266067	C₂	semidirect
36. #72266066	C₂²	semidirect
37. #72266065	C₂²	semidirect
38. #72266065	C₂²	semidirect
39. #72266039	C₂	semidirect
40. #72266035	C₂²	semidirect
41. #72266035	C₂²	semidirect
42. #72266035	C₂²	semidirect
43. #72266029	C₂²	semidirect
44. #72266028	C₂²	semidirect
45. #72266028	C₂²	semidirect
46. #72266028	C₂²	semidirect
47. #72266028	C₂²	semidirect
48. #72266028	C₂²	semidirect
49. #72266020	C₂	semidirect
50. #72266012	C₂²	semidirect
51. #72266012	C₂²	semidirect
52. #72266006	C₂	semidirect
53. #72266005	C₂²	semidirect
54. C₂×#201687	C₂²	semidirect
55. #72259008	C₂²	semidirect
56. #72259008	C₂²	semidirect
59. #72258613	C₂²	semidirect
60. #72258613	C₂²	semidirect
61. #72258613	C₂²	semidirect
62. C₂²×#245225	C₂	semidirect
68. #72241143	C₂²	semidirect
71. #72240619	C₂²	semidirect
72. #72240619	C₂²	semidirect
73. #72240619	C₂²	semidirect
74. #72240617	C₂²	semidirect
75. #72240568	C₂²	semidirect
76. C₂×#6370693	C₂²	semidirect
79. #72238531	C₂²	semidirect
80. #72238031	C₂²	semidirect
81. C₂×#233541	C₂²	semidirect
82. C₂×#233541	C₂²	semidirect
83. C₂×#233541	C₂²	semidirect
84. C₂×#201664	C₂²	semidirect
85. #72234689	C₂²	semidirect
86. #72234668	C₂²	semidirect
87. #72234668	C₂²	semidirect
88. #72234668	C₂²	semidirect
91. #72234629	C₂²	semidirect
92. C₂×#6628892	C₂²	semidirect
94. #72225801	C₂²	semidirect
95. #72225796	C₂²	semidirect
96. #72225796	C₂²	semidirect
97. #72225796	C₂²	semidirect
98. #72225796	C₂²	semidirect
99. #72225791	C₂²	semidirect
100. #72225783	C₂²	semidirect
125. C₂×#32898	D₄	semidirect
126. C₂×#32898	D₄	semidirect
163. #405104	D₄	semidirect
164. #393929	D₄	semidirect
165. #359695	D₄	semidirect
166. #359428	D₄	semidirect
186. C₂×#10336	D₄	semidirect
201. C₂⁸	#41	semidirect
210. C₂³×#120	#41	semidirect
212. C₂⁴×C₂²⋊C₄	#41	semidirect
213. C₂⁴×C₂²⋊C₄	#41	semidirect
214. C₂×#2405	C₂×D₄	semidirect
222. C₂×#2403	C₂×D₄	semidirect
225. C₂²×#386	#41	semidirect
226. C₂×#2280	C₂×D₄	semidirect
227. C₂²×#379	C₂×D₄	semidirect
242. C₂×#1819	C₂×D₄	semidirect
252. C₂×#1781	C₂×D₄	semidirect
253. #14681	C₂×D₄	semidirect
254. #14679	C₂×D₄	semidirect
255. #13867	C₂×D₄	semidirect
256. #10725	C₂×D₄	semidirect
257. #10725	C₂×D₄	semidirect
258. #10725	C₂×D₄	semidirect
295. #2403	#120	semidirect
296. #2403	#120	semidirect
297. #2403	#120	semidirect
466. C₂⁴	#23996	semidirect

Maximal subgroups

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

subgroup	index
#72266118	2
#72266117	2
#72266116	2
#72266115	2
#72266114	2
#72266113	2
#72266112	2
#72266110	2
#72266102	2
#72266096	2
#72266094	2
#72266084	2
#72266080	2
#72266078	2
#72266067	2
#72266039	2
#72266020	2
#72266006	2
C₂²×#245225	2