Subgroups — #26204159

Order 12032.

836 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254536	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254306	C₂	1	1	yes	maximal, characteristic
3	#20253948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689495	C₂	1	1	yes	maximal, characteristic, complemented
5	#20253782	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243038	C₂	1	2	yes	maximal, complemented
7	#20243024	C₂	1	2	yes	maximal, complemented
8	#20242988	C₂	1	2	yes	maximal, complemented
9	#20242979	C₂	1	2	yes	maximal, complemented
10	M₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625335	—	2	2	no	—
13	#15689673	C₂²	1	1	yes	characteristic
14	C₂×#13094024	C₂²	1	1	yes	characteristic
15	#15689526	C₂²	1	2	yes	complemented
16	#15689519	C₂²	1	1	yes	characteristic, complemented
17	#15689499	C₂²	1	2	yes	—
18	#15689497	C₂²	1	1	yes	characteristic, complemented
19	#15689495	—	2	2	no	—
20	#15689495	C₂²	1	2	yes	—
21	#15689495	C₂²	1	2	yes	—
22	#15689483	—	2	2	no	—
23	#15689474	C₂²	1	2	yes	complemented
24	#15689473	C₂²	1	2	yes	complemented
25	#15689473	C₂²	1	1	yes	characteristic, complemented
26	#15689471	C₂²	1	1	yes	characteristic, complemented
27	#15689470	C₂²	1	2	yes	complemented
28	#15689469	C₂²	1	2	yes	—
29	#15689456	—	2	2	no	—
30	#15689418	—	2	2	no	—
31	#15689354	—	2	2	no	—
32	#15689315	—	2	2	no	—
33	#15689257	—	2	2	no	—
34	C₄×#10625336	—	2	2	no	—
35	#15689176	C₂²	1	1	yes	characteristic
36	#15689125	—	2	2	no	—
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688844	C₂²	1	2	yes	complemented
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
40	C₄₇×#533	C₂²	1	1	yes	characteristic
41	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#490	—	2	2	no	—
43	C₄₇×#486	C₂²	1	2	yes	—
44	C₄₇×#486	C₂²	1	2	yes	—
45	C₄₇×#418	—	2	2	no	—
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	C₂²×Dic₉₄	—	2	1	no	—
49	C₂×#10625335	—	2	4	no	—
50	C₂×#10625335	—	2	4	no	—
51	C₂×#10625335	—	4	8	no	—
52	C₂×#10625336	—	2	2	no	—
53	C₂×#10625334	—	2	4	no	—
54	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
55	#13094024	—	2	1	no	—
56	#13094024	—	2	1	no	—
57	#13094024	—	2	1	no	—
58	#13094024	C₂³	1	1	yes	characteristic
59	#13094024	C₂³	1	2	yes	—
60	#13094021	C₂³	1	1	yes	characteristic
61	#13094012	—	2	1	no	—
62	#13093998	—	2	1	no	—
63	#13093998	—	2	1	no	—
64	C₄×D₁₈₈	—	2	1	no	—
65	C₄×D₁₈₈	—	2	1	no	—
66	C₂×C₄⋊Dic₄₇	—	2	1	no	—
67	C₂×C₄⋊Dic₄₇	—	2	1	no	—
68	#13093957	—	2	4	no	—
69	#13093955	—	2	2	no	—
70	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
71	#13093949	—	2	4	no	—
72	#13093948	—	2	2	no	—
73	#13093948	—	2	4	no	—
74	#13093946	—	2	4	no	—
75	#13093945	—	2	4	no	—
76	#13093944	—	2	2	no	—
77	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
78	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
81	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₄₇	—	2	1	no	—
83	C₂²×D₄×C₄₇	—	2	1	no	—
84	C₂²×D₄×C₄₇	—	2	1	no	—
85	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
86	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
88	#127×C₄₇	—	2	1	no	—
89	#127×C₄₇	—	2	1	no	—
90	#127×C₄₇	—	2	1	no	—
91	#127×C₄₇	C₂³	1	2	yes	—
92	#125×C₄₇	—	2	1	no	—
93	C₂²⋊Q₈×C₄₇	—	2	1	no	—
94	C₂²⋊Q₈×C₄₇	—	2	1	no	—
95	C₄×Q₈×C₄₇	—	2	1	no	—
96	C₄×Q₈×C₄₇	—	2	1	no	—
97	#117×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	#102×C₄₇	—	2	4	no	—
100	#102×C₄₇	—	2	4	no	—
101	#97×C₄₇	D₄	1	2	yes	—
102	C₄×C₈×C₄₇	C₂³	1	2	yes	—
103	C₂⁴×C₄₇	—	4	1	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×Q₈×C₄₇	—	2	1	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	4	4	no	—
110	C₂×D₄×C₄₇	—	4	1	no	—
111	C₂×D₄×C₄₇	—	4	1	no	—
112	C₂×D₄×C₄₇	—	4	1	no	—
113	C₂×D₄×C₄₇	—	4	4	no	—
114	C₂×D₄×C₄₇	—	8	2	no	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₄₇	—	4	1	no	—
119	C₂²×Dic₄₇	—	4	1	no	—
120	#10625350	—	4	4	no	—
121	C₂×D₁₈₈	—	2	1	no	—
122	C₂×D₁₈₈	—	2	1	no	—
123	C₂×D₁₈₈	—	2	1	no	—
124	C₂×C₄×D₄₇	—	4	1	no	—
125	C₂×Dic₉₄	—	2	1	no	—
126	C₂×Dic₉₄	—	2	2	no	—
127	C₂×Dic₉₄	—	4	4	no	—
128	C₂×Dic₉₄	—	4	1	no	—
129	M₁₆×C₄₇	—	2	4	no	—
130	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
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	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	4	1	no	—
136	C₄⋊C₄×C₄₇	—	4	1	no	—
137	C₂²⋊C₄×C₄₇	—	4	1	no	—
138	C₄²×C₄₇	—	4	1	no	—
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
143	#10625336	—	4	4	no	—
144	#10625335	—	4	8	no	—
145	#10625335	—	4	8	no	—
146	#10625334	—	8	4	no	—
147	(C₂×D₄₇)⋊C₄	—	4	1	no	—
148	(C₂×D₄₇)⋊C₄	—	4	1	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	C₄⋊Dic₄₇	—	2	2	no	—
151	C₄⋊Dic₄₇	—	2	1	no	—
152	C₄⋊Dic₄₇	—	2	2	no	—
153	C₄⋊Dic₄₇	—	4	1	no	—
154	C₄⋊Dic₄₇	—	4	1	no	—
155	C₂×C₄₇⋊C₈	—	2	4	no	—
156	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
157	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
158	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	—	8	2	no	—
161	C₂³×C₄₇	—	8	2	no	—
162	C₂³×C₄₇	—	8	2	no	—
163	C₂³×C₄₇	#127	1	1	yes	characteristic
164	C₂²×D₄₇	—	4	1	no	—
165	Q₈×C₄₇	—	4	2	no	—
166	Q₈×C₄₇	—	4	2	no	—
167	D₄×C₄₇	—	4	4	no	—
168	D₄×C₄₇	—	4	4	no	—
169	D₄×C₄₇	—	4	4	no	—
170	D₄×C₄₇	—	8	2	no	—
171	D₄×C₄₇	—	8	2	no	—
172	D₄×C₄₇	—	8	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
178	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
179	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
180	C₂×C₄×C₄₇	#135	1	4	yes	—
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂²⋊D₄₇	—	8	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	—	4	1	no	—
187	C₂×Dic₄₇	—	8	2	no	—
188	D₁₈₈	—	4	2	no	—
189	D₁₈₈	—	4	2	no	—
190	D₁₈₈	—	4	2	no	—
191	C₄×D₄₇	—	8	2	no	—
192	Dic₉₄	—	4	2	no	—
193	Dic₉₄	—	4	4	no	—
194	Dic₉₄	—	8	2	no	—
195	C₈×C₄₇	—	2	4	no	—
196	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	—	2	4	no	—
198	C₄₇⋊C₈	AGL(1,ℤ/8)	1	4	yes	—
199	#19625	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	8	2	no	—
203	C₂²×C₄₇	—	8	2	no	—
204	C₂²×C₄₇	—	8	2	no	—
205	C₂²×C₄₇	—	16	4	no	—
206	C₂²×C₄₇	#495	1	2	yes	—
207	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
208	C₂×D₄₇	—	8	1	no	—
209	C₂×D₄₇	—	8	1	no	—
210	C₂×D₄₇	—	8	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	8	1	no	—
214	C₄×C₄₇	—	8	1	no	—
215	C₄×C₄₇	#495	1	2	yes	—
216	C₄×C₄₇	C₂×#135	1	2	yes	—
217	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
218	C₄×C₄₇	#577	1	2	yes	—
219	Dic₄₇	—	8	1	no	—
220	Dic₄₇	—	8	2	no	—
221	#3230	—	47	1	no	—
222	#3205	—	47	1	no	—
223	#3167	—	47	1	no	—
224	C₂×#492	—	47	1	no	—
225	#3141	—	47	1	no	—
226	#3138	D₄₇	1	1	yes	characteristic, complemented
227	#1719	—	47	2	no	—
228	#1717	—	47	2	no	—
229	#1708	—	47	2	no	—
230	#1706	—	47	2	no	—
231	C₈×M₁₆	—	47	1	no	—
232	C₂×C₄₇	—	2	2	no	—
233	C₂×C₄₇	—	16	2	no	—
234	C₂×C₄₇	C₂×#495	1	1	yes	characteristic
235	C₂×C₄₇	#3151	1	1	yes	characteristic
236	C₂×C₄₇	#3154	1	1	yes	characteristic
237	D₄₇	—	16	1	no	—
238	C₂²×SD₁₆	—	94	2	no	—
239	#533	C₂×D₄₇	1	1	yes	characteristic
240	#532	—	47	1	no	—
241	C₂×C₄⋊Q₈	—	47	1	no	—
242	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
243	#500	—	47	2	no	—
244	#498	—	47	1	no	—
245	#493	—	47	2	no	—
246	#492	—	47	1	no	—
247	#492	—	47	2	no	—
248	#492	—	47	2	no	—
249	#492	—	94	2	no	—
250	#490	—	2	2	no	—
251	#489	—	94	2	no	—
252	#487	—	47	1	no	—
253	#487	—	47	2	no	—
254	#487	—	47	2	no	—
255	#486	—	47	1	no	—
256	#486	—	47	2	no	—
257	#486	—	47	2	no	—
258	#486	C₂×D₄₇	1	2	yes	—
259	#486	C₂×D₄₇	1	2	yes	—
260	#484	—	94	2	no	—
261	#477	—	94	2	no	—
262	#465	—	94	2	no	—
263	#459	—	94	2	no	—
264	#447	—	94	2	no	—
265	C₄×SD₁₆	—	94	2	no	—
266	#431	—	47	1	no	—
267	#418	—	2	2	no	—
268	#417	—	94	2	no	—
269	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
270	C₂×C₄×C₈	—	47	1	no	—
271	#322	—	47	2	no	—
272	C₈²	—	47	2	no	—
273	C₄₇	#19625	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	94	1	no	—
275	C₂²×Q₈	—	94	1	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂×SD₁₆	—	94	4	no	—
280	C₂×SD₁₆	—	94	4	no	—
281	C₂×SD₁₆	—	94	2	no	—
282	C₂×SD₁₆	—	188	8	no	—
283	C₂×D₈	—	94	4	no	—
284	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
285	C₂²×C₈	—	47	2	no	—
286	C₄⋊Q₈	—	47	2	no	—
287	C₄⋊Q₈	—	47	1	no	—
288	C₄⋊Q₈	—	94	1	no	—
289	C₄⋊Q₈	—	94	1	no	—
290	C₄⋊Q₈	—	94	1	no	—
291	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
293	#127	—	2	1	no	—
294	#127	—	2	1	no	—
295	#127	—	2	1	no	—
296	#127	—	47	1	no	—
297	#127	C₂²×D₄₇	1	2	yes	—
298	#125	—	2	1	no	—
299	#124	—	94	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	2	1	no	—
302	#121	—	94	1	no	—
303	#121	—	94	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×D₄	—	94	1	no	—
307	C₄×D₄	—	94	1	no	—
308	#117	—	2	1	no	—
309	C₂×C₄⋊C₄	—	94	1	no	—
310	C₂×C₄⋊C₄	—	94	1	no	—
311	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
312	#107	—	94	4	no	—
313	#106	—	94	2	no	—
314	C₄⋊C₈	—	47	2	no	—
315	#103	—	94	2	no	—
316	#103	—	94	4	no	—
317	#103	—	94	4	no	—
318	#102	—	2	4	no	—
319	#102	—	2	4	no	—
320	#102	—	94	2	no	—
321	#102	—	94	4	no	—
322	#102	—	94	4	no	—
323	C₂²⋊C₈	—	47	2	no	—
324	#97	C₂²⋊D₄₇	1	2	yes	—
325	C₄×C₈	—	47	2	no	—
326	C₄×C₈	—	47	1	no	—
327	C₄×C₈	—	47	2	no	—
328	C₄×C₈	—	47	1	no	—
329	C₄×C₈	C₂²×D₄₇	1	2	yes	—
330	C₂⁴	—	4	1	no	—
331	#41	—	188	4	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	94	2	no	—
335	C₂×Q₈	—	94	1	no	—
336	C₂×Q₈	—	188	4	no	—
337	C₂×Q₈	—	188	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	—	94	1	no	—
348	C₂×D₄	—	94	1	no	—
349	C₂×D₄	—	94	1	no	—
350	C₂×D₄	—	188	1	no	—
351	C₂²×C₄	—	188	1	no	—
352	C₂²×C₄	—	188	1	no	—
353	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
356	SD₁₆	—	188	8	no	—
357	SD₁₆	—	188	4	no	—
358	SD₁₆	—	188	8	no	—
359	D₈	—	376	4	no	—
360	M₁₆	—	2	4	no	—
361	C₂×C₈	—	47	2	no	—
362	C₂×C₈	—	47	2	no	—
363	C₂×C₈	—	47	4	no	—
364	C₂×C₈	—	94	4	no	—
365	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	—	94	1	no	—
373	C₄⋊C₄	—	94	1	no	—
374	C₄⋊C₄	—	94	2	no	—
375	C₄⋊C₄	—	94	2	no	—
376	C₄⋊C₄	—	188	1	no	—
377	C₄⋊C₄	—	188	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	188	1	no	—
380	C₂²⋊C₄	—	188	1	no	—
381	C₄²	—	4	1	no	—
382	C₄²	D₄×D₄₇	1	1	yes	characteristic
383	C₄²	D₄×D₄₇	1	1	yes	characteristic
384	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
385	C₄²	C₂³×D₄₇	1	1	yes	characteristic
386	C₂³	—	4	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	—	8	2	no	—
389	C₂³	—	8	2	no	—
390	C₂³	—	188	1	no	—
391	C₂³	#13094020	1	1	yes	characteristic
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	376	2	no	—
395	Q₈	—	188	2	no	—
396	Q₈	—	188	4	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	4	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	376	2	no	—
404	D₄	—	188	2	no	—
405	D₄	—	188	2	no	—
406	D₄	—	188	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	376	2	no	—
412	C₂×C₄	—	376	2	no	—
413	C₂×C₄	—	188	1	no	—
414	C₂×C₄	—	188	2	no	—
415	C₂×C₄	#13094020	1	1	yes	characteristic
416	C₂×C₄	#13094020	1	1	yes	characteristic
417	C₂×C₄	#13094020	1	1	yes	characteristic
418	C₂×C₄	#13094044	1	4	yes	—
419	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
420	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	47	4	no	—
424	C₈	—	94	2	no	—
425	C₈	—	94	4	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	16	4	no	—
432	C₂²	—	376	1	no	—
433	C₂²	—	376	1	no	—
434	C₂²	—	376	1	no	—
435	C₂²	#15689505	1	2	yes	—
436	C₂²	C₂×#13094020	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	1	no	—
441	C₄	—	376	1	no	—
442	C₄	—	376	2	no	—
443	C₄	#15689505	1	2	yes	—
444	C₄	C₂×#13094044	1	2	yes	—
445	C₄	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
446	C₄	#15689933	1	2	yes	—
447	C₂	—	2	2	no	—
448	C₂	—	16	2	no	—
449	C₂	—	752	1	no	—
450	C₂	C₂×#15689505	1	1	yes	characteristic
451	C₂	#20253836	1	1	yes	characteristic
452	C₂	#20253862	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3138	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	#20254306	C₂
hypercenter	#3138	D₄₇
hypocenter	C₄₇	#19625
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3138

Complements

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

N	H ≅ G/N	type
1. #20254536	C₂	semidirect
3. #20253948	C₂	semidirect
4. C₂×#15689495	C₂	semidirect
5. #20253782	C₂	semidirect
6. #20243038	C₂	semidirect
7. #20243024	C₂	semidirect
8. #20242988	C₂	semidirect
9. #20242979	C₂	semidirect
10. M₁₆×C₄₇⋊C₈	C₂	semidirect
11. C₄₇×#3138	C₂	semidirect
15. #15689526	C₂²	semidirect
16. #15689519	C₂²	semidirect
18. #15689497	C₂²	semidirect
23. #15689474	C₂²	semidirect
24. #15689473	C₂²	semidirect
25. #15689473	C₂²	semidirect
26. #15689471	C₂²	semidirect
27. #15689470	C₂²	semidirect
38. #15688844	C₂²	semidirect
39. C₈×C₄₇⋊C₈	C₂²	semidirect
226. #3138	D₄₇	semidirect
273. C₄₇	#19625	semidirect

Maximal subgroups

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

subgroup	index
#20254536	2
#20254306	2
#20253948	2
C₂×#15689495	2
#20253782	2
#20243038	2
#20243024	2
#20242988	2
#20242979	2
M₁₆×C₄₇⋊C₈	2
C₄₇×#3138	2
#19625	47