Subgroups — C₂×C₄₇×#1477 #26057134

Order 12032.

1370 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1477	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇×Q₈⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×D₄⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₇	C₄	1	1	yes	characteristic
8	C₂³×C₈×C₄₇	—	2	1	no	—
9	C₄×#41×C₄₇	—	2	2	no	—
10	C₄×#41×C₄₇	—	2	2	no	—
11	C₄×#41×C₄₇	C₄	1	4	yes	—
12	C₄×#41×C₄₇	C₂²	1	4	yes	—
13	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₇	—	2	1	no	—
16	C₂×C₄×D₄×C₄₇	—	2	1	no	—
17	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₇	—	2	1	no	—
20	C₂×#117×C₄₇	C₄	1	1	yes	characteristic
21	C₂²×C₄²×C₄₇	—	2	1	no	—
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#431	—	2	2	no	—
24	C₄₇×#431	C₂²	1	4	yes	complemented
25	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
26	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
27	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
28	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	complemented
30	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
31	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
32	C₄₇×Q₈⋊C₈	C₂²	1	8	yes	complemented
33	C₄₇×D₄⋊C₈	C₂²	1	8	yes	complemented
34	C₂×#41×C₄₇	—	2	2	no	—
35	C₂×#41×C₄₇	—	2	4	no	—
36	C₂×#41×C₄₇	C₈	1	8	yes	complemented
37	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
38	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₄₇	—	2	1	no	—
40	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	—	2	1	no	—
42	C₂³×C₄×C₄₇	—	2	1	no	—
43	C₂³×C₄×C₄₇	—	2	1	no	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₄₇	—	2	4	no	—
48	C₂²×C₈×C₄₇	—	2	2	no	—
49	C₂²×C₈×C₄₇	—	2	2	no	—
50	C₂²×C₈×C₄₇	—	4	4	no	—
51	C₄×Q₈×C₄₇	—	2	2	no	—
52	C₄×Q₈×C₄₇	—	2	1	no	—
53	C₄×Q₈×C₄₇	—	2	1	no	—
54	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
55	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
57	C₄×D₄×C₄₇	—	2	4	no	—
58	C₄×D₄×C₄₇	—	2	4	no	—
59	C₄×D₄×C₄₇	—	2	4	no	—
60	C₄×D₄×C₄₇	—	2	4	no	—
61	C₄×D₄×C₄₇	—	2	2	no	—
62	C₄×D₄×C₄₇	—	2	1	no	—
63	C₄×D₄×C₄₇	—	2	1	no	—
64	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
65	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₄₇	C₂³	1	2	yes	—
67	#117×C₄₇	—	2	2	no	—
68	#117×C₄₇	—	2	4	no	—
69	#117×C₄₇	—	2	4	no	—
70	#117×C₄₇	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	—	2	1	no	—
81	C₂×C₄²×C₄₇	—	2	4	no	—
82	C₂×C₄²×C₄₇	—	2	4	no	—
83	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	D₄	1	2	yes	—
87	C₂×C₄²×C₄₇	D₄	1	2	yes	—
88	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	—	2	2	no	—
92	C₄⋊C₈×C₄₇	—	2	4	no	—
93	C₄⋊C₈×C₄₇	—	2	4	no	—
94	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
95	C₂²⋊C₈×C₄₇	—	2	4	no	—
96	C₄×C₈×C₄₇	—	2	2	no	—
97	C₄×C₈×C₄₇	C₂³	1	4	yes	—
98	C₂⁴×C₄₇	—	2	1	no	—
99	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
100	#41×C₄₇	—	2	16	no	—
101	#41×C₄₇	—	2	8	no	—
102	#41×C₄₇	C₂×C₈	1	16	yes	complemented
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	complemented
106	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₄₇	—	2	8	no	—
108	C₂×D₄×C₄₇	—	2	4	no	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	C₂×C₈	1	4	yes	complemented
112	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	8	no	—
115	C₂²×C₄×C₄₇	—	2	4	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	4	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	4	2	no	—
124	C₂²×C₄×C₄₇	—	4	4	no	—
125	C₂²×C₄×C₄₇	—	4	2	no	—
126	C₂²×C₄×C₄₇	—	4	2	no	—
127	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
134	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
135	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₇	—	2	4	no	—
142	C₂×C₈×C₄₇	—	2	4	no	—
143	C₂×C₈×C₄₇	—	4	4	no	—
144	C₂×C₈×C₄₇	—	4	8	no	—
145	C₂×C₈×C₄₇	—	4	4	no	—
146	C₄⋊C₄×C₄₇	—	2	4	no	—
147	C₄⋊C₄×C₄₇	—	2	2	no	—
148	C₄⋊C₄×C₄₇	—	2	1	no	—
149	C₄⋊C₄×C₄₇	—	2	1	no	—
150	C₄⋊C₄×C₄₇	—	2	2	no	—
151	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
152	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₄₇	—	2	4	no	—
154	C₂²⋊C₄×C₄₇	—	2	4	no	—
155	C₂²⋊C₄×C₄₇	—	2	2	no	—
156	C₂²⋊C₄×C₄₇	—	2	2	no	—
157	C₄²×C₄₇	—	2	4	no	—
158	C₄²×C₄₇	—	2	4	no	—
159	C₄²×C₄₇	—	2	2	no	—
160	C₄²×C₄₇	—	2	2	no	—
161	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
162	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
163	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
164	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
165	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₄₇	C₂×D₄	1	2	yes	—
167	C₄²×C₄₇	C₂×D₄	1	2	yes	—
168	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂³×C₄₇	—	2	2	no	—
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	2	no	—
174	C₂³×C₄₇	—	2	4	no	—
175	C₂³×C₄₇	—	4	2	no	—
176	C₂³×C₄₇	—	4	2	no	—
177	C₂³×C₄₇	C₂²⋊C₈	1	4	yes	—
178	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	Q₈×C₄₇	—	2	2	no	—
181	Q₈×C₄₇	—	2	4	no	—
182	Q₈×C₄₇	C₂²×C₈	1	4	yes	complemented
183	D₄×C₄₇	—	2	16	no	—
184	D₄×C₄₇	—	2	2	no	—
185	D₄×C₄₇	—	2	4	no	—
186	D₄×C₄₇	C₂²×C₈	1	4	yes	complemented
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	16	no	—
195	C₂×C₄×C₄₇	—	2	4	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	4	2	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	8	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	4	no	—
206	C₂×C₄×C₄₇	C₂²⋊C₈	1	4	yes	—
207	C₂×C₄×C₄₇	C₂²⋊C₈	1	8	yes	—
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
215	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
216	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
217	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
218	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
219	C₂×C₄×C₄₇	#137	1	2	yes	—
220	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
223	C₈×C₄₇	—	4	4	no	—
224	C₈×C₄₇	—	4	4	no	—
225	C₂×#1477	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂²×C₄₇	—	2	2	no	—
227	C₂²×C₄₇	—	2	2	no	—
228	C₂²×C₄₇	—	2	8	no	—
229	C₂²×C₄₇	—	2	4	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	4	2	no	—
232	C₂²×C₄₇	—	4	8	no	—
233	C₂²×C₄₇	C₂×C₂²⋊C₈	1	4	yes	—
234	C₂²×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
235	C₂²×C₄₇	#417	1	2	yes	—
236	C₂²×C₄₇	#421	1	2	yes	—
237	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
238	C₄×C₄₇	—	2	4	no	—
239	C₄×C₄₇	—	2	2	no	—
240	C₄×C₄₇	—	2	1	no	—
241	C₄×C₄₇	—	2	2	no	—
242	C₄×C₄₇	—	2	1	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	—	4	2	no	—
245	C₄×C₄₇	C₂×C₂²⋊C₈	1	4	yes	—
246	C₄×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
247	C₄×C₄₇	#417	1	2	yes	—
248	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
249	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
250	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
252	C₂×C₄×#41	C₂×C₄₇	1	1	yes	characteristic
253	C₂×#431	C₂×C₄₇	1	1	yes	characteristic, complemented
254	C₂²×C₄⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
255	#1477	C₂×C₄₇	1	8	yes	direct product factor
256	C₂×Q₈⋊C₈	C₂×C₄₇	1	2	yes	complemented
257	C₂×D₄⋊C₈	C₂×C₄₇	1	2	yes	complemented
258	C₂×C₄₇	—	2	4	no	—
259	C₂×C₄₇	—	4	4	no	—
260	C₂×C₄₇	#1477	1	4	yes	direct product factor
261	C₂×C₄₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic
262	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
263	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
264	C₂²×#41	C₄×C₄₇	1	1	yes	characteristic
265	C₂³×C₈	—	2	1	no	—
266	C₄×#41	—	2	2	no	—
267	C₄×#41	—	2	2	no	—
268	C₄×#41	C₄×C₄₇	1	4	yes	—
269	C₄×#41	C₂²×C₄₇	1	4	yes	—
270	C₂×C₄×Q₈	C₄×C₄₇	1	1	yes	characteristic
271	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
272	C₂×C₄×D₄	—	2	1	no	—
273	C₂×C₄×D₄	—	2	1	no	—
274	C₂×C₄×D₄	C₄×C₄₇	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
276	C₂×#117	—	2	1	no	—
277	C₂×#117	C₄×C₄₇	1	1	yes	characteristic
278	C₂²×C₄²	—	2	1	no	—
279	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
280	#431	—	2	2	no	—
281	#431	C₂²×C₄₇	1	4	yes	complemented
282	C₂×C₄⋊C₈	—	2	2	no	—
283	C₂×C₄⋊C₈	—	2	1	no	—
284	C₂×C₄⋊C₈	—	2	1	no	—
285	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
286	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
287	C₂×C₂²⋊C₈	—	2	1	no	—
288	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	—
289	Q₈⋊C₈	C₂²×C₄₇	1	8	yes	complemented
290	D₄⋊C₈	C₂²×C₄₇	1	8	yes	complemented
291	C₄₇	C₂×#1477	1	1	yes	characteristic, direct product factor, Sylow
292	C₂×#41	—	2	2	no	—
293	C₂×#41	—	2	4	no	—
294	C₂×#41	C₈×C₄₇	1	8	yes	complemented
295	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
296	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
303	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
304	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	—	2	4	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	4	4	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×Q₈	C₂×C₄×C₄₇	1	4	yes	—
313	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
314	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
315	C₄×D₄	—	2	4	no	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
323	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
324	C₄×D₄	C₂³×C₄₇	1	2	yes	—
325	#117	—	2	2	no	—
326	#117	—	2	4	no	—
327	#117	—	2	4	no	—
328	#117	C₂×C₄×C₄₇	1	4	yes	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	—	2	4	no	—
340	C₂×C₄²	—	2	4	no	—
341	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
342	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
343	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
344	C₂×C₄²	D₄×C₄₇	1	2	yes	—
345	C₂×C₄²	D₄×C₄₇	1	2	yes	—
346	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
349	C₄⋊C₈	—	2	2	no	—
350	C₄⋊C₈	—	2	4	no	—
351	C₄⋊C₈	—	2	4	no	—
352	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
353	C₂²⋊C₈	—	2	4	no	—
354	C₄×C₈	—	2	2	no	—
355	C₄×C₈	C₂³×C₄₇	1	4	yes	—
356	C₂⁴	—	2	1	no	—
357	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
358	#41	—	2	8	no	—
359	#41	—	2	16	no	—
360	#41	C₂×C₈×C₄₇	1	16	yes	complemented
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	C₂×C₈×C₄₇	1	4	yes	complemented
364	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	C₂×C₈×C₄₇	1	4	yes	complemented
370	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	4	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
386	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
387	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
388	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
389	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
390	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
391	C₂²×C₄	C₂×C₈×C₄₇	1	4	yes	—
392	C₂²×C₄	M₁₆×C₄₇	1	4	yes	—
393	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	4	no	—
401	C₂×C₈	—	4	4	no	—
402	C₂×C₈	—	4	8	no	—
403	C₂×C₈	—	4	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
410	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₄²	—	2	4	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
420	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
421	C₄²	C₂²⋊C₄×C₄₇	1	2	yes	—
422	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
423	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₄₇	1	2	yes	—
426	C₄²	C₂×D₄×C₄₇	1	2	yes	—
427	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
428	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	C₂²⋊C₈×C₄₇	1	4	yes	—
436	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
437	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	Q₈	—	2	4	no	—
440	Q₈	C₂²×C₈×C₄₇	1	4	yes	complemented
441	D₄	—	2	16	no	—
442	D₄	—	2	2	no	—
443	D₄	—	2	4	no	—
444	D₄	C₂²×C₈×C₄₇	1	4	yes	complemented
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	16	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	C₂²⋊C₈×C₄₇	1	4	yes	—
465	C₂×C₄	C₂²⋊C₈×C₄₇	1	8	yes	—
466	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
467	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
468	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
469	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
470	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
471	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₈×C₄₇	1	2	yes	—
473	C₂×C₄	C₂²×C₈×C₄₇	1	4	yes	—
474	C₂×C₄	C₂×M₁₆×C₄₇	1	2	yes	—
475	C₂×C₄	C₂×M₁₆×C₄₇	1	4	yes	—
476	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
477	C₂×C₄	#137×C₄₇	1	2	yes	—
478	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
480	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
481	C₈	—	4	4	no	—
482	C₈	—	4	4	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	8	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	8	no	—
490	C₂²	C₂×C₂²⋊C₈×C₄₇	1	4	yes	—
491	C₂²	C₂×C₂²⋊C₈×C₄₇	1	2	yes	—
492	C₂²	C₄₇×#417	1	2	yes	—
493	C₂²	C₄₇×#421	1	2	yes	—
494	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
495	C₄	—	2	4	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	1	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	C₂×C₂²⋊C₈×C₄₇	1	4	yes	—
503	C₄	C₂×C₂²⋊C₈×C₄₇	1	2	yes	—
504	C₄	C₄₇×#417	1	2	yes	—
505	C₄	C₂³×C₈×C₄₇	1	1	yes	characteristic
506	C₄	C₂²×M₁₆×C₄₇	1	1	yes	characteristic
507	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
508	C₄	C₂×#137×C₄₇	1	1	yes	characteristic
509	C₂	—	2	4	no	—
510	C₂	—	4	4	no	—
511	C₂	C₄₇×#1477	1	4	yes	direct product factor
512	C₂	C₂²×C₂²⋊C₈×C₄₇	1	1	yes	characteristic
513	C₂	C₂×C₄₇×#417	1	1	yes	characteristic
514	C₂	C₂×C₄₇×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂×D₄
commutator	C₄	C₂³×C₈×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#431	C₂	semidirect
3. C₂²×C₄⋊C₈×C₄₇	C₂	semidirect
4. C₄₇×#1477	C₂	direct (N × H)
5. C₂×C₄₇×Q₈⋊C₈	C₂	semidirect
6. C₂×C₄₇×D₄⋊C₈	C₂	semidirect
24. C₄₇×#431	C₂²	semidirect
29. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
32. C₄₇×Q₈⋊C₈	C₂²	semidirect
33. C₄₇×D₄⋊C₈	C₂²	semidirect
36. C₂×#41×C₄₇	C₈	semidirect
102. #41×C₄₇	C₂×C₈	semidirect
105. C₂×Q₈×C₄₇	C₂×C₈	semidirect
111. C₂×D₄×C₄₇	C₂×C₈	semidirect
182. Q₈×C₄₇	C₂²×C₈	semidirect
186. D₄×C₄₇	C₂²×C₈	semidirect
225. C₂×#1477	C₄₇	direct (N × H)
253. C₂×#431	C₂×C₄₇	semidirect
254. C₂²×C₄⋊C₈	C₂×C₄₇	semidirect
255. #1477	C₂×C₄₇	direct (N × H)
256. C₂×Q₈⋊C₈	C₂×C₄₇	semidirect
257. C₂×D₄⋊C₈	C₂×C₄₇	semidirect
260. C₂×C₄₇	#1477	direct (N × H)
281. #431	C₂²×C₄₇	semidirect
286. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
289. Q₈⋊C₈	C₂²×C₄₇	semidirect
290. D₄⋊C₈	C₂²×C₄₇	semidirect
291. C₄₇	C₂×#1477	direct (N × H)
294. C₂×#41	C₈×C₄₇	semidirect
360. #41	C₂×C₈×C₄₇	semidirect
363. C₂×Q₈	C₂×C₈×C₄₇	semidirect
369. C₂×D₄	C₂×C₈×C₄₇	semidirect
440. Q₈	C₂²×C₈×C₄₇	semidirect
444. D₄	C₂²×C₈×C₄₇	semidirect
511. C₂	C₄₇×#1477	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×C₄×#41×C₄₇	2
C₂×C₄₇×#431	2
C₂²×C₄⋊C₈×C₄₇	2
C₄₇×#1477	2
C₂×C₄₇×Q₈⋊C₈	2
C₂×C₄₇×D₄⋊C₈	2
C₂×#1477	47

Subgroups — C2×C47×#1477 #26057134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1477 #26057134