Subgroups — #72240136

Order 2048.

At least 7326 conjugacy classes of subgroups; only the 404 normal subgroups are shown.

The subgroup lattice has 354 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72240134	C₂	1	1	yes	maximal, characteristic, complemented
2	#72240132	C₂	1	1	yes	maximal, characteristic, complemented
3	#72240130	C₂	1	1	yes	maximal, characteristic
4	#72236988	C₂	1	1	yes	maximal, characteristic, complemented
5	#72236441	C₂	1	1	yes	maximal, characteristic, complemented
6	#72235186	C₂	1	1	yes	maximal, characteristic, complemented
7	#72234596	C₂	1	1	yes	maximal, characteristic, complemented
8	#72233098	C₂	1	2	yes	maximal, complemented
9	#72233007	C₂	1	2	yes	maximal, complemented
10	#72213274	C₂	1	2	yes	maximal, complemented
11	#72210462	C₂	1	2	yes	maximal, complemented
12	#7626202	C₂²	1	1	yes	characteristic
13	C₂×#21746	C₂²	1	1	yes	characteristic
14	#5486611	C₄	1	1	yes	characteristic, complemented
15	#5069375	C₄	1	1	yes	characteristic, complemented
16	#5065220	C₄	1	1	yes	characteristic, complemented
17	#4894596	C₂²	1	1	yes	characteristic
18	#4312024	C₂²	1	1	yes	characteristic
19	#4128936	C₄	1	1	yes	characteristic, complemented
20	#4117631	C₄	1	1	yes	characteristic, complemented
21	#4035548	C₄	1	1	yes	characteristic, complemented
22	#2227686	C₄	1	1	yes	characteristic, complemented
23	#2108839	C₄	1	1	yes	characteristic, complemented
24	#616961	C₂²	1	1	yes	characteristic
25	#616960	C₂²	1	1	yes	characteristic
26	#604823	C₂²	1	1	yes	characteristic
27	#581603	C₂²	1	1	yes	characteristic
28	#516383	C₂²	1	1	yes	characteristic
29	#496225	C₂²	1	2	yes	—
30	#493370	C₂²	1	2	yes	—
31	#359509	C₂²	1	2	yes	—
32	#201664	C₂²	1	2	yes	—
33	C₂×#8547	C₂²	1	1	yes	characteristic
34	C₂×#8541	C₂²	1	1	yes	characteristic
35	#128073	C₂²	1	2	yes	—
36	#128073	C₂²	1	2	yes	—
37	#128073	C₂²	1	2	yes	—
38	#128009	C₂²	1	2	yes	—
39	#108238	C₂²	1	2	yes	—
40	#106766	C₂²	1	2	yes	—
41	#106766	C₂²	1	2	yes	—
42	#106766	C₂²	1	2	yes	—
43	C₂²×#535	C₂³	1	1	yes	characteristic
44	C₂²×#534	D₄	1	1	yes	characteristic
45	C₂³×#120	C₂³	1	1	yes	characteristic
46	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
47	C₂×#2404	D₄	1	1	yes	characteristic
48	C₂×#2404	D₄	1	1	yes	characteristic
49	C₂×#2403	D₄	1	1	yes	characteristic
50	C₂×#2403	C₂³	1	1	yes	characteristic
51	#34171	C₂³	1	2	yes	—
52	C₂²×#379	D₄	1	1	yes	characteristic
53	C₂×#1783	C₂³	1	2	yes	—
54	C₂×#1781	C₂³	1	2	yes	—
55	C₂×#1781	C₂³	1	2	yes	—
56	#17273	C₂×C₄	1	1	yes	characteristic, complemented
57	#17272	C₂×C₄	1	1	yes	characteristic, complemented
58	#17137	C₂×C₄	1	1	yes	characteristic, complemented
59	#17136	C₂×C₄	1	1	yes	characteristic, complemented
60	#15948	C₂×C₄	1	1	yes	characteristic
61	#15948	C₂×C₄	1	1	yes	characteristic
62	#15948	D₄	1	1	yes	characteristic
63	#15948	D₄	1	1	yes	characteristic
64	#15947	C₂×C₄	1	1	yes	characteristic
65	#15947	C₂×C₄	1	1	yes	characteristic
66	#15947	D₄	1	1	yes	characteristic
67	#15947	D₄	1	1	yes	characteristic
68	#15784	C₂×C₄	1	1	yes	characteristic, complemented
69	#15313	C₂×C₄	1	1	yes	characteristic, complemented
70	#15259	C₂×C₄	1	1	yes	characteristic
71	#15259	C₂×C₄	1	1	yes	characteristic
72	#15259	C₂×C₄	1	1	yes	characteristic, complemented
73	#15259	D₄	1	1	yes	characteristic
74	#15259	D₄	1	1	yes	characteristic
75	#15258	C₂×C₄	1	1	yes	characteristic
76	#15258	C₂×C₄	1	1	yes	characteristic
77	#15258	C₂×C₄	1	1	yes	characteristic, complemented
78	#15258	D₄	1	1	yes	characteristic
79	#15258	D₄	1	1	yes	characteristic
80	#14666	C₂×C₄	1	1	yes	characteristic, complemented
81	#14662	C₂×C₄	1	1	yes	characteristic, complemented
82	#14516	C₂×C₄	1	1	yes	characteristic, complemented
83	#14419	C₂×C₄	1	1	yes	characteristic, complemented
84	#14419	C₂×C₄	1	1	yes	characteristic, complemented
85	#14358	C₂×C₄	1	1	yes	characteristic, complemented
86	#14335	D₄	1	1	yes	characteristic
87	#14335	C₂³	1	1	yes	characteristic
88	#14255	C₂×C₄	1	1	yes	characteristic
89	#14255	C₂×C₄	1	1	yes	characteristic
90	#14255	D₄	1	1	yes	characteristic
91	#14255	D₄	1	1	yes	characteristic
92	#14169	C₂×C₄	1	1	yes	characteristic, complemented
93	#14134	C₂×C₄	1	1	yes	characteristic
94	#14134	C₂×C₄	1	1	yes	characteristic
95	#14134	C₂×C₄	1	1	yes	characteristic, complemented
96	#14134	D₄	1	1	yes	characteristic
97	#14134	D₄	1	1	yes	characteristic
98	#13869	D₄	1	1	yes	characteristic
99	#13869	D₄	1	1	yes	characteristic
100	#13868	D₄	1	1	yes	characteristic
101	#13868	D₄	1	1	yes	characteristic
102	#13867	D₄	1	1	yes	characteristic
103	#13867	C₂³	1	1	yes	characteristic
104	#13867	C₂³	1	1	yes	characteristic
105	#13867	C₂³	1	1	yes	characteristic
106	C₂⁷	C₂×D₄	1	1	yes	characteristic
107	C₂³×#41	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
112	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
113	C₂²×#127	C₂×D₄	1	1	yes	characteristic
114	C₂²×#124	C₂²×C₄	1	1	yes	characteristic
115	C₂²×#124	C₂×D₄	1	1	yes	characteristic
116	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
123	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
124	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
125	C₂²×#120	C₂×D₄	1	1	yes	characteristic
126	C₂²×#120	C₂×D₄	1	1	yes	characteristic
127	C₂²×#120	C₂×D₄	1	1	yes	characteristic
128	C₂²×#120	C₂×D₄	1	1	yes	characteristic
129	C₂²×#120	C₂×D₄	1	1	yes	characteristic
130	C₂²×#120	C₂×D₄	1	1	yes	characteristic
131	C₂²×#120	C₂×D₄	1	1	yes	characteristic
132	C₂²×#117	C₂×D₄	1	1	yes	characteristic
133	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
136	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
137	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
139	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
140	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
141	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
142	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
143	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
144	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
145	C₂²×#99	#41	1	4	yes	complemented
146	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
154	#2309	#41	1	4	yes	complemented
155	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×#386	C₂²×C₄	1	1	yes	characteristic
158	C₂×#386	C₂×D₄	1	1	yes	characteristic
159	C₂×#381	C₂×D₄	1	1	yes	characteristic
160	C₂×#381	C₂×D₄	1	1	yes	characteristic
161	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#379	C₂×D₄	1	1	yes	characteristic
164	C₂×#379	C₂×D₄	1	1	yes	characteristic
165	C₂×#379	C₂×D₄	1	1	yes	characteristic
166	C₂×#379	C₂×D₄	1	1	yes	characteristic
167	#1440	C₂²⋊C₄	1	1	yes	characteristic
168	#1440	C₂²⋊C₄	1	1	yes	characteristic
169	#1440	C₂²⋊C₄	1	1	yes	characteristic
170	#1440	C₂²⋊C₄	1	1	yes	characteristic
171	#1440	C₂²⋊C₄	1	1	yes	characteristic
172	#1440	C₂²⋊C₄	1	1	yes	characteristic
173	#1440	C₂²⋊C₄	1	1	yes	characteristic
174	#1440	C₂²⋊C₄	1	1	yes	characteristic
175	#1438	C₂²⋊C₄	1	1	yes	characteristic
176	#1438	C₂²⋊C₄	1	1	yes	characteristic
177	#1438	C₂²⋊C₄	1	1	yes	characteristic
178	#1438	C₂²⋊C₄	1	1	yes	characteristic
179	#1438	C₂²⋊C₄	1	1	yes	characteristic
180	#1438	C₂²⋊C₄	1	1	yes	characteristic
181	#1438	C₂²⋊C₄	1	1	yes	characteristic
182	#1438	C₂²⋊C₄	1	1	yes	characteristic
183	#1438	C₂²×C₄	1	1	yes	characteristic
184	#1438	C₂²×C₄	1	1	yes	characteristic
185	#1438	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
192	#1438	C₂×D₄	1	1	yes	characteristic
193	#1438	C₂×D₄	1	1	yes	characteristic
194	#1438	C₂×D₄	1	1	yes	characteristic
195	#1438	C₂×D₄	1	1	yes	characteristic
196	#1438	C₂×D₄	1	1	yes	characteristic
197	#1438	C₂×D₄	1	1	yes	characteristic
198	#1438	C₂×D₄	1	1	yes	characteristic
199	#1437	C₂²⋊C₄	1	1	yes	characteristic
200	#1437	C₂²⋊C₄	1	1	yes	characteristic
201	#1437	C₂²⋊C₄	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	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂⁶	#120	1	1	yes	characteristic
211	C₂⁶	#120	1	1	yes	characteristic
212	C₂⁶	#120	1	1	yes	characteristic
213	C₂⁶	#120	1	1	yes	characteristic
214	C₂⁶	C₂²×D₄	1	1	yes	characteristic
215	C₂⁶	C₂²×D₄	1	1	yes	characteristic
216	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×D₄	C₂×C₂²⋊C₄	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	#120	1	1	yes	characteristic
223	C₂³×D₄	#120	1	1	yes	characteristic
224	C₂³×D₄	#120	1	1	yes	characteristic
225	C₂³×D₄	#120	1	1	yes	characteristic
226	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
227	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
228	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
229	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
230	C₂³×D₄	C₂×#41	1	2	yes	—
231	C₂³×D₄	C₂×#41	1	2	yes	—
232	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
233	C₂³×D₄	2₋¹⁺⁴	1	2	yes	—
234	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂⁴×C₄	#120	1	1	yes	characteristic
236	C₂⁴×C₄	#120	1	1	yes	characteristic
237	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	#120	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
263	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
264	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂⁵	#379	1	1	yes	characteristic
271	C₂⁵	#379	1	1	yes	characteristic
272	C₂⁵	#379	1	1	yes	characteristic
273	C₂⁵	#379	1	1	yes	characteristic
274	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
275	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
276	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
277	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
278	C₂⁵	#458	1	1	yes	characteristic
279	C₂⁵	#458	1	1	yes	characteristic
280	C₂⁵	#458	1	1	yes	characteristic
281	C₂⁵	#458	1	1	yes	characteristic
282	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
283	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
284	C₂⁵	C₂×#120	1	1	yes	characteristic
285	C₂⁵	C₂×#120	1	1	yes	characteristic
286	C₂⁵	C₂×#120	1	1	yes	characteristic
287	C₂⁵	#525	1	1	yes	characteristic
288	C₂⁵	#525	1	1	yes	characteristic
289	C₂⁵	#535	1	1	yes	characteristic
290	C₂⁵	#536	1	1	yes	characteristic
291	C₂⁵	#546	1	2	yes	—
292	C₂⁵	#547	1	2	yes	—
293	C₂²×D₄	C₄×#41	1	2	yes	—
294	C₂²×D₄	#520	1	2	yes	—
295	C₂²×D₄	#532	1	2	yes	—
296	C₂²×D₄	#537	1	2	yes	—
297	C₂²×D₄	#546	1	2	yes	—
298	C₂²×D₄	#546	1	2	yes	—
299	C₂²×D₄	#547	1	2	yes	—
300	C₂²×D₄	#547	1	2	yes	—
301	C₂³×C₄	#379	1	1	yes	characteristic
302	C₂³×C₄	#379	1	1	yes	characteristic
303	C₂³×C₄	#379	1	1	yes	characteristic
304	C₂³×C₄	#379	1	1	yes	characteristic
305	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
306	C₂³×C₄	C₂×#120	1	1	yes	characteristic
307	C₂³×C₄	#546	1	2	yes	—
308	C₂³×C₄	#547	1	2	yes	—
309	C₂⁴	#1790	1	1	yes	characteristic
310	C₂⁴	#1790	1	1	yes	characteristic
311	C₂⁴	#1790	1	1	yes	characteristic
312	C₂⁴	#1790	1	1	yes	characteristic
313	C₂⁴	#1790	1	1	yes	characteristic
314	C₂⁴	#1790	1	1	yes	characteristic
315	C₂⁴	#1790	1	1	yes	characteristic
316	C₂⁴	#1790	1	1	yes	characteristic
317	C₂⁴	C₂×#379	1	1	yes	characteristic
318	C₂⁴	#2297	1	1	yes	characteristic
319	C₂⁴	#2311	1	1	yes	characteristic
320	C₂⁴	#2339	1	2	yes	—
321	C₂⁴	#2404	1	1	yes	characteristic
322	C₂⁴	#2404	1	1	yes	characteristic
323	C₂⁴	#2406	1	1	yes	characteristic
324	C₂⁴	#2406	1	1	yes	characteristic
325	C₂⁴	#2430	1	2	yes	—
326	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
327	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
328	C₂⁴	C₂×#458	1	1	yes	characteristic
329	C₂⁴	C₂×#458	1	1	yes	characteristic
330	C₂²×C₄	#2339	1	2	yes	—
331	C₂²×C₄	#2430	1	2	yes	—
332	C₂³	#12753	1	2	yes	—
333	C₂³	#12753	1	2	yes	—
334	C₂³	#12754	1	2	yes	—
335	C₂³	#13956	1	1	yes	characteristic
336	C₂³	C₂×#1790	1	1	yes	characteristic
337	C₂³	C₂×#1790	1	1	yes	characteristic
338	C₂³	#23984	1	1	yes	characteristic
339	C₂³	#23985	1	1	yes	characteristic
340	C₂³	#23996	1	2	yes	—
341	C₂³	#24112	1	1	yes	characteristic
342	C₂³	#24112	1	1	yes	characteristic
343	C₂²	#363909	1	1	yes	characteristic
344	C₂²	#363953	1	1	yes	characteristic
345	C₂²	#363969	1	1	yes	characteristic
346	C₂²	C₂×#12753	1	1	yes	characteristic
347	C₂²	C₂×#12753	1	1	yes	characteristic
348	C₂²	C₂×#12754	1	1	yes	characteristic
349	C₂²	#493562	1	1	yes	characteristic
350	C₂	#72238858	1	1	yes	characteristic
351	C₂	#72238859	1	1	yes	characteristic
352	C₂	#72238862	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#363909
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72240130	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
1. #72240134	C₂	semidirect
2. #72240132	C₂	semidirect
4. #72236988	C₂	semidirect
5. #72236441	C₂	semidirect
6. #72235186	C₂	semidirect
7. #72234596	C₂	semidirect
8. #72233098	C₂	semidirect
9. #72233007	C₂	semidirect
10. #72213274	C₂	semidirect
11. #72210462	C₂	semidirect
14. #5486611	C₄	semidirect
15. #5069375	C₄	semidirect
16. #5065220	C₄	semidirect
19. #4128936	C₄	semidirect
20. #4117631	C₄	semidirect
21. #4035548	C₄	semidirect
22. #2227686	C₄	semidirect
23. #2108839	C₄	semidirect
56. #17273	C₂×C₄	semidirect
57. #17272	C₂×C₄	semidirect
58. #17137	C₂×C₄	semidirect
59. #17136	C₂×C₄	semidirect
68. #15784	C₂×C₄	semidirect
69. #15313	C₂×C₄	semidirect
72. #15259	C₂×C₄	semidirect
77. #15258	C₂×C₄	semidirect
80. #14666	C₂×C₄	semidirect
81. #14662	C₂×C₄	semidirect
82. #14516	C₂×C₄	semidirect
83. #14419	C₂×C₄	semidirect
84. #14419	C₂×C₄	semidirect
85. #14358	C₂×C₄	semidirect
92. #14169	C₂×C₄	semidirect
95. #14134	C₂×C₄	semidirect
145. C₂²×#99	#41	semidirect
154. #2309	#41	semidirect

Maximal subgroups

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

subgroup	index
#72240134	2
#72240132	2
#72240130	2
#72236988	2
#72236441	2
#72235186	2
#72234596	2
#72233098	2
#72233007	2
#72213274	2
#72210462	2