Subgroups — #26200209

Order 12032.

638 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	#500×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253200	C₂	1	2	yes	maximal
3	C₈×#10625352	C₂	1	1	yes	maximal, characteristic
4	#20242793	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242791	C₂	1	2	yes	maximal, complemented
6	#20242789	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242787	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242785	C₂	1	2	yes	maximal, complemented
9	#20242145	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242067	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1675	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊Q₈×D₄₇	C₂²	1	2	yes	—
13	C₄×#10625352	C₂²	1	1	yes	characteristic
14	#15689528	C₂²	1	1	yes	characteristic
15	#15689527	—	2	1	no	—
16	#15689527	—	2	1	no	—
17	#15689526	C₂²	1	2	yes	—
18	#15689419	C₂²	1	2	yes	—
19	#15689415	C₂²	1	2	yes	—
20	#15689413	C₂²	1	2	yes	—
21	#15689407	—	2	2	no	—
22	#15689401	—	2	2	no	—
23	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
24	#15689247	C₂²	1	1	yes	characteristic
25	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₄₇	—	2	1	no	—
27	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
28	#15689175	C₂²	1	1	yes	characteristic
29	#15689173	—	2	1	no	—
30	#15689162	—	2	2	no	—
31	#107×D₄₇	—	2	1	no	—
32	#107×D₄₇	—	2	1	no	—
33	#15689145	C₂²	1	2	yes	—
34	#15689121	—	2	2	no	—
35	C₂×C₈×Dic₄₇	—	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	#15688872	C₂²	1	2	yes	—
40	#15688871	C₂²	1	2	yes	—
41	#15688871	C₂²	1	2	yes	—
42	C₄₇×#500	C₂²	1	1	yes	characteristic
43	C₄₇×#476	C₂²	1	2	yes	—
44	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	1	yes	characteristic
46	C₄₇×#333	C₂²	1	2	yes	—
47	C₂×#10625352	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₄₇	—	2	2	no	—
49	C₂×#10625324	—	2	2	no	—
50	C₂²×C₄₇⋊C₈	—	2	1	no	—
51	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
52	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
53	#13094024	C₂³	1	2	yes	—
54	#13094023	—	2	2	no	—
55	#13094023	—	2	2	no	—
56	#13094022	—	2	2	no	—
57	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
58	#13093989	D₄	1	1	yes	characteristic
59	D₄×Dic₄₇	D₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₄₇	—	2	1	no	—
61	(C₂²⋊D₄₇)⋊C₄	—	2	1	no	—
62	#13093982	D₄	1	1	yes	characteristic
63	#13093980	—	2	1	no	—
64	C₄⋊C₄×D₄₇	—	2	2	no	—
65	C₄⋊C₄×D₄₇	—	2	2	no	—
66	C₂×C₄×Dic₄₇	—	2	1	no	—
67	C₄²×D₄₇	C₂³	1	1	yes	characteristic
68	#13093958	—	2	1	no	—
69	#13093958	—	2	1	no	—
70	#13093958	—	2	2	no	—
71	#13093957	—	2	2	no	—
72	#13093957	—	2	2	no	—
73	#13093957	—	2	2	no	—
74	#13093955	—	2	2	no	—
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
77	Dic₄₇⋊C₈	—	2	1	no	—
78	Dic₄₇⋊C₈	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	1	no	—
80	#13093949	—	2	2	no	—
81	#13093947	—	2	2	no	—
82	#13093945	—	2	2	no	—
83	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
84	(C₂×D₄₇)⋊C₈	—	2	1	no	—
85	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₈×Dic₄₇	—	2	1	no	—
87	C₈×Dic₄₇	—	2	1	no	—
88	C₈×Dic₄₇	—	2	1	no	—
89	C₈×Dic₄₇	D₄	1	1	yes	characteristic
90	C₈×Dic₄₇	D₄	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	—	2	1	no	—
92	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
93	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
94	#107×C₄₇	—	2	1	no	—
95	#107×C₄₇	—	2	1	no	—
96	#106×C₄₇	—	2	2	no	—
97	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
98	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
99	#102×C₄₇	—	2	2	no	—
100	C₂²⋊C₈×C₄₇	—	2	1	no	—
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂×C₂²⋊D₄₇	—	2	1	no	—
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	1	no	—
108	Q₈×D₄₇	—	8	4	no	—
109	#10625352	—	2	2	no	—
110	#10625352	Q₁₆	1	4	yes	—
111	C₂×C₄×D₄₇	—	4	2	no	—
112	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
115	C₂×Dic₉₄	—	2	2	no	—
116	C₂×Dic₉₄	—	4	2	no	—
117	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	4	2	no	—
121	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²⋊C₄×C₄₇	—	2	1	no	—
127	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂²⋊Dic₄₇	—	2	1	no	—
129	(C₂×D₄₇)⋊C₄	—	2	1	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
133	Dic₄₇⋊C₄	—	2	1	no	—
134	Dic₄₇⋊C₄	—	2	1	no	—
135	Dic₄₇⋊C₄	—	4	2	no	—
136	Dic₄₇⋊C₄	—	4	2	no	—
137	C₄×Dic₄₇	—	2	1	no	—
138	C₄×Dic₄₇	—	2	1	no	—
139	C₄×Dic₄₇	—	2	1	no	—
140	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₄₇	#41	1	1	yes	characteristic
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	4	2	no	—
146	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
148	#10625324	—	4	4	no	—
149	C₈×D₄₇	—	2	2	no	—
150	C₈×D₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	2	1	no	—
152	C₂²×D₄₇	#121	1	1	yes	characteristic
153	Q₈×C₄₇	—	8	2	no	—
154	D₄×C₄₇	—	2	1	no	—
155	D₄×C₄₇	C₂×Q₁₆	1	2	yes	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	4	1	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂²⋊D₄₇	—	2	4	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	4	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	#121	1	1	yes	characteristic
170	C₂×Dic₄₇	#121	1	1	yes	characteristic
171	C₂×Dic₄₇	#121	1	1	yes	characteristic
172	C₄×D₄₇	—	2	1	no	—
173	C₄×D₄₇	—	2	1	no	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	8	4	no	—
176	C₄×D₄₇	C₂×Q₁₆	1	2	yes	—
177	C₄×D₄₇	#135	1	2	yes	—
178	Dic₉₄	—	2	1	no	—
179	Dic₉₄	—	8	4	no	—
180	Dic₉₄	—	8	2	no	—
181	Dic₉₄	C₂×Q₁₆	1	2	yes	—
182	C₈×C₄₇	—	2	1	no	—
183	C₈×C₄₇	—	4	2	no	—
184	C₈×C₄₇	—	4	1	no	—
185	C₈×C₄₇	#137	1	2	yes	—
186	C₄₇⋊C₈	—	2	1	no	—
187	C₄₇⋊C₈	—	4	2	no	—
188	C₄₇⋊C₈	—	4	1	no	—
189	C₄₇⋊C₈	#137	1	2	yes	—
190	#19272	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	4	1	no	—
193	C₂²×C₄₇	—	4	1	no	—
194	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
195	C₂×D₄₇	—	2	1	no	—
196	C₂×D₄₇	—	2	1	no	—
197	C₂×D₄₇	#467	1	2	yes	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	4	1	no	—
200	C₄×C₄₇	—	8	2	no	—
201	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
202	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
203	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
204	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
205	Dic₄₇	—	2	1	no	—
206	Dic₄₇	—	2	2	no	—
207	Dic₄₇	—	4	1	no	—
208	Dic₄₇	—	8	2	no	—
209	Dic₄₇	#467	1	2	yes	—
210	Dic₄₇	#472	1	2	yes	—
211	C₂×#500	—	47	1	no	—
212	#3079	—	47	2	no	—
213	C₈×#41	—	47	1	no	—
214	#1676	—	47	1	no	—
215	#1676	—	47	1	no	—
216	#1676	—	47	2	no	—
217	#1675	—	47	2	no	—
218	#1675	—	47	1	no	—
219	#1675	D₄₇	1	1	yes	characteristic, complemented
220	#1567	—	47	1	no	—
221	#1548	—	47	2	no	—
222	C₂×C₄₇	—	4	2	no	—
223	C₂×C₄₇	#3039	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#467	1	1	yes	characteristic
225	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
226	D₄₇	—	2	2	no	—
227	C₂×C₄⋊Q₈	—	47	2	no	—
228	C₄×#41	—	47	1	no	—
229	#500	—	47	2	no	—
230	#500	—	47	1	no	—
231	#500	—	94	1	no	—
232	#500	—	94	1	no	—
233	#500	C₂×D₄₇	1	1	yes	characteristic
234	#477	—	47	2	no	—
235	#477	—	47	2	no	—
236	#476	—	47	2	no	—
237	#476	C₂×D₄₇	1	2	yes	—
238	#475	—	94	2	no	—
239	#474	—	94	2	no	—
240	C₈×Q₈	—	47	1	no	—
241	C₈×Q₈	—	47	1	no	—
242	C₈×D₄	—	47	1	no	—
243	C₈×D₄	—	94	1	no	—
244	C₈×D₄	—	94	1	no	—
245	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
246	#431	—	47	1	no	—
247	#431	—	94	1	no	—
248	#428	—	94	2	no	—
249	C₂×#107	—	94	1	no	—
250	C₂×#107	—	94	1	no	—
251	#423	—	47	2	no	—
252	#417	—	94	2	no	—
253	C₂×C₄×C₈	—	47	1	no	—
254	C₂×C₄×C₈	—	94	1	no	—
255	#335	—	47	2	no	—
256	#335	—	47	1	no	—
257	#335	C₂×D₄₇	1	1	yes	characteristic
258	#333	—	47	2	no	—
259	#333	—	47	2	no	—
260	#333	—	47	2	no	—
261	#333	C₂×D₄₇	1	2	yes	—
262	C₄₇	#19272	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	47	1	no	—
264	C₂²×Q₈	—	94	2	no	—
265	C₂×M₁₆	—	94	2	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	—	47	1	no	—
269	C₂²×C₈	—	94	1	no	—
270	C₄⋊Q₈	—	47	2	no	—
271	C₄⋊Q₈	—	94	2	no	—
272	C₄⋊Q₈	—	94	2	no	—
273	C₄⋊Q₈	—	94	2	no	—
274	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
275	C₄×Q₈	—	47	1	no	—
276	C₄×Q₈	—	47	1	no	—
277	C₄×D₄	—	47	1	no	—
278	C₄×D₄	—	94	1	no	—
279	C₄×D₄	—	94	1	no	—
280	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
281	#117	—	47	1	no	—
282	#117	—	94	1	no	—
283	C₂×C₄⋊C₄	—	94	2	no	—
284	C₂×C₄⋊C₄	—	94	2	no	—
285	C₂×C₄²	—	47	1	no	—
286	C₂×C₄²	—	94	1	no	—
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	94	2	no	—
290	#107	—	94	2	no	—
291	#107	—	94	2	no	—
292	#107	—	94	2	no	—
293	#107	—	94	1	no	—
294	#107	—	94	1	no	—
295	#106	—	2	2	no	—
296	#106	—	94	2	no	—
297	C₄⋊C₈	—	47	1	no	—
298	C₄⋊C₈	—	47	2	no	—
299	C₄⋊C₈	—	94	2	no	—
300	C₄⋊C₈	—	94	1	no	—
301	C₄⋊C₈	—	94	1	no	—
302	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
303	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
304	#103	—	94	2	no	—
305	#103	—	94	2	no	—
306	#102	—	2	2	no	—
307	#102	—	94	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	94	1	no	—
310	C₂²⋊C₈	—	94	1	no	—
311	C₄×C₈	—	47	1	no	—
312	C₄×C₈	—	47	1	no	—
313	C₄×C₈	—	47	1	no	—
314	C₄×C₈	—	94	1	no	—
315	C₄×C₈	—	94	1	no	—
316	C₄×C₈	—	94	1	no	—
317	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
318	#41	—	47	4	no	—
319	#41	—	94	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	47	1	no	—
322	C₂×Q₈	—	94	2	no	—
323	C₂×Q₈	—	376	4	no	—
324	C₂×Q₈	—	188	2	no	—
325	C₂×D₄	—	94	1	no	—
326	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	47	1	no	—
329	C₂²×C₄	—	47	1	no	—
330	C₂²×C₄	—	47	1	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	—	94	1	no	—
333	C₂²×C₄	—	188	2	no	—
334	M₁₆	—	188	4	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	47	1	no	—
339	C₂×C₈	—	47	1	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	94	1	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	188	2	no	—
345	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
346	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	47	1	no	—
350	C₄⋊C₄	—	94	1	no	—
351	C₄⋊C₄	—	94	1	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	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	94	1	no	—
359	C₂²⋊C₄	—	94	1	no	—
360	C₄²	—	47	1	no	—
361	C₄²	—	47	1	no	—
362	C₄²	—	47	1	no	—
363	C₄²	—	94	1	no	—
364	C₄²	—	94	1	no	—
365	C₄²	—	94	1	no	—
366	C₄²	C₂³×D₄₇	1	1	yes	characteristic
367	C₂³	—	2	1	no	—
368	C₂³	—	47	1	no	—
369	Q₈	—	8	2	no	—
370	Q₈	—	47	2	no	—
371	Q₈	—	94	1	no	—
372	Q₈	—	376	2	no	—
373	Q₈	—	376	4	no	—
374	D₄	—	2	1	no	—
375	D₄	—	94	4	no	—
376	D₄	Q₁₆×D₄₇	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	47	1	no	—
382	C₂×C₄	—	47	1	no	—
383	C₂×C₄	—	47	2	no	—
384	C₂×C₄	—	47	2	no	—
385	C₂×C₄	—	47	1	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	4	no	—
388	C₂×C₄	—	94	1	no	—
389	C₂×C₄	—	94	1	no	—
390	C₂×C₄	—	94	1	no	—
391	C₂×C₄	—	94	1	no	—
392	C₂×C₄	—	376	4	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	1	no	—
401	C₈	—	47	2	no	—
402	C₈	—	94	1	no	—
403	C₈	—	188	2	no	—
404	C₈	—	188	1	no	—
405	C₈	#13094053	1	2	yes	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	47	2	no	—
410	C₂²	—	94	1	no	—
411	C₂²	—	94	1	no	—
412	C₂²	#121×D₄₇	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	8	2	no	—
416	C₄	—	47	2	no	—
417	C₄	—	47	2	no	—
418	C₄	—	94	2	no	—
419	C₄	—	94	1	no	—
420	C₄	—	376	2	no	—
421	C₄	—	188	1	no	—
422	C₄	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
423	C₄	#135×D₄₇	1	1	yes	characteristic
424	C₄	#137×D₄₇	1	1	yes	characteristic
425	C₄	C₂×#13094053	1	1	yes	characteristic
426	C₂	—	4	2	no	—
427	C₂	—	94	2	no	—
428	C₂	#20252870	1	1	yes	characteristic
429	C₂	#467×D₄₇	1	1	yes	characteristic
430	C₂	#472×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₄₇
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1675	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#10625352	D₄
hypercenter	#1675	D₄₇
hypocenter	C₄₇	#19272
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1675

Complements

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

N	H ≅ G/N	type
1. #500×D₄₇	C₂	semidirect
4. #20242793	C₂	semidirect
5. #20242791	C₂	semidirect
6. #20242789	C₂	semidirect
7. #20242787	C₂	semidirect
8. #20242785	C₂	semidirect
9. #20242145	C₂	semidirect
10. #20242067	C₂	semidirect
11. C₄₇×#1675	C₂	semidirect
219. #1675	D₄₇	semidirect
262. C₄₇	#19272	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
#20253200	2
C₈×#10625352	2
#20242793	2
#20242791	2
#20242789	2
#20242787	2
#20242785	2
#20242145	2
#20242067	2
C₄₇×#1675	2
#19272	47