Subgroups — #26275264

Order 12032.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20248424	C₂	1	1	yes	maximal, characteristic
2	#20246347	C₂	1	1	yes	maximal, characteristic
3	#20244928	C₂	1	2	yes	maximal
4	#20244764	C₂	1	2	yes	maximal
5	#20244149	C₂	1	1	yes	maximal, characteristic
6	#20244148	C₂	1	2	yes	maximal
7	#20244106	C₂	1	1	yes	maximal, characteristic
8	#20243968	C₂	1	2	yes	maximal
9	#20243390	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093949	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1844	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094015	—	2	1	no	—
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₂×#13093955	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×#13093949	C₂²	1	1	yes	characteristic
18	C₂×#13093949	C₂²	1	1	yes	characteristic
19	C₂×#13093947	C₂²	1	2	yes	—
20	#15689056	—	2	2	no	—
21	#15689028	C₂²	1	2	yes	—
22	#15689022	C₂²	1	2	yes	—
23	#15689019	—	2	1	no	—
24	#15689004	—	2	2	no	—
25	#15688992	C₂²	1	2	yes	—
26	#15688988	—	2	1	no	—
27	C₄⋊C₄×Dic₄₇	—	2	1	no	—
28	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688886	C₂²	1	1	yes	characteristic
32	#15688886	C₂²	1	1	yes	characteristic
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	C₂×#106×C₄₇	C₂²	1	2	yes	—
37	C₂×#106×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#384	C₂²	1	1	yes	characteristic
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	#13094015	—	4	4	no	—
44	C₄×Dic₉₄	—	2	2	no	—
45	C₄×Dic₉₄	Q₈	1	4	yes	—
46	C₂×C₄⋊Dic₄₇	—	2	2	no	—
47	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
52	C₂×Dic₄₇⋊C₄	—	2	1	no	—
53	C₂×Dic₄₇⋊C₄	—	2	2	no	—
54	C₂×Dic₄₇⋊C₄	—	2	2	no	—
55	C₂×C₄×Dic₄₇	—	2	1	no	—
56	C₂×C₄×Dic₄₇	—	2	1	no	—
57	C₂×C₄×Dic₄₇	—	2	2	no	—
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	#13093955	—	4	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	Dic₄₇⋊C₈	—	2	4	no	—
62	#13093949	—	2	2	no	—
63	#13093949	—	2	2	no	—
64	#13093947	—	4	2	no	—
65	C₄₇⋊#95	—	2	1	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	D₄	1	2	yes	—
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	#106×C₄₇	—	2	4	no	—
81	#106×C₄₇	—	4	2	no	—
82	C₄×C₈×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
88	C₂²×Dic₄₇	—	2	1	no	—
89	C₂²×Dic₄₇	—	2	1	no	—
90	C₂²×Dic₄₇	—	2	1	no	—
91	C₂²×Dic₄₇	—	2	1	no	—
92	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
93	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
94	C₂×Dic₉₄	—	2	1	no	—
95	C₂×Dic₉₄	—	2	1	no	—
96	C₂×Dic₉₄	—	2	1	no	—
97	C₂×Dic₉₄	—	2	1	no	—
98	C₂×Dic₉₄	—	2	1	no	—
99	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	—	2	1	no	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	#41	1	2	yes	—
105	C₂×C₈×C₄₇	#41	1	2	yes	—
106	C₄⋊C₄×C₄₇	—	2	2	no	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	4	2	no	—
111	C₄⋊C₄×C₄₇	—	4	2	no	—
112	C₄⋊C₄×C₄₇	—	8	1	no	—
113	C₄⋊C₄×C₄₇	—	8	1	no	—
114	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
115	C₄²×C₄₇	#41	1	2	yes	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	1	no	—
118	C₄⋊Dic₄₇	—	2	1	no	—
119	C₄⋊Dic₄₇	—	2	1	no	—
120	C₄⋊Dic₄₇	—	2	1	no	—
121	C₄⋊Dic₄₇	—	2	1	no	—
122	C₄⋊Dic₄₇	—	4	4	no	—
123	C₄⋊Dic₄₇	SD₁₆	1	4	yes	—
124	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
125	Dic₄₇⋊C₄	—	2	4	no	—
126	Dic₄₇⋊C₄	—	4	4	no	—
127	Dic₄₇⋊C₄	—	8	2	no	—
128	C₄×Dic₄₇	—	2	4	no	—
129	C₄×Dic₄₇	—	2	2	no	—
130	C₄×Dic₄₇	—	2	2	no	—
131	C₄×Dic₄₇	—	4	2	no	—
132	C₄×Dic₄₇	—	8	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
148	C₂×C₄×C₄₇	#137	1	2	yes	—
149	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	2	no	—
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	4	1	no	—
163	C₂×Dic₄₇	—	4	1	no	—
164	C₂×Dic₄₇	—	4	1	no	—
165	C₂×Dic₄₇	—	4	1	no	—
166	C₂×Dic₄₇	—	4	1	no	—
167	C₂×Dic₄₇	—	4	1	no	—
168	C₂×Dic₄₇	—	4	1	no	—
169	C₂×Dic₄₇	—	4	1	no	—
170	C₂×Dic₄₇	—	4	1	no	—
171	C₂×Dic₄₇	—	4	1	no	—
172	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
173	Dic₉₄	—	2	2	no	—
174	Dic₉₄	—	2	2	no	—
175	Dic₉₄	—	4	1	no	—
176	Dic₉₄	—	4	1	no	—
177	C₈×C₄₇	—	2	2	no	—
178	C₈×C₄₇	—	2	2	no	—
179	C₄₇⋊C₈	—	4	2	no	—
180	#26088	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
182	C₂²×C₄₇	#547	1	1	yes	characteristic
183	C₂²×C₄₇	#550	1	1	yes	characteristic
184	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
186	C₂²×C₄₇	#577	1	1	yes	characteristic
187	C₂²×C₄₇	#577	1	1	yes	characteristic
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	8	2	no	—
190	C₄×C₄₇	—	8	2	no	—
191	C₄×C₄₇	#475	1	4	yes	—
192	C₄×C₄₇	#533	1	1	yes	characteristic
193	C₄×C₄₇	#544	1	1	yes	characteristic
194	C₄×C₄₇	#552	1	1	yes	characteristic
195	C₄×C₄₇	#553	1	1	yes	characteristic
196	Dic₄₇	—	2	4	no	—
197	Dic₄₇	—	4	2	no	—
198	Dic₄₇	—	4	2	no	—
199	Dic₄₇	—	4	2	no	—
200	Dic₄₇	—	8	1	no	—
201	Dic₄₇	—	8	1	no	—
202	#2552	—	47	1	no	—
203	#2355	—	47	1	no	—
204	#2096	—	47	2	no	—
205	#2066	—	47	2	no	—
206	#1948	—	47	2	no	—
207	#1948	—	47	1	no	—
208	#1939	—	47	1	no	—
209	#1919	—	47	2	no	—
210	#1844	D₄₇	1	1	yes	characteristic
211	#1803	—	47	1	no	—
212	C₄×#103	—	47	1	no	—
213	C₂×C₄₇	#2441	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#475	1	1	yes	characteristic
215	C₂×C₄₇	#3084	1	1	yes	characteristic
216	C₂×C₄₇	#3335	1	1	yes	characteristic
217	C₂×C₄₇	#3356	1	1	yes	characteristic
218	C₂×C₄₇	#3392	1	1	yes	characteristic
219	C₂×C₄₇	#3400	1	1	yes	characteristic
220	C₂×#125	—	94	1	no	—
221	C₂×C₄×Q₈	—	47	1	no	—
222	C₂×#106	—	47	2	no	—
223	C₂×#106	C₂×D₄₇	1	2	yes	—
224	C₂×#106	C₂×D₄₇	1	2	yes	—
225	C₂×C₄⋊C₈	—	47	2	no	—
226	C₂×C₄⋊C₈	—	47	1	no	—
227	C₂×#103	—	47	1	no	—
228	C₂×#103	—	47	1	no	—
229	C₂×#103	—	47	2	no	—
230	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
231	#398	—	94	2	no	—
232	#391	—	47	2	no	—
233	#389	—	47	2	no	—
234	#389	—	94	1	no	—
235	#387	—	94	2	no	—
236	#384	—	47	2	no	—
237	#384	C₂×D₄₇	1	1	yes	characteristic
238	#384	C₂×D₄₇	1	1	yes	characteristic
239	#382	—	94	1	no	—
240	C₄×C₄⋊C₄	—	47	1	no	—
241	C₄×C₄⋊C₄	—	47	2	no	—
242	C₄×C₄⋊C₄	—	47	1	no	—
243	C₄×C₄⋊C₄	—	94	1	no	—
244	#340	—	47	1	no	—
245	#340	—	47	1	no	—
246	#340	—	47	2	no	—
247	#340	—	47	2	no	—
248	#336	—	47	2	no	—
249	C₄₇	#26088	1	1	yes	characteristic, complemented, Sylow
250	C₂²×Q₈	—	47	1	no	—
251	C₂²×C₈	—	47	2	no	—
252	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
253	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
254	#125	—	188	4	no	—
255	C₄×Q₈	—	47	4	no	—
256	C₄×Q₈	—	94	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	47	1	no	—
262	C₂×C₄⋊C₄	—	47	1	no	—
263	C₂×C₄⋊C₄	—	47	1	no	—
264	C₂×C₄⋊C₄	—	47	1	no	—
265	C₂×C₄⋊C₄	—	47	1	no	—
266	C₂×C₄⋊C₄	—	94	1	no	—
267	C₂×C₄⋊C₄	—	94	2	no	—
268	C₂×C₄⋊C₄	—	94	2	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
272	C₂×C₄²	—	47	2	no	—
273	C₂×C₄²	—	94	1	no	—
274	C₂×C₄²	—	94	2	no	—
275	C₂×C₄²	—	94	1	no	—
276	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
277	#106	—	2	4	no	—
278	#106	—	4	2	no	—
279	#106	—	188	2	no	—
280	C₄⋊C₈	—	94	4	no	—
281	C₄⋊C₈	—	94	2	no	—
282	#103	—	94	2	no	—
283	#103	—	94	2	no	—
284	#103	—	188	2	no	—
285	C₄×C₈	—	2	2	no	—
286	#95	—	47	2	no	—
287	#95	—	94	2	no	—
288	#95	—	94	2	no	—
289	#95	—	94	2	no	—
290	#95	—	94	2	no	—
291	#95	—	94	1	no	—
292	C₂×Q₈	—	47	2	no	—
293	C₂×Q₈	—	94	1	no	—
294	C₂×Q₈	—	94	1	no	—
295	C₂×Q₈	—	94	1	no	—
296	C₂×Q₈	—	94	1	no	—
297	C₂×Q₈	—	94	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	47	2	no	—
301	C₂²×C₄	—	47	2	no	—
302	C₂²×C₄	—	94	1	no	—
303	C₂²×C₄	—	94	1	no	—
304	C₂²×C₄	—	94	1	no	—
305	C₂²×C₄	—	94	1	no	—
306	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	94	2	no	—
314	C₂×C₈	—	94	2	no	—
315	C₂×C₈	—	94	2	no	—
316	C₂×C₈	#10625352	1	2	yes	—
317	C₂×C₈	#10625354	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	8	1	no	—
325	C₄⋊C₄	—	8	1	no	—
326	C₄⋊C₄	—	47	4	no	—
327	C₄⋊C₄	—	47	2	no	—
328	C₄⋊C₄	—	94	4	no	—
329	C₄⋊C₄	—	94	2	no	—
330	C₄⋊C₄	—	94	1	no	—
331	C₄⋊C₄	—	94	1	no	—
332	C₄⋊C₄	—	94	1	no	—
333	C₄⋊C₄	—	94	1	no	—
334	C₄⋊C₄	—	94	1	no	—
335	C₄⋊C₄	—	376	2	no	—
336	C₄⋊C₄	—	188	4	no	—
337	C₄⋊C₄	—	188	4	no	—
338	C₄²	—	94	4	no	—
339	C₄²	—	94	2	no	—
340	C₄²	—	94	2	no	—
341	C₄²	—	376	2	no	—
342	C₄²	—	188	2	no	—
343	C₄²	#10625350	1	2	yes	—
344	C₄²	Q₈×D₄₇	1	2	yes	—
345	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
346	Q₈	—	94	2	no	—
347	Q₈	—	94	2	no	—
348	Q₈	—	188	1	no	—
349	Q₈	—	188	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	47	4	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	2	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	188	1	no	—
367	C₂×C₄	—	188	1	no	—
368	C₂×C₄	—	188	1	no	—
369	C₂×C₄	—	188	1	no	—
370	C₂×C₄	—	188	1	no	—
371	C₂×C₄	—	188	1	no	—
372	C₂×C₄	—	188	1	no	—
373	C₂×C₄	—	188	1	no	—
374	C₂×C₄	—	188	1	no	—
375	C₂×C₄	—	188	1	no	—
376	C₂×C₄	#13094002	1	2	yes	—
377	C₂×C₄	#13094002	1	2	yes	—
378	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
379	C₂×C₄	#13094053	1	2	yes	—
380	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
382	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
383	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
384	C₂×C₄	#13094069	1	1	yes	characteristic
385	C₂×C₄	#13094072	1	1	yes	characteristic
386	C₈	—	2	2	no	—
387	C₈	—	2	2	no	—
388	C₈	—	188	2	no	—
389	C₂²	C₂×#13094002	1	1	yes	characteristic
390	C₂²	#15689776	1	1	yes	characteristic
391	C₂²	#15689793	1	1	yes	characteristic
392	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
393	C₂²	C₂×#13094053	1	1	yes	characteristic
394	C₂²	#15689929	1	1	yes	characteristic
395	C₂²	#15689929	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	94	4	no	—
400	C₄	—	376	1	no	—
401	C₄	—	376	1	no	—
402	C₄	—	188	2	no	—
403	C₄	—	188	2	no	—
404	C₄	—	188	2	no	—
405	C₄	#15689407	1	4	yes	—
406	C₄	#15689678	1	1	yes	characteristic
407	C₄	#15689750	1	1	yes	characteristic
408	C₄	#15689808	1	1	yes	characteristic
409	C₄	#15689821	1	1	yes	characteristic
410	C₂	#20247104	1	1	yes	characteristic
411	C₂	C₂×#15689407	1	1	yes	characteristic
412	C₂	#20253255	1	1	yes	characteristic
413	C₂	#20255744	1	1	yes	characteristic
414	C₂	#20256002	1	1	yes	characteristic
415	C₂	#20256366	1	1	yes	characteristic
416	C₂	#20256446	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1844	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
hypercenter	#1844	D₄₇
hypocenter	C₄₇	#26088
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

Complements

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

N	H ≅ G/N	type
249. C₄₇	#26088	semidirect

Maximal subgroups

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

subgroup	index
#20248424	2
#20246347	2
#20244928	2
#20244764	2
#20244149	2
#20244148	2
#20244106	2
#20243968	2
#20243390	2
C₄×#13093949	2
C₄₇×#1844	2
#26088	47