Subgroups — C₂×#20252489 #27081241

Order 12032.

1794 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	C₂×#15689680	C₂	1	1	yes	maximal, characteristic
2	#20252489	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689253	C₂	1	2	yes	maximal, complemented
4	C₂×#15689250	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×Dic₉₄	C₂	1	2	yes	maximal, complemented
6	C₂×#15689247	C₂	1	2	yes	maximal, complemented
7	C₂×#15689181	C₂	1	4	yes	maximal
8	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic
10	#15689680	C₄	1	8	yes	—
11	#15689680	C₂²	1	8	yes	—
12	C₂×#13094024	C₄	1	1	yes	characteristic
13	C₂×#13094024	C₄	1	1	yes	characteristic
14	C₂×#13094016	C₄	1	2	yes	—
15	C₂×#13094003	C₄	1	2	yes	—
16	C₂×#13094003	C₄	1	2	yes	—
17	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
18	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
19	C₂×#13093983	C₂²	1	2	yes	—
20	#15689253	C₂²	1	16	yes	complemented
21	#15689250	C₂²	1	16	yes	complemented
22	C₈×Dic₉₄	C₂²	1	16	yes	complemented
23	#15689247	C₂²	1	16	yes	complemented
24	#15689181	C₂²	1	32	yes	—
25	#15689176	C₂²	1	8	yes	—
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
29	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
30	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
31	C₂×#13093934	C₂²	1	4	yes	—
32	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
33	C₂×C₈×Dic₄₇	C₂²	1	4	yes	—
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#431	C₂²	1	8	yes	—
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
40	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
41	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	#13094024	C₂×C₄	1	8	yes	—
45	#13094024	C₂×C₄	1	8	yes	—
46	#13094016	C₂×C₄	1	16	yes	—
47	#13094003	C₂×C₄	1	16	yes	—
48	#13094003	C₂×C₄	1	16	yes	—
49	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
50	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
51	C₄×Dic₉₄	C₂³	1	8	yes	—
52	C₄×Dic₉₄	C₂³	1	8	yes	—
53	#13093983	C₂×C₄	1	8	yes	—
54	#13093983	C₂³	1	8	yes	—
55	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
59	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
60	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
61	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
64	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
65	Dic₄₇⋊C₈	C₂³	1	16	yes	—
66	Dic₄₇⋊C₈	C₂³	1	16	yes	—
67	C₂²⋊(C₄₇⋊C₈)	C₂³	1	8	yes	—
68	#13093934	C₂³	1	16	yes	—
69	C₄×C₄₇⋊C₈	C₂³	1	8	yes	—
70	C₈×Dic₄₇	C₂³	1	16	yes	—
71	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
82	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
83	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
84	C₂²⋊C₈×C₄₇	C₂³	1	8	yes	—
85	C₄×C₈×C₄₇	C₂³	1	8	yes	—
86	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
102	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
103	C₂×Dic₉₄	—	2	8	no	—
104	C₂×Dic₉₄	—	2	8	no	—
105	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
106	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
107	C₂×C₈×C₄₇	—	2	4	no	—
108	C₂×C₈×C₄₇	—	2	4	no	—
109	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
110	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
111	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
113	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
115	C₄²×C₄₇	C₂⁴	1	2	yes	—
116	C₄²×C₄₇	C₂⁴	1	2	yes	—
117	C₂²⋊Dic₄₇	C₂²×C₄	1	16	yes	—
118	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
119	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
120	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
121	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
122	Dic₄₇⋊C₄	C₂²×C₄	1	16	yes	—
123	Dic₄₇⋊C₄	C₂²×C₄	1	16	yes	—
124	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
125	C₄×Dic₄₇	C₂⁴	1	8	yes	—
126	C₂×C₄₇⋊C₈	—	2	4	no	—
127	C₂×C₄₇⋊C₈	—	2	4	no	—
128	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
129	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
134	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	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	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	#131	1	4	yes	—
144	C₂×C₄×C₄₇	#131	1	4	yes	—
145	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
146	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
147	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
151	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
152	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
153	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
154	C₂×Dic₄₇	—	2	8	no	—
155	C₂×Dic₄₇	—	2	8	no	—
156	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
157	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
158	Dic₉₄	—	2	16	no	—
159	Dic₉₄	—	2	16	no	—
160	C₈×C₄₇	—	2	4	no	—
161	C₈×C₄₇	—	2	4	no	—
162	C₄₇⋊C₈	—	2	4	no	—
163	C₄₇⋊C₈	—	2	4	no	—
164	C₂×#2986	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	4	4	no	—
169	C₂²×C₄₇	#519	1	2	yes	—
170	C₂²×C₄₇	C₂×#131	1	2	yes	—
171	C₂²×C₄₇	C₂×#131	1	2	yes	—
172	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
173	C₄×C₄₇	—	2	2	no	—
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	—	2	2	no	—
176	C₄×C₄₇	#519	1	2	yes	—
177	C₄×C₄₇	C₂×#131	1	4	yes	—
178	C₄×C₄₇	C₂×#131	1	4	yes	—
179	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
180	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
181	Dic₄₇	—	2	8	no	—
182	Dic₄₇	—	2	8	no	—
183	C₂×#533	—	47	1	no	—
184	#2986	—	47	16	no	—
185	C₂×#446	—	47	2	no	—
186	C₂×#446	—	47	2	no	—
187	C₂×C₈×Q₈	—	47	2	no	—
188	C₂×C₈×Q₈	—	47	2	no	—
189	C₂×#433	—	47	4	no	—
190	C₂×#431	—	47	1	no	—
191	C₂×#431	D₄₇	1	1	yes	characteristic
192	C₂×C₄₇	—	4	2	no	—
193	C₂×C₄₇	#2986	1	4	yes	complemented
194	C₂×C₄₇	C₂×#519	1	1	yes	characteristic
195	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
196	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
197	#533	—	47	8	no	—
198	#533	—	47	8	no	—
199	C₂×C₄⋊Q₈	—	47	1	no	—
200	C₂×C₄⋊Q₈	—	47	1	no	—
201	C₂×#125	—	47	2	no	—
202	C₂×C₂²⋊Q₈	—	47	2	no	—
203	C₂×C₂²⋊Q₈	—	47	2	no	—
204	C₂×C₄×Q₈	—	47	2	no	—
205	C₂×C₄×Q₈	—	47	2	no	—
206	C₂×#117	—	47	2	no	—
207	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
208	#446	—	47	16	no	—
209	#446	—	47	16	no	—
210	C₈×Q₈	—	47	16	no	—
211	C₈×Q₈	—	47	16	no	—
212	#433	—	47	32	no	—
213	#431	—	47	8	no	—
214	#431	C₂×D₄₇	1	8	yes	—
215	C₂×C₄⋊C₈	—	47	4	no	—
216	C₂×C₄⋊C₈	—	47	4	no	—
217	C₂×C₄⋊C₈	—	47	1	no	—
218	C₂×C₄⋊C₈	—	47	1	no	—
219	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
221	C₂×C₂²⋊C₈	—	47	2	no	—
222	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
223	C₂×#97	—	47	4	no	—
224	C₂×C₄×C₈	—	47	4	no	—
225	C₂×C₄×C₈	—	47	2	no	—
226	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
227	C₄₇	C₂×#2986	1	1	yes	characteristic, complemented, Sylow
228	C₂²×Q₈	—	47	2	no	—
229	C₂²×Q₈	—	47	2	no	—
230	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
231	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
232	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
233	C₂²×C₈	—	47	2	no	—
234	C₂²×C₈	—	47	2	no	—
235	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
236	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
237	C₄⋊Q₈	—	47	8	no	—
238	C₄⋊Q₈	—	47	8	no	—
239	#125	—	47	16	no	—
240	C₂²⋊Q₈	—	47	16	no	—
241	C₂²⋊Q₈	—	47	16	no	—
242	C₄×Q₈	—	47	8	no	—
243	C₄×Q₈	—	47	8	no	—
244	C₄×Q₈	—	47	8	no	—
245	C₄×Q₈	—	47	8	no	—
246	#117	—	47	8	no	—
247	#117	—	47	8	no	—
248	C₂×C₄⋊C₄	—	47	2	no	—
249	C₂×C₄⋊C₄	—	47	2	no	—
250	C₂×C₄⋊C₄	—	47	4	no	—
251	C₂×C₄⋊C₄	—	47	4	no	—
252	C₂×C₄⋊C₄	—	47	2	no	—
253	C₂×C₄⋊C₄	—	47	2	no	—
254	C₂×C₂²⋊C₄	—	47	4	no	—
255	C₂×C₄²	—	47	4	no	—
256	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
257	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
258	C₂×C₄²	C₄×D₄₇	1	4	yes	—
259	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
260	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	C₄⋊C₈	—	47	16	no	—
263	C₄⋊C₈	—	47	16	no	—
264	C₄⋊C₈	—	47	4	no	—
265	C₄⋊C₈	—	47	4	no	—
266	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
267	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
268	C₂²⋊C₈	—	47	8	no	—
269	C₂²⋊C₈	C₂²×D₄₇	1	8	yes	—
270	#97	—	47	16	no	—
271	C₄×C₈	—	47	16	no	—
272	C₄×C₈	—	47	8	no	—
273	C₄×C₈	C₂²×D₄₇	1	8	yes	—
274	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
275	C₂×Q₈	—	47	8	no	—
276	C₂×Q₈	—	47	8	no	—
277	C₂×Q₈	—	94	8	no	—
278	C₂×Q₈	—	94	8	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	47	4	no	—
284	C₂²×C₄	—	47	4	no	—
285	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
287	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
290	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
291	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
294	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	47	4	no	—
298	C₂×C₈	—	47	4	no	—
299	C₂×C₈	—	94	4	no	—
300	C₂×C₈	—	94	4	no	—
301	C₂×C₈	C₂³×D₄₇	1	4	yes	—
302	C₂×C₈	C₂³×D₄₇	1	4	yes	—
303	C₄⋊C₄	—	47	16	no	—
304	C₄⋊C₄	—	47	16	no	—
305	C₄⋊C₄	—	47	8	no	—
306	C₄⋊C₄	—	47	8	no	—
307	C₄⋊C₄	—	47	8	no	—
308	C₄⋊C₄	—	47	8	no	—
309	C₂²⋊C₄	—	47	16	no	—
310	C₄²	—	47	8	no	—
311	C₄²	—	47	8	no	—
312	C₄²	C₂×C₄×D₄₇	1	2	yes	—
313	C₄²	C₂×C₄×D₄₇	1	2	yes	—
314	C₄²	C₂×C₄×D₄₇	1	4	yes	—
315	C₄²	C₂×C₄×D₄₇	1	4	yes	—
316	C₄²	C₂³×D₄₇	1	2	yes	—
317	C₄²	C₂³×D₄₇	1	2	yes	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
322	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
323	Q₈	—	94	16	no	—
324	Q₈	—	94	16	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	47	8	no	—
334	C₂×C₄	—	47	8	no	—
335	C₂×C₄	—	94	8	no	—
336	C₂×C₄	—	94	8	no	—
337	C₂×C₄	#13094030	1	4	yes	—
338	C₂×C₄	#13094032	1	4	yes	—
339	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
340	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
341	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
342	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
344	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
345	C₂×C₄	#13094071	1	2	yes	—
346	C₂×C₄	#13094071	1	2	yes	—
347	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
348	C₈	—	2	4	no	—
349	C₈	—	2	4	no	—
350	C₈	—	94	4	no	—
351	C₈	—	94	4	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	4	4	no	—
356	C₂²	#15689600	1	2	yes	—
357	C₂²	C₂×#13094030	1	2	yes	—
358	C₂²	C₂×#13094032	1	2	yes	—
359	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	94	8	no	—
364	C₄	—	94	8	no	—
365	C₄	#15689600	1	2	yes	—
366	C₄	C₂×#13094030	1	4	yes	—
367	C₄	C₂×#13094032	1	4	yes	—
368	C₄	C₂×#13094071	1	1	yes	characteristic
369	C₄	C₂×#13094071	1	1	yes	characteristic
370	C₂	—	4	2	no	—
371	C₂	#20252489	1	4	yes	direct product factor
372	C₂	C₂×#15689600	1	1	yes	characteristic
373	C₂	C₂²×#13094030	1	1	yes	characteristic
374	C₂	C₂²×#13094032	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#431	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#431	D₄₇
hypocenter	C₄₇	C₂×#2986
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
2. #20252489	C₂	direct (N × H)
3. C₂×#15689253	C₂	semidirect
4. C₂×#15689250	C₂	semidirect
5. C₂×C₈×Dic₉₄	C₂	semidirect
6. C₂×#15689247	C₂	semidirect
20. #15689253	C₂²	semidirect
21. #15689250	C₂²	semidirect
22. C₈×Dic₉₄	C₂²	semidirect
23. #15689247	C₂²	semidirect
193. C₂×C₄₇	#2986	semidirect
227. C₄₇	C₂×#2986	semidirect
371. C₂	#20252489	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689680	2
#20252489	2
C₂×#15689253	2
C₂×#15689250	2
C₂×C₈×Dic₉₄	2
C₂×#15689247	2
C₂×#15689181	2
C₂×#15689176	2
C₂×C₄₇×#431	2
C₂×#2986	47

Subgroups — C2×#20252489 #27081241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252489 #27081241