Subgroups — #26105824

Order 12032.

734 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
3	#20245784	C₂	1	1	yes	maximal, characteristic
4	#20241229	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241228	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625324	—	2	1	no	—
9	C₂²×C₈×D₄₇	—	2	1	no	—
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×Dic₄₇⋊C₈	—	2	1	no	—
13	C₄⋊C₈×D₄₇	—	2	2	no	—
14	C₄⋊C₈×D₄₇	C₄	1	4	yes	complemented
15	C₄×#10625324	—	2	2	no	—
16	C₄×#10625324	C₄	1	4	yes	complemented
17	C₂×#13093934	—	2	1	no	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	#15688990	—	2	1	no	—
20	#15688988	C₄	1	2	yes	—
21	#15688985	—	2	1	no	—
22	#15688980	C₄	1	2	yes	—
23	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
25	#15688969	—	2	1	no	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
32	C₂×#10625324	—	2	8	no	—
33	C₂×#10625324	—	2	4	no	—
34	C₂²×C₄₇⋊C₈	—	2	1	no	—
35	C₂²×C₄₇⋊C₈	—	2	1	no	—
36	C₂×C₈×D₄₇	—	2	4	no	—
37	C₂×C₈×D₄₇	—	4	2	no	—
38	C₂×C₈×D₄₇	—	4	2	no	—
39	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
40	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
41	C₂×C₄×Dic₄₇	—	2	1	no	—
42	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
44	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
45	C₄²×D₄₇	C₂×C₄	1	2	yes	—
46	C₄²×D₄₇	C₂×C₄	1	2	yes	—
47	C₄²×D₄₇	D₄	1	2	yes	—
48	C₄²×D₄₇	Q₈	1	2	yes	—
49	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
51	Dic₄₇⋊C₈	—	2	4	no	—
52	#13093934	—	2	4	no	—
53	C₄×C₄₇⋊C₈	—	2	1	no	—
54	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
55	C₄₇⋊#95	—	2	1	no	—
56	C₄₇⋊#95	—	2	2	no	—
57	C₄₇⋊#95	—	2	2	no	—
58	C₄₇⋊#95	—	2	2	no	—
59	C₂²×C₈×C₄₇	—	2	1	no	—
60	C₂²×C₈×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₄₇	—	2	1	no	—
63	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₄₇	—	2	1	no	—
65	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
66	C₄×C₈×C₄₇	—	2	1	no	—
67	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
68	#95×C₄₇	—	2	1	no	—
69	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×D₄₇	—	2	4	no	—
79	C₂×C₄×D₄₇	—	2	2	no	—
80	C₂×C₄×D₄₇	—	2	2	no	—
81	C₂×C₄×D₄₇	—	2	1	no	—
82	C₂×C₄×D₄₇	—	2	1	no	—
83	C₂×C₄×D₄₇	—	2	1	no	—
84	C₂×C₄×D₄₇	—	2	1	no	—
85	C₂×C₄×D₄₇	C₄²	1	2	yes	—
86	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
87	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
88	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
89	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
90	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
91	C₂×C₈×C₄₇	—	2	4	no	—
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	2	2	no	—
94	C₂×C₈×C₄₇	—	4	1	no	—
95	C₂×C₈×C₄₇	—	4	1	no	—
96	C₄⋊C₄×C₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	—	2	2	no	—
98	C₄²×C₄₇	—	4	1	no	—
99	C₄²×C₄₇	—	4	1	no	—
100	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
104	(C₂×D₄₇)⋊C₄	—	4	4	no	—
105	C₄⋊Dic₄₇	—	2	2	no	—
106	C₄⋊Dic₄₇	—	2	2	no	—
107	C₄×Dic₄₇	—	4	1	no	—
108	C₄×Dic₄₇	—	4	1	no	—
109	C₄×Dic₄₇	C₄²	1	2	yes	—
110	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
111	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
112	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
113	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
114	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
115	C₂×C₄₇⋊C₈	—	2	4	no	—
116	C₂×C₄₇⋊C₈	—	2	2	no	—
117	C₂×C₄₇⋊C₈	—	2	2	no	—
118	C₂×C₄₇⋊C₈	—	4	1	no	—
119	C₂×C₄₇⋊C₈	—	4	1	no	—
120	#10625324	—	2	16	no	—
121	C₈×D₄₇	—	4	8	no	—
122	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×D₄₇	—	2	2	no	—
124	C₂²×D₄₇	—	2	1	no	—
125	C₂²×D₄₇	—	2	1	no	—
126	C₂²×D₄₇	#95	1	2	yes	—
127	C₂²×D₄₇	#104	1	4	yes	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	4	2	no	—
130	C₂×C₄×C₄₇	—	4	2	no	—
131	C₂×C₄×C₄₇	—	4	2	no	—
132	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
133	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	#131	1	2	yes	—
139	C₂×C₄×C₄₇	#131	1	2	yes	—
140	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
144	C₂×Dic₄₇	—	2	2	no	—
145	C₂×Dic₄₇	—	2	1	no	—
146	C₂×Dic₄₇	—	2	1	no	—
147	C₂×Dic₄₇	—	2	2	no	—
148	C₂×Dic₄₇	—	4	2	no	—
149	C₂×Dic₄₇	—	4	2	no	—
150	C₂×Dic₄₇	—	4	2	no	—
151	C₂×Dic₄₇	#95	1	2	yes	—
152	C₂×Dic₄₇	#95	1	2	yes	—
153	C₂×Dic₄₇	#95	1	2	yes	—
154	C₄×D₄₇	—	2	4	no	—
155	C₄×D₄₇	—	2	4	no	—
156	C₄×D₄₇	—	2	2	no	—
157	C₄×D₄₇	—	2	2	no	—
158	C₄×D₄₇	—	2	2	no	—
159	C₄×D₄₇	—	2	2	no	—
160	C₄×D₄₇	—	2	4	no	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	2	2	no	—
163	C₈×C₄₇	—	2	4	no	—
164	C₈×C₄₇	—	4	2	no	—
165	C₄₇⋊C₈	—	2	4	no	—
166	C₄₇⋊C₈	—	4	2	no	—
167	#7895	—	47	1	no	maximal, Sylow
168	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
169	C₂²×C₄₇	#408	1	2	yes	—
170	C₂²×C₄₇	#417	1	1	yes	characteristic
171	C₂²×C₄₇	#417	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#104	1	2	yes	—
173	C₂×D₄₇	—	2	2	no	—
174	C₂×D₄₇	—	2	2	no	—
175	C₂×D₄₇	—	2	4	no	—
176	C₂×D₄₇	—	2	4	no	—
177	C₂×D₄₇	#339	1	4	yes	—
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	—	2	1	no	—
180	C₄×C₄₇	—	8	2	no	—
181	C₄×C₄₇	#405	1	1	yes	characteristic
182	C₄×C₄₇	#405	1	1	yes	characteristic
183	C₄×C₄₇	#418	1	1	yes	characteristic
184	C₄×C₄₇	#419	1	1	yes	characteristic
185	C₄×C₄₇	#424	1	2	yes	—
186	C₄×C₄₇	#428	1	1	yes	characteristic
187	C₄×C₄₇	#428	1	1	yes	characteristic
188	Dic₄₇	—	2	2	no	—
189	Dic₄₇	—	2	2	no	—
190	Dic₄₇	—	2	2	no	—
191	Dic₄₇	—	8	2	no	—
192	C₂²×C₄⋊C₈	—	47	1	no	—
193	C₂×C₄×M₁₆	—	47	1	no	—
194	#2283	—	47	1	no	—
195	#1279	—	47	1	no	—
196	#1279	—	47	1	no	—
197	#1279	—	47	1	no	—
198	#1279	D₄₇	1	1	yes	characteristic, complemented
199	C₂×C₄₇	#1483	1	2	yes	—
200	C₂×C₄₇	#1483	1	2	yes	—
201	C₂×C₄₇	#1729	1	1	yes	characteristic
202	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
203	C₂×C₄₇	#1736	1	1	yes	characteristic
204	D₄₇	—	2	4	no	—
205	C₂²×M₁₆	—	94	1	no	—
206	C₂³×C₈	—	94	1	no	—
207	C₂²×C₄²	—	47	1	no	—
208	C₂×C₄⋊C₈	—	47	1	no	—
209	C₂×C₄⋊C₈	—	47	4	no	—
210	C₂×C₄⋊C₈	—	94	2	no	—
211	C₂×C₄⋊C₈	—	94	1	no	—
212	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
213	C₄×M₁₆	—	47	4	no	—
214	C₄×M₁₆	—	94	2	no	—
215	C₂×#97	—	94	1	no	—
216	C₂×C₄×C₈	—	47	1	no	—
217	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
218	#383	—	94	1	no	—
219	#382	—	47	2	no	—
220	#381	—	94	1	no	—
221	#380	—	47	2	no	—
222	C₄×C₄⋊C₄	—	47	1	no	—
223	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
224	C₄×C₂²⋊C₄	—	94	1	no	—
225	#376	—	94	1	no	—
226	C₄₇	#7895	1	1	yes	characteristic, complemented, Sylow
227	C₂³×C₄	—	47	1	no	—
228	C₂³×C₄	—	47	1	no	—
229	C₂³×C₄	—	47	1	no	—
230	C₂×M₁₆	—	94	4	no	—
231	C₂×M₁₆	—	94	8	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	2	1	no	—
234	C₂²×C₈	—	94	4	no	—
235	C₂²×C₈	—	94	1	no	—
236	C₂²×C₈	—	94	1	no	—
237	C₂²×C₈	—	188	2	no	—
238	C₂²×C₈	—	188	2	no	—
239	C₂×C₄⋊C₄	—	47	2	no	—
240	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
241	C₂×C₂²⋊C₄	—	94	2	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	—	47	1	no	—
244	C₂×C₄²	—	47	1	no	—
245	C₂×C₄²	—	47	1	no	—
246	C₂×C₄²	—	47	2	no	—
247	C₂×C₄²	—	47	2	no	—
248	C₂×C₄²	—	47	2	no	—
249	C₂×C₄²	—	47	2	no	—
250	C₂×C₄²	—	94	1	no	—
251	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	47	2	no	—
254	C₄⋊C₈	—	94	4	no	—
255	C₄⋊C₈	—	94	1	no	—
256	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
257	#97	—	94	4	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	47	2	no	—
260	C₄×C₈	—	94	1	no	—
261	C₄×C₈	C₄×D₄₇	1	2	yes	—
262	#95	—	2	1	no	—
263	#95	—	94	2	no	—
264	#95	—	94	2	no	—
265	#95	—	94	2	no	—
266	#95	—	94	1	no	—
267	C₂⁴	—	47	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	47	1	no	—
270	C₂²×C₄	—	47	1	no	—
271	C₂²×C₄	—	47	1	no	—
272	C₂²×C₄	—	47	2	no	—
273	C₂²×C₄	—	47	2	no	—
274	C₂²×C₄	—	47	2	no	—
275	C₂²×C₄	—	47	2	no	—
276	C₂²×C₄	—	47	2	no	—
277	C₂²×C₄	—	47	2	no	—
278	C₂²×C₄	—	94	4	no	—
279	C₂²×C₄	—	94	2	no	—
280	C₂²×C₄	—	94	2	no	—
281	C₂²×C₄	—	94	1	no	—
282	C₂²×C₄	—	94	1	no	—
283	C₂²×C₄	—	94	1	no	—
284	C₂²×C₄	—	94	1	no	—
285	C₂²×C₄	—	94	2	no	—
286	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
287	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
288	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
289	M₁₆	—	94	16	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	94	4	no	—
296	C₂×C₈	—	94	2	no	—
297	C₂×C₈	—	94	2	no	—
298	C₂×C₈	—	188	8	no	—
299	C₂×C₈	—	188	1	no	—
300	C₂×C₈	—	188	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	94	2	no	—
304	C₄⋊C₄	—	94	2	no	—
305	C₂²⋊C₄	—	188	4	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	—	47	2	no	—
309	C₄²	—	47	2	no	—
310	C₄²	—	47	2	no	—
311	C₄²	—	47	2	no	—
312	C₄²	—	47	2	no	—
313	C₄²	—	47	2	no	—
314	C₄²	—	188	1	no	—
315	C₄²	—	188	1	no	—
316	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
317	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
318	C₄²	D₄×D₄₇	1	1	yes	characteristic
319	C₄²	Q₈×D₄₇	1	1	yes	characteristic
320	C₂³	—	47	2	no	—
321	C₂³	—	47	4	no	—
322	C₂³	—	94	2	no	—
323	C₂³	—	94	1	no	—
324	C₂³	—	94	1	no	—
325	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	47	2	no	—
331	C₂×C₄	—	47	2	no	—
332	C₂×C₄	—	47	2	no	—
333	C₂×C₄	—	94	4	no	—
334	C₂×C₄	—	94	4	no	—
335	C₂×C₄	—	94	2	no	—
336	C₂×C₄	—	94	1	no	—
337	C₂×C₄	—	94	1	no	—
338	C₂×C₄	—	94	2	no	—
339	C₂×C₄	—	94	2	no	—
340	C₂×C₄	—	94	2	no	—
341	C₂×C₄	—	94	2	no	—
342	C₂×C₄	—	94	2	no	—
343	C₂×C₄	—	94	4	no	—
344	C₂×C₄	—	94	2	no	—
345	C₂×C₄	—	94	2	no	—
346	C₂×C₄	—	188	2	no	—
347	C₂×C₄	—	188	2	no	—
348	C₂×C₄	—	188	2	no	—
349	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
350	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
351	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
352	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
353	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
354	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
355	C₂×C₄	#13094030	1	2	yes	—
356	C₂×C₄	#13094032	1	2	yes	—
357	C₂×C₄	#13094048	1	1	yes	characteristic
358	C₂×C₄	#13094051	1	1	yes	characteristic
359	C₂×C₄	#13094053	1	1	yes	characteristic
360	C₂×C₄	#13094056	1	1	yes	characteristic
361	C₈	—	2	4	no	—
362	C₈	—	4	2	no	—
363	C₈	—	94	4	no	—
364	C₈	—	188	2	no	—
365	C₂²	—	47	4	no	—
366	C₂²	—	94	4	no	—
367	C₂²	—	94	4	no	—
368	C₂²	—	94	2	no	—
369	C₂²	—	94	2	no	—
370	C₂²	#95×D₄₇	1	1	yes	characteristic
371	C₂²	#15689088	1	2	yes	—
372	C₂²	#15689121	1	1	yes	characteristic
373	C₂²	#15689123	1	1	yes	characteristic
374	C₂²	#104×D₄₇	1	2	yes	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	8	2	no	—
378	C₄	—	94	2	no	—
379	C₄	—	94	2	no	—
380	C₄	—	94	2	no	—
381	C₄	—	376	2	no	—
382	C₄	#15689077	1	1	yes	characteristic
383	C₄	#15689080	1	1	yes	characteristic
384	C₄	#15689126	1	1	yes	characteristic
385	C₄	#15689130	1	1	yes	characteristic
386	C₄	#15689148	1	2	yes	—
387	C₄	#15689162	1	1	yes	characteristic
388	C₄	#15689164	1	1	yes	characteristic
389	C₂	—	94	4	no	—
390	C₂	#20241798	1	2	yes	—
391	C₂	#20241800	1	2	yes	—
392	C₂	#20243083	1	1	yes	characteristic
393	C₂	#339×D₄₇	1	1	yes	characteristic
394	C₂	#20243106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1279	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1279	D₄₇
hypocenter	C₄₇	#7895
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #20241229	C₂	semidirect
5. #20241228	C₂	semidirect
6. #20241227	C₂	semidirect
7. C₄₇×#1279	C₂	semidirect
14. C₄⋊C₈×D₄₇	C₄	semidirect
16. C₄×#10625324	C₄	semidirect
198. #1279	D₄₇	semidirect
226. C₄₇	#7895	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₈×D₄₇	2
C₂×C₄×#10625324	2
#20245784	2
#20241229	2
#20241228	2
#20241227	2
C₄₇×#1279	2
#7895	47