Subgroups — #26200204

Order 12032.

702 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252872	C₂	1	2	yes	maximal
3	C₈×#10625354	C₂	1	1	yes	maximal, characteristic
4	#20242782	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242780	C₂	1	2	yes	maximal, complemented
6	#20242778	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242776	C₂	1	2	yes	maximal, complemented
8	#20242774	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242145	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242058	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1674	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094056	—	2	2	no	—
13	C₄⋊Q₈×D₄₇	C₂²	1	2	yes	—
14	C₄×#10625354	C₂²	1	1	yes	characteristic
15	#15689528	C₂²	1	1	yes	characteristic
16	#15689527	—	2	1	no	—
17	#15689527	—	2	1	no	—
18	#15689526	C₂²	1	2	yes	—
19	#15689333	C₂²	1	2	yes	—
20	#15689331	—	2	2	no	—
21	#15689329	C₂²	1	2	yes	—
22	#15689327	—	2	2	no	—
23	#15689325	C₂²	1	2	yes	—
24	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₈×D₁₈₈	—	2	1	no	—
26	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
27	#15689188	—	2	1	no	—
28	#15689188	C₂²	1	1	yes	characteristic
29	#15689175	—	2	1	no	—
30	#15689175	C₂²	1	1	yes	characteristic
31	#107×D₄₇	—	2	1	no	—
32	#107×D₄₇	—	2	1	no	—
33	#15689145	C₂²	1	2	yes	—
34	#15689130	—	2	2	no	—
35	C₄×C₈×D₄₇	—	2	1	no	—
36	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
37	#15688876	C₂²	1	1	yes	characteristic
38	#15688875	C₂²	1	2	yes	—
39	#15688870	C₂²	1	2	yes	—
40	#15688869	C₂²	1	2	yes	—
41	#15688868	C₂²	1	2	yes	—
42	C₄₇×#500	C₂²	1	1	yes	characteristic
43	C₄₇×#462	C₂²	1	2	yes	—
44	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	1	yes	characteristic
46	C₄₇×#332	C₂²	1	2	yes	—
47	C₂×#10625354	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₄₇	—	2	2	no	—
49	#13094056	—	4	8	no	—
50	C₂×#10625337	—	2	2	no	—
51	C₂×#10625325	—	2	2	no	—
52	C₂×#10625336	—	2	2	no	—
53	C₂×#10625324	—	2	2	no	—
54	C₂×C₈×D₄₇	—	2	1	no	—
55	C₂×C₈×D₄₇	—	2	1	no	—
56	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
57	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
58	#13094024	C₂³	1	2	yes	—
59	#13094023	—	2	2	no	—
60	#13094023	—	2	2	no	—
61	#13094022	—	2	2	no	—
62	Q₈×Dic₄₇	D₄	1	1	yes	characteristic
63	C₄×D₁₈₈	—	2	1	no	—
64	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
65	#13093986	—	2	1	no	—
66	#13093986	D₄	1	1	yes	characteristic
67	#13093982	—	2	1	no	—
68	#13093982	D₄	1	1	yes	characteristic
69	C₄⋊C₄×D₄₇	—	2	2	no	—
70	C₄⋊C₄×D₄₇	—	2	2	no	—
71	C₄²×D₄₇	—	2	1	no	—
72	C₄²×D₄₇	C₂³	1	1	yes	characteristic
73	#13093958	—	2	1	no	—
74	#13093958	—	2	1	no	—
75	#13093957	—	2	2	no	—
76	#13093957	—	2	2	no	—
77	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
78	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
79	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
80	Dic₄₇⋊C₈	—	2	2	no	—
81	#13093949	—	2	2	no	—
82	#13093948	—	2	2	no	—
83	#13093947	—	2	2	no	—
84	(C₂×D₄₇)⋊C₈	—	2	1	no	—
85	(C₂×D₄₇)⋊C₈	—	2	1	no	—
86	(C₂×D₄₇)⋊C₈	—	2	1	no	—
87	C₄×C₄₇⋊C₈	—	2	1	no	—
88	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
89	C₈×Dic₄₇	—	2	1	no	—
90	C₈×Dic₄₇	D₄	1	1	yes	characteristic
91	C₈×Dic₄₇	D₄	1	1	yes	characteristic
92	C₂×Q₁₆×C₄₇	—	2	2	no	—
93	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
94	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
95	#107×C₄₇	—	2	1	no	—
96	#107×C₄₇	—	2	1	no	—
97	C₄⋊C₈×C₄₇	—	2	1	no	—
98	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
99	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
100	#103×C₄₇	—	2	2	no	—
101	C₄×C₈×C₄₇	—	2	1	no	—
102	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
105	#10625354	—	2	2	no	—
106	#10625354	D₈	1	4	yes	—
107	Q₈×D₄₇	—	4	4	no	—
108	Q₈×D₄₇	—	4	4	no	—
109	C₂×D₁₈₈	—	2	1	no	—
110	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×C₄×D₄₇	—	2	1	no	—
114	C₂×C₄×D₄₇	—	4	2	no	—
115	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
118	C₂×Dic₉₄	—	2	2	no	—
119	C₂×Dic₉₄	—	4	2	no	—
120	Q₁₆×C₄₇	—	4	4	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	—	2	1	no	—
130	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
131	#10625337	—	4	4	no	—
132	#10625336	—	4	4	no	—
133	(C₂×D₄₇)⋊C₄	—	2	1	no	—
134	(C₂×D₄₇)⋊C₄	—	2	1	no	—
135	(C₂×D₄₇)⋊C₄	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
140	Dic₄₇⋊C₄	—	4	2	no	—
141	Dic₄₇⋊C₄	—	4	2	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
145	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
146	C₄×Dic₄₇	#41	1	1	yes	characteristic
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
151	#10625325	—	4	4	no	—
152	#10625324	—	4	4	no	—
153	C₈×D₄₇	—	2	2	no	—
154	C₈×D₄₇	—	2	2	no	—
155	C₈×D₄₇	—	4	2	no	—
156	C₈×D₄₇	—	4	2	no	—
157	C₂²×D₄₇	—	2	1	no	—
158	C₂²×D₄₇	#121	1	1	yes	characteristic
159	Q₈×C₄₇	—	2	1	no	—
160	Q₈×C₄₇	—	4	2	no	—
161	Q₈×C₄₇	—	4	2	no	—
162	Q₈×C₄₇	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂×Dic₄₇	—	2	1	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	#121	1	1	yes	characteristic
172	C₂×Dic₄₇	#121	1	1	yes	characteristic
173	C₂×Dic₄₇	#121	1	1	yes	characteristic
174	D₁₈₈	—	2	4	no	—
175	D₁₈₈	—	2	1	no	—
176	D₁₈₈	C₂×D₈	1	2	yes	—
177	C₄×D₄₇	—	2	1	no	—
178	C₄×D₄₇	—	2	1	no	—
179	C₄×D₄₇	—	2	4	no	—
180	C₄×D₄₇	—	2	2	no	—
181	C₄×D₄₇	—	4	1	no	—
182	C₄×D₄₇	—	4	1	no	—
183	C₄×D₄₇	—	4	2	no	—
184	C₄×D₄₇	—	8	4	no	—
185	C₄×D₄₇	C₂×D₈	1	2	yes	—
186	C₄×D₄₇	#135	1	2	yes	—
187	Dic₉₄	—	4	2	no	—
188	Dic₉₄	—	4	2	no	—
189	Dic₉₄	—	8	4	no	—
190	C₈×C₄₇	—	2	1	no	—
191	C₈×C₄₇	—	4	2	no	—
192	C₈×C₄₇	—	4	1	no	—
193	C₈×C₄₇	#137	1	2	yes	complemented
194	C₄₇⋊C₈	—	2	1	no	—
195	C₄₇⋊C₈	—	4	2	no	—
196	C₄₇⋊C₈	—	4	1	no	—
197	C₄₇⋊C₈	#137	1	2	yes	complemented
198	#19271	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
200	C₂×D₄₇	—	2	1	no	—
201	C₂×D₄₇	—	2	1	no	—
202	C₂×D₄₇	—	2	2	no	—
203	C₂×D₄₇	—	4	1	no	—
204	C₂×D₄₇	—	4	1	no	—
205	C₂×D₄₇	#466	1	2	yes	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	4	1	no	—
209	C₄×C₄₇	—	8	2	no	—
210	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
211	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
212	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
213	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
214	Dic₄₇	—	2	1	no	—
215	Dic₄₇	—	4	1	no	—
216	Dic₄₇	—	8	2	no	—
217	Dic₄₇	#466	1	2	yes	—
218	Dic₄₇	#473	1	2	yes	—
219	C₂×#500	—	47	1	no	—
220	#3039	—	47	2	no	—
221	C₈×#41	—	47	1	no	—
222	#1674	—	47	2	no	—
223	#1674	—	47	1	no	—
224	#1674	D₄₇	1	1	yes	characteristic, complemented
225	#1673	—	47	1	no	—
226	#1673	—	47	1	no	—
227	#1673	—	47	2	no	—
228	#1567	—	47	1	no	—
229	#1546	—	47	2	no	—
230	C₂×C₄₇	#3039	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
232	C₂×C₄₇	C₂×#473	1	1	yes	characteristic
233	D₄₇	—	2	2	no	—
234	D₄₇	—	4	2	no	—
235	C₂×#137	—	94	2	no	—
236	C₂×C₄⋊Q₈	—	47	2	no	—
237	C₄×#41	—	47	1	no	—
238	#500	—	47	2	no	—
239	#500	—	47	1	no	—
240	#500	—	94	1	no	—
241	#500	—	94	1	no	—
242	#500	C₂×D₄₇	1	1	yes	characteristic
243	#462	—	47	2	no	—
244	#462	—	94	2	no	—
245	#462	C₂×D₄₇	1	2	yes	—
246	#461	—	47	2	no	—
247	#461	—	47	2	no	—
248	#461	—	94	2	no	—
249	C₈×Q₈	—	47	1	no	—
250	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic
251	C₈×D₄	—	47	1	no	—
252	C₈×D₄	—	47	1	no	—
253	C₈×D₄	—	94	1	no	—
254	C₈×D₄	—	94	1	no	—
255	#431	—	47	1	no	—
256	#431	—	94	1	no	—
257	C₂×#107	—	94	1	no	—
258	C₂×#107	—	94	1	no	—
259	#423	—	47	2	no	—
260	#419	—	94	2	no	—
261	C₂×C₄×C₈	—	47	1	no	—
262	C₂×C₄×C₈	—	94	1	no	—
263	#335	—	47	2	no	—
264	#335	—	47	1	no	—
265	#335	C₂×D₄₇	1	1	yes	characteristic
266	#332	—	47	2	no	—
267	#332	—	47	2	no	—
268	#332	—	47	2	no	—
269	#332	C₂×D₄₇	1	2	yes	—
270	C₄₇	#19271	1	1	yes	characteristic, complemented, Sylow
271	C₂×#41	—	47	1	no	—
272	C₂²×Q₈	—	94	2	no	—
273	#137	—	188	8	no	—
274	C₂×Q₁₆	—	2	2	no	—
275	C₂×Q₁₆	—	94	2	no	—
276	C₂×SD₁₆	—	94	2	no	—
277	C₂×SD₁₆	—	94	2	no	—
278	C₂×M₁₆	—	94	2	no	—
279	C₂²×C₈	—	47	1	no	—
280	C₂²×C₈	—	47	1	no	—
281	C₂²×C₈	—	94	1	no	—
282	C₂²×C₈	—	94	1	no	—
283	C₄⋊Q₈	—	47	2	no	—
284	C₄⋊Q₈	—	94	2	no	—
285	C₄⋊Q₈	—	94	2	no	—
286	C₄⋊Q₈	—	94	2	no	—
287	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
288	C₄×Q₈	—	47	1	no	—
289	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
290	C₄×D₄	—	47	1	no	—
291	C₄×D₄	—	47	1	no	—
292	C₄×D₄	—	94	1	no	—
293	C₄×D₄	—	94	1	no	—
294	#117	—	47	1	no	—
295	#117	—	94	1	no	—
296	C₂×C₄⋊C₄	—	94	2	no	—
297	C₂×C₄⋊C₄	—	94	2	no	—
298	C₂×C₄²	—	47	1	no	—
299	C₂×C₄²	—	94	1	no	—
300	#107	—	2	1	no	—
301	#107	—	2	1	no	—
302	#107	—	94	2	no	—
303	#107	—	94	2	no	—
304	#107	—	94	1	no	—
305	#107	—	94	1	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	47	1	no	—
308	C₄⋊C₈	—	47	2	no	—
309	C₄⋊C₈	—	94	1	no	—
310	C₄⋊C₈	—	94	2	no	—
311	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
313	#103	—	2	2	no	—
314	#103	—	94	2	no	—
315	#103	—	94	2	no	—
316	#103	—	94	2	no	—
317	C₂²⋊C₈	—	94	1	no	—
318	C₂²⋊C₈	—	94	1	no	—
319	C₂²⋊C₈	—	94	1	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	—	47	1	no	—
322	C₄×C₈	—	47	1	no	—
323	C₄×C₈	—	47	1	no	—
324	C₄×C₈	—	94	1	no	—
325	C₄×C₈	—	94	1	no	—
326	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
327	#41	—	47	4	no	—
328	#41	—	94	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	94	2	no	—
331	C₂×Q₈	—	188	2	no	—
332	C₂×Q₈	—	188	4	no	—
333	C₂×Q₈	—	188	4	no	—
334	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
335	C₂×D₄	—	47	1	no	—
336	C₂×D₄	—	94	1	no	—
337	C₂²×C₄	—	47	1	no	—
338	C₂²×C₄	—	47	1	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	94	1	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	—	94	1	no	—
343	C₂²×C₄	—	188	2	no	—
344	Q₁₆	—	4	4	no	—
345	Q₁₆	—	188	4	no	—
346	SD₁₆	—	188	4	no	—
347	SD₁₆	—	188	4	no	—
348	M₁₆	—	188	4	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	47	1	no	—
352	C₂×C₈	—	47	1	no	—
353	C₂×C₈	—	94	2	no	—
354	C₂×C₈	—	94	2	no	—
355	C₂×C₈	—	94	1	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	188	2	no	—
358	C₂×C₈	—	188	2	no	—
359	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
360	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	47	1	no	—
365	C₄⋊C₄	—	94	1	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	188	2	no	—
369	C₄⋊C₄	—	188	2	no	—
370	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
371	C₂²⋊C₄	—	94	1	no	—
372	C₂²⋊C₄	—	94	1	no	—
373	C₂²⋊C₄	—	94	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	47	1	no	—
376	C₄²	—	47	1	no	—
377	C₄²	—	47	1	no	—
378	C₄²	—	94	1	no	—
379	C₄²	—	94	1	no	—
380	C₄²	C₂³×D₄₇	1	1	yes	characteristic
381	C₂³	—	47	1	no	—
382	C₂³	—	94	1	no	—
383	Q₈	—	2	1	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	376	4	no	—
387	Q₈	—	188	2	no	—
388	Q₈	—	188	2	no	—
389	Q₈	D₈×D₄₇	1	2	yes	—
390	D₄	—	47	2	no	—
391	D₄	—	94	4	no	—
392	D₄	—	94	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	47	1	no	—
397	C₂×C₄	—	47	1	no	—
398	C₂×C₄	—	47	2	no	—
399	C₂×C₄	—	47	2	no	—
400	C₂×C₄	—	47	1	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	94	4	no	—
403	C₂×C₄	—	94	1	no	—
404	C₂×C₄	—	94	1	no	—
405	C₂×C₄	—	94	1	no	—
406	C₂×C₄	—	376	4	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	—	188	1	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	47	2	no	—
418	C₈	—	94	1	no	—
419	C₈	—	188	2	no	—
420	C₈	—	188	1	no	—
421	C₈	#13094056	1	2	yes	complemented
422	C₂²	—	47	2	no	—
423	C₂²	—	94	1	no	—
424	C₂²	—	94	1	no	—
425	C₂²	—	94	2	no	—
426	C₂²	—	188	1	no	—
427	C₂²	—	188	1	no	—
428	C₂²	#121×D₄₇	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	47	2	no	—
434	C₄	—	47	2	no	—
435	C₄	—	94	1	no	—
436	C₄	—	376	2	no	—
437	C₄	—	188	1	no	—
438	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
439	C₄	#135×D₄₇	1	1	yes	characteristic
440	C₄	#137×D₄₇	1	1	yes	characteristic
441	C₄	C₂×#13094056	1	1	yes	characteristic
442	C₂	—	94	2	no	—
443	C₂	—	188	2	no	—
444	C₂	#20252872	1	1	yes	characteristic
445	C₂	#466×D₄₇	1	1	yes	characteristic
446	C₂	#473×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₄₇
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1674	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#10625354	D₄
hypercenter	#1674	D₄₇
hypocenter	C₄₇	#19271
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1674

Complements

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

N	H ≅ G/N	type
1. #500×D₄₇	C₂	semidirect
4. #20242782	C₂	semidirect
5. #20242780	C₂	semidirect
6. #20242778	C₂	semidirect
7. #20242776	C₂	semidirect
8. #20242774	C₂	semidirect
9. #20242145	C₂	semidirect
10. #20242058	C₂	semidirect
11. C₄₇×#1674	C₂	semidirect
193. C₈×C₄₇	#137	semidirect
197. C₄₇⋊C₈	#137	semidirect
224. #1674	D₄₇	semidirect
270. C₄₇	#19271	semidirect
421. C₈	#13094056	semidirect

Maximal subgroups

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

subgroup	index
#500×D₄₇	2
#20252872	2
C₈×#10625354	2
#20242782	2
#20242780	2
#20242778	2
#20242776	2
#20242774	2
#20242145	2
#20242058	2
C₄₇×#1674	2
#19271	47