Subgroups — #26198728

Order 12032.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253974	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253178	C₂	1	2	yes	maximal
3	C₈×#10625350	C₂	1	1	yes	maximal, characteristic
4	#20242847	C₂	1	2	yes	maximal, complemented
5	#20242840	C₂	1	2	yes	maximal, complemented
6	#20242793	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242788	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242759	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242754	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242046	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689680	C₂²	1	2	yes	—
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689528	C₂²	1	1	yes	characteristic
15	#15689503	C₂²	1	1	yes	characteristic
16	#15689474	C₂²	1	2	yes	—
17	#15689431	—	2	2	no	—
18	#15689424	—	2	2	no	—
19	#15689419	C₂²	1	2	yes	—
20	#15689414	C₂²	1	2	yes	—
21	#15689409	C₂²	1	2	yes	—
22	#15689404	C₂²	1	2	yes	—
23	#15689364	—	2	1	no	—
24	#15689364	—	2	1	no	—
25	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
26	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
27	C₄×Dic₁₈₈	—	2	1	no	—
28	C₄×Dic₁₈₈	—	2	1	no	—
29	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
30	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₄₇	—	2	1	no	—
32	C₈×C₂²⋊D₄₇	—	2	1	no	—
33	#15689176	C₂²	1	1	yes	characteristic
34	#15689174	—	2	1	no	—
35	#15689161	—	2	2	no	—
36	#15689120	—	2	2	no	—
37	C₄×C₈×D₄₇	—	2	1	no	—
38	#15688871	C₂²	1	2	yes	—
39	#15688871	C₂²	1	2	yes	—
40	#15688868	C₂²	1	2	yes	—
41	#15688868	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#335	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	1	yes	characteristic
46	C₄₇×#335	C₂²	1	2	yes	—
47	C₂×#10625350	D₄	1	1	yes	characteristic
48	C₂×Dic₁₈₈	—	2	1	no	—
49	C₂×Dic₁₈₈	—	2	1	no	—
50	C₂×C₈×D₄₇	—	2	1	no	—
51	C₂×C₈×D₄₇	—	2	1	no	—
52	#13094024	C₂³	1	2	yes	—
53	#13094024	C₂³	1	2	yes	—
54	#13094016	—	2	2	no	—
55	#13094003	—	2	2	no	—
56	#13094003	—	2	2	no	—
57	C₄×Dic₉₄	—	2	2	no	—
58	C₄×Dic₉₄	—	2	2	no	—
59	C₄×Dic₉₄	D₄	1	1	yes	characteristic
60	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
61	C₄×D₁₈₈	D₄	1	1	yes	characteristic
62	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
63	C₄×C₂²⋊D₄₇	—	2	1	no	—
64	C₄×C₂²⋊D₄₇	—	2	1	no	—
65	#13093983	—	2	2	no	—
66	#13093983	D₄	1	1	yes	characteristic
67	#13093981	—	2	1	no	—
68	C₄²×D₄₇	—	2	1	no	—
69	#13093958	—	2	1	no	—
70	#13093958	—	2	1	no	—
71	#13093958	—	2	2	no	—
72	#13093958	—	2	2	no	—
73	#13093956	—	2	2	no	—
74	#13093956	—	2	2	no	—
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₄₇⋊C₈	—	2	1	no	—
78	Dic₄₇⋊C₈	—	2	1	no	—
79	#13093949	—	2	2	no	—
80	#13093949	—	2	2	no	—
81	#13093949	—	2	2	no	—
82	#13093949	—	2	2	no	—
83	#13093946	—	2	2	no	—
84	#13093946	—	2	2	no	—
85	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
86	(C₂×D₄₇)⋊C₈	—	2	1	no	—
87	(C₂×D₄₇)⋊C₈	—	2	1	no	—
88	C₄×C₄₇⋊C₈	—	2	1	no	—
89	C₈×Dic₄₇	—	2	1	no	—
90	C₈×Dic₄₇	—	2	1	no	—
91	C₂²×C₈×C₄₇	—	2	2	no	—
92	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	—	2	2	no	—
96	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
98	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₇	—	2	1	no	—
106	#10625350	—	2	2	no	—
107	#10625350	Q₁₆	1	4	yes	complemented
108	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₄₇	—	2	1	no	—
110	C₂×C₄×D₄₇	—	2	1	no	—
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×Dic₉₄	—	2	2	no	—
113	C₂×Dic₉₄	—	2	2	no	—
114	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	4	1	no	—
119	C₂×C₈×C₄₇	—	4	4	no	—
120	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₇	#41	1	1	yes	characteristic
127	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂²⋊Dic₄₇	—	2	1	no	—
129	C₂²⋊Dic₄₇	—	4	2	no	—
130	(C₂×D₄₇)⋊C₄	—	2	1	no	—
131	(C₂×D₄₇)⋊C₄	—	2	1	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
137	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
138	Dic₄₇⋊C₄	—	2	1	no	—
139	Dic₄₇⋊C₄	—	2	1	no	—
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	—	2	1	no	—
145	C₄×Dic₄₇	—	4	2	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	Dic₁₈₈	—	4	2	no	—
149	Dic₁₈₈	—	4	2	no	—
150	C₈×D₄₇	—	4	2	no	—
151	C₈×D₄₇	—	4	2	no	—
152	C₂³×C₄₇	#121	1	1	yes	characteristic
153	C₂²×D₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
161	C₂×C₄×C₄₇	#135	1	2	yes	—
162	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂²⋊D₄₇	—	2	4	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	2	1	no	—
168	C₂×Dic₄₇	—	2	1	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	D₁₈₈	—	2	1	no	—
172	D₁₈₈	C₂×Q₁₆	1	2	yes	—
173	C₄×D₄₇	—	2	4	no	—
174	C₄×D₄₇	—	4	2	no	—
175	C₄×D₄₇	—	4	1	no	—
176	C₄×D₄₇	—	4	1	no	—
177	Dic₉₄	—	2	1	no	—
178	Dic₉₄	—	4	2	no	—
179	Dic₉₄	—	4	2	no	—
180	Dic₉₄	—	8	2	no	—
181	Dic₉₄	C₂×Q₁₆	1	2	yes	—
182	C₈×C₄₇	—	2	1	no	—
183	C₈×C₄₇	—	2	1	no	—
184	C₈×C₄₇	—	2	1	no	—
185	C₈×C₄₇	—	4	2	no	—
186	C₈×C₄₇	—	4	2	no	—
187	C₈×C₄₇	#135	1	2	yes	—
188	C₄₇⋊C₈	—	4	1	no	—
189	C₄₇⋊C₈	—	4	1	no	—
190	#19126	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	#467	1	2	yes	—
194	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
195	C₂×D₄₇	—	2	2	no	—
196	C₂×D₄₇	—	4	1	no	—
197	C₂×D₄₇	—	4	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	#467	1	2	yes	—
202	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
203	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
204	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
205	C₄×C₄₇	#575	1	1	yes	characteristic
206	Dic₄₇	—	2	2	no	—
207	Dic₄₇	—	4	1	no	—
208	Dic₄₇	—	4	1	no	—
209	Dic₄₇	—	8	2	no	—
210	Dic₄₇	—	8	2	no	—
211	#3170	—	47	1	no	—
212	#3076	—	47	2	no	—
213	C₈×#41	—	47	1	no	—
214	#1684	—	47	2	no	—
215	#1683	—	47	2	no	—
216	#1676	—	47	1	no	—
217	#1675	—	47	1	no	—
218	#1670	—	47	1	no	—
219	#1669	—	47	1	no	—
220	C₂×#335	D₄₇	1	1	yes	characteristic, complemented
221	#1542	—	47	2	no	—
222	C₂×C₄₇	—	2	2	no	—
223	C₂×C₄₇	#3035	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#467	1	1	yes	characteristic
225	C₂×C₄₇	#3067	1	1	yes	characteristic
226	D₄₇	—	4	2	no	—
227	#533	—	47	2	no	—
228	C₄×#41	—	47	1	no	—
229	#500	—	47	1	no	—
230	#494	—	47	1	no	—
231	#487	—	47	2	no	—
232	#479	—	94	2	no	—
233	#478	—	94	2	no	—
234	#477	—	47	2	no	—
235	#476	—	47	2	no	—
236	#475	—	47	2	no	—
237	#474	—	47	2	no	—
238	#467	—	94	1	no	—
239	#467	—	94	1	no	—
240	C₈×Q₈	—	47	1	no	—
241	C₈×Q₈	—	47	1	no	—
242	C₄×Q₁₆	—	94	1	no	—
243	C₄×Q₁₆	—	94	1	no	—
244	C₈×D₄	—	47	1	no	—
245	C₈×D₄	—	47	1	no	—
246	C₈×D₄	—	94	1	no	—
247	C₈×D₄	—	94	1	no	—
248	#431	—	47	1	no	—
249	#431	—	94	1	no	—
250	#427	—	94	2	no	—
251	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
252	#416	—	94	2	no	—
253	C₂×C₄×C₈	—	94	1	no	—
254	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
255	#335	C₂×D₄₇	1	1	yes	characteristic
256	#335	C₂×D₄₇	1	1	yes	characteristic
257	#335	C₂×D₄₇	1	2	yes	—
258	#333	—	47	2	no	—
259	#333	—	47	2	no	—
260	#332	—	47	2	no	—
261	#332	—	47	2	no	—
262	C₄₇	#19126	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	47	1	no	—
264	C₂×Q₁₆	—	94	1	no	—
265	C₂×Q₁₆	—	94	1	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	94	1	no	—
268	C₂²×C₈	—	94	1	no	—
269	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
270	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
271	C₄⋊Q₈	—	47	2	no	—
272	C₄⋊Q₈	—	47	2	no	—
273	#125	—	94	2	no	—
274	C₂²⋊Q₈	—	94	2	no	—
275	C₂²⋊Q₈	—	94	2	no	—
276	C₄×Q₈	—	47	1	no	—
277	C₄×Q₈	—	47	1	no	—
278	C₄×Q₈	—	94	2	no	—
279	C₄×Q₈	—	94	2	no	—
280	C₄×D₄	—	47	1	no	—
281	C₄×D₄	—	47	1	no	—
282	C₄×D₄	—	94	1	no	—
283	C₄×D₄	—	94	1	no	—
284	#117	—	47	1	no	—
285	#117	—	94	1	no	—
286	#117	—	94	2	no	—
287	C₂×C₄²	—	94	1	no	—
288	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
289	#107	—	94	2	no	—
290	#107	—	94	2	no	—
291	#107	—	94	1	no	—
292	#107	—	94	1	no	—
293	#106	—	94	2	no	—
294	#106	—	94	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	47	1	no	—
297	C₄⋊C₈	—	47	1	no	—
298	C₄⋊C₈	—	94	1	no	—
299	C₄⋊C₈	—	94	1	no	—
300	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
301	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
302	#103	—	94	2	no	—
303	#103	—	94	2	no	—
304	#103	—	94	2	no	—
305	#103	—	94	2	no	—
306	#102	—	94	2	no	—
307	#102	—	94	2	no	—
308	C₂²⋊C₈	—	94	1	no	—
309	C₂²⋊C₈	—	94	1	no	—
310	C₂²⋊C₈	—	94	1	no	—
311	C₄×C₈	—	94	1	no	—
312	C₄×C₈	—	94	1	no	—
313	C₄×C₈	—	94	1	no	—
314	C₄×C₈	D₁₈₈	1	1	yes	characteristic
315	C₄×C₈	D₁₈₈	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
318	#41	—	47	4	no	—
319	#41	—	94	2	no	—
320	C₂×Q₈	—	47	1	no	—
321	C₂×Q₈	—	94	2	no	—
322	C₂×Q₈	—	94	2	no	—
323	C₂×D₄	—	47	1	no	—
324	C₂×D₄	—	94	1	no	—
325	C₂²×C₄	—	94	1	no	—
326	C₂²×C₄	—	94	1	no	—
327	C₂²×C₄	—	94	1	no	—
328	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
330	C₂²×C₄	#10625354	1	1	yes	characteristic
331	Q₁₆	—	188	2	no	—
332	Q₁₆	—	188	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	4	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	—	188	2	no	—
341	C₂×C₈	—	188	2	no	—
342	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
343	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
344	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
345	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
346	C₄⋊C₄	—	47	1	no	—
347	C₄⋊C₄	—	47	1	no	—
348	C₄⋊C₄	—	94	1	no	—
349	C₄⋊C₄	—	94	1	no	—
350	C₄⋊C₄	—	94	2	no	—
351	C₄⋊C₄	—	94	2	no	—
352	C₄⋊C₄	—	94	2	no	—
353	C₄⋊C₄	—	94	2	no	—
354	C₄⋊C₄	—	188	2	no	—
355	C₄⋊C₄	—	188	2	no	—
356	C₂²⋊C₄	—	94	1	no	—
357	C₂²⋊C₄	—	94	1	no	—
358	C₂²⋊C₄	—	94	1	no	—
359	C₂²⋊C₄	—	188	2	no	—
360	C₄²	—	94	1	no	—
361	C₄²	—	94	1	no	—
362	C₄²	—	94	1	no	—
363	C₄²	—	188	2	no	—
364	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
365	C₄²	D₄×D₄₇	1	1	yes	characteristic
366	C₄²	#10625354	1	1	yes	characteristic
367	C₄²	C₂³×D₄₇	1	1	yes	characteristic
368	C₂³	—	94	1	no	—
369	C₂³	#13093999	1	1	yes	characteristic
370	Q₈	—	47	2	no	—
371	Q₈	—	94	1	no	—
372	Q₈	—	376	2	no	—
373	Q₈	—	188	2	no	—
374	Q₈	—	188	2	no	—
375	D₄	—	47	2	no	—
376	D₄	—	94	4	no	—
377	D₄	—	94	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	94	1	no	—
382	C₂×C₄	—	94	4	no	—
383	C₂×C₄	—	94	1	no	—
384	C₂×C₄	—	94	1	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	—	188	2	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	1	no	—
389	C₂×C₄	—	188	1	no	—
390	C₂×C₄	#13093999	1	1	yes	characteristic
391	C₂×C₄	#13093999	1	1	yes	characteristic
392	C₂×C₄	#13093999	1	1	yes	characteristic
393	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
394	C₂×C₄	#13094043	1	2	yes	—
395	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
397	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	188	1	no	—
404	C₈	—	188	1	no	—
405	C₈	#13094046	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	94	2	no	—
409	C₂²	—	188	1	no	—
410	C₂²	—	188	1	no	—
411	C₂²	#15689365	1	2	yes	—
412	C₂²	C₂×#13093999	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	94	2	no	—
417	C₄	—	376	2	no	—
418	C₄	—	376	2	no	—
419	C₄	—	188	1	no	—
420	C₄	—	188	1	no	—
421	C₄	#15689365	1	2	yes	—
422	C₄	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
423	C₄	C₂×#13094043	1	1	yes	characteristic
424	C₄	C₂×#13094046	1	1	yes	characteristic
425	C₄	#15689923	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	188	2	no	—
428	C₂	#20252845	1	1	yes	characteristic
429	C₂	C₂×#15689365	1	1	yes	characteristic
430	C₂	#20253109	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093999
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#335	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#10625350	D₄
hypercenter	C₂×#335	D₄₇
hypocenter	C₄₇	#19126
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
1. #20253974	C₂	semidirect
4. #20242847	C₂	semidirect
5. #20242840	C₂	semidirect
6. #20242793	C₂	semidirect
7. #20242788	C₂	semidirect
8. #20242759	C₂	semidirect
9. #20242754	C₂	semidirect
10. #20242046	C₂	semidirect
11. C₂×C₄₇×#335	C₂	semidirect
107. #10625350	Q₁₆	semidirect
220. C₂×#335	D₄₇	semidirect
262. C₄₇	#19126	semidirect

Maximal subgroups

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

subgroup	index
#20253974	2
#20253178	2
C₈×#10625350	2
#20242847	2
#20242840	2
#20242793	2
#20242788	2
#20242759	2
#20242754	2
#20242046	2
C₂×C₄₇×#335	2
#19126	47