Subgroups — #72240158

Order 2048.

At least 9084 conjugacy classes of subgroups; only the 452 normal subgroups are shown.

The subgroup lattice has 369 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72240151	C₂	1	1	yes	maximal, characteristic
2	#72240134	C₂	1	1	yes	maximal, characteristic, complemented
3	#72240132	C₂	1	1	yes	maximal, characteristic, complemented
4	#72236467	C₂	1	1	yes	maximal, characteristic, complemented
5	#72235186	C₂	1	1	yes	maximal, characteristic, complemented
6	#72234596	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233140	C₂	1	2	yes	maximal, complemented
8	#72233098	C₂	1	2	yes	maximal, complemented
9	#72225994	C₂	1	1	yes	maximal, characteristic, complemented
10	#72213274	C₂	1	2	yes	maximal, complemented
11	#72210566	C₂	1	2	yes	maximal, complemented
12	C₂×#52004	C₂²	1	1	yes	characteristic
13	C₂×#34980	C₂²	1	1	yes	characteristic
14	#7626202	C₂²	1	1	yes	characteristic, complemented
15	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
16	#5021162	C₄	1	1	yes	characteristic, complemented
17	#4941255	C₄	1	1	yes	characteristic, complemented
18	#4867137	C₂²	1	1	yes	characteristic
19	#4607564	C₄	1	1	yes	characteristic, complemented
20	#4312024	C₂²	1	1	yes	characteristic
21	#2924619	C₄	1	1	yes	characteristic, complemented
22	#2039305	C₄	1	1	yes	characteristic, complemented
23	#2032505	C₄	1	1	yes	characteristic, complemented
24	#1418393	C₄	1	1	yes	characteristic, complemented
25	#647656	C₄	1	1	yes	characteristic, complemented
26	#616961	C₂²	1	1	yes	characteristic
27	#616960	C₂²	1	1	yes	characteristic
28	#604823	C₂²	1	1	yes	characteristic
29	#496225	C₂²	1	2	yes	—
30	#496225	C₂²	1	2	yes	complemented
31	#496225	C₂²	1	2	yes	complemented
32	#493370	C₂²	1	2	yes	complemented
33	#359509	C₂²	1	2	yes	complemented
34	#201664	C₂²	1	2	yes	—
35	#201664	C₂²	1	2	yes	complemented
36	#201664	C₂²	1	2	yes	complemented
37	C₂×#8547	C₂²	1	1	yes	characteristic, complemented
38	C₂×#8541	C₂²	1	1	yes	characteristic, complemented
39	#128073	C₂²	1	2	yes	complemented
40	#128009	C₂²	1	2	yes	complemented
41	#108238	C₂²	1	2	yes	complemented
42	#106766	C₂²	1	2	yes	complemented
43	C₂⁵×D₄	D₄	1	1	yes	characteristic
44	C₂²×D₄²	C₂×C₄	1	1	yes	characteristic, complemented
45	C₂²×#535	C₂³	1	1	yes	characteristic
46	C₂²×#534	D₄	1	1	yes	characteristic
47	C₂³×#120	C₂³	1	1	yes	characteristic
48	C₂×#2684	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×#2684	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×#2849	C₂×C₄	1	1	yes	characteristic
51	C₂×#2849	D₄	1	1	yes	characteristic
52	C₂×#2846	C₂×C₄	1	1	yes	characteristic
53	C₂×#2846	D₄	1	1	yes	characteristic
54	C₂×#2404	D₄	1	1	yes	characteristic
55	C₂×#2404	D₄	1	1	yes	characteristic
56	C₂×#2405	D₄	1	1	yes	characteristic
57	C₂×#2405	D₄	1	1	yes	characteristic
58	C₂×#2410	C₂×C₄	1	1	yes	characteristic
59	C₂×#2410	C₂×C₄	1	1	yes	characteristic
60	C₂×#2410	D₄	1	1	yes	characteristic
61	C₂×#2410	D₄	1	1	yes	characteristic
62	C₂×#2403	D₄	1	1	yes	characteristic
63	C₂×#2403	C₂³	1	1	yes	characteristic
64	C₂×#2403	C₂³	1	1	yes	characteristic
65	C₂×#2403	C₂³	1	1	yes	characteristic
66	C₂×#2380	C₂×C₄	1	1	yes	characteristic, complemented
67	#34171	C₂³	1	2	yes	—
68	C₂²×#379	D₄	1	1	yes	characteristic
69	C₂×#1783	C₂³	1	2	yes	—
70	C₂×#1781	C₂³	1	2	yes	—
71	C₂×#1781	C₂³	1	2	yes	—
72	#16014	C₂×C₄	1	1	yes	characteristic, complemented
73	#15948	C₂×C₄	1	1	yes	characteristic
74	#15948	C₂×C₄	1	1	yes	characteristic
75	#15948	D₄	1	1	yes	characteristic
76	#15948	D₄	1	1	yes	characteristic
77	#15947	C₂×C₄	1	1	yes	characteristic
78	#15947	C₂×C₄	1	1	yes	characteristic
79	#15947	C₂×C₄	1	1	yes	characteristic, complemented
80	#15947	D₄	1	1	yes	characteristic
81	#15947	D₄	1	1	yes	characteristic
82	#15784	C₂×C₄	1	1	yes	characteristic, complemented
83	#15313	C₂×C₄	1	1	yes	characteristic, complemented
84	#15266	C₂×C₄	1	1	yes	characteristic, complemented
85	#15266	C₂×C₄	1	1	yes	characteristic, complemented
86	#15259	C₂×C₄	1	1	yes	characteristic
87	#15259	C₂×C₄	1	1	yes	characteristic
88	#15259	C₂×C₄	1	1	yes	characteristic, complemented
89	#15259	D₄	1	1	yes	characteristic
90	#15259	D₄	1	1	yes	characteristic
91	#15258	C₂×C₄	1	1	yes	characteristic
92	#15258	C₂×C₄	1	1	yes	characteristic
93	#15258	C₂×C₄	1	1	yes	characteristic, complemented
94	#15258	D₄	1	1	yes	characteristic
95	#15258	D₄	1	1	yes	characteristic
96	#14666	C₂×C₄	1	1	yes	characteristic, complemented
97	#14516	C₂×C₄	1	1	yes	characteristic, complemented
98	#14358	C₂×C₄	1	1	yes	characteristic, complemented
99	#14335	D₄	1	1	yes	characteristic
100	#14335	C₂³	1	1	yes	characteristic
101	#14134	C₂×C₄	1	1	yes	characteristic, complemented
102	#13868	D₄	1	1	yes	characteristic
103	#13868	D₄	1	1	yes	characteristic
104	#13867	D₄	1	1	yes	characteristic
105	#13867	C₂³	1	1	yes	characteristic
106	#9497	D₄	1	8	yes	complemented
107	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
108	C₂⁷	C₂×D₄	1	1	yes	characteristic
109	C₂³×#41	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	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×D₄	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
118	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
120	C₂²×#127	C₂×D₄	1	1	yes	characteristic
121	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
122	C₂²×#124	C₂×D₄	1	1	yes	characteristic
123	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
130	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
131	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
132	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
133	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
134	C₂²×#120	C₂×D₄	1	1	yes	characteristic
135	C₂²×#120	C₂×D₄	1	1	yes	characteristic
136	C₂²×#120	C₂×D₄	1	1	yes	characteristic
137	C₂²×#120	C₂×D₄	1	1	yes	characteristic
138	C₂²×#120	C₂×D₄	1	1	yes	characteristic
139	C₂²×#120	C₂×D₄	1	1	yes	characteristic
140	C₂²×#120	C₂×D₄	1	1	yes	characteristic
141	C₂²×#120	C₂×D₄	1	1	yes	characteristic
142	C₂²×#120	C₂×D₄	1	1	yes	characteristic
143	C₂²×#117	C₂×D₄	1	1	yes	characteristic
144	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
148	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
149	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
150	#2403	C₂×D₄	1	4	yes	—
151	#2403	#41	1	4	yes	—
152	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
160	#2309	C₂×D₄	1	4	yes	complemented
161	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#386	C₂²×C₄	1	1	yes	characteristic
164	C₂×#386	C₂²×C₄	1	1	yes	characteristic
165	C₂×#386	C₂²×C₄	1	1	yes	characteristic
166	C₂×#386	C₂×D₄	1	1	yes	characteristic
167	C₂×#386	C₂×D₄	1	1	yes	characteristic
168	C₂×#386	C₂×D₄	1	1	yes	characteristic
169	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
173	C₂×#381	C₂×D₄	1	1	yes	characteristic
174	C₂×#381	C₂×D₄	1	1	yes	characteristic
175	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
176	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
177	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
179	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×#379	C₂×D₄	1	1	yes	characteristic
182	C₂×#379	C₂×D₄	1	1	yes	characteristic
183	C₂×#379	C₂×D₄	1	1	yes	characteristic
184	C₂×#379	C₂×D₄	1	1	yes	characteristic
185	#1781	C₂×D₄	1	4	yes	complemented
186	#1438	C₂²⋊C₄	1	1	yes	characteristic
187	#1438	C₂²⋊C₄	1	1	yes	characteristic
188	#1438	C₂²⋊C₄	1	1	yes	characteristic
189	#1438	C₂²⋊C₄	1	1	yes	characteristic
190	#1438	C₂²⋊C₄	1	1	yes	characteristic
191	#1438	C₂²⋊C₄	1	1	yes	characteristic
192	#1438	C₂²⋊C₄	1	1	yes	characteristic
193	#1438	C₂²⋊C₄	1	1	yes	characteristic
194	#1438	C₂²×C₄	1	1	yes	characteristic
195	#1438	C₂²×C₄	1	1	yes	characteristic
196	#1438	C₂²×C₄	1	1	yes	characteristic
197	#1438	C₂²×C₄	1	1	yes	characteristic
198	#1438	C₂×D₄	1	1	yes	characteristic
199	#1438	C₂×D₄	1	1	yes	characteristic
200	#1438	C₂×D₄	1	1	yes	characteristic
201	#1438	C₂×D₄	1	1	yes	characteristic
202	#1437	C₂²⋊C₄	1	1	yes	characteristic
203	#1437	C₂²⋊C₄	1	1	yes	characteristic
204	#1437	C₂²⋊C₄	1	1	yes	characteristic
205	#1437	C₂²⋊C₄	1	1	yes	characteristic
206	#1437	C₂²⋊C₄	1	1	yes	characteristic
207	#1437	C₂²⋊C₄	1	1	yes	characteristic
208	#1437	C₂²⋊C₄	1	1	yes	characteristic
209	#1437	C₂²⋊C₄	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	#120	1	1	yes	characteristic
216	C₂⁶	#120	1	1	yes	characteristic
217	C₂⁶	#120	1	1	yes	characteristic
218	C₂⁶	#120	1	1	yes	characteristic
219	C₂⁶	C₂²×D₄	1	1	yes	characteristic
220	C₂⁶	C₂²×D₄	1	1	yes	characteristic
221	C₂³×Q₈	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	#120	1	1	yes	characteristic
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	2	yes	—
232	C₂³×D₄	#123	1	2	yes	—
233	C₂³×D₄	C₂³×C₄	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	#120	1	1	yes	characteristic
245	C₂⁴×C₄	#120	1	1	yes	characteristic
246	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
247	C₂×#120	C₄×D₄	1	4	yes	—
248	C₂×#120	#121	1	4	yes	—
249	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	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	#120	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
271	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	#386	C₄×D₄	1	4	yes	—
274	#386	#121	1	4	yes	—
275	#379	#120	1	2	yes	—
276	#379	#123	1	2	yes	—
277	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂⁵	#379	1	1	yes	characteristic
282	C₂⁵	#379	1	1	yes	characteristic
283	C₂⁵	#379	1	1	yes	characteristic
284	C₂⁵	#379	1	1	yes	characteristic
285	C₂⁵	#386	1	2	yes	—
286	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
287	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
288	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
289	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
290	C₂⁵	#458	1	1	yes	characteristic
291	C₂⁵	#458	1	1	yes	characteristic
292	C₂⁵	#458	1	1	yes	characteristic
293	C₂⁵	#458	1	1	yes	characteristic
294	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
296	C₂⁵	C₂×#120	1	1	yes	characteristic
297	C₂⁵	C₂×#120	1	1	yes	characteristic
298	C₂⁵	C₂×#120	1	1	yes	characteristic
299	C₂⁵	C₂×#120	1	1	yes	characteristic
300	C₂⁵	C₂×#123	1	1	yes	characteristic
301	C₂⁵	#534	1	1	yes	characteristic
302	C₂⁵	#534	1	1	yes	characteristic
303	C₂⁵	D₄²	1	2	yes	—
304	C₂⁵	#546	1	2	yes	—
305	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
306	C₂²×D₄	#518	1	2	yes	—
307	C₂²×D₄	C₂×#121	1	2	yes	—
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	#386	1	2	yes	—
318	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
319	C₂³×C₄	C₂×#120	1	1	yes	characteristic
320	C₂³×C₄	D₄²	1	2	yes	—
321	C₂³×C₄	#546	1	2	yes	—
322	C₂×C₂²⋊C₄	#386	1	2	yes	—
323	C₂×C₂²⋊C₄	#386	1	2	yes	—
324	C₂⁴	#1790	1	1	yes	characteristic
325	C₂⁴	#1790	1	1	yes	characteristic
326	C₂⁴	#1790	1	1	yes	characteristic
327	C₂⁴	#1790	1	1	yes	characteristic
328	C₂⁴	#1790	1	1	yes	characteristic
329	C₂⁴	#1790	1	1	yes	characteristic
330	C₂⁴	#1790	1	1	yes	characteristic
331	C₂⁴	#1790	1	1	yes	characteristic
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	#2403	1	1	yes	characteristic
337	C₂⁴	#2403	1	1	yes	characteristic
338	C₂⁴	#2405	1	1	yes	characteristic
339	C₂⁴	#2405	1	1	yes	characteristic
340	C₂⁴	#2410	1	2	yes	—
341	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
342	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
343	C₂⁴	C₂×#458	1	1	yes	characteristic
344	C₂⁴	C₂×#458	1	1	yes	characteristic
345	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
346	C₂²×C₄	#2410	1	2	yes	—
347	C₂³	#12753	1	2	yes	—
348	C₂³	#12753	1	2	yes	—
349	C₂³	#12753	1	2	yes	—
350	C₂³	#13867	1	1	yes	characteristic
351	C₂³	C₂×#1790	1	1	yes	characteristic
352	C₂³	C₂×#1790	1	1	yes	characteristic
353	C₂³	#21776	1	2	yes	—
354	C₂³	#23900	1	1	yes	characteristic
355	C₂³	#23901	1	1	yes	characteristic
356	C₂³	#24056	1	1	yes	characteristic
357	C₂³	#24056	1	1	yes	characteristic
358	C₂²	#359528	1	1	yes	characteristic
359	C₂²	#359552	1	1	yes	characteristic
360	C₂²	#359591	1	1	yes	characteristic
361	C₂²	C₂×#12753	1	1	yes	characteristic
362	C₂²	C₂×#12753	1	1	yes	characteristic
363	C₂²	C₂×#12753	1	1	yes	characteristic
364	C₂²	#493562	1	1	yes	characteristic
365	C₂	#72218088	1	1	yes	characteristic
366	C₂	#72235131	1	1	yes	characteristic
367	C₂	#72240111	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#359552
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72240151	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#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
2. #72240134	C₂	semidirect
3. #72240132	C₂	semidirect
4. #72236467	C₂	semidirect
5. #72235186	C₂	semidirect
6. #72234596	C₂	semidirect
7. #72233140	C₂	semidirect
8. #72233098	C₂	semidirect
9. #72225994	C₂	semidirect
10. #72213274	C₂	semidirect
11. #72210566	C₂	semidirect
14. #7626202	C₂²	semidirect
15. C₂×#21746	C₂²	semidirect
16. #5021162	C₄	semidirect
17. #4941255	C₄	semidirect
19. #4607564	C₄	semidirect
21. #2924619	C₄	semidirect
22. #2039305	C₄	semidirect
23. #2032505	C₄	semidirect
24. #1418393	C₄	semidirect
25. #647656	C₄	semidirect
30. #496225	C₂²	semidirect
31. #496225	C₂²	semidirect
32. #493370	C₂²	semidirect
33. #359509	C₂²	semidirect
35. #201664	C₂²	semidirect
36. #201664	C₂²	semidirect
37. C₂×#8547	C₂²	semidirect
38. C₂×#8541	C₂²	semidirect
39. #128073	C₂²	semidirect
40. #128009	C₂²	semidirect
41. #108238	C₂²	semidirect
42. #106766	C₂²	semidirect
44. C₂²×D₄²	C₂×C₄	semidirect
48. C₂×#2684	C₂×C₄	semidirect
49. C₂×#2684	C₂×C₄	semidirect
66. C₂×#2380	C₂×C₄	semidirect
72. #16014	C₂×C₄	semidirect
79. #15947	C₂×C₄	semidirect
82. #15784	C₂×C₄	semidirect
83. #15313	C₂×C₄	semidirect
84. #15266	C₂×C₄	semidirect
85. #15266	C₂×C₄	semidirect
88. #15259	C₂×C₄	semidirect
93. #15258	C₂×C₄	semidirect
96. #14666	C₂×C₄	semidirect
97. #14516	C₂×C₄	semidirect
98. #14358	C₂×C₄	semidirect
101. #14134	C₂×C₄	semidirect
106. #9497	D₄	semidirect
160. #2309	C₂×D₄	semidirect
185. #1781	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72240151	2
#72240134	2
#72240132	2
#72236467	2
#72235186	2
#72234596	2
#72233140	2
#72233098	2
#72225994	2
#72213274	2
#72210566	2