Subgroups — C₂×#20242045 #26184576

Order 12032.

1050 conjugacy classes of subgroups.

The subgroup lattice has 400 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	#20242045	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688872	C₂	1	2	yes	maximal, complemented
5	C₂×#15688869	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₇⋊C₈	—	2	1	no	—
8	#15689176	—	2	2	no	—
9	#15689176	C₂²	1	4	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
16	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
17	#15688872	C₂²	1	8	yes	complemented
18	#15688869	C₂²	1	8	yes	complemented
19	C₄₇×#533	—	2	2	no	—
20	C₄₇×#533	—	2	2	no	—
21	C₄₇×#533	C₄	1	4	yes	—
22	C₄₇×#533	C₂²	1	4	yes	—
23	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₄₇	—	2	1	no	—
26	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
28	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
29	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	—
30	C₂×#117×C₄₇	—	2	1	no	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₂²×C₄₇⋊C₈	—	2	4	no	—
35	C₂²×C₄₇⋊C₈	—	4	4	no	—
36	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
37	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
38	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
39	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
40	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
41	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
42	C₄×C₄₇⋊C₈	—	2	4	no	—
43	C₂²×Q₈×C₄₇	—	2	1	no	—
44	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
48	C₄⋊Q₈×C₄₇	—	2	1	no	—
49	C₄⋊Q₈×C₄₇	—	2	1	no	—
50	C₄⋊Q₈×C₄₇	—	2	1	no	—
51	C₄⋊Q₈×C₄₇	—	2	1	no	—
52	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
53	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
54	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
56	#125×C₄₇	—	2	4	no	—
57	#125×C₄₇	—	2	4	no	—
58	C₂²⋊Q₈×C₄₇	—	2	4	no	—
59	C₂²⋊Q₈×C₄₇	—	2	4	no	—
60	C₂²⋊Q₈×C₄₇	—	2	4	no	—
61	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
62	C₄×Q₈×C₄₇	—	2	4	no	—
63	C₄×Q₈×C₄₇	—	2	4	no	—
64	C₄×Q₈×C₄₇	—	2	4	no	—
65	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
66	#117×C₄₇	—	2	4	no	—
67	#117×C₄₇	—	2	4	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₄²×C₄₇	—	2	2	no	—
76	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	D₄	1	2	yes	—
81	C₂×C₄²×C₄₇	D₄	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
84	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	—	4	4	no	—
89	C₂×Q₈×C₄₇	—	4	4	no	—
90	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	4	2	no	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
102	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	8	no	—
113	C₄⋊C₄×C₄₇	—	2	8	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
119	C₂²⋊C₄×C₄₇	—	2	8	no	—
120	C₄²×C₄₇	—	2	8	no	—
121	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
123	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
125	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₄₇	C₂×D₄	1	2	yes	—
127	C₄²×C₄₇	C₂×D₄	1	2	yes	—
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
131	C₂×C₄₇⋊C₈	—	2	4	no	—
132	C₂×C₄₇⋊C₈	—	2	4	no	—
133	C₂×C₄₇⋊C₈	—	4	8	no	—
134	C₂×C₄₇⋊C₈	—	4	4	no	—
135	C₂×C₄₇⋊C₈	—	4	4	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	#103	1	4	yes	—
139	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	Q₈×C₄₇	—	4	4	no	—
142	Q₈×C₄₇	—	4	4	no	—
143	Q₈×C₄₇	—	4	4	no	—
144	Q₈×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	#103	1	8	yes	—
157	C₂×C₄×C₄₇	#103	1	4	yes	—
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
165	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
167	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
168	C₂×C₄×C₄₇	#135	1	4	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₄₇⋊C₈	—	4	4	no	—
173	C₄₇⋊C₈	—	4	4	no	—
174	C₂×#1542	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	—	2	8	no	—
176	C₂²×C₄₇	—	2	2	no	—
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	#413	1	2	yes	—
179	C₂²×C₄₇	C₂×#103	1	4	yes	—
180	C₂²×C₄₇	C₂×#103	1	2	yes	—
181	C₂²×C₄₇	#416	1	2	yes	—
182	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	C₄×C₄₇	—	2	2	no	—
184	C₄×C₄₇	—	2	1	no	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	2	2	no	—
187	C₄×C₄₇	—	4	4	no	—
188	C₄×C₄₇	—	4	4	no	—
189	C₄×C₄₇	C₂×#103	1	4	yes	—
190	C₄×C₄₇	C₂×#103	1	2	yes	—
191	C₄×C₄₇	#416	1	2	yes	—
192	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
193	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
194	C₄×C₄₇	C₂×#135	1	2	yes	—
195	C₂×#533	D₄₇	1	1	yes	characteristic
196	C₂×#431	—	47	1	no	—
197	C₂²×C₄⋊C₈	—	47	1	no	—
198	#1542	—	47	8	no	—
199	C₂×#333	—	47	2	no	—
200	C₂×#332	—	47	2	no	—
201	C₂×C₄₇	—	2	4	no	—
202	C₂×C₄₇	#1542	1	4	yes	complemented
203	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
204	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
205	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
206	C₂³×C₈	—	94	1	no	—
207	#533	—	2	2	no	—
208	#533	—	2	2	no	—
209	#533	Dic₄₇	1	4	yes	—
210	#533	C₂×D₄₇	1	4	yes	—
211	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
213	C₂×#125	—	2	1	no	—
214	C₂×C₂²⋊Q₈	—	2	1	no	—
215	C₂×C₂²⋊Q₈	Dic₄₇	1	2	yes	—
216	C₂×C₄×Q₈	—	2	1	no	—
217	C₂×C₄×Q₈	Dic₄₇	1	2	yes	—
218	C₂×#117	—	2	1	no	—
219	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
220	#431	—	47	4	no	—
221	#431	—	94	2	no	—
222	C₂×C₄⋊C₈	—	47	2	no	—
223	C₂×C₄⋊C₈	—	47	2	no	—
224	C₂×C₄⋊C₈	—	47	4	no	—
225	C₂×C₄⋊C₈	—	94	1	no	—
226	C₂×C₄⋊C₈	—	94	2	no	—
227	C₂×C₂²⋊C₈	—	94	1	no	—
228	C₂×C₄×C₈	—	94	1	no	—
229	#333	—	47	8	no	—
230	#332	—	47	8	no	—
231	C₄₇	C₂×#1542	1	1	yes	characteristic, complemented, Sylow
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
234	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
235	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
236	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
237	C₂²×C₈	—	94	2	no	—
238	C₂²×C₈	—	94	4	no	—
239	C₂²×C₈	—	94	2	no	—
240	C₂²×C₈	—	188	4	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
246	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
247	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
248	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
249	#125	—	2	4	no	—
250	#125	—	2	4	no	—
251	C₂²⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	C₂²⋊Q₈	—	2	4	no	—
254	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	C₂×Dic₄₇	1	8	yes	—
259	#117	—	2	4	no	—
260	#117	—	2	4	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
270	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
271	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
272	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
273	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
274	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
275	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
276	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
277	C₄⋊C₈	—	47	4	no	—
278	C₄⋊C₈	—	47	4	no	—
279	C₄⋊C₈	—	94	4	no	—
280	C₄⋊C₈	—	94	2	no	—
281	C₄⋊C₈	—	94	2	no	—
282	C₂²⋊C₈	—	94	4	no	—
283	C₄×C₈	—	94	4	no	—
284	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	#10625336	1	4	yes	—
296	C₂²×C₄	#10625337	1	4	yes	—
297	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
299	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
301	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
302	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
305	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
306	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
308	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂×C₈	—	94	4	no	—
310	C₂×C₈	—	94	4	no	—
311	C₂×C₈	—	188	8	no	—
312	C₂×C₈	—	188	4	no	—
313	C₂×C₈	—	188	4	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
324	C₂²⋊C₄	—	2	8	no	—
325	C₄²	—	2	8	no	—
326	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
327	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
328	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
329	C₄²	C₂²×Dic₄₇	1	2	yes	—
330	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
331	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
332	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
333	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
334	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
335	C₄²	C₂³×D₄₇	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	#13093948	1	4	yes	—
339	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
340	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	4	4	no	—
344	Q₈	—	4	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	#13093948	1	8	yes	—
357	C₂×C₄	#13093948	1	4	yes	—
358	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
359	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
360	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
362	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
363	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂×#10625336	1	4	yes	—
365	C₂×C₄	C₂×#10625336	1	2	yes	—
366	C₂×C₄	C₂×#10625337	1	4	yes	—
367	C₂×C₄	C₂×#10625337	1	2	yes	—
368	C₂×C₄	#13094044	1	4	yes	—
369	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
372	C₈	—	188	4	no	—
373	C₈	—	188	4	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	#15689107	1	2	yes	—
378	C₂²	C₂×#13093948	1	4	yes	—
379	C₂²	C₂×#13093948	1	2	yes	—
380	C₂²	#15689119	1	2	yes	—
381	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	4	no	—
388	C₄	C₂×#13093948	1	2	yes	—
389	C₄	C₂×#13093948	1	4	yes	—
390	C₄	#15689119	1	2	yes	—
391	C₄	C₂²×#10625336	1	1	yes	characteristic
392	C₄	C₂²×#10625337	1	1	yes	characteristic
393	C₄	C₂×#13094044	1	2	yes	—
394	C₂	—	2	4	no	—
395	C₂	#20242045	1	4	yes	direct product factor
396	C₂	C₂×#15689107	1	1	yes	characteristic
397	C₂	C₂²×#13093948	1	1	yes	characteristic
398	C₂	C₂×#15689119	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₄₇
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×#1542
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×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. #20242045	C₂	direct (N × H)
4. C₂×#15688872	C₂	semidirect
5. C₂×#15688869	C₂	semidirect
17. #15688872	C₂²	semidirect
18. #15688869	C₂²	semidirect
202. C₂×C₄₇	#1542	semidirect
231. C₄₇	C₂×#1542	semidirect
395. C₂	#20242045	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
#20242045	2
C₂×#15688872	2
C₂×#15688869	2
C₂×C₄₇×#533	2
C₂×#1542	47

Subgroups — C2×#20242045 #26184576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242045 #26184576