Subgroups — C₄×C₄⋊C₈×D₄₇ #26214147

Order 12032.

1550 conjugacy classes of subgroups.

The subgroup lattice has 388 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	2	yes	maximal
2	C₂×C₄×C₈×D₄₇	C₂	1	2	yes	maximal
3	C₄³×D₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
5	C₄×Dic₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243236	C₂	1	2	yes	maximal, complemented
8	#336×D₄₇	C₂	1	2	yes	maximal
9	C₄×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₄₇	C₂²	1	4	yes	—
11	C₂×C₄²×D₄₇	C₄	1	2	yes	—
12	C₂×C₄²×D₄₇	C₄	1	2	yes	—
13	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
18	C₄⋊C₈×D₄₇	C₄	1	16	yes	direct product factor
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₇	C₂²	1	4	yes	—
21	C₄×C₈×D₄₇	—	2	8	no	—
22	C₄²×Dic₄₇	C₄	1	2	yes	—
23	C₄²×Dic₄₇	C₄	1	2	yes	—
24	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
27	#15688878	C₂²	1	2	yes	—
28	#15688877	C₂²	1	4	yes	—
29	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
31	C₄³×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#336	C₂²	1	2	yes	—
33	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
35	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
37	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
38	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
39	C₂×C₈×D₄₇	—	2	8	no	—
40	C₂×C₈×D₄₇	—	2	8	no	—
41	C₂×C₈×D₄₇	C₂×C₄	1	16	yes	—
42	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
43	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
44	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
45	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
46	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
55	C₄²×D₄₇	—	2	8	no	—
56	C₄²×D₄₇	—	2	4	no	—
57	C₄²×D₄₇	C₈	1	16	yes	complemented
58	C₄²×D₄₇	C₂×C₄	1	8	yes	—
59	C₄²×D₄₇	D₄	1	4	yes	—
60	C₄²×D₄₇	Q₈	1	4	yes	—
61	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
62	Dic₄₇⋊C₈	C₂×C₄	1	16	yes	complemented
63	C₄×C₄₇⋊C₈	—	2	4	no	—
64	C₈×Dic₄₇	—	2	8	no	—
65	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
72	C₄×C₈×C₄₇	—	2	4	no	—
73	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
79	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
81	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
84	C₂×C₄×D₄₇	—	2	4	no	—
85	C₂×C₄×D₄₇	—	2	4	no	—
86	C₂×C₄×D₄₇	—	2	4	no	—
87	C₂×C₄×D₄₇	C₄²	1	4	yes	—
88	C₂×C₄×D₄₇	C₄²	1	4	yes	—
89	C₂×C₄×D₄₇	C₄⋊C₄	1	8	yes	—
90	C₂×C₄×D₄₇	C₂×C₈	1	8	yes	—
91	C₂×C₄×D₄₇	C₂×C₈	1	8	yes	—
92	C₂×C₄×D₄₇	C₂×C₈	1	8	yes	—
93	C₂×C₄×D₄₇	M₁₆	1	8	yes	—
94	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
95	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
96	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
97	C₂×C₄×D₄₇	#41	1	4	yes	—
98	C₂×C₈×C₄₇	—	2	4	no	—
99	C₂×C₈×C₄₇	—	2	4	no	—
100	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
101	C₄²×C₄₇	—	2	4	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄²×C₄₇	C₂×C₈	1	8	yes	complemented
104	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
105	C₄²×C₄₇	C₂×D₄	1	2	yes	—
106	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
107	C₄×Dic₄₇	—	2	4	no	—
108	C₄×Dic₄₇	—	2	2	no	—
109	C₄×Dic₄₇	—	2	4	no	—
110	C₄×Dic₄₇	—	2	4	no	—
111	C₄×Dic₄₇	—	2	4	no	—
112	C₄×Dic₄₇	C₄²	1	4	yes	—
113	C₄×Dic₄₇	C₄²	1	4	yes	—
114	C₄×Dic₄₇	C₄⋊C₄	1	8	yes	—
115	C₄×Dic₄₇	C₂×C₈	1	8	yes	complemented
116	C₄×Dic₄₇	C₂×C₈	1	8	yes	complemented
117	C₄×Dic₄₇	C₂×C₈	1	8	yes	complemented
118	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
119	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
120	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	2	4	no	—
123	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
124	C₈×D₄₇	—	2	32	no	—
125	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
126	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
127	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂²×D₄₇	#117	1	2	yes	—
129	C₂²×D₄₇	C₂²×C₈	1	4	yes	—
130	C₂²×D₄₇	C₂×M₁₆	1	4	yes	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
138	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
139	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
140	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
141	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
145	C₂×Dic₄₇	—	2	2	no	—
146	C₂×Dic₄₇	—	2	2	no	—
147	C₂×Dic₄₇	—	2	2	no	—
148	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
149	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
150	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
151	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
152	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
153	C₂×Dic₄₇	#117	1	2	yes	—
154	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
155	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
156	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
157	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
158	C₄×D₄₇	—	2	8	no	—
159	C₄×D₄₇	—	2	16	no	—
160	C₄×D₄₇	C₄×C₈	1	16	yes	complemented
161	C₄×D₄₇	C₄⋊C₈	1	32	yes	direct product factor
162	C₄×D₄₇	C₄×D₄	1	8	yes	—
163	C₄×D₄₇	C₄×Q₈	1	8	yes	—
164	C₈×C₄₇	—	2	8	no	—
165	C₄₇⋊C₈	—	2	8	no	—
166	C₂×C₄×C₄⋊C₈	—	47	1	no	maximal, Sylow
167	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
168	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
170	C₂²×C₄₇	C₂³×C₈	1	2	yes	—
171	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
172	C₂×D₄₇	C₄×C₄⋊C₄	1	4	yes	—
173	C₂×D₄₇	C₂×C₄×C₈	1	4	yes	—
174	C₂×D₄₇	C₄×M₁₆	1	4	yes	—
175	C₂×D₄₇	C₂×C₄⋊C₈	1	8	yes	—
176	C₂×D₄₇	#431	1	8	yes	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	4	no	—
179	C₄×C₄₇	C₂×C₄×C₈	1	4	yes	complemented
180	C₄×C₄₇	C₂×C₄⋊C₈	1	8	yes	complemented
181	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
182	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
183	Dic₄₇	—	2	2	no	—
184	Dic₄₇	—	2	4	no	—
185	Dic₄₇	C₄×C₄⋊C₄	1	4	yes	—
186	Dic₄₇	C₂×C₄×C₈	1	4	yes	complemented
187	Dic₄₇	C₂×C₄⋊C₈	1	8	yes	complemented
188	C₂²×C₄⋊C₈	—	47	2	no	—
189	C₂²×C₄×C₈	—	47	2	no	—
190	C₂×C₄³	—	47	1	no	—
191	C₄×C₄⋊C₈	—	47	2	no	—
192	C₄×C₄⋊C₈	—	47	2	no	—
193	C₄×C₄⋊C₈	—	47	1	no	—
194	C₄×C₄⋊C₈	—	47	2	no	—
195	C₄×C₄⋊C₈	D₄₇	1	1	yes	characteristic, direct product factor
196	C₂×#336	—	47	2	no	—
197	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₄₇	C₂²×C₄×C₈	1	1	yes	characteristic
199	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
200	C₂×C₄₇	C₂²×C₄⋊C₈	1	2	yes	—
201	C₂×C₄₇	C₂×#431	1	2	yes	—
202	D₄₇	C₄×C₄⋊C₈	1	8	yes	direct product factor
203	C₂³×C₈	—	47	4	no	—
204	C₂²×C₄²	—	47	2	no	—
205	C₂²×C₄²	—	47	1	no	—
206	C₂²×C₄²	—	47	1	no	—
207	C₂²×C₄²	—	47	2	no	—
208	C₂²×C₄²	—	47	1	no	—
209	C₂×C₄⋊C₈	—	47	4	no	—
210	C₂×C₄⋊C₈	—	47	2	no	—
211	C₂×C₄⋊C₈	—	47	16	no	—
212	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
213	C₂×C₄×C₈	—	47	4	no	—
214	C₂×C₄×C₈	—	47	2	no	—
215	C₂×C₄×C₈	—	94	8	no	—
216	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
217	C₄³	—	47	2	no	—
218	C₄³	—	47	2	no	—
219	C₄³	—	47	1	no	—
220	C₄³	—	47	1	no	—
221	C₄³	—	47	1	no	—
222	C₄³	C₂×D₄₇	1	1	yes	characteristic
223	#336	—	47	4	no	—
224	#336	—	47	2	no	—
225	#336	C₂×D₄₇	1	2	yes	—
226	C₄₇	C₂×C₄×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
227	C₂³×C₄	—	47	1	no	—
228	C₂³×C₄	—	47	2	no	—
229	C₂³×C₄	—	47	1	no	—
230	C₂³×C₄	—	47	1	no	—
231	C₂³×C₄	—	47	2	no	—
232	C₂²×C₈	—	47	4	no	—
233	C₂²×C₈	—	47	16	no	—
234	C₂²×C₈	—	94	8	no	—
235	C₂²×C₈	—	94	8	no	—
236	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
237	C₂×C₄²	—	47	1	no	—
238	C₂×C₄²	—	47	1	no	—
239	C₂×C₄²	—	47	2	no	—
240	C₂×C₄²	—	47	2	no	—
241	C₂×C₄²	—	47	2	no	—
242	C₂×C₄²	—	47	2	no	—
243	C₂×C₄²	—	47	1	no	—
244	C₂×C₄²	—	47	1	no	—
245	C₂×C₄²	—	47	16	no	—
246	C₂×C₄²	—	47	8	no	—
247	C₂×C₄²	—	47	4	no	—
248	C₂×C₄²	—	47	4	no	—
249	C₂×C₄²	—	47	2	no	—
250	C₂×C₄²	—	47	2	no	—
251	C₂×C₄²	—	47	2	no	—
252	C₂×C₄²	—	47	2	no	—
253	C₂×C₄²	—	47	1	no	—
254	C₂×C₄²	—	94	8	no	—
255	C₂×C₄²	—	94	4	no	—
256	C₂×C₄²	C₄×D₄₇	1	2	yes	—
257	C₂×C₄²	C₄×D₄₇	1	2	yes	—
258	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
259	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
260	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
261	C₄⋊C₈	—	47	16	no	—
262	C₄⋊C₈	—	47	8	no	—
263	C₄⋊C₈	C₄×D₄₇	1	8	yes	direct product factor
264	C₄×C₈	—	2	4	no	—
265	C₄×C₈	—	94	8	no	—
266	C₄×C₈	—	94	4	no	—
267	C₂⁴	—	47	1	no	—
268	C₂²×C₄	—	47	1	no	—
269	C₂²×C₄	—	47	1	no	—
270	C₂²×C₄	—	47	2	no	—
271	C₂²×C₄	—	47	4	no	—
272	C₂²×C₄	—	47	8	no	—
273	C₂²×C₄	—	47	8	no	—
274	C₂²×C₄	—	47	8	no	—
275	C₂²×C₄	—	47	8	no	—
276	C₂²×C₄	—	47	4	no	—
277	C₂²×C₄	—	47	2	no	—
278	C₂²×C₄	—	47	2	no	—
279	C₂²×C₄	—	47	4	no	—
280	C₂²×C₄	—	47	1	no	—
281	C₂²×C₄	—	47	2	no	—
282	C₂²×C₄	—	47	4	no	—
283	C₂²×C₄	—	47	8	no	—
284	C₂²×C₄	—	94	4	no	—
285	C₂²×C₄	—	94	4	no	—
286	C₂²×C₄	—	94	4	no	—
287	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
289	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
291	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	47	8	no	—
295	C₂×C₈	—	94	32	no	—
296	C₂×C₈	—	94	4	no	—
297	C₂×C₈	—	94	4	no	—
298	C₂×C₈	C₂×C₄×D₄₇	1	8	yes	—
299	C₄²	—	2	4	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	47	4	no	—
302	C₄²	—	47	4	no	—
303	C₄²	—	47	8	no	—
304	C₄²	—	47	8	no	—
305	C₄²	—	47	8	no	—
306	C₄²	—	47	8	no	—
307	C₄²	—	47	4	no	—
308	C₄²	—	47	2	no	—
309	C₄²	—	47	2	no	—
310	C₄²	—	94	4	no	—
311	C₄²	—	94	4	no	—
312	C₄²	—	94	4	no	—
313	C₄²	—	94	4	no	—
314	C₄²	—	94	2	no	—
315	C₄²	C₈×D₄₇	1	8	yes	complemented
316	C₄²	C₂×C₄×D₄₇	1	4	yes	—
317	C₄²	D₄×D₄₇	1	2	yes	—
318	C₄²	Q₈×D₄₇	1	2	yes	—
319	C₂³	—	47	2	no	—
320	C₂³	—	47	2	no	—
321	C₂³	—	47	2	no	—
322	C₂³	—	47	4	no	—
323	C₂³	—	47	4	no	—
324	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	47	2	no	—
329	C₂×C₄	—	47	2	no	—
330	C₂×C₄	—	47	4	no	—
331	C₂×C₄	—	47	2	no	—
332	C₂×C₄	—	47	2	no	—
333	C₂×C₄	—	47	4	no	—
334	C₂×C₄	—	47	4	no	—
335	C₂×C₄	—	47	4	no	—
336	C₂×C₄	—	47	16	no	—
337	C₂×C₄	—	47	8	no	—
338	C₂×C₄	—	47	8	no	—
339	C₂×C₄	—	47	32	no	—
340	C₂×C₄	—	47	2	no	—
341	C₂×C₄	—	47	4	no	—
342	C₂×C₄	—	94	16	no	—
343	C₂×C₄	—	94	8	no	—
344	C₂×C₄	—	94	2	no	—
345	C₂×C₄	—	94	2	no	—
346	C₂×C₄	—	94	2	no	—
347	C₂×C₄	C₄²×D₄₇	1	2	yes	—
348	C₂×C₄	C₄²×D₄₇	1	2	yes	—
349	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
350	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
351	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
352	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
353	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
354	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
355	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
357	C₂×C₄	#41×D₄₇	1	2	yes	—
358	C₈	—	2	8	no	—
359	C₈	—	94	8	no	—
360	C₂²	—	47	8	no	—
361	C₂²	—	47	8	no	—
362	C₂²	—	47	4	no	—
363	C₂²	—	47	4	no	—
364	C₂²	—	47	4	no	—
365	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
366	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
367	C₂²	#117×D₄₇	1	1	yes	characteristic
368	C₂²	C₂²×C₈×D₄₇	1	2	yes	—
369	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
370	C₄	—	2	4	no	—
371	C₄	—	2	2	no	—
372	C₄	—	47	8	no	—
373	C₄	—	47	4	no	—
374	C₄	—	47	4	no	—
375	C₄	—	94	4	no	—
376	C₄	—	94	2	no	—
377	C₄	C₄×C₈×D₄₇	1	4	yes	complemented
378	C₄	C₄⋊C₈×D₄₇	1	8	yes	direct product factor
379	C₄	C₄×D₄×D₄₇	1	2	yes	—
380	C₄	C₄×Q₈×D₄₇	1	2	yes	—
381	C₂	—	47	8	no	—
382	C₂	C₄×C₄⋊C₄×D₄₇	1	1	yes	characteristic
383	C₂	C₂×C₄×C₈×D₄₇	1	1	yes	characteristic
384	C₂	C₄×M₁₆×D₄₇	1	1	yes	characteristic
385	C₂	C₂×C₄⋊C₈×D₄₇	1	2	yes	—
386	C₂	#431×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₄₇
commutator	C₂×C₄₇	C₂²×C₄×C₈
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₄⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₄⋊C₈	D₄₇
hypocenter	C₄₇	C₂×C₄×C₄⋊C₈
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₄⋊C₈×Dic₄₇	C₂	semidirect
5. C₄×Dic₄₇⋊C₈	C₂	semidirect
6. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
7. #20243236	C₂	semidirect
9. C₄×C₄⋊C₈×C₄₇	C₂	semidirect
18. C₄⋊C₈×D₄₇	C₄	direct (N × H)
57. C₄²×D₄₇	C₈	semidirect
61. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
62. Dic₄₇⋊C₈	C₂×C₄	semidirect
71. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
103. C₄²×C₄₇	C₂×C₈	semidirect
115. C₄×Dic₄₇	C₂×C₈	semidirect
116. C₄×Dic₄₇	C₂×C₈	semidirect
117. C₄×Dic₄₇	C₂×C₈	semidirect
160. C₄×D₄₇	C₄×C₈	semidirect
161. C₄×D₄₇	C₄⋊C₈	direct (N × H)
179. C₄×C₄₇	C₂×C₄×C₈	semidirect
180. C₄×C₄₇	C₂×C₄⋊C₈	semidirect
186. Dic₄₇	C₂×C₄×C₈	semidirect
187. Dic₄₇	C₂×C₄⋊C₈	semidirect
195. C₄×C₄⋊C₈	D₄₇	direct (N × H)
202. D₄₇	C₄×C₄⋊C₈	direct (N × H)
226. C₄₇	C₂×C₄×C₄⋊C₈	semidirect
263. C₄⋊C₈	C₄×D₄₇	direct (N × H)
315. C₄²	C₈×D₄₇	semidirect
377. C₄	C₄×C₈×D₄₇	semidirect
378. C₄	C₄⋊C₈×D₄₇	direct (N × H)

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×C₈×D₄₇	2
C₄³×D₄₇	2
C₄⋊C₈×Dic₄₇	2
C₄×Dic₄₇⋊C₈	2
C₄×C₄⋊(C₄₇⋊C₈)	2
#20243236	2
#336×D₄₇	2
C₄×C₄⋊C₈×C₄₇	2
C₂×C₄×C₄⋊C₈	47

Subgroups — C4×C4⋊C8×D47 #26214147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊C₈×D₄₇ #26214147