Subgroups — C₂×#20243263 #26214215

Order 12032.

1310 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093935	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13093935	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#20243263	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	8	yes	complemented
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
15	C₂×#13093935	—	2	4	no	—
16	C₂×#13093935	C₄	1	8	yes	complemented
17	C₂×#13093935	C₂²	1	4	yes	—
18	C₂×#13093935	C₂²	1	4	yes	—
19	C₂×C₄×C₄₇⋊C₈	—	2	4	no	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
21	#15688878	C₂²	1	4	yes	—
22	#15688878	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₄₇	C₄	1	4	yes	—
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
29	C₂×#95×C₄₇	C₄	1	2	yes	—
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₂²×C₄₇⋊C₈	—	2	2	no	—
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
37	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
38	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
39	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
40	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
41	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	16	yes	complemented
47	#13093935	—	2	8	no	—
48	#13093935	C₂×C₄	1	16	yes	complemented
49	C₄×C₄₇⋊C₈	—	2	8	no	—
50	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
51	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₄₇	—	2	2	no	—
58	C₂×C₄²×C₄₇	—	2	2	no	—
59	C₂×C₄²×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	—	2	2	no	—
61	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
69	#95×C₄₇	C₂×C₄	1	8	yes	—
70	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	—	2	4	no	—
72	C₂²×C₄×C₄₇	—	2	4	no	—
73	C₂²×C₄×C₄₇	—	2	4	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	C₄²	1	4	yes	—
79	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
80	C₂²×C₄×C₄₇	M₁₆	1	8	yes	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	2	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	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₄₇	#41	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₄⋊C₄×C₄₇	—	2	16	no	—
94	C₄²×C₄₇	—	2	4	no	—
95	C₄²×C₄₇	—	2	4	no	—
96	C₄²×C₄₇	—	2	2	no	—
97	C₄²×C₄₇	—	2	2	no	—
98	C₄²×C₄₇	—	2	2	no	—
99	C₄²×C₄₇	—	2	2	no	—
100	C₄²×C₄₇	C₄²	1	8	yes	—
101	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
102	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂×C₄₇⋊C₈	—	2	8	no	—
104	C₂×C₄₇⋊C₈	—	2	8	no	—
105	C₂×C₄₇⋊C₈	—	2	8	no	—
106	C₂×C₄₇⋊C₈	—	2	2	no	—
107	C₂×C₄₇⋊C₈	—	2	2	no	—
108	C₂×C₄₇⋊C₈	—	2	2	no	—
109	C₂×C₄₇⋊C₈	—	2	2	no	—
110	C₂×C₄₇⋊C₈	—	2	2	no	—
111	C₂×C₄₇⋊C₈	—	2	2	no	—
112	C₂×C₄₇⋊C₈	C₄⋊C₄	1	16	yes	complemented
113	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
114	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
115	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
116	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
117	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
118	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
119	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
120	C₂³×C₄₇	C₄×D₄	1	2	yes	—
121	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
122	C₂³×C₄₇	C₂×M₁₆	1	4	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	4	no	—
129	C₂×C₄×C₄₇	—	2	8	no	—
130	C₂×C₄×C₄₇	—	2	8	no	—
131	C₂×C₄×C₄₇	—	2	16	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	4	8	no	—
136	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
137	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
138	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
140	C₂×C₄×C₄₇	#117	1	4	yes	—
141	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
142	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
144	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×M₁₆	1	8	yes	—
146	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₄₇⋊C₈	—	2	4	no	—
153	C₄₇⋊C₈	—	2	4	no	—
154	C₄₇⋊C₈	—	2	4	no	—
155	C₄₇⋊C₈	C₂×C₄⋊C₄	1	8	yes	complemented
156	C₂×#1771	—	47	1	no	maximal, Sylow
157	C₂²×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
158	C₂²×C₄₇	C₄×M₁₆	1	4	yes	—
159	C₂²×C₄₇	#405	1	4	yes	—
160	C₂²×C₄₇	#435	1	8	yes	—
161	C₂²×C₄₇	#446	1	8	yes	—
162	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
163	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
164	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
165	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
166	C₂²×C₄₇	C₂×#131	1	2	yes	—
167	C₄×C₄₇	—	2	4	no	—
168	C₄×C₄₇	—	2	4	no	—
169	C₄×C₄₇	—	2	8	no	—
170	C₄×C₄₇	—	4	4	no	—
171	C₄×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
172	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
173	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
174	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
175	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
176	C₂²×C₄⋊C₈	—	47	1	no	—
177	C₂²×#97	—	47	1	no	—
178	C₂²×#97	—	47	1	no	—
179	C₂²×C₄×C₈	—	47	1	no	—
180	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
181	#1771	—	47	8	no	—
182	C₂×#336	—	47	1	no	—
183	C₂×#336	—	47	1	no	—
184	C₂×C₄₇	#1771	1	8	yes	complemented
185	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
187	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
188	C₂×C₄₇	C₂×#435	1	2	yes	—
189	C₂×C₄₇	C₂×#446	1	2	yes	—
190	C₂³×C₈	—	47	1	no	—
191	C₂³×C₈	—	47	1	no	—
192	C₂³×C₈	—	47	1	no	—
193	C₂³×C₈	—	47	1	no	—
194	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
195	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
196	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
197	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
198	C₂×C₄⋊C₈	—	47	8	no	—
199	C₂×C₄⋊C₈	—	47	4	no	—
200	C₂×#97	—	47	8	no	—
201	C₂×#97	—	47	4	no	—
202	C₂×#97	—	47	4	no	—
203	C₂×#97	—	94	4	no	—
204	C₂×C₄×C₈	—	47	4	no	—
205	C₂×C₄×C₈	—	94	4	no	—
206	C₄×C₄⋊C₄	Dic₄₇	1	4	yes	—
207	C₄×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
208	C₂×#95	Dic₄₇	1	2	yes	—
209	#336	—	47	4	no	—
210	#336	—	47	4	no	—
211	C₄₇	C₂×#1771	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
213	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
214	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
215	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
216	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
217	C₂²×C₈	—	47	4	no	—
218	C₂²×C₈	—	47	4	no	—
219	C₂²×C₈	—	47	4	no	—
220	C₂²×C₈	—	47	2	no	—
221	C₂²×C₈	—	47	4	no	—
222	C₂²×C₈	—	47	4	no	—
223	C₂²×C₈	—	47	4	no	—
224	C₂²×C₈	—	47	2	no	—
225	C₂²×C₈	—	47	2	no	—
226	C₂²×C₈	—	47	2	no	—
227	C₂²×C₈	—	94	2	no	—
228	C₂²×C₈	—	94	2	no	—
229	C₂²×C₈	—	94	2	no	—
230	C₂²×C₈	—	94	2	no	—
231	C₂²×C₈	—	94	2	no	—
232	C₂²×C₈	—	94	2	no	—
233	C₂×C₄⋊C₄	—	2	8	no	—
234	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	C₄×D₄₇	1	4	yes	—
240	C₂×C₄²	C₄×D₄₇	1	4	yes	—
241	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
242	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
243	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
244	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
245	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
246	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
247	C₄⋊C₈	—	47	16	no	—
248	#97	—	47	16	no	—
249	#97	—	94	8	no	—
250	C₄×C₈	—	94	8	no	—
251	#95	C₂×Dic₄₇	1	8	yes	—
252	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	#10625329	1	8	yes	—
261	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
262	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
263	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
264	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
265	C₂²×C₄	D₄×D₄₇	1	2	yes	—
266	C₂²×C₄	#10625352	1	2	yes	—
267	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
268	C₂²×C₄	#10625354	1	2	yes	—
269	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
270	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
271	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
272	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
273	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
274	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
275	C₂×C₈	—	47	16	no	—
276	C₂×C₈	—	47	4	no	—
277	C₂×C₈	—	47	4	no	—
278	C₂×C₈	—	47	4	no	—
279	C₂×C₈	—	47	4	no	—
280	C₂×C₈	—	47	4	no	—
281	C₂×C₈	—	47	4	no	—
282	C₂×C₈	—	94	8	no	—
283	C₂×C₈	—	94	8	no	—
284	C₂×C₈	—	94	8	no	—
285	C₂×C₈	—	94	2	no	—
286	C₂×C₈	—	94	2	no	—
287	C₂×C₈	—	94	2	no	—
288	C₂×C₈	—	94	2	no	—
289	C₂×C₈	—	94	2	no	—
290	C₂×C₈	—	94	2	no	—
291	C₄⋊C₄	—	2	16	no	—
292	C₄²	—	2	4	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	C₄×Dic₄₇	1	8	yes	—
299	C₄²	C₂×C₄×D₄₇	1	4	yes	—
300	C₄²	C₂×C₄×D₄₇	1	4	yes	—
301	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
302	C₂³	D₄×Dic₄₇	1	2	yes	—
303	C₂³	Q₈×Dic₄₇	1	2	yes	—
304	C₂³	C₂×#10625329	1	4	yes	—
305	C₂³	#13094031	1	4	yes	—
306	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	16	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
319	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
320	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
321	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
322	C₂×C₄	#13093982	1	4	yes	—
323	C₂×C₄	#13093986	1	4	yes	—
324	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
325	C₂×C₄	#13093989	1	4	yes	—
326	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
327	C₂×C₄	C₂×#10625329	1	8	yes	—
328	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
330	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
331	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
332	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
333	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
334	C₈	—	47	8	no	—
335	C₈	—	94	4	no	—
336	C₈	—	94	4	no	—
337	C₈	—	94	4	no	—
338	C₂²	C₄⋊C₄×Dic₄₇	1	4	yes	—
339	C₂²	C₄×#10625329	1	4	yes	—
340	C₂²	#15689079	1	4	yes	—
341	C₂²	#15689195	1	8	yes	—
342	C₂²	#15689254	1	8	yes	—
343	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
344	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
345	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
346	C₂²	C₂²×#10625329	1	2	yes	—
347	C₂²	C₂×#13094031	1	2	yes	—
348	C₄	—	2	4	no	—
349	C₄	—	2	4	no	—
350	C₄	—	2	8	no	—
351	C₄	—	4	4	no	—
352	C₄	C₄⋊C₄×Dic₄₇	1	4	yes	—
353	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
354	C₄	C₂×#13093982	1	1	yes	characteristic
355	C₄	C₂×#13093986	1	1	yes	characteristic
356	C₄	C₂×#13093989	1	1	yes	characteristic
357	C₂	#20243263	1	8	yes	direct product factor
358	C₂	C₂×C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
359	C₂	C₂×C₄×#10625329	1	1	yes	characteristic
360	C₂	C₂×#15689079	1	1	yes	characteristic
361	C₂	C₂×#15689195	1	2	yes	—
362	C₂	C₂×#15689254	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₂×#1771
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
5. #20243263	C₂	direct (N × H)
13. C₂×C₄⋊(C₄₇⋊C₈)	C₄	semidirect
16. C₂×#13093935	C₄	semidirect
46. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
48. #13093935	C₂×C₄	semidirect
112. C₂×C₄₇⋊C₈	C₄⋊C₄	semidirect
155. C₄₇⋊C₈	C₂×C₄⋊C₄	semidirect
184. C₂×C₄₇	#1771	semidirect
211. C₄₇	C₂×#1771	semidirect
357. C₂	#20243263	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×C₄⋊(C₄₇⋊C₈)	2
C₂²×#13093935	2
C₂²×C₄×C₄₇⋊C₈	2
#20243263	2
C₂×#15688878	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₂×#1771	47

Subgroups — C2×#20243263 #26214215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243263 #26214215