Subgroups — #26214280

Order 12032.

1138 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689079	C₂	1	2	yes	maximal
3	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
4	#20243263	C₂	1	4	yes	maximal, complemented
5	#20243257	C₂	1	2	yes	maximal, complemented
6	C₄⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
7	#20243085	C₂	1	2	yes	maximal
8	C₄₇×#2285	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	8	yes	complemented
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	#15689079	—	2	8	no	—
17	C₄×#10625329	C₄	1	8	yes	complemented
18	C₂×#13093935	C₂²	1	4	yes	—
19	C₂×#13093935	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	#15688878	C₂²	1	4	yes	—
23	#15688878	C₂²	1	4	yes	—
24	C₂×#117×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#384	C₄	1	2	yes	—
27	C₄₇×#382	C₄	1	2	yes	—
28	C₄₇×#380	C₄	1	2	yes	—
29	C₄₇×#380	C₄	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
31	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625329	C₂×C₄	1	4	yes	—
35	C₂×#10625329	C₂×C₄	1	4	yes	—
36	C₂×#10625329	D₄	1	4	yes	—
37	C₂×#10625329	Q₈	1	4	yes	—
38	C₂²×C₄₇⋊C₈	—	2	4	no	—
39	C₂²×C₄₇⋊C₈	—	2	4	no	—
40	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
46	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
47	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
48	#13093935	—	2	8	no	—
49	#13093935	C₂×C₄	1	8	yes	—
50	C₄×C₄₇⋊C₈	—	2	8	no	—
51	C₄×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
52	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	#117×C₄₇	—	2	4	no	—
56	#117×C₄₇	—	2	4	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	#95×C₄₇	C₂×C₄	1	4	yes	—
69	#95×C₄₇	C₂×C₄	1	4	yes	—
70	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	—	2	4	no	—
72	C₂²×C₄×C₄₇	—	4	2	no	—
73	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
74	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
75	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
76	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₄₇	#41	1	2	yes	—
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
88	C₄⋊C₄×C₄₇	—	2	8	no	—
89	C₄⋊C₄×C₄₇	—	2	8	no	—
90	C₄⋊C₄×C₄₇	—	4	4	no	—
91	C₂²⋊C₄×C₄₇	—	2	8	no	—
92	C₄²×C₄₇	—	2	4	no	—
93	C₄²×C₄₇	—	2	4	no	—
94	C₄²×C₄₇	C₄²	1	4	yes	—
95	C₄²×C₄₇	C₄²	1	4	yes	—
96	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
97	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
98	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
99	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
100	#10625329	—	2	8	no	—
101	#10625329	C₄⋊C₄	1	16	yes	complemented
102	C₂×C₄₇⋊C₈	—	2	16	no	—
103	C₂×C₄₇⋊C₈	—	2	2	no	—
104	C₂×C₄₇⋊C₈	—	2	2	no	—
105	C₂×C₄₇⋊C₈	—	2	2	no	—
106	C₂×C₄₇⋊C₈	—	2	2	no	—
107	C₂×C₄₇⋊C₈	—	2	2	no	—
108	C₂×C₄₇⋊C₈	—	2	2	no	—
109	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
110	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
111	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
112	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
113	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
114	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
115	C₂³×C₄₇	—	2	2	no	—
116	C₂³×C₄₇	—	2	2	no	—
117	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
118	C₂³×C₄₇	C₄×D₄	1	2	yes	—
119	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
120	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
121	C₂×C₄×C₄₇	—	2	2	no	—
122	C₂×C₄×C₄₇	—	2	2	no	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	8	no	—
125	C₂×C₄×C₄₇	—	2	8	no	—
126	C₂×C₄×C₄₇	—	2	8	no	—
127	C₂×C₄×C₄₇	—	2	8	no	—
128	C₂×C₄×C₄₇	—	4	4	no	—
129	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
130	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
131	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
135	C₂×C₄×C₄₇	#117	1	4	yes	—
136	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
137	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
138	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
139	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
140	C₂×C₄×C₄₇	#131	1	4	yes	—
141	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
147	C₄₇⋊C₈	—	2	4	no	—
148	C₄₇⋊C₈	—	2	4	no	—
149	C₄₇⋊C₈	—	2	4	no	—
150	C₄₇⋊C₈	C₂×C₄⋊C₄	1	8	yes	—
151	#20441	—	47	1	no	maximal, Sylow
152	C₂²×C₄₇	—	2	2	no	—
153	C₂²×C₄₇	—	2	2	no	—
154	C₂²×C₄₇	—	2	4	no	—
155	C₂²×C₄₇	—	2	4	no	—
156	C₂²×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
157	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
158	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
159	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
160	C₂²×C₄₇	C₂×#131	1	2	yes	—
161	C₂²×C₄₇	#568	1	2	yes	—
162	C₄×C₄₇	—	2	2	no	—
163	C₄×C₄₇	—	2	2	no	—
164	C₄×C₄₇	—	2	2	no	—
165	C₄×C₄₇	—	4	8	no	—
166	C₄×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
167	C₄×C₄₇	#405	1	4	yes	complemented
168	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
170	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
171	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
172	C₂²×C₄⋊C₈	—	47	1	no	—
173	C₂×#405	—	47	2	no	—
174	C₂×C₄×M₁₆	—	47	1	no	—
175	#2285	D₄₇	1	1	yes	characteristic
176	#1771	—	47	4	no	—
177	#1770	—	47	2	no	—
178	C₈×C₄⋊C₄	—	47	2	no	—
179	#1729	—	47	2	no	—
180	C₂×C₄₇	—	2	4	no	—
181	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
183	C₂×C₄₇	#2873	1	1	yes	characteristic
184	C₂×C₄₇	#2935	1	2	yes	—
185	C₂×C₄₇	#2962	1	2	yes	—
186	C₂²×M₁₆	—	47	1	no	—
187	C₂²×M₁₆	—	47	1	no	—
188	C₂³×C₈	—	47	2	no	—
189	C₂×#117	C₂×D₄₇	1	2	yes	—
190	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
191	C₂×C₄⋊C₈	—	47	8	no	—
192	C₂×C₄⋊C₈	—	47	1	no	—
193	C₂×C₄⋊C₈	—	47	1	no	—
194	C₂×C₄⋊C₈	—	47	2	no	—
195	#405	—	94	8	no	—
196	C₄×M₁₆	—	47	8	no	—
197	C₂×#97	—	47	2	no	—
198	C₂×#97	—	47	4	no	—
199	C₂×C₄×C₈	—	47	2	no	—
200	C₂×C₄×C₈	—	47	4	no	—
201	#384	Dic₄₇	1	2	yes	—
202	#382	Dic₄₇	1	2	yes	—
203	#380	Dic₄₇	1	2	yes	—
204	#380	Dic₄₇	1	2	yes	—
205	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
206	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
207	#336	—	47	4	no	—
208	#336	—	47	4	no	—
209	C₄₇	#20441	1	1	yes	characteristic, complemented, Sylow
210	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
211	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
212	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
213	C₂×M₁₆	—	47	4	no	—
214	C₂×M₁₆	—	47	4	no	—
215	C₂×M₁₆	—	47	4	no	—
216	C₂×M₁₆	—	47	4	no	—
217	C₂×M₁₆	—	94	2	no	—
218	C₂×M₁₆	—	94	2	no	—
219	C₂²×C₈	—	47	2	no	—
220	C₂²×C₈	—	47	8	no	—
221	C₂²×C₈	—	47	2	no	—
222	C₂²×C₈	—	47	2	no	—
223	C₂²×C₈	—	47	2	no	—
224	C₂²×C₈	—	94	4	no	—
225	C₂²×C₈	—	94	4	no	—
226	#117	—	2	4	no	—
227	#117	—	2	4	no	—
228	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
229	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
230	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
231	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
232	C₂×C₄²	C₄×D₄₇	1	4	yes	—
233	C₂×C₄²	C₄×D₄₇	1	4	yes	—
234	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
237	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
238	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
239	C₄⋊C₈	—	47	4	no	—
240	C₄⋊C₈	—	47	4	no	—
241	C₄⋊C₈	—	47	8	no	—
242	#97	—	47	8	no	—
243	#97	—	94	8	no	—
244	C₄×C₈	—	47	8	no	—
245	C₄×C₈	—	94	8	no	—
246	#95	C₂×Dic₄₇	1	4	yes	—
247	#95	C₂×Dic₄₇	1	4	yes	—
248	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
252	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
253	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
254	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
255	C₂²×C₄	D₄×D₄₇	1	2	yes	—
256	C₂²×C₄	#10625352	1	2	yes	—
257	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
258	C₂²×C₄	#10625354	1	2	yes	—
259	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
260	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
262	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
264	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
265	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
266	M₁₆	—	47	16	no	—
267	M₁₆	—	94	8	no	—
268	C₂×C₈	—	47	4	no	—
269	C₂×C₈	—	47	4	no	—
270	C₂×C₈	—	47	4	no	—
271	C₂×C₈	—	47	4	no	—
272	C₂×C₈	—	47	4	no	—
273	C₂×C₈	—	47	4	no	—
274	C₂×C₈	—	94	16	no	—
275	C₂×C₈	—	94	2	no	—
276	C₂×C₈	—	94	2	no	—
277	C₂×C₈	—	94	2	no	—
278	C₂×C₈	—	94	2	no	—
279	C₂×C₈	—	94	2	no	—
280	C₂×C₈	—	94	2	no	—
281	C₄⋊C₄	—	2	8	no	—
282	C₄⋊C₄	—	2	8	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₂²⋊C₄	—	2	8	no	—
285	C₄²	—	2	4	no	—
286	C₄²	—	2	4	no	—
287	C₄²	C₄×Dic₄₇	1	4	yes	—
288	C₄²	C₄×Dic₄₇	1	4	yes	—
289	C₄²	C₂×C₄×D₄₇	1	2	yes	—
290	C₄²	C₂×C₄×D₄₇	1	2	yes	—
291	C₄²	C₂×C₄×D₄₇	1	2	yes	—
292	C₄²	C₂×C₄×D₄₇	1	2	yes	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	2	no	—
295	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
296	C₂³	D₄×Dic₄₇	1	2	yes	—
297	C₂³	Q₈×Dic₄₇	1	2	yes	—
298	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
308	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
309	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
310	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
311	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
312	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
313	C₂×C₄	#13093982	1	4	yes	—
314	C₂×C₄	#13093986	1	4	yes	—
315	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
316	C₂×C₄	#13093989	1	4	yes	—
317	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
318	C₂×C₄	#13094031	1	4	yes	—
319	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
320	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
321	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
322	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
323	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
324	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
325	C₈	—	47	8	no	—
326	C₈	—	94	4	no	—
327	C₈	—	94	4	no	—
328	C₈	—	94	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	4	no	—
333	C₂²	C₄⋊C₄×Dic₄₇	1	4	yes	—
334	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
335	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
336	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
337	C₂²	C₂×#13094031	1	2	yes	—
338	C₂²	#15689890	1	2	yes	—
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	4	8	no	—
343	C₄	C₄⋊C₄×Dic₄₇	1	4	yes	—
344	C₄	#15689079	1	4	yes	complemented
345	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
346	C₄	C₂×#13093982	1	1	yes	characteristic
347	C₄	C₂×#13093986	1	1	yes	characteristic
348	C₄	C₂×#13093989	1	1	yes	characteristic
349	C₂	—	2	4	no	—
350	C₂	C₂×C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
351	C₂	C₂×#15689079	1	1	yes	characteristic
352	C₂	#20251807	1	1	yes	characteristic
353	C₂	#20252132	1	2	yes	—
354	C₂	#20252337	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#2285	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2285	D₄₇
hypocenter	C₄₇	#20441
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2285

Complements

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

N	H ≅ G/N	type
4. #20243263	C₂	semidirect
5. #20243257	C₂	semidirect
6. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
12. C₂×C₄⋊(C₄₇⋊C₈)	C₄	semidirect
17. C₄×#10625329	C₄	semidirect
101. #10625329	C₄⋊C₄	semidirect
167. C₄×C₄₇	#405	semidirect
209. C₄₇	#20441	semidirect
344. C₄	#15689079	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂×#15689079	2
C₂×C₄×#10625329	2
#20243263	2
#20243257	2
C₄⋊C₄×C₄₇⋊C₈	2
#20243085	2
C₄₇×#2285	2
#20441	47