Subgroups — #26224373

Order 12032.

882 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689489	C₂	1	1	yes	maximal, characteristic
2	#20246113	C₂	1	1	yes	maximal, characteristic
3	#20244354	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244193	C₂	1	1	yes	maximal, characteristic
5	#20244084	C₂	1	2	yes	maximal, complemented
6	#20244070	C₂	1	2	yes	maximal, complemented
7	#20243523	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243216	C₂	1	2	yes	maximal, complemented
9	C₄×#13093944	C₂	1	2	yes	maximal, complemented
10	#20243075	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094021	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
14	#15689489	C₄	1	8	yes	complemented
15	C₂×#13093944	C₂²	1	2	yes	—
16	C₂×#13093944	C₂²	1	2	yes	—
17	C₂×#13093944	C₂²	1	2	yes	—
18	C₂×#13093944	C₂²	1	2	yes	—
19	C₂×#13093935	C₂²	1	1	yes	characteristic
20	C₂×#13093935	C₂²	1	1	yes	characteristic
21	C₂×#13093935	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15689025	C₂²	1	2	yes	—
26	#15689001	—	2	2	no	—
27	#15689001	—	2	2	no	—
28	#15688989	C₂²	1	1	yes	characteristic
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#389	—	2	2	no	—
35	C₄₇×#389	C₂²	1	2	yes	—
36	C₄₇×#387	—	2	2	no	—
37	C₄₇×#384	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#376	C₂²	1	1	yes	characteristic
40	C₂²×D₁₈₈	—	2	2	no	—
41	C₂²×D₁₈₈	C₂³	1	2	yes	—
42	C₂²×C₄×D₄₇	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	#13094021	—	2	2	no	—
48	#13094021	C₂×C₄	1	4	yes	—
49	C₄×D₁₈₈	—	2	4	no	—
50	C₄×D₁₈₈	—	2	4	no	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
53	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
54	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
55	#13093944	—	2	4	no	—
56	#13093944	—	2	4	no	—
57	#13093944	C₂×C₄	1	8	yes	complemented
58	#13093944	C₂×C₄	1	8	yes	complemented
59	#13093935	—	2	2	no	—
60	#13093935	—	2	2	no	—
61	#13093935	C₂×C₄	1	4	yes	complemented
62	C₄×C₄₇⋊C₈	—	2	2	no	—
63	C₄×C₄₇⋊C₈	—	2	2	no	—
64	C₄×C₄₇⋊C₈	—	2	2	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	#125×C₄₇	—	2	2	no	—
67	#125×C₄₇	C₂×C₄	1	4	yes	complemented
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	#95×C₄₇	—	2	2	no	—
78	#95×C₄₇	—	2	2	no	—
79	#95×C₄₇	D₄	1	2	yes	—
80	#95×C₄₇	D₄	1	2	yes	—
81	C₂³×D₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
89	C₂²×Dic₄₇	—	2	2	no	—
90	C₂×D₁₈₈	—	2	2	no	—
91	C₂×D₁₈₈	—	2	2	no	—
92	C₂×D₁₈₈	—	2	2	no	—
93	C₂×D₁₈₈	—	2	2	no	—
94	C₂×D₁₈₈	—	2	2	no	—
95	C₂×D₁₈₈	—	2	8	no	—
96	C₂×D₁₈₈	—	8	2	no	—
97	C₂×D₁₈₈	—	8	2	no	—
98	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
99	C₂×C₄×D₄₇	—	4	4	no	—
100	C₂×C₄×D₄₇	—	8	2	no	—
101	C₂×C₄×D₄₇	—	8	2	no	—
102	C₄⋊C₄×C₄₇	—	2	8	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	2	no	—
105	C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₄⋊C₄×C₄₇	—	8	2	no	—
107	C₄⋊C₄×C₄₇	—	8	2	no	—
108	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
109	C₄²×C₄₇	—	2	1	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	—	8	2	no	—
112	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
113	C₄²×C₄₇	#41	1	2	yes	—
114	C₄²×C₄₇	#41	1	2	yes	—
115	C₄²×C₄₇	#41	1	2	yes	—
116	(C₂×D₄₇)⋊C₄	—	4	4	no	—
117	(C₂×D₄₇)⋊C₄	—	8	2	no	—
118	(C₂×D₄₇)⋊C₄	—	8	2	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₂×C₄₇⋊C₈	—	2	1	no	—
122	C₂×C₄₇⋊C₈	—	2	1	no	—
123	C₂×C₄₇⋊C₈	—	2	1	no	—
124	C₂×C₄₇⋊C₈	—	2	1	no	—
125	C₂×C₄₇⋊C₈	—	2	1	no	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	1	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₄₇⋊C₈	#41	1	2	yes	—
132	C₂×C₄₇⋊C₈	#41	1	2	yes	—
133	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
134	C₂²×D₄₇	—	2	4	no	—
135	C₂²×D₄₇	—	4	2	no	—
136	C₂²×D₄₇	—	4	2	no	—
137	C₂²×D₄₇	—	4	2	no	—
138	C₂²×D₄₇	—	4	2	no	—
139	C₂²×D₄₇	—	4	2	no	—
140	C₂²×D₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
156	C₂×C₄×C₄₇	#124	1	4	yes	—
157	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	D₁₈₈	—	2	4	no	—
167	D₁₈₈	—	2	4	no	—
168	D₁₈₈	—	4	2	no	—
169	D₁₈₈	—	4	2	no	—
170	D₁₈₈	—	8	8	no	—
171	C₄×D₄₇	—	8	8	no	—
172	C₄₇⋊C₈	—	2	2	no	—
173	C₄₇⋊C₈	—	2	2	no	—
174	C₄₇⋊C₈	—	2	2	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	#21652	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
179	C₂²×C₄₇	#532	1	1	yes	characteristic
180	C₂²×C₄₇	#576	1	2	yes	—
181	C₂²×C₄₇	#577	1	2	yes	—
182	C₂×D₄₇	—	4	4	no	—
183	C₂×D₄₇	—	4	4	no	—
184	C₂×D₄₇	—	4	4	no	—
185	C₂×D₄₇	—	8	2	no	—
186	C₂×D₄₇	—	8	2	no	—
187	C₂×D₄₇	—	8	2	no	—
188	C₂×D₄₇	—	8	2	no	—
189	C₄×C₄₇	—	2	4	no	—
190	C₄×C₄₇	—	2	4	no	—
191	C₄×C₄₇	—	4	1	no	—
192	C₄×C₄₇	—	4	1	no	—
193	C₄×C₄₇	—	4	4	no	—
194	C₄×C₄₇	—	8	2	no	—
195	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
196	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
197	C₄×C₄₇	#529	1	1	yes	characteristic
198	C₄×C₄₇	#529	1	1	yes	characteristic
199	Dic₄₇	—	8	2	no	—
200	C₂×#490	—	47	1	no	—
201	#2330	D₄₇	1	1	yes	characteristic, complemented
202	#2328	—	47	1	no	—
203	#1991	—	47	1	no	—
204	#1957	—	47	1	no	—
205	#1936	—	47	2	no	—
206	#1934	—	47	2	no	—
207	#1836	—	47	1	no	—
208	#1762	—	47	2	no	—
209	C₄×#102	—	47	2	no	—
210	#1726	—	47	1	no	—
211	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
212	C₂×C₄₇	#2946	1	2	yes	—
213	C₂×C₄₇	#3136	1	2	yes	—
214	C₂×C₄₇	#3174	1	1	yes	characteristic
215	C₂×C₄₇	#3176	1	1	yes	characteristic
216	D₄₇	—	8	4	no	—
217	C₂×#127	—	47	1	no	—
218	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
219	C₂×C₄×D₄	—	47	2	no	—
220	#490	—	47	8	no	—
221	C₂×#102	—	47	2	no	—
222	C₂×#102	—	47	2	no	—
223	C₂×#102	—	47	2	no	—
224	C₂×#102	—	47	2	no	—
225	C₂×#97	—	47	1	no	—
226	C₂×#97	—	47	1	no	—
227	C₂×#97	—	47	1	no	—
228	C₂×C₄×C₈	—	47	1	no	—
229	C₂×C₄×C₈	—	47	1	no	—
230	C₂×C₄×C₈	—	47	1	no	—
231	#390	—	47	2	no	—
232	#389	—	2	2	no	—
233	#389	C₂×D₄₇	1	2	yes	—
234	#387	—	2	2	no	—
235	#386	—	94	2	no	—
236	#386	—	94	2	no	—
237	#384	C₂×D₄₇	1	1	yes	characteristic
238	#382	—	47	1	no	—
239	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
240	#376	C₂×D₄₇	1	1	yes	characteristic
241	#340	—	47	2	no	—
242	#340	—	47	2	no	—
243	#340	—	47	2	no	—
244	#340	—	47	2	no	—
245	C₄₇	#21652	1	1	yes	characteristic, complemented, Sylow
246	C₂²×D₄	—	47	2	no	—
247	C₂²×D₄	—	94	2	no	—
248	C₂³×C₄	—	94	2	no	—
249	C₂²×C₈	—	47	1	no	—
250	C₂²×C₈	—	47	1	no	—
251	C₂²×C₈	—	47	1	no	—
252	C₂²×C₈	—	47	1	no	—
253	#127	—	47	4	no	—
254	#127	—	94	2	no	—
255	#125	—	2	2	no	—
256	#125	C₄×D₄₇	1	4	yes	complemented
257	C₄×D₄	—	94	4	no	—
258	C₄×D₄	—	94	4	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	47	2	no	—
263	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	94	2	no	—
266	C₂×C₂²⋊C₄	—	94	2	no	—
267	C₂×C₂²⋊C₄	—	94	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
270	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
271	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
272	#102	—	47	8	no	—
273	#102	—	47	8	no	—
274	#102	—	94	4	no	—
275	#102	—	94	4	no	—
276	#97	—	47	4	no	—
277	#97	—	94	2	no	—
278	#97	—	94	2	no	—
279	C₄×C₈	—	94	2	no	—
280	C₄×C₈	—	94	2	no	—
281	C₄×C₈	—	94	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	94	2	no	—
285	#95	C₂²⋊D₄₇	1	2	yes	—
286	#95	C₂²⋊D₄₇	1	2	yes	—
287	C₂⁴	—	94	2	no	—
288	C₂×D₄	—	47	4	no	—
289	C₂×D₄	—	94	8	no	—
290	C₂×D₄	—	94	2	no	—
291	C₂×D₄	—	94	2	no	—
292	C₂×D₄	—	94	2	no	—
293	C₂×D₄	—	94	2	no	—
294	C₂×D₄	—	94	2	no	—
295	C₂×D₄	—	376	2	no	—
296	C₂×D₄	—	376	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	94	2	no	—
300	C₂²×C₄	—	376	2	no	—
301	C₂²×C₄	—	376	2	no	—
302	C₂²×C₄	—	188	4	no	—
303	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
306	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
307	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
308	C₂×C₈	—	47	2	no	—
309	C₂×C₈	—	47	2	no	—
310	C₂×C₈	—	47	2	no	—
311	C₂×C₈	—	47	2	no	—
312	C₂×C₈	—	94	1	no	—
313	C₂×C₈	—	94	1	no	—
314	C₂×C₈	—	94	1	no	—
315	C₂×C₈	—	94	1	no	—
316	C₂×C₈	—	94	1	no	—
317	C₂×C₈	—	94	1	no	—
318	C₂×C₈	—	94	1	no	—
319	C₂×C₈	—	94	1	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	8	2	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₄⋊C₄	—	94	2	no	—
327	C₄⋊C₄	—	94	2	no	—
328	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
329	C₂²⋊C₄	—	376	2	no	—
330	C₂²⋊C₄	—	376	2	no	—
331	C₂²⋊C₄	—	188	4	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	8	2	no	—
335	C₄²	C₂×C₄×D₄₇	1	2	yes	—
336	C₄²	#10625350	1	2	yes	—
337	C₄²	#10625354	1	2	yes	—
338	C₄²	#10625354	1	2	yes	—
339	C₂³	—	94	4	no	—
340	C₂³	—	188	2	no	—
341	C₂³	—	188	2	no	—
342	C₂³	—	188	2	no	—
343	C₂³	—	188	2	no	—
344	C₂³	—	188	2	no	—
345	C₂³	—	188	2	no	—
346	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
347	D₄	—	94	4	no	—
348	D₄	—	94	4	no	—
349	D₄	—	376	8	no	—
350	D₄	—	188	2	no	—
351	D₄	—	188	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	376	8	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	—	188	2	no	—
370	C₂×C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
371	C₂×C₄	#13094013	1	4	yes	—
372	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
374	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
376	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
377	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
378	C₈	—	94	2	no	—
379	C₈	—	94	2	no	—
380	C₈	—	94	2	no	—
381	C₈	—	94	2	no	—
382	C₂²	—	376	2	no	—
383	C₂²	—	376	2	no	—
384	C₂²	—	376	2	no	—
385	C₂²	—	376	2	no	—
386	C₂²	—	188	4	no	—
387	C₂²	—	188	4	no	—
388	C₂²	—	188	4	no	—
389	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
390	C₂²	C₂×#13094013	1	1	yes	characteristic
391	C₂²	#15689669	1	1	yes	characteristic
392	C₂²	#15689926	1	2	yes	—
393	C₂²	#15689931	1	2	yes	—
394	C₄	—	2	4	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	4	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	8	2	no	—
400	C₄	—	376	2	no	—
401	C₄	C₄×#10625354	1	1	yes	characteristic
402	C₄	C₄×#10625354	1	1	yes	characteristic
403	C₄	#15689660	1	1	yes	characteristic
404	C₄	#15689660	1	1	yes	characteristic
405	C₂	—	376	4	no	—
406	C₂	C₄×#13094013	1	1	yes	characteristic
407	C₂	#20252216	1	2	yes	—
408	C₂	#20253747	1	2	yes	—
409	C₂	#20254017	1	1	yes	characteristic
410	C₂	#20254032	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2330	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#13094021	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2330	D₄₇
hypocenter	C₄₇	#21652
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #376 ◁ #2330

Complements

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

N	H ≅ G/N	type
3. #20244354	C₂	semidirect
5. #20244084	C₂	semidirect
6. #20244070	C₂	semidirect
7. #20243523	C₂	semidirect
8. #20243216	C₂	semidirect
9. C₄×#13093944	C₂	semidirect
10. #20243075	C₂	semidirect
11. C₄₇×#2330	C₂	semidirect
14. #15689489	C₄	semidirect
57. #13093944	C₂×C₄	semidirect
58. #13093944	C₂×C₄	semidirect
61. #13093935	C₂×C₄	semidirect
67. #125×C₄₇	C₂×C₄	semidirect
201. #2330	D₄₇	semidirect
245. C₄₇	#21652	semidirect
256. #125	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689489	2
#20246113	2
#20244354	2
#20244193	2
#20244084	2
#20244070	2
#20243523	2
#20243216	2
C₄×#13093944	2
#20243075	2
C₄₇×#2330	2
#21652	47