Subgroups — #27080058

Order 12032.

2198 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252046	C₂	1	16	yes	maximal, complemented
2	#20252026	C₂	1	4	yes	maximal, complemented
3	#20252021	C₂	1	4	yes	maximal, complemented
4	#20251952	C₂	1	2	yes	maximal, complemented
5	C₂×#15689087	C₂	1	2	yes	maximal
6	#20251807	C₂	1	2	yes	maximal, complemented
7	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625329	C₂²	1	4	yes	—
9	#15689184	C₂²	1	32	yes	complemented
10	#15689180	C₂²	1	16	yes	complemented
11	#15689176	C₂²	1	16	yes	complemented
12	#15689150	C₂²	1	16	yes	complemented
13	#15689147	C₂²	1	8	yes	complemented
14	#15689087	C₂²	1	4	yes	—
15	#15689087	C₂²	1	4	yes	—
16	#15689087	C₂²	1	8	yes	—
17	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	8	yes	—
18	#15689079	C₂²	1	16	yes	complemented
19	C₄×#10625329	C₂²	1	8	yes	complemented
20	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₇	C₄	1	8	yes	—
22	C₂×#117×C₄₇	C₄	1	2	yes	—
23	C₂×#117×C₄₇	C₄	1	2	yes	—
24	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₄₇	C₂²	1	2	yes	—
26	C₂×#117×C₄₇	C₂²	1	8	yes	—
27	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
30	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
31	C₂×#10625329	—	2	16	no	—
32	C₂×#10625329	C₂³	1	8	yes	—
33	C₂×#10625329	C₂³	1	8	yes	—
34	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	—
35	C₄⋊(C₄₇⋊C₈)	C₂³	1	32	yes	complemented
36	C₂²⋊(C₄₇⋊C₈)	C₂³	1	16	yes	—
37	C₂²⋊(C₄₇⋊C₈)	C₂³	1	16	yes	—
38	#13093935	C₂³	1	16	yes	complemented
39	C₄×C₄₇⋊C₈	C₂³	1	16	yes	complemented
40	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	—	2	8	no	—
42	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	#117×C₄₇	C₂×C₄	1	8	yes	—
52	#117×C₄₇	C₂×C₄	1	16	yes	—
53	#117×C₄₇	C₂×C₄	1	16	yes	—
54	#117×C₄₇	C₂×C₄	1	4	yes	—
55	#117×C₄₇	C₂×C₄	1	4	yes	—
56	#117×C₄₇	C₂³	1	4	yes	—
57	#117×C₄₇	C₂³	1	4	yes	—
58	#117×C₄₇	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
62	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
65	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
66	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
73	C₂⁴×C₄₇	—	2	4	no	—
74	C₂⁴×C₄₇	—	4	4	no	—
75	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
76	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
77	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	16	no	—
83	C₂²×C₄×C₄₇	—	2	16	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	4	8	no	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	8	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
105	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
106	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
107	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
108	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
109	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
110	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
111	C₄²×C₄₇	C₂²×C₄	1	16	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
113	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
114	C₄²×C₄₇	C₂⁴	1	4	yes	—
115	C₄²×C₄₇	C₂⁴	1	4	yes	—
116	#10625329	—	2	16	no	—
117	#10625329	—	2	16	no	—
118	C₂×C₄₇⋊C₈	—	2	16	no	—
119	C₂×C₄₇⋊C₈	C₂⁴	1	16	yes	—
120	C₂³×C₄₇	—	2	2	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	8	no	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	8	no	—
125	C₂³×C₄₇	—	4	2	no	—
126	C₂³×C₄₇	—	4	4	no	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	4	16	no	—
129	C₂³×C₄₇	#117	1	4	yes	—
130	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
131	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
132	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
133	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	16	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	2	8	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	—	4	8	no	—
147	C₂×C₄×C₄₇	#117	1	4	yes	—
148	C₂×C₄×C₄₇	#117	1	8	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
152	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
156	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
157	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
158	C₄₇⋊C₈	—	2	16	no	—
159	#60124	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	—	2	8	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	—	2	2	no	—
164	C₂²×C₄₇	—	2	4	no	—
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	4	no	—
167	C₂²×C₄₇	—	4	4	no	—
168	C₂²×C₄₇	—	4	16	no	—
169	C₂²×C₄₇	—	4	4	no	—
170	C₂²×C₄₇	C₂×#117	1	2	yes	—
171	C₂²×C₄₇	C₂×#117	1	4	yes	—
172	C₂²×C₄₇	#568	1	4	yes	—
173	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	—	2	2	no	—
176	C₄×C₄₇	—	2	8	no	—
177	C₄×C₄₇	—	2	8	no	—
178	C₄×C₄₇	C₂×#117	1	2	yes	—
179	C₄×C₄₇	C₂×#117	1	4	yes	—
180	C₄×C₄₇	C₂²×#41	1	2	yes	—
181	C₂²×#117	D₄₇	1	1	yes	characteristic
182	#2924	—	47	16	no	—
183	#2921	—	47	4	no	—
184	#2920	—	47	4	no	—
185	#2905	—	47	2	no	—
186	C₂×#407	—	47	2	no	—
187	#2873	—	47	2	no	—
188	C₂×C₄₇	—	2	2	no	—
189	C₂×C₄₇	—	2	4	no	—
190	C₂×C₄₇	—	2	4	no	—
191	C₂×C₄₇	—	4	2	no	—
192	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
193	C₂×C₄₇	C₂×#568	1	2	yes	—
194	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
195	C₂²×M₁₆	—	47	4	no	—
196	C₂×#117	Dic₄₇	1	8	yes	—
197	C₂×#117	Dic₄₇	1	2	yes	—
198	C₂×#117	Dic₄₇	1	2	yes	—
199	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
200	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
201	C₂×#117	C₂×D₄₇	1	2	yes	—
202	C₂×#117	C₂×D₄₇	1	8	yes	—
203	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
204	C₂²×C₂²⋊C₄	Dic₄₇	1	2	yes	—
205	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
206	#433	—	47	32	no	—
207	#432	—	47	16	no	—
208	#431	—	47	16	no	—
209	#424	—	47	16	no	—
210	#423	—	47	8	no	—
211	#407	—	47	4	no	—
212	#407	—	47	4	no	—
213	#407	—	47	8	no	—
214	C₂×C₂²⋊C₈	—	47	8	no	—
215	#405	—	47	16	no	—
216	C₄×M₁₆	—	47	8	no	—
217	C₄₇	#60124	1	1	yes	characteristic, complemented, Sylow
218	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
219	C₂³×C₄	—	2	8	no	—
220	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
222	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
223	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
224	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
225	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
226	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
227	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
228	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
229	C₂×M₁₆	—	47	8	no	—
230	C₂×M₁₆	—	47	8	no	—
231	C₂×M₁₆	—	94	16	no	—
232	C₂²×C₈	—	47	8	no	—
233	#117	C₂×Dic₄₇	1	8	yes	—
234	#117	C₂×Dic₄₇	1	16	yes	—
235	#117	C₂×Dic₄₇	1	16	yes	—
236	#117	C₂×Dic₄₇	1	4	yes	—
237	#117	C₂×Dic₄₇	1	4	yes	—
238	#117	C₂²×D₄₇	1	4	yes	—
239	#117	C₂²×D₄₇	1	4	yes	—
240	#117	C₂²×D₄₇	1	8	yes	—
241	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
242	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
243	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
244	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
245	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	—
247	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
248	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
249	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
250	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
251	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
252	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
253	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
254	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
255	C₄⋊C₈	—	47	32	no	—
256	C₂²⋊C₈	—	47	16	no	—
257	C₂²⋊C₈	—	47	16	no	—
258	#97	—	47	16	no	—
259	C₄×C₈	—	47	16	no	—
260	C₂⁴	—	2	4	no	—
261	C₂⁴	—	4	4	no	—
262	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
263	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
264	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
265	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	16	no	—
270	C₂²×C₄	—	2	16	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	8	no	—
274	C₂²×C₄	#10625350	1	8	yes	—
275	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
277	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
278	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
279	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
280	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
281	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
282	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
283	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
284	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
285	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
286	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
288	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
289	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
290	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
292	M₁₆	—	94	16	no	—
293	M₁₆	—	94	16	no	—
294	C₂×C₈	—	47	16	no	—
295	C₂×C₈	—	94	16	no	—
296	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	—
297	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
298	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
299	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
300	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
301	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
302	C₄²	C₂²×Dic₄₇	1	16	yes	—
303	C₄²	C₂²×Dic₄₇	1	4	yes	—
304	C₄²	C₂²×Dic₄₇	1	4	yes	—
305	C₄²	C₂³×D₄₇	1	4	yes	—
306	C₄²	C₂³×D₄₇	1	4	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	8	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	8	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	16	no	—
316	C₂³	#13093983	1	4	yes	—
317	C₂³	C₂³×Dic₄₇	1	2	yes	—
318	C₂³	C₂³×Dic₄₇	1	2	yes	—
319	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
320	C₂³	C₂³×Dic₄₇	1	2	yes	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	#13093983	1	4	yes	—
335	C₂×C₄	#13093983	1	8	yes	—
336	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
337	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
338	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
339	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
340	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
341	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
342	C₂×C₄	C₂×#10625350	1	8	yes	—
343	C₂×C₄	C₂×#10625350	1	4	yes	—
344	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
345	C₈	—	94	16	no	—
346	C₂²	—	2	8	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	16	no	—
355	C₂²	—	4	4	no	—
356	C₂²	C₂×#13093983	1	2	yes	—
357	C₂²	C₂×#13093983	1	4	yes	—
358	C₂²	#15689890	1	4	yes	—
359	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	8	no	—
363	C₄	—	2	8	no	—
364	C₄	C₂×#13093983	1	2	yes	—
365	C₄	C₂×#13093983	1	4	yes	—
366	C₄	C₂²×#10625350	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	4	no	—
369	C₂	—	2	4	no	—
370	C₂	—	4	2	no	—
371	C₂	C₂²×#13093983	1	1	yes	characteristic
372	C₂	C₂×#15689890	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂²×#117×C₄₇	C₂
prime radical	C₂⁵×C₄₇	C₂×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×#117	D₄₇
hypocenter	C₄₇	#60124
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. #20252046	C₂	semidirect
2. #20252026	C₂	semidirect
3. #20252021	C₂	semidirect
4. #20251952	C₂	semidirect
6. #20251807	C₂	semidirect
9. #15689184	C₂²	semidirect
10. #15689180	C₂²	semidirect
11. #15689176	C₂²	semidirect
12. #15689150	C₂²	semidirect
13. #15689147	C₂²	semidirect
18. #15689079	C₂²	semidirect
19. C₄×#10625329	C₂²	semidirect
35. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
38. #13093935	C₂³	semidirect
39. C₄×C₄₇⋊C₈	C₂³	semidirect
217. C₄₇	#60124	semidirect

Maximal subgroups

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

subgroup	index
#20252046	2
#20252026	2
#20252021	2
#20251952	2
C₂×#15689087	2
#20251807	2
C₂²×#117×C₄₇	2
#60124	47