Subgroups — C₄₇×#17426 #26057124

Order 12032.

996 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#554	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2974	C₂	1	2	yes	maximal
3	C₄₇×#1472	C₂	1	4	yes	maximal, complemented
4	C₄₇×#1470	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1463	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#324	C₂	1	2	yes	maximal, complemented
9	C₄₇×#554	—	2	2	no	—
10	C₄₇×#554	—	2	4	no	—
11	C₄₇×#554	—	2	2	no	—
12	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
13	C₂×#125×C₄₇	C₄	1	1	yes	characteristic
14	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
23	C₄₇×#436	—	2	2	no	—
24	C₄₇×#435	—	2	4	no	—
25	C₈×D₄×C₄₇	—	2	2	no	—
26	C₄₇×#432	C₂²	1	2	yes	—
27	C₄₇×#431	C₂²	1	2	yes	—
28	C₄₇×#407	C₂²	1	4	yes	—
29	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
30	C₄₇×#324	C₂²	1	1	yes	characteristic
31	C₄₇×#324	C₂²	1	2	yes	—
32	C₄₇×#324	C₂²	1	4	yes	—
33	C₄₇×#324	C₂²	1	1	yes	characteristic
34	C₄₇×#324	C₂²	1	2	yes	—
35	C₄₇×#324	C₂²	1	4	yes	—
36	C₄₇×#324	C₂²	1	2	yes	—
37	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
39	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
43	C₂×M₁₆×C₄₇	—	2	4	no	—
44	C₂²×C₈×C₄₇	—	2	4	no	—
45	C₄⋊Q₈×C₄₇	—	2	2	no	—
46	C₄⋊Q₈×C₄₇	—	2	2	no	—
47	#125×C₄₇	—	2	2	no	—
48	#125×C₄₇	—	2	2	no	—
49	#125×C₄₇	—	2	2	no	—
50	#125×C₄₇	—	2	2	no	—
51	C₂²⋊Q₈×C₄₇	—	2	4	no	—
52	C₂²⋊Q₈×C₄₇	—	2	4	no	—
53	C₂²⋊Q₈×C₄₇	—	2	4	no	—
54	C₂²⋊Q₈×C₄₇	—	2	4	no	—
55	C₂²⋊Q₈×C₄₇	—	2	4	no	—
56	C₂²⋊Q₈×C₄₇	—	2	4	no	—
57	C₄×Q₈×C₄₇	—	2	2	no	—
58	C₄×Q₈×C₄₇	—	2	2	no	—
59	C₄×D₄×C₄₇	—	2	2	no	—
60	C₄×D₄×C₄₇	—	2	1	no	—
61	C₄×D₄×C₄₇	—	2	1	no	—
62	C₄×D₄×C₄₇	—	2	2	no	—
63	C₄×D₄×C₄₇	—	2	1	no	—
64	C₄×D₄×C₄₇	—	2	1	no	—
65	C₄×D₄×C₄₇	D₄	1	2	yes	—
66	C₄×D₄×C₄₇	D₄	1	4	yes	—
67	C₄×D₄×C₄₇	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₄₇	—	2	2	no	—
88	C₄⋊C₈×C₄₇	—	2	2	no	—
89	C₂²⋊C₈×C₄₇	—	2	4	no	—
90	C₂²⋊C₈×C₄₇	—	2	4	no	—
91	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
92	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
93	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
94	#97×C₄₇	—	2	2	no	—
95	C₄×C₈×C₄₇	—	2	2	no	—
96	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	4	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	—	4	1	no	—
101	C₂×Q₈×C₄₇	—	8	2	no	—
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
104	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	4	2	no	—
112	C₂²×C₄×C₄₇	—	8	2	no	—
113	C₂²×C₄×C₄₇	—	8	2	no	—
114	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
126	M₁₆×C₄₇	—	8	4	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	4	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	8	4	no	—
131	C₄⋊C₄×C₄₇	—	2	4	no	—
132	C₄⋊C₄×C₄₇	—	2	4	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	4	no	—
139	C₄⋊C₄×C₄₇	—	2	4	no	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	2	4	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
144	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
145	C₂²⋊C₄×C₄₇	—	2	2	no	—
146	C₂²⋊C₄×C₄₇	—	2	2	no	—
147	C₂²⋊C₄×C₄₇	—	2	2	no	—
148	C₂²⋊C₄×C₄₇	—	2	2	no	—
149	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
150	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
151	C₄²×C₄₇	—	2	1	no	—
152	C₄²×C₄₇	—	2	1	no	—
153	C₄²×C₄₇	—	2	1	no	—
154	C₄²×C₄₇	—	2	1	no	—
155	C₄²×C₄₇	C₂×D₄	1	2	yes	—
156	C₄²×C₄₇	C₂×D₄	1	2	yes	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	2	4	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	Q₈×C₄₇	—	4	4	no	—
165	Q₈×C₄₇	—	8	4	no	—
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	—	2	2	no	—
168	D₄×C₄₇	#101	1	4	yes	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	4	4	no	—
184	C₂×C₄×C₄₇	—	4	4	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	4	no	—
188	C₂×C₄×C₄₇	—	4	4	no	—
189	C₂×C₄×C₄₇	—	4	1	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	1	no	—
192	C₂×C₄×C₄₇	—	8	2	no	—
193	C₂×C₄×C₄₇	—	8	2	no	—
194	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
197	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	#131	1	2	yes	—
199	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
200	C₈×C₄₇	—	4	2	no	—
201	C₈×C₄₇	—	4	4	no	—
202	C₈×C₄₇	—	4	2	no	—
203	#17426	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₄₇	—	2	2	no	—
205	C₂²×C₄₇	—	2	1	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	2	2	no	—
210	C₂²×C₄₇	—	2	2	no	—
211	C₂²×C₄₇	—	4	4	no	—
212	C₂²×C₄₇	—	4	4	no	—
213	C₂²×C₄₇	C₂×#101	1	4	yes	—
214	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
216	C₂²×C₄₇	#568	1	1	yes	characteristic
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	2	2	no	—
220	C₄×C₄₇	—	2	4	no	—
221	C₄×C₄₇	—	2	1	no	—
222	C₄×C₄₇	—	4	2	no	—
223	C₄×C₄₇	—	4	1	no	—
224	C₄×C₄₇	—	4	1	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	4	1	no	—
227	C₄×C₄₇	C₂×#101	1	2	yes	—
228	C₂×#554	C₂×C₄₇	1	1	yes	characteristic
229	#2974	C₂×C₄₇	1	2	yes	—
230	#1472	C₂×C₄₇	1	4	yes	complemented
231	#1470	C₂×C₄₇	1	2	yes	complemented
232	#1467	C₂×C₄₇	1	1	yes	characteristic, complemented
233	#1463	C₂×C₄₇	1	2	yes	complemented
234	#1461	C₂×C₄₇	1	1	yes	characteristic, complemented
235	C₂×#324	C₂×C₄₇	1	2	yes	complemented
236	C₂×C₄₇	—	2	1	no	—
237	C₂×C₄₇	—	2	1	no	—
238	C₂×C₄₇	—	2	4	no	—
239	C₂×C₄₇	—	4	2	no	—
240	C₂×C₄₇	#2880	1	1	yes	characteristic
241	C₂×C₄₇	#2883	1	1	yes	characteristic
242	C₂×C₄₇	C₂²×#101	1	1	yes	characteristic
243	#554	—	2	2	no	—
244	#554	—	2	4	no	—
245	#554	—	2	2	no	—
246	C₂×C₄⋊Q₈	C₄×C₄₇	1	1	yes	characteristic
247	C₂×#125	C₄×C₄₇	1	1	yes	characteristic
248	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
249	C₂×C₂²⋊Q₈	C₄×C₄₇	1	2	yes	—
250	C₂×C₂²⋊Q₈	C₄×C₄₇	1	2	yes	—
251	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
252	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
253	C₂×C₄×D₄	C₄×C₄₇	1	1	yes	characteristic
254	C₂×C₄×D₄	C₄×C₄₇	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
257	#436	—	2	2	no	—
258	#435	—	2	4	no	—
259	C₈×D₄	—	2	2	no	—
260	#432	C₂²×C₄₇	1	2	yes	—
261	#431	C₂²×C₄₇	1	2	yes	—
262	#407	C₂²×C₄₇	1	4	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
264	#324	C₂²×C₄₇	1	1	yes	characteristic
265	#324	C₂²×C₄₇	1	2	yes	—
266	#324	C₂²×C₄₇	1	4	yes	—
267	#324	C₂²×C₄₇	1	1	yes	characteristic
268	#324	C₂²×C₄₇	1	2	yes	—
269	#324	C₂²×C₄₇	1	4	yes	—
270	#324	C₂²×C₄₇	1	2	yes	—
271	C₄₇	#17426	1	1	yes	characteristic, direct product factor, Sylow
272	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
273	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
274	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
275	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
276	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
277	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
278	C₂×M₁₆	—	2	4	no	—
279	C₂²×C₈	—	2	4	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	#125	—	2	2	no	—
283	#125	—	2	2	no	—
284	#125	—	2	2	no	—
285	#125	—	2	2	no	—
286	C₂²⋊Q₈	—	2	4	no	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	D₄×C₄₇	1	2	yes	—
301	C₄×D₄	D₄×C₄₇	1	4	yes	—
302	C₄×D₄	D₄×C₄₇	1	2	yes	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
311	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
318	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
319	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
320	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	—	2	4	no	—
325	C₂²⋊C₈	—	2	4	no	—
326	C₂²⋊C₈	C₂³×C₄₇	1	2	yes	—
327	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
328	C₂²⋊C₈	C₂³×C₄₇	1	2	yes	—
329	#97	—	2	2	no	—
330	C₄×C₈	—	2	2	no	—
331	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	1	no	—
336	C₂×Q₈	—	8	2	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	C₂²⋊C₄×C₄₇	1	2	yes	—
339	C₂×D₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
340	C₂×D₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	8	2	no	—
348	C₂²×C₄	—	8	2	no	—
349	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
351	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
359	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
361	M₁₆	—	8	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	8	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
379	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
385	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×D₄×C₄₇	1	2	yes	—
391	C₄²	C₂×D₄×C₄₇	1	2	yes	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	4	2	no	—
396	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
397	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
398	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
399	Q₈	—	4	4	no	—
400	Q₈	—	8	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	2	no	—
403	D₄	#101×C₄₇	1	4	yes	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
430	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
431	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
433	C₂×C₄	#131×C₄₇	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
435	C₈	—	4	2	no	—
436	C₈	—	4	4	no	—
437	C₈	—	4	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	4	no	—
447	C₂²	C₂×#101×C₄₇	1	4	yes	—
448	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
449	C₂²	C₂×#131×C₄₇	1	1	yes	characteristic
450	C₂²	C₄₇×#568	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	4	no	—
455	C₄	—	2	1	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	1	no	—
461	C₄	C₂×#101×C₄₇	1	2	yes	—
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	—	2	4	no	—
465	C₂	—	4	2	no	—
466	C₂	C₄₇×#2880	1	1	yes	characteristic
467	C₂	C₄₇×#2883	1	1	yes	characteristic
468	C₂	C₂²×#101×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×D₄×C₄₇	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ 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
3. C₄₇×#1472	C₂	semidirect
4. C₄₇×#1470	C₂	semidirect
5. C₄₇×#1467	C₂	semidirect
6. C₄₇×#1463	C₂	semidirect
7. C₄₇×#1461	C₂	semidirect
8. C₂×C₄₇×#324	C₂	semidirect
203. #17426	C₄₇	direct (N × H)
230. #1472	C₂×C₄₇	semidirect
231. #1470	C₂×C₄₇	semidirect
232. #1467	C₂×C₄₇	semidirect
233. #1463	C₂×C₄₇	semidirect
234. #1461	C₂×C₄₇	semidirect
235. C₂×#324	C₂×C₄₇	semidirect
271. C₄₇	#17426	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×#554	2
C₄₇×#2974	2
C₄₇×#1472	2
C₄₇×#1470	2
C₄₇×#1467	2
C₄₇×#1463	2
C₄₇×#1461	2
C₂×C₄₇×#324	2
#17426	47

Subgroups — C47×#17426 #26057124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17426 #26057124