Subgroups — C₂×C₄₇×#2463 #26074352

Order 12032.

3958 conjugacy classes of subgroups.

The subgroup lattice has 536 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	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2463	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₇×#394	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#393	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇×#392	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₇×#388	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₇×#387	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#386	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₇×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
13	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₄₇	—	2	16	no	—
17	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	16	yes	complemented
18	C₂×C₄×D₄×C₄₇	—	2	16	no	—
19	C₂×C₄×D₄×C₄₇	C₂²	1	16	yes	complemented
20	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
31	C₄₇×#394	C₂²	1	16	yes	complemented
32	C₄₇×#393	C₂²	1	8	yes	complemented
33	C₄₇×#392	C₂²	1	8	yes	—
34	C₄₇×#388	C₂²	1	16	yes	complemented
35	C₄₇×#387	C₂²	1	16	yes	complemented
36	C₄₇×#386	C₂²	1	16	yes	complemented
37	C₄₇×#385	C₂²	1	8	yes	complemented
38	C₂×#95×C₄₇	C₂²	1	2	yes	—
39	C₂×#95×C₄₇	C₂²	1	2	yes	—
40	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#95×C₄₇	C₂²	1	2	yes	—
42	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
43	C₂⁵×C₄₇	C₂³	1	2	yes	—
44	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₄₇	—	2	8	no	—
46	C₂²×Q₈×C₄₇	—	4	2	no	—
47	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
48	C₂²×D₄×C₄₇	—	2	8	no	—
49	C₂²×D₄×C₄₇	—	2	8	no	—
50	C₂²×D₄×C₄₇	—	2	8	no	—
51	C₂²×D₄×C₄₇	—	2	8	no	—
52	C₂²×D₄×C₄₇	—	4	2	no	—
53	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
54	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
55	C₂³×C₄×C₄₇	—	2	8	no	—
56	C₂³×C₄×C₄₇	—	2	8	no	—
57	C₂³×C₄×C₄₇	—	2	8	no	—
58	C₂³×C₄×C₄₇	—	4	2	no	—
59	C₂³×C₄×C₄₇	—	4	4	no	—
60	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
65	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
66	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
68	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
69	C₂²⋊Q₈×C₄₇	—	2	64	no	—
70	C₄×D₄×C₄₇	—	2	64	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
73	C₂×C₄⋊C₄×C₄₇	D₄	1	16	yes	complemented
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
82	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
84	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
91	C₂×C₄²×C₄₇	—	2	8	no	—
92	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
93	#95×C₄₇	C₂³	1	8	yes	—
94	#95×C₄₇	C₂³	1	8	yes	—
95	#95×C₄₇	C₂³	1	4	yes	—
96	#95×C₄₇	C₂³	1	8	yes	—
97	#95×C₄₇	C₂³	1	4	yes	—
98	C₂⁴×C₄₇	—	2	4	no	—
99	C₂⁴×C₄₇	—	2	4	no	—
100	C₂⁴×C₄₇	—	2	4	no	—
101	C₂⁴×C₄₇	—	2	4	no	—
102	C₂⁴×C₄₇	—	2	4	no	—
103	C₂⁴×C₄₇	—	2	4	no	—
104	C₂⁴×C₄₇	—	2	2	no	—
105	C₂⁴×C₄₇	—	2	4	no	—
106	C₂⁴×C₄₇	—	2	2	no	—
107	C₂⁴×C₄₇	—	2	4	no	—
108	C₂⁴×C₄₇	#41	1	4	yes	—
109	C₂⁴×C₄₇	#41	1	8	yes	—
110	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
111	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
112	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂×Q₈×C₄₇	—	2	16	no	—
114	C₂×Q₈×C₄₇	—	4	4	no	—
115	C₂×Q₈×C₄₇	—	4	16	no	—
116	C₂×D₄×C₄₇	—	2	64	no	—
117	C₂×D₄×C₄₇	—	2	16	no	—
118	C₂×D₄×C₄₇	—	2	16	no	—
119	C₂×D₄×C₄₇	—	2	16	no	—
120	C₂×D₄×C₄₇	—	2	16	no	—
121	C₂×D₄×C₄₇	—	4	4	no	—
122	C₂×D₄×C₄₇	—	4	16	no	—
123	C₂²×C₄×C₄₇	—	2	4	no	—
124	C₂²×C₄×C₄₇	—	2	4	no	—
125	C₂²×C₄×C₄₇	—	2	4	no	—
126	C₂²×C₄×C₄₇	—	2	4	no	—
127	C₂²×C₄×C₄₇	—	2	4	no	—
128	C₂²×C₄×C₄₇	—	2	4	no	—
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	—	2	4	no	—
131	C₂²×C₄×C₄₇	—	2	4	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	2	4	no	—
134	C₂²×C₄×C₄₇	—	2	4	no	—
135	C₂²×C₄×C₄₇	—	2	4	no	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	4	no	—
139	C₂²×C₄×C₄₇	—	2	16	no	—
140	C₂²×C₄×C₄₇	—	2	16	no	—
141	C₂²×C₄×C₄₇	—	2	16	no	—
142	C₂²×C₄×C₄₇	—	4	4	no	—
143	C₂²×C₄×C₄₇	—	4	8	no	—
144	C₂²×C₄×C₄₇	—	4	16	no	—
145	C₂²×C₄×C₄₇	—	4	32	no	—
146	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
147	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
148	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
149	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
156	C₄⋊C₄×C₄₇	—	2	16	no	—
157	C₄⋊C₄×C₄₇	—	2	16	no	—
158	C₄⋊C₄×C₄₇	C₂×D₄	1	32	yes	complemented
159	C₂²⋊C₄×C₄₇	—	2	8	no	—
160	C₂²⋊C₄×C₄₇	—	2	16	no	—
161	C₂²⋊C₄×C₄₇	—	2	16	no	—
162	C₂²⋊C₄×C₄₇	—	2	16	no	—
163	C₂²⋊C₄×C₄₇	—	2	16	no	—
164	C₂²⋊C₄×C₄₇	—	2	16	no	—
165	C₂²⋊C₄×C₄₇	—	4	4	no	—
166	C₄²×C₄₇	—	2	16	no	—
167	C₂³×C₄₇	—	2	16	no	—
168	C₂³×C₄₇	—	2	16	no	—
169	C₂³×C₄₇	—	2	8	no	—
170	C₂³×C₄₇	—	2	16	no	—
171	C₂³×C₄₇	—	2	16	no	—
172	C₂³×C₄₇	—	2	4	no	—
173	C₂³×C₄₇	—	2	4	no	—
174	C₂³×C₄₇	—	2	4	no	—
175	C₂³×C₄₇	—	2	4	no	—
176	C₂³×C₄₇	—	2	4	no	—
177	C₂³×C₄₇	—	2	4	no	—
178	C₂³×C₄₇	—	2	2	no	—
179	C₂³×C₄₇	—	2	4	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	2	4	no	—
182	C₂³×C₄₇	—	4	8	no	—
183	C₂³×C₄₇	—	4	8	no	—
184	C₂³×C₄₇	—	4	8	no	—
185	C₂³×C₄₇	—	4	4	no	—
186	C₂³×C₄₇	—	4	8	no	—
187	C₂³×C₄₇	—	4	8	no	—
188	C₂³×C₄₇	—	4	4	no	—
189	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
190	C₂³×C₄₇	C₂×#41	1	4	yes	—
191	C₂³×C₄₇	C₂×#41	1	8	yes	—
192	C₂³×C₄₇	C₂×#41	1	2	yes	—
193	C₂³×C₄₇	C₂×#41	1	4	yes	—
194	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
195	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
196	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
197	Q₈×C₄₇	—	4	16	no	—
198	D₄×C₄₇	—	2	64	no	—
199	D₄×C₄₇	—	4	16	no	—
200	C₂×C₄×C₄₇	—	2	16	no	—
201	C₂×C₄×C₄₇	—	2	16	no	—
202	C₂×C₄×C₄₇	—	2	16	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	4	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	2	4	no	—
211	C₂×C₄×C₄₇	—	2	4	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	4	no	—
215	C₂×C₄×C₄₇	—	2	4	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	4	no	—
219	C₂×C₄×C₄₇	—	4	16	no	—
220	C₂×C₄×C₄₇	—	4	32	no	—
221	C₂×C₄×C₄₇	—	4	8	no	—
222	C₂×C₄×C₄₇	—	4	4	no	—
223	C₂×C₄×C₄₇	—	4	8	no	—
224	C₂×C₄×C₄₇	—	4	4	no	—
225	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
226	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
227	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
228	C₂×#2463	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂²×C₄₇	—	2	8	no	—
230	C₂²×C₄₇	—	2	8	no	—
231	C₂²×C₄₇	—	2	4	no	—
232	C₂²×C₄₇	—	2	8	no	—
233	C₂²×C₄₇	—	2	8	no	—
234	C₂²×C₄₇	—	4	4	no	—
235	C₂²×C₄₇	—	4	4	no	—
236	C₂²×C₄₇	—	4	4	no	—
237	C₂²×C₄₇	—	4	2	no	—
238	C₂²×C₄₇	—	4	4	no	—
239	C₂²×C₄₇	—	4	4	no	—
240	C₂²×C₄₇	—	4	2	no	—
241	C₂²×C₄₇	—	4	16	no	—
242	C₂²×C₄₇	—	4	32	no	—
243	C₂²×C₄₇	#525	1	8	yes	—
244	C₂²×C₄₇	#539	1	4	yes	—
245	C₂²×C₄₇	D₄²	1	4	yes	—
246	C₂²×C₄₇	#548	1	8	yes	—
247	C₂²×C₄₇	#551	1	4	yes	—
248	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
249	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
250	C₂²×C₄₇	C₂²×#41	1	2	yes	—
251	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
252	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
253	C₄×C₄₇	—	2	8	no	—
254	C₄×C₄₇	—	2	8	no	—
255	C₄×C₄₇	—	2	8	no	—
256	C₄×C₄₇	—	4	4	no	—
257	C₄×C₄₇	—	4	2	no	—
258	C₄×C₄₇	—	4	4	no	—
259	C₄×C₄₇	—	4	2	no	—
260	C₂²×C₂²⋊Q₈	C₂×C₄₇	1	2	yes	complemented
261	C₂²×C₄×D₄	C₂×C₄₇	1	2	yes	complemented
262	#2463	C₂×C₄₇	1	16	yes	direct product factor
263	C₂×#394	C₂×C₄₇	1	2	yes	complemented
264	C₂×#393	C₂×C₄₇	1	1	yes	characteristic, complemented
265	C₂×#392	C₂×C₄₇	1	1	yes	characteristic
266	C₂×#388	C₂×C₄₇	1	2	yes	complemented
267	C₂×#387	C₂×C₄₇	1	2	yes	complemented
268	C₂×#386	C₂×C₄₇	1	2	yes	complemented
269	C₂×#385	C₂×C₄₇	1	1	yes	characteristic, complemented
270	C₂×C₄₇	—	4	4	no	—
271	C₂×C₄₇	—	4	8	no	—
272	C₂×C₄₇	#2463	1	8	yes	direct product factor
273	C₂×C₄₇	C₂×#525	1	2	yes	—
274	C₂×C₄₇	C₂×#539	1	1	yes	characteristic
275	C₂×C₄₇	C₂×D₄²	1	1	yes	characteristic
276	C₂×C₄₇	C₂×#548	1	2	yes	—
277	C₂×C₄₇	C₂×#551	1	1	yes	characteristic
278	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
279	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
280	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
281	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
282	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
283	C₂×C₂²⋊Q₈	—	2	16	no	—
284	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	16	yes	complemented
285	C₂×C₄×D₄	—	2	16	no	—
286	C₂×C₄×D₄	C₂²×C₄₇	1	16	yes	complemented
287	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
288	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
289	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
290	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
291	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
292	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
293	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
294	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
295	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
296	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
297	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
298	#394	C₂²×C₄₇	1	16	yes	complemented
299	#393	C₂²×C₄₇	1	8	yes	complemented
300	#392	C₂²×C₄₇	1	8	yes	—
301	#388	C₂²×C₄₇	1	16	yes	complemented
302	#387	C₂²×C₄₇	1	16	yes	complemented
303	#386	C₂²×C₄₇	1	16	yes	complemented
304	#385	C₂²×C₄₇	1	8	yes	complemented
305	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
306	C₂×#95	C₂²×C₄₇	1	2	yes	—
307	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
308	C₂×#95	C₂²×C₄₇	1	2	yes	—
309	C₂×#95	C₂²×C₄₇	1	2	yes	—
310	C₄₇	C₂×#2463	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁵	C₂³×C₄₇	1	2	yes	—
312	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
313	C₂²×Q₈	—	2	8	no	—
314	C₂²×Q₈	—	4	2	no	—
315	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
316	C₂²×D₄	—	2	8	no	—
317	C₂²×D₄	—	2	8	no	—
318	C₂²×D₄	—	2	8	no	—
319	C₂²×D₄	—	2	8	no	—
320	C₂²×D₄	—	4	2	no	—
321	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
322	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
323	C₂³×C₄	—	2	8	no	—
324	C₂³×C₄	—	2	8	no	—
325	C₂³×C₄	—	2	8	no	—
326	C₂³×C₄	—	4	2	no	—
327	C₂³×C₄	—	4	4	no	—
328	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
330	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
331	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
333	C₂³×C₄	C₂³×C₄₇	1	8	yes	—
334	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
335	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
336	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
337	C₂²⋊Q₈	—	2	64	no	—
338	C₄×D₄	—	2	64	no	—
339	C₂×C₄⋊C₄	—	2	8	no	—
340	C₂×C₄⋊C₄	—	2	8	no	—
341	C₂×C₄⋊C₄	D₄×C₄₇	1	16	yes	complemented
342	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
343	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
344	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	—	2	8	no	—
347	C₂×C₂²⋊C₄	—	2	8	no	—
348	C₂×C₂²⋊C₄	—	2	8	no	—
349	C₂×C₂²⋊C₄	—	2	8	no	—
350	C₂×C₂²⋊C₄	—	2	8	no	—
351	C₂×C₂²⋊C₄	—	4	2	no	—
352	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
359	C₂×C₄²	—	2	8	no	—
360	C₂×C₄²	C₂³×C₄₇	1	8	yes	—
361	#95	C₂³×C₄₇	1	8	yes	—
362	#95	C₂³×C₄₇	1	8	yes	—
363	#95	C₂³×C₄₇	1	4	yes	—
364	#95	C₂³×C₄₇	1	8	yes	—
365	#95	C₂³×C₄₇	1	4	yes	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	2	4	no	—
371	C₂⁴	—	2	4	no	—
372	C₂⁴	—	2	2	no	—
373	C₂⁴	—	2	4	no	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	#41×C₄₇	1	4	yes	—
377	C₂⁴	#41×C₄₇	1	8	yes	—
378	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
379	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
380	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
381	C₂×Q₈	—	2	16	no	—
382	C₂×Q₈	—	4	4	no	—
383	C₂×Q₈	—	4	16	no	—
384	C₂×D₄	—	2	64	no	—
385	C₂×D₄	—	2	16	no	—
386	C₂×D₄	—	2	16	no	—
387	C₂×D₄	—	2	16	no	—
388	C₂×D₄	—	2	16	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	16	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	16	no	—
408	C₂²×C₄	—	2	16	no	—
409	C₂²×C₄	—	2	16	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	8	no	—
412	C₂²×C₄	—	4	16	no	—
413	C₂²×C₄	—	4	32	no	—
414	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
415	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
416	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
417	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
420	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
423	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
424	C₄⋊C₄	—	2	16	no	—
425	C₄⋊C₄	—	2	16	no	—
426	C₄⋊C₄	C₂×D₄×C₄₇	1	32	yes	complemented
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	16	no	—
429	C₂²⋊C₄	—	2	16	no	—
430	C₂²⋊C₄	—	2	16	no	—
431	C₂²⋊C₄	—	2	16	no	—
432	C₂²⋊C₄	—	2	16	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₄²	—	2	16	no	—
435	C₂³	—	2	16	no	—
436	C₂³	—	2	16	no	—
437	C₂³	—	2	8	no	—
438	C₂³	—	2	16	no	—
439	C₂³	—	2	16	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	4	8	no	—
451	C₂³	—	4	8	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	4	no	—
454	C₂³	—	4	8	no	—
455	C₂³	—	4	8	no	—
456	C₂³	—	4	4	no	—
457	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
458	C₂³	C₂×#41×C₄₇	1	4	yes	—
459	C₂³	C₂×#41×C₄₇	1	8	yes	—
460	C₂³	C₂×#41×C₄₇	1	2	yes	—
461	C₂³	C₂×#41×C₄₇	1	4	yes	—
462	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
463	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
464	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
465	Q₈	—	4	16	no	—
466	D₄	—	2	64	no	—
467	D₄	—	4	16	no	—
468	C₂×C₄	—	2	16	no	—
469	C₂×C₄	—	2	16	no	—
470	C₂×C₄	—	2	16	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	4	16	no	—
488	C₂×C₄	—	4	32	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
494	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
495	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
496	C₂²	—	2	8	no	—
497	C₂²	—	2	8	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	8	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	16	no	—
509	C₂²	—	4	32	no	—
510	C₂²	C₄₇×#525	1	8	yes	—
511	C₂²	C₄₇×#539	1	4	yes	—
512	C₂²	D₄²×C₄₇	1	4	yes	—
513	C₂²	C₄₇×#548	1	8	yes	—
514	C₂²	C₄₇×#551	1	4	yes	—
515	C₂²	C₂³×D₄×C₄₇	1	2	yes	—
516	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
517	C₂²	C₂²×#41×C₄₇	1	2	yes	—
518	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
519	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
520	C₄	—	2	8	no	—
521	C₄	—	2	8	no	—
522	C₄	—	2	8	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	2	no	—
527	C₂	—	4	4	no	—
528	C₂	—	4	8	no	—
529	C₂	C₄₇×#2463	1	8	yes	direct product factor
530	C₂	C₂×C₄₇×#525	1	2	yes	—
531	C₂	C₂×C₄₇×#539	1	1	yes	characteristic
532	C₂	C₂×D₄²×C₄₇	1	1	yes	characteristic
533	C₂	C₂×C₄₇×#548	1	2	yes	—
534	C₂	C₂×C₄₇×#551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂×C₄₇×#392	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
1. C₂²×C₂²⋊Q₈×C₄₇	C₂	semidirect
2. C₂²×C₄×D₄×C₄₇	C₂	semidirect
3. C₄₇×#2463	C₂	direct (N × H)
4. C₂×C₄₇×#394	C₂	semidirect
5. C₂×C₄₇×#393	C₂	semidirect
7. C₂×C₄₇×#388	C₂	semidirect
8. C₂×C₄₇×#387	C₂	semidirect
9. C₂×C₄₇×#386	C₂	semidirect
10. C₂×C₄₇×#385	C₂	semidirect
17. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
19. C₂×C₄×D₄×C₄₇	C₂²	semidirect
31. C₄₇×#394	C₂²	semidirect
32. C₄₇×#393	C₂²	semidirect
34. C₄₇×#388	C₂²	semidirect
35. C₄₇×#387	C₂²	semidirect
36. C₄₇×#386	C₂²	semidirect
37. C₄₇×#385	C₂²	semidirect
73. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
158. C₄⋊C₄×C₄₇	C₂×D₄	semidirect
228. C₂×#2463	C₄₇	direct (N × H)
260. C₂²×C₂²⋊Q₈	C₂×C₄₇	semidirect
261. C₂²×C₄×D₄	C₂×C₄₇	semidirect
262. #2463	C₂×C₄₇	direct (N × H)
263. C₂×#394	C₂×C₄₇	semidirect
264. C₂×#393	C₂×C₄₇	semidirect
266. C₂×#388	C₂×C₄₇	semidirect
267. C₂×#387	C₂×C₄₇	semidirect
268. C₂×#386	C₂×C₄₇	semidirect
269. C₂×#385	C₂×C₄₇	semidirect
272. C₂×C₄₇	#2463	direct (N × H)
284. C₂×C₂²⋊Q₈	C₂²×C₄₇	semidirect
286. C₂×C₄×D₄	C₂²×C₄₇	semidirect
298. #394	C₂²×C₄₇	semidirect
299. #393	C₂²×C₄₇	semidirect
301. #388	C₂²×C₄₇	semidirect
302. #387	C₂²×C₄₇	semidirect
303. #386	C₂²×C₄₇	semidirect
304. #385	C₂²×C₄₇	semidirect
310. C₄₇	C₂×#2463	direct (N × H)
341. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
426. C₄⋊C₄	C₂×D₄×C₄₇	semidirect
529. C₂	C₄₇×#2463	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
C₂²×C₄×D₄×C₄₇	2
C₄₇×#2463	2
C₂×C₄₇×#394	2
C₂×C₄₇×#393	2
C₂×C₄₇×#392	2
C₂×C₄₇×#388	2
C₂×C₄₇×#387	2
C₂×C₄₇×#386	2
C₂×C₄₇×#385	2
C₂×#2463	47

Subgroups — C2×C47×#2463 #26074352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2463 #26074352