Subgroups — #26252370

Order 12032.

1294 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689408	C₂	1	2	yes	maximal, complemented
3	#20244721	C₂	1	2	yes	maximal, complemented
4	#20244529	C₂	1	2	yes	maximal, complemented
5	#20244340	C₂	1	2	yes	maximal, complemented
6	#20243696	C₂	1	2	yes	maximal
7	#20243580	C₂	1	2	yes	maximal
8	#20243368	C₂	1	1	yes	maximal, characteristic
9	C₄×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×Dic₉₄	—	2	1	no	—
11	C₂×#13094024	—	2	8	no	—
12	C₂×#13094024	—	2	1	no	—
13	C₂×#13094024	—	2	1	no	—
14	C₂×#13094024	C₂²	1	2	yes	—
15	C₂×#13094024	C₂²	1	2	yes	—
16	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
17	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
18	#15689408	—	2	8	no	—
19	C₂×#13093955	C₂²	1	4	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×#13093948	C₂²	1	4	yes	—
22	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
23	#15688885	C₂²	1	4	yes	—
24	#15688885	C₂²	1	4	yes	—
25	#15688878	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#391	C₂²	1	1	yes	characteristic
30	C₄₇×#389	C₂²	1	1	yes	characteristic
31	C₄₇×#387	—	2	1	no	—
32	C₄₇×#385	—	2	1	no	—
33	C₄₇×#380	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
37	C₂²×Dic₉₄	—	2	8	no	—
38	C₂²×Dic₉₄	—	2	2	no	—
39	C₂²×Dic₉₄	—	2	2	no	—
40	C₂²×Dic₉₄	—	4	4	no	—
41	C₂²×Dic₉₄	—	4	4	no	—
42	C₂³×Dic₄₇	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
44	#13094024	—	2	8	no	—
45	#13094024	—	2	8	no	—
46	#13094024	—	2	4	no	—
47	#13094024	—	2	8	no	—
48	#13094024	D₄	1	8	yes	—
49	C₂×C₄⋊Dic₄₇	—	2	8	no	—
50	C₂×C₄⋊Dic₄₇	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄⋊Dic₄₇	—	2	8	no	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
55	#13093955	—	2	8	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
57	#13093948	—	2	8	no	—
58	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
59	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂²⋊Q₈×C₄₇	—	2	2	no	—
64	C₂²⋊Q₈×C₄₇	Q₈	1	4	yes	complemented
65	C₄×Q₈×C₄₇	—	2	4	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄²×C₄₇	—	2	4	no	—
75	C₂×C₄²×C₄₇	—	2	1	no	—
76	C₂×C₄²×C₄₇	—	2	1	no	—
77	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	#95×C₄₇	—	2	1	no	—
82	#95×C₄₇	—	2	1	no	—
83	#95×C₄₇	—	2	1	no	—
84	#95×C₄₇	—	2	1	no	—
85	#95×C₄₇	—	2	1	no	—
86	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₄₇	—	2	1	no	—
88	C₂×Q₈×C₄₇	—	2	2	no	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	complemented
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	SD₁₆	1	4	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	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂²×Dic₄₇	—	2	8	no	—
112	C₂²×Dic₄₇	—	2	4	no	—
113	C₂²×Dic₄₇	—	4	4	no	—
114	C₂²×Dic₄₇	—	4	4	no	—
115	C₂×Dic₉₄	—	2	8	no	—
116	C₂×Dic₉₄	—	2	8	no	—
117	C₂×Dic₉₄	—	4	4	no	—
118	C₂×Dic₉₄	—	4	32	no	—
119	C₂×Dic₉₄	—	4	4	no	—
120	C₂×Dic₉₄	—	4	4	no	—
121	C₂×Dic₉₄	—	4	4	no	—
122	C₄⋊C₄×C₄₇	—	2	4	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	4	2	no	—
127	C₄⋊C₄×C₄₇	—	4	2	no	—
128	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	complemented
129	C₂²⋊C₄×C₄₇	—	2	4	no	—
130	C₂²⋊C₄×C₄₇	—	4	2	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	—	4	2	no	—
135	C₄²×C₄₇	—	4	2	no	—
136	C₄²×C₄₇	C₂×D₄	1	4	yes	—
137	C₄⋊Dic₄₇	—	2	8	no	—
138	C₄⋊Dic₄₇	—	2	8	no	—
139	C₄⋊Dic₄₇	—	2	8	no	—
140	C₄⋊Dic₄₇	—	2	4	no	—
141	C₄⋊Dic₄₇	C₂×D₄	1	8	yes	—
142	C₂×C₄₇⋊C₈	—	2	4	no	—
143	C₂×C₄₇⋊C₈	—	2	4	no	—
144	C₂×C₄₇⋊C₈	—	2	4	no	—
145	C₂³×C₄₇	—	2	1	no	—
146	C₂³×C₄₇	—	2	1	no	—
147	C₂³×C₄₇	—	2	1	no	—
148	C₂³×C₄₇	—	2	1	no	—
149	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
150	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
151	C₂³×C₄₇	#137	1	2	yes	—
152	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₄₇	—	2	4	no	—
154	Q₈×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	2	8	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	#120	1	2	yes	—
180	C₂×C₄×C₄₇	#120	1	2	yes	—
181	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
182	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
183	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
184	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
185	C₂×C₄×C₄₇	#137	1	2	yes	—
186	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
190	C₂×Dic₄₇	—	2	8	no	—
191	C₂×Dic₄₇	—	4	16	no	—
192	C₂×Dic₄₇	—	4	4	no	—
193	C₂×Dic₄₇	—	4	4	no	—
194	Dic₉₄	—	4	16	no	—
195	Dic₉₄	—	4	16	no	—
196	C₄₇⋊C₈	—	4	4	no	—
197	#24301	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	2	2	no	—
204	C₂²×C₄₇	#475	1	4	yes	complemented
205	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
207	C₂²×C₄₇	#536	1	1	yes	characteristic
208	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	4	2	no	—
217	C₄×C₄₇	—	4	2	no	—
218	C₄×C₄₇	—	8	1	no	—
219	C₄×C₄₇	—	8	1	no	—
220	C₄×C₄₇	#450	1	4	yes	—
221	C₄×C₄₇	#548	1	2	yes	—
222	C₄×C₄₇	D₄×Q₈	1	2	yes	—
223	Dic₄₇	—	4	8	no	—
224	C₂²×C₄⋊Q₈	—	47	1	no	—
225	C₂×#475	—	47	2	no	—
226	C₄×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
227	#2058	—	47	2	no	—
228	#2024	—	47	2	no	—
229	#1988	—	47	2	no	—
230	#1872	—	47	2	no	—
231	#1853	—	47	2	no	—
232	#1797	—	47	1	no	—
233	C₂×C₄₇	—	2	4	no	—
234	C₂×C₄₇	#2409	1	1	yes	characteristic
235	C₂×C₄₇	C₂×#450	1	1	yes	characteristic
236	C₂×C₄₇	#3004	1	1	yes	characteristic
237	C₂×C₄₇	C₂×#475	1	1	yes	characteristic
238	C₂×C₄₇	#3079	1	1	yes	characteristic
239	C₂×C₄₇	#3229	1	1	yes	characteristic
240	C₂×C₄₇	#3239	1	1	yes	characteristic
241	C₂³×Q₈	—	94	1	no	—
242	C₂×C₄⋊Q₈	—	47	2	no	—
243	C₂×C₄⋊Q₈	—	47	2	no	—
244	C₂×C₄⋊Q₈	—	94	8	no	—
245	C₂×C₄⋊Q₈	—	94	1	no	—
246	C₂×C₄⋊Q₈	—	94	1	no	—
247	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	—	47	2	no	—
250	C₂²×C₄⋊C₄	—	94	1	no	—
251	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
252	#475	—	94	8	no	—
253	C₂×#106	—	47	4	no	—
254	C₂×C₄⋊C₈	—	47	2	no	—
255	C₂×#103	—	47	4	no	—
256	C₂×C₂²⋊C₈	—	47	2	no	—
257	#391	C₂×D₄₇	1	1	yes	characteristic
258	#389	C₂×D₄₇	1	1	yes	characteristic
259	#387	—	2	1	no	—
260	#385	—	2	1	no	—
261	#380	C₂×D₄₇	1	1	yes	characteristic
262	C₄×C₄⋊C₄	—	2	1	no	—
263	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	—	2	1	no	—
265	#340	—	47	4	no	—
266	#340	—	47	4	no	—
267	#336	—	47	2	no	—
268	C₄₇	#24301	1	1	yes	characteristic, complemented, Sylow
269	C₂²×Q₈	—	94	8	no	—
270	C₂²×Q₈	—	94	2	no	—
271	C₂²×Q₈	—	94	2	no	—
272	C₂²×Q₈	—	188	4	no	—
273	C₂²×Q₈	—	188	4	no	—
274	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
275	C₂³×C₄	—	94	2	no	—
276	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
277	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
278	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
279	C₂²×C₈	—	47	4	no	—
280	C₄⋊Q₈	—	47	8	no	—
281	C₄⋊Q₈	—	94	8	no	—
282	C₄⋊Q₈	—	94	8	no	—
283	C₄⋊Q₈	—	94	8	no	—
284	C₄⋊Q₈	—	94	4	no	—
285	C₂²⋊Q₈	—	2	2	no	—
286	C₂²⋊Q₈	Dic₉₄	1	4	yes	complemented
287	C₄×Q₈	—	2	4	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	47	4	no	—
292	C₂×C₄⋊C₄	—	94	8	no	—
293	C₂×C₄⋊C₄	—	94	8	no	—
294	C₂×C₄⋊C₄	—	94	2	no	—
295	C₂×C₄⋊C₄	—	94	2	no	—
296	C₂×C₄⋊C₄	—	94	2	no	—
297	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₄²	—	2	4	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
306	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
307	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
308	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
309	#106	—	94	8	no	—
310	C₄⋊C₈	—	94	4	no	—
311	#103	—	94	8	no	—
312	C₂²⋊C₈	—	94	4	no	—
313	#95	—	2	1	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	94	8	no	—
323	C₂×Q₈	—	94	8	no	—
324	C₂×Q₈	—	188	4	no	—
325	C₂×Q₈	—	188	32	no	—
326	C₂×Q₈	—	188	4	no	—
327	C₂×Q₈	—	188	4	no	—
328	C₂×Q₈	—	188	4	no	—
329	C₂×Q₈	C₂×Dic₉₄	1	2	yes	complemented
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	94	8	no	—
342	C₂²×C₄	—	94	4	no	—
343	C₂²×C₄	—	188	4	no	—
344	C₂²×C₄	—	188	4	no	—
345	C₂²×C₄	#10625336	1	4	yes	—
346	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
347	C₂²×C₄	#10625350	1	2	yes	—
348	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
354	C₂×C₈	—	94	4	no	—
355	C₂×C₈	—	94	4	no	—
356	C₂×C₈	—	94	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	47	8	no	—
364	C₄⋊C₄	—	94	8	no	—
365	C₄⋊C₄	—	94	8	no	—
366	C₄⋊C₄	—	94	8	no	—
367	C₄⋊C₄	—	94	4	no	—
368	C₄⋊C₄	C₂×Dic₉₄	1	2	yes	complemented
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	2	no	—
375	C₄²	—	4	2	no	—
376	C₄²	D₄×D₄₇	1	4	yes	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	#13094003	1	2	yes	—
382	C₂³	C₂×#10625336	1	2	yes	—
383	C₂³	#13094054	1	2	yes	—
384	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
385	Q₈	—	2	4	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	188	16	no	—
388	Q₈	—	188	16	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	94	8	no	—
414	C₂×C₄	—	188	16	no	—
415	C₂×C₄	—	188	4	no	—
416	C₂×C₄	—	188	4	no	—
417	C₂×C₄	#13093992	1	2	yes	—
418	C₂×C₄	#13093992	1	2	yes	—
419	C₂×C₄	#13094003	1	2	yes	—
420	C₂×C₄	C₂×#10625336	1	2	yes	—
421	C₂×C₄	C₂×#10625336	1	2	yes	—
422	C₂×C₄	#13094049	1	2	yes	—
423	C₂×C₄	#13094054	1	2	yes	—
424	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
425	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
426	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
427	C₂×C₄	#13094071	1	2	yes	—
428	C₈	—	188	4	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	#15689408	1	4	yes	complemented
436	C₂²	C₂×#13093992	1	1	yes	characteristic
437	C₂²	C₂×#13094003	1	1	yes	characteristic
438	C₂²	#15689694	1	1	yes	characteristic
439	C₂²	C₂²×#10625336	1	1	yes	characteristic
440	C₂²	C₂×#13094049	1	1	yes	characteristic
441	C₂²	C₂×#13094054	1	1	yes	characteristic
442	C₂²	C₂×#13094054	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	1	no	—
451	C₄	—	188	8	no	—
452	C₄	#15689273	1	4	yes	—
453	C₄	#15689782	1	2	yes	—
454	C₄	D₄×Dic₉₄	1	2	yes	—
455	C₂	—	2	4	no	—
456	C₂	#20246753	1	1	yes	characteristic
457	C₂	C₂×#15689273	1	1	yes	characteristic
458	C₂	#20252621	1	1	yes	characteristic
459	C₂	C₂×#15689408	1	1	yes	characteristic
460	C₂	#20253203	1	1	yes	characteristic
461	C₂	#20254529	1	1	yes	characteristic
462	C₂	#20254615	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₂²⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
hypercenter	C₄×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	#24301
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×#15689408	C₂	semidirect
3. #20244721	C₂	semidirect
4. #20244529	C₂	semidirect
5. #20244340	C₂	semidirect
64. C₂²⋊Q₈×C₄₇	Q₈	semidirect
90. C₂×Q₈×C₄₇	C₂×Q₈	semidirect
128. C₄⋊C₄×C₄₇	C₂×Q₈	semidirect
204. C₂²×C₄₇	#475	semidirect
268. C₄₇	#24301	semidirect
286. C₂²⋊Q₈	Dic₉₄	semidirect
329. C₂×Q₈	C₂×Dic₉₄	semidirect
368. C₄⋊C₄	C₂×Dic₉₄	semidirect
435. C₂²	#15689408	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13094024	2
C₂×#15689408	2
#20244721	2
#20244529	2
#20244340	2
#20243696	2
#20243580	2
#20243368	2
C₄×C₂²⋊Q₈×C₄₇	2
#24301	47