Subgroups — #72263561

Order 2048.

At least 10378 conjugacy classes of subgroups; only the 728 normal subgroups are shown.

The subgroup lattice has 613 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263547	C₂	1	1	yes	maximal, characteristic
2	#72238031	C₂	1	1	yes	maximal, characteristic, complemented
3	#72236717	C₂	1	1	yes	maximal, characteristic, complemented
4	#72236704	C₂	1	1	yes	maximal, characteristic, complemented
5	#72236670	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#496225	C₂	1	1	yes	maximal, characteristic, complemented
7	#72236530	C₂	1	4	yes	maximal, complemented
8	C₂×#201664	C₂	1	1	yes	maximal, characteristic, complemented
9	#72213274	C₂	1	4	yes	maximal, complemented
10	C₂×#35222	C₂²	1	1	yes	characteristic
11	C₂²×#2403	C₂²	1	1	yes	characteristic
12	C₂×#34171	C₂²	1	1	yes	characteristic
13	C₂²×#1783	C₂²	1	1	yes	characteristic
14	C₂²×#1781	C₂²	1	1	yes	characteristic
15	C₂²×#1781	C₂²	1	1	yes	characteristic
16	#4866529	C₄	1	2	yes	complemented
17	#4866528	C₄	1	2	yes	complemented
18	#4327960	C₂²	1	2	yes	—
19	#4312024	C₂²	1	2	yes	—
20	#846393	C₄	1	1	yes	characteristic, complemented
21	#846389	C₄	1	1	yes	characteristic, complemented
22	#846061	C₄	1	1	yes	characteristic, complemented
23	#846057	C₄	1	1	yes	characteristic, complemented
24	#517411	C₂²	1	1	yes	characteristic
25	#496225	C₂²	1	4	yes	—
26	#493883	C₂²	1	2	yes	complemented
27	#493370	C₂²	1	2	yes	complemented
28	#359869	C₂²	1	2	yes	complemented
29	#359509	C₂²	1	2	yes	complemented
30	#201664	C₂²	1	4	yes	—
31	#128073	C₂²	1	4	yes	complemented
32	#106766	C₂²	1	4	yes	complemented
33	C₂⁵×D₄	D₄	1	1	yes	characteristic
34	C₂⁵×D₄	C₂³	1	1	yes	characteristic
35	C₂²×#535	D₄	1	1	yes	characteristic
36	C₂²×#535	C₂³	1	1	yes	characteristic
37	C₂²×#525	D₄	1	1	yes	characteristic
38	C₂³×#120	C₂×C₄	1	1	yes	characteristic
39	C₂³×#120	D₄	1	1	yes	characteristic
40	C₂³×#100	D₄	1	2	yes	complemented
41	C₂³×#99	D₄	1	2	yes	complemented
42	C₂×#2435	C₂×C₄	1	1	yes	characteristic
43	C₂×#2435	C₂×C₄	1	1	yes	characteristic
44	C₂×#2435	D₄	1	1	yes	characteristic
45	C₂×#2435	D₄	1	1	yes	characteristic
46	C₂×#2433	C₂×C₄	1	1	yes	characteristic
47	C₂×#2433	C₂×C₄	1	1	yes	characteristic
48	C₂×#2433	D₄	1	1	yes	characteristic
49	C₂×#2433	D₄	1	1	yes	characteristic
50	C₂×#2403	C₂×C₄	1	2	yes	—
51	C₂×#2403	D₄	1	2	yes	—
52	C₂×#2403	D₄	1	2	yes	—
53	C₂×#2403	C₂³	1	2	yes	—
54	#34171	D₄	1	2	yes	complemented
55	#34171	C₂³	1	2	yes	—
56	C₂×#2309	D₄	1	1	yes	characteristic
57	C₂×#2309	D₄	1	2	yes	complemented
58	C₂×#2309	C₂³	1	1	yes	characteristic
59	C₂²×#386	C₂×C₄	1	1	yes	characteristic
60	C₂²×#386	D₄	1	1	yes	characteristic
61	C₂×#2280	D₄	1	1	yes	characteristic
62	C₂²×#379	D₄	1	1	yes	characteristic
63	C₂²×#379	D₄	1	1	yes	characteristic
64	C₂²×#379	D₄	1	1	yes	characteristic
65	C₂×#1783	D₄	1	2	yes	complemented
66	C₂×#1783	C₂³	1	2	yes	—
67	C₂×#1781	D₄	1	2	yes	complemented
68	C₂×#1781	D₄	1	2	yes	complemented
69	C₂×#1781	D₄	1	2	yes	complemented
70	C₂×#1781	C₂³	1	2	yes	—
71	C₂×#1781	C₂³	1	2	yes	—
72	#16074	C₂×C₄	1	2	yes	complemented
73	#15784	C₂×C₄	1	2	yes	complemented
74	#15342	C₂×C₄	1	2	yes	complemented
75	#15313	C₂×C₄	1	2	yes	complemented
76	#15281	C₂×C₄	1	2	yes	complemented
77	#15281	C₂×C₄	1	2	yes	complemented
78	#15259	C₂×C₄	1	2	yes	complemented
79	#15258	C₂×C₄	1	2	yes	complemented
80	#14335	C₂×C₄	1	2	yes	—
81	#14335	D₄	1	2	yes	—
82	#13867	C₂×C₄	1	1	yes	characteristic
83	#13867	C₂×C₄	1	1	yes	characteristic
84	#13867	D₄	1	1	yes	characteristic
85	#13867	D₄	1	1	yes	characteristic
86	#13867	D₄	1	2	yes	—
87	#13867	C₂³	1	2	yes	—
88	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
89	C₂⁷	C₂×D₄	1	1	yes	characteristic
90	C₂⁷	C₂×D₄	1	1	yes	characteristic
91	C₂³×#41	C₂×D₄	1	1	yes	characteristic
92	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
93	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
94	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
95	C₂⁴×D₄	C₂×D₄	1	2	yes	—
96	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
97	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
98	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
99	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
102	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
103	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
104	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
105	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×D₄	#41	1	1	yes	characteristic
114	C₂⁴×D₄	#41	1	1	yes	characteristic
115	C₂⁴×D₄	#41	1	1	yes	characteristic
116	C₂⁴×D₄	#41	1	1	yes	characteristic
117	C₂⁴×D₄	#41	1	1	yes	characteristic
118	C₂⁴×D₄	#41	1	1	yes	characteristic
119	C₂⁴×D₄	#41	1	1	yes	characteristic
120	C₂⁴×D₄	#41	1	1	yes	characteristic
121	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
122	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
123	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
124	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
127	C₂²×#127	C₂×D₄	1	1	yes	characteristic
128	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
131	C₂²×#124	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×#120	C₂²⋊C₄	1	2	yes	—
137	C₂²×#120	C₂²⋊C₄	1	2	yes	—
138	C₂²×#120	C₂²×C₄	1	2	yes	—
139	C₂²×#120	C₂×D₄	1	2	yes	—
140	C₂²×#117	C₂×D₄	1	1	yes	characteristic
141	C₂²×#117	C₂×D₄	1	1	yes	characteristic
142	C₂²×#117	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
148	C₂²×#100	C₂×D₄	1	4	yes	—
149	C₂²×#99	C₂×D₄	1	4	yes	—
150	#2309	C₂×D₄	1	4	yes	—
151	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×#390	C₂²×C₄	1	1	yes	characteristic
156	C₂×#390	C₂²×C₄	1	1	yes	characteristic
157	C₂×#390	C₂×D₄	1	1	yes	characteristic
158	C₂×#390	C₂×D₄	1	1	yes	characteristic
159	C₂×#386	C₂²⋊C₄	1	2	yes	—
160	C₂×#386	C₂²⋊C₄	1	2	yes	—
161	C₂×#386	C₂²×C₄	1	2	yes	—
162	C₂×#386	C₂×D₄	1	2	yes	—
163	C₂×#379	C₂²⋊C₄	1	2	yes	—
164	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×#379	C₂²⋊C₄	1	2	yes	—
167	C₂×#379	C₂²⋊C₄	1	2	yes	—
168	C₂×#379	C₂×D₄	1	2	yes	—
169	C₂×#379	C₂×D₄	1	2	yes	—
170	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
174	#1781	C₂×D₄	1	4	yes	—
175	#1438	C₂²⋊C₄	1	2	yes	—
176	#1438	C₂²⋊C₄	1	2	yes	—
177	#1438	C₂²⋊C₄	1	2	yes	—
178	#1438	C₂²⋊C₄	1	2	yes	—
179	#1438	C₂²×C₄	1	2	yes	—
180	#1438	C₂²×C₄	1	2	yes	—
181	#1438	C₂×D₄	1	2	yes	—
182	#1438	C₂×D₄	1	2	yes	—
183	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂⁶	#120	1	1	yes	characteristic
189	C₂⁶	#120	1	1	yes	characteristic
190	C₂⁶	#120	1	1	yes	characteristic
191	C₂⁶	#120	1	1	yes	characteristic
192	C₂⁶	#120	1	1	yes	characteristic
193	C₂⁶	#120	1	1	yes	characteristic
194	C₂⁶	#120	1	1	yes	characteristic
195	C₂⁶	#120	1	1	yes	characteristic
196	C₂⁶	#120	1	1	yes	characteristic
197	C₂⁶	#121	1	1	yes	characteristic
198	C₂⁶	#121	1	1	yes	characteristic
199	C₂⁶	#121	1	1	yes	characteristic
200	C₂⁶	#121	1	1	yes	characteristic
201	C₂⁶	#121	1	1	yes	characteristic
202	C₂⁶	#121	1	1	yes	characteristic
203	C₂⁶	#121	1	1	yes	characteristic
204	C₂⁶	#121	1	1	yes	characteristic
205	C₂⁶	#123	1	1	yes	characteristic
206	C₂⁶	#123	1	1	yes	characteristic
207	C₂⁶	#124	1	1	yes	characteristic
208	C₂⁶	#124	1	1	yes	characteristic
209	C₂⁶	#127	1	1	yes	characteristic
210	C₂⁶	#127	1	1	yes	characteristic
211	C₂⁶	C₂²×D₄	1	1	yes	characteristic
212	C₂⁶	C₂²×D₄	1	1	yes	characteristic
213	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
222	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
223	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
224	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
225	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
226	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
227	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
228	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
229	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
230	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
231	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
232	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
233	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
234	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
235	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
236	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
237	C₂³×D₄	#120	1	1	yes	characteristic
238	C₂³×D₄	#120	1	1	yes	characteristic
239	C₂³×D₄	#120	1	1	yes	characteristic
240	C₂³×D₄	#120	1	1	yes	characteristic
241	C₂³×D₄	#120	1	1	yes	characteristic
242	C₂³×D₄	#120	1	1	yes	characteristic
243	C₂³×D₄	#120	1	1	yes	characteristic
244	C₂³×D₄	#120	1	1	yes	characteristic
245	C₂³×D₄	#120	1	1	yes	characteristic
246	C₂³×D₄	#120	1	1	yes	characteristic
247	C₂³×D₄	#120	1	1	yes	characteristic
248	C₂³×D₄	#120	1	1	yes	characteristic
249	C₂³×D₄	#120	1	1	yes	characteristic
250	C₂³×D₄	#120	1	1	yes	characteristic
251	C₂³×D₄	#120	1	1	yes	characteristic
252	C₂³×D₄	#120	1	1	yes	characteristic
253	C₂³×D₄	#120	1	1	yes	characteristic
254	C₂³×D₄	#120	1	1	yes	characteristic
255	C₂³×D₄	#121	1	1	yes	characteristic
256	C₂³×D₄	#121	1	1	yes	characteristic
257	C₂³×D₄	#121	1	1	yes	characteristic
258	C₂³×D₄	#121	1	1	yes	characteristic
259	C₂³×D₄	#121	1	1	yes	characteristic
260	C₂³×D₄	#121	1	1	yes	characteristic
261	C₂³×D₄	#121	1	1	yes	characteristic
262	C₂³×D₄	#121	1	1	yes	characteristic
263	C₂³×D₄	#121	1	1	yes	characteristic
264	C₂³×D₄	#121	1	1	yes	characteristic
265	C₂³×D₄	#121	1	1	yes	characteristic
266	C₂³×D₄	#121	1	1	yes	characteristic
267	C₂³×D₄	#121	1	1	yes	characteristic
268	C₂³×D₄	#121	1	1	yes	characteristic
269	C₂³×D₄	#121	1	1	yes	characteristic
270	C₂³×D₄	#121	1	1	yes	characteristic
271	C₂³×D₄	#121	1	1	yes	characteristic
272	C₂³×D₄	#121	1	1	yes	characteristic
273	C₂³×D₄	#121	1	1	yes	characteristic
274	C₂³×D₄	#121	1	1	yes	characteristic
275	C₂³×D₄	#121	1	1	yes	characteristic
276	C₂³×D₄	#121	1	1	yes	characteristic
277	C₂³×D₄	#121	1	1	yes	characteristic
278	C₂³×D₄	#121	1	1	yes	characteristic
279	C₂³×D₄	#121	1	1	yes	characteristic
280	C₂³×D₄	#121	1	1	yes	characteristic
281	C₂³×D₄	#121	1	1	yes	characteristic
282	C₂³×D₄	#121	1	1	yes	characteristic
283	C₂³×D₄	#121	1	1	yes	characteristic
284	C₂³×D₄	#121	1	1	yes	characteristic
285	C₂³×D₄	#121	1	1	yes	characteristic
286	C₂³×D₄	#121	1	1	yes	characteristic
287	C₂³×D₄	#121	1	1	yes	characteristic
288	C₂³×D₄	#121	1	1	yes	characteristic
289	C₂³×D₄	#121	1	1	yes	characteristic
290	C₂³×D₄	#121	1	1	yes	characteristic
291	C₂³×D₄	#123	1	1	yes	characteristic
292	C₂³×D₄	#123	1	1	yes	characteristic
293	C₂³×D₄	#123	1	1	yes	characteristic
294	C₂³×D₄	#123	1	1	yes	characteristic
295	C₂³×D₄	#123	1	1	yes	characteristic
296	C₂³×D₄	#123	1	1	yes	characteristic
297	C₂³×D₄	#123	1	1	yes	characteristic
298	C₂³×D₄	#123	1	1	yes	characteristic
299	C₂³×D₄	#123	1	1	yes	characteristic
300	C₂³×D₄	#123	1	1	yes	characteristic
301	C₂³×D₄	#123	1	1	yes	characteristic
302	C₂³×D₄	#123	1	1	yes	characteristic
303	C₂³×D₄	#124	1	1	yes	characteristic
304	C₂³×D₄	#124	1	1	yes	characteristic
305	C₂³×D₄	#124	1	1	yes	characteristic
306	C₂³×D₄	#124	1	1	yes	characteristic
307	C₂³×D₄	#124	1	1	yes	characteristic
308	C₂³×D₄	#124	1	1	yes	characteristic
309	C₂³×D₄	#127	1	1	yes	characteristic
310	C₂³×D₄	#127	1	1	yes	characteristic
311	C₂³×D₄	#127	1	1	yes	characteristic
312	C₂³×D₄	#127	1	1	yes	characteristic
313	C₂³×D₄	#127	1	1	yes	characteristic
314	C₂³×D₄	#127	1	1	yes	characteristic
315	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
316	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
317	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
318	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
319	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
320	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
321	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
322	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
323	C₂³×D₄	C₂×#41	1	1	yes	characteristic
324	C₂³×D₄	C₂×#41	1	1	yes	characteristic
325	C₂³×D₄	C₂×#41	1	1	yes	characteristic
326	C₂³×D₄	C₂×#41	1	1	yes	characteristic
327	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
329	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
330	C₂⁴×C₄	#120	1	1	yes	characteristic
331	C₂⁴×C₄	#120	1	1	yes	characteristic
332	C₂⁴×C₄	#120	1	1	yes	characteristic
333	C₂⁴×C₄	#120	1	1	yes	characteristic
334	C₂⁴×C₄	#120	1	1	yes	characteristic
335	C₂⁴×C₄	#121	1	1	yes	characteristic
336	C₂⁴×C₄	#121	1	1	yes	characteristic
337	C₂⁴×C₄	#121	1	1	yes	characteristic
338	C₂⁴×C₄	#121	1	1	yes	characteristic
339	C₂⁴×C₄	#123	1	1	yes	characteristic
340	C₂⁴×C₄	#123	1	1	yes	characteristic
341	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
345	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
346	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
347	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
348	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
349	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
351	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
352	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
353	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
354	C₂⁵	#379	1	1	yes	characteristic
355	C₂⁵	#379	1	1	yes	characteristic
356	C₂⁵	#379	1	1	yes	characteristic
357	C₂⁵	#379	1	1	yes	characteristic
358	C₂⁵	#379	1	1	yes	characteristic
359	C₂⁵	#379	1	1	yes	characteristic
360	C₂⁵	#386	1	1	yes	characteristic
361	C₂⁵	#386	1	1	yes	characteristic
362	C₂⁵	#386	1	1	yes	characteristic
363	C₂⁵	#386	1	1	yes	characteristic
364	C₂⁵	#386	1	1	yes	characteristic
365	C₂⁵	#386	1	1	yes	characteristic
366	C₂⁵	#386	1	1	yes	characteristic
367	C₂⁵	#386	1	1	yes	characteristic
368	C₂⁵	#390	1	1	yes	characteristic
369	C₂⁵	#390	1	1	yes	characteristic
370	C₂⁵	#390	1	1	yes	characteristic
371	C₂⁵	#390	1	1	yes	characteristic
372	C₂⁵	#390	1	1	yes	characteristic
373	C₂⁵	#390	1	1	yes	characteristic
374	C₂⁵	#390	1	1	yes	characteristic
375	C₂⁵	#390	1	1	yes	characteristic
376	C₂⁵	#392	1	1	yes	characteristic
377	C₂⁵	#392	1	1	yes	characteristic
378	C₂⁵	#392	1	1	yes	characteristic
379	C₂⁵	#392	1	1	yes	characteristic
380	C₂⁵	#392	1	1	yes	characteristic
381	C₂⁵	#392	1	1	yes	characteristic
382	C₂⁵	#392	1	1	yes	characteristic
383	C₂⁵	#392	1	1	yes	characteristic
384	C₂⁵	#392	1	1	yes	characteristic
385	C₂⁵	#392	1	1	yes	characteristic
386	C₂⁵	#392	1	1	yes	characteristic
387	C₂⁵	#392	1	1	yes	characteristic
388	C₂⁵	#392	1	1	yes	characteristic
389	C₂⁵	#392	1	1	yes	characteristic
390	C₂⁵	#394	1	1	yes	characteristic
391	C₂⁵	#394	1	1	yes	characteristic
392	C₂⁵	#394	1	1	yes	characteristic
393	C₂⁵	#394	1	1	yes	characteristic
394	C₂⁵	#394	1	1	yes	characteristic
395	C₂⁵	#394	1	1	yes	characteristic
396	C₂⁵	#394	1	1	yes	characteristic
397	C₂⁵	#394	1	1	yes	characteristic
398	C₂⁵	#394	1	1	yes	characteristic
399	C₂⁵	#394	1	1	yes	characteristic
400	C₂⁵	#394	1	1	yes	characteristic
401	C₂⁵	#394	1	1	yes	characteristic
402	C₂⁵	#394	1	1	yes	characteristic
403	C₂⁵	#394	1	1	yes	characteristic
404	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
405	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
406	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
407	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
408	C₂⁵	#458	1	1	yes	characteristic
409	C₂⁵	#458	1	1	yes	characteristic
410	C₂⁵	#458	1	1	yes	characteristic
411	C₂⁵	#458	1	1	yes	characteristic
412	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
413	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
414	C₂⁵	C₂×#120	1	1	yes	characteristic
415	C₂⁵	C₂×#120	1	1	yes	characteristic
416	C₂⁵	C₂×#120	1	1	yes	characteristic
417	C₂⁵	C₂×#120	1	1	yes	characteristic
418	C₂⁵	C₂×#121	1	1	yes	characteristic
419	C₂⁵	C₂×#121	1	1	yes	characteristic
420	C₂⁵	C₂×#121	1	1	yes	characteristic
421	C₂⁵	C₂×#121	1	1	yes	characteristic
422	C₂⁵	C₂×#123	1	1	yes	characteristic
423	C₂⁵	C₂×#124	1	1	yes	characteristic
424	C₂⁵	C₂×#127	1	1	yes	characteristic
425	C₂²×D₄	#386	1	1	yes	characteristic
426	C₂²×D₄	#386	1	1	yes	characteristic
427	C₂²×D₄	#386	1	1	yes	characteristic
428	C₂²×D₄	#386	1	1	yes	characteristic
429	C₂²×D₄	#386	1	1	yes	characteristic
430	C₂²×D₄	#386	1	1	yes	characteristic
431	C₂²×D₄	#386	1	1	yes	characteristic
432	C₂²×D₄	#386	1	1	yes	characteristic
433	C₂²×D₄	#386	1	1	yes	characteristic
434	C₂²×D₄	#386	1	1	yes	characteristic
435	C₂²×D₄	#386	1	1	yes	characteristic
436	C₂²×D₄	#386	1	1	yes	characteristic
437	C₂²×D₄	#386	1	1	yes	characteristic
438	C₂²×D₄	#386	1	1	yes	characteristic
439	C₂²×D₄	#386	1	1	yes	characteristic
440	C₂²×D₄	#386	1	1	yes	characteristic
441	C₂²×D₄	#390	1	1	yes	characteristic
442	C₂²×D₄	#390	1	1	yes	characteristic
443	C₂²×D₄	#390	1	1	yes	characteristic
444	C₂²×D₄	#390	1	1	yes	characteristic
445	C₂²×D₄	#390	1	1	yes	characteristic
446	C₂²×D₄	#390	1	1	yes	characteristic
447	C₂²×D₄	#390	1	1	yes	characteristic
448	C₂²×D₄	#390	1	1	yes	characteristic
449	C₂²×D₄	#392	1	1	yes	characteristic
450	C₂²×D₄	#392	1	1	yes	characteristic
451	C₂²×D₄	#392	1	1	yes	characteristic
452	C₂²×D₄	#392	1	1	yes	characteristic
453	C₂²×D₄	#392	1	1	yes	characteristic
454	C₂²×D₄	#392	1	1	yes	characteristic
455	C₂²×D₄	#392	1	1	yes	characteristic
456	C₂²×D₄	#392	1	1	yes	characteristic
457	C₂²×D₄	#392	1	1	yes	characteristic
458	C₂²×D₄	#392	1	1	yes	characteristic
459	C₂²×D₄	#392	1	1	yes	characteristic
460	C₂²×D₄	#392	1	1	yes	characteristic
461	C₂²×D₄	#394	1	1	yes	characteristic
462	C₂²×D₄	#394	1	1	yes	characteristic
463	C₂²×D₄	#394	1	1	yes	characteristic
464	C₂²×D₄	#394	1	1	yes	characteristic
465	C₂²×D₄	#394	1	1	yes	characteristic
466	C₂²×D₄	#394	1	1	yes	characteristic
467	C₂²×D₄	#394	1	1	yes	characteristic
468	C₂²×D₄	#394	1	1	yes	characteristic
469	C₂²×D₄	#394	1	1	yes	characteristic
470	C₂²×D₄	#394	1	1	yes	characteristic
471	C₂²×D₄	#394	1	1	yes	characteristic
472	C₂²×D₄	#394	1	1	yes	characteristic
473	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
474	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
475	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
476	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
477	C₂²×D₄	C₂×#120	1	1	yes	characteristic
478	C₂²×D₄	C₂×#120	1	1	yes	characteristic
479	C₂²×D₄	C₂×#121	1	1	yes	characteristic
480	C₂²×D₄	C₂×#121	1	1	yes	characteristic
481	C₂²×D₄	C₂×#121	1	1	yes	characteristic
482	C₂²×D₄	C₂×#121	1	1	yes	characteristic
483	C₂²×D₄	C₂×#121	1	1	yes	characteristic
484	C₂²×D₄	C₂×#121	1	1	yes	characteristic
485	C₂²×D₄	C₂×#123	1	1	yes	characteristic
486	C₂²×D₄	C₂×#123	1	1	yes	characteristic
487	C₂²×D₄	C₂×#124	1	1	yes	characteristic
488	C₂²×D₄	C₂×#127	1	1	yes	characteristic
489	C₂³×C₄	#379	1	1	yes	characteristic
490	C₂³×C₄	#379	1	1	yes	characteristic
491	C₂³×C₄	#386	1	1	yes	characteristic
492	C₂³×C₄	#386	1	1	yes	characteristic
493	C₂³×C₄	#386	1	1	yes	characteristic
494	C₂³×C₄	#386	1	1	yes	characteristic
495	C₂³×C₄	#386	1	1	yes	characteristic
496	C₂³×C₄	#386	1	1	yes	characteristic
497	C₂³×C₄	#386	1	1	yes	characteristic
498	C₂³×C₄	#386	1	1	yes	characteristic
499	C₂³×C₄	#392	1	1	yes	characteristic
500	C₂³×C₄	#392	1	1	yes	characteristic
501	C₂³×C₄	#392	1	1	yes	characteristic
502	C₂³×C₄	#392	1	1	yes	characteristic
503	C₂³×C₄	#392	1	1	yes	characteristic
504	C₂³×C₄	#392	1	1	yes	characteristic
505	C₂³×C₄	#394	1	1	yes	characteristic
506	C₂³×C₄	#394	1	1	yes	characteristic
507	C₂³×C₄	#394	1	1	yes	characteristic
508	C₂³×C₄	#394	1	1	yes	characteristic
509	C₂³×C₄	#394	1	1	yes	characteristic
510	C₂³×C₄	#394	1	1	yes	characteristic
511	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
512	C₂³×C₄	C₂×#120	1	1	yes	characteristic
513	C₂³×C₄	C₂×#120	1	1	yes	characteristic
514	C₂³×C₄	C₂×#121	1	1	yes	characteristic
515	C₂³×C₄	C₂×#121	1	1	yes	characteristic
516	C₂³×C₄	C₂×#123	1	1	yes	characteristic
517	C₂⁴	#1438	1	1	yes	characteristic
518	C₂⁴	#1438	1	1	yes	characteristic
519	C₂⁴	#1438	1	1	yes	characteristic
520	C₂⁴	#1438	1	1	yes	characteristic
521	C₂⁴	#1438	1	1	yes	characteristic
522	C₂⁴	#1438	1	1	yes	characteristic
523	C₂⁴	#1438	1	1	yes	characteristic
524	C₂⁴	#1438	1	1	yes	characteristic
525	C₂⁴	#1438	1	1	yes	characteristic
526	C₂⁴	#1438	1	1	yes	characteristic
527	C₂⁴	#1438	1	1	yes	characteristic
528	C₂⁴	#1438	1	1	yes	characteristic
529	C₂⁴	#1790	1	1	yes	characteristic
530	C₂⁴	#1790	1	1	yes	characteristic
531	C₂⁴	#1790	1	1	yes	characteristic
532	C₂⁴	#1790	1	1	yes	characteristic
533	C₂⁴	#1790	1	1	yes	characteristic
534	C₂⁴	#1790	1	1	yes	characteristic
535	C₂⁴	#1790	1	1	yes	characteristic
536	C₂⁴	#1790	1	1	yes	characteristic
537	C₂⁴	#2021	1	1	yes	characteristic
538	C₂⁴	#2021	1	1	yes	characteristic
539	C₂⁴	#2021	1	1	yes	characteristic
540	C₂⁴	#2021	1	1	yes	characteristic
541	C₂⁴	#2022	1	1	yes	characteristic
542	C₂⁴	#2022	1	1	yes	characteristic
543	C₂⁴	#2022	1	1	yes	characteristic
544	C₂⁴	#2022	1	1	yes	characteristic
545	C₂⁴	#2044	1	1	yes	characteristic
546	C₂⁴	#2044	1	1	yes	characteristic
547	C₂⁴	#2044	1	1	yes	characteristic
548	C₂⁴	#2044	1	1	yes	characteristic
549	C₂⁴	#2044	1	1	yes	characteristic
550	C₂⁴	#2044	1	1	yes	characteristic
551	C₂⁴	#2044	1	1	yes	characteristic
552	C₂⁴	#2044	1	1	yes	characteristic
553	C₂⁴	C₂×#379	1	1	yes	characteristic
554	C₂⁴	C₂×#386	1	1	yes	characteristic
555	C₂⁴	C₂×#386	1	1	yes	characteristic
556	C₂⁴	C₂×#390	1	1	yes	characteristic
557	C₂⁴	C₂×#390	1	1	yes	characteristic
558	C₂⁴	C₂×#392	1	1	yes	characteristic
559	C₂⁴	C₂×#392	1	1	yes	characteristic
560	C₂⁴	C₂×#392	1	1	yes	characteristic
561	C₂⁴	C₂×#394	1	1	yes	characteristic
562	C₂⁴	C₂×#394	1	1	yes	characteristic
563	C₂⁴	C₂×#394	1	1	yes	characteristic
564	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
565	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
566	C₂⁴	C₂×#458	1	1	yes	characteristic
567	C₂⁴	C₂×#458	1	1	yes	characteristic
568	C₂×D₄	#1913	1	4	yes	—
569	C₂×D₄	#3026	1	4	yes	—
570	C₂²×C₄	#1438	1	1	yes	characteristic
571	C₂²×C₄	#1438	1	1	yes	characteristic
572	C₂²×C₄	#1438	1	1	yes	characteristic
573	C₂²×C₄	#1438	1	1	yes	characteristic
574	C₂²×C₄	C₂×#386	1	1	yes	characteristic
575	C₂²×C₄	C₂×#386	1	1	yes	characteristic
576	C₂²×C₄	C₂×#392	1	1	yes	characteristic
577	C₂²×C₄	C₂×#394	1	1	yes	characteristic
578	C₂³	#10972	1	2	yes	—
579	C₂³	#10972	1	2	yes	—
580	C₂³	#10995	1	1	yes	characteristic
581	C₂³	#10995	1	1	yes	characteristic
582	C₂³	#10995	1	1	yes	characteristic
583	C₂³	#10995	1	1	yes	characteristic
584	C₂³	#10995	1	1	yes	characteristic
585	C₂³	#10995	1	1	yes	characteristic
586	C₂³	#10995	1	1	yes	characteristic
587	C₂³	#10995	1	1	yes	characteristic
588	C₂³	#12753	1	2	yes	—
589	C₂³	#12753	1	2	yes	—
590	C₂³	C₂×#1438	1	1	yes	characteristic
591	C₂³	C₂×#1790	1	1	yes	characteristic
592	C₂³	C₂×#1790	1	1	yes	characteristic
593	C₂³	#20960	1	2	yes	—
594	C₂³	C₂×#2021	1	1	yes	characteristic
595	C₂³	C₂×#2022	1	1	yes	characteristic
596	C₂³	#23444	1	2	yes	—
597	C₂³	C₂×#2044	1	1	yes	characteristic
598	C₂³	C₂×#2044	1	1	yes	characteristic
599	C₂×C₄	C₂×#1913	1	2	yes	—
600	C₂×C₄	#23444	1	2	yes	—
601	C₂²	#147811	1	2	yes	—
602	C₂²	#147811	1	2	yes	—
603	C₂²	C₂×#10972	1	1	yes	characteristic
604	C₂²	C₂×#10995	1	1	yes	characteristic
605	C₂²	#357530	1	1	yes	characteristic
606	C₂²	C₂×#12753	1	1	yes	characteristic
607	C₂²	C₂×#12753	1	1	yes	characteristic
608	C₂²	#493562	1	2	yes	—
609	C₂	C₂×#147811	1	1	yes	characteristic
610	C₂	#72236453	1	1	yes	characteristic
611	C₂	#72256609	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#10995
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72263547	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #72238031	C₂	semidirect
3. #72236717	C₂	semidirect
4. #72236704	C₂	semidirect
5. #72236670	C₂	semidirect
6. C₂×#496225	C₂	semidirect
7. #72236530	C₂	semidirect
8. C₂×#201664	C₂	semidirect
9. #72213274	C₂	semidirect
16. #4866529	C₄	semidirect
17. #4866528	C₄	semidirect
20. #846393	C₄	semidirect
21. #846389	C₄	semidirect
22. #846061	C₄	semidirect
23. #846057	C₄	semidirect
26. #493883	C₂²	semidirect
27. #493370	C₂²	semidirect
28. #359869	C₂²	semidirect
29. #359509	C₂²	semidirect
31. #128073	C₂²	semidirect
32. #106766	C₂²	semidirect
40. C₂³×#100	D₄	semidirect
41. C₂³×#99	D₄	semidirect
54. #34171	D₄	semidirect
57. C₂×#2309	D₄	semidirect
65. C₂×#1783	D₄	semidirect
67. C₂×#1781	D₄	semidirect
68. C₂×#1781	D₄	semidirect
69. C₂×#1781	D₄	semidirect
72. #16074	C₂×C₄	semidirect
73. #15784	C₂×C₄	semidirect
74. #15342	C₂×C₄	semidirect
75. #15313	C₂×C₄	semidirect
76. #15281	C₂×C₄	semidirect
77. #15281	C₂×C₄	semidirect
78. #15259	C₂×C₄	semidirect
79. #15258	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72263547	2
#72238031	2
#72236717	2
#72236704	2
#72236670	2
C₂×#496225	2
#72236530	2
C₂×#201664	2
#72213274	2