Subgroups — #26204281

Order 12032.

750 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	#20254529	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254326	C₂	1	1	yes	maximal, characteristic
3	#20253770	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253764	C₂	1	1	yes	maximal, characteristic
5	C₂×#15689470	C₂	1	1	yes	maximal, characteristic
6	#20243051	C₂	1	2	yes	maximal, complemented
7	#20243044	C₂	1	2	yes	maximal, complemented
8	#20243001	C₂	1	2	yes	maximal, complemented
9	#20242991	C₂	1	2	yes	maximal, complemented
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094024	C₂²	1	1	yes	characteristic
13	C₂×#13094021	C₂²	1	1	yes	characteristic
14	#15689519	C₂²	1	2	yes	complemented
15	#15689497	C₂²	1	2	yes	—
16	#15689493	—	2	2	no	—
17	#15689489	—	2	2	no	—
18	#15689475	C₂²	1	2	yes	complemented
19	#15689475	C₂²	1	2	yes	complemented
20	#15689473	C₂²	1	2	yes	complemented
21	#15689471	C₂²	1	2	yes	—
22	#15689471	C₂²	1	2	yes	—
23	#15689471	C₂²	1	2	yes	—
24	#15689470	—	2	2	no	—
25	#15689470	C₂²	1	2	yes	—
26	#15689470	C₂²	1	2	yes	—
27	#15689451	—	2	2	no	—
28	#15689408	—	2	2	no	—
29	#15689323	—	2	2	no	—
30	#15689273	—	2	2	no	—
31	#15689176	C₂²	1	1	yes	characteristic
32	#15689131	—	2	2	no	—
33	#15689127	—	2	2	no	—
34	C₂×#13093946	—	2	2	no	—
35	C₄×#10625329	C₂²	1	1	yes	characteristic
36	#15688845	C₂²	1	2	yes	complemented
37	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
38	C₄₇×#533	C₂²	1	1	yes	characteristic
39	C₄₇×#533	C₂²	1	1	yes	characteristic
40	C₄₇×#500	C₂²	1	1	yes	characteristic, complemented
41	C₄₇×#494	C₂²	1	1	yes	characteristic, complemented
42	C₄₇×#487	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×#487	C₂²	1	1	yes	characteristic, complemented
44	C₄₇×#467	—	2	2	no	—
45	C₄×Q₁₆×C₄₇	—	2	2	no	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂²×Dic₉₄	—	2	1	no	—
48	C₂²×D₁₈₈	—	2	1	no	—
49	C₂²×D₁₈₈	—	2	1	no	—
50	C₂²×D₁₈₈	—	2	1	no	—
51	C₂×#10625336	—	2	4	no	—
52	C₂×#10625329	D₄	1	2	yes	—
53	#13094024	—	2	1	no	—
54	#13094024	—	2	1	no	—
55	#13094024	—	2	1	no	—
56	#13094024	C₂³	1	2	yes	—
57	#13094021	—	2	1	no	—
58	#13094021	—	2	1	no	—
59	#13094021	—	2	1	no	—
60	#13094021	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₄₇	—	2	1	no	—
62	C₂×C₄⋊Dic₄₇	—	2	1	no	—
63	#13093955	—	2	4	no	—
64	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
65	#13093948	—	2	4	no	—
66	#13093947	—	2	4	no	—
67	#13093947	—	2	4	no	—
68	#13093946	—	2	4	no	—
69	#13093946	—	2	4	no	—
70	#13093944	—	2	4	no	—
71	#13093944	—	2	4	no	—
72	#13093944	—	2	4	no	—
73	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
74	#13093935	D₄	1	2	yes	—
75	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
76	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
77	C₂×Q₁₆×C₄₇	—	2	2	no	—
78	C₂²×C₈×C₄₇	D₄	1	2	yes	—
79	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
83	#125×C₄₇	—	2	1	no	—
84	#125×C₄₇	—	2	1	no	—
85	C₂²⋊Q₈×C₄₇	—	2	1	no	—
86	C₂²⋊Q₈×C₄₇	—	2	1	no	—
87	C₂²⋊Q₈×C₄₇	—	2	1	no	—
88	C₂²⋊Q₈×C₄₇	—	2	1	no	—
89	C₄×Q₈×C₄₇	—	2	1	no	—
90	C₄×Q₈×C₄₇	—	2	1	no	—
91	C₄×Q₈×C₄₇	—	2	1	no	—
92	C₄×Q₈×C₄₇	—	2	1	no	—
93	#117×C₄₇	—	2	1	no	—
94	#117×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	#107×C₄₇	—	2	2	no	—
97	#103×C₄₇	—	2	2	no	—
98	#103×C₄₇	—	2	2	no	—
99	C₄×C₈×C₄₇	D₄	1	2	yes	—
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂³×D₄₇	—	4	1	no	—
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×Q₈×C₄₇	—	2	1	no	—
106	C₂×Q₈×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×Dic₄₇	—	4	1	no	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	2	2	no	—
113	C₂×D₁₈₈	—	2	2	no	—
114	C₂×D₁₈₈	—	4	4	no	—
115	C₂×D₁₈₈	—	4	4	no	—
116	C₂×D₁₈₈	—	4	1	no	—
117	C₂×D₁₈₈	—	4	1	no	—
118	C₂×D₁₈₈	—	4	1	no	—
119	C₂×D₁₈₈	—	8	2	no	—
120	C₂×Dic₉₄	—	2	2	no	—
121	C₂×Dic₉₄	—	4	4	no	—
122	C₂×Dic₉₄	—	4	1	no	—
123	Q₁₆×C₄₇	—	4	4	no	—
124	C₂×C₈×C₄₇	—	4	2	no	—
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	—	2	1	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	4	1	no	—
136	C₄⋊C₄×C₄₇	—	4	1	no	—
137	C₄⋊C₄×C₄₇	—	4	1	no	—
138	C₄⋊C₄×C₄₇	—	4	1	no	—
139	C₂²⋊C₄×C₄₇	—	4	1	no	—
140	C₂²⋊C₄×C₄₇	—	4	1	no	—
141	C₄²×C₄₇	—	4	1	no	—
142	C₄²×C₄₇	—	4	1	no	—
143	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
147	#10625336	—	8	4	no	—
148	C₄⋊Dic₄₇	—	2	2	no	—
149	C₄⋊Dic₄₇	—	2	2	no	—
150	C₄⋊Dic₄₇	—	4	1	no	—
151	C₄⋊Dic₄₇	—	4	1	no	—
152	#10625329	—	2	4	no	—
153	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
155	C₂³×C₄₇	#127	1	1	yes	characteristic
156	C₂²×D₄₇	—	4	2	no	—
157	C₂²×D₄₇	—	8	2	no	—
158	C₂²×D₄₇	—	8	2	no	—
159	C₂²×D₄₇	—	8	2	no	—
160	Q₈×C₄₇	—	4	2	no	—
161	Q₈×C₄₇	—	4	2	no	—
162	Q₈×C₄₇	—	4	2	no	—
163	Q₈×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
172	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
173	C₂×C₄×C₄₇	#135	1	4	yes	—
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	8	2	no	—
179	D₁₈₈	—	4	4	no	—
180	D₁₈₈	—	4	4	no	—
181	D₁₈₈	—	4	4	no	—
182	D₁₈₈	—	8	2	no	—
183	D₁₈₈	—	8	2	no	—
184	D₁₈₈	—	8	2	no	—
185	Dic₉₄	—	4	4	no	—
186	Dic₉₄	—	8	2	no	—
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₄₇⋊C₈	—	2	4	no	—
190	C₄₇⋊C₈	—	2	4	no	—
191	#19637	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	#495	1	2	yes	—
195	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
196	C₂×D₄₇	—	8	2	no	—
197	C₂×D₄₇	—	8	2	no	—
198	C₂×D₄₇	—	8	2	no	—
199	C₂×D₄₇	—	16	4	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	8	1	no	—
203	C₄×C₄₇	—	8	1	no	—
204	C₄×C₄₇	—	8	1	no	—
205	C₄×C₄₇	—	8	1	no	—
206	C₄×C₄₇	#495	1	2	yes	—
207	C₄×C₄₇	C₂×#135	1	2	yes	—
208	C₄×C₄₇	#575	1	2	yes	—
209	C₄×C₄₇	#577	1	2	yes	—
210	Dic₄₇	—	8	2	no	—
211	#3229	—	47	1	no	—
212	#3208	—	47	1	no	—
213	#3170	D₄₇	1	1	yes	characteristic, complemented
214	#3139	—	47	1	no	—
215	#3138	—	47	1	no	—
216	C₂×#486	—	47	1	no	—
217	#1720	—	47	2	no	—
218	#1719	—	47	2	no	—
219	#1711	—	47	2	no	—
220	#1708	—	47	2	no	—
221	C₈×M₁₆	—	47	1	no	—
222	C₂×C₄₇	—	2	2	no	—
223	C₂×C₄₇	C₂×#495	1	1	yes	characteristic
224	C₂×C₄₇	#3153	1	1	yes	characteristic
225	C₂×C₄₇	#3154	1	1	yes	characteristic
226	D₄₇	—	16	2	no	—
227	#533	C₂×D₄₇	1	1	yes	characteristic
228	#533	C₂×D₄₇	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	—	47	1	no	—
230	C₂×#127	—	47	1	no	—
231	#500	C₂×D₄₇	1	1	yes	characteristic, complemented
232	#498	—	47	2	no	—
233	#494	C₂×D₄₇	1	1	yes	characteristic, complemented
234	#492	—	47	2	no	—
235	#491	—	94	2	no	—
236	#490	—	94	2	no	—
237	#487	—	47	2	no	—
238	#487	—	47	2	no	—
239	#487	—	47	2	no	—
240	#487	C₂×D₄₇	1	1	yes	characteristic, complemented
241	#487	C₂×D₄₇	1	1	yes	characteristic, complemented
242	#486	—	47	2	no	—
243	#486	—	47	2	no	—
244	#486	—	47	2	no	—
245	#486	—	47	2	no	—
246	#486	—	47	2	no	—
247	#486	—	94	2	no	—
248	#483	—	94	2	no	—
249	#475	—	94	2	no	—
250	#467	—	2	2	no	—
251	#460	—	94	2	no	—
252	#450	—	94	2	no	—
253	C₄×Q₁₆	—	2	2	no	—
254	#431	—	47	1	no	—
255	#419	—	94	2	no	—
256	#418	—	94	2	no	—
257	C₂×#102	—	94	2	no	—
258	C₄×M₁₆	—	47	1	no	—
259	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
260	#322	—	47	2	no	—
261	C₈²	—	47	2	no	—
262	C₄₇	#19637	1	1	yes	characteristic, complemented, Sylow
263	C₂²×Q₈	—	94	1	no	—
264	C₂²×D₄	—	94	1	no	—
265	C₂²×D₄	—	94	1	no	—
266	C₂²×D₄	—	94	1	no	—
267	C₂×Q₁₆	—	2	2	no	—
268	C₂×SD₁₆	—	94	4	no	—
269	C₂×M₁₆	—	47	2	no	—
270	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
271	C₄⋊Q₈	—	47	2	no	—
272	C₄⋊Q₈	—	94	1	no	—
273	C₄⋊Q₈	—	94	1	no	—
274	C₄⋊Q₈	—	94	1	no	—
275	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
276	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
277	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
278	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
279	#127	—	47	2	no	—
280	#127	—	94	1	no	—
281	#127	—	94	1	no	—
282	#127	—	94	1	no	—
283	#125	—	2	1	no	—
284	#125	—	2	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	C₂²⋊Q₈	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	#117	—	2	1	no	—
294	#117	—	2	1	no	—
295	C₂×C₄⋊C₄	—	94	1	no	—
296	C₂×C₄⋊C₄	—	94	1	no	—
297	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
298	#107	—	2	2	no	—
299	#106	—	94	4	no	—
300	C₄⋊C₈	—	47	2	no	—
301	#103	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	94	4	no	—
304	#103	—	94	4	no	—
305	#103	—	94	4	no	—
306	#102	—	94	4	no	—
307	#102	—	94	4	no	—
308	#102	—	94	4	no	—
309	#102	—	94	4	no	—
310	#102	—	94	4	no	—
311	C₂²⋊C₈	—	47	2	no	—
312	#97	—	47	2	no	—
313	C₄×C₈	—	47	2	no	—
314	C₄×C₈	—	47	2	no	—
315	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
316	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
318	C₂⁴	—	188	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	94	2	no	—
324	C₂×Q₈	—	188	4	no	—
325	C₂×Q₈	—	188	1	no	—
326	C₂×D₄	—	94	2	no	—
327	C₂×D₄	—	94	2	no	—
328	C₂×D₄	—	94	2	no	—
329	C₂×D₄	—	376	2	no	—
330	C₂×D₄	—	188	4	no	—
331	C₂×D₄	—	188	1	no	—
332	C₂×D₄	—	188	1	no	—
333	C₂×D₄	—	188	1	no	—
334	C₂×D₄	—	188	4	no	—
335	C₂²×C₄	—	188	1	no	—
336	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
339	Q₁₆	—	4	4	no	—
340	SD₁₆	—	376	4	no	—
341	M₁₆	—	94	4	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	47	4	no	—
344	C₂×C₈	—	47	4	no	—
345	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
346	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	94	2	no	—
360	C₄⋊C₄	—	94	2	no	—
361	C₄⋊C₄	—	188	1	no	—
362	C₄⋊C₄	—	188	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	4	1	no	—
367	C₄²	D₄×D₄₇	1	1	yes	characteristic
368	C₄²	D₄×D₄₇	1	1	yes	characteristic
369	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
370	C₄²	C₂³×D₄₇	1	1	yes	characteristic
371	C₂³	—	376	2	no	—
372	C₂³	—	376	2	no	—
373	C₂³	—	376	2	no	—
374	C₂³	—	188	2	no	—
375	C₂³	#13094020	1	1	yes	characteristic
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	376	2	no	—
381	Q₈	—	188	4	no	—
382	D₄	—	376	2	no	—
383	D₄	—	376	2	no	—
384	D₄	—	376	2	no	—
385	D₄	—	188	4	no	—
386	D₄	—	188	4	no	—
387	D₄	—	188	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	376	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	#13094020	1	1	yes	characteristic
397	C₂×C₄	#13094020	1	1	yes	characteristic
398	C₂×C₄	#13094020	1	1	yes	characteristic
399	C₂×C₄	#13094047	1	4	yes	—
400	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	2	no	—
405	C₈	—	94	4	no	—
406	C₈	—	94	4	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	376	2	no	—
410	C₂²	—	376	2	no	—
411	C₂²	—	376	2	no	—
412	C₂²	—	752	4	no	—
413	C₂²	#15689508	1	2	yes	—
414	C₂²	C₂×#13094020	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	1	no	—
421	C₄	—	376	2	no	—
422	C₄	#15689508	1	2	yes	—
423	C₄	C₂×#13094047	1	2	yes	—
424	C₄	#15689921	1	2	yes	—
425	C₄	#15689930	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	752	2	no	—
428	C₂	C₂×#15689508	1	1	yes	characteristic
429	C₂	#20253856	1	1	yes	characteristic
430	C₂	#20253865	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3170	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	C₂×#13094021	C₂²
hypercenter	#3170	D₄₇
hypocenter	C₄₇	#19637
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3170

Complements

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

N	H ≅ G/N	type
1. #20254529	C₂	semidirect
3. #20253770	C₂	semidirect
6. #20243051	C₂	semidirect
7. #20243044	C₂	semidirect
8. #20243001	C₂	semidirect
9. #20242991	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
11. C₄₇×#3170	C₂	semidirect
14. #15689519	C₂²	semidirect
18. #15689475	C₂²	semidirect
19. #15689475	C₂²	semidirect
20. #15689473	C₂²	semidirect
36. #15688845	C₂²	semidirect
37. C₈×C₄₇⋊C₈	C₂²	semidirect
40. C₄₇×#500	C₂²	semidirect
41. C₄₇×#494	C₂²	semidirect
42. C₄₇×#487	C₂²	semidirect
43. C₄₇×#487	C₂²	semidirect
213. #3170	D₄₇	semidirect
231. #500	C₂×D₄₇	semidirect
233. #494	C₂×D₄₇	semidirect
240. #487	C₂×D₄₇	semidirect
241. #487	C₂×D₄₇	semidirect
262. C₄₇	#19637	semidirect

Maximal subgroups

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

subgroup	index
#20254529	2
#20254326	2
#20253770	2
#20253764	2
C₂×#15689470	2
#20243051	2
#20243044	2
#20243001	2
#20242991	2
C₈×#10625329	2
C₄₇×#3170	2
#19637	47