Subgroups — #26108939

Order 12032.

682 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20243368	C₂	1	2	yes	maximal
2	C₂×#15688849	C₂	1	2	yes	maximal
3	#20241231	C₂	1	2	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
6	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
7	#15688878	—	2	2	no	—
8	#15688849	—	2	4	no	—
9	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₄₇	C₄	1	1	yes	characteristic
12	C₂²×C₄²×C₄₇	C₄	1	1	yes	characteristic
13	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
14	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
15	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
16	C₂×#95×C₄₇	C₄	1	1	yes	characteristic
17	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄₇⋊C₈	—	2	4	no	—
19	C₄⋊(C₄₇⋊C₈)	—	4	4	no	—
20	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
21	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
22	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
30	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
31	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
32	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
33	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
34	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₄₇	Q₈	1	2	yes	—
36	C₂×C₄²×C₄₇	—	2	1	no	—
37	C₂×C₄²×C₄₇	—	2	1	no	—
38	C₂×C₄²×C₄₇	—	2	2	no	—
39	C₂×C₄²×C₄₇	—	2	1	no	—
40	C₂×C₄²×C₄₇	—	2	1	no	—
41	C₂×C₄²×C₄₇	—	4	2	no	—
42	C₂×C₄²×C₄₇	—	4	2	no	—
43	C₂×C₄²×C₄₇	C₈	1	4	yes	complemented
44	C₂×C₄²×C₄₇	D₄	1	2	yes	—
45	C₂×C₄²×C₄₇	D₄	1	2	yes	—
46	#95×C₄₇	—	2	2	no	—
47	#95×C₄₇	—	2	2	no	—
48	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	—	2	1	no	—
50	C₂²×C₄×C₄₇	—	2	1	no	—
51	C₂²×C₄×C₄₇	—	2	1	no	—
52	C₂²×C₄×C₄₇	—	2	1	no	—
53	C₂²×C₄×C₄₇	—	2	2	no	—
54	C₂²×C₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	—	2	1	no	—
56	C₂²×C₄×C₄₇	—	2	1	no	—
57	C₂²×C₄×C₄₇	—	2	1	no	—
58	C₂²×C₄×C₄₇	—	2	1	no	—
59	C₂²×C₄×C₄₇	—	2	1	no	—
60	C₂²×C₄×C₄₇	—	2	1	no	—
61	C₂²×C₄×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	—	2	1	no	—
63	C₂²×C₄×C₄₇	—	4	1	no	—
64	C₂²×C₄×C₄₇	—	4	1	no	—
65	C₂²×C₄×C₄₇	—	4	1	no	—
66	C₂²×C₄×C₄₇	—	4	1	no	—
67	C₂²×C₄×C₄₇	—	4	1	no	—
68	C₂²×C₄×C₄₇	—	4	1	no	—
69	C₂²×C₄×C₄₇	—	4	1	no	—
70	C₂²×C₄×C₄₇	—	4	1	no	—
71	C₂²×C₄×C₄₇	—	4	1	no	—
72	C₂²×C₄×C₄₇	—	4	1	no	—
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
78	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
81	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
82	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
83	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₄⋊C₄×C₄₇	—	2	8	no	—
89	C₄⋊C₄×C₄₇	—	2	4	no	—
90	C₄⋊C₄×C₄₇	—	2	4	no	—
91	C₄²×C₄₇	—	2	4	no	—
92	C₄²×C₄₇	—	2	4	no	—
93	C₄²×C₄₇	—	2	4	no	—
94	C₄²×C₄₇	—	4	2	no	—
95	C₄²×C₄₇	—	4	2	no	—
96	C₄²×C₄₇	—	4	2	no	—
97	C₂×C₄₇⋊C₈	—	4	4	no	—
98	C₂×C₄₇⋊C₈	—	4	4	no	—
99	C₂×C₄₇⋊C₈	—	4	4	no	—
100	C₂³×C₄₇	—	2	1	no	—
101	C₂³×C₄₇	—	2	1	no	—
102	C₂³×C₄₇	—	2	1	no	—
103	C₂³×C₄₇	—	2	1	no	—
104	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂³×C₄₇	#117	1	1	yes	characteristic
107	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
108	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
109	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
110	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
111	C₂×C₄×C₄₇	—	2	2	no	—
112	C₂×C₄×C₄₇	—	2	2	no	—
113	C₂×C₄×C₄₇	—	2	2	no	—
114	C₂×C₄×C₄₇	—	2	2	no	—
115	C₂×C₄×C₄₇	—	2	1	no	—
116	C₂×C₄×C₄₇	—	2	2	no	—
117	C₂×C₄×C₄₇	—	2	1	no	—
118	C₂×C₄×C₄₇	—	2	2	no	—
119	C₂×C₄×C₄₇	—	2	2	no	—
120	C₂×C₄×C₄₇	—	2	2	no	—
121	C₂×C₄×C₄₇	—	2	4	no	—
122	C₂×C₄×C₄₇	—	2	4	no	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	2	no	—
125	C₂×C₄×C₄₇	—	2	2	no	—
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	—	4	1	no	—
130	C₂×C₄×C₄₇	—	4	1	no	—
131	C₂×C₄×C₄₇	—	4	2	no	—
132	C₂×C₄×C₄₇	—	4	2	no	—
133	C₂×C₄×C₄₇	—	4	2	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	—	4	1	no	—
138	C₂×C₄×C₄₇	—	4	1	no	—
139	C₂×C₄×C₄₇	—	4	1	no	—
140	C₂×C₄×C₄₇	—	4	1	no	—
141	C₂×C₄×C₄₇	—	4	1	no	—
142	C₂×C₄×C₄₇	—	4	1	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
147	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
148	C₂×C₄×C₄₇	#99	1	2	yes	—
149	C₂×C₄×C₄₇	#101	1	2	yes	—
150	C₂×C₄×C₄₇	C₄⋊C₈	1	4	yes	complemented
151	C₂×C₄×C₄₇	#121	1	2	yes	—
152	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
153	C₄₇⋊C₈	—	8	4	no	—
154	#8558	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	—	2	1	no	—
156	C₂²×C₄₇	—	2	1	no	—
157	C₂²×C₄₇	—	2	1	no	—
158	C₂²×C₄₇	—	2	1	no	—
159	C₂²×C₄₇	—	2	1	no	—
160	C₂²×C₄₇	—	2	1	no	—
161	C₂²×C₄₇	—	2	1	no	—
162	C₂²×C₄₇	—	2	1	no	—
163	C₂²×C₄₇	—	2	1	no	—
164	C₂²×C₄₇	—	2	1	no	—
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	#380	1	1	yes	characteristic
168	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
169	C₂²×C₄₇	#407	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×#99	1	1	yes	characteristic
171	C₂²×C₄₇	#410	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
173	C₂²×C₄₇	#413	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
175	C₂²×C₄₇	#423	1	1	yes	characteristic
176	C₂²×C₄₇	#431	1	1	yes	characteristic
177	C₂²×C₄₇	#432	1	1	yes	characteristic
178	C₄×C₄₇	—	2	4	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	4	2	no	—
184	C₄×C₄₇	—	4	2	no	—
185	C₄×C₄₇	—	4	2	no	—
186	C₄×C₄₇	#324	1	4	yes	complemented
187	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
188	#1797	—	47	2	no	—
189	C₂×#324	—	47	2	no	—
190	#1280	—	47	2	no	—
191	C₂×C₄₇	—	2	1	no	—
192	C₂×C₄₇	—	2	1	no	—
193	C₂×C₄₇	—	2	1	no	—
194	C₂×C₄₇	—	2	1	no	—
195	C₂×C₄₇	C₂×#324	1	1	yes	characteristic
196	C₂×C₄₇	#1458	1	1	yes	characteristic
197	C₂×C₄₇	#1465	1	1	yes	characteristic
198	C₂×C₄₇	#1467	1	1	yes	characteristic
199	C₂×C₄₇	#1797	1	1	yes	characteristic
200	C₂×C₄₇	#1799	1	1	yes	characteristic
201	C₂×C₄₇	#1801	1	1	yes	characteristic
202	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
204	C₂²×C₄²	Dic₄₇	1	1	yes	characteristic
205	C₂²×C₄²	Dic₄₇	1	1	yes	characteristic
206	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
207	C₂×C₄⋊C₈	—	94	2	no	—
208	C₂×C₂²⋊C₈	—	47	4	no	—
209	C₄×C₄⋊C₄	—	2	2	no	—
210	C₄×C₄⋊C₄	—	2	2	no	—
211	C₂×#95	Dic₄₇	1	1	yes	characteristic
212	C₂×#95	C₂×D₄₇	1	1	yes	characteristic
213	#336	—	94	2	no	—
214	#324	—	94	4	no	—
215	C₄₇	#8558	1	1	yes	characteristic, complemented, Sylow
216	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
217	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
218	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
219	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
220	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
223	C₂²×C₈	—	94	4	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	Dic₉₄	1	2	yes	—
230	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	—	2	1	no	—
236	C₂×C₄²	—	4	2	no	—
237	C₂×C₄²	—	4	2	no	—
238	C₂×C₄²	C₄₇⋊C₈	1	4	yes	complemented
239	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
240	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
241	C₄⋊C₈	—	188	4	no	—
242	C₂²⋊C₈	—	94	4	no	—
243	C₂²⋊C₈	—	94	4	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
272	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
273	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
274	C₂²×C₄	#10625329	1	2	yes	—
275	C₂²×C₄	#10625329	1	2	yes	—
276	C₂²×C₄	#10625329	1	2	yes	—
277	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
278	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
279	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
280	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
284	C₂²×C₄	#10625350	1	2	yes	—
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
286	C₂×C₈	—	188	4	no	—
287	C₂×C₈	—	188	4	no	—
288	C₂×C₈	—	188	4	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄²	—	2	4	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	2	4	no	—
295	C₄²	—	4	2	no	—
296	C₄²	—	4	2	no	—
297	C₄²	—	4	2	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
303	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
304	C₂³	#13093983	1	1	yes	characteristic
305	C₂³	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
306	C₂³	C₂×#10625329	1	1	yes	characteristic
307	C₂³	C₂×#10625329	1	1	yes	characteristic
308	C₂³	C₂×#10625329	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
345	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
346	C₂×C₄	#13093939	1	2	yes	—
347	C₂×C₄	#13093943	1	2	yes	—
348	C₂×C₄	C₄⋊(C₄₇⋊C₈)	1	4	yes	complemented
349	C₂×C₄	#13093998	1	2	yes	—
350	C₂×C₄	#13094003	1	2	yes	—
351	C₈	—	376	4	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	#15688983	1	1	yes	characteristic
365	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
366	C₂²	#15689087	1	1	yes	characteristic
367	C₂²	C₂×#13093939	1	1	yes	characteristic
368	C₂²	#15689097	1	1	yes	characteristic
369	C₂²	C₂×#13093943	1	1	yes	characteristic
370	C₂²	#15689107	1	1	yes	characteristic
371	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
372	C₂²	#15689147	1	1	yes	characteristic
373	C₂²	#15689176	1	1	yes	characteristic
374	C₂²	#15689180	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	4	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	#15688849	1	4	yes	complemented
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	C₂×#15688849	1	1	yes	characteristic
389	C₂	#20241702	1	1	yes	characteristic
390	C₂	#20241726	1	1	yes	characteristic
391	C₂	#20241732	1	1	yes	characteristic
392	C₂	#20243368	1	1	yes	characteristic
393	C₂	#20243376	1	1	yes	characteristic
394	C₂	#20243384	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂³×C₄₇	C₂²×C₈
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#8558
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
43. C₂×C₄²×C₄₇	C₈	semidirect
150. C₂×C₄×C₄₇	C₄⋊C₈	semidirect
186. C₄×C₄₇	#324	semidirect
215. C₄₇	#8558	semidirect
238. C₂×C₄²	C₄₇⋊C₈	semidirect
348. C₂×C₄	C₄⋊(C₄₇⋊C₈)	semidirect
383. C₄	#15688849	semidirect

Maximal subgroups

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

subgroup	index
#20243368	2
C₂×#15688849	2
#20241231	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#8558	47