Subgroups — #72317676

Order 2048.

At least 8770 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	#72317671	C₂	1	1	yes	maximal, characteristic, complemented
2	#72317668	C₂	1	4	yes	maximal, complemented
3	#72317660	C₂	1	2	yes	maximal, complemented
4	#72317653	C₂	1	1	yes	maximal, characteristic, complemented
5	#72317649	C₂	1	1	yes	maximal, characteristic, complemented
6	#72317643	C₂	1	4	yes	maximal, complemented
7	#72263425	C₂	1	2	yes	maximal, complemented
8	#72262562	C₂	1	1	yes	maximal, characteristic, complemented
9	#72262500	C₂	1	1	yes	maximal, characteristic, complemented
10	#72240175	C₂	1	4	yes	maximal, complemented
11	C₂×#508087	C₂	1	2	yes	maximal, complemented
12	#72232733	C₂	1	1	yes	maximal, characteristic, complemented
13	#72231467	C₂	1	2	yes	maximal, complemented
14	#72227862	C₂	1	4	yes	maximal, complemented
15	#72216616	C₂	1	1	yes	maximal, characteristic
16	#10586472	C₂²	1	1	yes	characteristic
17	C₂²×#2684	C₂²	1	1	yes	characteristic, complemented
18	C₂×D₄×#120	C₂²	1	1	yes	characteristic
19	#6516837	C₂²	1	2	yes	—
20	#6512843	C₂²	1	2	yes	—
21	#6500010	C₂²	1	2	yes	—
22	#6499867	C₂²	1	2	yes	—
23	#6470225	C₂²	1	2	yes	—
24	C₂×#24056	C₂²	1	2	yes	complemented
25	C₂×#23900	C₂²	1	2	yes	—
26	C₂×#23907	C₂²	1	2	yes	complemented
27	#6385971	C₂²	1	1	yes	characteristic
28	#2924786	C₂²	1	2	yes	complemented
29	#2924619	C₂²	1	2	yes	complemented
30	#2032743	C₂²	1	2	yes	complemented
31	#2032505	C₂²	1	2	yes	complemented
32	#848801	C₂²	1	1	yes	characteristic, complemented
33	#847893	C₂²	1	1	yes	characteristic, complemented
34	#663621	C₂²	1	1	yes	characteristic
35	#649042	C₂²	1	1	yes	characteristic
36	#531607	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	#347052	C₂²	1	4	yes	complemented
44	#347048	C₂²	1	4	yes	complemented
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	complemented
50	#186808	C₂²	1	2	yes	complemented
51	#144421	C₂²	1	8	yes	complemented
52	#144415	C₂²	1	8	yes	complemented
53	#144412	C₂²	1	8	yes	complemented
54	#144388	C₂²	1	8	yes	complemented
55	#139848	C₂²	1	4	yes	complemented
56	#139828	C₂²	1	4	yes	complemented
57	#139795	C₂²	1	4	yes	complemented
58	#139773	C₂²	1	8	yes	complemented
59	#139720	C₂²	1	4	yes	complemented
60	#139700	C₂²	1	8	yes	complemented
61	#134020	C₂²	1	2	yes	complemented
62	#133893	C₂²	1	2	yes	complemented
63	#133849	C₂²	1	2	yes	complemented
64	#133822	C₂²	1	2	yes	complemented
65	#128073	C₂²	1	2	yes	complemented
66	#128058	C₂²	1	2	yes	complemented
67	C₂⁵×D₄	D₄	1	1	yes	characteristic
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
74	C₂³×#120	C₂³	1	1	yes	characteristic
75	C₂²×B(4,𝔽₂)	D₄	1	4	yes	—
76	C₂×#2684	C₂³	1	2	yes	complemented
77	C₂×#2684	C₂³	1	2	yes	complemented
78	C₂×#2849	D₄	1	1	yes	characteristic, complemented
79	C₂×#2847	C₂³	1	1	yes	characteristic
80	C₂×#2846	D₄	1	1	yes	characteristic
81	C₂×#2846	C₂³	1	1	yes	characteristic
82	C₂×#2436	D₄	1	1	yes	characteristic, complemented
83	C₂×#2409	D₄	1	1	yes	characteristic, complemented
84	C₂×#2433	C₂³	1	1	yes	characteristic
85	C₂×#2408	D₄	1	1	yes	characteristic
86	C₂×#2410	D₄	1	1	yes	characteristic
87	C₂×#2410	C₂³	1	1	yes	characteristic
88	C₂×#2403	D₄	1	1	yes	characteristic
89	C₂×#2403	C₂³	1	1	yes	characteristic
90	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
91	C₂×C₄×#120	D₄	1	1	yes	characteristic
92	C₂²×#386	D₄	1	1	yes	characteristic, complemented
93	C₂²×#386	C₂³	1	1	yes	characteristic
94	#24056	C₂³	1	4	yes	—
95	#24056	C₂³	1	8	yes	—
96	#23907	C₂³	1	8	yes	—
97	#23900	D₄	1	8	yes	—
98	#23900	C₂³	1	4	yes	—
99	#23900	C₂³	1	4	yes	—
100	#23900	C₂³	1	4	yes	—
101	#21793	C₂³	1	2	yes	—
102	#21746	C₂³	1	2	yes	—
103	C₂×#1889	D₄	1	4	yes	—
104	C₂×#1783	C₂³	1	2	yes	—
105	C₂×#1781	C₂³	1	2	yes	—
106	C₂×#1781	C₂³	1	2	yes	—
107	#16014	C₂³	1	2	yes	complemented
108	#15984	D₄	1	2	yes	complemented
109	#15984	C₂³	1	2	yes	—
110	#15948	C₂³	1	2	yes	—
111	#15784	C₂³	1	2	yes	complemented
112	#15673	D₄	1	2	yes	complemented
113	#15673	C₂³	1	2	yes	—
114	#15266	C₂³	1	2	yes	complemented
115	#15261	D₄	1	2	yes	complemented
116	#15259	D₄	1	2	yes	complemented
117	#15259	C₂³	1	2	yes	—
118	#15259	C₂³	1	2	yes	complemented
119	#14698	D₄	1	1	yes	characteristic, complemented
120	#14358	C₂³	1	2	yes	complemented
121	#14134	D₄	1	1	yes	characteristic, complemented
122	#14134	C₂³	1	2	yes	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	8	yes	complemented
128	#12852	C₂³	1	4	yes	complemented
129	#12694	C₂³	1	8	yes	complemented
130	#12687	C₂³	1	4	yes	complemented
131	#12687	C₂³	1	4	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	C₂⁷	C₂×D₄	1	1	yes	characteristic
143	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
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
150	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
152	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
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	complemented
158	C₂²×#124	C₂⁴	1	2	yes	—
159	C₂²×#123	C₂×D₄	1	2	yes	complemented
160	C₂²×#121	C₂×D₄	1	1	yes	characteristic
161	C₂²×#121	C₂×D₄	1	1	yes	characteristic
162	C₂²×#121	C₂×D₄	1	1	yes	characteristic
163	C₂²×#121	C₂⁴	1	1	yes	characteristic
164	C₂²×#120	C₂×D₄	1	4	yes	—
165	C₂²×#120	C₂×D₄	1	4	yes	—
166	C₂²×#120	C₂×D₄	1	1	yes	characteristic
167	C₂²×#120	C₂×D₄	1	1	yes	characteristic
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
172	C₂²×#120	C₂×D₄	1	1	yes	characteristic
173	C₂²×#120	C₂×D₄	1	1	yes	characteristic
174	C₂²×#120	C₂×D₄	1	1	yes	characteristic
175	C₂²×#120	C₂⁴	1	1	yes	characteristic
176	C₂²×#120	C₂⁴	1	1	yes	characteristic
177	C₂²×#120	C₂⁴	1	1	yes	characteristic
178	C₂²×#120	C₂⁴	1	1	yes	characteristic
179	C₂×#518	C₂×D₄	1	2	yes	—
180	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×D₄	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, complemented
185	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
186	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
187	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	—
188	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	—
189	C₂²×#99	C₂×D₄	1	4	yes	—
190	C₂×#395	C₂×D₄	1	2	yes	complemented
191	C₂×#393	C₂×D₄	1	2	yes	complemented
192	C₂×#393	C₂×D₄	1	2	yes	complemented
193	C₂×#393	C₂×D₄	1	2	yes	complemented
194	C₂×#386	C₂×D₄	1	1	yes	characteristic
195	C₂×#386	C₂×D₄	1	1	yes	characteristic
196	C₂×#386	C₂×D₄	1	2	yes	complemented
197	C₂×#386	C₂×D₄	1	2	yes	complemented
198	C₂×#386	C₂×D₄	1	2	yes	complemented
199	C₂×#386	C₂⁴	1	1	yes	characteristic
200	C₂×#386	C₂⁴	1	2	yes	—
201	C₂×#385	C₂×D₄	1	1	yes	characteristic
202	C₂×#381	C₂×D₄	1	2	yes	complemented
203	C₂×#380	C₂×D₄	1	1	yes	characteristic
204	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
205	C₂×#379	C₂×D₄	1	1	yes	characteristic
206	C₂×#379	C₂×D₄	1	1	yes	characteristic
207	C₂×#379	C₂×D₄	1	1	yes	characteristic
208	C₂×#379	C₂×D₄	1	1	yes	characteristic
209	C₂×#379	C₂×D₄	1	1	yes	characteristic
210	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
212	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
213	#1889	C₂×D₄	1	8	yes	—
214	#1889	C₂×D₄	1	8	yes	—
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	complemented
220	#1438	C₂×D₄	1	2	yes	complemented
221	#1438	C₂×D₄	1	2	yes	complemented
222	#1438	C₂×D₄	1	2	yes	complemented
223	#1438	C₂×D₄	1	2	yes	complemented
224	#1438	C₂×D₄	1	2	yes	complemented
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	#120	1	4	yes	—
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	1	yes	characteristic
237	C₂⁶	C₂²×D₄	1	1	yes	characteristic
238	C₂⁶	C₂²×D₄	1	1	yes	characteristic
239	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
240	C₂³×Q₈	C₂²×D₄	1	2	yes	—
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	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	1	yes	characteristic
254	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
255	C₂³×D₄	C₂²×D₄	1	2	yes	—
256	C₂³×D₄	C₂²×D₄	1	2	yes	—
257	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
258	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
259	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
260	C₂³×D₄	C₂⁵	1	1	yes	characteristic
261	C₂⁴×C₄	#120	1	1	yes	characteristic
262	C₂⁴×C₄	#120	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	2	yes	—
267	C₂×#120	#120	1	2	yes	—
268	C₂×#120	#120	1	2	yes	—
269	C₂×#120	#120	1	2	yes	—
270	C₂×#120	#120	1	2	yes	—
271	C₂×#120	C₂²×D₄	1	4	yes	—
272	C₂×#120	C₂²×D₄	1	4	yes	—
273	#518	C₂²×D₄	1	4	yes	—
274	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
278	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
279	C₂²×C₂²⋊C₄	#120	1	4	yes	—
280	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
285	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
286	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
287	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
288	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
289	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
290	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
291	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
292	C₂²×C₄²	#120	1	1	yes	characteristic
293	C₂²×C₄²	C₂²×D₄	1	2	yes	—
294	C₂×#99	C₂²×D₄	1	8	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	2	yes	—
302	C₂⁵	C₂×#120	1	2	yes	—
303	C₂⁵	C₂×#120	1	1	yes	characteristic
304	C₂⁵	C₂×#120	1	1	yes	characteristic
305	C₂⁵	C₂×#120	1	1	yes	characteristic
306	C₂⁵	#534	1	2	yes	—
307	C₂⁵	D₄²	1	2	yes	—
308	C₂⁵	D₄²	1	2	yes	—
309	C₂⁵	C₂³×D₄	1	1	yes	characteristic
310	C₂⁵	C₂³×D₄	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	1	yes	characteristic
314	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
315	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
316	C₂²×D₄	C₂×#120	1	1	yes	characteristic
317	C₂²×D₄	C₂×#120	1	1	yes	characteristic
318	C₂²×D₄	#534	1	1	yes	characteristic
319	C₂²×D₄	#534	1	1	yes	characteristic
320	C₂²×D₄	D₄²	1	2	yes	—
321	C₂²×D₄	D₄²	1	2	yes	—
322	C₂²×D₄	D₄²	1	2	yes	—
323	C₂²×D₄	D₄²	1	2	yes	—
324	C₂²×D₄	C₂³×D₄	1	2	yes	—
325	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
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	1	yes	characteristic
331	C₂³×C₄	C₂×#120	1	1	yes	characteristic
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	2	yes	—
339	C₂⁴	#2403	1	1	yes	characteristic
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	#2197	1	4	yes	—
352	C₂×D₄	#3026	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	#23903	1	2	yes	—
362	C₂³	C₂×#2197	1	2	yes	—
363	C₂³	C₂×#2197	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×#3026	1	2	yes	—
369	C₂×C₄	#23903	1	2	yes	—
370	C₂×C₄	C₂×#2197	1	2	yes	—
371	C₂²	#499789	1	4	yes	—
372	C₂²	C₂×#23900	1	1	yes	characteristic
373	C₂²	C₂×#23903	1	1	yes	characteristic
374	C₂²	#6437629	1	1	yes	characteristic
375	C₂²	C₂²×#2197	1	1	yes	characteristic
376	C₂²	C₂×#33551	1	1	yes	characteristic
377	C₂²	#7622886	1	2	yes	—
378	C₂	C₂×#499789	1	1	yes	characteristic
379	C₂	#72317558	1	1	yes	characteristic
380	C₂	#72317607	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
prime radical	#72216616	C₂
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. #72317671	C₂	semidirect
2. #72317668	C₂	semidirect
3. #72317660	C₂	semidirect
4. #72317653	C₂	semidirect
5. #72317649	C₂	semidirect
6. #72317643	C₂	semidirect
7. #72263425	C₂	semidirect
8. #72262562	C₂	semidirect
9. #72262500	C₂	semidirect
10. #72240175	C₂	semidirect
11. C₂×#508087	C₂	semidirect
12. #72232733	C₂	semidirect
13. #72231467	C₂	semidirect
14. #72227862	C₂	semidirect
17. C₂²×#2684	C₂²	semidirect
24. C₂×#24056	C₂²	semidirect
26. C₂×#23907	C₂²	semidirect
28. #2924786	C₂²	semidirect
29. #2924619	C₂²	semidirect
30. #2032743	C₂²	semidirect
31. #2032505	C₂²	semidirect
32. #848801	C₂²	semidirect
33. #847893	C₂²	semidirect
36. #531607	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
43. #347052	C₂²	semidirect
44. #347048	C₂²	semidirect
45. #346459	C₂²	semidirect
46. #346456	C₂²	semidirect
49. #187928	C₂²	semidirect
50. #186808	C₂²	semidirect
51. #144421	C₂²	semidirect
52. #144415	C₂²	semidirect
53. #144412	C₂²	semidirect
54. #144388	C₂²	semidirect
55. #139848	C₂²	semidirect
56. #139828	C₂²	semidirect
57. #139795	C₂²	semidirect
58. #139773	C₂²	semidirect
59. #139720	C₂²	semidirect
60. #139700	C₂²	semidirect
61. #134020	C₂²	semidirect
62. #133893	C₂²	semidirect
63. #133849	C₂²	semidirect
64. #133822	C₂²	semidirect
65. #128073	C₂²	semidirect
66. #128058	C₂²	semidirect
76. C₂×#2684	C₂³	semidirect
77. C₂×#2684	C₂³	semidirect
78. C₂×#2849	D₄	semidirect
82. C₂×#2436	D₄	semidirect
83. C₂×#2409	D₄	semidirect
92. C₂²×#386	D₄	semidirect
107. #16014	C₂³	semidirect
108. #15984	D₄	semidirect
111. #15784	C₂³	semidirect
112. #15673	D₄	semidirect
114. #15266	C₂³	semidirect
115. #15261	D₄	semidirect
116. #15259	D₄	semidirect
118. #15259	C₂³	semidirect
119. #14698	D₄	semidirect
120. #14358	C₂³	semidirect
121. #14134	D₄	semidirect
122. #14134	C₂³	semidirect
124. #13867	D₄	semidirect
126. C₄×#386	D₄	semidirect
127. #12852	C₂³	semidirect
128. #12852	C₂³	semidirect
129. #12694	C₂³	semidirect
130. #12687	C₂³	semidirect
131. #12687	C₂³	semidirect
132. #12687	C₂³	semidirect
139. #7307	C₂³	semidirect
140. #7304	C₂³	semidirect
144. C₂⁴×Q₈	C₂×D₄	semidirect
153. C₂⁵×C₄	C₂×D₄	semidirect
157. C₂²×#124	C₂×D₄	semidirect
159. C₂²×#123	C₂×D₄	semidirect
184. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
185. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
186. C₂³×C₄²	C₂×D₄	semidirect
190. C₂×#395	C₂×D₄	semidirect
191. C₂×#393	C₂×D₄	semidirect
192. C₂×#393	C₂×D₄	semidirect
193. C₂×#393	C₂×D₄	semidirect
196. C₂×#386	C₂×D₄	semidirect
197. C₂×#386	C₂×D₄	semidirect
198. C₂×#386	C₂×D₄	semidirect
202. C₂×#381	C₂×D₄	semidirect
204. C₂×#380	C₂×D₄	semidirect
210. C₂×#379	C₂×D₄	semidirect
212. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
219. #1440	C₂×D₄	semidirect
220. #1438	C₂×D₄	semidirect
221. #1438	C₂×D₄	semidirect
222. #1438	C₂×D₄	semidirect
223. #1438	C₂×D₄	semidirect
224. #1438	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
#72317671	2
#72317668	2
#72317660	2
#72317653	2
#72317649	2
#72317643	2
#72263425	2
#72262562	2
#72262500	2
#72240175	2
C₂×#508087	2
#72232733	2
#72231467	2
#72227862	2
#72216616	2