Subgroups — C₄₇×#24312 #26064010

Order 12032.

1170 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3077	C₂	1	2	yes	maximal, complemented
3	C₄×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2060	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2027	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1994	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1887	C₂	1	2	yes	maximal
8	C₄₇×#1856	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1800	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#554	—	2	2	no	—
11	C₄₇×#554	—	2	4	no	—
12	D₄×Q₈×C₄₇	—	2	2	no	—
13	C₄₇×#544	C₂²	1	2	yes	—
14	C₄₇×#543	—	2	2	no	—
15	C₄₇×#533	C₂²	1	2	yes	—
16	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
18	C₄₇×#518	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₄₇	—	2	2	no	—
20	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#478	—	2	4	no	—
23	C₄₇×#476	—	2	2	no	—
24	C₄₇×#474	—	2	2	no	—
25	C₄₇×#428	C₂²	1	4	yes	—
26	C₄₇×#423	C₂²	1	2	yes	—
27	C₄₇×#418	C₂²	1	4	yes	—
28	C₂×#100×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#390	—	2	2	no	—
30	C₄₇×#390	C₂²	1	1	yes	characteristic
31	C₄₇×#390	C₂²	1	1	yes	characteristic
32	C₄₇×#384	C₂²	1	1	yes	characteristic
33	C₄³×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#343	C₂²	1	2	yes	—
35	C₄₇×#339	C₂²	1	4	yes	—
36	C₄₇×#339	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₇	—	2	2	no	—
38	C₂²×D₄×C₄₇	—	2	2	no	—
39	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	—	2	1	no	—
42	C₂³×C₄×C₄₇	D₄	1	2	yes	—
43	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
44	C₄⋊Q₈×C₄₇	—	2	4	no	—
45	C₄⋊Q₈×C₄₇	D₄	1	2	yes	complemented
46	C₄⋊Q₈×C₄₇	D₄	1	2	yes	complemented
47	#127×C₄₇	—	2	2	no	—
48	#127×C₄₇	Q₈	1	4	yes	complemented
49	#125×C₄₇	—	2	4	no	—
50	#125×C₄₇	D₄	1	4	yes	complemented
51	C₂²⋊Q₈×C₄₇	—	2	4	no	—
52	C₂²⋊Q₈×C₄₇	—	2	4	no	—
53	C₂²⋊Q₈×C₄₇	—	2	8	no	—
54	C₂²⋊Q₈×C₄₇	—	2	8	no	—
55	C₂²⋊Q₈×C₄₇	—	2	2	no	—
56	C₂²⋊Q₈×C₄₇	—	2	4	no	—
57	C₂²⋊Q₈×C₄₇	—	2	2	no	—
58	C₄×Q₈×C₄₇	—	2	2	no	—
59	C₄×Q₈×C₄₇	—	2	2	no	—
60	C₄×D₄×C₄₇	—	2	4	no	—
61	C₄×D₄×C₄₇	—	2	4	no	—
62	C₄×D₄×C₄₇	—	2	2	no	—
63	C₄×D₄×C₄₇	—	2	2	no	—
64	C₄×D₄×C₄₇	—	2	2	no	—
65	C₄×D₄×C₄₇	—	2	2	no	—
66	C₄×D₄×C₄₇	—	4	8	no	—
67	#117×C₄₇	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
78	C₂×C₄²×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	#107×C₄₇	—	2	4	no	—
84	#106×C₄₇	—	2	4	no	—
85	C₄⋊C₈×C₄₇	—	2	2	no	—
86	C₄⋊C₈×C₄₇	—	2	2	no	—
87	#102×C₄₇	—	2	4	no	—
88	#102×C₄₇	—	2	4	no	—
89	#100×C₄₇	—	2	4	no	—
90	C₂⁴×C₄₇	—	2	1	no	—
91	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
92	C₂×Q₈×C₄₇	—	2	4	no	—
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	8	4	no	—
96	C₂×D₄×C₄₇	—	2	8	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	1	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	4	4	no	—
103	C₂×D₄×C₄₇	—	4	4	no	—
104	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	—
105	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	complemented
106	C₂×D₄×C₄₇	#41	1	2	yes	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	4	4	no	—
115	C₂²×C₄×C₄₇	—	4	4	no	—
116	C₂²×C₄×C₄₇	—	4	1	no	—
117	C₂²×C₄×C₄₇	—	4	1	no	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₄₇	—	2	4	no	—
123	M₁₆×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	—	2	4	no	—
126	C₄⋊C₄×C₄₇	—	2	8	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	4	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	4	4	no	—
134	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
135	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
136	C₂²⋊C₄×C₄₇	—	2	8	no	—
137	C₂²⋊C₄×C₄₇	—	2	4	no	—
138	C₂²⋊C₄×C₄₇	—	2	4	no	—
139	C₂²⋊C₄×C₄₇	—	4	4	no	—
140	C₂²⋊C₄×C₄₇	—	4	4	no	—
141	C₂²⋊C₄×C₄₇	—	4	2	no	—
142	C₄²×C₄₇	—	2	4	no	—
143	C₄²×C₄₇	—	2	4	no	—
144	C₄²×C₄₇	—	2	1	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	—	4	2	no	—
147	C₄²×C₄₇	C₂×D₄	1	2	yes	—
148	C₄²×C₄₇	C₂×D₄	1	2	yes	—
149	C₄²×C₄₇	C₂×Q₈	1	2	yes	complemented
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	4	2	no	—
154	C₂³×C₄₇	—	4	2	no	—
155	C₂³×C₄₇	—	4	2	no	—
156	C₂³×C₄₇	—	4	2	no	—
157	C₂³×C₄₇	—	4	1	no	—
158	C₂³×C₄₇	—	4	1	no	—
159	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
160	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₄₇	—	4	4	no	—
162	Q₈×C₄₇	—	8	2	no	—
163	Q₈×C₄₇	—	8	4	no	—
164	D₄×C₄₇	—	2	4	no	—
165	D₄×C₄₇	—	2	4	no	—
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	—	4	16	no	—
168	D₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	4	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	8	2	no	—
185	C₂×C₄×C₄₇	—	8	2	no	—
186	C₂×C₄×C₄₇	—	8	4	no	—
187	C₂×C₄×C₄₇	—	8	4	no	—
188	C₂×C₄×C₄₇	—	8	2	no	—
189	C₂×C₄×C₄₇	#120	1	2	yes	—
190	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
191	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
196	C₈×C₄₇	—	4	4	no	—
197	#24312	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	4	no	—
201	C₂²×C₄₇	—	4	4	no	—
202	C₂²×C₄₇	—	4	4	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	8	2	no	—
207	C₂²×C₄₇	—	8	2	no	—
208	C₂²×C₄₇	—	8	1	no	—
209	C₂²×C₄₇	—	8	1	no	—
210	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
212	C₂²×C₄₇	#536	1	1	yes	characteristic
213	C₄×C₄₇	—	2	4	no	—
214	C₄×C₄₇	—	2	1	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	4	2	no	—
217	C₄×C₄₇	—	4	2	no	—
218	C₄×C₄₇	—	4	4	no	—
219	C₄×C₄₇	—	4	4	no	—
220	C₄×C₄₇	—	8	1	no	—
221	C₄×C₄₇	#453	1	2	yes	—
222	C₄×C₄₇	#548	1	2	yes	—
223	C₄×C₄₇	D₄×Q₈	1	2	yes	—
224	#3501	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#3077	C₂×C₄₇	1	2	yes	complemented
226	C₄×#127	C₂×C₄₇	1	1	yes	characteristic
227	#2060	C₂×C₄₇	1	2	yes	complemented
228	#2027	C₂×C₄₇	1	2	yes	complemented
229	#1994	C₂×C₄₇	1	2	yes	complemented
230	#1887	C₂×C₄₇	1	2	yes	—
231	#1856	C₂×C₄₇	1	2	yes	complemented
232	#1800	C₂×C₄₇	1	1	yes	characteristic, complemented
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	2	1	no	—
235	C₂×C₄₇	—	4	4	no	—
236	C₂×C₄₇	—	8	2	no	—
237	C₂×C₄₇	#2409	1	1	yes	characteristic
238	C₂×C₄₇	C₂×#453	1	1	yes	characteristic
239	C₂×C₄₇	#3018	1	1	yes	characteristic
240	#554	—	2	2	no	—
241	#554	—	2	4	no	—
242	D₄×Q₈	—	2	2	no	—
243	#544	C₂²×C₄₇	1	2	yes	—
244	#543	—	2	2	no	—
245	#533	C₂²×C₄₇	1	2	yes	—
246	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	—	2	2	no	—
248	#518	C₂²×C₄₇	1	2	yes	—
249	C₂×C₄×D₄	—	2	2	no	—
250	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
252	#478	—	2	4	no	—
253	#476	—	2	2	no	—
254	#474	—	2	2	no	—
255	#428	C₂²×C₄₇	1	4	yes	—
256	#423	C₂²×C₄₇	1	2	yes	—
257	#418	C₂²×C₄₇	1	4	yes	—
258	C₂×#100	C₂²×C₄₇	1	2	yes	—
259	#390	—	2	2	no	—
260	#390	C₂²×C₄₇	1	1	yes	characteristic
261	#390	C₂²×C₄₇	1	1	yes	characteristic
262	#384	C₂²×C₄₇	1	1	yes	characteristic
263	C₄³	C₂²×C₄₇	1	1	yes	characteristic
264	#343	C₂²×C₄₇	1	2	yes	—
265	#339	C₂²×C₄₇	1	4	yes	—
266	#339	C₂²×C₄₇	1	4	yes	—
267	C₄₇	#24312	1	1	yes	characteristic, direct product factor, Sylow
268	C₂²×Q₈	—	2	2	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
271	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	D₄×C₄₇	1	2	yes	—
274	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
275	C₄⋊Q₈	—	2	4	no	—
276	C₄⋊Q₈	D₄×C₄₇	1	2	yes	complemented
277	C₄⋊Q₈	D₄×C₄₇	1	2	yes	complemented
278	#127	—	2	2	no	—
279	#127	Q₈×C₄₇	1	4	yes	complemented
280	#125	—	2	4	no	—
281	#125	D₄×C₄₇	1	4	yes	complemented
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	—	2	4	no	—
284	C₂²⋊Q₈	—	2	8	no	—
285	C₂²⋊Q₈	—	2	8	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	2	4	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	4	8	no	—
298	#117	C₂³×C₄₇	1	4	yes	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	4	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
314	#107	—	2	4	no	—
315	#106	—	2	4	no	—
316	C₄⋊C₈	—	2	2	no	—
317	C₄⋊C₈	—	2	2	no	—
318	#102	—	2	4	no	—
319	#102	—	2	4	no	—
320	#100	—	2	4	no	—
321	C₂⁴	—	2	1	no	—
322	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	8	4	no	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	C₂×Q₈×C₄₇	1	2	yes	—
336	C₂×D₄	C₂×Q₈×C₄₇	1	2	yes	complemented
337	C₂×D₄	#41×C₄₇	1	2	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
353	M₁₆	—	2	4	no	—
354	M₁₆	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	8	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
366	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
367	C₂²⋊C₄	—	2	8	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	2	no	—
378	C₄²	C₂×D₄×C₄₇	1	2	yes	—
379	C₄²	C₂×D₄×C₄₇	1	2	yes	—
380	C₄²	C₂×Q₈×C₄₇	1	2	yes	complemented
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	C₂²⋊Q₈×C₄₇	1	4	yes	—
391	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
392	Q₈	—	4	4	no	—
393	Q₈	—	8	2	no	—
394	Q₈	—	8	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	4	16	no	—
399	D₄	—	4	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	8	2	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	#120×C₄₇	1	2	yes	—
421	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
422	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
424	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
426	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
427	C₈	—	4	4	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
441	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
442	C₂²	C₄₇×#536	1	1	yes	characteristic
443	C₄	—	2	4	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	4	no	—
450	C₄	—	8	1	no	—
451	C₄	C₄₇×#453	1	2	yes	—
452	C₄	C₄₇×#548	1	2	yes	—
453	C₄	D₄×Q₈×C₄₇	1	2	yes	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	4	4	no	—
457	C₂	—	8	2	no	—
458	C₂	C₄₇×#2409	1	1	yes	characteristic
459	C₂	C₂×C₄₇×#453	1	1	yes	characteristic
460	C₂	C₄₇×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×#127×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3501	C₂	semidirect
2. C₄₇×#3077	C₂	semidirect
4. C₄₇×#2060	C₂	semidirect
5. C₄₇×#2027	C₂	semidirect
6. C₄₇×#1994	C₂	semidirect
8. C₄₇×#1856	C₂	semidirect
9. C₄₇×#1800	C₂	semidirect
45. C₄⋊Q₈×C₄₇	D₄	semidirect
46. C₄⋊Q₈×C₄₇	D₄	semidirect
48. #127×C₄₇	Q₈	semidirect
50. #125×C₄₇	D₄	semidirect
105. C₂×D₄×C₄₇	C₂×Q₈	semidirect
149. C₄²×C₄₇	C₂×Q₈	semidirect
197. #24312	C₄₇	direct (N × H)
224. #3501	C₂×C₄₇	semidirect
225. #3077	C₂×C₄₇	semidirect
227. #2060	C₂×C₄₇	semidirect
228. #2027	C₂×C₄₇	semidirect
229. #1994	C₂×C₄₇	semidirect
231. #1856	C₂×C₄₇	semidirect
232. #1800	C₂×C₄₇	semidirect
267. C₄₇	#24312	direct (N × H)
276. C₄⋊Q₈	D₄×C₄₇	semidirect
277. C₄⋊Q₈	D₄×C₄₇	semidirect
279. #127	Q₈×C₄₇	semidirect
281. #125	D₄×C₄₇	semidirect
336. C₂×D₄	C₂×Q₈×C₄₇	semidirect
380. C₄²	C₂×Q₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3501	2
C₄₇×#3077	2
C₄×#127×C₄₇	2
C₄₇×#2060	2
C₄₇×#2027	2
C₄₇×#1994	2
C₄₇×#1887	2
C₄₇×#1856	2
C₄₇×#1800	2
#24312	47

Subgroups — C47×#24312 #26064010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24312 #26064010