Subgroups — C₄₇×#8095 #26047793

Order 12032.

674 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2285	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1303	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₄₇	—	2	1	no	—
6	C₂×#117×C₄₇	—	2	1	no	—
7	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
8	C₄₇×#431	—	2	1	no	—
9	C₄₇×#431	—	2	1	no	—
10	C₄₇×#431	C₄	1	2	yes	complemented
11	C₄₇×#431	C₂²	1	2	yes	—
12	C₄₇×#423	—	2	1	no	—
13	C₄₇×#423	—	2	1	no	—
14	C₄₇×#423	C₄	1	2	yes	complemented
15	C₄₇×#423	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
17	C₂×C₄⋊C₈×C₄₇	C₄	1	2	yes	complemented
18	C₂×C₄⋊C₈×C₄₇	C₄	1	2	yes	complemented
19	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
20	C₂×C₄×C₈×C₄₇	—	2	1	no	—
21	C₄₇×#384	—	2	1	no	—
22	C₄₇×#382	C₄	1	2	yes	—
23	C₄₇×#380	—	2	1	no	—
24	C₄₇×#380	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
26	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
27	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₄₇	—	2	2	no	—
31	C₂×M₁₆×C₄₇	—	2	2	no	—
32	C₂×M₁₆×C₄₇	—	4	2	no	—
33	C₂×M₁₆×C₄₇	—	4	2	no	—
34	C₂²×C₈×C₄₇	—	2	2	no	—
35	C₂²×C₈×C₄₇	—	2	2	no	—
36	#117×C₄₇	—	4	2	no	—
37	#117×C₄₇	—	4	2	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
42	C₂×C₄²×C₄₇	—	2	2	no	—
43	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
53	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₄₇	—	2	2	no	—
56	C₄⋊C₈×C₄₇	—	2	2	no	—
57	C₄⋊C₈×C₄₇	—	2	2	no	—
58	C₄⋊C₈×C₄₇	—	2	2	no	—
59	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
60	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
61	C₂²⋊C₈×C₄₇	—	2	2	no	—
62	C₂²⋊C₈×C₄₇	—	2	2	no	—
63	C₄×C₈×C₄₇	—	2	2	no	—
64	C₄×C₈×C₄₇	—	2	2	no	—
65	#95×C₄₇	—	2	2	no	—
66	#95×C₄₇	C₂×C₄	1	4	yes	—
67	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	—	2	4	no	—
69	C₂²×C₄×C₄₇	—	4	2	no	—
70	C₂²×C₄×C₄₇	—	4	2	no	—
71	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	D₈	1	2	yes	—
87	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
89	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	M₁₆×C₄₇	—	4	4	no	—
94	M₁₆×C₄₇	—	4	2	no	—
95	M₁₆×C₄₇	—	4	2	no	—
96	C₂×C₈×C₄₇	—	2	4	no	—
97	C₂×C₈×C₄₇	—	2	4	no	—
98	C₂×C₈×C₄₇	—	4	4	no	—
99	C₂×C₈×C₄₇	—	4	4	no	—
100	C₄⋊C₄×C₄₇	—	4	4	no	—
101	C₄⋊C₄×C₄₇	—	4	4	no	—
102	C₄⋊C₄×C₄₇	—	4	4	no	—
103	C₂²⋊C₄×C₄₇	—	4	4	no	—
104	C₄²×C₄₇	—	4	2	no	—
105	C₄²×C₄₇	—	4	2	no	—
106	C₄²×C₄₇	C₄²	1	1	yes	characteristic
107	C₄²×C₄₇	C₄²	1	1	yes	characteristic
108	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
122	C₂³×C₄₇	—	4	1	no	—
123	C₂³×C₄₇	—	4	1	no	—
124	C₂³×C₄₇	#95	1	1	yes	characteristic
125	C₂³×C₄₇	#95	1	1	yes	characteristic
126	C₂³×C₄₇	#102	1	2	yes	—
127	C₂³×C₄₇	#103	1	2	yes	—
128	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
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	—	2	2	no	—
135	C₂×C₄×C₄₇	—	4	1	no	—
136	C₂×C₄×C₄₇	—	4	1	no	—
137	C₂×C₄×C₄₇	—	4	1	no	—
138	C₂×C₄×C₄₇	—	4	1	no	—
139	C₂×C₄×C₄₇	—	4	1	no	—
140	C₂×C₄×C₄₇	—	4	1	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	4	4	no	—
143	C₂×C₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#102	1	2	yes	—
151	C₂×C₄×C₄₇	#102	1	2	yes	—
152	C₂×C₄×C₄₇	#102	1	2	yes	—
153	C₂×C₄×C₄₇	#103	1	2	yes	—
154	C₂×C₄×C₄₇	#103	1	2	yes	—
155	C₂×C₄×C₄₇	#103	1	2	yes	—
156	C₂×C₄×C₄₇	#106	1	2	yes	—
157	C₂×C₄×C₄₇	#106	1	2	yes	—
158	C₂×C₄×C₄₇	#107	1	2	yes	—
159	C₂×C₄×C₄₇	#107	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
170	C₈×C₄₇	—	4	4	no	—
171	C₈×C₄₇	—	4	4	no	—
172	#8095	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₇	—	2	1	no	—
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	#340	1	2	yes	—
182	C₂²×C₄₇	#340	1	2	yes	—
183	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	8	4	no	—
193	C₄×C₄₇	#340	1	2	yes	—
194	C₄×C₄₇	#340	1	2	yes	—
195	C₄×C₄₇	#344	1	2	yes	—
196	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
197	C₄×C₄₇	C₂×#103	1	1	yes	characteristic
198	C₄×C₄₇	#421	1	2	yes	—
199	C₄×C₄₇	C₂×#106	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#107	1	1	yes	characteristic
201	C₂×#431	C₂×C₄₇	1	1	yes	characteristic
202	C₂×#423	C₂×C₄₇	1	1	yes	characteristic
203	#2285	C₂×C₄₇	1	1	yes	characteristic
204	#1303	C₂×C₄₇	1	4	yes	complemented
205	C₂×C₄₇	—	2	1	no	—
206	C₂×C₄₇	—	2	2	no	—
207	C₂×C₄₇	—	2	2	no	—
208	C₂×C₄₇	—	2	1	no	—
209	C₂×C₄₇	#1733	1	1	yes	characteristic
210	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#344	1	1	yes	characteristic
212	C₂²×M₁₆	—	2	1	no	—
213	C₂×#117	—	2	1	no	—
214	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
215	#431	—	2	1	no	—
216	#431	—	2	1	no	—
217	#431	C₄×C₄₇	1	2	yes	complemented
218	#431	C₂²×C₄₇	1	2	yes	—
219	#423	—	2	1	no	—
220	#423	—	2	1	no	—
221	#423	C₄×C₄₇	1	2	yes	complemented
222	#423	C₂²×C₄₇	1	2	yes	—
223	C₂×C₄⋊C₈	—	2	1	no	—
224	C₂×C₄⋊C₈	C₄×C₄₇	1	2	yes	complemented
225	C₂×C₄⋊C₈	C₄×C₄₇	1	2	yes	complemented
226	C₂×C₂²⋊C₈	—	2	1	no	—
227	C₂×C₄×C₈	—	2	1	no	—
228	#384	—	2	1	no	—
229	#382	C₄×C₄₇	1	2	yes	—
230	#380	—	2	1	no	—
231	#380	C₄×C₄₇	1	2	yes	—
232	C₄×C₄⋊C₄	—	2	1	no	—
233	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
234	C₄₇	#8095	1	1	yes	characteristic, direct product factor, Sylow
235	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
237	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	4	2	no	—
241	C₂×M₁₆	—	4	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	#117	—	4	2	no	—
245	#117	—	4	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
252	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
253	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
254	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
257	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
260	C₂×C₄²	Q₈×C₄₇	1	1	yes	characteristic
261	C₂×C₄²	Q₈×C₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
268	C₄⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₂²⋊C₈	—	2	2	no	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	C₂×C₄×C₄₇	1	4	yes	—
275	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₄²×C₄₇	1	1	yes	characteristic
280	C₂²×C₄	C₄²×C₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
283	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₄⋊C₄×C₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₄⋊C₄×C₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₄⋊C₄×C₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₄⋊C₄×C₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₄⋊C₄×C₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊C₄×C₄₇	1	1	yes	characteristic
294	C₂²×C₄	D₈×C₄₇	1	2	yes	—
295	C₂²×C₄	SD₁₆×C₄₇	1	2	yes	—
296	C₂²×C₄	SD₁₆×C₄₇	1	2	yes	—
297	C₂²×C₄	Q₁₆×C₄₇	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
301	M₁₆	—	4	2	no	—
302	M₁₆	—	4	2	no	—
303	M₁₆	—	4	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	4	4	no	—
307	C₂×C₈	—	4	4	no	—
308	C₄⋊C₄	—	4	4	no	—
309	C₄⋊C₄	—	4	4	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₄²	—	4	2	no	—
313	C₄²	—	4	2	no	—
314	C₄²	C₄²×C₄₇	1	1	yes	characteristic
315	C₄²	C₄²×C₄₇	1	1	yes	characteristic
316	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
317	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
318	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
319	C₄²	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
320	C₄²	C₄⋊C₄×C₄₇	1	1	yes	characteristic
321	C₄²	C₄⋊C₄×C₄₇	1	1	yes	characteristic
322	C₄²	C₄⋊C₄×C₄₇	1	1	yes	characteristic
323	C₄²	C₄⋊C₄×C₄₇	1	1	yes	characteristic
324	C₄²	C₄⋊C₄×C₄₇	1	1	yes	characteristic
325	C₄²	C₄⋊C₄×C₄₇	1	1	yes	characteristic
326	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
327	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
328	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
329	C₄²	C₂×Q₈×C₄₇	1	1	yes	characteristic
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	#95×C₄₇	1	1	yes	characteristic
333	C₂³	#95×C₄₇	1	1	yes	characteristic
334	C₂³	#102×C₄₇	1	2	yes	—
335	C₂³	#103×C₄₇	1	2	yes	—
336	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	#95×C₄₇	1	1	yes	characteristic
353	C₂×C₄	#95×C₄₇	1	1	yes	characteristic
354	C₂×C₄	#95×C₄₇	1	1	yes	characteristic
355	C₂×C₄	#95×C₄₇	1	1	yes	characteristic
356	C₂×C₄	#95×C₄₇	1	1	yes	characteristic
357	C₂×C₄	#95×C₄₇	1	1	yes	characteristic
358	C₂×C₄	#102×C₄₇	1	2	yes	—
359	C₂×C₄	#102×C₄₇	1	2	yes	—
360	C₂×C₄	#102×C₄₇	1	2	yes	—
361	C₂×C₄	#103×C₄₇	1	2	yes	—
362	C₂×C₄	#103×C₄₇	1	2	yes	—
363	C₂×C₄	#103×C₄₇	1	2	yes	—
364	C₂×C₄	#106×C₄₇	1	2	yes	—
365	C₂×C₄	#106×C₄₇	1	2	yes	—
366	C₂×C₄	#107×C₄₇	1	2	yes	—
367	C₂×C₄	#107×C₄₇	1	2	yes	—
368	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
369	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×D₈×C₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂×SD₁₆×C₄₇	1	1	yes	characteristic
376	C₂×C₄	C₂×SD₁₆×C₄₇	1	1	yes	characteristic
377	C₂×C₄	C₂×Q₁₆×C₄₇	1	1	yes	characteristic
378	C₈	—	4	4	no	—
379	C₈	—	4	4	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	C₄₇×#340	1	2	yes	—
389	C₂²	C₄₇×#340	1	2	yes	—
390	C₂²	C₂×#95×C₄₇	1	1	yes	characteristic
391	C₂²	C₂×#102×C₄₇	1	1	yes	characteristic
392	C₂²	C₂×#103×C₄₇	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	8	4	no	—
400	C₄	C₄₇×#340	1	2	yes	—
401	C₄	C₄₇×#340	1	2	yes	—
402	C₄	C₄₇×#344	1	2	yes	—
403	C₄	C₂×#102×C₄₇	1	1	yes	characteristic
404	C₄	C₂×#103×C₄₇	1	1	yes	characteristic
405	C₄	C₄₇×#421	1	2	yes	—
406	C₄	C₂×#106×C₄₇	1	1	yes	characteristic
407	C₄	C₂×#107×C₄₇	1	1	yes	characteristic
408	C₂	—	2	1	no	—
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	2	1	no	—
412	C₂	C₄₇×#1733	1	1	yes	characteristic
413	C₂	C₂×C₄₇×#340	1	1	yes	characteristic
414	C₂	C₂×C₄₇×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₄₇
Frattini, cosocle	C₂×C₄²	C₂³×C₄₇
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₇×#1303	C₂	semidirect
10. C₄₇×#431	C₄	semidirect
14. C₄₇×#423	C₄	semidirect
17. C₂×C₄⋊C₈×C₄₇	C₄	semidirect
18. C₂×C₄⋊C₈×C₄₇	C₄	semidirect
172. #8095	C₄₇	direct (N × H)
204. #1303	C₂×C₄₇	semidirect
217. #431	C₄×C₄₇	semidirect
221. #423	C₄×C₄₇	semidirect
224. C₂×C₄⋊C₈	C₄×C₄₇	semidirect
225. C₂×C₄⋊C₈	C₄×C₄₇	semidirect
234. C₄₇	#8095	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×C₄₇×#431	2
C₂×C₄₇×#423	2
C₄₇×#2285	2
C₄₇×#1303	2
#8095	47

Subgroups — C47×#8095 #26047793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#8095 #26047793