Subgroups — C₂×#20243568 #26216929

Order 12032.

1854 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#20243568	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688878	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₇⋊C₈	—	2	8	no	—
8	C₂³×C₄₇⋊C₈	—	2	4	no	—
9	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	4	yes	—
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	8	yes	complemented
15	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
17	#15688878	C₂²	1	8	yes	complemented
18	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₄₇	C₄	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₄₇	C₄	1	1	yes	characteristic
21	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
22	C₄×C₂²⋊C₄×C₄₇	C₄	1	4	yes	—
23	C₄×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
24	C₂×#95×C₄₇	C₄	1	2	yes	—
25	C₂²×C₄₇⋊C₈	—	2	32	no	—
26	C₂²×C₄₇⋊C₈	—	2	8	no	—
27	C₂²×C₄₇⋊C₈	—	2	4	no	—
28	C₂²×C₄₇⋊C₈	—	2	4	no	—
29	C₂²×C₄₇⋊C₈	—	2	16	no	—
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂²×C₄₇⋊C₈	—	2	4	no	—
33	C₂²×C₄₇⋊C₈	—	2	4	no	—
34	C₂²×C₄₇⋊C₈	D₄	1	8	yes	—
35	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
36	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
37	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
38	C₄⋊(C₄₇⋊C₈)	—	2	16	no	—
39	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
40	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	—	2	4	no	—
42	C₂³×C₄×C₄₇	—	2	4	no	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₄₇	D₄	1	4	yes	—
48	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₄₇	C₈	1	8	yes	complemented
53	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
54	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₄₇	—	2	4	no	—
56	C₂×C₄²×C₄₇	—	2	4	no	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
59	#95×C₄₇	C₂×C₄	1	8	yes	—
60	C₂⁴×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	—	2	4	no	—
62	C₂⁴×C₄₇	C₄⋊C₄	1	4	yes	—
63	C₂⁴×C₄₇	C₂×C₈	1	4	yes	—
64	C₂⁴×C₄₇	M₁₆	1	4	yes	—
65	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
66	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	—	2	4	no	—
68	C₂²×C₄×C₄₇	—	2	4	no	—
69	C₂²×C₄×C₄₇	—	2	4	no	—
70	C₂²×C₄×C₄₇	—	2	8	no	—
71	C₂²×C₄×C₄₇	—	2	8	no	—
72	C₂²×C₄×C₄₇	—	2	16	no	—
73	C₂²×C₄×C₄₇	—	2	8	no	—
74	C₂²×C₄×C₄₇	—	2	4	no	—
75	C₂²×C₄×C₄₇	—	2	4	no	—
76	C₂²×C₄×C₄₇	—	2	4	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	8	yes	—
81	C₂²×C₄×C₄₇	C₂×C₈	1	8	yes	complemented
82	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₂²⋊C₄×C₄₇	—	2	8	no	—
94	C₂²⋊C₄×C₄₇	C₂×C₈	1	16	yes	complemented
95	C₄²×C₄₇	—	2	8	no	—
96	C₄²×C₄₇	—	2	4	no	—
97	C₄²×C₄₇	—	2	4	no	—
98	C₂×C₄₇⋊C₈	—	2	32	no	—
99	C₂×C₄₇⋊C₈	—	2	16	no	—
100	C₂×C₄₇⋊C₈	—	2	4	no	—
101	C₂×C₄₇⋊C₈	—	2	4	no	—
102	C₂×C₄₇⋊C₈	—	2	2	no	—
103	C₂×C₄₇⋊C₈	—	2	2	no	—
104	C₂×C₄₇⋊C₈	—	2	4	no	—
105	C₂×C₄₇⋊C₈	—	2	4	no	—
106	C₂×C₄₇⋊C₈	—	4	4	no	—
107	C₂×C₄₇⋊C₈	—	4	4	no	—
108	C₂×C₄₇⋊C₈	C₂×D₄	1	8	yes	—
109	C₂³×C₄₇	—	2	4	no	—
110	C₂³×C₄₇	—	2	4	no	—
111	C₂³×C₄₇	—	2	8	no	—
112	C₂³×C₄₇	—	2	8	no	—
113	C₂³×C₄₇	—	2	16	no	—
114	C₂³×C₄₇	—	2	16	no	—
115	C₂³×C₄₇	C₄⋊C₈	1	16	yes	complemented
116	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
117	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
118	C₂³×C₄₇	C₄×D₄	1	4	yes	—
119	C₂³×C₄₇	C₂²×C₈	1	4	yes	—
120	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
121	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
122	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
123	C₂³×C₄₇	#131	1	4	yes	—
124	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	2	4	no	—
127	C₂×C₄×C₄₇	—	2	4	no	—
128	C₂×C₄×C₄₇	—	2	8	no	—
129	C₂×C₄×C₄₇	—	2	16	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	8	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	16	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	—	4	8	no	—
138	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
139	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
140	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
141	C₂×C₄×C₄₇	#120	1	4	yes	—
142	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
143	C₂×C₄×C₄₇	#123	1	4	yes	—
144	C₂×C₄×C₄₇	C₂²×C₈	1	8	yes	complemented
145	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
146	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
149	C₄₇⋊C₈	—	2	8	no	—
150	C₄₇⋊C₈	—	4	2	no	—
151	C₄₇⋊C₈	—	4	2	no	—
152	C₂×#1850	—	47	1	no	maximal, Sylow
153	C₂²×C₄₇	—	2	32	no	—
154	C₂²×C₄₇	—	2	4	no	—
155	C₂²×C₄₇	—	2	8	no	—
156	C₂²×C₄₇	—	2	8	no	—
157	C₂²×C₄₇	—	2	4	no	—
158	C₂²×C₄₇	#385	1	4	yes	—
159	C₂²×C₄₇	C₂×C₄⋊C₈	1	4	yes	—
160	C₂²×C₄₇	C₂×C₄⋊C₈	1	8	yes	complemented
161	C₂²×C₄₇	#424	1	4	yes	—
162	C₂²×C₄₇	C₈×D₄	1	8	yes	—
163	C₂²×C₄₇	#435	1	8	yes	—
164	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
166	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
167	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
168	C₂²×C₄₇	C₂×#131	1	2	yes	—
169	C₄×C₄₇	—	2	8	no	—
170	C₄×C₄₇	—	2	4	no	—
171	C₄×C₄₇	—	4	4	no	—
172	C₄×C₄₇	#385	1	4	yes	—
173	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
174	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
175	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
176	C₂⁴×C₈	—	47	1	no	—
177	C₂²×C₄⋊C₈	—	47	2	no	—
178	C₂²×C₂²⋊C₈	—	47	1	no	—
179	C₂×C₄×C₂²⋊C₄	D₄₇	1	1	yes	characteristic
180	#1850	—	47	8	no	—
181	C₂×#336	—	47	2	no	—
182	C₂×C₄₇	—	2	8	no	—
183	C₂×C₄₇	#1850	1	8	yes	complemented
184	C₂×C₄₇	C₂×#385	1	1	yes	characteristic
185	C₂×C₄₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
186	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
187	C₂×C₄₇	C₂×C₈×D₄	1	2	yes	—
188	C₂×C₄₇	C₂×#435	1	2	yes	—
189	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
190	C₂³×C₈	—	47	2	no	—
191	C₂³×C₈	—	47	4	no	—
192	C₂³×C₈	—	47	1	no	—
193	C₂³×C₈	—	47	1	no	—
194	C₂³×C₈	—	94	8	no	—
195	C₂³×C₈	—	94	4	no	—
196	C₂²×C₂²⋊C₄	Dic₄₇	1	1	yes	characteristic
197	C₂²×C₂²⋊C₄	Dic₄₇	1	1	yes	characteristic
198	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
199	C₂×C₄⋊C₈	—	47	8	no	—
200	C₂×C₄⋊C₈	—	94	8	no	—
201	C₂×C₂²⋊C₈	—	47	4	no	—
202	C₂×C₂²⋊C₈	—	94	4	no	—
203	C₄×C₂²⋊C₄	Dic₄₇	1	4	yes	—
204	C₄×C₂²⋊C₄	C₂×D₄₇	1	4	yes	—
205	C₂×#95	Dic₄₇	1	2	yes	—
206	#336	—	47	8	no	—
207	C₄₇	C₂×#1850	1	1	yes	characteristic, complemented, Sylow
208	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	—	2	4	no	—
211	C₂³×C₄	Dic₉₄	1	4	yes	—
212	C₂³×C₄	D₁₈₈	1	4	yes	—
213	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
214	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
215	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
216	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
217	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
218	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
219	C₂²×C₈	—	47	8	no	—
220	C₂²×C₈	—	47	4	no	—
221	C₂²×C₈	—	47	2	no	—
222	C₂²×C₈	—	47	2	no	—
223	C₂²×C₈	—	94	16	no	—
224	C₂²×C₈	—	94	32	no	—
225	C₂²×C₈	—	94	8	no	—
226	C₂²×C₈	—	94	4	no	—
227	C₂²×C₈	—	94	4	no	—
228	C₂²×C₈	—	94	2	no	—
229	C₂²×C₈	—	94	2	no	—
230	C₂²×C₈	—	94	4	no	—
231	C₂²×C₈	—	94	4	no	—
232	C₂×C₂²⋊C₄	—	2	4	no	—
233	C₂×C₂²⋊C₄	C₄₇⋊C₈	1	8	yes	complemented
234	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
235	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	—	2	4	no	—
238	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
239	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
240	C₄⋊C₈	—	94	16	no	—
241	C₂²⋊C₈	—	94	8	no	—
242	#95	C₂×Dic₄₇	1	8	yes	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	C₂×C₄₇⋊C₈	1	4	yes	—
246	C₂⁴	#10625329	1	4	yes	—
247	C₂⁴	C₄⋊Dic₄₇	1	4	yes	—
248	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
249	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	16	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	C₂×C₄₇⋊C₈	1	8	yes	complemented
263	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
264	C₂²×C₄	C₄⋊Dic₄₇	1	8	yes	—
265	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
266	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
267	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
268	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
269	C₂²×C₄	D₄×D₄₇	1	4	yes	—
270	C₂²×C₄	#10625352	1	4	yes	—
271	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
272	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
273	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
274	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
275	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
276	C₂×C₈	—	47	8	no	—
277	C₂×C₈	—	94	32	no	—
278	C₂×C₈	—	94	16	no	—
279	C₂×C₈	—	94	4	no	—
280	C₂×C₈	—	94	4	no	—
281	C₂×C₈	—	94	4	no	—
282	C₂×C₈	—	94	2	no	—
283	C₂×C₈	—	94	2	no	—
284	C₂×C₈	—	94	4	no	—
285	C₂×C₈	—	188	4	no	—
286	C₂×C₈	—	188	4	no	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	C₂×C₄₇⋊C₈	1	16	yes	complemented
289	C₄²	—	2	8	no	—
290	C₄²	—	2	4	no	—
291	C₄²	—	2	4	no	—
292	C₂³	—	2	8	no	—
293	C₂³	—	2	4	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	8	no	—
296	C₂³	—	2	16	no	—
297	C₂³	—	2	16	no	—
298	C₂³	C₄⋊(C₄₇⋊C₈)	1	16	yes	complemented
299	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
300	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
301	C₂³	D₄×Dic₄₇	1	4	yes	—
302	C₂³	C₂²×C₄₇⋊C₈	1	4	yes	—
303	C₂³	C₂²×C₄₇⋊C₈	1	2	yes	—
304	C₂³	C₂×#10625329	1	4	yes	—
305	C₂³	C₂×#10625329	1	2	yes	—
306	C₂³	#13094031	1	4	yes	—
307	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	16	no	—
313	C₂×C₄	—	2	16	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	4	8	no	—
321	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
322	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
323	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
324	C₂×C₄	#13093994	1	4	yes	—
325	C₂×C₄	#13094001	1	8	yes	—
326	C₂×C₄	#13094008	1	4	yes	—
327	C₂×C₄	C₂²×C₄₇⋊C₈	1	8	yes	complemented
328	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
329	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
330	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
331	C₂×C₄	C₂×#10625352	1	2	yes	—
332	C₈	—	94	8	no	—
333	C₈	—	188	2	no	—
334	C₈	—	188	2	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	32	no	—
338	C₂²	—	2	8	no	—
339	C₂²	—	2	8	no	—
340	C₂²	#15688998	1	4	yes	—
341	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	4	yes	—
342	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	8	yes	complemented
343	C₂²	#15689150	1	4	yes	—
344	C₂²	D₄×C₄₇⋊C₈	1	8	yes	—
345	C₂²	#15689195	1	8	yes	—
346	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
347	C₂²	C₂×D₄×Dic₄₇	1	2	yes	—
348	C₂²	C₂³×C₄₇⋊C₈	1	1	yes	characteristic
349	C₂²	C₂²×#10625329	1	1	yes	characteristic
350	C₂²	C₂×#13094031	1	2	yes	—
351	C₄	—	2	4	no	—
352	C₄	—	2	8	no	—
353	C₄	—	4	4	no	—
354	C₄	#15688998	1	4	yes	—
355	C₄	C₂×#13093994	1	1	yes	characteristic
356	C₄	C₂×#13094001	1	2	yes	—
357	C₄	C₂×#13094008	1	1	yes	characteristic
358	C₂	—	2	8	no	—
359	C₂	#20243568	1	8	yes	direct product factor
360	C₂	C₂×#15688998	1	1	yes	characteristic
361	C₂	C₂²×C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
362	C₂	C₂×#15689150	1	1	yes	characteristic
363	C₂	C₂×D₄×C₄₇⋊C₈	1	2	yes	—
364	C₂	C₂×#15689195	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×C₂²⋊C₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂²×C₄
prime radical	C₂⁵×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×C₂²⋊C₄	D₄₇
hypocenter	C₄₇	C₂×#1850
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
4. #20243568	C₂	direct (N × H)
5. C₂×#15688878	C₂	semidirect
14. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
17. #15688878	C₂²	semidirect
52. C₂×C₂²⋊C₄×C₄₇	C₈	semidirect
81. C₂²×C₄×C₄₇	C₂×C₈	semidirect
94. C₂²⋊C₄×C₄₇	C₂×C₈	semidirect
115. C₂³×C₄₇	C₄⋊C₈	semidirect
144. C₂×C₄×C₄₇	C₂²×C₈	semidirect
160. C₂²×C₄₇	C₂×C₄⋊C₈	semidirect
183. C₂×C₄₇	#1850	semidirect
207. C₄₇	C₂×#1850	semidirect
233. C₂×C₂²⋊C₄	C₄₇⋊C₈	semidirect
262. C₂²×C₄	C₂×C₄₇⋊C₈	semidirect
288. C₂²⋊C₄	C₂×C₄₇⋊C₈	semidirect
298. C₂³	C₄⋊(C₄₇⋊C₈)	semidirect
327. C₂×C₄	C₂²×C₄₇⋊C₈	semidirect
342. C₂²	C₂×C₄⋊(C₄₇⋊C₈)	semidirect
359. C₂	#20243568	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄₇⋊C₈	2
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂²×C₂²⋊(C₄₇⋊C₈)	2
#20243568	2
C₂×#15688878	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₂×#1850	47

Subgroups — C2×#20243568 #26216929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243568 #26216929