Subgroups — #26186294

Order 12032.

712 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252364	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242225	C₂	1	2	yes	maximal, complemented
4	#20242218	C₂	1	2	yes	maximal, complemented
5	#20242212	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal, complemented
7	#20242173	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241831	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241801	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3105	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	—	2	1	no	—
13	#15689254	C₂²	1	1	yes	characteristic, complemented
14	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
15	#15689201	C₂²	1	1	yes	characteristic, complemented
16	#15689195	—	2	1	no	—
17	D₄×C₄₇⋊C₈	—	2	1	no	—
18	D₄×C₄₇⋊C₈	—	2	1	no	—
19	D₄×C₄₇⋊C₈	—	2	1	no	—
20	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
21	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
23	#15689184	—	2	1	no	—
24	#15689180	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
27	#15689079	—	2	1	no	—
28	C₄×#10625329	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	#15688876	C₂²	1	2	yes	complemented
31	#15688874	C₂²	1	2	yes	complemented
32	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
34	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
36	#15688845	C₂²	1	2	yes	complemented
37	#15688844	C₂²	1	2	yes	complemented
38	C₄₇×#529	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#484	C₄	1	1	yes	characteristic
41	C₄₇×#481	C₄	1	1	yes	characteristic
42	C₄₇×#478	C₄	1	2	yes	—
43	C₄₇×#463	C₄	1	2	yes	—
44	C₄₇×#450	C₄	1	1	yes	characteristic
45	C₄₇×#447	C₄	1	1	yes	characteristic
46	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
47	C₄×D₈×C₄₇	C₂²	1	2	yes	—
48	C₄₇×#431	C₂²	1	1	yes	characteristic
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂²×C₄₇⋊C₈	—	2	1	no	—
52	C₂²×C₄₇⋊C₈	—	2	1	no	—
53	C₂²×C₄₇⋊C₈	—	2	2	no	—
54	C₂²×C₄₇⋊C₈	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	—	4	4	no	—
56	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
58	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
59	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
69	#13093935	—	2	1	no	—
70	#13093935	—	2	1	no	—
71	#13093935	—	2	1	no	—
72	C₄×C₄₇⋊C₈	—	2	1	no	—
73	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
74	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
75	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
76	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
77	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₄₇	—	2	1	no	—
80	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
82	#126×C₄₇	—	2	1	no	—
83	#125×C₄₇	C₂×C₄	1	1	yes	characteristic
84	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
85	#123×C₄₇	—	2	1	no	—
86	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
87	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₄×D₄×C₄₇	—	2	1	no	—
90	C₄×D₄×C₄₇	—	2	1	no	—
91	C₄×D₄×C₄₇	—	2	1	no	—
92	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₄₇	C₂³	1	2	yes	—
94	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
95	#117×C₄₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	#107×C₄₇	C₂×C₄	1	2	yes	—
100	#106×C₄₇	C₂×C₄	1	2	yes	—
101	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
102	#103×C₄₇	C₂×C₄	1	2	yes	—
103	#102×C₄₇	C₂×C₄	1	2	yes	—
104	#102×C₄₇	C₂×C₄	1	2	yes	—
105	#102×C₄₇	C₂×C₄	1	2	yes	—
106	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₄×C₈×C₄₇	C₂³	1	2	yes	—
109	C₂⁴×C₄₇	—	2	1	no	—
110	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₄×C₄₇	—	2	4	no	—
112	C₂×D₄×C₄₇	—	2	1	no	—
113	C₂×D₄×C₄₇	—	2	1	no	—
114	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	4	2	no	—
121	C₂²×C₄×C₄₇	—	4	2	no	—
122	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
125	SD₁₆×C₄₇	—	2	4	no	—
126	D₈×C₄₇	—	2	4	no	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	—	2	1	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²⋊C₄×C₄₇	—	2	1	no	—
138	C₂²⋊C₄×C₄₇	—	2	2	no	—
139	C₂²⋊C₄×C₄₇	—	2	1	no	—
140	C₂²⋊C₄×C₄₇	—	2	1	no	—
141	C₂²⋊C₄×C₄₇	—	2	1	no	—
142	C₂²⋊C₄×C₄₇	—	2	2	no	—
143	C₂²⋊C₄×C₄₇	—	2	1	no	—
144	C₄²×C₄₇	—	2	1	no	—
145	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₇	#41	1	1	yes	characteristic
148	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
149	#10625329	—	4	2	no	—
150	#10625329	—	4	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	4	1	no	—
157	C₂×C₄₇⋊C₈	—	4	2	no	—
158	C₂×C₄₇⋊C₈	—	4	4	no	—
159	C₂×C₄₇⋊C₈	—	4	2	no	—
160	C₂×C₄₇⋊C₈	—	4	4	no	—
161	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂³×C₄₇	—	2	4	no	—
166	C₂³×C₄₇	—	2	2	no	—
167	C₂³×C₄₇	—	2	1	no	—
168	C₂³×C₄₇	—	4	2	no	—
169	C₂³×C₄₇	—	4	2	no	—
170	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
171	Q₈×C₄₇	—	2	2	no	—
172	D₄×C₄₇	—	2	4	no	—
173	D₄×C₄₇	—	2	2	no	—
174	D₄×C₄₇	—	2	2	no	—
175	D₄×C₄₇	—	4	2	no	—
176	D₄×C₄₇	#131	1	4	yes	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	4	4	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	1	no	—
189	C₂×C₄×C₄₇	—	4	1	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	2	2	no	—
199	C₄₇⋊C₈	—	2	1	no	—
200	C₄₇⋊C₈	—	2	1	no	—
201	C₄₇⋊C₈	—	2	1	no	—
202	C₄₇⋊C₈	—	4	2	no	—
203	C₄₇⋊C₈	—	4	2	no	—
204	C₄₇⋊C₈	—	4	1	no	—
205	C₄₇⋊C₈	—	4	1	no	—
206	C₄₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
207	#17914	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	—	2	1	no	—
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	—	2	4	no	—
211	C₂²×C₄₇	—	4	8	no	—
212	C₂²×C₄₇	—	4	2	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	—	4	1	no	—
215	C₂²×C₄₇	—	4	1	no	—
216	C₂²×C₄₇	—	4	1	no	—
217	C₂²×C₄₇	#444	1	2	yes	—
218	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	—	2	1	no	—
222	C₄×C₄₇	—	2	1	no	—
223	C₄×C₄₇	—	4	1	no	—
224	C₄×C₄₇	—	4	1	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	4	1	no	—
227	C₄×C₄₇	C₂×#131	1	2	yes	—
228	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₄×C₄₇	#575	1	1	yes	characteristic
230	#3105	D₄₇	1	1	yes	characteristic
231	#2966	—	47	1	no	—
232	C₂×C₈×D₄	—	47	1	no	—
233	#1582	—	47	2	no	—
234	#1581	—	47	2	no	—
235	#1580	—	47	2	no	—
236	SD₁₆⋊C₈	—	47	2	no	—
237	#1573	—	47	1	no	—
238	#1490	—	47	1	no	—
239	#1483	—	47	1	no	—
240	#1451	—	47	1	no	—
241	C₂×C₄₇	—	2	2	no	—
242	C₂×C₄₇	—	4	4	no	—
243	C₂×C₄₇	—	8	1	no	—
244	C₂×C₄₇	#2929	1	1	yes	characteristic
245	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
247	C₂³×C₈	—	94	1	no	—
248	#529	C₂×D₄₇	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
250	#484	Dic₄₇	1	1	yes	characteristic
251	#481	Dic₄₇	1	1	yes	characteristic
252	#478	Dic₄₇	1	2	yes	—
253	#463	Dic₄₇	1	2	yes	—
254	#450	Dic₄₇	1	1	yes	characteristic
255	#447	Dic₄₇	1	1	yes	characteristic
256	#446	—	47	1	no	—
257	C₈×Q₈	—	47	1	no	—
258	C₄×SD₁₆	C₂×D₄₇	1	2	yes	—
259	C₄×D₈	C₂×D₄₇	1	2	yes	—
260	#436	—	47	1	no	—
261	#435	—	94	1	no	—
262	C₈×D₄	—	47	2	no	—
263	C₈×D₄	—	47	1	no	—
264	C₈×D₄	—	47	2	no	—
265	C₈×D₄	—	94	1	no	—
266	C₈×D₄	—	94	1	no	—
267	C₈×D₄	—	94	1	no	—
268	#433	—	94	1	no	—
269	#432	—	47	1	no	—
270	#431	C₂×D₄₇	1	1	yes	characteristic
271	C₂×C₄⋊C₈	—	47	1	no	—
272	C₂×C₂²⋊C₈	—	94	1	no	—
273	#405	—	94	1	no	—
274	C₄×M₁₆	—	47	1	no	—
275	C₂×C₄×C₈	—	47	1	no	—
276	#335	—	47	2	no	—
277	#334	—	47	2	no	—
278	Q₈⋊C₈	—	47	2	no	—
279	D₄⋊C₈	—	47	2	no	—
280	D₄⋊C₈	—	47	2	no	—
281	D₄⋊C₈	—	47	2	no	—
282	#322	—	47	2	no	—
283	#322	—	47	2	no	—
284	C₄₇	#17914	1	1	yes	characteristic, complemented, Sylow
285	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
288	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
289	C₂×M₁₆	—	94	1	no	—
290	C₂×M₁₆	—	94	1	no	—
291	C₂²×C₈	—	47	1	no	—
292	C₂²×C₈	—	47	1	no	—
293	C₂²×C₈	—	94	2	no	—
294	C₂²×C₈	—	94	2	no	—
295	C₂²×C₈	—	94	1	no	—
296	C₂²×C₈	—	94	1	no	—
297	C₂²×C₈	—	188	4	no	—
298	#126	—	2	1	no	—
299	#125	C₂×Dic₄₇	1	1	yes	characteristic
300	#124	C₂×Dic₄₇	1	1	yes	characteristic
301	#123	—	2	1	no	—
302	C₂²⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
303	#121	C₂×Dic₄₇	1	1	yes	characteristic
304	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
309	C₄×D₄	C₂²×D₄₇	1	2	yes	—
310	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
311	#117	—	2	1	no	—
312	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
315	#107	C₂×Dic₄₇	1	2	yes	—
316	#106	C₂×Dic₄₇	1	2	yes	—
317	C₄⋊C₈	—	47	1	no	—
318	C₄⋊C₈	—	47	1	no	—
319	C₄⋊C₈	—	47	2	no	—
320	C₄⋊C₈	—	94	1	no	—
321	C₄⋊C₈	—	94	1	no	—
322	C₄⋊C₈	—	94	1	no	—
323	C₄⋊C₈	C₂×Dic₄₇	1	2	yes	—
324	#103	C₂×Dic₄₇	1	2	yes	—
325	#102	C₂×Dic₄₇	1	2	yes	—
326	#102	C₂×Dic₄₇	1	2	yes	—
327	#102	C₂×Dic₄₇	1	2	yes	—
328	C₂²⋊C₈	—	94	2	no	—
329	C₂²⋊C₈	—	94	2	no	—
330	C₂²⋊C₈	—	94	1	no	—
331	C₂²⋊C₈	—	94	1	no	—
332	C₂²⋊C₈	—	94	1	no	—
333	C₂²⋊C₈	C₂×Dic₄₇	1	1	yes	characteristic
334	C₂²⋊C₈	C₂×Dic₄₇	1	1	yes	characteristic
335	#97	—	94	1	no	—
336	#97	—	94	1	no	—
337	#97	—	94	1	no	—
338	C₄×C₈	—	47	1	no	—
339	C₄×C₈	—	47	1	no	—
340	C₄×C₈	—	47	1	no	—
341	C₄×C₈	—	47	1	no	—
342	C₄×C₈	—	47	2	no	—
343	C₄×C₈	—	94	1	no	—
344	C₄×C₈	C₂²×D₄₇	1	2	yes	—
345	C₂⁴	—	2	1	no	—
346	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
351	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
359	C₂²×C₄	#10625352	1	1	yes	characteristic
360	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
361	SD₁₆	—	2	4	no	—
362	D₈	—	2	4	no	—
363	M₁₆	—	188	2	no	—
364	M₁₆	—	188	2	no	—
365	C₂×C₈	—	47	1	no	—
366	C₂×C₈	—	47	1	no	—
367	C₂×C₈	—	47	1	no	—
368	C₂×C₈	—	47	1	no	—
369	C₂×C₈	—	94	2	no	—
370	C₂×C₈	—	94	1	no	—
371	C₂×C₈	—	94	1	no	—
372	C₂×C₈	—	94	2	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	188	4	no	—
375	C₂×C₈	—	188	1	no	—
376	C₂×C₈	—	188	2	no	—
377	C₂×C₈	—	188	4	no	—
378	C₂×C₈	—	188	2	no	—
379	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
380	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
387	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
388	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	D₄×D₄₇	1	1	yes	characteristic
398	C₄²	#10625352	1	1	yes	characteristic
399	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
400	C₄²	C₂³×D₄₇	1	1	yes	characteristic
401	C₂³	—	2	4	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	2	no	—
412	D₄	#13094031	1	4	yes	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
428	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
429	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	47	2	no	—
436	C₈	—	94	1	no	—
437	C₈	—	94	1	no	—
438	C₈	—	94	1	no	—
439	C₈	—	188	2	no	—
440	C₈	—	188	2	no	—
441	C₈	—	188	1	no	—
442	C₈	—	188	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	#15689245	1	2	yes	—
453	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	C₂×#13094031	1	2	yes	—
463	C₄	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
464	C₄	#15689919	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	4	4	no	—
467	C₂	—	8	1	no	—
468	C₂	#20252083	1	1	yes	characteristic
469	C₂	AGL(1,ℤ/8)×Dic₄₇	1	1	yes	characteristic
470	C₂	C₂×#15689245	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3105	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₄₇×#447	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3105	D₄₇
hypocenter	C₄₇	#17914
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #20252364	C₂	semidirect
2. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
3. #20242225	C₂	semidirect
4. #20242218	C₂	semidirect
5. #20242212	C₂	semidirect
6. SD₁₆⋊(C₄₇⋊C₈)	C₂	semidirect
7. #20242173	C₂	semidirect
8. #20241831	C₂	semidirect
9. #20241801	C₂	semidirect
10. #20241678	C₂	semidirect
13. #15689254	C₂²	semidirect
14. Q₈×C₄₇⋊C₈	C₂²	semidirect
15. #15689201	C₂²	semidirect
22. D₄×C₄₇⋊C₈	C₂²	semidirect
30. #15688876	C₂²	semidirect
31. #15688874	C₂²	semidirect
32. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
35. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
36. #15688845	C₂²	semidirect
37. #15688844	C₂²	semidirect
284. C₄₇	#17914	semidirect

Maximal subgroups

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

subgroup	index
#20252364	2
C₂×D₄×C₄₇⋊C₈	2
#20242225	2
#20242218	2
#20242212	2
SD₁₆⋊(C₄₇⋊C₈)	2
#20242173	2
#20241831	2
#20241801	2
#20241678	2
C₄₇×#3105	2
#17914	47