Subgroups — #26198961

Order 12032.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253711	C₂	1	1	yes	maximal, characteristic
2	#20253428	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253420	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689253	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242971	C₂	1	2	yes	maximal, complemented
6	#20242957	C₂	1	2	yes	maximal, complemented
7	#20242943	C₂	1	2	yes	maximal, complemented
8	#20242929	C₂	1	2	yes	maximal, complemented
9	#20242043	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242035	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689680	C₂²	1	1	yes	characteristic
13	#15689673	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	#15689478	—	2	1	no	—
16	#15689478	—	2	1	no	—
17	#15689474	C₂²	1	1	yes	characteristic
18	#15689474	C₂²	1	1	yes	characteristic
19	#15689470	C₂²	1	1	yes	characteristic
20	#15689470	C₂²	1	1	yes	characteristic
21	#15689459	—	2	1	no	—
22	#15689442	—	2	1	no	—
23	#15689419	C₂²	1	2	yes	—
24	#15689409	C₂²	1	2	yes	—
25	#15689334	C₂²	1	2	yes	—
26	#15689324	C₂²	1	2	yes	—
27	#15689281	—	2	1	no	—
28	#15689264	—	2	1	no	—
29	#15689253	—	2	1	no	—
30	#15689253	—	2	1	no	—
31	#15689253	C₂²	1	2	yes	—
32	#15689253	C₂²	1	2	yes	—
33	C₄×Dic₁₈₈	—	2	2	no	—
34	C₄×#10625325	—	2	2	no	—
35	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×Dic₄₇⋊C₈	—	2	1	no	—
37	#15689120	—	2	1	no	—
38	#15689120	—	2	1	no	—
39	C₂×#13093934	—	2	1	no	—
40	#15688871	C₂²	1	2	yes	—
41	#15688870	C₂²	1	2	yes	—
42	#15688868	C₂²	1	2	yes	—
43	#15688866	C₂²	1	2	yes	—
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₄₇×#431	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#335	C₂²	1	2	yes	—
48	C₄₇×#334	C₂²	1	2	yes	—
49	C₂×#10625350	—	2	1	no	—
50	C₂²×Dic₉₄	D₄	1	1	yes	characteristic
51	C₂×Dic₁₈₈	—	2	2	no	—
52	C₂×#10625325	—	2	2	no	—
53	C₂²×C₄₇⋊C₈	—	2	1	no	—
54	#13094024	C₂³	1	1	yes	characteristic
55	#13094024	C₂³	1	1	yes	characteristic
56	#13094024	C₂³	1	1	yes	characteristic
57	#13094021	C₂³	1	1	yes	characteristic
58	#13094016	—	2	1	no	—
59	#13094012	—	2	1	no	—
60	#13094003	—	2	1	no	—
61	#13094003	—	2	1	no	—
62	#13093998	—	2	1	no	—
63	#13093998	—	2	1	no	—
64	C₄×Dic₉₄	—	2	1	no	—
65	C₄×Dic₉₄	—	2	1	no	—
66	C₄×Dic₉₄	—	2	1	no	—
67	C₄×Dic₉₄	—	2	1	no	—
68	C₄×Dic₉₄	D₄	1	2	yes	—
69	C₄×Dic₉₄	C₂³	1	2	yes	—
70	C₄×D₁₈₈	—	2	1	no	—
71	C₄×D₁₈₈	—	2	1	no	—
72	#13093983	—	2	1	no	—
73	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
74	C₂×Dic₄₇⋊C₄	—	2	1	no	—
75	C₂×C₄×Dic₄₇	—	2	1	no	—
76	#13093958	—	2	2	no	—
77	#13093956	—	2	2	no	—
78	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
79	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
80	Dic₄₇⋊C₈	—	2	2	no	—
81	Dic₄₇⋊C₈	—	2	2	no	—
82	#13093949	—	2	2	no	—
83	#13093949	—	2	2	no	—
84	#13093949	—	2	1	no	—
85	#13093949	—	2	1	no	—
86	#13093949	—	2	1	no	—
87	#13093949	—	2	1	no	—
88	#13093949	—	2	2	no	—
89	#13093946	—	2	1	no	—
90	#13093946	—	2	1	no	—
91	#13093946	—	2	1	no	—
92	#13093946	—	2	1	no	—
93	#13093946	—	2	2	no	—
94	#13093934	—	2	2	no	—
95	#13093934	—	2	2	no	—
96	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
100	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
101	C₂²⋊C₈×C₄₇	—	2	1	no	—
102	C₂²⋊C₈×C₄₇	—	2	1	no	—
103	C₄×C₈×C₄₇	—	2	1	no	—
104	C₄×C₈×C₄₇	—	2	1	no	—
105	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
106	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₇	—	4	1	no	—
113	C₂²×Dic₄₇	—	2	1	no	—
114	C₂²×Dic₄₇	—	2	1	no	—
115	#10625350	—	4	2	no	—
116	#10625350	—	4	2	no	—
117	C₂×D₁₈₈	—	2	1	no	—
118	C₂×D₁₈₈	—	2	1	no	—
119	C₂×D₁₈₈	—	2	1	no	—
120	C₂×C₄×D₄₇	—	4	1	no	—
121	C₂×Dic₉₄	—	2	1	no	—
122	C₂×Dic₉₄	—	2	1	no	—
123	C₂×Dic₉₄	—	2	1	no	—
124	C₂×Dic₉₄	—	2	1	no	—
125	C₂×Dic₉₄	—	4	2	no	—
126	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	2	2	no	—
131	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₇	#41	1	1	yes	characteristic
138	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₄₇	—	4	1	no	—
140	(C₂×D₄₇)⋊C₄	—	4	1	no	—
141	(C₂×D₄₇)⋊C₄	—	4	1	no	—
142	C₄⋊Dic₄₇	—	2	1	no	—
143	C₄⋊Dic₄₇	—	2	1	no	—
144	C₄⋊Dic₄₇	—	2	1	no	—
145	C₄⋊Dic₄₇	—	2	1	no	—
146	C₄⋊Dic₄₇	—	2	1	no	—
147	C₄⋊Dic₄₇	—	2	1	no	—
148	C₄⋊Dic₄₇	—	2	1	no	—
149	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
150	Dic₄₇⋊C₄	—	2	2	no	—
151	Dic₄₇⋊C₄	—	2	2	no	—
152	Dic₄₇⋊C₄	—	4	1	no	—
153	Dic₄₇⋊C₄	—	4	1	no	—
154	C₄×Dic₄₇	—	2	2	no	—
155	C₄×Dic₄₇	—	2	2	no	—
156	C₄×Dic₄₇	—	4	1	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	4	2	no	—
159	Dic₁₈₈	—	4	4	no	—
160	#10625325	—	4	4	no	—
161	C₂³×C₄₇	#121	1	1	yes	characteristic
162	C₂²×D₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#135	1	2	yes	—
169	C₂×C₄×C₄₇	#137	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₄₇	—	8	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	1	no	—
179	C₂×Dic₄₇	—	4	1	no	—
180	C₂×Dic₄₇	—	4	1	no	—
181	D₁₈₈	—	4	1	no	—
182	D₁₈₈	—	4	1	no	—
183	D₁₈₈	—	4	2	no	—
184	D₁₈₈	—	8	1	no	—
185	C₄×D₄₇	—	8	2	no	—
186	Dic₉₄	—	2	2	no	—
187	Dic₉₄	—	2	2	no	—
188	Dic₉₄	—	4	2	no	—
189	Dic₉₄	—	4	1	no	—
190	Dic₉₄	—	4	1	no	—
191	Dic₉₄	—	4	2	no	—
192	Dic₉₄	—	8	1	no	—
193	C₈×C₄₇	—	2	1	no	—
194	C₈×C₄₇	—	2	1	no	—
195	C₈×C₄₇	—	2	1	no	—
196	C₈×C₄₇	—	2	1	no	—
197	C₈×C₄₇	—	4	2	no	—
198	C₈×C₄₇	—	4	2	no	—
199	C₄₇⋊C₈	—	4	2	no	—
200	#19155	—	47	1	no	maximal, Sylow
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	#464	1	2	yes	—
204	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
205	C₂×D₄₇	—	8	1	no	—
206	C₂×D₄₇	—	8	1	no	—
207	C₂×D₄₇	—	8	1	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	#464	1	2	yes	—
212	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
213	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
214	C₄×C₄₇	#575	1	2	yes	—
215	Dic₄₇	—	4	2	no	—
216	Dic₄₇	—	4	2	no	—
217	Dic₄₇	—	8	1	no	—
218	Dic₄₇	—	8	1	no	—
219	Dic₄₇	—	8	1	no	—
220	#3131	—	47	1	no	—
221	#3104	—	47	1	no	—
222	#3103	—	47	1	no	—
223	C₂×#446	—	47	1	no	—
224	#1704	—	47	2	no	—
225	#1702	—	47	2	no	—
226	#1700	—	47	2	no	—
227	#1698	—	47	2	no	—
228	#1564	D₄₇	1	1	yes	characteristic, complemented
229	#1542	—	47	1	no	—
230	#1540	—	47	1	no	—
231	C₂×C₄₇	—	2	2	no	—
232	C₂×C₄₇	C₂×#464	1	1	yes	characteristic
233	C₂×C₄₇	#3054	1	1	yes	characteristic
234	C₂×C₄₇	#3067	1	1	yes	characteristic
235	D₄₇	—	16	1	no	—
236	#533	—	47	1	no	—
237	#532	—	47	1	no	—
238	C₂×C₄×Q₈	—	47	1	no	—
239	#488	—	94	1	no	—
240	#488	—	94	1	no	—
241	#487	—	47	1	no	—
242	#487	—	47	1	no	—
243	#486	—	47	1	no	—
244	#486	—	47	1	no	—
245	#484	—	94	1	no	—
246	#481	—	94	1	no	—
247	#477	—	47	2	no	—
248	#475	—	47	2	no	—
249	#462	—	47	2	no	—
250	#460	—	47	2	no	—
251	#451	—	94	1	no	—
252	#448	—	94	1	no	—
253	#446	—	47	2	no	—
254	#446	—	47	2	no	—
255	#446	—	94	1	no	—
256	#446	—	94	1	no	—
257	C₄×Q₁₆	—	94	2	no	—
258	C₄×SD₁₆	—	94	2	no	—
259	#431	C₂×D₄₇	1	1	yes	characteristic
260	#431	C₂×D₄₇	1	1	yes	characteristic
261	C₂×C₄⋊C₈	—	47	1	no	—
262	C₂×C₄⋊C₈	—	94	1	no	—
263	#416	—	94	1	no	—
264	#416	—	94	1	no	—
265	C₂×#97	—	94	1	no	—
266	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
267	#335	C₂×D₄₇	1	2	yes	—
268	#334	C₂×D₄₇	1	2	yes	—
269	#333	—	47	2	no	—
270	#332	—	47	2	no	—
271	#332	—	47	2	no	—
272	#331	—	47	2	no	—
273	C₄₇	#19155	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	94	1	no	—
275	C₂²×Q₈	—	47	1	no	—
276	C₂×Q₁₆	—	94	2	no	—
277	C₂×SD₁₆	—	94	2	no	—
278	C₂²×C₈	—	94	1	no	—
279	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
280	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
281	C₄⋊Q₈	—	47	1	no	—
282	C₄⋊Q₈	—	47	1	no	—
283	C₄⋊Q₈	—	47	1	no	—
284	#127	—	47	1	no	—
285	#125	—	94	1	no	—
286	#124	—	94	1	no	—
287	C₂²⋊Q₈	—	94	1	no	—
288	C₂²⋊Q₈	—	94	1	no	—
289	#121	—	94	1	no	—
290	#121	—	94	1	no	—
291	C₄×Q₈	—	47	2	no	—
292	C₄×Q₈	—	47	2	no	—
293	C₄×Q₈	—	94	1	no	—
294	C₄×Q₈	—	94	1	no	—
295	C₄×Q₈	—	94	1	no	—
296	C₄×Q₈	—	94	1	no	—
297	C₄×D₄	—	94	1	no	—
298	C₄×D₄	—	94	1	no	—
299	#117	—	94	1	no	—
300	C₂×C₄⋊C₄	—	47	1	no	—
301	C₂×C₄⋊C₄	—	94	1	no	—
302	C₂×C₄²	—	94	1	no	—
303	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
304	#107	—	94	2	no	—
305	#106	—	94	2	no	—
306	C₄⋊C₈	—	47	2	no	—
307	C₄⋊C₈	—	94	2	no	—
308	C₄⋊C₈	—	94	2	no	—
309	C₄⋊C₈	—	94	1	no	—
310	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
311	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
312	#103	—	94	2	no	—
313	#103	—	94	2	no	—
314	#103	—	94	2	no	—
315	#103	—	94	1	no	—
316	#103	—	94	1	no	—
317	#103	—	94	1	no	—
318	#103	—	94	1	no	—
319	#102	—	94	2	no	—
320	#102	—	94	1	no	—
321	#102	—	94	1	no	—
322	#102	—	94	1	no	—
323	#102	—	94	1	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	#97	—	94	2	no	—
327	#97	—	94	2	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	2	1	no	—
330	C₄×C₈	D₁₈₈	1	1	yes	characteristic
331	C₄×C₈	D₁₈₈	1	1	yes	characteristic
332	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	#41	—	188	2	no	—
335	#41	—	188	2	no	—
336	C₂×Q₈	—	47	2	no	—
337	C₂×Q₈	—	94	1	no	—
338	C₂×Q₈	—	94	1	no	—
339	C₂×Q₈	—	94	1	no	—
340	C₂×Q₈	—	94	1	no	—
341	C₂×Q₈	—	188	2	no	—
342	C₂×D₄	—	94	1	no	—
343	C₂×D₄	—	94	1	no	—
344	C₂×D₄	—	94	1	no	—
345	C₂×D₄	—	188	1	no	—
346	C₂²×C₄	—	94	1	no	—
347	C₂²×C₄	—	94	1	no	—
348	C₂²×C₄	—	188	1	no	—
349	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
351	C₂²×C₄	#10625354	1	1	yes	characteristic
352	Q₁₆	—	188	4	no	—
353	SD₁₆	—	188	4	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	94	2	no	—
359	C₂×C₈	—	188	2	no	—
360	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
361	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
362	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
363	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
364	C₄⋊C₄	—	47	2	no	—
365	C₄⋊C₄	—	94	2	no	—
366	C₄⋊C₄	—	94	1	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	94	1	no	—
369	C₄⋊C₄	—	94	1	no	—
370	C₄⋊C₄	—	94	1	no	—
371	C₄⋊C₄	—	94	1	no	—
372	C₄⋊C₄	—	94	1	no	—
373	C₄⋊C₄	—	94	1	no	—
374	C₄⋊C₄	—	188	1	no	—
375	C₄⋊C₄	—	188	1	no	—
376	C₂²⋊C₄	—	188	1	no	—
377	C₂²⋊C₄	—	188	1	no	—
378	C₂²⋊C₄	—	188	1	no	—
379	C₄²	—	94	2	no	—
380	C₄²	—	94	2	no	—
381	C₄²	—	188	1	no	—
382	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
383	C₄²	D₄×D₄₇	1	1	yes	characteristic
384	C₄²	#10625354	1	1	yes	characteristic
385	C₄²	C₂³×D₄₇	1	1	yes	characteristic
386	C₂³	—	188	1	no	—
387	C₂³	#13093999	1	1	yes	characteristic
388	Q₈	—	94	2	no	—
389	Q₈	—	94	2	no	—
390	Q₈	—	376	1	no	—
391	Q₈	—	188	2	no	—
392	Q₈	—	188	1	no	—
393	Q₈	—	188	1	no	—
394	Q₈	—	188	2	no	—
395	D₄	—	376	1	no	—
396	D₄	—	376	2	no	—
397	D₄	—	188	1	no	—
398	D₄	—	188	1	no	—
399	D₄	—	188	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	94	2	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	376	2	no	—
405	C₂×C₄	—	188	1	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	1	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	—	188	2	no	—
410	C₂×C₄	#13093999	1	1	yes	characteristic
411	C₂×C₄	#13093999	1	1	yes	characteristic
412	C₂×C₄	#13093999	1	1	yes	characteristic
413	C₂×C₄	#13094046	1	2	yes	—
414	C₂×C₄	#13094057	1	2	yes	—
415	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
417	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₈	—	188	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	376	1	no	—
428	C₂²	—	376	1	no	—
429	C₂²	—	376	1	no	—
430	C₂²	#15689346	1	2	yes	—
431	C₂²	C₂×#13093999	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	376	1	no	—
436	C₄	—	376	1	no	—
437	C₄	—	376	1	no	—
438	C₄	—	188	2	no	—
439	C₄	—	188	2	no	—
440	C₄	#15689346	1	2	yes	—
441	C₄	C₂×#13094046	1	1	yes	characteristic
442	C₄	C₂×#13094057	1	1	yes	characteristic
443	C₄	#15689920	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	752	1	no	—
446	C₂	C₂×#15689346	1	1	yes	characteristic
447	C₂	#20252998	1	1	yes	characteristic
448	C₂	#20253109	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093999
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1564	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#15689673	C₂²
hypercenter	#1564	D₄₇
hypocenter	C₄₇	#19155
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
2. #20253428	C₂	semidirect
4. C₂×#15689253	C₂	semidirect
5. #20242971	C₂	semidirect
6. #20242957	C₂	semidirect
7. #20242943	C₂	semidirect
8. #20242929	C₂	semidirect
9. #20242043	C₂	semidirect
11. C₄₇×#1564	C₂	semidirect
228. #1564	D₄₇	semidirect
273. C₄₇	#19155	semidirect

Maximal subgroups

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

subgroup	index
#20253711	2
#20253428	2
#20253420	2
C₂×#15689253	2
#20242971	2
#20242957	2
#20242943	2
#20242929	2
#20242043	2
#20242035	2
C₄₇×#1564	2
#19155	47