Subgroups — #72233185

Order 2048.

At least 9744 conjugacy classes of subgroups; only the 482 normal subgroups are shown.

The subgroup lattice has 371 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72233171	C₂	1	1	yes	maximal, characteristic, complemented
2	#72233159	C₂	1	1	yes	maximal, characteristic, complemented
3	#72233145	C₂	1	2	yes	maximal, complemented
4	#72233106	C₂	1	1	yes	maximal, characteristic, complemented
5	#72233040	C₂	1	1	yes	maximal, characteristic, complemented
6	#72233001	C₂	1	2	yes	maximal, complemented
7	#72232717	C₂	1	1	yes	maximal, characteristic, complemented
8	#72219261	C₂	1	1	yes	maximal, characteristic
9	#72218306	C₂	1	2	yes	maximal, complemented
10	#72216625	C₂	1	1	yes	maximal, characteristic, complemented
11	#72213256	C₂	1	2	yes	maximal, complemented
12	C₂²×#3484	C₂²	1	1	yes	characteristic
13	C₂×#37644	C₂²	1	1	yes	characteristic
14	C₂×D₄×#120	C₂²	1	1	yes	characteristic
15	C₂×#35346	C₄	1	1	yes	characteristic, complemented
16	#6385983	C₂²	1	1	yes	characteristic, complemented
17	#6385971	C₂²	1	1	yes	characteristic, complemented
18	#4930494	C₄	1	1	yes	characteristic, complemented
19	#4929118	C₄	1	1	yes	characteristic, complemented
20	#688032	C₂²	1	1	yes	characteristic
21	#687584	C₂²	1	1	yes	characteristic
22	#648360	C₄	1	1	yes	characteristic, complemented
23	#647670	C₄	1	1	yes	characteristic, complemented
24	#616969	C₄	1	1	yes	characteristic, complemented
25	#612424	C₂²	1	1	yes	characteristic
26	C₂×#15947	C₄	1	1	yes	characteristic, complemented
27	#535282	C₂²	1	1	yes	characteristic
28	#518030	C₄	1	1	yes	characteristic, complemented
29	#496225	C₂²	1	2	yes	complemented
30	#496225	C₂²	1	2	yes	complemented
31	#493357	C₂²	1	2	yes	—
32	#493357	C₂²	1	2	yes	—
33	#493357	C₂²	1	2	yes	complemented
34	#493357	C₂²	1	2	yes	complemented
35	#392113	C₂²	1	2	yes	complemented
36	#392109	C₂²	1	2	yes	complemented
37	#188087	C₂²	1	1	yes	characteristic, complemented
38	#188035	C₂²	1	1	yes	characteristic, complemented
39	#128073	C₂²	1	2	yes	complemented
40	#128073	C₂²	1	2	yes	complemented
41	#106660	C₂²	1	2	yes	complemented
42	#106654	C₂²	1	2	yes	complemented
43	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
44	C₂⁵×D₄	C₂³	1	1	yes	characteristic
45	C₂²×D₄²	C₂³	1	1	yes	characteristic
46	C₂²×#534	C₂³	1	1	yes	characteristic
47	C₂²×#534	C₂³	1	1	yes	characteristic
48	C₂³×#120	C₂×C₄	1	1	yes	characteristic
49	C₂³×#120	C₂×C₄	1	1	yes	characteristic
50	C₂³×#120	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂³×#120	C₂×C₄	1	1	yes	characteristic, complemented
52	C₂³×#120	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂³×#120	D₄	1	1	yes	characteristic
54	C₂³×#120	D₄	1	1	yes	characteristic
55	C₂²×#518	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂×#2847	D₄	1	1	yes	characteristic
57	C₂×#2846	C₂×C₄	1	1	yes	characteristic
58	C₂×#2846	D₄	1	1	yes	characteristic
59	C₂×#2846	D₄	1	1	yes	characteristic
60	C₂×#2539	D₄	1	1	yes	characteristic
61	C₂×#2534	D₄	1	1	yes	characteristic
62	C₂×#2433	D₄	1	1	yes	characteristic
63	C₂×#2408	D₄	1	1	yes	characteristic
64	C₂×#2412	D₄	1	1	yes	characteristic
65	C₂×#2405	D₄	1	1	yes	characteristic
66	C₂×#2410	C₂×C₄	1	1	yes	characteristic
67	C₂×#2410	C₂×C₄	1	1	yes	characteristic
68	C₂×#2410	C₂×C₄	1	1	yes	characteristic
69	C₂×#2410	D₄	1	1	yes	characteristic
70	C₂×#2403	C₂×C₄	1	1	yes	characteristic
71	C₂×#2403	C₂×C₄	1	1	yes	characteristic
72	C₂×#2403	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×#2403	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂×#2403	D₄	1	1	yes	characteristic
75	C₂×#2403	C₂³	1	1	yes	characteristic
76	C₂×#2617	D₄	1	1	yes	characteristic
77	C₂×#2613	C₂×C₄	1	1	yes	characteristic
78	C₂×D₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×D₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×#2321	D₄	1	1	yes	characteristic
81	C₂×#2308	C₂×C₄	1	1	yes	characteristic, complemented
82	C₂×C₄×#120	D₄	1	1	yes	characteristic
83	C₂×#2121	D₄	1	8	yes	complemented
84	C₂×#1783	C₂³	1	2	yes	—
85	C₂×#1783	C₂³	1	2	yes	—
86	C₂×#1781	C₂³	1	2	yes	—
87	C₂×#1781	C₂³	1	2	yes	—
88	#15950	D₄	1	1	yes	characteristic
89	#15948	D₄	1	1	yes	characteristic
90	#15947	D₄	1	1	yes	characteristic
91	#15261	D₄	1	1	yes	characteristic
92	#15260	D₄	1	1	yes	characteristic
93	#15258	D₄	1	1	yes	characteristic
94	#15257	D₄	1	1	yes	characteristic
95	#15257	D₄	1	1	yes	characteristic
96	#14679	C₂×C₄	1	1	yes	characteristic, complemented
97	#14262	C₂×C₄	1	1	yes	characteristic, complemented
98	#14255	C₂×C₄	1	1	yes	characteristic
99	#13877	C₂×C₄	1	1	yes	characteristic, complemented
100	#13867	C₂×C₄	1	1	yes	characteristic, complemented
101	#13867	C₂×C₄	1	1	yes	characteristic, complemented
102	#13867	C₂³	1	1	yes	characteristic
103	C₂×#1438	C₂×C₄	1	1	yes	characteristic
104	C₂×#1438	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×#1438	C₂×C₄	1	1	yes	characteristic, complemented
106	C₂²⋊C₄²	C₂×C₄	1	1	yes	characteristic, complemented
107	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic, complemented
108	C₂⁷	C₂²×C₄	1	1	yes	characteristic
109	C₂⁷	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
112	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
114	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
115	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
120	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
121	C₂×#534	C₂×D₄	1	4	yes	—
122	C₂×#534	#41	1	4	yes	—
123	C₂²×#127	C₂×D₄	1	1	yes	characteristic
124	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic, complemented
125	C₂²×#123	C₂×D₄	1	1	yes	characteristic
126	C₂²×#123	C₂×D₄	1	1	yes	characteristic
127	C₂²×#123	C₂×D₄	1	1	yes	characteristic
128	C₂²×#123	C₂×D₄	1	1	yes	characteristic
129	C₂²×#121	C₂×D₄	1	1	yes	characteristic
130	C₂²×#121	C₂×D₄	1	1	yes	characteristic
131	C₂²×#121	C₂×D₄	1	1	yes	characteristic
132	C₂²×#121	C₂×D₄	1	1	yes	characteristic
133	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
143	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
144	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
145	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
146	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
147	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
148	C₂²×#120	C₂×D₄	1	1	yes	characteristic
149	C₂²×#120	C₂×D₄	1	1	yes	characteristic
150	C₂²×#120	C₂×D₄	1	1	yes	characteristic
151	C₂²×#120	C₂×D₄	1	1	yes	characteristic
152	C₂²×#120	C₂×D₄	1	1	yes	characteristic
153	C₂²×#120	C₂×D₄	1	1	yes	characteristic
154	C₂²×#120	C₂×D₄	1	1	yes	characteristic
155	C₂²×#120	C₂×D₄	1	1	yes	characteristic
156	C₂²×#120	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
159	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
160	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
161	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
162	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
163	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
164	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
165	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
166	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
167	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₂²×#100	C₂×D₄	1	4	yes	complemented
169	C₂²×#99	C₂×D₄	1	4	yes	complemented
170	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
173	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
174	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
175	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
176	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
177	C₂×#386	C₂×D₄	1	1	yes	characteristic
178	C₂×#386	C₂×D₄	1	1	yes	characteristic
179	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic, complemented
181	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic, complemented
182	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
183	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic, complemented
184	C₂×#380	C₂×D₄	1	1	yes	characteristic
185	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
186	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
187	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
188	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
189	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
190	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
191	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
192	C₂×#379	C₂²×C₄	1	1	yes	characteristic
193	C₂×#379	C₂²×C₄	1	1	yes	characteristic
194	C₂×#379	C₂²×C₄	1	1	yes	characteristic
195	C₂×#379	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
197	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
198	#1440	C₂²⋊C₄	1	1	yes	characteristic, complemented
199	#1440	C₂²⋊C₄	1	1	yes	characteristic, complemented
200	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
201	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
202	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
203	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
204	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
205	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
206	#1438	C₂×D₄	1	1	yes	characteristic
207	#1438	C₂×D₄	1	1	yes	characteristic
208	#1438	C₂×D₄	1	1	yes	characteristic
209	#1438	C₂×D₄	1	1	yes	characteristic
210	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂⁶	#120	1	1	yes	characteristic
218	C₂⁶	C₂³×C₄	1	1	yes	characteristic
219	C₂⁶	C₂²×D₄	1	1	yes	characteristic
220	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×D₄	C₄×D₄	1	4	yes	—
228	C₂³×D₄	#120	1	1	yes	characteristic
229	C₂³×D₄	#120	1	1	yes	characteristic
230	C₂³×D₄	#120	1	1	yes	characteristic
231	C₂³×D₄	#120	1	1	yes	characteristic
232	C₂³×D₄	#120	1	1	yes	characteristic
233	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
234	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
235	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
236	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
237	C₂³×D₄	C₂²×D₄	1	2	yes	—
238	C₂³×D₄	C₂×#41	1	2	yes	—
239	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
240	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
241	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂⁴×C₄	#120	1	1	yes	characteristic
247	C₂⁴×C₄	#120	1	1	yes	characteristic
248	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
249	C₂×#123	#120	1	2	yes	—
250	C₂×#123	#121	1	4	yes	—
251	C₂×#123	#123	1	2	yes	—
252	C₂×#120	#99	1	2	yes	—
253	C₂×#120	#99	1	2	yes	—
254	C₂×#120	#120	1	2	yes	—
255	C₂×#120	#121	1	4	yes	—
256	C₂×#120	#123	1	2	yes	—
257	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	C₄×D₄	1	4	yes	—
277	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
278	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
279	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
282	C₂²×C₄²	#120	1	1	yes	characteristic
283	#386	#99	1	2	yes	—
284	#386	#99	1	2	yes	—
285	C₂⁵	#379	1	1	yes	characteristic
286	C₂⁵	#379	1	1	yes	characteristic
287	C₂⁵	#379	1	1	yes	characteristic
288	C₂⁵	#386	1	2	yes	—
289	C₂⁵	C₂×#99	1	2	yes	—
290	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
291	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
293	C₂⁵	C₂×C₄×D₄	1	2	yes	—
294	C₂⁵	#518	1	2	yes	—
295	C₂⁵	C₂×#120	1	1	yes	characteristic
296	C₂⁵	C₂×#120	1	1	yes	characteristic
297	C₂⁵	D₄²	1	2	yes	—
298	C₂⁵	#546	1	2	yes	—
299	C₂²×D₄	C₂×#99	1	1	yes	characteristic
300	C₂²×D₄	C₂×#99	1	1	yes	characteristic
301	C₂²×D₄	C₂×#99	1	1	yes	characteristic
302	C₂²×D₄	C₂×#99	1	1	yes	characteristic
303	C₂²×D₄	C₂×#120	1	1	yes	characteristic
304	C₂²×D₄	C₂×#121	1	2	yes	—
305	C₂²×D₄	C₂×#123	1	1	yes	characteristic
306	C₂²×D₄	#534	1	1	yes	characteristic
307	C₂²×D₄	#534	1	1	yes	characteristic
308	C₂²×D₄	#534	1	2	yes	—
309	C₂²×D₄	D₄²	1	2	yes	—
310	C₂²×D₄	D₄²	1	2	yes	—
311	C₂²×D₄	#546	1	2	yes	—
312	C₂²×D₄	#546	1	2	yes	—
313	C₂³×C₄	#379	1	1	yes	characteristic
314	C₂³×C₄	#379	1	1	yes	characteristic
315	C₂³×C₄	#379	1	1	yes	characteristic
316	C₂³×C₄	#379	1	1	yes	characteristic
317	C₂³×C₄	#379	1	1	yes	characteristic
318	C₂³×C₄	#386	1	2	yes	—
319	C₂³×C₄	C₂×#99	1	2	yes	—
320	C₂³×C₄	C₂×#120	1	1	yes	characteristic
321	C₂³×C₄	C₂×#120	1	1	yes	characteristic
322	C₂³×C₄	D₄²	1	2	yes	—
323	C₂³×C₄	#546	1	2	yes	—
324	#120	B(4,𝔽₂)	1	8	yes	—
325	C₂×C₂²⋊C₄	#386	1	2	yes	—
326	C₂×C₂²⋊C₄	#386	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
329	C₂⁴	#1781	1	1	yes	characteristic
330	C₂⁴	#1781	1	1	yes	characteristic
331	C₂⁴	#1889	1	4	yes	complemented
332	C₂⁴	C₂×#379	1	1	yes	characteristic
333	C₂⁴	C₂×#386	1	1	yes	characteristic
334	C₂⁴	#2308	1	1	yes	characteristic
335	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
336	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
337	C₂⁴	#2403	1	1	yes	characteristic
338	C₂⁴	#2405	1	1	yes	characteristic
339	C₂⁴	#2410	1	2	yes	—
340	C₂⁴	C₂²×#99	1	1	yes	characteristic
341	C₂⁴	C₂²×#99	1	1	yes	characteristic
342	C₂⁴	#2883	1	2	yes	—
343	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
344	C₂²×C₄	#1781	1	1	yes	characteristic
345	C₂²×C₄	#1781	1	1	yes	characteristic
346	C₂²×C₄	#2403	1	1	yes	characteristic
347	C₂²×C₄	#2405	1	1	yes	characteristic
348	C₂²×C₄	#2410	1	2	yes	—
349	C₂²⋊C₄	#1889	1	4	yes	complemented
350	C₂³	#12705	1	2	yes	complemented
351	C₂³	#13867	1	1	yes	characteristic
352	C₂³	C₂×#1781	1	1	yes	characteristic
353	C₂³	#20585	1	1	yes	characteristic
354	C₂³	C₂×#1889	1	2	yes	—
355	C₂³	#21776	1	2	yes	—
356	C₂³	D₄×#99	1	2	yes	—
357	C₂³	D₄×#99	1	2	yes	—
358	C₂³	#23900	1	2	yes	—
359	C₂×C₄	#23900	1	2	yes	—
360	C₂²	#359501	1	1	yes	characteristic
361	C₂²	#359579	1	1	yes	characteristic
362	C₂²	#359591	1	1	yes	characteristic
363	C₂²	C₂×#12705	1	1	yes	characteristic
364	C₂²	#493391	1	1	yes	characteristic
365	C₂²	#493474	1	1	yes	characteristic
366	C₂²	#493477	1	1	yes	characteristic
367	C₂	#72216625	1	1	yes	characteristic
368	C₂	#72233183	1	1	yes	characteristic
369	C₂	#72233184	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#359579
commutator	C₂⁶	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72219261	C₂
LCS	G ▷ C₂⁶ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂×D₄×#120 ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72233171	C₂	semidirect
2. #72233159	C₂	semidirect
3. #72233145	C₂	semidirect
4. #72233106	C₂	semidirect
5. #72233040	C₂	semidirect
6. #72233001	C₂	semidirect
7. #72232717	C₂	semidirect
9. #72218306	C₂	semidirect
10. #72216625	C₂	semidirect
11. #72213256	C₂	semidirect
15. C₂×#35346	C₄	semidirect
16. #6385983	C₂²	semidirect
17. #6385971	C₂²	semidirect
18. #4930494	C₄	semidirect
19. #4929118	C₄	semidirect
22. #648360	C₄	semidirect
23. #647670	C₄	semidirect
24. #616969	C₄	semidirect
26. C₂×#15947	C₄	semidirect
28. #518030	C₄	semidirect
29. #496225	C₂²	semidirect
30. #496225	C₂²	semidirect
33. #493357	C₂²	semidirect
34. #493357	C₂²	semidirect
35. #392113	C₂²	semidirect
36. #392109	C₂²	semidirect
37. #188087	C₂²	semidirect
38. #188035	C₂²	semidirect
39. #128073	C₂²	semidirect
40. #128073	C₂²	semidirect
41. #106660	C₂²	semidirect
42. #106654	C₂²	semidirect
43. C₂³×H(5,𝔽₂)	C₂×C₄	semidirect
50. C₂³×#120	C₂×C₄	semidirect
51. C₂³×#120	C₂×C₄	semidirect
52. C₂³×#120	C₂×C₄	semidirect
55. C₂²×#518	C₂×C₄	semidirect
72. C₂×#2403	C₂×C₄	semidirect
73. C₂×#2403	C₂×C₄	semidirect
81. C₂×#2308	C₂×C₄	semidirect
83. C₂×#2121	D₄	semidirect
96. #14679	C₂×C₄	semidirect
97. #14262	C₂×C₄	semidirect
99. #13877	C₂×C₄	semidirect
100. #13867	C₂×C₄	semidirect
101. #13867	C₂×C₄	semidirect
104. C₂×#1438	C₂×C₄	semidirect
105. C₂×#1438	C₂×C₄	semidirect
106. C₂²⋊C₄²	C₂×C₄	semidirect
107. C₂⁷	C₂²⋊C₄	semidirect
124. C₂²×#123	C₂²⋊C₄	semidirect
142. C₂²×#120	C₂²⋊C₄	semidirect
143. C₂²×#120	C₂²⋊C₄	semidirect
144. C₂²×#120	C₂²⋊C₄	semidirect
145. C₂²×#120	C₂²⋊C₄	semidirect
146. C₂²×#120	C₂²⋊C₄	semidirect
159. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
160. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
161. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
162. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
168. C₂²×#100	C₂×D₄	semidirect
169. C₂²×#99	C₂×D₄	semidirect
173. C₂×#386	C₂²⋊C₄	semidirect
174. C₂×#386	C₂²⋊C₄	semidirect
175. C₂×#386	C₂²⋊C₄	semidirect
176. C₂×#386	C₂²⋊C₄	semidirect
180. C₂×#385	C₂²⋊C₄	semidirect
181. C₂×#385	C₂²⋊C₄	semidirect
182. C₂×#381	C₂²⋊C₄	semidirect
183. C₂×#380	C₂²⋊C₄	semidirect
188. C₂×#379	C₂²⋊C₄	semidirect
189. C₂×#379	C₂²⋊C₄	semidirect
190. C₂×#379	C₂²⋊C₄	semidirect
191. C₂×#379	C₂²⋊C₄	semidirect
196. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
198. #1440	C₂²⋊C₄	semidirect
199. #1440	C₂²⋊C₄	semidirect
200. #1438	C₂²⋊C₄	semidirect
201. #1438	C₂²⋊C₄	semidirect
202. #1438	C₂²⋊C₄	semidirect
203. #1438	C₂²⋊C₄	semidirect
204. #1438	C₂²⋊C₄	semidirect
205. #1438	C₂²⋊C₄	semidirect
331. C₂⁴	#1889	semidirect
349. C₂²⋊C₄	#1889	semidirect
350. C₂³	#12705	semidirect

Maximal subgroups

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

subgroup	index
#72233171	2
#72233159	2
#72233145	2
#72233106	2
#72233040	2
#72233001	2
#72232717	2
#72219261	2
#72218306	2
#72216625	2
#72213256	2