Subgroups — C₄₇×#21374 #26061072

Order 12032.

1442 conjugacy classes of subgroups.

The subgroup lattice has 422 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	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1985	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1955	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1870	C₂	1	4	yes	maximal, complemented
7	C₄×C₂²⋊C₈×C₄₇	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₄₇	C₄	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
10	C₄×#41×C₄₇	—	2	4	no	—
11	C₄×#41×C₄₇	—	2	4	no	—
12	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₇	C₄	1	1	yes	characteristic
19	C₂×#117×C₄₇	C₄	1	2	yes	—
20	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#431	—	2	4	no	—
23	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₇	C₂²	1	8	yes	—
26	C₄×M₁₆×C₄₇	—	2	4	no	—
27	C₂×#97×C₄₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
30	C₄₇×#336	C₂²	1	8	yes	—
31	C₂×#41×C₄₇	—	2	4	no	—
32	C₂×#41×C₄₇	—	2	8	no	—
33	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₄₇	—	2	4	no	—
43	C₂×M₁₆×C₄₇	—	2	8	no	—
44	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
45	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
46	C₄×Q₈×C₄₇	—	2	4	no	—
47	C₄×Q₈×C₄₇	—	2	2	no	—
48	C₄×Q₈×C₄₇	—	2	2	no	—
49	C₄×D₄×C₄₇	—	2	8	no	—
50	C₄×D₄×C₄₇	—	2	4	no	—
51	C₄×D₄×C₄₇	—	2	4	no	—
52	C₄×D₄×C₄₇	—	2	4	no	—
53	C₄×D₄×C₄₇	—	2	2	no	—
54	C₄×D₄×C₄₇	—	2	2	no	—
55	#117×C₄₇	—	2	4	no	—
56	#117×C₄₇	—	2	8	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₄₇	—	2	4	no	—
65	C₂×C₄²×C₄₇	—	2	4	no	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	D₄	1	4	yes	—
71	C₂×C₄²×C₄₇	D₄	1	4	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₄₇	—	2	4	no	—
76	C₂²⋊C₈×C₄₇	—	2	4	no	—
77	C₂²⋊C₈×C₄₇	—	2	16	no	—
78	#97×C₄₇	—	2	4	no	—
79	C₄×C₈×C₄₇	—	2	4	no	—
80	C₄×C₈×C₄₇	—	2	4	no	—
81	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
83	#41×C₄₇	—	2	32	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	2	4	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	2	4	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	8	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	8	no	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	M₁₆	1	8	yes	complemented
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
115	M₁₆×C₄₇	—	2	16	no	—
116	C₂×C₈×C₄₇	—	2	4	no	—
117	C₂×C₈×C₄₇	—	2	4	no	—
118	C₂×C₈×C₄₇	—	2	4	no	—
119	C₂×C₈×C₄₇	—	2	8	no	—
120	C₂×C₈×C₄₇	#41	1	8	yes	complemented
121	C₄⋊C₄×C₄₇	—	2	4	no	—
122	C₄⋊C₄×C₄₇	—	2	4	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₂²⋊C₄×C₄₇	—	2	4	no	—
126	C₂²⋊C₄×C₄₇	—	2	4	no	—
127	C₂²⋊C₄×C₄₇	—	2	4	no	—
128	C₄²×C₄₇	—	2	4	no	—
129	C₄²×C₄₇	—	2	4	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
133	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
134	C₄²×C₄₇	C₂×D₄	1	2	yes	—
135	C₄²×C₄₇	C₂×D₄	1	2	yes	—
136	C₄²×C₄₇	C₂×D₄	1	2	yes	—
137	C₄²×C₄₇	C₂×D₄	1	2	yes	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
147	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
148	Q₈×C₄₇	—	2	8	no	—
149	D₄×C₄₇	—	2	8	no	—
150	D₄×C₄₇	—	2	16	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	8	no	—
159	C₂×C₄×C₄₇	—	2	16	no	—
160	C₂×C₄×C₄₇	—	2	8	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	4	4	no	—
166	C₂×C₄×C₄₇	—	4	4	no	—
167	C₂×C₄×C₄₇	—	4	8	no	—
168	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
174	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
175	C₂×C₄×C₄₇	#131	1	4	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
179	C₈×C₄₇	—	2	8	no	—
180	C₈×C₄₇	—	4	4	no	—
181	#21374	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	4	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	2	8	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	4	4	no	—
189	C₂²×C₄₇	—	4	4	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₄₇	C₄×#41	1	2	yes	—
193	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
194	C₂²×C₄₇	C₂×#131	1	2	yes	—
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	—	2	4	no	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	—	4	2	no	—
201	C₄×C₄₇	#407	1	4	yes	—
202	C₄×C₄₇	#408	1	4	yes	—
203	C₄×C₄₇	#525	1	2	yes	—
204	C₄×C₄₇	#532	1	2	yes	—
205	C₂×C₄×#41	C₂×C₄₇	1	1	yes	characteristic
206	C₂×#431	C₂×C₄₇	1	1	yes	characteristic, complemented
207	C₂×C₄×M₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
208	#1985	C₂×C₄₇	1	2	yes	complemented
209	#1955	C₂×C₄₇	1	2	yes	complemented
210	#1870	C₂×C₄₇	1	4	yes	complemented
211	C₄×C₂²⋊C₈	C₂×C₄₇	1	4	yes	complemented
212	C₂×C₄₇	—	4	2	no	—
213	C₂×C₄₇	—	4	4	no	—
214	C₂×C₄₇	#2297	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#407	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#408	1	1	yes	characteristic
217	C₂×C₄₇	#2965	1	4	yes	—
218	C₂²×#41	C₄×C₄₇	1	1	yes	characteristic
219	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
220	C₄×#41	—	2	4	no	—
221	C₄×#41	—	2	4	no	—
222	C₂×C₄×Q₈	C₄×C₄₇	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
224	C₂×C₄×D₄	C₄×C₄₇	1	2	yes	—
225	C₂×C₄×D₄	C₄×C₄₇	1	1	yes	characteristic
226	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
227	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
228	C₂×#117	C₄×C₄₇	1	1	yes	characteristic
229	C₂×#117	C₄×C₄₇	1	2	yes	—
230	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
231	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
232	#431	—	2	4	no	—
233	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
234	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₄₇	1	8	yes	—
236	C₄×M₁₆	—	2	4	no	—
237	C₂×#97	C₂²×C₄₇	1	2	yes	—
238	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	—
239	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	—
240	#336	C₂²×C₄₇	1	8	yes	—
241	C₄₇	#21374	1	1	yes	characteristic, direct product factor, Sylow
242	C₂×#41	—	2	4	no	—
243	C₂×#41	—	2	8	no	—
244	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
245	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
246	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
247	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
248	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
249	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
250	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
251	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
252	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	—	2	8	no	—
255	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
256	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×Q₈	—	2	2	no	—
260	C₄×D₄	—	2	8	no	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	—	2	4	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	#117	—	2	4	no	—
267	#117	—	2	8	no	—
268	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
273	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
274	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
275	C₂×C₄²	—	2	4	no	—
276	C₂×C₄²	—	2	4	no	—
277	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
278	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
279	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
280	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
281	C₂×C₄²	D₄×C₄₇	1	4	yes	—
282	C₂×C₄²	D₄×C₄₇	1	4	yes	—
283	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
284	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
286	C₄⋊C₈	—	2	4	no	—
287	C₂²⋊C₈	—	2	4	no	—
288	C₂²⋊C₈	—	2	16	no	—
289	#97	—	2	4	no	—
290	C₄×C₈	—	2	4	no	—
291	C₄×C₈	—	2	4	no	—
292	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
293	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
294	#41	—	2	32	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
313	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
314	C₂²×C₄	M₁₆×C₄₇	1	8	yes	complemented
315	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
317	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
321	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
326	M₁₆	—	2	16	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	2	8	no	—
331	C₂×C₈	#41×C₄₇	1	8	yes	complemented
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₄²	—	2	4	no	—
340	C₄²	—	2	4	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
344	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
345	C₄²	C₂×D₄×C₄₇	1	2	yes	—
346	C₄²	C₂×D₄×C₄₇	1	2	yes	—
347	C₄²	C₂×D₄×C₄₇	1	2	yes	—
348	C₄²	C₂×D₄×C₄₇	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	4	no	—
356	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
357	C₂³	C₂×M₁₆×C₄₇	1	4	yes	—
358	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
359	Q₈	—	2	8	no	—
360	D₄	—	2	8	no	—
361	D₄	—	2	16	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	16	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
381	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
382	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
384	C₂×C₄	C₂×M₁₆×C₄₇	1	4	yes	—
385	C₂×C₄	C₂×M₁₆×C₄₇	1	4	yes	—
386	C₂×C₄	#131×C₄₇	1	4	yes	—
387	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
390	C₈	—	2	8	no	—
391	C₈	—	4	4	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	8	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
402	C₂²	C₄×#41×C₄₇	1	2	yes	—
403	C₂²	C₂²×M₁₆×C₄₇	1	2	yes	—
404	C₂²	C₂×#131×C₄₇	1	2	yes	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	4	no	—
408	C₄	—	2	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	C₄₇×#407	1	4	yes	—
412	C₄	C₄₇×#408	1	4	yes	—
413	C₄	C₄₇×#525	1	2	yes	—
414	C₄	C₄₇×#532	1	2	yes	—
415	C₂	—	4	2	no	—
416	C₂	—	4	4	no	—
417	C₂	C₄₇×#2297	1	1	yes	characteristic
418	C₂	C₂×C₄₇×#407	1	1	yes	characteristic
419	C₂	C₂×C₄₇×#408	1	1	yes	characteristic
420	C₂	C₄₇×#2965	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²×C₄₇	C₂³
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×#41×C₄₇	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×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. C₂×C₄×M₁₆×C₄₇	C₂	semidirect
4. C₄₇×#1985	C₂	semidirect
5. C₄₇×#1955	C₂	semidirect
6. C₄₇×#1870	C₂	semidirect
7. C₄×C₂²⋊C₈×C₄₇	C₂	semidirect
103. C₂²×C₄×C₄₇	M₁₆	semidirect
120. C₂×C₈×C₄₇	#41	semidirect
181. #21374	C₄₇	direct (N × H)
206. C₂×#431	C₂×C₄₇	semidirect
207. C₂×C₄×M₁₆	C₂×C₄₇	semidirect
208. #1985	C₂×C₄₇	semidirect
209. #1955	C₂×C₄₇	semidirect
210. #1870	C₂×C₄₇	semidirect
211. C₄×C₂²⋊C₈	C₂×C₄₇	semidirect
241. C₄₇	#21374	direct (N × H)
314. C₂²×C₄	M₁₆×C₄₇	semidirect
331. C₂×C₈	#41×C₄₇	semidirect

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
C₂×C₄×M₁₆×C₄₇	2
C₄₇×#1985	2
C₄₇×#1955	2
C₄₇×#1870	2
C₄×C₂²⋊C₈×C₄₇	2
#21374	47

Subgroups — C47×#21374 #26061072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21374 #26061072