Subgroups — C₄₇×#13867 #26053565

Order 12032.

7150 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#386	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#379	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#379	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1438	C₂	1	4	yes	maximal, complemented
7	C₄₇×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
9	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₇	—	2	4	no	—
11	C₂³×D₄×C₄₇	—	2	4	no	—
12	C₂³×D₄×C₄₇	—	2	16	no	—
13	C₂³×D₄×C₄₇	C₄	1	8	yes	complemented
14	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
15	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊C₄×C₄₇	—	2	4	no	—
19	C₂²×C₂²⋊C₄×C₄₇	—	2	8	no	—
20	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	complemented
25	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
26	C₄₇×#386	—	2	16	no	—
27	C₄₇×#379	—	2	4	no	—
28	C₄₇×#379	—	2	8	no	—
29	C₂×#95×C₄₇	C₂²	1	8	yes	complemented
30	C₂⁵×C₄₇	—	2	4	no	—
31	C₂⁵×C₄₇	—	2	8	no	—
32	C₂⁵×C₄₇	—	2	8	no	—
33	C₂⁵×C₄₇	—	2	2	no	—
34	C₂⁵×C₄₇	—	2	2	no	—
35	C₂⁵×C₄₇	—	2	4	no	—
36	C₂⁵×C₄₇	—	2	4	no	—
37	C₂⁵×C₄₇	—	2	4	no	—
38	C₂⁵×C₄₇	—	4	4	no	—
39	C₂⁵×C₄₇	—	4	4	no	—
40	C₂⁵×C₄₇	C₂×C₄	1	4	yes	—
41	C₂⁵×C₄₇	C₂×C₄	1	4	yes	complemented
42	C₂⁵×C₄₇	D₄	1	4	yes	—
43	C₂⁵×C₄₇	D₄	1	4	yes	—
44	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
45	C₂⁵×C₄₇	C₂³	1	2	yes	—
46	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
47	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₄₇	—	2	64	no	—
49	C₂²×D₄×C₄₇	—	2	64	no	—
50	C₂²×D₄×C₄₇	—	2	32	no	—
51	C₂²×D₄×C₄₇	—	2	4	no	—
52	C₂²×D₄×C₄₇	—	2	4	no	—
53	C₂²×D₄×C₄₇	—	2	8	no	—
54	C₂²×D₄×C₄₇	—	2	4	no	—
55	C₂²×D₄×C₄₇	—	2	8	no	—
56	C₂²×D₄×C₄₇	—	2	4	no	—
57	C₂²×D₄×C₄₇	—	2	64	no	—
58	C₂²×D₄×C₄₇	—	2	8	no	—
59	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
60	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
61	C₂²×D₄×C₄₇	D₄	1	16	yes	—
62	C₂³×C₄×C₄₇	—	2	2	no	—
63	C₂³×C₄×C₄₇	—	2	2	no	—
64	C₂³×C₄×C₄₇	—	2	8	no	—
65	C₂³×C₄×C₄₇	—	2	4	no	—
66	C₂³×C₄×C₄₇	—	2	8	no	—
67	C₂³×C₄×C₄₇	—	2	8	no	—
68	C₂³×C₄×C₄₇	—	4	4	no	—
69	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	complemented
70	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
71	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
72	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	32	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
83	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
86	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
87	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
88	C₂×C₂²⋊C₄×C₄₇	D₄	1	8	yes	complemented
89	#95×C₄₇	—	2	16	no	—
90	C₂⁴×C₄₇	—	2	2	no	—
91	C₂⁴×C₄₇	—	2	4	no	—
92	C₂⁴×C₄₇	—	2	2	no	—
93	C₂⁴×C₄₇	—	2	4	no	—
94	C₂⁴×C₄₇	—	2	4	no	—
95	C₂⁴×C₄₇	—	2	16	no	—
96	C₂⁴×C₄₇	—	2	16	no	—
97	C₂⁴×C₄₇	—	2	16	no	—
98	C₂⁴×C₄₇	—	2	8	no	—
99	C₂⁴×C₄₇	—	2	16	no	—
100	C₂⁴×C₄₇	—	2	16	no	—
101	C₂⁴×C₄₇	—	2	8	no	—
102	C₂⁴×C₄₇	—	2	16	no	—
103	C₂⁴×C₄₇	—	2	16	no	—
104	C₂⁴×C₄₇	—	2	16	no	—
105	C₂⁴×C₄₇	—	2	8	no	—
106	C₂⁴×C₄₇	—	2	2	no	—
107	C₂⁴×C₄₇	—	2	4	no	—
108	C₂⁴×C₄₇	—	2	2	no	—
109	C₂⁴×C₄₇	—	2	2	no	—
110	C₂⁴×C₄₇	—	2	4	no	—
111	C₂⁴×C₄₇	—	2	4	no	—
112	C₂⁴×C₄₇	—	2	2	no	—
113	C₂⁴×C₄₇	—	2	4	no	—
114	C₂⁴×C₄₇	—	2	4	no	—
115	C₂⁴×C₄₇	—	2	8	no	—
116	C₂⁴×C₄₇	—	2	16	no	—
117	C₂⁴×C₄₇	—	4	8	no	—
118	C₂⁴×C₄₇	—	4	8	no	—
119	C₂⁴×C₄₇	—	4	8	no	—
120	C₂⁴×C₄₇	—	4	8	no	—
121	C₂⁴×C₄₇	—	4	32	no	—
122	C₂⁴×C₄₇	—	4	32	no	—
123	C₂⁴×C₄₇	—	4	32	no	—
124	C₂⁴×C₄₇	—	4	32	no	—
125	C₂⁴×C₄₇	—	4	8	no	—
126	C₂⁴×C₄₇	—	4	8	no	—
127	C₂⁴×C₄₇	—	4	4	no	—
128	C₂⁴×C₄₇	—	4	8	no	—
129	C₂⁴×C₄₇	—	4	4	no	—
130	C₂⁴×C₄₇	C₂²⋊C₄	1	16	yes	complemented
131	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
132	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
133	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
136	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
137	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
138	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
139	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
140	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
141	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
142	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
143	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
144	C₂⁴×C₄₇	#41	1	4	yes	—
145	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂×D₄×C₄₇	—	2	256	no	—
147	C₂×D₄×C₄₇	—	2	32	no	—
148	C₂×D₄×C₄₇	—	2	32	no	—
149	C₂×D₄×C₄₇	—	2	16	no	—
150	C₂×D₄×C₄₇	—	2	16	no	—
151	C₂×D₄×C₄₇	—	2	16	no	—
152	C₂×D₄×C₄₇	—	2	16	no	—
153	C₂×D₄×C₄₇	—	2	32	no	—
154	C₂×D₄×C₄₇	—	2	32	no	—
155	C₂×D₄×C₄₇	—	2	16	no	—
156	C₂×D₄×C₄₇	C₂²⋊C₄	1	32	yes	complemented
157	C₂²×C₄×C₄₇	—	2	16	no	—
158	C₂²×C₄×C₄₇	—	2	16	no	—
159	C₂²×C₄×C₄₇	—	2	8	no	—
160	C₂²×C₄×C₄₇	—	2	2	no	—
161	C₂²×C₄×C₄₇	—	2	2	no	—
162	C₂²×C₄×C₄₇	—	2	4	no	—
163	C₂²×C₄×C₄₇	—	2	16	no	—
164	C₂²×C₄×C₄₇	—	2	16	no	—
165	C₂²×C₄×C₄₇	—	2	4	no	—
166	C₂²×C₄×C₄₇	—	2	4	no	—
167	C₂²×C₄×C₄₇	—	2	8	no	—
168	C₂²×C₄×C₄₇	—	2	8	no	—
169	C₂²×C₄×C₄₇	—	2	4	no	—
170	C₂²×C₄×C₄₇	—	2	4	no	—
171	C₂²×C₄×C₄₇	—	2	8	no	—
172	C₂²×C₄×C₄₇	—	2	4	no	—
173	C₂²×C₄×C₄₇	—	2	8	no	—
174	C₂²×C₄×C₄₇	—	4	32	no	—
175	C₂²×C₄×C₄₇	—	4	8	no	—
176	C₂²×C₄×C₄₇	—	4	8	no	—
177	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
178	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
179	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	complemented
180	C₂²⋊C₄×C₄₇	—	2	16	no	—
181	C₂²⋊C₄×C₄₇	—	2	16	no	—
182	C₂²⋊C₄×C₄₇	—	4	32	no	—
183	C₂²⋊C₄×C₄₇	—	4	8	no	—
184	C₂²⋊C₄×C₄₇	—	4	8	no	—
185	C₂²⋊C₄×C₄₇	—	4	8	no	—
186	C₂³×C₄₇	—	2	4	no	—
187	C₂³×C₄₇	—	2	4	no	—
188	C₂³×C₄₇	—	2	4	no	—
189	C₂³×C₄₇	—	2	4	no	—
190	C₂³×C₄₇	—	2	2	no	—
191	C₂³×C₄₇	—	2	4	no	—
192	C₂³×C₄₇	—	2	4	no	—
193	C₂³×C₄₇	—	2	4	no	—
194	C₂³×C₄₇	—	2	2	no	—
195	C₂³×C₄₇	—	2	4	no	—
196	C₂³×C₄₇	—	2	4	no	—
197	C₂³×C₄₇	—	2	4	no	—
198	C₂³×C₄₇	—	2	4	no	—
199	C₂³×C₄₇	—	2	16	no	—
200	C₂³×C₄₇	—	2	16	no	—
201	C₂³×C₄₇	—	2	16	no	—
202	C₂³×C₄₇	—	2	16	no	—
203	C₂³×C₄₇	—	2	32	no	—
204	C₂³×C₄₇	—	2	4	no	—
205	C₂³×C₄₇	—	2	4	no	—
206	C₂³×C₄₇	—	2	4	no	—
207	C₂³×C₄₇	—	2	8	no	—
208	C₂³×C₄₇	—	2	4	no	—
209	C₂³×C₄₇	—	2	4	no	—
210	C₂³×C₄₇	—	2	8	no	—
211	C₂³×C₄₇	—	2	2	no	—
212	C₂³×C₄₇	—	2	4	no	—
213	C₂³×C₄₇	—	2	4	no	—
214	C₂³×C₄₇	—	2	8	no	—
215	C₂³×C₄₇	—	2	8	no	—
216	C₂³×C₄₇	—	2	4	no	—
217	C₂³×C₄₇	—	2	2	no	—
218	C₂³×C₄₇	—	2	4	no	—
219	C₂³×C₄₇	—	2	4	no	—
220	C₂³×C₄₇	—	2	16	no	—
221	C₂³×C₄₇	—	2	16	no	—
222	C₂³×C₄₇	—	2	32	no	—
223	C₂³×C₄₇	—	2	32	no	—
224	C₂³×C₄₇	—	4	16	no	—
225	C₂³×C₄₇	—	4	64	no	—
226	C₂³×C₄₇	—	4	64	no	—
227	C₂³×C₄₇	—	4	32	no	—
228	C₂³×C₄₇	—	4	32	no	—
229	C₂³×C₄₇	—	4	64	no	—
230	C₂³×C₄₇	—	4	16	no	—
231	C₂³×C₄₇	—	4	32	no	—
232	C₂³×C₄₇	—	4	32	no	—
233	C₂³×C₄₇	—	4	64	no	—
234	C₂³×C₄₇	—	4	2	no	—
235	C₂³×C₄₇	—	4	4	no	—
236	C₂³×C₄₇	—	4	2	no	—
237	C₂³×C₄₇	—	4	4	no	—
238	C₂³×C₄₇	—	4	4	no	—
239	C₂³×C₄₇	—	4	8	no	—
240	C₂³×C₄₇	—	4	8	no	—
241	C₂³×C₄₇	—	4	8	no	—
242	C₂³×C₄₇	—	4	8	no	—
243	C₂³×C₄₇	—	4	16	no	—
244	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
245	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
246	C₂³×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
247	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
248	C₂³×C₄₇	C₂×C₂²⋊C₄	1	8	yes	complemented
249	C₂³×C₄₇	C₄×D₄	1	8	yes	—
250	C₂³×C₄₇	#120	1	8	yes	—
251	C₂³×C₄₇	#120	1	8	yes	—
252	C₂³×C₄₇	#120	1	4	yes	—
253	C₂³×C₄₇	#121	1	8	yes	—
254	C₂³×C₄₇	#123	1	4	yes	—
255	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
256	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
257	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
258	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
259	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
260	C₂³×C₄₇	C₂×#41	1	2	yes	—
261	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
262	D₄×C₄₇	—	2	64	no	—
263	D₄×C₄₇	—	2	64	no	—
264	C₂×C₄×C₄₇	—	2	32	no	—
265	C₂×C₄×C₄₇	—	2	4	no	—
266	C₂×C₄×C₄₇	—	2	4	no	—
267	C₂×C₄×C₄₇	—	2	8	no	—
268	C₂×C₄×C₄₇	—	2	8	no	—
269	C₂×C₄×C₄₇	—	2	8	no	—
270	C₂×C₄×C₄₇	—	2	16	no	—
271	C₂×C₄×C₄₇	—	4	32	no	—
272	C₂×C₄×C₄₇	—	4	4	no	—
273	C₂×C₄×C₄₇	—	4	4	no	—
274	C₂×C₄×C₄₇	—	4	8	no	—
275	C₂×C₄×C₄₇	—	4	4	no	—
276	C₂×C₄×C₄₇	—	4	4	no	—
277	C₂×C₄×C₄₇	—	4	4	no	—
278	C₂×C₄×C₄₇	—	4	8	no	—
279	C₂×C₄×C₄₇	—	4	8	no	—
280	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	complemented
281	#13867	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂²×C₄₇	—	2	4	no	—
283	C₂²×C₄₇	—	2	4	no	—
284	C₂²×C₄₇	—	2	16	no	—
285	C₂²×C₄₇	—	2	16	no	—
286	C₂²×C₄₇	—	2	8	no	—
287	C₂²×C₄₇	—	2	8	no	—
288	C₂²×C₄₇	—	2	8	no	—
289	C₂²×C₄₇	—	2	8	no	—
290	C₂²×C₄₇	—	2	16	no	—
291	C₂²×C₄₇	—	2	16	no	—
292	C₂²×C₄₇	—	2	4	no	—
293	C₂²×C₄₇	—	2	4	no	—
294	C₂²×C₄₇	—	2	4	no	—
295	C₂²×C₄₇	—	2	16	no	—
296	C₂²×C₄₇	—	2	4	no	—
297	C₂²×C₄₇	—	2	8	no	—
298	C₂²×C₄₇	—	2	4	no	—
299	C₂²×C₄₇	—	4	64	no	—
300	C₂²×C₄₇	—	4	64	no	—
301	C₂²×C₄₇	—	4	4	no	—
302	C₂²×C₄₇	—	4	8	no	—
303	C₂²×C₄₇	—	4	8	no	—
304	C₂²×C₄₇	—	4	4	no	—
305	C₂²×C₄₇	—	4	8	no	—
306	C₂²×C₄₇	—	4	4	no	—
307	C₂²×C₄₇	—	4	8	no	—
308	C₂²×C₄₇	—	4	8	no	—
309	C₂²×C₄₇	—	4	16	no	—
310	C₂²×C₄₇	—	4	4	no	—
311	C₂²×C₄₇	#379	1	8	yes	complemented
312	C₂²×C₄₇	#386	1	8	yes	complemented
313	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
314	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	2	yes	—
315	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
316	C₂²×C₄₇	#518	1	2	yes	—
317	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
318	C₂²×C₄₇	C₂×#120	1	2	yes	—
319	C₂²×C₄₇	C₂×#120	1	2	yes	—
320	C₂²×C₄₇	C₂×#121	1	2	yes	—
321	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
322	C₂²×C₄₇	#534	1	2	yes	—
323	C₂²×C₄₇	#534	1	2	yes	—
324	C₂²×C₄₇	D₄²	1	8	yes	—
325	C₂²×C₄₇	#546	1	8	yes	—
326	C₄×C₄₇	—	2	8	no	—
327	C₄×C₄₇	—	4	8	no	—
328	C₄×C₄₇	—	8	4	no	—
329	C₂⁴×D₄	C₂×C₄₇	1	1	yes	characteristic
330	C₂³×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
331	C₂×#386	C₂×C₄₇	1	4	yes	complemented
332	C₂×#379	C₂×C₄₇	1	1	yes	characteristic, complemented
333	C₂×#379	C₂×C₄₇	1	2	yes	complemented
334	#1438	C₂×C₄₇	1	4	yes	complemented
335	C₂²⋊#95	C₂×C₄₇	1	2	yes	complemented
336	C₂×C₄₇	—	2	8	no	—
337	C₂×C₄₇	—	2	8	no	—
338	C₂×C₄₇	—	4	4	no	—
339	C₂×C₄₇	—	4	8	no	—
340	C₂×C₄₇	C₂×#379	1	1	yes	characteristic
341	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
342	C₂×C₄₇	#2308	1	1	yes	characteristic
343	C₂×C₄₇	D₄×C₂²⋊C₄	1	4	yes	—
344	C₂×C₄₇	#2403	1	2	yes	—
345	C₂×C₄₇	#2405	1	2	yes	—
346	C₂×C₄₇	#2410	1	4	yes	—
347	C₂⁶	C₂²×C₄₇	1	1	yes	characteristic
348	C₂⁶	C₂²×C₄₇	1	1	yes	characteristic
349	C₂³×D₄	—	2	4	no	—
350	C₂³×D₄	—	2	4	no	—
351	C₂³×D₄	—	2	16	no	—
352	C₂³×D₄	C₄×C₄₇	1	8	yes	complemented
353	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
354	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
355	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
356	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	complemented
357	C₂²×C₂²⋊C₄	—	2	4	no	—
358	C₂²×C₂²⋊C₄	—	2	8	no	—
359	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
360	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
361	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	complemented
362	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	complemented
363	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	complemented
364	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	complemented
365	#386	—	2	16	no	—
366	#379	—	2	4	no	—
367	#379	—	2	8	no	—
368	C₂×#95	C₂²×C₄₇	1	8	yes	complemented
369	C₄₇	#13867	1	1	yes	characteristic, direct product factor, Sylow
370	C₂⁵	—	2	4	no	—
371	C₂⁵	—	2	8	no	—
372	C₂⁵	—	2	8	no	—
373	C₂⁵	—	2	2	no	—
374	C₂⁵	—	2	2	no	—
375	C₂⁵	—	2	4	no	—
376	C₂⁵	—	2	4	no	—
377	C₂⁵	—	2	4	no	—
378	C₂⁵	—	4	4	no	—
379	C₂⁵	—	4	4	no	—
380	C₂⁵	C₂×C₄×C₄₇	1	4	yes	—
381	C₂⁵	C₂×C₄×C₄₇	1	4	yes	complemented
382	C₂⁵	D₄×C₄₇	1	4	yes	—
383	C₂⁵	D₄×C₄₇	1	4	yes	—
384	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
385	C₂⁵	C₂³×C₄₇	1	2	yes	—
386	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
387	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
388	C₂²×D₄	—	2	64	no	—
389	C₂²×D₄	—	2	64	no	—
390	C₂²×D₄	—	2	32	no	—
391	C₂²×D₄	—	2	4	no	—
392	C₂²×D₄	—	2	4	no	—
393	C₂²×D₄	—	2	8	no	—
394	C₂²×D₄	—	2	4	no	—
395	C₂²×D₄	—	2	8	no	—
396	C₂²×D₄	—	2	4	no	—
397	C₂²×D₄	—	2	64	no	—
398	C₂²×D₄	—	2	8	no	—
399	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	—
400	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	complemented
401	C₂²×D₄	D₄×C₄₇	1	16	yes	—
402	C₂³×C₄	—	2	2	no	—
403	C₂³×C₄	—	2	2	no	—
404	C₂³×C₄	—	2	8	no	—
405	C₂³×C₄	—	2	4	no	—
406	C₂³×C₄	—	2	8	no	—
407	C₂³×C₄	—	2	8	no	—
408	C₂³×C₄	—	4	4	no	—
409	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	complemented
410	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
411	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
412	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
413	C₂×C₂²⋊C₄	—	2	32	no	—
414	C₂×C₂²⋊C₄	—	2	4	no	—
415	C₂×C₂²⋊C₄	—	2	4	no	—
416	C₂×C₂²⋊C₄	—	2	4	no	—
417	C₂×C₂²⋊C₄	—	2	8	no	—
418	C₂×C₂²⋊C₄	—	2	4	no	—
419	C₂×C₂²⋊C₄	—	2	4	no	—
420	C₂×C₂²⋊C₄	—	2	4	no	—
421	C₂×C₂²⋊C₄	—	2	4	no	—
422	C₂×C₂²⋊C₄	—	2	16	no	—
423	C₂×C₂²⋊C₄	—	2	8	no	—
424	C₂×C₂²⋊C₄	—	2	4	no	—
425	C₂×C₂²⋊C₄	—	2	16	no	—
426	C₂×C₂²⋊C₄	—	4	8	no	—
427	C₂×C₂²⋊C₄	—	4	4	no	—
428	C₂×C₂²⋊C₄	D₄×C₄₇	1	8	yes	complemented
429	#95	—	2	16	no	—
430	C₂⁴	—	2	2	no	—
431	C₂⁴	—	2	4	no	—
432	C₂⁴	—	2	2	no	—
433	C₂⁴	—	2	4	no	—
434	C₂⁴	—	2	4	no	—
435	C₂⁴	—	2	16	no	—
436	C₂⁴	—	2	16	no	—
437	C₂⁴	—	2	16	no	—
438	C₂⁴	—	2	8	no	—
439	C₂⁴	—	2	16	no	—
440	C₂⁴	—	2	16	no	—
441	C₂⁴	—	2	8	no	—
442	C₂⁴	—	2	16	no	—
443	C₂⁴	—	2	16	no	—
444	C₂⁴	—	2	16	no	—
445	C₂⁴	—	2	8	no	—
446	C₂⁴	—	2	2	no	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	—	2	2	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	—	2	4	no	—
451	C₂⁴	—	2	4	no	—
452	C₂⁴	—	2	2	no	—
453	C₂⁴	—	2	4	no	—
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	2	8	no	—
456	C₂⁴	—	2	16	no	—
457	C₂⁴	—	4	8	no	—
458	C₂⁴	—	4	8	no	—
459	C₂⁴	—	4	8	no	—
460	C₂⁴	—	4	8	no	—
461	C₂⁴	—	4	32	no	—
462	C₂⁴	—	4	32	no	—
463	C₂⁴	—	4	32	no	—
464	C₂⁴	—	4	32	no	—
465	C₂⁴	—	4	8	no	—
466	C₂⁴	—	4	8	no	—
467	C₂⁴	—	4	4	no	—
468	C₂⁴	—	4	8	no	—
469	C₂⁴	—	4	4	no	—
470	C₂⁴	C₂²⋊C₄×C₄₇	1	16	yes	complemented
471	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
472	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
473	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
474	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
475	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
476	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
477	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
478	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
479	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
480	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
481	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
482	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
483	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
484	C₂⁴	#41×C₄₇	1	4	yes	—
485	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
486	C₂×D₄	—	2	256	no	—
487	C₂×D₄	—	2	32	no	—
488	C₂×D₄	—	2	32	no	—
489	C₂×D₄	—	2	16	no	—
490	C₂×D₄	—	2	16	no	—
491	C₂×D₄	—	2	16	no	—
492	C₂×D₄	—	2	16	no	—
493	C₂×D₄	—	2	32	no	—
494	C₂×D₄	—	2	32	no	—
495	C₂×D₄	—	2	16	no	—
496	C₂×D₄	C₂²⋊C₄×C₄₇	1	32	yes	complemented
497	C₂²×C₄	—	2	16	no	—
498	C₂²×C₄	—	2	16	no	—
499	C₂²×C₄	—	2	8	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	16	no	—
504	C₂²×C₄	—	2	16	no	—
505	C₂²×C₄	—	2	8	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	8	no	—
509	C₂²×C₄	—	2	8	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	8	no	—
514	C₂²×C₄	—	4	32	no	—
515	C₂²×C₄	—	4	8	no	—
516	C₂²×C₄	—	4	8	no	—
517	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
518	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
519	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	complemented
520	C₂²⋊C₄	—	2	16	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	4	32	no	—
523	C₂²⋊C₄	—	4	8	no	—
524	C₂²⋊C₄	—	4	8	no	—
525	C₂²⋊C₄	—	4	8	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	16	no	—
540	C₂³	—	2	16	no	—
541	C₂³	—	2	16	no	—
542	C₂³	—	2	16	no	—
543	C₂³	—	2	32	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	8	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	8	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	8	no	—
555	C₂³	—	2	8	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	2	16	no	—
561	C₂³	—	2	16	no	—
562	C₂³	—	2	32	no	—
563	C₂³	—	2	32	no	—
564	C₂³	—	4	16	no	—
565	C₂³	—	4	64	no	—
566	C₂³	—	4	64	no	—
567	C₂³	—	4	32	no	—
568	C₂³	—	4	32	no	—
569	C₂³	—	4	64	no	—
570	C₂³	—	4	16	no	—
571	C₂³	—	4	32	no	—
572	C₂³	—	4	32	no	—
573	C₂³	—	4	64	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	4	no	—
576	C₂³	—	4	2	no	—
577	C₂³	—	4	4	no	—
578	C₂³	—	4	4	no	—
579	C₂³	—	4	8	no	—
580	C₂³	—	4	8	no	—
581	C₂³	—	4	8	no	—
582	C₂³	—	4	8	no	—
583	C₂³	—	4	16	no	—
584	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
585	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
586	C₂³	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
587	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
588	C₂³	C₂×C₂²⋊C₄×C₄₇	1	8	yes	complemented
589	C₂³	C₄×D₄×C₄₇	1	8	yes	—
590	C₂³	#120×C₄₇	1	8	yes	—
591	C₂³	#120×C₄₇	1	8	yes	—
592	C₂³	#120×C₄₇	1	4	yes	—
593	C₂³	#121×C₄₇	1	8	yes	—
594	C₂³	#123×C₄₇	1	4	yes	—
595	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
596	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
597	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
598	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
599	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
600	C₂³	C₂×#41×C₄₇	1	2	yes	—
601	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
602	D₄	—	2	64	no	—
603	D₄	—	2	64	no	—
604	C₂×C₄	—	2	32	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	8	no	—
608	C₂×C₄	—	2	8	no	—
609	C₂×C₄	—	2	8	no	—
610	C₂×C₄	—	2	16	no	—
611	C₂×C₄	—	4	32	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	4	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	4	4	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	—	4	8	no	—
620	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	complemented
621	C₂²	—	2	4	no	—
622	C₂²	—	2	4	no	—
623	C₂²	—	2	4	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	2	16	no	—
626	C₂²	—	2	16	no	—
627	C₂²	—	2	8	no	—
628	C₂²	—	2	8	no	—
629	C₂²	—	2	8	no	—
630	C₂²	—	2	8	no	—
631	C₂²	—	2	16	no	—
632	C₂²	—	2	16	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	8	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	16	no	—
638	C₂²	—	4	64	no	—
639	C₂²	—	4	64	no	—
640	C₂²	—	4	4	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	8	no	—
643	C₂²	—	4	8	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	8	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	8	no	—
648	C₂²	—	4	8	no	—
649	C₂²	—	4	16	no	—
650	C₂²	C₄₇×#379	1	8	yes	complemented
651	C₂²	C₄₇×#386	1	8	yes	complemented
652	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
653	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	2	yes	—
654	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
655	C₂²	C₄₇×#518	1	2	yes	—
656	C₂²	C₂×#120×C₄₇	1	2	yes	—
657	C₂²	C₂×#120×C₄₇	1	2	yes	—
658	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
659	C₂²	C₂×#121×C₄₇	1	2	yes	—
660	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
661	C₂²	C₄₇×#534	1	2	yes	—
662	C₂²	C₄₇×#534	1	2	yes	—
663	C₂²	D₄²×C₄₇	1	8	yes	—
664	C₂²	C₄₇×#546	1	8	yes	—
665	C₄	—	2	8	no	—
666	C₄	—	4	8	no	—
667	C₄	—	8	4	no	—
668	C₂	—	2	8	no	—
669	C₂	—	2	8	no	—
670	C₂	—	4	4	no	—
671	C₂	—	4	8	no	—
672	C₂	C₂×C₄₇×#379	1	1	yes	characteristic
673	C₂	C₂×C₄₇×#386	1	1	yes	characteristic
674	C₂	C₄₇×#2308	1	1	yes	characteristic
675	C₂	D₄×C₂²⋊C₄×C₄₇	1	4	yes	—
676	C₂	C₄₇×#2403	1	2	yes	—
677	C₂	C₄₇×#2405	1	2	yes	—
678	C₂	C₄₇×#2410	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂⁴×D₄×C₄₇	C₂
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
2. C₂³×C₂²⋊C₄×C₄₇	C₂	semidirect
3. C₂×C₄₇×#386	C₂	semidirect
4. C₂×C₄₇×#379	C₂	semidirect
5. C₂×C₄₇×#379	C₂	semidirect
6. C₄₇×#1438	C₂	semidirect
7. C₄₇×C₂²⋊#95	C₂	semidirect
13. C₂³×D₄×C₄₇	C₄	semidirect
17. C₂⁴×C₄×C₄₇	C₂²	semidirect
22. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
23. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
24. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
25. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
29. C₂×#95×C₄₇	C₂²	semidirect
41. C₂⁵×C₄₇	C₂×C₄	semidirect
60. C₂²×D₄×C₄₇	C₂×C₄	semidirect
69. C₂³×C₄×C₄₇	C₂×C₄	semidirect
88. C₂×C₂²⋊C₄×C₄₇	D₄	semidirect
130. C₂⁴×C₄₇	C₂²⋊C₄	semidirect
156. C₂×D₄×C₄₇	C₂²⋊C₄	semidirect
179. C₂²×C₄×C₄₇	C₂×D₄	semidirect
248. C₂³×C₄₇	C₂×C₂²⋊C₄	semidirect
280. C₂×C₄×C₄₇	C₂×C₂²⋊C₄	semidirect
281. #13867	C₄₇	direct (N × H)
311. C₂²×C₄₇	#379	semidirect
312. C₂²×C₄₇	#386	semidirect
330. C₂³×C₂²⋊C₄	C₂×C₄₇	semidirect
331. C₂×#386	C₂×C₄₇	semidirect
332. C₂×#379	C₂×C₄₇	semidirect
333. C₂×#379	C₂×C₄₇	semidirect
334. #1438	C₂×C₄₇	semidirect
335. C₂²⋊#95	C₂×C₄₇	semidirect
352. C₂³×D₄	C₄×C₄₇	semidirect
356. C₂⁴×C₄	C₂²×C₄₇	semidirect
361. C₂²×C₂²⋊C₄	C₂²×C₄₇	semidirect
362. C₂²×C₂²⋊C₄	C₂²×C₄₇	semidirect
363. C₂²×C₂²⋊C₄	C₂²×C₄₇	semidirect
364. C₂²×C₂²⋊C₄	C₂²×C₄₇	semidirect
368. C₂×#95	C₂²×C₄₇	semidirect
369. C₄₇	#13867	direct (N × H)
381. C₂⁵	C₂×C₄×C₄₇	semidirect
400. C₂²×D₄	C₂×C₄×C₄₇	semidirect
409. C₂³×C₄	C₂×C₄×C₄₇	semidirect
428. C₂×C₂²⋊C₄	D₄×C₄₇	semidirect
470. C₂⁴	C₂²⋊C₄×C₄₇	semidirect
496. C₂×D₄	C₂²⋊C₄×C₄₇	semidirect
519. C₂²×C₄	C₂×D₄×C₄₇	semidirect
588. C₂³	C₂×C₂²⋊C₄×C₄₇	semidirect
620. C₂×C₄	C₂×C₂²⋊C₄×C₄₇	semidirect
650. C₂²	C₄₇×#379	semidirect
651. C₂²	C₄₇×#386	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₄₇	2
C₂³×C₂²⋊C₄×C₄₇	2
C₂×C₄₇×#386	2
C₂×C₄₇×#379	2
C₄₇×#1438	2
C₄₇×C₂²⋊#95	2
#13867	47

Subgroups — C47×#13867 #26053565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13867 #26053565