Subgroups — C₂×#20242059 #26184600

Order 12032.

1246 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
3	#20242059	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688868	C₂	1	4	yes	maximal, complemented
5	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₉₄	—	2	1	no	—
7	C₂²×#10625329	—	2	1	no	—
8	C₂×#13094024	—	2	1	no	—
9	C₂×#13094024	—	2	2	no	—
10	C₂×#13094024	—	2	1	no	—
11	C₂×#13094024	—	2	2	no	—
12	C₂×#13094024	C₄	1	2	yes	—
13	C₂×#13094024	C₄	1	4	yes	—
14	C₂×#13094024	C₂²	1	2	yes	—
15	C₂×#13094024	C₂²	1	4	yes	—
16	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
17	C₂²×C₄⋊Dic₄₇	C₄	1	2	yes	—
18	#15689147	—	2	2	no	—
19	#15689147	C₂²	1	4	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	#15688868	C₂²	1	16	yes	complemented
23	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#431	—	2	2	no	—
25	C₄₇×#431	C₂²	1	4	yes	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
28	C₂×C₄×C₈×C₄₇	—	2	1	no	—
29	C₂²×Dic₉₄	—	2	4	no	—
30	C₂²×Dic₉₄	—	2	2	no	—
31	C₂²×Dic₉₄	—	2	2	no	—
32	C₂²×Dic₉₄	—	2	4	no	—
33	C₂²×Dic₉₄	—	4	4	no	—
34	C₂²×Dic₉₄	—	4	4	no	—
35	C₂³×Dic₄₇	—	2	2	no	—
36	C₂×#10625329	—	2	4	no	—
37	C₂×#10625329	—	4	4	no	—
38	C₂²×C₄₇⋊C₈	—	2	2	no	—
39	#13094024	—	2	4	no	—
40	#13094024	—	2	4	no	—
41	#13094024	—	2	4	no	—
42	#13094024	—	2	2	no	—
43	#13094024	—	2	4	no	—
44	#13094024	—	2	2	no	—
45	#13094024	—	2	4	no	—
46	#13094024	C₂×C₄	1	4	yes	—
47	#13094024	C₂×C₄	1	8	yes	—
48	#13094024	C₂³	1	4	yes	—
49	C₂×C₄⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄⋊Dic₄₇	—	2	4	no	—
51	C₂×C₄⋊Dic₄₇	—	2	4	no	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄⋊Dic₄₇	—	2	4	no	—
54	C₂×C₄⋊Dic₄₇	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
57	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
60	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₄₇	—	2	2	no	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	D₄	1	2	yes	—
68	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	D₄	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
72	C₄⋊C₈×C₄₇	—	2	2	no	—
73	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
74	C₂²⋊C₈×C₄₇	—	2	4	no	—
75	C₄×C₈×C₄₇	—	2	4	no	—
76	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	D₈	1	4	yes	—
86	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×Dic₄₇	—	2	8	no	—
94	C₂²×Dic₄₇	—	2	4	no	—
95	C₂²×Dic₄₇	—	4	8	no	—
96	C₂×Dic₉₄	—	2	4	no	—
97	C₂×Dic₉₄	—	2	8	no	—
98	C₂×Dic₉₄	—	2	4	no	—
99	C₂×Dic₉₄	—	4	16	no	—
100	C₂×Dic₉₄	—	4	8	no	—
101	C₂×Dic₉₄	—	4	4	no	—
102	C₂×Dic₉₄	—	4	8	no	—
103	C₂×Dic₉₄	—	4	8	no	—
104	C₂×Dic₉₄	—	4	4	no	—
105	C₂×C₈×C₄₇	—	2	4	no	—
106	C₂×C₈×C₄₇	—	4	4	no	—
107	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
108	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
109	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
110	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
111	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₄₇	C₂×D₄	1	2	yes	—
113	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂×D₄	1	2	yes	—
116	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₄⋊Dic₄₇	—	2	8	no	—
118	C₄⋊Dic₄₇	—	2	4	no	—
119	C₄⋊Dic₄₇	—	2	4	no	—
120	C₄⋊Dic₄₇	—	2	8	no	—
121	C₄⋊Dic₄₇	—	2	4	no	—
122	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
123	#10625329	—	4	8	no	—
124	C₂×C₄₇⋊C₈	—	2	4	no	—
125	C₂×C₄₇⋊C₈	—	4	4	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	#102	1	4	yes	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	#101	1	4	yes	—
138	C₂×C₄×C₄₇	#102	1	8	yes	—
139	C₂×C₄×C₄₇	#102	1	4	yes	—
140	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
148	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
149	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
150	C₂×C₄×C₄₇	#137	1	4	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×Dic₄₇	—	2	8	no	—
155	C₂×Dic₄₇	—	4	16	no	—
156	C₂×Dic₄₇	—	4	8	no	—
157	Dic₉₄	—	4	4	no	—
158	Dic₉₄	—	4	4	no	—
159	Dic₉₄	—	4	8	no	—
160	Dic₉₄	—	4	16	no	—
161	C₈×C₄₇	—	4	4	no	—
162	C₄₇⋊C₈	—	4	4	no	—
163	C₂×#1546	—	47	1	no	maximal, Sylow
164	C₂²×C₄₇	—	2	8	no	—
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	C₂×#101	1	2	yes	—
168	C₂²×C₄₇	C₂×#102	1	4	yes	—
169	C₂²×C₄₇	C₂×#102	1	2	yes	—
170	C₂²×C₄₇	#419	1	2	yes	—
171	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₄×C₄₇	—	2	1	no	—
173	C₄×C₄₇	—	2	1	no	—
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	C₂×#101	1	4	yes	—
176	C₄×C₄₇	C₂×#102	1	2	yes	—
177	C₄×C₄₇	C₂×#102	1	4	yes	—
178	C₄×C₄₇	#419	1	2	yes	—
179	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
180	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
181	C₄×C₄₇	C₂×#137	1	2	yes	—
182	Dic₄₇	—	4	8	no	—
183	C₂²×C₄⋊Q₈	—	47	1	no	—
184	C₂×#431	D₄₇	1	1	yes	characteristic
185	C₂×#423	—	47	1	no	—
186	#1546	—	47	8	no	—
187	C₂×#332	—	47	4	no	—
188	C₂×C₄₇	—	2	4	no	—
189	C₂×C₄₇	#1546	1	4	yes	complemented
190	C₂×C₄₇	C₂²×#101	1	1	yes	characteristic
191	C₂×C₄₇	C₂²×#102	1	1	yes	characteristic
192	C₂×C₄₇	C₂×#419	1	1	yes	characteristic
193	C₂³×Q₈	—	94	1	no	—
194	C₂²×M₁₆	—	94	1	no	—
195	C₂×C₄⋊Q₈	—	47	4	no	—
196	C₂×C₄⋊Q₈	—	47	2	no	—
197	C₂×C₄⋊Q₈	—	47	2	no	—
198	C₂×C₄⋊Q₈	—	47	4	no	—
199	C₂×C₄⋊Q₈	—	94	1	no	—
200	C₂×C₄⋊Q₈	—	94	2	no	—
201	C₂×C₄⋊Q₈	—	94	1	no	—
202	C₂×C₄⋊Q₈	—	94	2	no	—
203	C₂²×C₄⋊C₄	—	47	2	no	—
204	C₂²×C₄⋊C₄	—	94	1	no	—
205	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
206	#431	—	2	2	no	—
207	#431	C₂×D₄₇	1	4	yes	—
208	#423	—	47	4	no	—
209	#423	—	94	2	no	—
210	C₂×C₄⋊C₈	—	47	2	no	—
211	C₂×C₄⋊C₈	—	94	1	no	—
212	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
213	C₂×C₂²⋊C₈	—	2	1	no	—
214	C₂×C₄×C₈	—	2	1	no	—
215	#332	—	47	16	no	—
216	C₄₇	C₂×#1546	1	1	yes	characteristic, complemented, Sylow
217	C₂²×Q₈	—	94	4	no	—
218	C₂²×Q₈	—	94	2	no	—
219	C₂²×Q₈	—	94	4	no	—
220	C₂²×Q₈	—	94	2	no	—
221	C₂²×Q₈	—	188	4	no	—
222	C₂²×Q₈	—	188	4	no	—
223	C₂³×C₄	—	94	2	no	—
224	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
225	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
226	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
227	C₂×M₁₆	—	94	4	no	—
228	C₂×M₁₆	—	188	4	no	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	—	94	2	no	—
231	C₄⋊Q₈	—	47	4	no	—
232	C₄⋊Q₈	—	47	8	no	—
233	C₄⋊Q₈	—	47	4	no	—
234	C₄⋊Q₈	—	94	4	no	—
235	C₄⋊Q₈	—	94	4	no	—
236	C₄⋊Q₈	—	94	4	no	—
237	C₄⋊Q₈	—	94	2	no	—
238	C₄⋊Q₈	—	94	4	no	—
239	C₄⋊Q₈	—	94	4	no	—
240	C₄⋊Q₈	—	94	2	no	—
241	C₂×C₄⋊C₄	—	47	8	no	—
242	C₂×C₄⋊C₄	—	47	4	no	—
243	C₂×C₄⋊C₄	—	94	4	no	—
244	C₂×C₄⋊C₄	—	94	2	no	—
245	C₂×C₄⋊C₄	—	94	4	no	—
246	C₂×C₄⋊C₄	—	94	2	no	—
247	C₂×C₄⋊C₄	—	94	4	no	—
248	C₂×C₄⋊C₄	—	94	2	no	—
249	C₂×C₄²	C₄×D₄₇	1	2	yes	—
250	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
251	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
252	C₂×C₄²	D₁₈₈	1	2	yes	—
253	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
254	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
255	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
256	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	47	4	no	—
259	C₄⋊C₈	—	94	2	no	—
260	C₄⋊C₈	—	94	4	no	—
261	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
262	C₂²⋊C₈	—	2	4	no	—
263	C₄×C₈	—	2	4	no	—
264	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
265	C₂×Q₈	—	94	8	no	—
266	C₂×Q₈	—	94	4	no	—
267	C₂×Q₈	—	94	4	no	—
268	C₂×Q₈	—	188	16	no	—
269	C₂×Q₈	—	188	8	no	—
270	C₂×Q₈	—	188	4	no	—
271	C₂×Q₈	—	188	8	no	—
272	C₂×Q₈	—	188	8	no	—
273	C₂×Q₈	—	188	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	94	8	no	—
277	C₂²×C₄	—	94	4	no	—
278	C₂²×C₄	—	188	8	no	—
279	C₂²×C₄	#10625325	1	4	yes	—
280	C₂²×C₄	D₃₇₆	1	4	yes	—
281	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
282	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
283	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
286	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
288	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
290	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
292	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
293	M₁₆	—	188	8	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	4	4	no	—
296	C₂×C₈	—	94	4	no	—
297	C₂×C₈	—	188	4	no	—
298	C₄⋊C₄	—	47	8	no	—
299	C₄⋊C₄	—	94	4	no	—
300	C₄⋊C₄	—	94	8	no	—
301	C₄⋊C₄	—	94	8	no	—
302	C₄⋊C₄	—	94	4	no	—
303	C₄⋊C₄	—	94	4	no	—
304	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
305	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
306	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
307	C₄²	C₂×C₄×D₄₇	1	2	yes	—
308	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
309	C₄²	C₂×D₁₈₈	1	2	yes	—
310	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
311	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
312	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
313	C₄²	C₂³×D₄₇	1	1	yes	characteristic
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	#13093946	1	4	yes	—
317	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
318	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
319	Q₈	—	188	8	no	—
320	Q₈	—	188	16	no	—
321	Q₈	—	188	4	no	—
322	Q₈	—	188	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	94	8	no	—
330	C₂×C₄	—	188	16	no	—
331	C₂×C₄	—	188	8	no	—
332	C₂×C₄	#13093942	1	4	yes	—
333	C₂×C₄	#13093946	1	8	yes	—
334	C₂×C₄	#13093946	1	4	yes	—
335	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
336	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
338	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
339	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
342	C₂×C₄	C₂×D₃₇₆	1	4	yes	—
343	C₂×C₄	C₂×#10625325	1	4	yes	—
344	C₂×C₄	C₂×#10625325	1	2	yes	—
345	C₂×C₄	#13094054	1	4	yes	—
346	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
349	C₈	—	4	4	no	—
350	C₈	—	188	4	no	—
351	C₂²	—	2	8	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	C₂×#13093942	1	2	yes	—
355	C₂²	C₂×#13093946	1	4	yes	—
356	C₂²	C₂×#13093946	1	2	yes	—
357	C₂²	#15689131	1	2	yes	—
358	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	2	no	—
362	C₄	—	188	8	no	—
363	C₄	C₂×#13093942	1	4	yes	—
364	C₄	C₂×#13093946	1	2	yes	—
365	C₄	C₂×#13093946	1	4	yes	—
366	C₄	#15689131	1	2	yes	—
367	C₄	C₂²×D₃₇₆	1	1	yes	characteristic
368	C₄	C₂²×#10625325	1	1	yes	characteristic
369	C₄	C₂×#13094054	1	2	yes	—
370	C₂	—	2	4	no	—
371	C₂	#20242059	1	4	yes	direct product factor
372	C₂	C₂²×#13093942	1	1	yes	characteristic
373	C₂	C₂²×#13093946	1	1	yes	characteristic
374	C₂	C₂×#15689131	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#431	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#431	D₄₇
hypocenter	C₄₇	C₂×#1546
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #20242059	C₂	direct (N × H)
4. C₂×#15688868	C₂	semidirect
22. #15688868	C₂²	semidirect
189. C₂×C₄₇	#1546	semidirect
216. C₄₇	C₂×#1546	semidirect
371. C₂	#20242059	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13094024	2
C₂×#15689147	2
#20242059	2
C₂×#15688868	2
C₂×C₄₇×#431	2
C₂×#1546	47

Subgroups — C2×#20242059 #26184600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242059 #26184600