Subgroups — #26188087

Order 12032.

646 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253947	C₂	1	1	yes	maximal, characteristic
2	#20252335	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252134	C₂	1	1	yes	maximal, characteristic
4	#20242292	C₂	1	2	yes	maximal, complemented
5	#20242268	C₂	1	2	yes	maximal, complemented
6	#20242247	C₂	1	2	yes	maximal, complemented
7	#20242202	C₂	1	2	yes	maximal, complemented
8	C₂×#15688876	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241792	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241788	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094032	—	2	1	no	—
13	#15689680	C₂²	1	1	yes	characteristic
14	#15689673	C₂²	1	1	yes	characteristic
15	#15689521	C₄	1	1	yes	characteristic
16	#15689496	C₄	1	1	yes	characteristic
17	#15689474	C₄	1	1	yes	characteristic
18	#15689470	C₄	1	1	yes	characteristic
19	#15689352	C₄	1	2	yes	—
20	#15689352	C₄	1	2	yes	—
21	#15689253	C₂²	1	2	yes	—
22	#15689251	—	2	2	no	—
23	C₈×Dic₉₄	C₂²	1	2	yes	—
24	C₄×#10625325	C₂²	1	2	yes	—
25	C₄×#10625325	C₂²	1	2	yes	—
26	#15689202	C₂²	1	2	yes	—
27	#15689196	—	2	2	no	—
28	C₈×D₁₈₈	C₂²	1	2	yes	—
29	#15689151	—	2	1	no	—
30	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
32	#15689091	—	2	1	no	—
33	#15689081	—	2	1	no	—
34	#15688876	C₂²	1	1	yes	characteristic
35	#15688876	C₂²	1	1	yes	characteristic
36	#15688876	C₂²	1	1	yes	characteristic
37	#15688876	C₂²	1	1	yes	characteristic
38	#15688855	C₂²	1	2	yes	—
39	#15688855	C₂²	1	2	yes	—
40	#15688852	C₂²	1	2	yes	—
41	#15688852	C₂²	1	2	yes	—
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#322	C₂²	1	2	yes	—
46	C₄₇×#322	C₂²	1	2	yes	—
47	C₂×#10625350	—	2	1	no	—
48	C₂×#10625325	C₂×C₄	1	2	yes	—
49	C₂×#10625325	C₂×C₄	1	2	yes	—
50	#13094032	—	4	4	no	—
51	C₂×#10625324	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	—	2	1	no	—
53	C₂²×C₄₇⋊C₈	—	2	1	no	—
54	C₂×C₈×D₄₇	—	2	2	no	—
55	#13094024	C₂×C₄	1	1	yes	characteristic
56	#13094024	C₂×C₄	1	1	yes	characteristic
57	#13094024	C₂×C₄	1	1	yes	characteristic
58	#13094021	C₂×C₄	1	1	yes	characteristic
59	#13094016	—	2	1	no	—
60	#13094012	—	2	1	no	—
61	#13094003	—	2	1	no	—
62	#13094003	C₂×C₄	1	2	yes	—
63	#13093998	—	2	1	no	—
64	#13093998	C₂×C₄	1	2	yes	—
65	C₄×Dic₉₄	—	2	1	no	—
66	C₄×Dic₉₄	C₂³	1	2	yes	—
67	C₄×D₁₈₈	—	2	1	no	—
68	C₄×D₁₈₈	C₂³	1	2	yes	—
69	#13093983	—	2	1	no	—
70	#13093956	C₂×C₄	1	2	yes	—
71	#13093956	C₂×C₄	1	2	yes	—
72	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
73	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
74	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
78	Dic₄₇⋊C₈	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	2	no	—
80	#13093949	C₂×C₄	1	2	yes	—
81	#13093949	C₂×C₄	1	2	yes	—
82	#13093946	C₂×C₄	1	2	yes	—
83	#13093946	C₂×C₄	1	2	yes	—
84	(C₂×D₄₇)⋊C₈	—	2	2	no	—
85	(C₂×D₄₇)⋊C₈	—	2	2	no	—
86	#13093934	—	2	2	no	—
87	C₈×Dic₄₇	—	2	2	no	—
88	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
89	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
90	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	—	2	1	no	—
94	C₂²⋊C₈×C₄₇	—	2	1	no	—
95	#97×C₄₇	D₄	1	2	yes	—
96	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₄×C₈×C₄₇	C₂³	1	2	yes	—
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	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	2	no	—
106	#10625350	—	4	2	no	—
107	#10625350	—	4	2	no	—
108	C₂×D₁₈₈	—	2	1	no	—
109	C₂×D₁₈₈	—	2	1	no	—
110	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₄₇	—	2	2	no	—
112	C₂×Dic₉₄	—	2	1	no	—
113	C₂×Dic₉₄	—	2	1	no	—
114	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
115	M₁₆×C₄₇	—	2	2	no	—
116	M₁₆×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	4	1	no	—
120	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₇	#41	1	1	yes	characteristic
129	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
130	C₂²⋊Dic₄₇	—	2	2	no	—
131	(C₂×D₄₇)⋊C₄	—	2	2	no	—
132	(C₂×D₄₇)⋊C₄	—	2	2	no	—
133	C₄⋊Dic₄₇	—	2	1	no	—
134	C₄⋊Dic₄₇	—	2	1	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
138	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
139	Dic₄₇⋊C₄	—	2	2	no	—
140	Dic₄₇⋊C₄	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	4	2	no	—
147	C₂×C₄₇⋊C₈	—	4	2	no	—
148	#10625325	—	2	4	no	—
149	#10625325	—	4	2	no	—
150	#10625324	—	4	4	no	—
151	C₈×D₄₇	—	4	4	no	—
152	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
153	C₂²×D₄₇	—	2	2	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	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₄₇	#137	1	2	yes	—
162	C₂×C₄×C₄₇	C₂³×C₄	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	—	4	4	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	D₁₈₈	—	2	2	no	—
170	D₁₈₈	—	2	2	no	—
171	D₁₈₈	—	4	2	no	—
172	D₁₈₈	—	8	1	no	—
173	C₄×D₄₇	—	4	2	no	—
174	C₄×D₄₇	—	4	2	no	—
175	Dic₉₄	—	2	2	no	—
176	Dic₉₄	—	2	2	no	—
177	Dic₉₄	—	4	2	no	—
178	Dic₉₄	—	8	1	no	—
179	C₈×C₄₇	—	2	1	no	—
180	C₈×C₄₇	—	2	1	no	—
181	C₈×C₄₇	—	2	1	no	—
182	C₈×C₄₇	—	2	2	no	—
183	C₈×C₄₇	—	2	2	no	—
184	C₈×C₄₇	—	4	2	no	—
185	C₈×C₄₇	#131	1	2	yes	complemented
186	C₄₇⋊C₈	—	4	1	no	—
187	C₄₇⋊C₈	—	4	1	no	—
188	C₄₇⋊C₈	—	4	1	no	—
189	C₄₇⋊C₈	—	4	1	no	—
190	#18071	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	#440	1	2	yes	—
194	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂×D₄₇	—	4	2	no	—
196	C₂×D₄₇	—	4	2	no	—
197	C₂×D₄₇	—	4	2	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	#440	1	2	yes	—
202	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
203	C₄×C₄₇	#568	1	1	yes	characteristic
204	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
206	Dic₄₇	—	4	2	no	—
207	Dic₄₇	—	4	2	no	—
208	Dic₄₇	—	4	2	no	—
209	#3167	—	47	1	no	—
210	#2962	—	47	1	no	—
211	#2935	—	47	1	no	—
212	#1592	—	47	2	no	—
213	#1588	—	47	2	no	—
214	#1585	—	47	2	no	—
215	SD₁₆⋊C₈	—	47	2	no	—
216	C₂×#335	—	47	1	no	—
217	#1481	—	47	1	no	—
218	#1480	—	47	1	no	—
219	#1451	D₄₇	1	1	yes	characteristic, complemented
220	C₂×C₄₇	—	2	2	no	—
221	C₂×C₄₇	#2935	1	1	yes	characteristic
222	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
223	C₂×C₄₇	#2957	1	1	yes	characteristic
224	D₄₇	—	8	2	no	—
225	C₂×#131	—	94	1	no	—
226	#533	—	47	1	no	—
227	#532	—	47	1	no	—
228	#498	—	47	1	no	—
229	#492	—	47	1	no	—
230	#487	—	47	1	no	—
231	#486	—	47	1	no	—
232	#465	—	47	2	no	—
233	#465	—	47	2	no	—
234	#446	—	47	2	no	—
235	#446	—	94	2	no	—
236	C₈×Q₈	—	47	2	no	—
237	C₄×SD₁₆	—	47	2	no	—
238	C₄×SD₁₆	—	47	2	no	—
239	#436	—	47	2	no	—
240	#435	—	94	2	no	—
241	C₈×D₄	—	47	2	no	—
242	#431	C₂×D₄₇	1	1	yes	characteristic
243	#424	—	94	1	no	—
244	C₂×C₄⋊C₈	—	47	1	no	—
245	C₂×C₄⋊C₈	—	47	1	no	—
246	#408	—	94	1	no	—
247	#405	—	94	1	no	—
248	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
250	#335	—	47	1	no	—
251	#335	—	47	1	no	—
252	#335	—	47	1	no	—
253	#335	—	47	1	no	—
254	Q₈⋊C₈	—	47	2	no	—
255	Q₈⋊C₈	—	47	2	no	—
256	D₄⋊C₈	—	47	2	no	—
257	D₄⋊C₈	—	47	2	no	—
258	#322	C₂×D₄₇	1	2	yes	—
259	#322	C₂×D₄₇	1	2	yes	—
260	C₄₇	#18071	1	1	yes	characteristic, complemented, Sylow
261	C₂×#41	—	94	1	no	—
262	C₂×SD₁₆	—	47	2	no	—
263	C₂×SD₁₆	—	47	2	no	—
264	#131	—	188	4	no	—
265	C₂×M₁₆	—	94	2	no	—
266	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
267	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
268	C₂²×C₈	—	94	1	no	—
269	C₂²×C₈	—	94	1	no	—
270	C₂²×C₈	—	94	2	no	—
271	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
272	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
273	C₄⋊Q₈	—	47	1	no	—
274	C₄⋊Q₈	—	47	1	no	—
275	C₄⋊Q₈	—	47	1	no	—
276	#127	—	47	1	no	—
277	#125	—	94	1	no	—
278	#124	—	94	1	no	—
279	C₂²⋊Q₈	—	47	2	no	—
280	C₂²⋊Q₈	—	94	1	no	—
281	#121	—	47	2	no	—
282	#121	—	94	1	no	—
283	C₄×Q₈	—	47	2	no	—
284	C₄×Q₈	—	94	1	no	—
285	C₄×D₄	—	47	2	no	—
286	C₄×D₄	—	94	1	no	—
287	#117	—	94	1	no	—
288	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
289	#106	—	47	2	no	—
290	#106	—	47	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	47	1	no	—
293	C₄⋊C₈	—	47	1	no	—
294	C₄⋊C₈	—	47	1	no	—
295	C₄⋊C₈	—	47	1	no	—
296	C₄⋊C₈	—	94	2	no	—
297	C₄⋊C₈	—	94	2	no	—
298	C₄⋊C₈	—	94	1	no	—
299	C₄⋊C₈	—	94	1	no	—
300	#103	—	47	2	no	—
301	#103	—	47	2	no	—
302	#102	—	47	2	no	—
303	#102	—	47	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	94	2	no	—
306	C₂²⋊C₈	—	94	2	no	—
307	#97	—	94	2	no	—
308	#97	D₁₈₈	1	2	yes	—
309	C₄×C₈	—	94	2	no	—
310	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
311	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₄₇	1	2	yes	—
313	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₄₇	1	2	yes	—
316	#41	—	188	2	no	—
317	#41	—	188	2	no	—
318	C₂×Q₈	—	47	2	no	—
319	C₂×Q₈	—	94	1	no	—
320	C₂×Q₈	—	94	1	no	—
321	C₂×D₄	—	47	2	no	—
322	C₂×D₄	—	94	2	no	—
323	C₂×D₄	—	94	1	no	—
324	C₂×D₄	—	94	1	no	—
325	C₂²×C₄	—	94	2	no	—
326	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
328	C₂²×C₄	#10625350	1	1	yes	characteristic
329	SD₁₆	—	94	4	no	—
330	SD₁₆	—	188	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	188	4	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	—	94	1	no	—
341	C₂×C₈	—	188	4	no	—
342	C₂×C₈	—	188	2	no	—
343	C₂×C₈	—	188	2	no	—
344	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
345	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
346	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
347	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
348	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
349	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
350	C₄⋊C₄	—	47	2	no	—
351	C₄⋊C₄	—	47	2	no	—
352	C₄⋊C₄	—	94	2	no	—
353	C₄⋊C₄	—	94	1	no	—
354	C₄⋊C₄	—	94	1	no	—
355	C₄⋊C₄	—	94	1	no	—
356	C₄⋊C₄	—	94	1	no	—
357	C₄⋊C₄	—	94	2	no	—
358	C₂²⋊C₄	—	94	2	no	—
359	C₂²⋊C₄	—	94	2	no	—
360	C₂²⋊C₄	—	94	2	no	—
361	C₄²	—	94	2	no	—
362	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
363	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
364	C₄²	#10625350	1	1	yes	characteristic
365	C₄²	C₂³×D₄₇	1	1	yes	characteristic
366	C₂³	—	94	2	no	—
367	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
368	Q₈	—	94	2	no	—
369	Q₈	—	94	2	no	—
370	Q₈	—	376	1	no	—
371	Q₈	—	188	2	no	—
372	D₄	—	94	2	no	—
373	D₄	—	94	2	no	—
374	D₄	—	376	1	no	—
375	D₄	—	188	4	no	—
376	D₄	—	188	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	94	2	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	—	188	2	no	—
385	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
386	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
387	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
388	C₂×C₄	#13094052	1	2	yes	—
389	C₂×C₄	#13094057	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
392	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	4	2	no	—
399	C₈	—	188	1	no	—
400	C₈	—	188	1	no	—
401	C₈	—	188	1	no	—
402	C₈	—	188	1	no	—
403	C₈	#13094032	1	2	yes	complemented
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	188	2	no	—
407	C₂²	—	188	2	no	—
408	C₂²	—	188	2	no	—
409	C₂²	#15689225	1	2	yes	—
410	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	188	2	no	—
415	C₄	—	188	2	no	—
416	C₄	—	188	2	no	—
417	C₄	#15689225	1	2	yes	—
418	C₄	C₂×#13094032	1	1	yes	characteristic
419	C₄	#15689889	1	1	yes	characteristic
420	C₄	C₂×#13094052	1	1	yes	characteristic
421	C₄	C₂×#13094057	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	376	2	no	—
424	C₂	#20252134	1	1	yes	characteristic
425	C₂	C₂×#15689225	1	1	yes	characteristic
426	C₂	#20252306	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1451	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689673	C₂²
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1451	D₄₇
hypocenter	C₄₇	#18071
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #1451

Complements

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

N	H ≅ G/N	type
2. #20252335	C₂	semidirect
4. #20242292	C₂	semidirect
5. #20242268	C₂	semidirect
6. #20242247	C₂	semidirect
7. #20242202	C₂	semidirect
8. C₂×#15688876	C₂	semidirect
9. #20241792	C₂	semidirect
11. C₄₇×#1451	C₂	semidirect
185. C₈×C₄₇	#131	semidirect
219. #1451	D₄₇	semidirect
260. C₄₇	#18071	semidirect
403. C₈	#13094032	semidirect

Maximal subgroups

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

subgroup	index
#20253947	2
#20252335	2
#20252134	2
#20242292	2
#20242268	2
#20242247	2
#20242202	2
C₂×#15688876	2
#20241792	2
#20241788	2
C₄₇×#1451	2
#18071	47