Subgroups — #72235963

Order 2048.

At least 8310 conjugacy classes of subgroups; only the 1276 normal subgroups are shown.

The subgroup lattice has 395 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72235937	C₂	1	1	yes	maximal, characteristic, complemented
2	#72235930	C₂	1	1	yes	maximal, characteristic, complemented
3	#72235928	C₂	1	2	yes	maximal, complemented
4	#72235927	C₂	1	4	yes	maximal, complemented
5	#72235919	C₂	1	4	yes	maximal, complemented
6	#72235747	C₂	1	4	yes	maximal, complemented
7	#72235186	C₂	1	2	yes	maximal, complemented
8	#72234675	C₂	1	1	yes	maximal, characteristic, complemented
9	#72232667	C₂	1	2	yes	maximal, complemented
10	#72231950	C₂	1	2	yes	maximal, complemented
11	#72231810	C₂	1	2	yes	maximal, complemented
12	#72219034	C₂	1	2	yes	maximal, complemented
13	#72218455	C₂	1	2	yes	maximal, complemented
14	#72210511	C₂	1	2	yes	maximal, complemented
15	C₂×#62817	C₂²	1	1	yes	characteristic, complemented
16	C₂²×#3484	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄²	C₂²	1	1	yes	characteristic
18	#7642350	C₂²	1	2	yes	—
19	#7642350	C₂²	1	2	yes	complemented
20	#7642273	C₂²	1	2	yes	—
21	#7642257	C₂²	1	2	yes	complemented
22	#7630945	C₂²	1	2	yes	complemented
23	#7630939	C₂²	1	2	yes	—
24	C₂×#35347	C₂²	1	1	yes	characteristic, complemented
25	C₂×#35346	C₂²	1	1	yes	characteristic, complemented
26	#7626202	C₂²	1	1	yes	characteristic, complemented
27	#6628867	C₂²	1	4	yes	complemented
28	#6437445	C₂²	1	4	yes	complemented
29	#6346594	C₂²	1	4	yes	complemented
30	#6346594	C₂²	1	4	yes	complemented
31	#635987	C₂²	1	2	yes	complemented
32	#617709	C₂²	1	2	yes	complemented
33	#616961	C₂²	1	2	yes	—
34	#612429	C₂²	1	2	yes	complemented
35	#517411	C₂²	1	1	yes	characteristic, complemented
36	#515362	C₂²	1	1	yes	characteristic, complemented
37	#515285	C₂²	1	1	yes	characteristic, complemented
38	#393988	C₂²	1	8	yes	complemented
39	#392696	C₂²	1	4	yes	complemented
40	#392113	C₂²	1	2	yes	complemented
41	#359509	C₂²	1	4	yes	complemented
42	#234949	C₂²	1	8	yes	complemented
43	#234948	C₂²	1	8	yes	complemented
44	#201462	C₂²	1	4	yes	complemented
45	#201462	C₂²	1	4	yes	complemented
46	#201322	C₂²	1	4	yes	complemented
47	#201322	C₂²	1	4	yes	complemented
48	C₂×#8549	C₂²	1	2	yes	complemented
49	C₂×#8549	C₂²	1	2	yes	complemented
50	C₂×#8547	C₂²	1	2	yes	complemented
51	C₂×#8547	C₂²	1	2	yes	complemented
52	#186835	C₂²	1	4	yes	complemented
53	#185255	C₂²	1	4	yes	complemented
54	#185255	C₂²	1	4	yes	complemented
55	#184796	C₂²	1	2	yes	complemented
56	#184777	C₂²	1	2	yes	complemented
57	#112857	C₂²	1	8	yes	complemented
58	#111960	C₂²	1	8	yes	complemented
59	#111959	C₂²	1	8	yes	complemented
60	#108238	C₂²	1	4	yes	complemented
61	#106326	C₂²	1	4	yes	complemented
62	#106326	C₂²	1	4	yes	complemented
63	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
64	C₂⁵×D₄	D₄	1	1	yes	characteristic
65	C₂⁵×D₄	D₄	1	1	yes	characteristic
66	C₂⁵×D₄	D₄	1	1	yes	characteristic
67	C₂⁵×D₄	C₂³	1	1	yes	characteristic
68	C₂×#3490	C₂³	1	2	yes	—
69	C₂×#3490	C₂³	1	2	yes	—
70	C₂×#3484	D₄	1	4	yes	complemented
71	C₂×#3484	C₂³	1	2	yes	—
72	C₂²×#535	C₂³	1	2	yes	—
73	C₂³×#127	D₄	1	1	yes	characteristic
74	C₂²×#525	C₂³	1	2	yes	complemented
75	C₂³×#121	D₄	1	1	yes	characteristic
76	C₂³×#121	C₂³	1	1	yes	characteristic
77	C₂³×#121	C₂³	1	1	yes	characteristic
78	C₂³×#121	C₂³	1	1	yes	characteristic
79	C₂³×#120	D₄	1	1	yes	characteristic
80	C₂³×#120	D₄	1	1	yes	characteristic
81	C₂³×#120	C₂³	1	1	yes	characteristic
82	C₂³×#120	C₂³	1	1	yes	characteristic
83	C₂²×#518	C₂³	1	1	yes	characteristic, complemented
84	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
85	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
86	#60359	C₂³	1	8	yes	—
87	#36718	D₄	1	4	yes	complemented
88	#36717	D₄	1	4	yes	complemented
89	#36703	D₄	1	8	yes	complemented
90	#36614	C₂³	1	4	yes	—
91	#35395	D₄	1	8	yes	complemented
92	#35390	D₄	1	4	yes	complemented
93	#35367	D₄	1	4	yes	complemented
94	#35222	D₄	1	8	yes	complemented
95	#35222	C₂³	1	4	yes	—
96	#35057	C₂³	1	4	yes	—
97	#35050	C₂³	1	4	yes	—
98	C₂×#2406	C₂³	1	2	yes	complemented
99	C₂×#2404	C₂³	1	2	yes	—
100	C₂×#2404	C₂³	1	2	yes	—
101	C₂×#2404	C₂³	1	2	yes	complemented
102	#34176	C₂³	1	2	yes	—
103	#34176	C₂³	1	2	yes	—
104	#34171	D₄	1	4	yes	complemented
105	#34171	C₂³	1	2	yes	—
106	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
107	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
108	#20979	C₂³	1	8	yes	—
109	#20605	C₂³	1	8	yes	complemented
110	C₂×#1783	C₂³	1	4	yes	—
111	C₂×#1783	C₂³	1	4	yes	complemented
112	#20579	C₂³	1	4	yes	complemented
113	#17587	C₂³	1	8	yes	—
114	#17587	C₂³	1	8	yes	—
115	C₂×#1463	C₂³	1	4	yes	complemented
116	C₂×#1462	C₂³	1	4	yes	—
117	C₂×#1462	C₂³	1	4	yes	—
118	C₂×#1462	C₂³	1	4	yes	complemented
119	#15259	D₄	1	8	yes	complemented
120	#15258	D₄	1	8	yes	complemented
121	#14681	C₂³	1	2	yes	complemented
122	#14335	C₂³	1	2	yes	—
123	#13870	C₂³	1	2	yes	complemented
124	#13868	C₂³	1	2	yes	—
125	#13868	C₂³	1	2	yes	—
126	#13868	C₂³	1	2	yes	complemented
127	#10716	C₂³	1	8	yes	complemented
128	#7943	C₂³	1	8	yes	complemented
129	#7943	C₂³	1	8	yes	complemented
130	C₂⁷	C₂×D₄	1	1	yes	characteristic
131	C₂⁷	C₂×D₄	1	1	yes	characteristic
132	C₂⁷	C₂×D₄	1	1	yes	characteristic
133	C₂⁷	C₂×D₄	1	1	yes	characteristic
134	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
135	C₂³×#41	C₂⁴	1	2	yes	—
136	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
137	C₂⁴×D₄	C₂×D₄	1	4	yes	—
138	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
139	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
145	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
146	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
147	C₂⁴×D₄	C₂×D₄	1	4	yes	—
148	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
153	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
154	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
155	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
156	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
157	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
158	C₂×#543	C₂×D₄	1	2	yes	complemented
159	C₂×#543	C₂×D₄	1	2	yes	complemented
160	C₂×#538	C₂×D₄	1	4	yes	complemented
161	C₂×#538	C₂×D₄	1	4	yes	complemented
162	C₂×#535	C₂×D₄	1	8	yes	—
163	C₂×#535	C₂×D₄	1	4	yes	complemented
164	C₂×#534	C₂×D₄	1	2	yes	complemented
165	C₂×#534	C₂×D₄	1	2	yes	complemented
166	C₂²×#127	C₂×D₄	1	4	yes	complemented
167	C₂²×#124	C₂×D₄	1	4	yes	complemented
168	C₂×#525	C₂×D₄	1	8	yes	complemented
169	C₂×#525	C₂⁴	1	4	yes	—
170	C₂²×#121	C₂×D₄	1	4	yes	—
171	C₂²×#121	C₂×D₄	1	4	yes	—
172	C₂²×#120	C₂×D₄	1	8	yes	—
173	C₂²×#120	C₂×D₄	1	4	yes	—
174	C₂²×#120	C₂×D₄	1	4	yes	—
175	C₂×#518	C₂×D₄	1	2	yes	complemented
176	C₂×#518	C₂×D₄	1	4	yes	complemented
177	C₂²×#117	C₂⁴	1	2	yes	—
178	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
179	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
180	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
182	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
183	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
184	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
185	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
186	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
187	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
188	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
189	C₂×#407	C₂⁴	1	8	yes	—
190	#2591	C₂×D₄	1	8	yes	complemented
191	#2583	C₂×D₄	1	8	yes	complemented
192	#2561	C₂×D₄	1	8	yes	complemented
193	#2539	C₂×D₄	1	8	yes	complemented
194	#2435	C₂×D₄	1	8	yes	—
195	#2435	C₂×D₄	1	8	yes	—
196	#2433	C₂×D₄	1	8	yes	—
197	#2433	C₂×D₄	1	8	yes	—
198	C₂×#393	C₂×D₄	1	4	yes	complemented
199	C₂×#393	C₂×D₄	1	4	yes	complemented
200	C₂×#392	C₂×D₄	1	4	yes	complemented
201	C₂×#392	C₂×D₄	1	4	yes	complemented
202	#2312	C₂×D₄	1	4	yes	complemented
203	#2312	C₂×D₄	1	4	yes	complemented
204	#2309	C₂×D₄	1	8	yes	—
205	#2309	C₂×D₄	1	4	yes	complemented
206	#2280	C₂×D₄	1	8	yes	complemented
207	#2280	C₂⁴	1	4	yes	—
208	C₂×#381	C₂⁴	1	2	yes	—
209	C₂×#381	C₂⁴	1	2	yes	—
210	#2273	C₂×D₄	1	4	yes	complemented
211	#2273	C₂×D₄	1	4	yes	complemented
212	#1438	C₂×D₄	1	8	yes	complemented
213	#1437	C₂×D₄	1	8	yes	complemented
214	#1437	C₂×D₄	1	8	yes	complemented
215	C₂⁶	#120	1	4	yes	—
216	C₂⁶	#120	1	2	yes	—
217	C₂⁶	#120	1	4	yes	—
218	C₂⁶	#120	1	2	yes	—
219	C₂⁶	#120	1	2	yes	—
220	C₂⁶	#120	1	2	yes	—
221	C₂⁶	C₂²×D₄	1	1	yes	characteristic
222	C₂⁶	C₂²×D₄	1	1	yes	characteristic
223	C₂⁶	C₂²×D₄	1	1	yes	characteristic
224	C₂⁶	C₂²×D₄	1	1	yes	characteristic
225	C₂⁶	C₂²×D₄	1	1	yes	characteristic
226	C₂⁶	C₂²×D₄	1	1	yes	characteristic
227	C₂⁶	C₂²×D₄	1	1	yes	characteristic
228	C₂⁶	C₂²×D₄	1	1	yes	characteristic
229	C₂²×#41	C₂²×D₄	1	4	yes	—
230	C₂³×Q₈	C₂²×D₄	1	2	yes	—
231	C₂³×D₄	#120	1	2	yes	—
232	C₂³×D₄	#120	1	2	yes	—
233	C₂³×D₄	#120	1	4	yes	—
234	C₂³×D₄	#120	1	4	yes	—
235	C₂³×D₄	#120	1	4	yes	—
236	C₂³×D₄	#120	1	2	yes	—
237	C₂³×D₄	#120	1	2	yes	—
238	C₂³×D₄	#120	1	2	yes	—
239	C₂³×D₄	#120	1	2	yes	—
240	C₂³×D₄	#120	1	2	yes	—
241	C₂³×D₄	#120	1	2	yes	—
242	C₂³×D₄	#120	1	4	yes	—
243	C₂³×D₄	C₂²×D₄	1	4	yes	—
244	C₂³×D₄	C₂²×D₄	1	2	yes	—
245	C₂³×D₄	C₂²×D₄	1	2	yes	—
246	C₂³×D₄	C₂²×D₄	1	4	yes	—
247	C₂³×D₄	C₂²×D₄	1	4	yes	—
248	C₂³×D₄	C₂²×D₄	1	2	yes	—
249	C₂³×D₄	C₂²×D₄	1	4	yes	—
250	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
251	C₂⁴×C₄	#120	1	4	yes	—
252	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
253	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
254	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
255	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
256	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
257	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
258	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
259	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
260	C₂×#127	#120	1	16	yes	complemented
261	C₂×#124	#120	1	16	yes	complemented
262	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
263	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
264	C₂×#121	C₂²×D₄	1	4	yes	—
265	C₂×#121	C₂²×D₄	1	4	yes	—
266	C₂×#117	C₂²×D₄	1	4	yes	—
267	C₂×#117	C₂²×D₄	1	8	yes	—
268	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
269	C₂²×C₂²⋊C₄	#120	1	4	yes	—
270	C₂²×C₂²⋊C₄	#120	1	4	yes	—
271	C₂²×C₂²⋊C₄	#120	1	4	yes	—
272	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
273	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
274	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
275	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
276	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
277	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
278	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
279	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
280	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
281	C₂²×C₄²	C₂²×D₄	1	4	yes	—
282	#390	#120	1	16	yes	complemented
283	#390	#120	1	16	yes	complemented
284	C₄×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
285	C₄×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
286	C₂×#95	C₂²×D₄	1	4	yes	—
287	C₂×#95	C₂²×D₄	1	4	yes	—
288	C₂⁵	C₂×#120	1	2	yes	—
289	C₂⁵	C₂×#120	1	2	yes	—
290	C₂⁵	C₂×#120	1	2	yes	—
291	C₂⁵	C₂×#120	1	1	yes	characteristic
292	C₂⁵	C₂×#120	1	2	yes	—
293	C₂⁵	C₂×#120	1	2	yes	—
294	C₂⁵	C₂×#120	1	1	yes	characteristic
295	C₂⁵	C₂×#120	1	2	yes	—
296	C₂⁵	C₂×#120	1	2	yes	—
297	C₂⁵	C₂×#120	1	2	yes	—
298	C₂⁵	C₂×#120	1	1	yes	characteristic
299	C₂⁵	C₂×#120	1	2	yes	—
300	C₂⁵	C₂×#120	1	2	yes	—
301	C₂⁵	C₂×#120	1	2	yes	—
302	C₂⁵	C₂×#120	1	2	yes	—
303	C₂⁵	C₂×#120	1	2	yes	—
304	C₂⁵	C₂×#120	1	1	yes	characteristic
305	C₂⁵	C₂×#120	1	1	yes	characteristic
306	C₂⁵	C₂×#120	1	1	yes	characteristic
307	C₂⁵	#534	1	2	yes	—
308	C₂⁵	#534	1	2	yes	—
309	C₂⁵	#534	1	2	yes	—
310	C₂⁵	#534	1	2	yes	—
311	C₂⁵	C₂³×D₄	1	1	yes	characteristic
312	C₂²×Q₈	C₂×#120	1	4	yes	—
313	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
314	C₂²×D₄	C₂×#120	1	16	yes	—
315	C₂²×D₄	C₂×#120	1	4	yes	—
316	C₂²×D₄	D₄²	1	8	yes	—
317	C₂²×D₄	D₄²	1	8	yes	—
318	C₂³×C₄	C₂×#120	1	2	yes	—
319	C₂³×C₄	C₂×#120	1	2	yes	—
320	C₂³×C₄	C₂×#120	1	2	yes	—
321	C₂³×C₄	C₂×#120	1	2	yes	—
322	C₂³×C₄	C₂×#120	1	2	yes	—
323	C₂³×C₄	C₂×#120	1	2	yes	—
324	C₂³×C₄	C₂×#120	1	2	yes	—
325	C₂³×C₄	C₂×#120	1	2	yes	—
326	C₂³×C₄	#534	1	2	yes	—
327	C₂³×C₄	#534	1	2	yes	—
328	C₂³×C₄	C₂³×D₄	1	2	yes	—
329	C₂³×C₄	C₂³×D₄	1	2	yes	—
330	C₂³×C₄	C₂³×D₄	1	2	yes	—
331	C₂³×C₄	C₂³×D₄	1	2	yes	—
332	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
333	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
334	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
335	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
336	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
337	C₂×C₂²⋊C₄	D₄²	1	8	yes	—
338	C₂×C₂²⋊C₄	D₄²	1	8	yes	—
339	C₂×C₂²⋊C₄	D₄²	1	8	yes	—
340	C₂×C₂²⋊C₄	D₄²	1	8	yes	—
341	C₂×C₄²	C₂×#120	1	16	yes	—
342	C₂⁴	#2403	1	2	yes	—
343	C₂⁴	#2403	1	2	yes	—
344	C₂⁴	#2403	1	4	yes	—
345	C₂⁴	#2403	1	2	yes	—
346	C₂⁴	#2403	1	2	yes	—
347	C₂⁴	#2403	1	2	yes	—
348	C₂⁴	#2403	1	2	yes	—
349	C₂⁴	#2846	1	4	yes	—
350	C₂⁴	#2846	1	4	yes	—
351	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
352	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
353	C₂⁴	#3026	1	4	yes	—
354	C₂⁴	C₂²×#120	1	1	yes	characteristic
355	C₂⁴	C₂²×#120	1	1	yes	characteristic
356	C₂⁴	C₂²×#120	1	1	yes	characteristic
357	C₂⁴	C₂²×#120	1	1	yes	characteristic
358	C₂⁴	C₂×#534	1	1	yes	characteristic
359	C₂⁴	C₂×#534	1	1	yes	characteristic
360	C₂⁴	C₂×#534	1	1	yes	characteristic
361	C₂²×C₄	#2403	1	4	yes	—
362	C₂²×C₄	#2403	1	4	yes	—
363	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
364	C₂²×C₄	C₂²×#120	1	4	yes	—
365	C₂²×C₄	C₂×D₄²	1	4	yes	—
366	C₂²×C₄	C₂×D₄²	1	4	yes	—
367	C₂²×C₄	C₂×D₄²	1	4	yes	—
368	C₂²×C₄	#3484	1	4	yes	—
369	C₂²×C₄	#3484	1	4	yes	—
370	C₂²×C₄	#3484	1	4	yes	—
371	C₂³	#23897	1	4	yes	complemented
372	C₂³	#23900	1	4	yes	—
373	C₂³	#32898	1	8	yes	—
374	C₂³	C₂×#2403	1	1	yes	characteristic
375	C₂³	C₂×#2403	1	1	yes	characteristic
376	C₂³	C₂×#2403	1	1	yes	characteristic
377	C₂³	#34980	1	1	yes	characteristic
378	C₂³	#34980	1	1	yes	characteristic
379	C₂³	#34980	1	1	yes	characteristic
380	C₂³	C₂×#2846	1	1	yes	characteristic
381	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
382	C₂³	C₂×#3026	1	2	yes	—
383	C₂×C₄	D₄×#120	1	8	yes	—
384	C₂²	#612424	1	1	yes	characteristic
385	C₂²	C₂×#23897	1	2	yes	—
386	C₂²	#6437464	1	2	yes	—
387	C₂²	C₂×#23900	1	1	yes	characteristic
388	C₂²	#6437621	1	1	yes	characteristic
389	C₂²	#6470225	1	2	yes	—
390	C₂²	C₂×#32898	1	2	yes	—
391	C₂	#72210511	1	1	yes	characteristic
392	C₂	#72214832	1	1	yes	characteristic
393	C₂	#72235458	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#612424
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72235937	C₂	semidirect
2. #72235930	C₂	semidirect
3. #72235928	C₂	semidirect
4. #72235927	C₂	semidirect
5. #72235919	C₂	semidirect
6. #72235747	C₂	semidirect
7. #72235186	C₂	semidirect
8. #72234675	C₂	semidirect
9. #72232667	C₂	semidirect
10. #72231950	C₂	semidirect
11. #72231810	C₂	semidirect
12. #72219034	C₂	semidirect
13. #72218455	C₂	semidirect
14. #72210511	C₂	semidirect
15. C₂×#62817	C₂²	semidirect
16. C₂²×#3484	C₂²	semidirect
19. #7642350	C₂²	semidirect
21. #7642257	C₂²	semidirect
22. #7630945	C₂²	semidirect
24. C₂×#35347	C₂²	semidirect
25. C₂×#35346	C₂²	semidirect
26. #7626202	C₂²	semidirect
27. #6628867	C₂²	semidirect
28. #6437445	C₂²	semidirect
29. #6346594	C₂²	semidirect
30. #6346594	C₂²	semidirect
31. #635987	C₂²	semidirect
32. #617709	C₂²	semidirect
34. #612429	C₂²	semidirect
35. #517411	C₂²	semidirect
36. #515362	C₂²	semidirect
37. #515285	C₂²	semidirect
38. #393988	C₂²	semidirect
39. #392696	C₂²	semidirect
40. #392113	C₂²	semidirect
41. #359509	C₂²	semidirect
42. #234949	C₂²	semidirect
43. #234948	C₂²	semidirect
44. #201462	C₂²	semidirect
45. #201462	C₂²	semidirect
46. #201322	C₂²	semidirect
47. #201322	C₂²	semidirect
48. C₂×#8549	C₂²	semidirect
49. C₂×#8549	C₂²	semidirect
50. C₂×#8547	C₂²	semidirect
51. C₂×#8547	C₂²	semidirect
52. #186835	C₂²	semidirect
53. #185255	C₂²	semidirect
54. #185255	C₂²	semidirect
55. #184796	C₂²	semidirect
56. #184777	C₂²	semidirect
57. #112857	C₂²	semidirect
58. #111960	C₂²	semidirect
59. #111959	C₂²	semidirect
60. #108238	C₂²	semidirect
61. #106326	C₂²	semidirect
62. #106326	C₂²	semidirect
63. C₂³×H(5,𝔽₂)	C₂³	semidirect
70. C₂×#3484	D₄	semidirect
74. C₂²×#525	C₂³	semidirect
83. C₂²×#518	C₂³	semidirect
87. #36718	D₄	semidirect
88. #36717	D₄	semidirect
89. #36703	D₄	semidirect
91. #35395	D₄	semidirect
92. #35390	D₄	semidirect
93. #35367	D₄	semidirect
94. #35222	D₄	semidirect
98. C₂×#2406	C₂³	semidirect
101. C₂×#2404	C₂³	semidirect
104. #34171	D₄	semidirect
106. C₂×#2308	C₂³	semidirect
107. C₂×#2308	C₂³	semidirect
109. #20605	C₂³	semidirect
111. C₂×#1783	C₂³	semidirect
112. #20579	C₂³	semidirect
115. C₂×#1463	C₂³	semidirect
118. C₂×#1462	C₂³	semidirect
119. #15259	D₄	semidirect
120. #15258	D₄	semidirect
121. #14681	C₂³	semidirect
123. #13870	C₂³	semidirect
126. #13868	C₂³	semidirect
127. #10716	C₂³	semidirect
128. #7943	C₂³	semidirect
129. #7943	C₂³	semidirect
134. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
158. C₂×#543	C₂×D₄	semidirect
159. C₂×#543	C₂×D₄	semidirect
160. C₂×#538	C₂×D₄	semidirect
161. C₂×#538	C₂×D₄	semidirect
163. C₂×#535	C₂×D₄	semidirect
164. C₂×#534	C₂×D₄	semidirect
165. C₂×#534	C₂×D₄	semidirect
166. C₂²×#127	C₂×D₄	semidirect
167. C₂²×#124	C₂×D₄	semidirect
168. C₂×#525	C₂×D₄	semidirect
175. C₂×#518	C₂×D₄	semidirect
176. C₂×#518	C₂×D₄	semidirect
190. #2591	C₂×D₄	semidirect
191. #2583	C₂×D₄	semidirect
192. #2561	C₂×D₄	semidirect
193. #2539	C₂×D₄	semidirect
198. C₂×#393	C₂×D₄	semidirect
199. C₂×#393	C₂×D₄	semidirect
200. C₂×#392	C₂×D₄	semidirect
201. C₂×#392	C₂×D₄	semidirect
202. #2312	C₂×D₄	semidirect
203. #2312	C₂×D₄	semidirect
205. #2309	C₂×D₄	semidirect
206. #2280	C₂×D₄	semidirect
210. #2273	C₂×D₄	semidirect
211. #2273	C₂×D₄	semidirect
212. #1438	C₂×D₄	semidirect
213. #1437	C₂×D₄	semidirect
214. #1437	C₂×D₄	semidirect
260. C₂×#127	#120	semidirect
261. C₂×#124	#120	semidirect
282. #390	#120	semidirect
283. #390	#120	semidirect
371. C₂³	#23897	semidirect

Maximal subgroups

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

subgroup	index
#72235937	2
#72235930	2
#72235928	2
#72235927	2
#72235919	2
#72235747	2
#72235186	2
#72234675	2
#72232667	2
#72231950	2
#72231810	2
#72219034	2
#72218455	2
#72210511	2