Subgroups — #26107649

Order 12032.

1088 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20243368	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
6	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
8	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
9	#15688878	—	2	1	no	—
10	#15688878	—	2	1	no	—
11	Q₈⋊(C₄₇⋊C₈)	—	2	8	no	—
12	C₂³×Q₈×C₄₇	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₇	—	2	8	no	—
14	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
15	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
16	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	—
17	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
19	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
20	C₂²×C₄²×C₄₇	—	2	1	no	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
25	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
26	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
27	C₄×C₄₇⋊C₈	—	2	4	no	—
28	C₂²×Q₈×C₄₇	—	2	4	no	—
29	C₂²×Q₈×C₄₇	—	2	4	no	—
30	C₂²×Q₈×C₄₇	—	2	1	no	—
31	C₂²×Q₈×C₄₇	—	2	2	no	—
32	C₂²×Q₈×C₄₇	C₈	1	4	yes	complemented
33	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₄₇	—	2	1	no	—
35	C₂³×C₄×C₄₇	—	2	1	no	—
36	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₄×Q₈×C₄₇	—	2	8	no	—
40	C₄×Q₈×C₄₇	—	2	8	no	—
41	C₄×Q₈×C₄₇	—	2	4	no	—
42	C₄×Q₈×C₄₇	—	2	4	no	—
43	C₄×Q₈×C₄₇	—	2	4	no	—
44	C₄×Q₈×C₄₇	D₄	1	8	yes	—
45	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
50	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₄₇	—	2	8	no	—
52	C₂×C₄²×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	—	2	2	no	—
54	C₂×C₄²×C₄₇	—	2	4	no	—
55	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
59	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×Q₈×C₄₇	—	2	4	no	—
61	C₂×Q₈×C₄₇	—	2	16	no	—
62	C₂×Q₈×C₄₇	—	2	4	no	—
63	C₂×Q₈×C₄₇	—	2	16	no	—
64	C₂×Q₈×C₄₇	—	2	4	no	—
65	C₂×Q₈×C₄₇	—	2	2	no	—
66	C₂×Q₈×C₄₇	—	2	2	no	—
67	C₂×Q₈×C₄₇	—	2	2	no	—
68	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
69	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	—
70	C₂×Q₈×C₄₇	M₁₆	1	4	yes	—
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	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	4	1	no	—
84	C₂²×C₄×C₄₇	—	4	2	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
90	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
91	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₄⋊C₄×C₄₇	—	2	8	no	—
97	C₄⋊C₄×C₄₇	—	2	4	no	—
98	C₄⋊C₄×C₄₇	—	2	2	no	—
99	C₄⋊C₄×C₄₇	—	2	8	no	—
100	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
101	C₄²×C₄₇	—	2	8	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄²×C₄₇	—	2	8	no	—
104	C₄²×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	C₂×D₄	1	4	yes	—
107	C₂×C₄₇⋊C₈	—	2	4	no	—
108	C₂×C₄₇⋊C₈	—	4	2	no	—
109	C₂×C₄₇⋊C₈	—	4	2	no	—
110	C₂×C₄₇⋊C₈	—	4	2	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	2	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	2	1	no	—
115	C₂³×C₄₇	—	2	1	no	—
116	C₂³×C₄₇	—	2	1	no	—
117	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
118	C₂³×C₄₇	#103	1	2	yes	—
119	C₂³×C₄₇	#104	1	2	yes	—
120	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	Q₈×C₄₇	—	2	16	no	—
122	Q₈×C₄₇	—	2	4	no	—
123	Q₈×C₄₇	—	2	4	no	—
124	Q₈×C₄₇	—	2	4	no	—
125	Q₈×C₄₇	C₂²⋊C₈	1	8	yes	complemented
126	C₂×C₄×C₄₇	—	2	16	no	—
127	C₂×C₄×C₄₇	—	2	1	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	8	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
149	C₂×C₄×C₄₇	#103	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	#120	1	2	yes	—
152	C₂×C₄×C₄₇	#120	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#137	1	2	yes	—
159	C₄₇⋊C₈	—	4	4	no	—
160	C₄₇⋊C₈	—	8	2	no	—
161	#8311	—	47	1	no	maximal, Sylow
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	—	2	2	no	—
164	C₂²×C₄₇	—	2	2	no	—
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	Q₈⋊C₈	1	4	yes	complemented
169	C₂²×C₄₇	#379	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
171	C₂²×C₄₇	#407	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
173	C₂²×C₄₇	#419	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
175	C₂²×C₄₇	#421	1	1	yes	characteristic
176	C₄×C₄₇	—	2	8	no	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	4	1	no	—
181	C₄×C₄₇	—	4	4	no	—
182	C₄×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
183	C₄×C₄₇	#407	1	2	yes	—
184	C₄×C₄₇	#448	1	2	yes	—
185	C₄×C₄₇	#451	1	2	yes	—
186	C₂²×C₄×Q₈	D₄₇	1	1	yes	characteristic
187	#1797	—	47	1	no	—
188	C₄×C₂²⋊C₈	—	47	1	no	—
189	C₂×Q₈⋊C₈	—	47	4	no	—
190	C₂×C₄₇	—	2	4	no	—
191	C₂×C₄₇	C₂×Q₈⋊C₈	1	1	yes	characteristic
192	C₂×C₄₇	#1479	1	1	yes	characteristic
193	C₂×C₄₇	#1487	1	1	yes	characteristic
194	C₂×C₄₇	#1491	1	1	yes	characteristic
195	C₂×C₄₇	#1779	1	1	yes	characteristic
196	C₂×C₄₇	#1787	1	1	yes	characteristic
197	C₂×C₄₇	#1789	1	1	yes	characteristic
198	C₂³×Q₈	Dic₄₇	1	1	yes	characteristic
199	C₂×C₄×Q₈	—	2	8	no	—
200	C₂×C₄×Q₈	—	2	1	no	—
201	C₂×C₄×Q₈	—	2	1	no	—
202	C₂×C₄×Q₈	Dic₄₇	1	2	yes	—
203	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
204	C₂²×C₄⋊C₄	—	2	1	no	—
205	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
206	C₂²×C₄²	—	2	1	no	—
207	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
208	C₂×C₄⋊C₈	—	47	2	no	—
209	C₂×C₂²⋊C₈	—	94	1	no	—
210	C₂×C₂²⋊C₈	—	94	1	no	—
211	C₂×C₄×C₈	—	47	2	no	—
212	#336	—	94	1	no	—
213	#336	—	94	1	no	—
214	Q₈⋊C₈	—	94	8	no	—
215	C₄₇	#8311	1	1	yes	characteristic, complemented, Sylow
216	C₂²×Q₈	—	2	4	no	—
217	C₂²×Q₈	—	2	4	no	—
218	C₂²×Q₈	—	2	2	no	—
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	C₄₇⋊C₈	1	4	yes	complemented
221	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
222	C₂³×C₄	—	2	1	no	—
223	C₂³×C₄	—	2	1	no	—
224	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
226	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
227	C₂²×C₈	—	94	2	no	—
228	C₂²×C₈	—	94	2	no	—
229	C₄×Q₈	—	2	8	no	—
230	C₄×Q₈	—	2	8	no	—
231	C₄×Q₈	—	2	4	no	—
232	C₄×Q₈	—	2	4	no	—
233	C₄×Q₈	—	2	4	no	—
234	C₄×Q₈	C₂²⋊D₄₇	1	8	yes	—
235	C₂×C₄⋊C₄	—	2	8	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
241	C₂×C₄²	—	2	8	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
246	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
247	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
248	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
249	C₄⋊C₈	—	94	4	no	—
250	C₂²⋊C₈	—	94	4	no	—
251	C₂²⋊C₈	—	188	2	no	—
252	C₄×C₈	—	94	4	no	—
253	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	2	16	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	16	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	C₂×C₄₇⋊C₈	1	4	yes	—
263	C₂×Q₈	#10625329	1	4	yes	—
264	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
281	C₂²×C₄	#10625329	1	2	yes	—
282	C₂²×C₄	#10625336	1	2	yes	—
283	C₂²×C₄	#10625337	1	2	yes	—
284	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
290	C₂×C₈	—	94	4	no	—
291	C₂×C₈	—	188	2	no	—
292	C₂×C₈	—	188	2	no	—
293	C₂×C₈	—	188	2	no	—
294	C₂×C₈	—	188	2	no	—
295	C₂×C₈	—	188	2	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
301	C₄²	—	2	8	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	8	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
312	C₂³	#13093948	1	2	yes	—
313	C₂³	#13093951	1	2	yes	—
314	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
315	Q₈	—	2	16	no	—
316	Q₈	—	2	4	no	—
317	Q₈	—	2	4	no	—
318	Q₈	—	2	4	no	—
319	Q₈	C₂²⋊(C₄₇⋊C₈)	1	8	yes	complemented
320	C₂×C₄	—	2	16	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	8	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
343	C₂×C₄	#13093948	1	2	yes	—
344	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
345	C₂×C₄	#13093993	1	2	yes	—
346	C₂×C₄	#13093993	1	2	yes	—
347	C₂×C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
348	C₂×C₄	C₂×#10625329	1	2	yes	—
349	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
350	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
351	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
352	C₂×C₄	#13094055	1	2	yes	—
353	C₈	—	376	2	no	—
354	C₈	—	188	4	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	Q₈⋊(C₄₇⋊C₈)	1	4	yes	complemented
362	C₂²	#15688979	1	1	yes	characteristic
363	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
364	C₂²	#15689087	1	1	yes	characteristic
365	C₂²	C₂×#13093948	1	1	yes	characteristic
366	C₂²	#15689132	1	1	yes	characteristic
367	C₂²	C₂×#13093951	1	1	yes	characteristic
368	C₂²	#15689140	1	1	yes	characteristic
369	C₄	—	2	8	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	4	no	—
375	C₄	C₂×C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
376	C₄	#15689087	1	2	yes	—
377	C₄	#15689262	1	2	yes	—
378	C₄	#15689279	1	2	yes	—
379	C₂	—	2	4	no	—
380	C₂	C₂×Q₈⋊(C₄₇⋊C₈)	1	1	yes	characteristic
381	C₂	#20241783	1	1	yes	characteristic
382	C₂	#20241817	1	1	yes	characteristic
383	C₂	#20241835	1	1	yes	characteristic
384	C₂	#20243298	1	1	yes	characteristic
385	C₂	#20243323	1	1	yes	characteristic
386	C₂	#20243332	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂²×C₄×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂²×C₄×Q₈	D₄₇
hypocenter	C₄₇	#8311
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
32. C₂²×Q₈×C₄₇	C₈	semidirect
125. Q₈×C₄₇	C₂²⋊C₈	semidirect
168. C₂²×C₄₇	Q₈⋊C₈	semidirect
215. C₄₇	#8311	semidirect
220. C₂²×Q₈	C₄₇⋊C₈	semidirect
319. Q₈	C₂²⋊(C₄₇⋊C₈)	semidirect
361. C₂²	Q₈⋊(C₄₇⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
#20243368	2
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂²×C₄×Q₈×C₄₇	2
#8311	47