Subgroups — #26232921

Order 12032.

1034 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689851	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689254	C₂	1	1	yes	maximal, characteristic
3	#20244356	C₂	1	2	yes	maximal
4	#20244348	C₂	1	1	yes	maximal, characteristic
5	#20244345	C₂	1	2	yes	maximal
6	#20244340	C₂	1	1	yes	maximal, characteristic
7	#20243390	C₂	1	1	yes	maximal, characteristic
8	#20243390	C₂	1	2	yes	maximal
9	#20243221	C₂	1	2	yes	maximal
10	C₄×#13093947	C₂	1	1	yes	maximal, characteristic
11	Q₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
12	#15689851	—	2	4	no	—
13	#15689851	C₄	1	8	yes	complemented
14	C₂×#13094024	C₂²	1	1	yes	characteristic
15	C₂×#13094022	—	2	1	no	—
16	C₂×#13094016	C₂²	1	2	yes	—
17	C₂×#13094014	—	2	2	no	—
18	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
19	C₂×C₄×Dic₉₄	C₂²	1	2	yes	—
20	C₂×#13093989	—	2	1	no	—
21	#15689254	—	2	4	no	—
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
24	C₂×#13093947	C₂²	1	1	yes	characteristic
25	C₂×#13093947	C₂²	1	2	yes	—
26	C₂×#13093947	C₂²	1	1	yes	characteristic
27	C₂×#13093935	C₂²	1	2	yes	—
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	#15688885	C₂²	1	1	yes	characteristic
30	#15688885	C₂²	1	1	yes	characteristic
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
37	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#389	—	2	1	no	—
39	C₄₇×#389	—	2	2	no	—
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄₇×#384	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
44	C₂²×Dic₉₄	—	2	1	no	—
45	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	#13094024	—	2	2	no	—
50	#13094024	C₂×C₄	1	4	yes	—
51	#13094022	—	2	8	no	—
52	#13094016	—	2	4	no	—
53	#13094016	C₂×C₄	1	8	yes	—
54	#13094014	—	2	16	no	—
55	C₄×Dic₉₄	—	2	4	no	—
56	C₄×Dic₉₄	—	2	2	no	—
57	C₄×Dic₉₄	C₂×C₄	1	8	yes	—
58	C₄×Dic₉₄	C₂×C₄	1	4	yes	—
59	#13093989	—	2	8	no	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
63	C₂×Dic₄₇⋊C₄	—	2	2	no	—
64	C₂×Dic₄₇⋊C₄	—	2	1	no	—
65	C₂×Dic₄₇⋊C₄	—	2	2	no	—
66	C₂×Dic₄₇⋊C₄	—	2	2	no	—
67	C₂×C₄×Dic₄₇	—	2	2	no	—
68	C₂×C₄×Dic₄₇	—	2	1	no	—
69	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
70	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
71	#13093947	—	2	2	no	—
72	#13093947	—	2	4	no	—
73	#13093947	Q₈	1	4	yes	complemented
74	#13093935	—	2	4	no	—
75	C₄×C₄₇⋊C₈	—	2	2	no	—
76	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
77	C₄×Q₈×C₄₇	—	4	4	no	—
78	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
79	C₄×Q₈×C₄₇	D₄	1	4	yes	—
80	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	—	2	2	no	—
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
93	#95×C₄₇	—	2	2	no	—
94	#95×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	1	no	—
108	C₂²×Dic₄₇	—	2	2	no	—
109	C₂×Dic₉₄	—	2	1	no	—
110	C₂×Dic₉₄	—	2	1	no	—
111	C₂×Dic₉₄	—	2	1	no	—
112	C₂×Dic₉₄	—	2	4	no	—
113	C₂×Dic₉₄	—	4	2	no	—
114	C₂×Dic₉₄	—	4	2	no	—
115	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
116	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
117	C₂×Dic₉₄	#41	1	2	yes	—
118	C₄⋊C₄×C₄₇	—	2	1	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	4	4	no	—
124	C₄⋊C₄×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	—	8	2	no	—
126	C₄⋊C₄×C₄₇	—	8	1	no	—
127	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
128	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
129	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
130	C₄²×C₄₇	—	4	4	no	—
131	C₄²×C₄₇	—	4	2	no	—
132	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
133	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
134	C₄²×C₄₇	C₂×D₄	1	2	yes	—
135	C₄²×C₄₇	C₂×D₄	1	4	yes	—
136	C₄⋊Dic₄₇	—	2	4	no	—
137	C₄⋊Dic₄₇	—	2	1	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
140	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
141	Dic₄₇⋊C₄	—	2	8	no	—
142	Dic₄₇⋊C₄	—	2	4	no	—
143	Dic₄₇⋊C₄	—	2	8	no	—
144	Dic₄₇⋊C₄	—	2	8	no	—
145	C₄×Dic₄₇	—	2	8	no	—
146	C₄×Dic₄₇	—	2	4	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
156	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₄₇	—	2	8	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
174	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
178	C₂×C₄×C₄₇	#137	1	2	yes	—
179	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	2	2	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	—	2	4	no	—
190	C₂×Dic₄₇	—	4	2	no	—
191	C₂×Dic₄₇	—	4	2	no	—
192	C₂×Dic₄₇	—	4	1	no	—
193	C₂×Dic₄₇	—	4	1	no	—
194	Dic₉₄	—	2	2	no	—
195	Dic₉₄	—	2	2	no	—
196	Dic₉₄	—	2	2	no	—
197	Dic₉₄	—	4	8	no	—
198	Dic₉₄	C₄×Q₈	1	4	yes	complemented
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	—	4	1	no	—
201	C₄₇⋊C₈	—	4	2	no	—
202	#22524	—	47	1	no	maximal, Sylow
203	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₄₇	#548	1	1	yes	characteristic
205	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
208	C₂²×C₄₇	#577	1	1	yes	characteristic
209	C₂²×C₄₇	#578	1	1	yes	characteristic
210	C₄×C₄₇	—	2	4	no	—
211	C₄×C₄₇	—	2	4	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	4	2	no	—
214	C₄×C₄₇	—	8	2	no	—
215	C₄×C₄₇	—	8	1	no	—
216	C₄×C₄₇	#417	1	4	yes	—
217	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
218	C₄×C₄₇	#519	1	1	yes	characteristic
219	C₄×C₄₇	#548	1	1	yes	characteristic
220	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
221	Dic₄₇	—	2	4	no	—
222	Dic₄₇	—	4	4	no	—
223	Dic₄₇	—	4	2	no	—
224	C₂×#557	—	47	1	no	—
225	C₂×#446	—	47	1	no	—
226	Q₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic
227	#1992	—	47	2	no	—
228	#1990	—	47	1	no	—
229	#1989	—	47	2	no	—
230	#1988	—	47	1	no	—
231	#1803	—	47	1	no	—
232	#1803	—	47	2	no	—
233	#1763	—	47	2	no	—
234	C₄×#103	—	47	1	no	—
235	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
237	C₂×C₄₇	#2898	1	1	yes	characteristic
238	C₂×C₄₇	#3368	1	1	yes	characteristic
239	C₂×C₄₇	#3374	1	1	yes	characteristic
240	C₂×C₄₇	#3386	1	1	yes	characteristic
241	C₂×C₄₇	#3387	1	1	yes	characteristic
242	#557	—	47	8	no	—
243	#557	—	94	4	no	—
244	C₂×C₄⋊Q₈	—	47	1	no	—
245	C₂×C₄⋊Q₈	—	94	1	no	—
246	C₂×#125	—	47	2	no	—
247	C₂×#125	—	94	2	no	—
248	C₂×C₄×Q₈	—	2	1	no	—
249	C₂×C₄×Q₈	—	47	1	no	—
250	C₂×C₄×Q₈	—	47	2	no	—
251	C₂×C₄×Q₈	—	94	1	no	—
252	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
253	#446	—	94	4	no	—
254	C₂×C₄⋊C₈	—	47	1	no	—
255	C₂×C₄⋊C₈	—	47	2	no	—
256	C₂×#103	—	47	1	no	—
257	C₂×#103	—	47	1	no	—
258	C₂×#103	—	47	2	no	—
259	C₂×#97	—	47	2	no	—
260	C₂×C₄×C₈	—	47	1	no	—
261	#389	—	2	1	no	—
262	#389	—	2	2	no	—
263	#384	C₂×D₄₇	1	1	yes	characteristic
264	#384	C₂×D₄₇	1	2	yes	—
265	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
267	#340	—	47	2	no	—
268	#340	—	47	2	no	—
269	#340	—	47	2	no	—
270	#340	—	47	2	no	—
271	#340	—	47	1	no	—
272	#340	—	47	2	no	—
273	#340	—	47	1	no	—
274	C₄₇	#22524	1	1	yes	characteristic, complemented, Sylow
275	C₂²×Q₈	—	47	1	no	—
276	C₂²×Q₈	—	94	1	no	—
277	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
278	C₂²×C₈	—	47	1	no	—
279	C₂²×C₈	—	47	1	no	—
280	C₂²×C₈	—	47	2	no	—
281	C₄⋊Q₈	—	47	4	no	—
282	C₄⋊Q₈	—	94	8	no	—
283	C₄⋊Q₈	—	94	2	no	—
284	#125	—	47	8	no	—
285	#125	—	94	16	no	—
286	#125	—	94	4	no	—
287	C₄×Q₈	—	4	4	no	—
288	C₄×Q₈	—	47	8	no	—
289	C₄×Q₈	—	47	4	no	—
290	C₄×Q₈	—	94	8	no	—
291	C₄×Q₈	—	94	4	no	—
292	C₄×Q₈	—	94	2	no	—
293	C₄×Q₈	C₄×D₄₇	1	4	yes	—
294	C₄×Q₈	D₁₈₈	1	4	yes	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	47	1	no	—
300	C₂×C₄⋊C₄	—	47	2	no	—
301	C₂×C₄⋊C₄	—	94	1	no	—
302	C₂×C₄⋊C₄	—	94	2	no	—
303	C₂×C₄⋊C₄	—	94	2	no	—
304	C₂×C₄⋊C₄	—	94	2	no	—
305	C₂×C₄⋊C₄	—	94	1	no	—
306	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
308	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
310	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	94	2	no	—
314	C₂×C₄²	—	94	1	no	—
315	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
316	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
317	C₄⋊C₈	—	94	2	no	—
318	C₄⋊C₈	—	94	4	no	—
319	#103	—	47	4	no	—
320	#103	—	94	2	no	—
321	#103	—	94	4	no	—
322	#97	—	94	4	no	—
323	C₄×C₈	—	94	2	no	—
324	#95	—	2	2	no	—
325	#95	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	47	2	no	—
329	C₂×Q₈	—	47	2	no	—
330	C₂×Q₈	—	47	2	no	—
331	C₂×Q₈	—	94	4	no	—
332	C₂×Q₈	—	94	1	no	—
333	C₂×Q₈	—	94	1	no	—
334	C₂×Q₈	—	94	1	no	—
335	C₂×Q₈	—	188	2	no	—
336	C₂×Q₈	—	188	2	no	—
337	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	4	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	—	94	1	no	—
343	C₂²×C₄	—	94	2	no	—
344	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
345	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
347	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
349	C₂×C₈	—	47	2	no	—
350	C₂×C₈	—	94	1	no	—
351	C₂×C₈	—	94	1	no	—
352	C₂×C₈	—	94	1	no	—
353	C₂×C₈	—	94	2	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	—	94	2	no	—
356	C₂×C₈	—	94	1	no	—
357	C₂×C₈	—	94	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	8	2	no	—
366	C₄⋊C₄	—	8	1	no	—
367	C₄⋊C₄	—	47	2	no	—
368	C₄⋊C₄	—	47	4	no	—
369	C₄⋊C₄	—	94	4	no	—
370	C₄⋊C₄	—	94	8	no	—
371	C₄⋊C₄	—	94	8	no	—
372	C₄⋊C₄	—	94	8	no	—
373	C₄⋊C₄	—	94	4	no	—
374	C₄⋊C₄	—	94	1	no	—
375	C₄⋊C₄	—	94	2	no	—
376	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
377	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	8	yes	—
378	C₄⋊C₄	Q₈×D₄₇	1	2	yes	—
379	C₄²	—	4	4	no	—
380	C₄²	—	4	2	no	—
381	C₄²	—	94	8	no	—
382	C₄²	—	94	4	no	—
383	C₄²	C₂×C₄×D₄₇	1	4	yes	—
384	C₄²	C₂×C₄×D₄₇	1	2	yes	—
385	C₄²	C₂×D₁₈₈	1	2	yes	—
386	C₄²	C₂×D₁₈₈	1	4	yes	—
387	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
388	Q₈	—	2	8	no	—
389	Q₈	—	47	4	no	—
390	Q₈	—	94	2	no	—
391	Q₈	—	94	2	no	—
392	Q₈	—	94	2	no	—
393	Q₈	—	188	8	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	94	2	no	—
410	C₂×C₄	—	94	2	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	94	4	no	—
414	C₂×C₄	—	188	2	no	—
415	C₂×C₄	—	188	2	no	—
416	C₂×C₄	—	188	1	no	—
417	C₂×C₄	—	188	1	no	—
418	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
419	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
420	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
421	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
422	C₂×C₄	#13094050	1	2	yes	—
423	C₂×C₄	#13094055	1	2	yes	—
424	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
426	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
427	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
428	C₂×C₄	#13094071	1	1	yes	characteristic
429	C₂×C₄	#13094072	1	1	yes	characteristic
430	C₈	—	94	2	no	—
431	C₈	—	188	1	no	—
432	C₈	—	188	2	no	—
433	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
434	C₂²	#15689780	1	1	yes	characteristic
435	C₂²	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
436	C₂²	C₂×#13094050	1	1	yes	characteristic
437	C₂²	C₂×#13094055	1	1	yes	characteristic
438	C₂²	#15689934	1	1	yes	characteristic
439	C₂²	#15689938	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	4	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	1	no	—
446	C₄	—	94	4	no	—
447	C₄	—	188	2	no	—
448	C₄	—	188	4	no	—
449	C₄	#15689122	1	4	yes	—
450	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
451	C₄	#15689599	1	1	yes	characteristic
452	C₄	#15689785	1	1	yes	characteristic
453	C₄	Q₈×D₁₈₈	1	1	yes	characteristic
454	C₂	Q₈×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
455	C₂	C₂×#15689122	1	1	yes	characteristic
456	C₂	#20251918	1	1	yes	characteristic
457	C₂	#20256113	1	1	yes	characteristic
458	C₂	#20256187	1	1	yes	characteristic
459	C₂	#20256309	1	1	yes	characteristic
460	C₂	#20256316	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	Q₈×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	Q₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#22524
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ Q₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
13. #15689851	C₄	semidirect
73. #13093947	Q₈	semidirect
198. Dic₉₄	C₄×Q₈	semidirect
274. C₄₇	#22524	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689851	2
C₂×#15689254	2
#20244356	2
#20244348	2
#20244345	2
#20244340	2
#20243390	2
#20243221	2
C₄×#13093947	2
Q₈×C₄⋊C₄×C₄₇	2
#22524	47