Subgroups — #26214273

Order 12032.

1242 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₄₇	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243265	C₂	1	4	yes	maximal, complemented
5	#20243258	C₂	1	2	yes	maximal, complemented
6	#20243253	C₂	1	2	yes	maximal, complemented
7	#20243081	C₂	1	2	yes	maximal
8	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₄₇	C₄	1	2	yes	—
12	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
13	C₄×#10625329	C₄	1	8	yes	complemented
14	M₁₆×Dic₄₇	—	2	8	no	—
15	C₂×#13093935	C₂²	1	2	yes	—
16	C₂×#13093934	C₂²	1	4	yes	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×C₈×Dic₄₇	C₂²	1	4	yes	—
19	C₄×C₄⋊Dic₄₇	C₄	1	2	yes	—
20	C₄×C₄⋊Dic₄₇	C₄	1	2	yes	—
21	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
24	C₂×C₄₇⋊#95	C₄	1	2	yes	—
25	#15688877	C₂²	1	4	yes	—
26	#15688877	C₂²	1	4	yes	—
27	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#423	C₄	1	8	yes	complemented
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
31	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
32	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	C₂×C₄	1	4	yes	—
36	C₂×#10625329	C₂×C₄	1	4	yes	—
37	C₂×#10625329	D₄	1	4	yes	—
38	C₂×#10625329	Q₈	1	4	yes	—
39	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
40	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
41	C₂×C₄⋊Dic₄₇	—	2	8	no	—
42	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
45	C₂×C₄×Dic₄₇	—	2	4	no	—
46	C₂×C₄×Dic₄₇	—	2	4	no	—
47	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
48	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
50	#13093935	C₂×C₄	1	8	yes	complemented
51	#13093934	—	2	8	no	—
52	C₄×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
53	C₈×Dic₄₇	—	2	8	no	—
54	C₄₇⋊#95	C₂×C₄	1	2	yes	—
55	C₄₇⋊#95	C₂×C₄	1	4	yes	—
56	C₄₇⋊#95	C₂×C₄	1	2	yes	—
57	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₄₇	—	2	4	no	—
61	C₂×M₁₆×C₄₇	—	2	4	no	—
62	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	—
63	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
71	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
72	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	—	2	4	no	—
74	C₂²×C₄×C₄₇	—	4	2	no	—
75	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
76	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
89	C₂²×Dic₄₇	—	2	8	no	—
90	C₂²×Dic₄₇	—	2	8	no	—
91	C₂²×Dic₄₇	—	4	4	no	—
92	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
94	M₁₆×C₄₇	—	2	16	no	—
95	C₂×C₈×C₄₇	—	2	4	no	—
96	C₂×C₈×C₄₇	—	2	4	no	—
97	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
98	C₄²×C₄₇	C₄²	1	4	yes	—
99	C₄²×C₄₇	C₄²	1	4	yes	—
100	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
101	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
102	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
103	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
104	C₄⋊Dic₄₇	—	2	4	no	—
105	C₄⋊Dic₄₇	—	2	8	no	—
106	C₄⋊Dic₄₇	M₁₆	1	8	yes	complemented
107	C₄×Dic₄₇	—	2	8	no	—
108	C₄×Dic₄₇	—	2	2	no	—
109	C₄×Dic₄₇	—	2	2	no	—
110	C₄×Dic₄₇	—	2	2	no	—
111	C₄×Dic₄₇	—	2	2	no	—
112	#10625329	—	2	8	no	—
113	#10625329	C₄⋊C₄	1	16	yes	complemented
114	C₂×C₄₇⋊C₈	—	2	2	no	—
115	C₂×C₄₇⋊C₈	—	2	2	no	—
116	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
117	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
118	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
119	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
120	C₂³×C₄₇	—	2	2	no	—
121	C₂³×C₄₇	—	2	2	no	—
122	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
123	C₂³×C₄₇	C₄×D₄	1	2	yes	—
124	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
125	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	8	no	—
130	C₂×C₄×C₄₇	—	4	4	no	—
131	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₄₇	#117	1	4	yes	—
138	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
140	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
141	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
142	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
143	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
149	C₂×Dic₄₇	—	2	4	no	—
150	C₂×Dic₄₇	—	2	4	no	—
151	C₂×Dic₄₇	—	2	4	no	—
152	C₂×Dic₄₇	—	2	4	no	—
153	C₂×Dic₄₇	—	2	4	no	—
154	C₂×Dic₄₇	—	4	16	no	—
155	C₂×Dic₄₇	C₂×M₁₆	1	8	yes	—
156	C₈×C₄₇	—	2	8	no	—
157	C₄₇⋊C₈	—	2	4	no	—
158	C₄₇⋊C₈	C₂×C₄⋊C₄	1	8	yes	complemented
159	C₄⋊C₄×M₁₆	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	4	no	—
163	C₂²×C₄₇	—	2	4	no	—
164	C₂²×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
165	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
166	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
168	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
169	C₂²×C₄₇	#568	1	2	yes	—
170	C₄×C₄₇	—	2	2	no	—
171	C₄×C₄₇	—	2	2	no	—
172	C₄×C₄₇	—	2	2	no	—
173	C₄×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
174	C₄×C₄₇	C₄×M₁₆	1	4	yes	complemented
175	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
177	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
178	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
179	Dic₄₇	—	2	8	no	—
180	Dic₄₇	—	4	4	no	—
181	C₂×#423	D₄₇	1	1	yes	characteristic
182	C₂×C₄×M₁₆	—	47	1	no	—
183	C₂×C₄×M₁₆	—	47	2	no	—
184	C₂×C₄×C₄⋊C₄	—	47	1	no	—
185	#1771	—	47	4	no	—
186	#1770	—	47	2	no	—
187	C₈×C₄⋊C₄	—	47	2	no	—
188	#1728	—	47	2	no	—
189	C₂×C₄₇	—	2	4	no	—
190	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
192	C₂×C₄₇	#2873	1	1	yes	characteristic
193	C₂×C₄₇	D₄×M₁₆	1	2	yes	—
194	C₂×C₄₇	Q₈×M₁₆	1	2	yes	—
195	C₂²×M₁₆	—	47	1	no	—
196	C₂²×M₁₆	—	47	1	no	—
197	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
198	C₂²×C₄⋊C₄	—	47	2	no	—
199	C₂²×C₄²	—	47	2	no	—
200	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
201	#423	Dic₄₇	1	8	yes	complemented
202	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
203	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
204	C₄×M₁₆	—	47	8	no	—
205	C₄×M₁₆	—	94	8	no	—
206	C₂×#97	—	47	2	no	—
207	C₂×#97	—	47	4	no	—
208	C₂×C₄×C₈	—	47	2	no	—
209	C₂×C₄×C₈	—	47	4	no	—
210	C₄×C₄⋊C₄	—	47	2	no	—
211	C₄×C₄⋊C₄	—	47	2	no	—
212	C₄×C₄⋊C₄	—	47	1	no	—
213	C₄×C₄⋊C₄	—	47	1	no	—
214	C₄×C₄⋊C₄	—	47	2	no	—
215	C₂×#95	—	47	2	no	—
216	#336	—	47	4	no	—
217	#336	—	47	4	no	—
218	C₄₇	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₄	—	47	4	no	—
220	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
223	C₂×M₁₆	—	2	4	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂×M₁₆	—	47	4	no	—
226	C₂×M₁₆	—	47	4	no	—
227	C₂×M₁₆	—	47	4	no	—
228	C₂×M₁₆	—	47	4	no	—
229	C₂×M₁₆	—	94	2	no	—
230	C₂×M₁₆	—	94	2	no	—
231	C₂×M₁₆	C₂×Dic₄₇	1	8	yes	—
232	C₂²×C₈	—	47	2	no	—
233	C₂²×C₈	—	47	2	no	—
234	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
235	C₂×C₄⋊C₄	—	47	2	no	—
236	C₂×C₄⋊C₄	—	47	4	no	—
237	C₂×C₄⋊C₄	—	47	2	no	—
238	C₂×C₄⋊C₄	—	94	8	no	—
239	C₂×C₄²	—	47	4	no	—
240	C₂×C₄²	—	47	2	no	—
241	C₂×C₄²	—	47	2	no	—
242	C₂×C₄²	—	94	4	no	—
243	C₂×C₄²	—	94	4	no	—
244	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₄₇	1	4	yes	—
247	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
248	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
249	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
250	C₄⋊C₈	C₂×Dic₄₇	1	8	yes	complemented
251	C₄⋊C₈	C₂×Dic₄₇	1	8	yes	complemented
252	#97	—	47	8	no	—
253	#97	—	94	8	no	—
254	C₄×C₈	—	47	8	no	—
255	C₄×C₈	—	94	8	no	—
256	#95	—	47	2	no	—
257	#95	—	47	4	no	—
258	#95	—	47	2	no	—
259	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	47	4	no	—
263	C₂²×C₄	—	47	4	no	—
264	C₂²×C₄	—	94	8	no	—
265	C₂²×C₄	—	94	8	no	—
266	C₂²×C₄	—	188	4	no	—
267	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
268	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
269	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
275	C₂²×C₄	D₄×D₄₇	1	2	yes	—
276	C₂²×C₄	#10625352	1	2	yes	—
277	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
278	C₂²×C₄	#10625354	1	2	yes	—
279	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
280	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
281	M₁₆	—	2	16	no	—
282	M₁₆	—	47	16	no	—
283	M₁₆	—	94	8	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	47	4	no	—
287	C₂×C₈	—	47	4	no	—
288	C₂×C₈	—	47	4	no	—
289	C₂×C₈	—	47	4	no	—
290	C₂×C₈	—	94	2	no	—
291	C₂×C₈	—	94	2	no	—
292	C₂×C₈	C₂²×Dic₄₇	1	8	yes	—
293	C₄⋊C₄	—	47	8	no	—
294	C₄⋊C₄	—	94	8	no	—
295	C₄⋊C₄	—	94	4	no	—
296	C₄²	—	94	8	no	—
297	C₄²	—	94	2	no	—
298	C₄²	—	94	2	no	—
299	C₄²	—	94	2	no	—
300	C₄²	—	94	2	no	—
301	C₄²	C₄×Dic₄₇	1	4	yes	—
302	C₄²	C₄×Dic₄₇	1	4	yes	—
303	C₄²	C₂×C₄×D₄₇	1	2	yes	—
304	C₄²	C₂×C₄×D₄₇	1	2	yes	—
305	C₄²	C₂²×Dic₄₇	1	2	yes	—
306	C₄²	C₂²×Dic₄₇	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
310	C₂³	#13093986	1	2	yes	—
311	C₂³	#13093989	1	2	yes	—
312	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	47	8	no	—
319	C₂×C₄	—	94	4	no	—
320	C₂×C₄	—	94	4	no	—
321	C₂×C₄	—	94	4	no	—
322	C₂×C₄	—	94	4	no	—
323	C₂×C₄	—	94	4	no	—
324	C₂×C₄	—	188	16	no	—
325	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
326	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
327	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
328	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
329	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
330	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
331	C₂×C₄	#13093982	1	4	yes	—
332	C₂×C₄	#13093986	1	2	yes	—
333	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
334	C₂×C₄	#13093989	1	2	yes	—
335	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
336	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
337	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
338	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
339	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
340	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
341	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
342	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
343	C₈	—	2	8	no	—
344	C₈	—	47	8	no	—
345	C₈	—	94	4	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	C₄⋊C₄×Dic₄₇	1	4	yes	—
351	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
352	C₂²	C₂×#13093986	1	1	yes	characteristic
353	C₂²	C₂×#13093989	1	1	yes	characteristic
354	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
355	C₂²	#15689889	1	2	yes	—
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	94	8	no	—
360	C₄	—	188	4	no	—
361	C₄	C₄⋊C₄×Dic₄₇	1	4	yes	—
362	C₄	M₁₆×Dic₄₇	1	4	yes	complemented
363	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
364	C₄	C₂×#13093982	1	1	yes	characteristic
365	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
366	C₄	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
367	C₂	—	2	4	no	—
368	C₂	C₂×C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
369	C₂	C₂×M₁₆×Dic₄₇	1	1	yes	characteristic
370	C₂	#20251806	1	1	yes	characteristic
371	C₂	#20252123	1	2	yes	—
372	C₂	#20252339	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₄₇×#423	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#423	D₄₇
hypocenter	C₄₇	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
4. #20243265	C₂	semidirect
5. #20243258	C₂	semidirect
6. #20243253	C₂	semidirect
13. C₄×#10625329	C₄	semidirect
29. C₄₇×#423	C₄	semidirect
50. #13093935	C₂×C₄	semidirect
52. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
70. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
71. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
106. C₄⋊Dic₄₇	M₁₆	semidirect
113. #10625329	C₄⋊C₄	semidirect
158. C₄₇⋊C₈	C₂×C₄⋊C₄	semidirect
174. C₄×C₄₇	C₄×M₁₆	semidirect
201. #423	Dic₄₇	semidirect
218. C₄₇	C₄⋊C₄×M₁₆	semidirect
250. C₄⋊C₈	C₂×Dic₄₇	semidirect
251. C₄⋊C₈	C₂×Dic₄₇	semidirect
362. C₄	M₁₆×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625329	2
C₂×M₁₆×Dic₄₇	2
C₂×C₄×C₄⋊Dic₄₇	2
#20243265	2
#20243258	2
#20243253	2
#20243081	2
C₂×C₄₇×#423	2
C₄⋊C₄×M₁₆	47