Subgroups — #72263347

Order 2048.

At least 9859 conjugacy classes of subgroups; only the 614 normal subgroups are shown.

The subgroup lattice has 407 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263346	C₂	1	1	yes	maximal, characteristic, complemented
2	#72263345	C₂	1	2	yes	maximal, complemented
3	#72263344	C₂	1	2	yes	maximal, complemented
4	#72263343	C₂	1	2	yes	maximal, complemented
5	#72263342	C₂	1	2	yes	maximal, complemented
6	#72263155	C₂	1	1	yes	maximal, characteristic, complemented
7	#72263141	C₂	1	2	yes	maximal, complemented
8	#72262844	C₂	1	2	yes	maximal, complemented
9	#72256396	C₂	1	2	yes	maximal, complemented
10	#72234607	C₂	1	1	yes	maximal, characteristic, complemented
11	#72234143	C₂	1	2	yes	maximal, complemented
12	#72234108	C₂	1	2	yes	maximal, complemented
13	#72233177	C₂	1	2	yes	maximal, complemented
14	#72233165	C₂	1	2	yes	maximal, complemented
15	#72232866	C₂	1	1	yes	maximal, characteristic, complemented
16	#72232757	C₂	1	1	yes	maximal, characteristic, complemented
17	#72226358	C₂	1	1	yes	maximal, characteristic, complemented
18	#72216323	C₂	1	1	yes	maximal, characteristic, complemented
19	#72210587	C₂	1	2	yes	maximal, complemented
20	#10586472	C₂²	1	1	yes	characteristic, complemented
21	#6512701	C₂²	1	2	yes	complemented
22	#6499870	C₂²	1	2	yes	complemented
23	#6499867	C₂²	1	2	yes	—
24	#5486599	C₂²	1	1	yes	characteristic, complemented
25	#5486291	C₂²	1	1	yes	characteristic, complemented
26	#5236713	C₂²	1	1	yes	characteristic, complemented
27	#5064005	C₂²	1	1	yes	characteristic, complemented
28	#4607318	C₂²	1	1	yes	characteristic, complemented
29	#4466035	C₂²	1	1	yes	characteristic, complemented
30	#4420586	C₂²	1	1	yes	characteristic
31	#4420586	C₂²	1	1	yes	characteristic, complemented
32	#4117638	C₂²	1	1	yes	characteristic, complemented
33	#2177857	C₂²	1	1	yes	characteristic, complemented
34	#2032535	C₂²	1	1	yes	characteristic, complemented
35	#1420272	C₂²	1	1	yes	characteristic, complemented
36	#719145	C₂²	1	1	yes	characteristic
37	#647656	C₂²	1	1	yes	characteristic
38	#647656	C₂²	1	1	yes	characteristic, complemented
39	#511771	C₂²	1	4	yes	complemented
40	#508063	C₂²	1	4	yes	complemented
41	#347056	C₂²	1	2	yes	complemented
42	#347048	C₂²	1	2	yes	complemented
43	#347047	C₂²	1	2	yes	—
44	#347047	C₂²	1	2	yes	complemented
45	#347047	C₂²	1	2	yes	complemented
46	#347042	C₂²	1	2	yes	—
47	#347042	C₂²	1	2	yes	—
48	#347042	C₂²	1	2	yes	complemented
49	#346466	C₂²	1	2	yes	complemented
50	#346466	C₂²	1	2	yes	complemented
51	#346446	C₂²	1	2	yes	—
52	#346446	C₂²	1	2	yes	complemented
53	#188151	C₂²	1	1	yes	characteristic, complemented
54	#188035	C₂²	1	1	yes	characteristic, complemented
55	#188035	C₂²	1	1	yes	characteristic, complemented
56	#187949	C₂²	1	2	yes	complemented
57	#187940	C₂²	1	2	yes	complemented
58	#186819	C₂²	1	2	yes	complemented
59	#144655	C₂²	1	4	yes	complemented
60	#144655	C₂²	1	4	yes	complemented
61	#144404	C₂²	1	4	yes	complemented
62	#144404	C₂²	1	4	yes	complemented
63	#144387	C₂²	1	4	yes	complemented
64	#144386	C₂²	1	4	yes	complemented
65	#144367	C₂²	1	4	yes	complemented
66	#144366	C₂²	1	4	yes	complemented
67	#139830	C₂²	1	2	yes	complemented
68	#139830	C₂²	1	2	yes	complemented
69	#139819	C₂²	1	4	yes	complemented
70	#139790	C₂²	1	2	yes	complemented
71	#139790	C₂²	1	2	yes	complemented
72	#139790	C₂²	1	2	yes	complemented
73	#139788	C₂²	1	2	yes	complemented
74	#139774	C₂²	1	4	yes	complemented
75	#139773	C₂²	1	4	yes	complemented
76	#139718	C₂²	1	2	yes	complemented
77	#139718	C₂²	1	2	yes	complemented
78	#139716	C₂²	1	2	yes	complemented
79	#139716	C₂²	1	2	yes	complemented
80	#139716	C₂²	1	2	yes	complemented
81	#139714	C₂²	1	2	yes	complemented
82	#139706	C₂²	1	4	yes	complemented
83	#139702	C₂²	1	4	yes	complemented
84	#139700	C₂²	1	4	yes	complemented
85	#135548	C₂²	1	2	yes	complemented
86	#135524	C₂²	1	2	yes	complemented
87	#135522	C₂²	1	2	yes	complemented
88	#133853	C₂²	1	2	yes	complemented
89	#133825	C₂²	1	2	yes	complemented
90	#133822	C₂²	1	2	yes	complemented
91	#62832	C₂³	1	2	yes	—
92	#62817	C₂³	1	2	yes	—
93	#62817	C₂³	1	2	yes	—
94	C₂²×D₄²	C₂³	1	1	yes	characteristic
95	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
96	C₂³×#120	D₄	1	1	yes	characteristic, complemented
97	C₂³×#120	D₄	1	1	yes	characteristic, complemented
98	C₂×#2697	C₂³	1	1	yes	characteristic, complemented
99	C₂×#2846	C₂³	1	1	yes	characteristic
100	C₂×#2541	C₂³	1	1	yes	characteristic
101	C₂×#2535	D₄	1	1	yes	characteristic, complemented
102	C₂×#2403	D₄	1	1	yes	characteristic, complemented
103	C₂×#2403	D₄	1	1	yes	characteristic, complemented
104	C₂×#2613	C₂³	1	1	yes	characteristic
105	C₂×#2397	D₄	1	1	yes	characteristic, complemented
106	#24018	C₂³	1	4	yes	—
107	#23906	C₂³	1	4	yes	—
108	#23901	C₂³	1	4	yes	—
109	#23900	C₂³	1	4	yes	—
110	#23900	C₂³	1	4	yes	—
111	#23900	C₂³	1	4	yes	—
112	#21797	C₂³	1	2	yes	—
113	#21746	C₂³	1	2	yes	—
114	#21746	C₂³	1	2	yes	—
115	#17272	C₂³	1	1	yes	characteristic, complemented
116	#17272	C₂³	1	1	yes	characteristic, complemented
117	#15984	D₄	1	1	yes	characteristic, complemented
118	#15984	D₄	1	1	yes	characteristic, complemented
119	#15948	C₂³	1	1	yes	characteristic
120	#15948	C₂³	1	1	yes	characteristic, complemented
121	#15947	C₂³	1	1	yes	characteristic
122	#15947	C₂³	1	1	yes	characteristic
123	#15947	C₂³	1	1	yes	characteristic
124	#15947	C₂³	1	1	yes	characteristic, complemented
125	#15283	D₄	1	1	yes	characteristic, complemented
126	#15283	D₄	1	1	yes	characteristic, complemented
127	#15283	C₂³	1	1	yes	characteristic
128	#15283	C₂³	1	1	yes	characteristic
129	#15281	C₂³	1	1	yes	characteristic, complemented
130	#15281	C₂³	1	1	yes	characteristic, complemented
131	#15261	C₂³	1	1	yes	characteristic
132	#15261	C₂³	1	1	yes	characteristic, complemented
133	#15258	D₄	1	1	yes	characteristic, complemented
134	#15258	D₄	1	1	yes	characteristic, complemented
135	#15258	C₂³	1	1	yes	characteristic
136	#15258	C₂³	1	1	yes	characteristic
137	#15258	C₂³	1	1	yes	characteristic
138	#15258	C₂³	1	1	yes	characteristic
139	#15258	C₂³	1	1	yes	characteristic
140	#15258	C₂³	1	1	yes	characteristic, complemented
141	#15257	D₄	1	1	yes	characteristic, complemented
142	#15257	D₄	1	1	yes	characteristic, complemented
143	#15257	D₄	1	1	yes	characteristic, complemented
144	#15257	D₄	1	1	yes	characteristic, complemented
145	#15257	D₄	1	1	yes	characteristic, complemented
146	#15257	D₄	1	1	yes	characteristic, complemented
147	#14667	C₂³	1	1	yes	characteristic, complemented
148	#14657	C₂³	1	1	yes	characteristic
149	#14657	C₂³	1	1	yes	characteristic, complemented
150	#14506	C₂³	1	1	yes	characteristic, complemented
151	#14419	C₂³	1	1	yes	characteristic, complemented
152	#14358	C₂³	1	1	yes	characteristic, complemented
153	#14335	D₄	1	1	yes	characteristic, complemented
154	#14335	D₄	1	1	yes	characteristic, complemented
155	#14272	C₂³	1	1	yes	characteristic
156	#14134	C₂³	1	1	yes	characteristic
157	#14134	C₂³	1	1	yes	characteristic, complemented
158	#13905	D₄	1	1	yes	characteristic, complemented
159	#13867	D₄	1	1	yes	characteristic, complemented
160	#13867	D₄	1	1	yes	characteristic, complemented
161	#13785	D₄	1	1	yes	characteristic, complemented
162	#12856	C₂³	1	4	yes	complemented
163	#12693	C₂³	1	4	yes	complemented
164	#12688	C₂³	1	4	yes	complemented
165	#12687	C₂³	1	4	yes	complemented
166	#12687	C₂³	1	4	yes	complemented
167	#12687	C₂³	1	4	yes	complemented
168	#8547	C₂³	1	2	yes	—
169	#8547	C₂³	1	2	yes	—
170	#8546	C₂³	1	2	yes	—
171	#8546	C₂³	1	2	yes	—
172	#8541	C₂³	1	2	yes	—
173	#8541	C₂³	1	2	yes	—
174	#8534	C₂³	1	4	yes	—
175	#8534	C₂³	1	4	yes	—
176	#8534	C₂³	1	4	yes	—
177	#8534	C₂³	1	4	yes	—
178	#8453	C₂³	1	4	yes	—
179	#8453	C₂³	1	4	yes	—
180	#7307	C₂³	1	4	yes	complemented
181	#7307	C₂³	1	4	yes	complemented
182	#7304	C₂³	1	4	yes	complemented
183	#7304	C₂³	1	4	yes	complemented
184	#7304	C₂³	1	4	yes	complemented
185	#7304	C₂³	1	4	yes	complemented
186	C₂⁷	C₂×D₄	1	1	yes	characteristic
187	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
192	#3484	C₂⁴	1	4	yes	—
193	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
194	C₂²×#127	C₂⁴	1	1	yes	characteristic
195	C₂²×#127	C₂⁴	1	1	yes	characteristic
196	C₂²×#123	C₂⁴	1	1	yes	characteristic
197	C₂²×#121	C₂×D₄	1	1	yes	characteristic
198	C₂²×#121	C₂×D₄	1	1	yes	characteristic
199	C₂²×#121	C₂×D₄	1	1	yes	characteristic
200	C₂²×#121	C₂×D₄	1	1	yes	characteristic
201	C₂²×#120	C₂×D₄	1	1	yes	characteristic
202	C₂²×#120	C₂×D₄	1	1	yes	characteristic
203	C₂²×#120	C₂×D₄	1	1	yes	characteristic
204	C₂²×#120	C₂×D₄	1	1	yes	characteristic
205	C₂²×#120	C₂×D₄	1	1	yes	characteristic
206	C₂²×#120	C₂×D₄	1	1	yes	characteristic
207	C₂²×#120	C₂×D₄	1	1	yes	characteristic
208	C₂²×#120	C₂×D₄	1	1	yes	characteristic
209	C₂²×#120	C₂×D₄	1	1	yes	characteristic
210	C₂²×#120	C₂×D₄	1	1	yes	characteristic
211	C₂²×#120	C₂×D₄	1	1	yes	characteristic
212	C₂²×#120	C₂×D₄	1	1	yes	characteristic
213	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
214	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
215	C₂²×#120	C₂⁴	1	1	yes	characteristic
216	C₂²×#120	C₂⁴	1	1	yes	characteristic
217	C₂²×#120	C₂⁴	1	1	yes	characteristic
218	C₂²×#120	C₂⁴	1	1	yes	characteristic
219	C₂²×#120	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
223	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₂×#399	C₂×D₄	1	1	yes	characteristic
226	C₂×#399	C₂×D₄	1	1	yes	characteristic, complemented
227	C₂×#397	C₂×D₄	1	1	yes	characteristic
228	C₂×#397	C₂×D₄	1	1	yes	characteristic, complemented
229	C₂×#392	C₂×D₄	1	1	yes	characteristic
230	C₂×#392	C₂×D₄	1	1	yes	characteristic
231	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
232	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
233	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
234	C₂×#390	C₂⁴	1	1	yes	characteristic
235	C₂×#386	C₂×D₄	1	1	yes	characteristic
236	C₂×#386	C₂×D₄	1	1	yes	characteristic
237	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
238	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
239	C₂×#382	C₂×D₄	1	1	yes	characteristic, complemented
240	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
241	C₂×#379	C₂×D₄	1	1	yes	characteristic
242	C₂×#379	C₂×D₄	1	1	yes	characteristic
243	C₂×#379	C₂×D₄	1	1	yes	characteristic
244	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
245	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
246	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
247	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
248	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
249	C₂×#376	C₂×D₄	1	1	yes	characteristic, complemented
250	#1783	C₂⁴	1	4	yes	—
251	#1781	C₂⁴	1	4	yes	—
252	#1781	C₂⁴	1	4	yes	—
253	#1440	C₂×D₄	1	1	yes	characteristic
254	#1440	C₂×D₄	1	1	yes	characteristic
255	#1440	C₂×D₄	1	1	yes	characteristic, complemented
256	#1440	C₂×D₄	1	1	yes	characteristic, complemented
257	#1438	C₂×D₄	1	1	yes	characteristic
258	#1438	C₂×D₄	1	1	yes	characteristic
259	#1438	C₂×D₄	1	1	yes	characteristic
260	#1438	C₂×D₄	1	1	yes	characteristic
261	#1438	C₂×D₄	1	1	yes	characteristic
262	#1438	C₂×D₄	1	1	yes	characteristic
263	#1438	C₂×D₄	1	1	yes	characteristic
264	#1438	C₂×D₄	1	1	yes	characteristic
265	#1438	C₂×D₄	1	1	yes	characteristic
266	#1438	C₂×D₄	1	1	yes	characteristic
267	#1438	C₂×D₄	1	1	yes	characteristic
268	#1438	C₂×D₄	1	1	yes	characteristic
269	#1438	C₂×D₄	1	1	yes	characteristic, complemented
270	#1438	C₂×D₄	1	1	yes	characteristic, complemented
271	#1438	C₂×D₄	1	1	yes	characteristic, complemented
272	#1438	C₂×D₄	1	1	yes	characteristic, complemented
273	#1438	C₂×D₄	1	1	yes	characteristic, complemented
274	#1438	C₂×D₄	1	1	yes	characteristic, complemented
275	#1438	C₂⁴	1	1	yes	characteristic
276	#1438	C₂⁴	1	1	yes	characteristic
277	#1438	C₂⁴	1	1	yes	characteristic
278	#1438	C₂⁴	1	1	yes	characteristic
279	#1438	C₂⁴	1	1	yes	characteristic
280	#1438	C₂⁴	1	1	yes	characteristic
281	#1437	C₂×D₄	1	1	yes	characteristic
282	#1437	C₂×D₄	1	1	yes	characteristic
283	#1437	C₂×D₄	1	1	yes	characteristic
284	#1437	C₂×D₄	1	1	yes	characteristic
285	#1437	C₂×D₄	1	1	yes	characteristic, complemented
286	#1437	C₂×D₄	1	1	yes	characteristic, complemented
287	#1437	C₂×D₄	1	1	yes	characteristic, complemented
288	#1437	C₂×D₄	1	1	yes	characteristic, complemented
289	C₂⁶	#120	1	1	yes	characteristic
290	C₂⁶	#120	1	1	yes	characteristic
291	C₂⁶	C₂²×D₄	1	1	yes	characteristic
292	C₂⁶	C₂²×D₄	1	1	yes	characteristic
293	C₂⁶	C₂²×D₄	1	1	yes	characteristic
294	C₂⁶	C₂²×D₄	1	1	yes	characteristic
295	C₂⁶	C₂²×D₄	1	1	yes	characteristic
296	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	4	yes	—
297	C₂³×D₄	#120	1	1	yes	characteristic
298	C₂³×D₄	#120	1	1	yes	characteristic
299	C₂³×D₄	#120	1	1	yes	characteristic
300	C₂³×D₄	#120	1	1	yes	characteristic
301	C₂³×D₄	#120	1	1	yes	characteristic
302	C₂³×D₄	#120	1	1	yes	characteristic
303	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
304	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
305	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
306	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
307	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
308	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
309	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
310	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
311	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
312	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
313	C₂³×D₄	C₂⁵	1	1	yes	characteristic
314	C₂⁴×C₄	#120	1	1	yes	characteristic
315	C₂⁴×C₄	#120	1	1	yes	characteristic
316	C₂⁴×C₄	#120	1	1	yes	characteristic
317	C₂⁴×C₄	#120	1	1	yes	characteristic
318	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
319	#518	H(5,𝔽₂)	1	4	yes	—
320	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
321	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
325	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
340	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
342	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
343	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
344	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
345	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
346	C₂×#95	C₂²×D₄	1	1	yes	characteristic
347	C₂×#95	C₂²×D₄	1	1	yes	characteristic
348	C₂×#95	C₂²×D₄	1	1	yes	characteristic
349	C₂×#95	C₂²×D₄	1	1	yes	characteristic
350	C₂⁵	C₂×#120	1	1	yes	characteristic
351	C₂⁵	C₂×#120	1	1	yes	characteristic
352	C₂⁵	C₂×#120	1	1	yes	characteristic
353	C₂⁵	C₂×#120	1	1	yes	characteristic
354	C₂⁵	C₂×#120	1	1	yes	characteristic
355	C₂⁵	C₂×#120	1	1	yes	characteristic
356	C₂⁵	C₂³×D₄	1	1	yes	characteristic
357	C₂⁵	C₂³×D₄	1	1	yes	characteristic
358	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
359	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
360	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
361	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
362	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
363	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
364	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
365	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
366	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
367	C₂³×C₄	C₂×#120	1	1	yes	characteristic
368	C₂³×C₄	C₂×#120	1	1	yes	characteristic
369	C₂³×C₄	C₂×#120	1	1	yes	characteristic
370	C₂³×C₄	C₂×#120	1	1	yes	characteristic
371	C₂³×C₄	C₂×#120	1	1	yes	characteristic
372	C₂³×C₄	C₂×#120	1	1	yes	characteristic
373	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
374	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
375	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
376	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
377	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
378	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
379	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
380	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
381	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
382	C₂⁴	C₂²×#120	1	1	yes	characteristic
383	C₂⁴	#3484	1	2	yes	—
384	C₂⁴	#3484	1	2	yes	—
385	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
386	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
387	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
388	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
389	C₂²×C₄	#3484	1	2	yes	—
390	C₂³	#33551	1	2	yes	—
391	C₂³	#33557	1	2	yes	—
392	C₂³	#35346	1	1	yes	characteristic
393	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
394	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
395	C₂×C₄	#33551	1	2	yes	—
396	C₂²	#6499867	1	1	yes	characteristic
397	C₂²	#6499874	1	1	yes	characteristic
398	C₂²	#6499876	1	1	yes	characteristic
399	C₂²	C₂×#33551	1	1	yes	characteristic
400	C₂²	C₂×#33551	1	1	yes	characteristic
401	C₂²	C₂×#33557	1	1	yes	characteristic
402	C₂²	#7622875	1	1	yes	characteristic
403	C₂	#72233427	1	1	yes	characteristic
404	C₂	#72234418	1	1	yes	characteristic
405	C₂	#72238471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6499867
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72263346	C₂	semidirect
2. #72263345	C₂	semidirect
3. #72263344	C₂	semidirect
4. #72263343	C₂	semidirect
5. #72263342	C₂	semidirect
6. #72263155	C₂	semidirect
7. #72263141	C₂	semidirect
8. #72262844	C₂	semidirect
9. #72256396	C₂	semidirect
10. #72234607	C₂	semidirect
11. #72234143	C₂	semidirect
12. #72234108	C₂	semidirect
13. #72233177	C₂	semidirect
14. #72233165	C₂	semidirect
15. #72232866	C₂	semidirect
16. #72232757	C₂	semidirect
17. #72226358	C₂	semidirect
18. #72216323	C₂	semidirect
19. #72210587	C₂	semidirect
20. #10586472	C₂²	semidirect
21. #6512701	C₂²	semidirect
22. #6499870	C₂²	semidirect
24. #5486599	C₂²	semidirect
25. #5486291	C₂²	semidirect
26. #5236713	C₂²	semidirect
27. #5064005	C₂²	semidirect
28. #4607318	C₂²	semidirect
29. #4466035	C₂²	semidirect
31. #4420586	C₂²	semidirect
32. #4117638	C₂²	semidirect
33. #2177857	C₂²	semidirect
34. #2032535	C₂²	semidirect
35. #1420272	C₂²	semidirect
38. #647656	C₂²	semidirect
39. #511771	C₂²	semidirect
40. #508063	C₂²	semidirect
41. #347056	C₂²	semidirect
42. #347048	C₂²	semidirect
44. #347047	C₂²	semidirect
45. #347047	C₂²	semidirect
48. #347042	C₂²	semidirect
49. #346466	C₂²	semidirect
50. #346466	C₂²	semidirect
52. #346446	C₂²	semidirect
53. #188151	C₂²	semidirect
54. #188035	C₂²	semidirect
55. #188035	C₂²	semidirect
56. #187949	C₂²	semidirect
57. #187940	C₂²	semidirect
58. #186819	C₂²	semidirect
59. #144655	C₂²	semidirect
60. #144655	C₂²	semidirect
61. #144404	C₂²	semidirect
62. #144404	C₂²	semidirect
63. #144387	C₂²	semidirect
64. #144386	C₂²	semidirect
65. #144367	C₂²	semidirect
66. #144366	C₂²	semidirect
67. #139830	C₂²	semidirect
68. #139830	C₂²	semidirect
69. #139819	C₂²	semidirect
70. #139790	C₂²	semidirect
71. #139790	C₂²	semidirect
72. #139790	C₂²	semidirect
73. #139788	C₂²	semidirect
74. #139774	C₂²	semidirect
75. #139773	C₂²	semidirect
76. #139718	C₂²	semidirect
77. #139718	C₂²	semidirect
78. #139716	C₂²	semidirect
79. #139716	C₂²	semidirect
80. #139716	C₂²	semidirect
81. #139714	C₂²	semidirect
82. #139706	C₂²	semidirect
83. #139702	C₂²	semidirect
84. #139700	C₂²	semidirect
85. #135548	C₂²	semidirect
86. #135524	C₂²	semidirect
87. #135522	C₂²	semidirect
88. #133853	C₂²	semidirect
89. #133825	C₂²	semidirect
90. #133822	C₂²	semidirect
95. C₂²×D₄²	C₂³	semidirect
96. C₂³×#120	D₄	semidirect
97. C₂³×#120	D₄	semidirect
98. C₂×#2697	C₂³	semidirect
101. C₂×#2535	D₄	semidirect
102. C₂×#2403	D₄	semidirect
103. C₂×#2403	D₄	semidirect
105. C₂×#2397	D₄	semidirect
115. #17272	C₂³	semidirect
116. #17272	C₂³	semidirect
117. #15984	D₄	semidirect
118. #15984	D₄	semidirect
120. #15948	C₂³	semidirect
124. #15947	C₂³	semidirect
125. #15283	D₄	semidirect
126. #15283	D₄	semidirect
129. #15281	C₂³	semidirect
130. #15281	C₂³	semidirect
132. #15261	C₂³	semidirect
133. #15258	D₄	semidirect
134. #15258	D₄	semidirect
140. #15258	C₂³	semidirect
141. #15257	D₄	semidirect
142. #15257	D₄	semidirect
143. #15257	D₄	semidirect
144. #15257	D₄	semidirect
145. #15257	D₄	semidirect
146. #15257	D₄	semidirect
147. #14667	C₂³	semidirect
149. #14657	C₂³	semidirect
150. #14506	C₂³	semidirect
151. #14419	C₂³	semidirect
152. #14358	C₂³	semidirect
153. #14335	D₄	semidirect
154. #14335	D₄	semidirect
157. #14134	C₂³	semidirect
158. #13905	D₄	semidirect
159. #13867	D₄	semidirect
160. #13867	D₄	semidirect
161. #13785	D₄	semidirect
162. #12856	C₂³	semidirect
163. #12693	C₂³	semidirect
164. #12688	C₂³	semidirect
165. #12687	C₂³	semidirect
166. #12687	C₂³	semidirect
167. #12687	C₂³	semidirect
180. #7307	C₂³	semidirect
181. #7307	C₂³	semidirect
182. #7304	C₂³	semidirect
183. #7304	C₂³	semidirect
184. #7304	C₂³	semidirect
185. #7304	C₂³	semidirect
191. C₂⁴×D₄	C₂×D₄	semidirect
193. C₂²×#127	C₂×D₄	semidirect
213. C₂²×#120	C₂×D₄	semidirect
214. C₂²×#120	C₂×D₄	semidirect
222. C₂²×C₄×D₄	C₂×D₄	semidirect
226. C₂×#399	C₂×D₄	semidirect
228. C₂×#397	C₂×D₄	semidirect
231. C₂×#392	C₂×D₄	semidirect
232. C₂×#392	C₂×D₄	semidirect
233. C₂×#390	C₂×D₄	semidirect
237. C₂×#386	C₂×D₄	semidirect
238. C₂×#386	C₂×D₄	semidirect
239. C₂×#382	C₂×D₄	semidirect
240. C₂×#381	C₂×D₄	semidirect
244. C₂×#379	C₂×D₄	semidirect
245. C₂×#379	C₂×D₄	semidirect
246. C₂×#379	C₂×D₄	semidirect
247. C₂×#379	C₂×D₄	semidirect
248. C₂×C₄×C₄⋊C₄	C₂×D₄	semidirect
249. C₂×#376	C₂×D₄	semidirect
255. #1440	C₂×D₄	semidirect
256. #1440	C₂×D₄	semidirect
269. #1438	C₂×D₄	semidirect
270. #1438	C₂×D₄	semidirect
271. #1438	C₂×D₄	semidirect
272. #1438	C₂×D₄	semidirect
273. #1438	C₂×D₄	semidirect
274. #1438	C₂×D₄	semidirect
285. #1437	C₂×D₄	semidirect
286. #1437	C₂×D₄	semidirect
287. #1437	C₂×D₄	semidirect
288. #1437	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72263346	2
#72263345	2
#72263344	2
#72263343	2
#72263342	2
#72263155	2
#72263141	2
#72262844	2
#72256396	2
#72234607	2
#72234143	2
#72234108	2
#72233177	2
#72233165	2
#72232866	2
#72232757	2
#72226358	2
#72216323	2
#72210587	2