Subgroups — C₂×#20241791 #26182778

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#20241791	C₂	1	8	yes	maximal, direct product factor
4	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	4	yes	maximal, complemented
5	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	—	2	1	no	—
7	#15689176	—	2	2	no	—
8	#15689176	C₂²	1	4	yes	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
16	Q₈⋊(C₄₇⋊C₈)	C₂²	1	16	yes	complemented
17	C₄₇×#533	—	2	2	no	—
18	C₄₇×#533	—	2	2	no	—
19	C₄₇×#533	C₄	1	4	yes	—
20	C₄₇×#533	C₂²	1	4	yes	—
21	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
23	C₂×#125×C₄₇	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
26	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
27	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
28	C₂×#117×C₄₇	—	2	1	no	—
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	2	4	no	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	—	4	4	no	—
34	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
35	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
36	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
37	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
38	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
39	C₄×C₄₇⋊C₈	—	2	2	no	—
40	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
41	C₂²×Q₈×C₄₇	—	2	1	no	—
42	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₄⋊Q₈×C₄₇	—	2	2	no	—
47	C₄⋊Q₈×C₄₇	—	2	2	no	—
48	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
49	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
50	#125×C₄₇	—	2	4	no	—
51	#125×C₄₇	—	2	4	no	—
52	C₂²⋊Q₈×C₄₇	—	2	4	no	—
53	C₂²⋊Q₈×C₄₇	—	2	4	no	—
54	C₂²⋊Q₈×C₄₇	—	2	4	no	—
55	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
56	C₄×Q₈×C₄₇	—	2	4	no	—
57	C₄×Q₈×C₄₇	—	2	4	no	—
58	C₄×Q₈×C₄₇	—	2	2	no	—
59	C₄×Q₈×C₄₇	—	2	2	no	—
60	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
62	#117×C₄₇	—	2	4	no	—
63	#117×C₄₇	—	2	4	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	—	2	2	no	—
72	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	D₄	1	2	yes	—
77	C₂×C₄²×C₄₇	D₄	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	4	no	—
83	C₂×Q₈×C₄₇	—	2	8	no	—
84	C₂×Q₈×C₄₇	—	4	4	no	—
85	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
97	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	2	4	no	—
107	C₄⋊C₄×C₄₇	—	2	8	no	—
108	C₄⋊C₄×C₄₇	—	2	4	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	4	no	—
111	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
112	C₂²⋊C₄×C₄₇	—	2	8	no	—
113	C₄²×C₄₇	—	2	4	no	—
114	C₄²×C₄₇	—	2	4	no	—
115	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
116	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
118	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×D₄	1	2	yes	—
123	C₄²×C₄₇	C₂×D₄	1	2	yes	—
124	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂×C₄₇⋊C₈	—	2	4	no	—
126	C₂×C₄₇⋊C₈	—	2	4	no	—
127	C₂×C₄₇⋊C₈	—	4	4	no	—
128	C₂×C₄₇⋊C₈	—	4	8	no	—
129	C₂×C₄₇⋊C₈	—	4	4	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	#103	1	4	yes	—
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	Q₈×C₄₇	—	2	8	no	—
136	Q₈×C₄₇	—	4	8	no	—
137	Q₈×C₄₇	—	4	4	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	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	—	2	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	#103	1	8	yes	—
150	C₂×C₄×C₄₇	#103	1	4	yes	—
151	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	#131	1	4	yes	—
158	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
159	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
161	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
162	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₄₇⋊C₈	—	4	4	no	—
166	C₄₇⋊C₈	—	4	4	no	—
167	C₂×#1481	—	47	1	no	maximal, Sylow
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	2	8	no	—
171	C₂²×C₄₇	#408	1	2	yes	—
172	C₂²×C₄₇	C₂×#103	1	4	yes	—
173	C₂²×C₄₇	C₂×#103	1	2	yes	—
174	C₂²×C₄₇	#421	1	2	yes	—
175	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	2	1	no	—
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	4	4	no	—
181	C₄×C₄₇	—	4	4	no	—
182	C₄×C₄₇	#408	1	2	yes	—
183	C₄×C₄₇	C₂×#103	1	2	yes	—
184	C₄×C₄₇	C₂×#103	1	4	yes	—
185	C₄×C₄₇	C₂×#131	1	2	yes	—
186	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
187	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
188	C₂×#533	D₄₇	1	1	yes	characteristic
189	C₂×#431	—	47	1	no	—
190	C₂²×C₄⋊C₈	—	47	1	no	—
191	#1481	—	47	8	no	—
192	C₂×Q₈⋊C₈	—	47	4	no	—
193	C₂×C₄₇	—	2	4	no	—
194	C₂×C₄₇	#1481	1	4	yes	complemented
195	C₂×C₄₇	C₂×#408	1	1	yes	characteristic
196	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
197	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
198	C₂³×C₈	—	94	1	no	—
199	#533	—	2	2	no	—
200	#533	—	2	2	no	—
201	#533	Dic₄₇	1	4	yes	—
202	#533	C₂×D₄₇	1	4	yes	—
203	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic
205	C₂×#125	—	2	1	no	—
206	C₂×C₂²⋊Q₈	—	2	1	no	—
207	C₂×C₂²⋊Q₈	Dic₄₇	1	2	yes	—
208	C₂×C₄×Q₈	—	2	1	no	—
209	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
210	C₂×#117	—	2	1	no	—
211	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
212	#431	—	47	4	no	—
213	#431	—	94	2	no	—
214	C₂×C₄⋊C₈	—	47	2	no	—
215	C₂×C₄⋊C₈	—	47	4	no	—
216	C₂×C₄⋊C₈	—	94	2	no	—
217	C₂×C₄⋊C₈	—	94	1	no	—
218	C₂×C₄⋊C₈	—	94	1	no	—
219	C₂×C₂²⋊C₈	—	94	1	no	—
220	C₂×C₄×C₈	—	47	2	no	—
221	Q₈⋊C₈	—	47	16	no	—
222	C₄₇	C₂×#1481	1	1	yes	characteristic, complemented, Sylow
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
225	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
226	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
227	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
228	C₂²×C₈	—	94	4	no	—
229	C₂²×C₈	—	94	2	no	—
230	C₂²×C₈	—	94	2	no	—
231	C₂²×C₈	—	188	4	no	—
232	C₄⋊Q₈	—	2	2	no	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
235	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
236	#125	—	2	4	no	—
237	#125	—	2	4	no	—
238	C₂²⋊Q₈	—	2	4	no	—
239	C₂²⋊Q₈	—	2	4	no	—
240	C₂²⋊Q₈	—	2	4	no	—
241	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
242	C₄×Q₈	—	2	4	no	—
243	C₄×Q₈	—	2	4	no	—
244	C₄×Q₈	—	2	2	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₄×Q₈	C₂×Dic₄₇	1	4	yes	—
247	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
248	#117	—	2	4	no	—
249	#117	—	2	4	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
259	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
260	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
262	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
263	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
265	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
266	C₄⋊C₈	—	47	4	no	—
267	C₄⋊C₈	—	94	2	no	—
268	C₄⋊C₈	—	94	4	no	—
269	C₄⋊C₈	—	94	4	no	—
270	C₂²⋊C₈	—	94	4	no	—
271	C₄×C₈	—	47	4	no	—
272	C₄×C₈	—	94	2	no	—
273	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	#10625336	1	4	yes	—
284	C₂²×C₄	#10625337	1	4	yes	—
285	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
288	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
289	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
291	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
292	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
295	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
296	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂×C₈	—	94	4	no	—
298	C₂×C₈	—	94	4	no	—
299	C₂×C₈	—	188	4	no	—
300	C₂×C₈	—	188	8	no	—
301	C₂×C₈	—	188	4	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
310	C₂²⋊C₄	—	2	8	no	—
311	C₄²	—	2	4	no	—
312	C₄²	—	2	4	no	—
313	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
314	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
315	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
316	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
317	C₄²	C₂²×Dic₄₇	1	2	yes	—
318	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
319	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
320	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
321	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₄²	C₂³×D₄₇	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	#13093948	1	4	yes	—
326	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
327	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
328	Q₈	—	2	8	no	—
329	Q₈	—	4	8	no	—
330	Q₈	—	4	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	#13093948	1	8	yes	—
343	C₂×C₄	#13093948	1	4	yes	—
344	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
345	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
346	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
347	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
348	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
349	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
350	C₂×C₄	#13094031	1	4	yes	—
351	C₂×C₄	C₂×#10625336	1	4	yes	—
352	C₂×C₄	C₂×#10625336	1	2	yes	—
353	C₂×C₄	C₂×#10625337	1	4	yes	—
354	C₂×C₄	C₂×#10625337	1	2	yes	—
355	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
358	C₈	—	188	4	no	—
359	C₈	—	188	4	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	8	no	—
362	C₂²	—	2	2	no	—
363	C₂²	#15689090	1	2	yes	—
364	C₂²	C₂×#13093948	1	4	yes	—
365	C₂²	C₂×#13093948	1	2	yes	—
366	C₂²	#15689140	1	2	yes	—
367	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	2	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	2	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	4	no	—
374	C₄	#15689090	1	2	yes	—
375	C₄	C₂×#13093948	1	2	yes	—
376	C₄	C₂×#13093948	1	4	yes	—
377	C₄	C₂×#13094031	1	2	yes	—
378	C₄	C₂²×#10625336	1	1	yes	characteristic
379	C₄	C₂²×#10625337	1	1	yes	characteristic
380	C₂	—	2	4	no	—
381	C₂	#20241791	1	4	yes	direct product factor
382	C₂	C₂×#15689090	1	1	yes	characteristic
383	C₂	C₂²×#13093948	1	1	yes	characteristic
384	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	C₂×#1481
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #20241791	C₂	direct (N × H)
4. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
16. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
194. C₂×C₄₇	#1481	semidirect
222. C₄₇	C₂×#1481	semidirect
381. C₂	#20241791	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×#15689176	2
C₂²×C₄⋊(C₄₇⋊C₈)	2
#20241791	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂×C₄₇×#533	2
C₂×#1481	47

Subgroups — C2×#20241791 #26182778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241791 #26182778