Subgroups — C₄₇×#34972 #26074670

Order 12032.

2474 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2604	C₂	1	4	yes	maximal, complemented
4	C₄₇×#2565	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2545	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2501	C₂	1	1	yes	maximal, characteristic
8	C₄₇×#2436	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#2434	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#2413	C₂	1	4	yes	maximal, complemented
11	C₄₇×#2396	C₂	1	4	yes	maximal, complemented
12	C₄×C₄⋊Q₈×C₄₇	C₂	1	2	yes	maximal, complemented
13	C₄×#124×C₄₇	C₂	1	2	yes	maximal, complemented
14	C₄×#123×C₄₇	C₂	1	4	yes	maximal, complemented
15	C₄×#117×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#529	—	2	8	no	—
19	C₂×#126×C₄₇	C₂²	1	2	yes	—
20	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#124×C₄₇	C₂²	1	2	yes	—
23	C₂×#123×C₄₇	C₂²	1	4	yes	—
24	C₂×#123×C₄₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₄₇	—	2	8	no	—
28	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	2	yes	—
36	C₂×#117×C₄₇	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
40	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#400	C₂²	1	4	yes	—
42	C₄₇×#399	C₂²	1	4	yes	—
43	C₄₇×#398	C₂²	1	8	yes	—
44	C₄₇×#396	C₂²	1	8	yes	—
45	C₄₇×#395	C₂²	1	4	yes	—
46	C₄₇×#393	C₂²	1	4	yes	—
47	C₄₇×#391	C₂²	1	2	yes	—
48	C₄₇×#391	C₂²	1	2	yes	—
49	C₄₇×#391	C₂²	1	2	yes	—
50	C₄₇×#390	C₂²	1	2	yes	—
51	C₄₇×#389	C₂²	1	8	yes	—
52	C₄₇×#388	C₂²	1	8	yes	—
53	C₄₇×#388	C₂²	1	8	yes	—
54	C₄₇×#387	C₂²	1	8	yes	—
55	C₄₇×#386	C₂²	1	4	yes	—
56	C₄₇×#385	C₂²	1	4	yes	—
57	C₄₇×#384	C₂²	1	2	yes	—
58	C₄₇×#382	C₂²	1	2	yes	—
59	C₄₇×#381	C₂²	1	4	yes	—
60	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₄₇	C₂²	1	8	yes	—
63	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
67	C₄₇×#376	C₂²	1	2	yes	—
68	C₄³×C₄₇	C₂²	1	2	yes	—
69	C₂²×Q₈×C₄₇	—	2	8	no	—
70	C₂²×Q₈×C₄₇	—	2	4	no	—
71	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
72	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
74	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
75	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
77	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₇	—	2	8	no	—
83	#126×C₄₇	—	2	8	no	—
84	#125×C₄₇	—	2	4	no	—
85	#124×C₄₇	—	2	8	no	—
86	#124×C₄₇	—	2	4	no	—
87	#123×C₄₇	—	2	8	no	—
88	#123×C₄₇	—	2	16	no	—
89	C₂²⋊Q₈×C₄₇	—	2	4	no	—
90	#121×C₄₇	—	2	4	no	—
91	C₄×Q₈×C₄₇	—	2	8	no	—
92	C₄×Q₈×C₄₇	—	2	8	no	—
93	C₄×Q₈×C₄₇	—	2	8	no	—
94	C₄×Q₈×C₄₇	—	2	8	no	—
95	C₄×Q₈×C₄₇	—	2	4	no	—
96	C₄×D₄×C₄₇	—	2	8	no	—
97	C₄×D₄×C₄₇	—	2	4	no	—
98	#117×C₄₇	—	2	8	no	—
99	#117×C₄₇	—	2	8	no	—
100	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
101	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
102	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
114	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
122	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
123	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
124	C₂×C₄²×C₄₇	—	2	8	no	—
125	C₂×C₄²×C₄₇	D₄	1	8	yes	—
126	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
127	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
128	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
129	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
130	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
131	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
132	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
133	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
137	#95×C₄₇	C₂³	1	4	yes	—
138	#95×C₄₇	C₂³	1	2	yes	—
139	#95×C₄₇	C₂³	1	2	yes	—
140	#95×C₄₇	C₂³	1	8	yes	—
141	#95×C₄₇	C₂³	1	8	yes	—
142	#95×C₄₇	C₂³	1	8	yes	—
143	#95×C₄₇	C₂³	1	8	yes	—
144	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
145	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂×Q₈×C₄₇	—	2	32	no	—
147	C₂×Q₈×C₄₇	—	2	4	no	—
148	C₂×Q₈×C₄₇	—	2	4	no	—
149	C₂×Q₈×C₄₇	—	2	2	no	—
150	C₂×Q₈×C₄₇	—	2	8	no	—
151	C₂×Q₈×C₄₇	—	2	4	no	—
152	C₂×Q₈×C₄₇	—	2	4	no	—
153	C₂×Q₈×C₄₇	#41	1	8	yes	—
154	C₂×D₄×C₄₇	—	2	4	no	—
155	C₂×D₄×C₄₇	—	2	8	no	—
156	C₂×D₄×C₄₇	—	2	2	no	—
157	C₂×D₄×C₄₇	—	2	4	no	—
158	C₂²×C₄×C₄₇	—	2	4	no	—
159	C₂²×C₄×C₄₇	—	2	4	no	—
160	C₂²×C₄×C₄₇	—	2	8	no	—
161	C₂²×C₄×C₄₇	—	2	4	no	—
162	C₂²×C₄×C₄₇	—	2	4	no	—
163	C₂²×C₄×C₄₇	—	2	4	no	—
164	C₂²×C₄×C₄₇	—	2	8	no	—
165	C₂²×C₄×C₄₇	—	2	4	no	—
166	C₂²×C₄×C₄₇	—	2	8	no	—
167	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
183	C₄⋊C₄×C₄₇	—	2	8	no	—
184	C₄⋊C₄×C₄₇	—	2	8	no	—
185	C₄⋊C₄×C₄₇	—	2	4	no	—
186	C₄⋊C₄×C₄₇	—	2	4	no	—
187	C₄⋊C₄×C₄₇	—	2	4	no	—
188	C₄⋊C₄×C₄₇	—	2	4	no	—
189	C₄⋊C₄×C₄₇	—	2	2	no	—
190	C₄⋊C₄×C₄₇	—	2	4	no	—
191	C₄⋊C₄×C₄₇	—	2	2	no	—
192	C₄⋊C₄×C₄₇	—	2	4	no	—
193	C₄⋊C₄×C₄₇	—	2	8	no	—
194	C₄⋊C₄×C₄₇	—	2	16	no	—
195	C₄⋊C₄×C₄₇	—	2	16	no	—
196	C₂²⋊C₄×C₄₇	—	2	4	no	—
197	C₂²⋊C₄×C₄₇	—	2	4	no	—
198	C₂²⋊C₄×C₄₇	—	2	4	no	—
199	C₂²⋊C₄×C₄₇	—	2	4	no	—
200	C₂²⋊C₄×C₄₇	—	2	4	no	—
201	C₂²⋊C₄×C₄₇	—	2	4	no	—
202	C₂²⋊C₄×C₄₇	—	2	16	no	—
203	C₂²⋊C₄×C₄₇	—	2	16	no	—
204	C₂²⋊C₄×C₄₇	#41	1	8	yes	—
205	C₄²×C₄₇	—	2	8	no	—
206	C₄²×C₄₇	—	2	8	no	—
207	C₄²×C₄₇	—	2	4	no	—
208	C₄²×C₄₇	—	2	8	no	—
209	C₄²×C₄₇	—	2	4	no	—
210	C₄²×C₄₇	—	2	4	no	—
211	C₄²×C₄₇	—	2	8	no	—
212	C₄²×C₄₇	C₂×D₄	1	4	yes	—
213	C₄²×C₄₇	C₂×D₄	1	4	yes	—
214	C₄²×C₄₇	C₂×D₄	1	4	yes	—
215	C₄²×C₄₇	C₂×D₄	1	4	yes	—
216	C₂³×C₄₇	—	2	2	no	—
217	C₂³×C₄₇	—	2	2	no	—
218	C₂³×C₄₇	—	2	2	no	—
219	C₂³×C₄₇	—	2	4	no	—
220	C₂³×C₄₇	—	2	4	no	—
221	C₂³×C₄₇	—	2	4	no	—
222	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
223	C₂³×C₄₇	C₂×#41	1	4	yes	—
224	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
225	Q₈×C₄₇	—	2	16	no	—
226	Q₈×C₄₇	—	2	16	no	—
227	Q₈×C₄₇	—	4	4	no	—
228	D₄×C₄₇	—	4	8	no	—
229	D₄×C₄₇	—	4	4	no	—
230	C₂×C₄×C₄₇	—	2	16	no	—
231	C₂×C₄×C₄₇	—	2	8	no	—
232	C₂×C₄×C₄₇	—	2	4	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	4	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	2	2	no	—
237	C₂×C₄×C₄₇	—	2	4	no	—
238	C₂×C₄×C₄₇	—	2	4	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	2	8	no	—
241	C₂×C₄×C₄₇	—	2	8	no	—
242	C₂×C₄×C₄₇	—	2	4	no	—
243	C₂×C₄×C₄₇	—	2	2	no	—
244	C₂×C₄×C₄₇	—	2	2	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	4	no	—
247	C₂×C₄×C₄₇	—	2	4	no	—
248	C₂×C₄×C₄₇	—	2	8	no	—
249	C₂×C₄×C₄₇	—	2	4	no	—
250	C₂×C₄×C₄₇	—	2	4	no	—
251	C₂×C₄×C₄₇	—	2	4	no	—
252	C₂×C₄×C₄₇	—	2	4	no	—
253	C₂×C₄×C₄₇	—	4	8	no	—
254	C₂×C₄×C₄₇	—	4	8	no	—
255	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
262	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
263	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
264	C₂×C₄×C₄₇	2₋¹⁺⁴	1	4	yes	—
265	#34972	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂²×C₄₇	—	2	2	no	—
267	C₂²×C₄₇	—	2	2	no	—
268	C₂²×C₄₇	—	2	8	no	—
269	C₂²×C₄₇	—	4	2	no	—
270	C₂²×C₄₇	—	4	2	no	—
271	C₂²×C₄₇	—	4	2	no	—
272	C₂²×C₄₇	—	4	8	no	—
273	C₂²×C₄₇	#532	1	4	yes	—
274	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
275	C₂²×C₄₇	C₂²×#41	1	2	yes	—
276	C₂²×C₄₇	C₂²×#41	1	2	yes	—
277	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
278	C₄×C₄₇	—	2	2	no	—
279	C₄×C₄₇	—	2	8	no	—
280	C₄×C₄₇	—	2	2	no	—
281	C₄×C₄₇	—	2	2	no	—
282	C₄×C₄₇	—	2	2	no	—
283	C₄×C₄₇	—	2	8	no	—
284	C₄×C₄₇	—	4	2	no	—
285	C₄×C₄₇	—	4	4	no	—
286	C₄×C₄₇	—	4	2	no	—
287	C₄×C₄₇	—	4	2	no	—
288	C₄×C₄₇	—	4	4	no	—
289	C₄×C₄₇	#525	1	4	yes	—
290	C₄×C₄₇	#536	1	4	yes	—
291	C₂×#529	C₂×C₄₇	1	1	yes	characteristic
292	C₂²×C₄×Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
293	#2604	C₂×C₄₇	1	4	yes	complemented
294	#2565	C₂×C₄₇	1	2	yes	complemented
295	#2545	C₂×C₄₇	1	2	yes	complemented
296	#2503	C₂×C₄₇	1	1	yes	characteristic, complemented
297	#2501	C₂×C₄₇	1	1	yes	characteristic
298	#2436	C₂×C₄₇	1	1	yes	characteristic
299	#2434	C₂×C₄₇	1	1	yes	characteristic, complemented
300	#2413	C₂×C₄₇	1	4	yes	complemented
301	#2396	C₂×C₄₇	1	4	yes	complemented
302	C₄×C₄⋊Q₈	C₂×C₄₇	1	2	yes	complemented
303	C₄×#124	C₂×C₄₇	1	2	yes	complemented
304	C₄×#123	C₂×C₄₇	1	4	yes	complemented
305	C₄×#117	C₂×C₄₇	1	1	yes	characteristic, complemented
306	C₂×C₄₇	—	2	4	no	—
307	C₂×C₄₇	—	8	2	no	—
308	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
309	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
310	C₂×C₄₇	C₂×#536	1	1	yes	characteristic
311	C₂×C₄₇	#3482	1	4	yes	—
312	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
313	C₂×C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
314	#529	—	2	8	no	—
315	C₂×#126	C₂²×C₄₇	1	2	yes	—
316	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
317	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
318	C₂×#124	C₂²×C₄₇	1	2	yes	—
319	C₂×#123	C₂²×C₄₇	1	2	yes	—
320	C₂×#123	C₂²×C₄₇	1	4	yes	—
321	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
322	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
323	C₂×C₄×Q₈	—	2	8	no	—
324	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
325	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
326	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
327	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
328	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
329	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
330	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
331	C₂×#117	C₂²×C₄₇	1	2	yes	—
332	C₂×#117	C₂²×C₄₇	1	2	yes	—
333	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
334	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
335	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
336	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
337	#400	C₂²×C₄₇	1	4	yes	—
338	#399	C₂²×C₄₇	1	4	yes	—
339	#398	C₂²×C₄₇	1	8	yes	—
340	#396	C₂²×C₄₇	1	8	yes	—
341	#395	C₂²×C₄₇	1	4	yes	—
342	#393	C₂²×C₄₇	1	4	yes	—
343	#391	C₂²×C₄₇	1	2	yes	—
344	#391	C₂²×C₄₇	1	2	yes	—
345	#391	C₂²×C₄₇	1	2	yes	—
346	#390	C₂²×C₄₇	1	2	yes	—
347	#389	C₂²×C₄₇	1	8	yes	—
348	#388	C₂²×C₄₇	1	8	yes	—
349	#388	C₂²×C₄₇	1	8	yes	—
350	#387	C₂²×C₄₇	1	8	yes	—
351	#386	C₂²×C₄₇	1	4	yes	—
352	#385	C₂²×C₄₇	1	4	yes	—
353	#384	C₂²×C₄₇	1	2	yes	—
354	#382	C₂²×C₄₇	1	2	yes	—
355	#381	C₂²×C₄₇	1	4	yes	—
356	C₄×C₄⋊C₄	C₂²×C₄₇	1	8	yes	—
357	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
358	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
359	C₄×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
360	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
361	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
362	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
363	#376	C₂²×C₄₇	1	2	yes	—
364	C₄³	C₂²×C₄₇	1	2	yes	—
365	C₄₇	#34972	1	1	yes	characteristic, direct product factor, Sylow
366	C₂²×Q₈	—	2	8	no	—
367	C₂²×Q₈	—	2	4	no	—
368	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
369	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
370	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
371	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
372	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
374	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
375	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
376	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
378	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
379	C₄⋊Q₈	—	2	8	no	—
380	#126	—	2	8	no	—
381	#125	—	2	4	no	—
382	#124	—	2	8	no	—
383	#124	—	2	4	no	—
384	#123	—	2	8	no	—
385	#123	—	2	16	no	—
386	C₂²⋊Q₈	—	2	4	no	—
387	#121	—	2	4	no	—
388	C₄×Q₈	—	2	8	no	—
389	C₄×Q₈	—	2	8	no	—
390	C₄×Q₈	—	2	8	no	—
391	C₄×Q₈	—	2	8	no	—
392	C₄×Q₈	—	2	4	no	—
393	C₄×D₄	—	2	8	no	—
394	C₄×D₄	—	2	4	no	—
395	#117	—	2	8	no	—
396	#117	—	2	8	no	—
397	C₂×C₄⋊C₄	—	2	8	no	—
398	C₂×C₄⋊C₄	—	2	4	no	—
399	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
406	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
411	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
421	C₂×C₄²	—	2	8	no	—
422	C₂×C₄²	D₄×C₄₇	1	8	yes	—
423	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
424	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
425	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
426	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
427	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
428	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
429	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
430	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
434	#95	C₂³×C₄₇	1	4	yes	—
435	#95	C₂³×C₄₇	1	2	yes	—
436	#95	C₂³×C₄₇	1	2	yes	—
437	#95	C₂³×C₄₇	1	8	yes	—
438	#95	C₂³×C₄₇	1	8	yes	—
439	#95	C₂³×C₄₇	1	8	yes	—
440	#95	C₂³×C₄₇	1	8	yes	—
441	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
442	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
443	C₂×Q₈	—	2	32	no	—
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	2	4	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	8	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	#41×C₄₇	1	8	yes	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	8	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	8	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	8	no	—
464	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
465	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
466	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
468	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
480	C₄⋊C₄	—	2	8	no	—
481	C₄⋊C₄	—	2	8	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	8	no	—
491	C₄⋊C₄	—	2	16	no	—
492	C₄⋊C₄	—	2	16	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	16	no	—
500	C₂²⋊C₄	—	2	16	no	—
501	C₂²⋊C₄	#41×C₄₇	1	8	yes	—
502	C₄²	—	2	8	no	—
503	C₄²	—	2	8	no	—
504	C₄²	—	2	4	no	—
505	C₄²	—	2	8	no	—
506	C₄²	—	2	4	no	—
507	C₄²	—	2	4	no	—
508	C₄²	—	2	8	no	—
509	C₄²	C₂×D₄×C₄₇	1	4	yes	—
510	C₄²	C₂×D₄×C₄₇	1	4	yes	—
511	C₄²	C₂×D₄×C₄₇	1	4	yes	—
512	C₄²	C₂×D₄×C₄₇	1	4	yes	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
520	C₂³	C₂×#41×C₄₇	1	4	yes	—
521	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
522	Q₈	—	2	16	no	—
523	Q₈	—	2	16	no	—
524	Q₈	—	4	4	no	—
525	D₄	—	4	8	no	—
526	D₄	—	4	4	no	—
527	C₂×C₄	—	2	16	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	4	8	no	—
551	C₂×C₄	—	4	8	no	—
552	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
558	C₂×C₄	C₂×#41×C₄₇	1	8	yes	—
559	C₂×C₄	C₂×#41×C₄₇	1	8	yes	—
560	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
561	C₂×C₄	2₋¹⁺⁴×C₄₇	1	4	yes	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	8	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	8	no	—
569	C₂²	C₄₇×#532	1	4	yes	—
570	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
571	C₂²	C₂²×#41×C₄₇	1	2	yes	—
572	C₂²	C₂²×#41×C₄₇	1	2	yes	—
573	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	2	yes	—
574	C₄	—	2	2	no	—
575	C₄	—	2	8	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	8	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	4	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	4	no	—
585	C₄	C₄₇×#525	1	4	yes	—
586	C₄	C₄₇×#536	1	4	yes	—
587	C₂	—	2	4	no	—
588	C₂	—	8	2	no	—
589	C₂	C₂×C₄₇×#525	1	1	yes	characteristic
590	C₂	C₂×C₄₇×#532	1	1	yes	characteristic
591	C₂	C₂×C₄₇×#536	1	1	yes	characteristic
592	C₂	C₄₇×#3482	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
socle	C₂³×C₄₇	C₂⁵
prime radical	C₂×#121×C₄₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₄₇	C₂	semidirect
3. C₄₇×#2604	C₂	semidirect
4. C₄₇×#2565	C₂	semidirect
5. C₄₇×#2545	C₂	semidirect
6. C₄₇×#2503	C₂	semidirect
9. C₄₇×#2434	C₂	semidirect
10. C₄₇×#2413	C₂	semidirect
11. C₄₇×#2396	C₂	semidirect
12. C₄×C₄⋊Q₈×C₄₇	C₂	semidirect
13. C₄×#124×C₄₇	C₂	semidirect
14. C₄×#123×C₄₇	C₂	semidirect
15. C₄×#117×C₄₇	C₂	semidirect
265. #34972	C₄₇	direct (N × H)
292. C₂²×C₄×Q₈	C₂×C₄₇	semidirect
293. #2604	C₂×C₄₇	semidirect
294. #2565	C₂×C₄₇	semidirect
295. #2545	C₂×C₄₇	semidirect
296. #2503	C₂×C₄₇	semidirect
299. #2434	C₂×C₄₇	semidirect
300. #2413	C₂×C₄₇	semidirect
301. #2396	C₂×C₄₇	semidirect
302. C₄×C₄⋊Q₈	C₂×C₄₇	semidirect
303. C₄×#124	C₂×C₄₇	semidirect
304. C₄×#123	C₂×C₄₇	semidirect
305. C₄×#117	C₂×C₄₇	semidirect
365. C₄₇	#34972	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×#529	2
C₂²×C₄×Q₈×C₄₇	2
C₄₇×#2604	2
C₄₇×#2565	2
C₄₇×#2545	2
C₄₇×#2503	2
C₄₇×#2501	2
C₄₇×#2436	2
C₄₇×#2434	2
C₄₇×#2413	2
C₄₇×#2396	2
C₄×C₄⋊Q₈×C₄₇	2
C₄×#124×C₄₇	2
C₄×#123×C₄₇	2
C₄×#117×C₄₇	2
#34972	47

Subgroups — C47×#34972 #26074670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#34972 #26074670