Subgroups — #72317914

Order 2048.

At least 8614 conjugacy classes of subgroups; only the 790 normal subgroups are shown.

The subgroup lattice has 382 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72317906	C₂	1	1	yes	maximal, characteristic, complemented
2	#72317797	C₂	1	4	yes	maximal, complemented
3	#72317791	C₂	1	4	yes	maximal, complemented
4	#72317691	C₂	1	1	yes	maximal, characteristic, complemented
5	#72317686	C₂	1	2	yes	maximal, complemented
6	#72317653	C₂	1	1	yes	maximal, characteristic, complemented
7	#72263425	C₂	1	2	yes	maximal, complemented
8	#72262562	C₂	1	1	yes	maximal, characteristic, complemented
9	#72256552	C₂	1	1	yes	maximal, characteristic, complemented
10	#72240171	C₂	1	4	yes	maximal, complemented
11	#72240169	C₂	1	4	yes	maximal, complemented
12	C₂×#508087	C₂	1	2	yes	maximal, complemented
13	#72232741	C₂	1	1	yes	maximal, characteristic, complemented
14	#72225751	C₂	1	2	yes	maximal, complemented
15	#72216323	C₂	1	1	yes	maximal, characteristic, complemented
16	#10586472	C₂²	1	1	yes	characteristic
17	C₂²×#2684	C₂²	1	1	yes	characteristic, complemented
18	C₂×#36212	C₂²	1	1	yes	characteristic
19	#6524805	C₂²	1	2	yes	complemented
20	#6512843	C₂²	1	2	yes	complemented
21	#6508692	C₂²	1	2	yes	complemented
22	#6500010	C₂²	1	2	yes	complemented
23	#6470225	C₂²	1	2	yes	—
24	C₂×#24056	C₂²	1	2	yes	—
25	C₂×#23900	C₂²	1	2	yes	—
26	C₂×#23907	C₂²	1	2	yes	—
27	#6385971	C₂²	1	1	yes	characteristic
28	#4607728	C₂²	1	2	yes	complemented
29	#4607564	C₂²	1	2	yes	complemented
30	#2039947	C₂²	1	2	yes	complemented
31	#2039305	C₂²	1	2	yes	complemented
32	#848801	C₂²	1	1	yes	characteristic, complemented
33	#845297	C₂²	1	1	yes	characteristic, complemented
34	#649042	C₂²	1	1	yes	characteristic
35	#647656	C₂²	1	1	yes	characteristic
36	#559943	C₂²	1	1	yes	characteristic, complemented
37	#508087	C₂²	1	8	yes	complemented
38	#508087	C₂²	1	8	yes	complemented
39	#496225	C₂²	1	2	yes	complemented
40	C₂×#12852	C₂²	1	2	yes	complemented
41	C₂×#12694	C₂²	1	2	yes	complemented
42	C₂×#12687	C₂²	1	2	yes	complemented
43	#347043	C₂²	1	4	yes	—
44	#347042	C₂²	1	4	yes	—
45	#346459	C₂²	1	4	yes	complemented
46	#346456	C₂²	1	4	yes	complemented
47	#188087	C₂²	1	1	yes	characteristic
48	#188035	C₂²	1	1	yes	characteristic
49	#187928	C₂²	1	2	yes	—
50	#186808	C₂²	1	2	yes	—
51	#144415	C₂²	1	8	yes	complemented
52	#144412	C₂²	1	8	yes	complemented
53	#144388	C₂²	1	8	yes	complemented
54	#144366	C₂²	1	8	yes	complemented
55	#139816	C₂²	1	8	yes	complemented
56	#139795	C₂²	1	4	yes	complemented
57	#139793	C₂²	1	4	yes	complemented
58	#139764	C₂²	1	8	yes	complemented
59	#139720	C₂²	1	4	yes	complemented
60	#139716	C₂²	1	4	yes	complemented
61	#133972	C₂²	1	2	yes	complemented
62	#133925	C₂²	1	2	yes	complemented
63	#133893	C₂²	1	2	yes	complemented
64	#133849	C₂²	1	2	yes	complemented
65	#128073	C₂²	1	2	yes	complemented
66	#128058	C₂²	1	2	yes	complemented
67	C₂⁴×#41	D₄	1	1	yes	characteristic, complemented
68	#62818	C₂³	1	2	yes	—
69	#62817	C₂³	1	2	yes	—
70	C₂×#3484	C₂³	1	2	yes	—
71	C₂²×D₄²	C₂³	1	1	yes	characteristic
72	C₂³×#124	C₂³	1	1	yes	characteristic
73	C₂³×#120	D₄	1	1	yes	characteristic, complemented
74	C₂³×#120	C₂³	1	1	yes	characteristic
75	C₂×#2684	C₂³	1	2	yes	complemented
76	C₂×#2684	C₂³	1	2	yes	complemented
77	C₂×#2849	D₄	1	1	yes	characteristic, complemented
78	C₂×#2849	C₂³	1	1	yes	characteristic
79	C₂×#2847	C₂³	1	1	yes	characteristic
80	C₂×#2846	D₄	1	1	yes	characteristic, complemented
81	C₂×#2436	D₄	1	1	yes	characteristic, complemented
82	C₂×#2436	C₂³	1	1	yes	characteristic
83	C₂×#2409	D₄	1	1	yes	characteristic, complemented
84	C₂×#2409	D₄	1	1	yes	characteristic, complemented
85	C₂×#2410	D₄	1	1	yes	characteristic, complemented
86	C₂×#2410	C₂³	1	1	yes	characteristic
87	C₂×#2403	D₄	1	1	yes	characteristic, complemented
88	C₂×#2403	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
90	C₂×C₄×#120	D₄	1	1	yes	characteristic, complemented
91	C₂²×#386	D₄	1	1	yes	characteristic, complemented
92	C₂²×#386	C₂³	1	1	yes	characteristic
93	#24056	D₄	1	8	yes	complemented
94	#24056	C₂³	1	4	yes	—
95	#24056	C₂³	1	4	yes	—
96	#24056	C₂³	1	4	yes	—
97	#23907	C₂³	1	8	yes	—
98	#23900	C₂³	1	4	yes	—
99	#23900	C₂³	1	8	yes	—
100	#21793	C₂³	1	2	yes	—
101	#21746	C₂³	1	2	yes	—
102	C₂×#1867	D₄	1	4	yes	complemented
103	C₂×#1790	D₄	1	4	yes	complemented
104	C₂×#1783	C₂³	1	2	yes	—
105	C₂×#1781	C₂³	1	2	yes	—
106	C₂×#1781	C₂³	1	2	yes	—
107	#15947	C₂³	1	2	yes	—
108	#15947	C₂³	1	2	yes	complemented
109	#15784	C₂³	1	2	yes	complemented
110	#15673	D₄	1	2	yes	complemented
111	#15673	C₂³	1	2	yes	—
112	#15266	C₂³	1	2	yes	complemented
113	#15259	D₄	1	2	yes	complemented
114	#15259	C₂³	1	2	yes	—
115	#15259	C₂³	1	2	yes	complemented
116	#15258	D₄	1	2	yes	complemented
117	#15257	D₄	1	2	yes	complemented
118	#15257	C₂³	1	2	yes	—
119	#14698	D₄	1	1	yes	characteristic, complemented
120	#14666	C₂³	1	2	yes	complemented
121	#14516	C₂³	1	2	yes	complemented
122	#14134	D₄	1	1	yes	characteristic, complemented
123	#13902	C₂³	1	1	yes	characteristic
124	#13867	D₄	1	1	yes	characteristic, complemented
125	#13867	C₂³	1	1	yes	characteristic
126	C₄×#386	D₄	1	1	yes	characteristic, complemented
127	#12852	C₂³	1	4	yes	complemented
128	#12852	C₂³	1	4	yes	complemented
129	#12852	C₂³	1	4	yes	complemented
130	#12694	C₂³	1	8	yes	complemented
131	#12687	C₂³	1	8	yes	complemented
132	#12687	C₂³	1	4	yes	complemented
133	#8549	C₂³	1	2	yes	—
134	#8547	C₂³	1	2	yes	—
135	#8542	C₂³	1	2	yes	—
136	#8541	C₂³	1	2	yes	—
137	#8534	C₂³	1	8	yes	—
138	#8453	C₂³	1	8	yes	—
139	#7307	C₂³	1	8	yes	complemented
140	#7304	C₂³	1	8	yes	complemented
141	C₂⁷	C₂×D₄	1	1	yes	characteristic
142	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
143	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
145	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
146	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
147	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
150	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
151	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
152	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
153	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
154	#3484	C₂×D₄	1	4	yes	—
155	#3484	C₂⁴	1	4	yes	—
156	C₂²×#127	C₂×D₄	1	1	yes	characteristic
157	C₂²×#124	C₂×D₄	1	2	yes	—
158	C₂²×#124	C₂⁴	1	2	yes	—
159	C₂²×#121	C₂×D₄	1	1	yes	characteristic
160	C₂²×#121	C₂×D₄	1	1	yes	characteristic
161	C₂²×#121	C₂×D₄	1	1	yes	characteristic
162	C₂²×#121	C₂⁴	1	1	yes	characteristic
163	C₂²×#120	C₂×D₄	1	1	yes	characteristic
164	C₂²×#120	C₂×D₄	1	2	yes	—
165	C₂²×#120	C₂×D₄	1	2	yes	—
166	C₂²×#120	C₂×D₄	1	2	yes	—
167	C₂²×#120	C₂×D₄	1	2	yes	—
168	C₂²×#120	C₂×D₄	1	1	yes	characteristic
169	C₂²×#120	C₂×D₄	1	1	yes	characteristic
170	C₂²×#120	C₂×D₄	1	1	yes	characteristic
171	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
172	C₂²×#120	C₂⁴	1	2	yes	—
173	C₂²×#120	C₂⁴	1	1	yes	characteristic
174	C₂²×#120	C₂⁴	1	1	yes	characteristic
175	C₂×#518	C₂×D₄	1	2	yes	—
176	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
178	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
179	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
180	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
182	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
183	C₂²×#99	C₂×D₄	1	4	yes	—
184	C₂×#395	C₂×D₄	1	2	yes	complemented
185	C₂×#393	C₂×D₄	1	2	yes	complemented
186	C₂×#393	C₂×D₄	1	2	yes	complemented
187	C₂×#393	C₂×D₄	1	2	yes	complemented
188	C₂×#386	C₂×D₄	1	4	yes	—
189	C₂×#386	C₂×D₄	1	4	yes	—
190	C₂×#386	C₂×D₄	1	1	yes	characteristic
191	C₂×#386	C₂×D₄	1	1	yes	characteristic
192	C₂×#386	C₂×D₄	1	1	yes	characteristic
193	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
194	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
195	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
196	C₂×#386	C₂⁴	1	1	yes	characteristic
197	C₂×#386	C₂⁴	1	1	yes	characteristic
198	C₂×#386	C₂⁴	1	1	yes	characteristic
199	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
200	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
201	C₂×#385	C₂×D₄	1	1	yes	characteristic, complemented
202	C₂×#380	C₂×D₄	1	1	yes	characteristic
203	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
204	C₂×#379	C₂×D₄	1	1	yes	characteristic
205	C₂×#379	C₂×D₄	1	2	yes	—
206	C₂×#379	C₂×D₄	1	1	yes	characteristic
207	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
208	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
209	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
211	#1867	C₂×D₄	1	8	yes	complemented
212	#1867	C₂×D₄	1	8	yes	complemented
213	#1790	C₂×D₄	1	8	yes	complemented
214	#1790	C₂×D₄	1	8	yes	complemented
215	#1783	C₂⁴	1	4	yes	—
216	#1781	C₂×D₄	1	4	yes	—
217	#1781	C₂⁴	1	4	yes	—
218	#1781	C₂⁴	1	4	yes	—
219	#1440	C₂×D₄	1	2	yes	—
220	#1438	C₂×D₄	1	2	yes	—
221	#1438	C₂×D₄	1	2	yes	—
222	#1438	C₂×D₄	1	2	yes	—
223	#1438	C₂×D₄	1	2	yes	—
224	#1438	C₂×D₄	1	2	yes	—
225	#1438	C₂⁴	1	2	yes	—
226	#1438	C₂⁴	1	2	yes	—
227	#1437	C₂×D₄	1	2	yes	complemented
228	#1437	C₂×D₄	1	2	yes	complemented
229	#1437	C₂×D₄	1	2	yes	complemented
230	#1436	C₂×D₄	1	2	yes	complemented
231	C₂⁶	#120	1	1	yes	characteristic
232	C₂⁶	C₂²×D₄	1	1	yes	characteristic
233	C₂⁶	C₂²×D₄	1	1	yes	characteristic
234	C₂⁶	C₂²×D₄	1	1	yes	characteristic
235	C₂⁶	C₂²×D₄	1	1	yes	characteristic
236	C₂⁶	C₂²×D₄	1	2	yes	—
237	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
238	C₂³×Q₈	C₂²×D₄	1	2	yes	—
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	C₂²×D₄	1	1	yes	characteristic
248	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
249	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
250	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
251	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
252	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
253	C₂³×D₄	C₂²×D₄	1	2	yes	—
254	C₂³×D₄	C₂²×D₄	1	2	yes	—
255	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
256	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
257	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
258	C₂³×D₄	C₂⁵	1	1	yes	characteristic
259	C₂⁴×C₄	#120	1	1	yes	characteristic
260	C₂⁴×C₄	#120	1	1	yes	characteristic
261	C₂⁴×C₄	#120	1	4	yes	—
262	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
263	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
264	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
265	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
266	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
267	#518	C₂²×D₄	1	4	yes	—
268	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
273	C₂²×C₂²⋊C₄	#120	1	4	yes	—
274	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
278	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
279	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
281	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
282	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
283	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
285	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
286	C₂²×C₄²	#120	1	1	yes	characteristic
287	C₂²×C₄²	C₂²×D₄	1	2	yes	—
288	C₂×#99	C₂²×D₄	1	8	yes	—
289	#386	#120	1	2	yes	—
290	#386	#120	1	2	yes	—
291	#386	#120	1	2	yes	—
292	#386	#120	1	2	yes	—
293	#386	C₂²×D₄	1	4	yes	—
294	#386	C₂²×D₄	1	4	yes	—
295	C₂×#95	C₂²×D₄	1	2	yes	—
296	C₂×#95	C₂²×D₄	1	2	yes	—
297	C₂⁵	C₂×#120	1	1	yes	characteristic
298	C₂⁵	C₂×#120	1	1	yes	characteristic
299	C₂⁵	C₂×#120	1	2	yes	—
300	C₂⁵	C₂×#120	1	1	yes	characteristic
301	C₂⁵	C₂×#120	1	1	yes	characteristic
302	C₂⁵	C₂×#120	1	1	yes	characteristic
303	C₂⁵	C₂×#120	1	1	yes	characteristic
304	C₂⁵	#534	1	2	yes	—
305	C₂⁵	D₄²	1	2	yes	—
306	C₂⁵	D₄²	1	2	yes	—
307	C₂⁵	C₂³×D₄	1	1	yes	characteristic
308	C₂⁵	C₂³×D₄	1	1	yes	characteristic
309	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
310	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
311	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
312	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
313	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
314	C₂²×D₄	C₂×#120	1	1	yes	characteristic
315	C₂²×D₄	C₂×#120	1	1	yes	characteristic
316	C₂²×D₄	#534	1	1	yes	characteristic
317	C₂²×D₄	#534	1	1	yes	characteristic
318	C₂²×D₄	D₄²	1	2	yes	—
319	C₂²×D₄	D₄²	1	2	yes	—
320	C₂²×D₄	D₄²	1	2	yes	—
321	C₂²×D₄	D₄²	1	2	yes	—
322	C₂²×D₄	C₂³×D₄	1	2	yes	—
323	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
324	C₂³×C₄	C₂×#120	1	1	yes	characteristic
325	C₂³×C₄	C₂×#120	1	1	yes	characteristic
326	C₂³×C₄	C₂×#120	1	1	yes	characteristic
327	C₂³×C₄	C₂×#120	1	1	yes	characteristic
328	C₂³×C₄	C₂×#120	1	1	yes	characteristic
329	C₂³×C₄	C₂×#120	1	1	yes	characteristic
330	C₂³×C₄	C₂×#120	1	2	yes	—
331	C₂³×C₄	C₂×#120	1	2	yes	—
332	C₂³×C₄	D₄²	1	2	yes	—
333	C₂³×C₄	D₄²	1	2	yes	—
334	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
336	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
337	C₂⁴	#2403	1	2	yes	—
338	C₂⁴	#2403	1	1	yes	characteristic
339	C₂⁴	#2403	1	2	yes	—
340	C₂⁴	#2403	1	1	yes	characteristic
341	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
342	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
343	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
344	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
345	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
346	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
347	C₂⁴	C₂²×#120	1	1	yes	characteristic
348	C₂⁴	C₂²×#120	1	1	yes	characteristic
349	C₂⁴	C₂×#534	1	1	yes	characteristic
350	C₂⁴	C₂×D₄²	1	2	yes	—
351	C₂×D₄	#2199	1	4	yes	—
352	C₂×D₄	#3027	1	4	yes	—
353	C₂²×C₄	#2403	1	1	yes	characteristic
354	C₂²×C₄	#2403	1	1	yes	characteristic
355	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
356	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
357	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
358	C₂²×C₄	C₂×D₄²	1	2	yes	—
359	C₂³	#23900	1	2	yes	—
360	C₂³	#23900	1	2	yes	—
361	C₂³	#23904	1	2	yes	—
362	C₂³	C₂×#2199	1	2	yes	—
363	C₂³	C₂×#2199	1	2	yes	—
364	C₂³	#33551	1	2	yes	—
365	C₂³	C₂×#2403	1	1	yes	characteristic
366	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
367	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
368	C₂³	C₂×#3027	1	2	yes	—
369	C₂×C₄	#23904	1	2	yes	—
370	C₂×C₄	C₂×#2199	1	2	yes	—
371	C₂²	#499795	1	4	yes	—
372	C₂²	C₂×#23900	1	1	yes	characteristic
373	C₂²	C₂×#23904	1	1	yes	characteristic
374	C₂²	#6437629	1	1	yes	characteristic
375	C₂²	C₂²×#2199	1	1	yes	characteristic
376	C₂²	C₂×#33551	1	1	yes	characteristic
377	C₂²	#7622881	1	2	yes	—
378	C₂	C₂×#499795	1	1	yes	characteristic
379	C₂	#72317570	1	1	yes	characteristic
380	C₂	#72317603	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ 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. #72317906	C₂	semidirect
2. #72317797	C₂	semidirect
3. #72317791	C₂	semidirect
4. #72317691	C₂	semidirect
5. #72317686	C₂	semidirect
6. #72317653	C₂	semidirect
7. #72263425	C₂	semidirect
8. #72262562	C₂	semidirect
9. #72256552	C₂	semidirect
10. #72240171	C₂	semidirect
11. #72240169	C₂	semidirect
12. C₂×#508087	C₂	semidirect
13. #72232741	C₂	semidirect
14. #72225751	C₂	semidirect
15. #72216323	C₂	semidirect
17. C₂²×#2684	C₂²	semidirect
19. #6524805	C₂²	semidirect
20. #6512843	C₂²	semidirect
21. #6508692	C₂²	semidirect
22. #6500010	C₂²	semidirect
28. #4607728	C₂²	semidirect
29. #4607564	C₂²	semidirect
30. #2039947	C₂²	semidirect
31. #2039305	C₂²	semidirect
32. #848801	C₂²	semidirect
33. #845297	C₂²	semidirect
36. #559943	C₂²	semidirect
37. #508087	C₂²	semidirect
38. #508087	C₂²	semidirect
39. #496225	C₂²	semidirect
40. C₂×#12852	C₂²	semidirect
41. C₂×#12694	C₂²	semidirect
42. C₂×#12687	C₂²	semidirect
45. #346459	C₂²	semidirect
46. #346456	C₂²	semidirect
51. #144415	C₂²	semidirect
52. #144412	C₂²	semidirect
53. #144388	C₂²	semidirect
54. #144366	C₂²	semidirect
55. #139816	C₂²	semidirect
56. #139795	C₂²	semidirect
57. #139793	C₂²	semidirect
58. #139764	C₂²	semidirect
59. #139720	C₂²	semidirect
60. #139716	C₂²	semidirect
61. #133972	C₂²	semidirect
62. #133925	C₂²	semidirect
63. #133893	C₂²	semidirect
64. #133849	C₂²	semidirect
65. #128073	C₂²	semidirect
66. #128058	C₂²	semidirect
67. C₂⁴×#41	D₄	semidirect
73. C₂³×#120	D₄	semidirect
75. C₂×#2684	C₂³	semidirect
76. C₂×#2684	C₂³	semidirect
77. C₂×#2849	D₄	semidirect
80. C₂×#2846	D₄	semidirect
81. C₂×#2436	D₄	semidirect
83. C₂×#2409	D₄	semidirect
84. C₂×#2409	D₄	semidirect
85. C₂×#2410	D₄	semidirect
87. C₂×#2403	D₄	semidirect
89. C₂×D₄×C₂²⋊C₄	D₄	semidirect
90. C₂×C₄×#120	D₄	semidirect
91. C₂²×#386	D₄	semidirect
93. #24056	D₄	semidirect
102. C₂×#1867	D₄	semidirect
103. C₂×#1790	D₄	semidirect
108. #15947	C₂³	semidirect
109. #15784	C₂³	semidirect
110. #15673	D₄	semidirect
112. #15266	C₂³	semidirect
113. #15259	D₄	semidirect
115. #15259	C₂³	semidirect
116. #15258	D₄	semidirect
117. #15257	D₄	semidirect
119. #14698	D₄	semidirect
120. #14666	C₂³	semidirect
121. #14516	C₂³	semidirect
122. #14134	D₄	semidirect
124. #13867	D₄	semidirect
126. C₄×#386	D₄	semidirect
127. #12852	C₂³	semidirect
128. #12852	C₂³	semidirect
129. #12852	C₂³	semidirect
130. #12694	C₂³	semidirect
131. #12687	C₂³	semidirect
132. #12687	C₂³	semidirect
139. #7307	C₂³	semidirect
140. #7304	C₂³	semidirect
144. C₂⁴×Q₈	C₂×D₄	semidirect
149. C₂⁴×D₄	C₂×D₄	semidirect
152. C₂⁵×C₄	C₂×D₄	semidirect
153. C₂⁵×C₄	C₂×D₄	semidirect
171. C₂²×#120	C₂×D₄	semidirect
181. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
184. C₂×#395	C₂×D₄	semidirect
185. C₂×#393	C₂×D₄	semidirect
186. C₂×#393	C₂×D₄	semidirect
187. C₂×#393	C₂×D₄	semidirect
193. C₂×#386	C₂×D₄	semidirect
194. C₂×#386	C₂×D₄	semidirect
195. C₂×#386	C₂×D₄	semidirect
199. C₂×#385	C₂×D₄	semidirect
200. C₂×#385	C₂×D₄	semidirect
201. C₂×#385	C₂×D₄	semidirect
203. C₂×#380	C₂×D₄	semidirect
207. C₂×#379	C₂×D₄	semidirect
208. C₂×#379	C₂×D₄	semidirect
210. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
211. #1867	C₂×D₄	semidirect
212. #1867	C₂×D₄	semidirect
213. #1790	C₂×D₄	semidirect
214. #1790	C₂×D₄	semidirect
227. #1437	C₂×D₄	semidirect
228. #1437	C₂×D₄	semidirect
229. #1437	C₂×D₄	semidirect
230. #1436	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72317906	2
#72317797	2
#72317791	2
#72317691	2
#72317686	2
#72317653	2
#72263425	2
#72262562	2
#72256552	2
#72240171	2
#72240169	2
C₂×#508087	2
#72232741	2
#72225751	2
#72216323	2