Subgroups — C₂×C₄₇×#2561 #26074539

Order 12032.

4166 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2561	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₇×#397	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#393	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#388	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#381	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₇×#379	C₂	1	2	yes	maximal
9	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
12	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₇	—	2	8	no	—
15	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	8	yes	complemented
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊C₄×C₄₇	—	2	8	no	—
19	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
22	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
24	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
26	C₂²×C₄²×C₄₇	C₂²	1	2	yes	complemented
27	C₄₇×#397	C₂²	1	16	yes	complemented
28	C₄₇×#393	C₂²	1	16	yes	complemented
29	C₄₇×#388	C₂²	1	32	yes	complemented
30	C₄₇×#381	C₂²	1	16	yes	complemented
31	C₄₇×#379	C₂²	1	16	yes	—
32	C₄×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	complemented
33	C₂×#95×C₄₇	C₂²	1	2	yes	complemented
34	C₂×#95×C₄₇	C₂²	1	4	yes	complemented
35	C₂×#95×C₄₇	C₂²	1	4	yes	complemented
36	C₂⁵×C₄₇	—	2	4	no	—
37	C₂⁵×C₄₇	—	2	8	no	—
38	C₂⁵×C₄₇	—	2	8	no	—
39	C₂⁵×C₄₇	—	4	4	no	—
40	C₂⁵×C₄₇	C₂³	1	2	yes	—
41	C₂⁵×C₄₇	C₂³	1	4	yes	—
42	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₄₇	—	2	4	no	—
44	C₂²×Q₈×C₄₇	—	4	4	no	—
45	C₂²×Q₈×C₄₇	C₂³	1	4	yes	complemented
46	C₂³×C₄×C₄₇	—	2	4	no	—
47	C₂³×C₄×C₄₇	—	2	8	no	—
48	C₂³×C₄×C₄₇	—	4	4	no	—
49	C₂³×C₄×C₄₇	D₄	1	8	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
52	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
58	C₂²⋊Q₈×C₄₇	—	2	32	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	complemented
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	complemented
63	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	32	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
70	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
75	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
76	C₂×C₄²×C₄₇	—	4	4	no	—
77	C₂×C₄²×C₄₇	C₂³	1	8	yes	complemented
78	#95×C₄₇	C₂³	1	8	yes	complemented
79	#95×C₄₇	C₂³	1	16	yes	complemented
80	#95×C₄₇	C₂³	1	16	yes	complemented
81	C₂⁴×C₄₇	—	2	4	no	—
82	C₂⁴×C₄₇	—	2	4	no	—
83	C₂⁴×C₄₇	—	2	32	no	—
84	C₂⁴×C₄₇	—	2	8	no	—
85	C₂⁴×C₄₇	—	2	4	no	—
86	C₂⁴×C₄₇	—	2	16	no	—
87	C₂⁴×C₄₇	—	2	4	no	—
88	C₂⁴×C₄₇	—	2	8	no	—
89	C₂⁴×C₄₇	—	2	8	no	—
90	C₂⁴×C₄₇	—	2	16	no	—
91	C₂⁴×C₄₇	—	4	8	no	—
92	C₂⁴×C₄₇	—	4	64	no	—
93	C₂⁴×C₄₇	—	4	16	no	—
94	C₂⁴×C₄₇	—	4	16	no	—
95	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
96	C₂⁴×C₄₇	#41	1	8	yes	—
97	C₂⁴×C₄₇	#41	1	8	yes	—
98	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
99	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
100	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
101	C₂×Q₈×C₄₇	—	2	8	no	—
102	C₂×Q₈×C₄₇	—	4	8	no	—
103	C₂×Q₈×C₄₇	—	4	16	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	8	no	—
107	C₂²×C₄×C₄₇	—	2	4	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	8	no	—
111	C₂²×C₄×C₄₇	—	2	8	no	—
112	C₂²×C₄×C₄₇	—	2	8	no	—
113	C₂²×C₄×C₄₇	—	2	16	no	—
114	C₂²×C₄×C₄₇	—	2	8	no	—
115	C₂²×C₄×C₄₇	—	2	8	no	—
116	C₂²×C₄×C₄₇	—	2	8	no	—
117	C₂²×C₄×C₄₇	—	4	16	no	—
118	C₂²×C₄×C₄₇	—	4	8	no	—
119	C₂²×C₄×C₄₇	—	4	16	no	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₄₇	C₂×D₄	1	16	yes	—
123	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
129	C₄⋊C₄×C₄₇	—	2	8	no	—
130	C₄⋊C₄×C₄₇	—	2	16	no	—
131	C₂²⋊C₄×C₄₇	—	2	16	no	—
132	C₂²⋊C₄×C₄₇	—	2	32	no	—
133	C₂²⋊C₄×C₄₇	—	2	16	no	—
134	C₂²⋊C₄×C₄₇	—	2	16	no	—
135	C₂²⋊C₄×C₄₇	—	2	16	no	—
136	C₂²⋊C₄×C₄₇	—	4	16	no	—
137	C₄²×C₄₇	—	4	8	no	—
138	C₂³×C₄₇	—	2	8	no	—
139	C₂³×C₄₇	—	2	8	no	—
140	C₂³×C₄₇	—	2	32	no	—
141	C₂³×C₄₇	—	2	4	no	—
142	C₂³×C₄₇	—	2	4	no	—
143	C₂³×C₄₇	—	2	32	no	—
144	C₂³×C₄₇	—	2	16	no	—
145	C₂³×C₄₇	—	2	32	no	—
146	C₂³×C₄₇	—	2	4	no	—
147	C₂³×C₄₇	—	2	4	no	—
148	C₂³×C₄₇	—	2	8	no	—
149	C₂³×C₄₇	—	2	8	no	—
150	C₂³×C₄₇	—	4	64	no	—
151	C₂³×C₄₇	—	4	128	no	—
152	C₂³×C₄₇	—	4	16	no	—
153	C₂³×C₄₇	—	4	16	no	—
154	C₂³×C₄₇	—	4	8	no	—
155	C₂³×C₄₇	—	4	8	no	—
156	C₂³×C₄₇	—	4	16	no	—
157	C₂³×C₄₇	#124	1	16	yes	—
158	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
159	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
160	C₂³×C₄₇	C₂×#41	1	8	yes	—
161	C₂³×C₄₇	C₂×#41	1	8	yes	—
162	C₂³×C₄₇	C₂×#41	1	4	yes	—
163	C₂³×C₄₇	C₂×#41	1	4	yes	—
164	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
165	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
166	Q₈×C₄₇	—	4	16	no	—
167	C₂×C₄×C₄₇	—	2	8	no	—
168	C₂×C₄×C₄₇	—	2	8	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	8	no	—
175	C₂×C₄×C₄₇	—	2	8	no	—
176	C₂×C₄×C₄₇	—	2	8	no	—
177	C₂×C₄×C₄₇	—	2	8	no	—
178	C₂×C₄×C₄₇	—	2	8	no	—
179	C₂×C₄×C₄₇	—	2	8	no	—
180	C₂×C₄×C₄₇	—	4	16	no	—
181	C₂×C₄×C₄₇	—	4	8	no	—
182	C₂×C₄×C₄₇	—	4	16	no	—
183	C₂×C₄×C₄₇	—	4	8	no	—
184	C₂×C₄×C₄₇	—	4	8	no	—
185	C₂×C₄×C₄₇	—	4	16	no	—
186	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
188	C₂×#2561	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₄₇	—	2	32	no	—
190	C₂²×C₄₇	—	2	4	no	—
191	C₂²×C₄₇	—	2	4	no	—
192	C₂²×C₄₇	—	2	16	no	—
193	C₂²×C₄₇	—	2	8	no	—
194	C₂²×C₄₇	—	2	16	no	—
195	C₂²×C₄₇	—	4	64	no	—
196	C₂²×C₄₇	—	4	32	no	—
197	C₂²×C₄₇	—	4	4	no	—
198	C₂²×C₄₇	—	4	4	no	—
199	C₂²×C₄₇	—	4	8	no	—
200	C₂²×C₄₇	#525	1	4	yes	—
201	C₂²×C₄₇	C₂×#124	1	8	yes	—
202	C₂²×C₄₇	C₂×#124	1	4	yes	—
203	C₂²×C₄₇	#534	1	4	yes	—
204	C₂²×C₄₇	#551	1	16	yes	—
205	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
206	C₂²×C₄₇	C₂²×#41	1	2	yes	—
207	C₂²×C₄₇	C₂²×#41	1	2	yes	—
208	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	—	2	4	no	—
211	C₄×C₄₇	—	4	4	no	—
212	C₄×C₄₇	—	4	4	no	—
213	C₄×C₄₇	—	4	4	no	—
214	C₄×C₄₇	—	4	8	no	—
215	C₂²×C₂²⋊Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
216	C₂³×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic
217	#2561	C₂×C₄₇	1	16	yes	direct product factor
218	C₂×#397	C₂×C₄₇	1	2	yes	complemented
219	C₂×#393	C₂×C₄₇	1	2	yes	complemented
220	C₂×#388	C₂×C₄₇	1	4	yes	complemented
221	C₂×#381	C₂×C₄₇	1	2	yes	complemented
222	C₂×#379	C₂×C₄₇	1	2	yes	—
223	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
224	C₂×C₄₇	—	2	8	no	—
225	C₂×C₄₇	—	4	8	no	—
226	C₂×C₄₇	#2561	1	8	yes	direct product factor
227	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
228	C₂×C₄₇	C₂²×#124	1	1	yes	characteristic
229	C₂×C₄₇	C₂×#534	1	1	yes	characteristic
230	C₂×C₄₇	C₂×#551	1	4	yes	—
231	C₂⁶	C₂²×C₄₇	1	1	yes	characteristic
232	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
233	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
234	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	—	2	8	no	—
236	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	8	yes	complemented
237	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic, complemented
238	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
239	C₂²×C₂²⋊C₄	—	2	8	no	—
240	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
241	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
243	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
244	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
245	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
246	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
247	C₂²×C₄²	C₂²×C₄₇	1	2	yes	complemented
248	#397	C₂²×C₄₇	1	16	yes	complemented
249	#393	C₂²×C₄₇	1	16	yes	complemented
250	#388	C₂²×C₄₇	1	32	yes	complemented
251	#381	C₂²×C₄₇	1	16	yes	complemented
252	#379	C₂²×C₄₇	1	16	yes	—
253	C₄×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	complemented
254	C₂×#95	C₂²×C₄₇	1	2	yes	complemented
255	C₂×#95	C₂²×C₄₇	1	4	yes	complemented
256	C₂×#95	C₂²×C₄₇	1	4	yes	complemented
257	C₄₇	C₂×#2561	1	1	yes	characteristic, direct product factor, Sylow
258	C₂⁵	—	2	4	no	—
259	C₂⁵	—	2	8	no	—
260	C₂⁵	—	2	8	no	—
261	C₂⁵	—	4	4	no	—
262	C₂⁵	C₂³×C₄₇	1	2	yes	—
263	C₂⁵	C₂³×C₄₇	1	4	yes	—
264	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
265	C₂²×Q₈	—	2	4	no	—
266	C₂²×Q₈	—	4	4	no	—
267	C₂²×Q₈	C₂³×C₄₇	1	4	yes	complemented
268	C₂³×C₄	—	2	4	no	—
269	C₂³×C₄	—	2	8	no	—
270	C₂³×C₄	—	4	4	no	—
271	C₂³×C₄	D₄×C₄₇	1	8	yes	—
272	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
273	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
274	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
275	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
276	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
277	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
280	C₂²⋊Q₈	—	2	32	no	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	—	2	8	no	—
283	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	complemented
284	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	complemented
285	C₂×C₂²⋊C₄	—	2	8	no	—
286	C₂×C₂²⋊C₄	—	2	16	no	—
287	C₂×C₂²⋊C₄	—	2	8	no	—
288	C₂×C₂²⋊C₄	—	2	8	no	—
289	C₂×C₂²⋊C₄	—	2	8	no	—
290	C₂×C₂²⋊C₄	—	2	32	no	—
291	C₂×C₂²⋊C₄	—	4	8	no	—
292	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	—
298	C₂×C₄²	—	4	4	no	—
299	C₂×C₄²	C₂³×C₄₇	1	8	yes	complemented
300	#95	C₂³×C₄₇	1	8	yes	complemented
301	#95	C₂³×C₄₇	1	16	yes	complemented
302	#95	C₂³×C₄₇	1	16	yes	complemented
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	4	no	—
305	C₂⁴	—	2	32	no	—
306	C₂⁴	—	2	8	no	—
307	C₂⁴	—	2	4	no	—
308	C₂⁴	—	2	16	no	—
309	C₂⁴	—	2	4	no	—
310	C₂⁴	—	2	8	no	—
311	C₂⁴	—	2	8	no	—
312	C₂⁴	—	2	16	no	—
313	C₂⁴	—	4	8	no	—
314	C₂⁴	—	4	64	no	—
315	C₂⁴	—	4	16	no	—
316	C₂⁴	—	4	16	no	—
317	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
318	C₂⁴	#41×C₄₇	1	8	yes	—
319	C₂⁴	#41×C₄₇	1	8	yes	—
320	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
321	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
322	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
323	C₂×Q₈	—	2	8	no	—
324	C₂×Q₈	—	4	8	no	—
325	C₂×Q₈	—	4	16	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	16	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	4	16	no	—
340	C₂²×C₄	—	4	8	no	—
341	C₂²×C₄	—	4	16	no	—
342	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
343	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
344	C₂²×C₄	C₂×D₄×C₄₇	1	16	yes	—
345	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
346	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
347	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
348	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
349	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	16	no	—
353	C₂²⋊C₄	—	2	16	no	—
354	C₂²⋊C₄	—	2	32	no	—
355	C₂²⋊C₄	—	2	16	no	—
356	C₂²⋊C₄	—	2	16	no	—
357	C₂²⋊C₄	—	2	16	no	—
358	C₂²⋊C₄	—	4	16	no	—
359	C₄²	—	4	8	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	32	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	32	no	—
366	C₂³	—	2	16	no	—
367	C₂³	—	2	32	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	8	no	—
372	C₂³	—	4	64	no	—
373	C₂³	—	4	128	no	—
374	C₂³	—	4	16	no	—
375	C₂³	—	4	16	no	—
376	C₂³	—	4	8	no	—
377	C₂³	—	4	8	no	—
378	C₂³	—	4	16	no	—
379	C₂³	#124×C₄₇	1	16	yes	—
380	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
381	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
382	C₂³	C₂×#41×C₄₇	1	8	yes	—
383	C₂³	C₂×#41×C₄₇	1	8	yes	—
384	C₂³	C₂×#41×C₄₇	1	4	yes	—
385	C₂³	C₂×#41×C₄₇	1	4	yes	—
386	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
387	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
388	Q₈	—	4	16	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	4	16	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	16	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	16	no	—
408	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
409	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
410	C₂²	—	2	32	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	16	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	16	no	—
416	C₂²	—	4	64	no	—
417	C₂²	—	4	32	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	8	no	—
421	C₂²	C₄₇×#525	1	4	yes	—
422	C₂²	C₂×#124×C₄₇	1	8	yes	—
423	C₂²	C₂×#124×C₄₇	1	4	yes	—
424	C₂²	C₄₇×#534	1	4	yes	—
425	C₂²	C₄₇×#551	1	16	yes	—
426	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
427	C₂²	C₂²×#41×C₄₇	1	2	yes	—
428	C₂²	C₂²×#41×C₄₇	1	2	yes	—
429	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	2	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	4	4	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	4	8	no	—
436	C₂	—	2	8	no	—
437	C₂	—	4	8	no	—
438	C₂	C₄₇×#2561	1	8	yes	direct product factor
439	C₂	C₂×C₄₇×#525	1	1	yes	characteristic
440	C₂	C₂²×#124×C₄₇	1	1	yes	characteristic
441	C₂	C₂×C₄₇×#534	1	1	yes	characteristic
442	C₂	C₂×C₄₇×#551	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂⁶×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
1. C₂²×C₂²⋊Q₈×C₄₇	C₂	semidirect
3. C₄₇×#2561	C₂	direct (N × H)
4. C₂×C₄₇×#397	C₂	semidirect
5. C₂×C₄₇×#393	C₂	semidirect
6. C₂×C₄₇×#388	C₂	semidirect
7. C₂×C₄₇×#381	C₂	semidirect
9. C₂×C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
11. C₂³×Q₈×C₄₇	C₂²	semidirect
15. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
16. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
17. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
26. C₂²×C₄²×C₄₇	C₂²	semidirect
27. C₄₇×#397	C₂²	semidirect
28. C₄₇×#393	C₂²	semidirect
29. C₄₇×#388	C₂²	semidirect
30. C₄₇×#381	C₂²	semidirect
32. C₄×C₂²⋊C₄×C₄₇	C₂²	semidirect
33. C₂×#95×C₄₇	C₂²	semidirect
34. C₂×#95×C₄₇	C₂²	semidirect
35. C₂×#95×C₄₇	C₂²	semidirect
45. C₂²×Q₈×C₄₇	C₂³	semidirect
61. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
62. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
77. C₂×C₄²×C₄₇	C₂³	semidirect
78. #95×C₄₇	C₂³	semidirect
79. #95×C₄₇	C₂³	semidirect
80. #95×C₄₇	C₂³	semidirect
188. C₂×#2561	C₄₇	direct (N × H)
215. C₂²×C₂²⋊Q₈	C₂×C₄₇	semidirect
217. #2561	C₂×C₄₇	direct (N × H)
218. C₂×#397	C₂×C₄₇	semidirect
219. C₂×#393	C₂×C₄₇	semidirect
220. C₂×#388	C₂×C₄₇	semidirect
221. C₂×#381	C₂×C₄₇	semidirect
223. C₂×C₄×C₂²⋊C₄	C₂×C₄₇	semidirect
226. C₂×C₄₇	#2561	direct (N × H)
232. C₂³×Q₈	C₂²×C₄₇	semidirect
236. C₂×C₂²⋊Q₈	C₂²×C₄₇	semidirect
237. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
238. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
247. C₂²×C₄²	C₂²×C₄₇	semidirect
248. #397	C₂²×C₄₇	semidirect
249. #393	C₂²×C₄₇	semidirect
250. #388	C₂²×C₄₇	semidirect
251. #381	C₂²×C₄₇	semidirect
253. C₄×C₂²⋊C₄	C₂²×C₄₇	semidirect
254. C₂×#95	C₂²×C₄₇	semidirect
255. C₂×#95	C₂²×C₄₇	semidirect
256. C₂×#95	C₂²×C₄₇	semidirect
257. C₄₇	C₂×#2561	direct (N × H)
267. C₂²×Q₈	C₂³×C₄₇	semidirect
283. C₂×C₄⋊C₄	C₂³×C₄₇	semidirect
284. C₂×C₄⋊C₄	C₂³×C₄₇	semidirect
299. C₂×C₄²	C₂³×C₄₇	semidirect
300. #95	C₂³×C₄₇	semidirect
301. #95	C₂³×C₄₇	semidirect
302. #95	C₂³×C₄₇	semidirect
438. C₂	C₄₇×#2561	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₄₇	2
C₂³×C₂²⋊C₄×C₄₇	2
C₄₇×#2561	2
C₂×C₄₇×#397	2
C₂×C₄₇×#393	2
C₂×C₄₇×#388	2
C₂×C₄₇×#381	2
C₂×C₄₇×#379	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₂×#2561	47

Subgroups — C2×C47×#2561 #26074539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2561 #26074539