Subgroups — C₄₇×#17626 #26057324

Order 12032.

1254 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3496	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1517	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1510	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1507	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1502	C₂	1	2	yes	maximal, complemented
8	C₂×H(5,𝔽₂)×C₄₇	—	2	1	no	—
9	C₄₇×#547	C₄	1	4	yes	complemented
10	C₄₇×#546	—	2	4	no	—
11	D₄²×C₄₇	C₄	1	4	yes	complemented
12	C₄₇×#537	—	2	1	no	—
13	C₄₇×#534	—	2	2	no	—
14	C₄₇×#532	C₂²	1	2	yes	—
15	C₂×#121×C₄₇	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#436	—	2	4	no	—
18	C₄₇×#431	C₂²	1	2	yes	complemented
19	C₄₇×#407	C₂²	1	4	yes	complemented
20	C₄₇×#390	—	2	1	no	—
21	C₄₇×#388	—	2	2	no	—
22	C₄₇×#382	C₂²	1	1	yes	characteristic, complemented
23	C₄₇×#381	C₂²	1	2	yes	complemented
24	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
25	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
26	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
27	C₄₇×#327	C₂²	1	4	yes	complemented
28	C₄₇×#327	C₂²	1	4	yes	complemented
29	C₄₇×#327	C₂²	1	8	yes	complemented
30	H(5,𝔽₂)×C₄₇	—	4	4	no	—
31	H(5,𝔽₂)×C₄₇	—	4	4	no	—
32	C₂×#41×C₄₇	—	2	4	no	—
33	C₂×#41×C₄₇	—	2	2	no	—
34	C₂²×D₄×C₄₇	—	2	4	no	—
35	C₂²×D₄×C₄₇	—	2	4	no	—
36	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
39	C₂×M₁₆×C₄₇	—	2	4	no	—
40	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
41	#127×C₄₇	C₂×C₄	1	2	yes	—
42	#124×C₄₇	—	2	2	no	—
43	#123×C₄₇	—	2	8	no	—
44	C₂²⋊Q₈×C₄₇	—	2	4	no	—
45	#121×C₄₇	—	2	4	no	—
46	#121×C₄₇	—	2	4	no	—
47	#121×C₄₇	—	2	2	no	—
48	#121×C₄₇	—	2	4	no	—
49	#121×C₄₇	C₂×C₄	1	8	yes	—
50	#121×C₄₇	C₂³	1	4	yes	—
51	#120×C₄₇	—	2	8	no	—
52	C₄×D₄×C₄₇	—	2	2	no	—
53	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
54	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
55	C₄×D₄×C₄₇	D₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
64	C₂×C₄²×C₄₇	—	2	1	no	—
65	C₂×C₄²×C₄₇	—	2	2	no	—
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₄₇	—	2	2	no	—
68	C₂²⋊C₈×C₄₇	—	2	4	no	—
69	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
70	C₄×C₈×C₄₇	—	2	2	no	—
71	#95×C₄₇	—	2	2	no	—
72	#95×C₄₇	—	2	1	no	—
73	#95×C₄₇	C₂³	1	1	yes	characteristic
74	#95×C₄₇	C₂³	1	2	yes	—
75	#95×C₄₇	C₂³	1	1	yes	characteristic
76	C₂⁴×C₄₇	—	2	4	no	—
77	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
78	#41×C₄₇	—	4	16	no	—
79	#41×C₄₇	—	4	4	no	—
80	#41×C₄₇	—	4	4	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×D₄×C₄₇	—	2	8	no	—
83	C₂×D₄×C₄₇	—	2	4	no	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	4	16	no	—
90	C₂×D₄×C₄₇	—	4	8	no	—
91	C₂×D₄×C₄₇	—	4	8	no	—
92	C₂×D₄×C₄₇	—	8	4	no	—
93	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
94	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	8	2	no	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	M₁₆×C₄₇	—	8	4	no	—
108	C₂×C₈×C₄₇	—	2	4	no	—
109	C₄⋊C₄×C₄₇	—	2	4	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	4	2	no	—
112	C₄⋊C₄×C₄₇	—	4	2	no	—
113	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
114	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂²⋊C₄×C₄₇	—	2	8	no	—
116	C₂²⋊C₄×C₄₇	—	2	4	no	—
117	C₂²⋊C₄×C₄₇	—	2	4	no	—
118	C₂²⋊C₄×C₄₇	—	4	4	no	—
119	C₂²⋊C₄×C₄₇	—	8	2	no	—
120	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
121	C₄²×C₄₇	—	4	2	no	—
122	C₄²×C₄₇	—	8	2	no	—
123	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₇	C₂×D₄	1	2	yes	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	4	no	—
128	C₂³×C₄₇	—	4	2	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	8	no	—
131	C₂³×C₄₇	—	8	4	no	—
132	C₂³×C₄₇	—	8	4	no	—
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
134	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₄₇	—	4	4	no	—
136	D₄×C₄₇	—	2	8	no	—
137	D₄×C₄₇	—	4	4	no	—
138	D₄×C₄₇	—	4	16	no	—
139	D₄×C₄₇	—	4	4	no	—
140	D₄×C₄₇	—	4	4	no	—
141	D₄×C₄₇	—	4	4	no	—
142	D₄×C₄₇	—	8	2	no	—
143	D₄×C₄₇	—	8	4	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	1	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	4	8	no	—
153	C₂×C₄×C₄₇	—	4	1	no	—
154	C₂×C₄×C₄₇	—	4	8	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	1	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₈×C₄₇	—	4	4	no	—
169	#17626	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	—	2	4	no	—
173	C₂²×C₄₇	—	2	4	no	—
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	4	4	no	—
176	C₂²×C₄₇	—	4	4	no	—
177	C₂²×C₄₇	—	4	4	no	—
178	C₂²×C₄₇	—	8	2	no	—
179	C₂²×C₄₇	—	8	2	no	—
180	C₂²×C₄₇	—	16	8	no	—
181	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₄×C₄₇	—	2	1	no	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	2	4	no	—
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	4	2	no	—
189	C₄×C₄₇	—	4	4	no	—
190	C₄×C₄₇	—	8	1	no	—
191	C₄×C₄₇	—	8	2	no	—
192	C₄×C₄₇	#418	1	4	yes	—
193	#3496	C₂×C₄₇	1	1	yes	characteristic
194	#2975	C₂×C₄₇	1	1	yes	characteristic, complemented
195	#2357	C₂×C₄₇	1	1	yes	characteristic, complemented
196	#1517	C₂×C₄₇	1	2	yes	complemented
197	#1510	C₂×C₄₇	1	4	yes	complemented
198	#1507	C₂×C₄₇	1	4	yes	complemented
199	#1502	C₂×C₄₇	1	2	yes	complemented
200	C₂×C₄₇	—	2	1	no	—
201	C₂×C₄₇	—	2	1	no	—
202	C₂×C₄₇	—	4	4	no	—
203	C₂×C₄₇	—	8	4	no	—
204	C₂×C₄₇	#2883	1	1	yes	characteristic
205	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
206	C₂×C₄₇	#2901	1	1	yes	characteristic
207	C₂×H(5,𝔽₂)	—	2	1	no	—
208	#547	C₄×C₄₇	1	4	yes	complemented
209	#546	—	2	4	no	—
210	D₄²	C₄×C₄₇	1	4	yes	complemented
211	#537	—	2	1	no	—
212	#534	—	2	2	no	—
213	#532	C₂²×C₄₇	1	2	yes	—
214	C₂×#121	C₂²×C₄₇	1	4	yes	—
215	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
216	#436	—	2	4	no	—
217	#431	C₂²×C₄₇	1	2	yes	complemented
218	#407	C₂²×C₄₇	1	4	yes	complemented
219	#390	—	2	1	no	—
220	#388	—	2	2	no	—
221	#382	C₂²×C₄₇	1	1	yes	characteristic, complemented
222	#381	C₂²×C₄₇	1	2	yes	complemented
223	C₄×C₄⋊C₄	—	2	1	no	—
224	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic, complemented
225	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	complemented
226	#327	C₂²×C₄₇	1	4	yes	complemented
227	#327	C₂²×C₄₇	1	4	yes	complemented
228	#327	C₂²×C₄₇	1	8	yes	complemented
229	C₄₇	#17626	1	1	yes	characteristic, direct product factor, Sylow
230	H(5,𝔽₂)	—	4	4	no	—
231	H(5,𝔽₂)	—	4	4	no	—
232	C₂×#41	—	2	4	no	—
233	C₂×#41	—	2	2	no	—
234	C₂²×D₄	—	2	4	no	—
235	C₂²×D₄	—	2	4	no	—
236	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
237	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
239	C₂×M₁₆	—	2	4	no	—
240	C₄⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
241	#127	C₂×C₄×C₄₇	1	2	yes	—
242	#124	—	2	2	no	—
243	#123	—	2	8	no	—
244	C₂²⋊Q₈	—	2	4	no	—
245	#121	—	2	4	no	—
246	#121	—	2	4	no	—
247	#121	—	2	2	no	—
248	#121	—	2	4	no	—
249	#121	C₂×C₄×C₄₇	1	8	yes	—
250	#121	C₂³×C₄₇	1	4	yes	—
251	#120	—	2	8	no	—
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
254	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
255	C₄×D₄	D₄×C₄₇	1	4	yes	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
259	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
267	C₄⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	—	2	4	no	—
269	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
270	C₄×C₈	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	1	no	—
273	#95	C₂³×C₄₇	1	1	yes	characteristic
274	#95	C₂³×C₄₇	1	2	yes	—
275	#95	C₂³×C₄₇	1	1	yes	characteristic
276	C₂⁴	—	2	4	no	—
277	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
278	#41	—	4	16	no	—
279	#41	—	4	4	no	—
280	#41	—	4	4	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	16	no	—
290	C₂×D₄	—	4	8	no	—
291	C₂×D₄	—	4	8	no	—
292	C₂×D₄	—	8	4	no	—
293	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	—
294	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	8	2	no	—
301	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
302	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
307	M₁₆	—	8	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
314	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	8	2	no	—
320	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
321	C₄²	—	4	2	no	—
322	C₄²	—	8	2	no	—
323	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
324	C₄²	C₂×D₄×C₄₇	1	2	yes	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	8	no	—
331	C₂³	—	8	4	no	—
332	C₂³	—	8	4	no	—
333	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
334	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
335	Q₈	—	4	4	no	—
336	D₄	—	2	8	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	16	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	4	no	—
342	D₄	—	8	2	no	—
343	D₄	—	8	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
364	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
365	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
366	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
368	C₈	—	4	4	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	8	no	—
380	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
381	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
382	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	4	no	—
386	C₄	—	2	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	4	no	—
389	C₄	—	8	1	no	—
390	C₄	—	8	2	no	—
391	C₄	C₄₇×#418	1	4	yes	—
392	C₂	—	2	1	no	—
393	C₂	—	2	1	no	—
394	C₂	—	4	4	no	—
395	C₂	—	8	4	no	—
396	C₂	C₄₇×#2883	1	1	yes	characteristic
397	C₂	C₂×C₄₇×#418	1	1	yes	characteristic
398	C₂	C₄₇×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2975	C₂	semidirect
3. C₄₇×#2357	C₂	semidirect
4. C₄₇×#1517	C₂	semidirect
5. C₄₇×#1510	C₂	semidirect
6. C₄₇×#1507	C₂	semidirect
7. C₄₇×#1502	C₂	semidirect
9. C₄₇×#547	C₄	semidirect
11. D₄²×C₄₇	C₄	semidirect
18. C₄₇×#431	C₂²	semidirect
19. C₄₇×#407	C₂²	semidirect
22. C₄₇×#382	C₂²	semidirect
23. C₄₇×#381	C₂²	semidirect
25. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
26. C₄×C₂²⋊C₄×C₄₇	C₂²	semidirect
27. C₄₇×#327	C₂²	semidirect
28. C₄₇×#327	C₂²	semidirect
29. C₄₇×#327	C₂²	semidirect
169. #17626	C₄₇	direct (N × H)
194. #2975	C₂×C₄₇	semidirect
195. #2357	C₂×C₄₇	semidirect
196. #1517	C₂×C₄₇	semidirect
197. #1510	C₂×C₄₇	semidirect
198. #1507	C₂×C₄₇	semidirect
199. #1502	C₂×C₄₇	semidirect
208. #547	C₄×C₄₇	semidirect
210. D₄²	C₄×C₄₇	semidirect
217. #431	C₂²×C₄₇	semidirect
218. #407	C₂²×C₄₇	semidirect
221. #382	C₂²×C₄₇	semidirect
222. #381	C₂²×C₄₇	semidirect
224. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
225. C₄×C₂²⋊C₄	C₂²×C₄₇	semidirect
226. #327	C₂²×C₄₇	semidirect
227. #327	C₂²×C₄₇	semidirect
228. #327	C₂²×C₄₇	semidirect
229. C₄₇	#17626	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3496	2
C₄₇×#2975	2
C₄₇×#2357	2
C₄₇×#1517	2
C₄₇×#1510	2
C₄₇×#1507	2
C₄₇×#1502	2
#17626	47

Subgroups — C47×#17626 #26057324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17626 #26057324