Subgroups — C₂²×#15689195 #27080117

Order 12032.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689195	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13093935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	—	2	8	no	—
10	C₂²×#10625329	C₂²	1	12	yes	complemented
11	C₂³×C₄₇⋊C₈	—	2	8	no	—
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂³×C₄₇⋊C₈	C₂²	1	12	yes	complemented
17	#15689195	C₂²	1	64	yes	direct product factor
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	12	yes	complemented
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	12	yes	complemented
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	12	yes	complemented
21	C₂×#13093935	C₂²	1	12	yes	complemented
22	C₂³×D₄×C₄₇	C₄	1	1	yes	characteristic
23	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₇	C₄	1	12	yes	—
26	C₂×C₄×D₄×C₄₇	C₂²	1	12	yes	—
27	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₄₇	C₄	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₄₇	C₄	1	1	yes	characteristic
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#10625329	—	2	48	no	—
32	C₂×#10625329	C₂³	1	16	yes	complemented
33	C₂²×C₄₇⋊C₈	—	2	4	no	—
34	C₂²×C₄₇⋊C₈	—	2	4	no	—
35	C₂²×C₄₇⋊C₈	—	2	4	no	—
36	C₂²×C₄₇⋊C₈	—	2	48	no	—
37	C₂²×C₄₇⋊C₈	D₄	1	8	yes	complemented
38	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
39	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
40	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	16	yes	complemented
43	C₄⋊(C₄₇⋊C₈)	C₂³	1	16	yes	complemented
44	C₂²⋊(C₄₇⋊C₈)	C₂³	1	16	yes	complemented
45	C₂²⋊(C₄₇⋊C₈)	C₂³	1	16	yes	complemented
46	#13093935	C₂³	1	16	yes	complemented
47	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₄₇	—	2	8	no	—
50	C₂²×D₄×C₄₇	C₂×C₄	1	12	yes	—
51	C₂³×C₄×C₄₇	—	2	4	no	—
52	C₂³×C₄×C₄₇	—	2	4	no	—
53	C₂³×C₄×C₄₇	—	2	4	no	—
54	C₂³×C₄×C₄₇	—	2	4	no	—
55	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₇	C₂×C₄	1	6	yes	—
60	C₂³×C₄×C₄₇	C₂×C₄	1	6	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
62	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₄₇	C₂×C₄	1	48	yes	—
65	C₄×D₄×C₄₇	C₂³	1	16	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	12	yes	—
67	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	12	yes	—
68	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	12	yes	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	6	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	6	yes	—
71	C₂⁴×C₄₇	—	2	4	no	—
72	C₂⁴×C₄₇	—	2	4	no	—
73	C₂⁴×C₄₇	—	2	4	no	—
74	C₂⁴×C₄₇	—	2	4	no	—
75	C₂⁴×C₄₇	—	2	4	no	—
76	C₂⁴×C₄₇	M₁₆	1	8	yes	complemented
77	C₂⁴×C₄₇	C₂²×C₄	1	6	yes	—
78	C₂⁴×C₄₇	C₂²×C₄	1	6	yes	—
79	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂×D₄×C₄₇	—	2	48	no	—
81	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	24	no	—
87	C₂²×C₄×C₄₇	—	2	24	no	—
88	C₂²×C₄×C₄₇	—	2	12	no	—
89	C₂²×C₄×C₄₇	—	2	12	no	—
90	C₂²×C₄×C₄₇	—	2	12	no	—
91	C₂²×C₄×C₄₇	—	2	12	no	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	6	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	6	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	6	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	3	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₄₇	#41	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
104	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
105	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
106	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
107	C₄²×C₄₇	C₂²×C₄	1	12	yes	—
108	C₄²×C₄₇	C₂⁴	1	4	yes	—
109	#10625329	—	2	32	no	—
110	C₂×C₄₇⋊C₈	—	2	12	no	—
111	C₂×C₄₇⋊C₈	—	2	12	no	—
112	C₂×C₄₇⋊C₈	—	2	12	no	—
113	C₂×C₄₇⋊C₈	—	2	32	no	—
114	C₂×C₄₇⋊C₈	C₂×D₄	1	24	yes	complemented
115	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
116	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
117	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
118	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
119	C₂³×C₄₇	—	2	12	no	—
120	C₂³×C₄₇	—	2	12	no	—
121	C₂³×C₄₇	—	2	32	no	—
122	C₂³×C₄₇	—	2	12	no	—
123	C₂³×C₄₇	—	2	12	no	—
124	C₂³×C₄₇	—	2	12	no	—
125	C₂³×C₄₇	—	4	16	no	—
126	C₂³×C₄₇	C₄×D₄	1	4	yes	—
127	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
128	C₂³×C₄₇	C₂×M₁₆	1	24	yes	complemented
129	C₂³×C₄₇	#131	1	4	yes	—
130	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
131	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
132	C₂³×C₄₇	C₂³×C₄	1	3	yes	—
133	D₄×C₄₇	—	2	32	no	—
134	C₂×C₄×C₄₇	—	2	12	no	—
135	C₂×C₄×C₄₇	—	2	12	no	—
136	C₂×C₄×C₄₇	—	2	12	no	—
137	C₂×C₄×C₄₇	—	2	12	no	—
138	C₂×C₄×C₄₇	—	2	24	no	—
139	C₂×C₄×C₄₇	—	2	24	no	—
140	C₂×C₄×C₄₇	—	2	4	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	C₄×D₄	1	12	yes	—
145	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
146	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
147	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
148	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	3	yes	—
150	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
151	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
152	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
153	C₄₇⋊C₈	—	2	4	no	—
154	C₄₇⋊C₈	—	2	4	no	—
155	C₄₇⋊C₈	—	2	4	no	—
156	C₄₇⋊C₈	C₂²×D₄	1	8	yes	complemented
157	C₂²×#435	—	47	1	no	maximal, Sylow
158	C₂²×C₄₇	—	2	4	no	—
159	C₂²×C₄₇	—	2	48	no	—
160	C₂²×C₄₇	—	2	4	no	—
161	C₂²×C₄₇	—	2	4	no	—
162	C₂²×C₄₇	—	2	4	no	—
163	C₂²×C₄₇	—	2	4	no	—
164	C₂²×C₄₇	—	4	24	no	—
165	C₂²×C₄₇	#435	1	16	yes	complemented
166	C₂²×C₄₇	C₂×C₄×D₄	1	6	yes	—
167	C₂²×C₄₇	C₂²×M₁₆	1	6	yes	—
168	C₂²×C₄₇	C₂²×M₁₆	1	8	yes	complemented
169	C₂²×C₄₇	C₂×#131	1	6	yes	—
170	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
171	C₄×C₄₇	—	2	4	no	—
172	C₄×C₄₇	—	2	4	no	—
173	C₄×C₄₇	—	2	4	no	—
174	C₄×C₄₇	—	2	4	no	—
175	C₄×C₄₇	C₂×C₄×D₄	1	6	yes	—
176	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
177	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
178	C₂³×M₁₆	—	47	1	no	—
179	C₂⁴×C₈	—	47	1	no	—
180	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
181	C₂×#435	—	47	24	no	—
182	C₂²×C₄⋊C₈	—	47	1	no	—
183	C₂²×C₂²⋊C₈	—	47	1	no	—
184	C₂²×C₂²⋊C₈	—	47	1	no	—
185	C₂²×#97	—	47	1	no	—
186	C₂×C₄₇	—	2	8	no	—
187	C₂×C₄₇	—	4	4	no	—
188	C₂×C₄₇	C₂×#435	1	12	yes	complemented
189	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
190	C₂×C₄₇	C₂³×M₁₆	1	1	yes	characteristic
191	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
192	C₂³×D₄	Dic₄₇	1	1	yes	characteristic
193	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
194	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
195	C₂²×M₁₆	—	47	12	no	—
196	C₂²×M₁₆	—	94	8	no	—
197	C₂³×C₈	—	47	1	no	—
198	C₂³×C₈	—	47	12	no	—
199	C₂³×C₈	—	47	1	no	—
200	C₂³×C₈	—	47	1	no	—
201	C₂³×C₈	—	47	1	no	—
202	C₂³×C₈	—	94	8	no	—
203	C₂×C₄×D₄	Dic₄₇	1	12	yes	—
204	C₂×C₄×D₄	C₂×D₄₇	1	12	yes	—
205	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
206	C₂²×C₂²⋊C₄	Dic₄₇	1	1	yes	characteristic
207	C₂²×C₂²⋊C₄	Dic₄₇	1	1	yes	characteristic
208	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
209	#435	—	47	64	no	—
210	C₂×C₄⋊C₈	—	47	12	no	—
211	C₂×C₂²⋊C₈	—	47	12	no	—
212	C₂×C₂²⋊C₈	—	47	12	no	—
213	C₂×#97	—	47	12	no	—
214	C₄₇	C₂²×#435	1	1	yes	characteristic, complemented, Sylow
215	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
216	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
217	C₂²×D₄	—	2	8	no	—
218	C₂²×D₄	C₂×Dic₄₇	1	12	yes	—
219	C₂³×C₄	—	2	4	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
224	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
225	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
226	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
227	C₂³×C₄	C₂×Dic₄₇	1	6	yes	—
228	C₂³×C₄	C₂×Dic₄₇	1	6	yes	—
229	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
230	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
231	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
232	C₂×M₁₆	—	47	16	no	—
233	C₂×M₁₆	—	94	48	no	—
234	C₂²×C₈	—	47	8	no	—
235	C₂²×C₈	—	47	6	no	—
236	C₂²×C₈	—	47	6	no	—
237	C₂²×C₈	—	47	16	no	—
238	C₂²×C₈	—	47	6	no	—
239	C₂²×C₈	—	47	6	no	—
240	C₂²×C₈	—	94	48	no	—
241	C₂²×C₈	—	94	4	no	—
242	C₂²×C₈	—	94	4	no	—
243	C₂²×C₈	—	94	4	no	—
244	C₄×D₄	C₂×Dic₄₇	1	48	yes	—
245	C₄×D₄	C₂²×D₄₇	1	16	yes	—
246	C₂×C₄⋊C₄	C₂×Dic₄₇	1	12	yes	—
247	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	12	yes	—
248	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	12	yes	—
249	C₂×C₄²	C₂×Dic₄₇	1	6	yes	—
250	C₂×C₄²	C₂²×D₄₇	1	6	yes	—
251	C₄⋊C₈	—	47	16	no	—
252	C₂²⋊C₈	—	47	16	no	—
253	C₂²⋊C₈	—	47	16	no	—
254	#97	—	47	16	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	2	4	no	—
260	C₂⁴	#10625329	1	8	yes	complemented
261	C₂⁴	C₂²×Dic₄₇	1	6	yes	—
262	C₂⁴	C₂²×Dic₄₇	1	6	yes	—
263	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
264	C₂×D₄	—	2	48	no	—
265	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	24	no	—
271	C₂²×C₄	—	2	24	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	12	no	—
274	C₂²×C₄	—	2	12	no	—
275	C₂²×C₄	—	2	12	no	—
276	C₂²×C₄	D₄×D₄₇	1	4	yes	—
277	C₂²×C₄	#10625352	1	4	yes	—
278	C₂²×C₄	C₂²×Dic₄₇	1	6	yes	—
279	C₂²×C₄	C₂²×Dic₄₇	1	6	yes	—
280	C₂²×C₄	C₂²×Dic₄₇	1	6	yes	—
281	C₂²×C₄	C₂²×Dic₄₇	1	6	yes	—
282	C₂²×C₄	C₂²×Dic₄₇	1	12	yes	—
283	C₂²×C₄	C₂²×Dic₄₇	1	12	yes	—
284	C₂²×C₄	C₂²×Dic₄₇	1	3	yes	—
285	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
286	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
287	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
288	M₁₆	—	94	32	no	—
289	C₂×C₈	—	47	24	no	—
290	C₂×C₈	—	47	4	no	—
291	C₂×C₈	—	47	4	no	—
292	C₂×C₈	—	47	4	no	—
293	C₂×C₈	—	47	4	no	—
294	C₂×C₈	—	94	32	no	—
295	C₂×C₈	—	94	12	no	—
296	C₂×C₈	—	94	12	no	—
297	C₂×C₈	—	94	12	no	—
298	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	—
299	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
300	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
301	C₄²	C₂²×Dic₄₇	1	12	yes	—
302	C₄²	C₂³×D₄₇	1	4	yes	—
303	C₂³	—	2	12	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	32	no	—
306	C₂³	—	2	12	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	2	12	no	—
309	C₂³	—	4	16	no	—
310	C₂³	D₄×Dic₄₇	1	4	yes	—
311	C₂³	C₂×#10625329	1	4	yes	—
312	C₂³	C₂×#10625329	1	24	yes	complemented
313	C₂³	#13094031	1	4	yes	—
314	C₂³	C₂³×Dic₄₇	1	4	yes	—
315	C₂³	C₂³×Dic₄₇	1	4	yes	—
316	C₂³	C₂³×Dic₄₇	1	3	yes	—
317	D₄	—	2	32	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	24	no	—
323	C₂×C₄	—	2	24	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	D₄×Dic₄₇	1	12	yes	—
329	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
330	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
331	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
332	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
333	C₂×C₄	C₂³×Dic₄₇	1	3	yes	—
334	C₂×C₄	C₂×D₄×D₄₇	1	6	yes	—
335	C₂×C₄	C₂×#10625352	1	6	yes	—
336	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
337	C₈	—	47	8	no	—
338	C₈	—	94	4	no	—
339	C₈	—	94	4	no	—
340	C₈	—	94	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	48	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	24	no	—
348	C₂²	#15689195	1	16	yes	direct product factor
349	C₂²	C₂×D₄×Dic₄₇	1	6	yes	—
350	C₂²	C₂²×#10625329	1	6	yes	—
351	C₂²	C₂²×#10625329	1	8	yes	complemented
352	C₂²	C₂×#13094031	1	6	yes	—
353	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	C₂×D₄×Dic₄₇	1	6	yes	—
359	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
360	C₄	C₂²×#10625352	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	4	4	no	—
363	C₂	C₂×#15689195	1	12	yes	direct product factor
364	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
365	C₂	C₂³×#10625329	1	1	yes	characteristic
366	C₂	C₂²×#13094031	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂²×C₄
prime radical	C₂³×D₄×C₄₇	C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂²×#435
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#10625329	C₂	semidirect
2. C₂⁴×C₄₇⋊C₈	C₂	semidirect
3. C₂×#15689195	C₂	direct (N × H)
4. C₂²×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
5. C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
6. C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
7. C₂²×#13093935	C₂	semidirect
10. C₂²×#10625329	C₂²	semidirect
16. C₂³×C₄₇⋊C₈	C₂²	semidirect
17. #15689195	C₂²	direct (N × H)
18. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
19. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
20. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
21. C₂×#13093935	C₂²	semidirect
32. C₂×#10625329	C₂³	semidirect
37. C₂²×C₄₇⋊C₈	D₄	semidirect
42. C₂²×C₄₇⋊C₈	C₂³	semidirect
43. C₄⋊(C₄₇⋊C₈)	C₂³	semidirect
44. C₂²⋊(C₄₇⋊C₈)	C₂³	semidirect
45. C₂²⋊(C₄₇⋊C₈)	C₂³	semidirect
46. #13093935	C₂³	semidirect
76. C₂⁴×C₄₇	M₁₆	semidirect
114. C₂×C₄₇⋊C₈	C₂×D₄	semidirect
128. C₂³×C₄₇	C₂×M₁₆	semidirect
156. C₄₇⋊C₈	C₂²×D₄	semidirect
165. C₂²×C₄₇	#435	semidirect
168. C₂²×C₄₇	C₂²×M₁₆	semidirect
188. C₂×C₄₇	C₂×#435	semidirect
214. C₄₇	C₂²×#435	semidirect
260. C₂⁴	#10625329	semidirect
312. C₂³	C₂×#10625329	semidirect
348. C₂²	#15689195	direct (N × H)
351. C₂²	C₂²×#10625329	semidirect
363. C₂	C₂×#15689195	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10625329	2
C₂⁴×C₄₇⋊C₈	2
C₂×#15689195	2
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂²×C₂²⋊(C₄₇⋊C₈)	2
C₂²×#13093935	2
C₂²×C₄×D₄×C₄₇	2
C₂²×#435	47

Subgroups — C22×#15689195 #27080117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689195 #27080117