Subgroups — C₄₇×#13941 #26053639

Order 12032.

2374 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	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#390	C₂	1	2	yes	maximal
3	C₂×C₄₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1439	C₂	1	4	yes	maximal, complemented
6	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal, complemented
7	C₄₇×C₂²⋊#95	C₂	1	4	yes	maximal, complemented
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₄₇	—	2	4	no	—
11	C₂×C₄×D₄×C₄₇	—	2	4	no	—
12	C₂×C₄×D₄×C₄₇	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#390	—	2	8	no	—
21	C₄₇×#382	—	2	4	no	—
22	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	2	yes	—
26	C₂×#95×C₄₇	C₂²	1	8	yes	—
27	C₂⁵×C₄₇	C₂³	1	2	yes	—
28	C₂²×D₄×C₄₇	—	2	2	no	—
29	C₂²×D₄×C₄₇	—	2	2	no	—
30	C₂²×D₄×C₄₇	—	2	2	no	—
31	C₂²×D₄×C₄₇	—	2	2	no	—
32	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
33	C₂²×D₄×C₄₇	D₄	1	4	yes	—
34	C₂²×D₄×C₄₇	Q₈	1	4	yes	—
35	C₂³×C₄×C₄₇	—	2	4	no	—
36	C₂³×C₄×C₄₇	—	2	4	no	—
37	C₂³×C₄×C₄₇	—	4	8	no	—
38	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₄×D₄×C₄₇	—	2	32	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
58	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
59	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
60	C₂×C₄²×C₄₇	—	2	4	no	—
61	C₂×C₄²×C₄₇	—	2	4	no	—
62	C₂×C₄²×C₄₇	—	2	4	no	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	D₄	1	4	yes	—
65	C₂×C₄²×C₄₇	D₄	1	4	yes	—
66	#95×C₄₇	—	2	4	no	—
67	#95×C₄₇	—	2	4	no	—
68	#95×C₄₇	—	2	4	no	—
69	#95×C₄₇	—	4	8	no	—
70	C₂⁴×C₄₇	—	2	2	no	—
71	C₂⁴×C₄₇	—	2	2	no	—
72	C₂⁴×C₄₇	—	2	8	no	—
73	C₂⁴×C₄₇	—	2	2	no	—
74	C₂⁴×C₄₇	—	2	2	no	—
75	C₂⁴×C₄₇	—	2	8	no	—
76	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
77	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
78	C₂⁴×C₄₇	C₂×Q₈	1	4	yes	—
79	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
80	C₂×D₄×C₄₇	—	2	8	no	—
81	C₂×D₄×C₄₇	—	2	8	no	—
82	C₂×D₄×C₄₇	—	2	8	no	—
83	C₂×D₄×C₄₇	—	2	8	no	—
84	C₂×D₄×C₄₇	—	2	8	no	—
85	C₂×D₄×C₄₇	—	2	8	no	—
86	C₂×D₄×C₄₇	C₄⋊C₄	1	16	yes	complemented
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	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	8	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	16	no	—
99	C₂²×C₄×C₄₇	—	2	4	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	2	8	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	8	no	—
104	C₂²×C₄×C₄₇	—	4	16	no	—
105	C₂²×C₄×C₄₇	—	4	16	no	—
106	C₂²×C₄×C₄₇	—	4	16	no	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₄₇	#41	1	8	yes	—
120	C₂²×C₄×C₄₇	#41	1	2	yes	—
121	C₂²×C₄×C₄₇	#41	1	2	yes	—
122	C₄⋊C₄×C₄₇	—	2	16	no	—
123	C₄⋊C₄×C₄₇	—	2	8	no	—
124	C₄⋊C₄×C₄₇	—	4	8	no	—
125	C₂²⋊C₄×C₄₇	—	2	16	no	—
126	C₂²⋊C₄×C₄₇	—	4	32	no	—
127	C₄²×C₄₇	—	4	8	no	—
128	C₄²×C₄₇	C₂²⋊C₄	1	16	yes	complemented
129	C₂³×C₄₇	—	2	4	no	—
130	C₂³×C₄₇	—	2	4	no	—
131	C₂³×C₄₇	—	2	8	no	—
132	C₂³×C₄₇	—	2	8	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	—	2	4	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	—	2	16	no	—
138	C₂³×C₄₇	—	2	16	no	—
139	C₂³×C₄₇	—	4	4	no	—
140	C₂³×C₄₇	—	4	4	no	—
141	C₂³×C₄₇	—	4	4	no	—
142	C₂³×C₄₇	—	4	4	no	—
143	C₂³×C₄₇	—	4	8	no	—
144	C₂³×C₄₇	—	4	8	no	—
145	C₂³×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
146	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
151	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂³×C₄₇	C₂×#41	1	4	yes	—
154	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
155	D₄×C₄₇	—	2	32	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	8	no	—
164	C₂×C₄×C₄₇	—	2	8	no	—
165	C₂×C₄×C₄₇	—	2	8	no	—
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	4	32	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	—	4	4	no	—
170	C₂×C₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	—	4	4	no	—
172	C₂×C₄×C₄₇	—	4	4	no	—
173	C₂×C₄×C₄₇	—	4	4	no	—
174	C₂×C₄×C₄₇	—	4	4	no	—
175	C₂×C₄×C₄₇	—	4	4	no	—
176	C₂×C₄×C₄₇	—	4	4	no	—
177	C₂×C₄×C₄₇	—	4	8	no	—
178	C₂×C₄×C₄₇	—	4	8	no	—
179	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
180	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
181	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
182	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
183	C₂×C₄×C₄₇	#117	1	4	yes	—
184	C₂×C₄×C₄₇	#121	1	4	yes	—
185	C₂×C₄×C₄₇	#121	1	4	yes	—
186	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
187	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
188	#13941	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₄₇	—	2	16	no	—
190	C₂²×C₄₇	—	2	8	no	—
191	C₂²×C₄₇	—	4	4	no	—
192	C₂²×C₄₇	—	4	8	no	—
193	C₂²×C₄₇	—	4	8	no	—
194	C₂²×C₄₇	—	4	8	no	—
195	C₂²×C₄₇	—	4	8	no	—
196	C₂²×C₄₇	—	4	8	no	—
197	C₂²×C₄₇	—	4	4	no	—
198	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
200	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
201	C₂²×C₄₇	C₄×#41	1	2	yes	—
202	C₂²×C₄₇	#518	1	2	yes	—
203	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
207	C₂²×C₄₇	#525	1	2	yes	—
208	C₂²×C₄₇	#532	1	2	yes	—
209	C₂²×C₄₇	#535	1	2	yes	—
210	C₂²×C₄₇	#535	1	2	yes	—
211	C₂²×C₄₇	#546	1	4	yes	—
212	C₂²×C₄₇	#553	1	4	yes	—
213	C₂²×C₄₇	#554	1	4	yes	—
214	C₂²×C₄₇	#559	1	4	yes	—
215	C₄×C₄₇	—	2	4	no	—
216	C₄×C₄₇	—	2	4	no	—
217	C₄×C₄₇	—	4	4	no	—
218	C₄×C₄₇	—	4	8	no	—
219	C₄×C₄₇	—	8	4	no	—
220	C₄×C₄₇	#380	1	8	yes	—
221	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
222	C₂×#390	C₂×C₄₇	1	2	yes	—
223	C₂×#382	C₂×C₄₇	1	1	yes	characteristic, complemented
224	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#1439	C₂×C₄₇	1	4	yes	complemented
226	C₄⋊#95	C₂×C₄₇	1	2	yes	complemented
227	C₂²⋊#95	C₂×C₄₇	1	4	yes	complemented
228	C₂×C₄₇	—	4	8	no	—
229	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
230	C₂×C₄₇	#2297	1	1	yes	characteristic
231	C₂×C₄₇	#2309	1	1	yes	characteristic
232	C₂×C₄₇	#2349	1	2	yes	—
233	C₂×C₄₇	#2357	1	2	yes	—
234	C₂×C₄₇	#2535	1	2	yes	—
235	C₂×C₄₇	#2544	1	2	yes	—
236	C₂×C₄₇	#2566	1	2	yes	—
237	C₂×C₄₇	#2580	1	2	yes	—
238	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
240	C₂×C₄×D₄	—	2	4	no	—
241	C₂×C₄×D₄	—	2	4	no	—
242	C₂×C₄×D₄	C₄×C₄₇	1	8	yes	complemented
243	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
244	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
245	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
247	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
248	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
249	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
250	#390	—	2	8	no	—
251	#382	—	2	4	no	—
252	C₄×C₄⋊C₄	—	2	4	no	—
253	C₂×#95	C₂²×C₄₇	1	2	yes	—
254	C₂×#95	C₂²×C₄₇	1	2	yes	—
255	C₂×#95	C₂²×C₄₇	1	2	yes	—
256	C₂×#95	C₂²×C₄₇	1	8	yes	—
257	C₄₇	#13941	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁵	C₂³×C₄₇	1	2	yes	—
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	—	2	2	no	—
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
264	C₂²×D₄	D₄×C₄₇	1	4	yes	—
265	C₂²×D₄	Q₈×C₄₇	1	4	yes	—
266	C₂³×C₄	—	2	4	no	—
267	C₂³×C₄	—	2	4	no	—
268	C₂³×C₄	—	4	8	no	—
269	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	—
270	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
271	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
272	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
273	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
276	C₄×D₄	—	2	32	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	4	no	—
280	C₂×C₄⋊C₄	—	2	8	no	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	16	no	—
288	C₂×C₂²⋊C₄	—	2	16	no	—
289	C₂×C₂²⋊C₄	—	4	8	no	—
290	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
291	C₂×C₄²	—	2	4	no	—
292	C₂×C₄²	—	2	4	no	—
293	C₂×C₄²	—	2	4	no	—
294	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
295	C₂×C₄²	D₄×C₄₇	1	4	yes	—
296	C₂×C₄²	D₄×C₄₇	1	4	yes	—
297	#95	—	2	4	no	—
298	#95	—	2	4	no	—
299	#95	—	2	4	no	—
300	#95	—	4	8	no	—
301	C₂⁴	—	2	2	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	8	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	—	2	8	no	—
307	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
308	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
309	C₂⁴	C₂×Q₈×C₄₇	1	4	yes	—
310	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	C₄⋊C₄×C₄₇	1	16	yes	complemented
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	16	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	4	16	no	—
336	C₂²×C₄	—	4	16	no	—
337	C₂²×C₄	—	4	16	no	—
338	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
339	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
340	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
349	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
350	C₂²×C₄	#41×C₄₇	1	8	yes	—
351	C₂²×C₄	#41×C₄₇	1	2	yes	—
352	C₂²×C₄	#41×C₄₇	1	2	yes	—
353	C₄⋊C₄	—	2	16	no	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	4	8	no	—
356	C₂²⋊C₄	—	2	16	no	—
357	C₂²⋊C₄	—	4	32	no	—
358	C₄²	—	4	8	no	—
359	C₄²	C₂²⋊C₄×C₄₇	1	16	yes	complemented
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	16	no	—
369	C₂³	—	2	16	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	4	no	—
372	C₂³	—	4	4	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	8	no	—
375	C₂³	—	4	8	no	—
376	C₂³	C₂×C₄⋊C₄×C₄₇	1	8	yes	—
377	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
378	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
379	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
380	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
381	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
382	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
383	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
384	C₂³	C₂×#41×C₄₇	1	4	yes	—
385	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
386	D₄	—	2	32	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	4	32	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	8	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
411	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
412	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
413	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
414	C₂×C₄	#117×C₄₇	1	4	yes	—
415	C₂×C₄	#121×C₄₇	1	4	yes	—
416	C₂×C₄	#121×C₄₇	1	4	yes	—
417	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
418	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
419	C₂²	—	2	8	no	—
420	C₂²	—	2	16	no	—
421	C₂²	—	4	8	no	—
422	C₂²	—	4	8	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	8	no	—
426	C₂²	—	4	8	no	—
427	C₂²	—	4	8	no	—
428	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
429	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
430	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
431	C₂²	C₄×#41×C₄₇	1	2	yes	—
432	C₂²	C₄₇×#518	1	2	yes	—
433	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
434	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
435	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
436	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
437	C₂²	C₄₇×#525	1	2	yes	—
438	C₂²	C₄₇×#532	1	2	yes	—
439	C₂²	C₄₇×#535	1	2	yes	—
440	C₂²	C₄₇×#535	1	2	yes	—
441	C₂²	C₄₇×#546	1	4	yes	—
442	C₂²	C₄₇×#553	1	4	yes	—
443	C₂²	C₄₇×#554	1	4	yes	—
444	C₂²	C₄₇×#559	1	4	yes	—
445	C₄	—	2	4	no	—
446	C₄	—	2	4	no	—
447	C₄	—	4	8	no	—
448	C₄	—	4	4	no	—
449	C₄	—	8	4	no	—
450	C₄	C₄₇×#380	1	8	yes	—
451	C₂	—	4	8	no	—
452	C₂	C₂×C₄₇×#380	1	1	yes	characteristic
453	C₂	C₄₇×#2297	1	1	yes	characteristic
454	C₂	C₄₇×#2309	1	1	yes	characteristic
455	C₂	C₄₇×#2349	1	2	yes	—
456	C₂	C₄₇×#2357	1	2	yes	—
457	C₂	C₄₇×#2535	1	2	yes	—
458	C₂	C₄₇×#2544	1	2	yes	—
459	C₂	C₄₇×#2566	1	2	yes	—
460	C₂	C₄₇×#2580	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₇×#382	C₂	semidirect
4. C₂×C₄×C₄⋊C₄×C₄₇	C₂	semidirect
5. C₄₇×#1439	C₂	semidirect
6. C₄₇×C₄⋊#95	C₂	semidirect
7. C₄₇×C₂²⋊#95	C₂	semidirect
12. C₂×C₄×D₄×C₄₇	C₄	semidirect
86. C₂×D₄×C₄₇	C₄⋊C₄	semidirect
128. C₄²×C₄₇	C₂²⋊C₄	semidirect
188. #13941	C₄₇	direct (N × H)
223. C₂×#382	C₂×C₄₇	semidirect
224. C₂×C₄×C₄⋊C₄	C₂×C₄₇	semidirect
225. #1439	C₂×C₄₇	semidirect
226. C₄⋊#95	C₂×C₄₇	semidirect
227. C₂²⋊#95	C₂×C₄₇	semidirect
242. C₂×C₄×D₄	C₄×C₄₇	semidirect
257. C₄₇	#13941	direct (N × H)
317. C₂×D₄	C₄⋊C₄×C₄₇	semidirect
359. C₄²	C₂²⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₇	2
C₂×C₄₇×#390	2
C₂×C₄₇×#382	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1439	2
C₄₇×C₄⋊#95	2
C₄₇×C₂²⋊#95	2
#13941	47

Subgroups — C47×#13941 #26053639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13941 #26053639