Subgroups — C₂×C₄₇×#2611 #26074570

Order 12032.

2638 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2611	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₇×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#399	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₇×#398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#397	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#389	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#388	C₂	1	2	yes	maximal
10	C₂×C₄₇×#387	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#385	C₂	1	2	yes	maximal
12	C₂×C₄₇×#376	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#125×C₄₇	—	2	8	no	—
15	C₂×#125×C₄₇	C₂²	1	8	yes	complemented
16	C₂×#117×C₄₇	—	2	8	no	—
17	C₂×#117×C₄₇	C₂²	1	8	yes	—
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
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	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#400	C₂²	1	8	yes	complemented
34	C₄₇×#399	C₂²	1	8	yes	—
35	C₄₇×#398	C₂²	1	8	yes	complemented
36	C₄₇×#397	C₂²	1	8	yes	—
37	C₄₇×#389	C₂²	1	16	yes	complemented
38	C₄₇×#388	C₂²	1	16	yes	—
39	C₄₇×#387	C₂²	1	16	yes	complemented
40	C₄₇×#385	C₂²	1	16	yes	—
41	C₄₇×#376	C₂²	1	8	yes	complemented
42	C₂×#95×C₄₇	C₂²	1	2	yes	—
43	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#95×C₄₇	C₂²	1	2	yes	—
46	C₂×#95×C₄₇	C₂²	1	2	yes	—
47	C₂×#95×C₄₇	C₂²	1	2	yes	—
48	C₂×#95×C₄₇	C₂²	1	2	yes	—
49	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	—	2	4	no	—
51	C₂³×C₄×C₄₇	—	2	4	no	—
52	C₂³×C₄×C₄₇	—	2	4	no	—
53	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
58	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	#125×C₄₇	—	2	32	no	—
65	#117×C₄₇	—	2	32	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
90	C₂×C₄²×C₄₇	—	2	4	no	—
91	C₂×C₄²×C₄₇	—	2	8	no	—
92	C₂×C₄²×C₄₇	D₄	1	8	yes	—
93	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
94	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
95	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
96	#95×C₄₇	C₂³	1	8	yes	—
97	#95×C₄₇	C₂³	1	4	yes	—
98	#95×C₄₇	C₂³	1	4	yes	—
99	#95×C₄₇	C₂³	1	8	yes	—
100	#95×C₄₇	C₂³	1	8	yes	—
101	#95×C₄₇	C₂³	1	8	yes	—
102	#95×C₄₇	C₂³	1	8	yes	—
103	C₂⁴×C₄₇	—	2	2	no	—
104	C₂⁴×C₄₇	—	2	4	no	—
105	C₂⁴×C₄₇	—	2	2	no	—
106	C₂⁴×C₄₇	—	2	4	no	—
107	C₂⁴×C₄₇	#41	1	4	yes	—
108	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
109	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	—	2	32	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	4	no	—
114	C₂²×C₄×C₄₇	—	2	8	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	4	no	—
119	C₂²×C₄×C₄₇	—	2	4	no	—
120	C₂²×C₄×C₄₇	—	2	8	no	—
121	C₂²×C₄×C₄₇	—	2	8	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	2	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	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₄₇	#41	1	8	yes	—
139	C₂²×C₄×C₄₇	#41	1	4	yes	—
140	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
150	C₄⋊C₄×C₄₇	—	2	8	no	—
151	C₄⋊C₄×C₄₇	—	2	8	no	—
152	C₄⋊C₄×C₄₇	—	2	16	no	—
153	C₄⋊C₄×C₄₇	—	2	16	no	—
154	C₄⋊C₄×C₄₇	—	2	8	no	—
155	C₄⋊C₄×C₄₇	—	2	8	no	—
156	C₄⋊C₄×C₄₇	—	2	16	no	—
157	C₄⋊C₄×C₄₇	—	2	16	no	—
158	C₂²⋊C₄×C₄₇	—	2	16	no	—
159	C₂²⋊C₄×C₄₇	—	2	8	no	—
160	C₂²⋊C₄×C₄₇	—	2	8	no	—
161	C₂²⋊C₄×C₄₇	—	2	16	no	—
162	C₄²×C₄₇	—	2	8	no	—
163	C₄²×C₄₇	—	2	16	no	—
164	C₄²×C₄₇	C₂×D₄	1	16	yes	—
165	C₂³×C₄₇	—	2	8	no	—
166	C₂³×C₄₇	—	2	16	no	—
167	C₂³×C₄₇	—	2	2	no	—
168	C₂³×C₄₇	—	2	4	no	—
169	C₂³×C₄₇	—	2	2	no	—
170	C₂³×C₄₇	—	2	4	no	—
171	C₂³×C₄₇	—	4	4	no	—
172	C₂³×C₄₇	—	4	4	no	—
173	C₂³×C₄₇	—	4	8	no	—
174	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
175	C₂³×C₄₇	C₂×#41	1	4	yes	—
176	C₂³×C₄₇	C₂×#41	1	2	yes	—
177	C₂³×C₄₇	C₂×#41	1	2	yes	—
178	C₂³×C₄₇	C₂×#41	1	4	yes	—
179	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
180	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
181	C₂×C₄×C₄₇	—	2	32	no	—
182	C₂×C₄×C₄₇	—	2	8	no	—
183	C₂×C₄×C₄₇	—	2	8	no	—
184	C₂×C₄×C₄₇	—	2	8	no	—
185	C₂×C₄×C₄₇	—	2	8	no	—
186	C₂×C₄×C₄₇	—	2	16	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	2	4	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	4	no	—
194	C₂×C₄×C₄₇	—	2	4	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	4	no	—
198	C₂×C₄×C₄₇	—	2	4	no	—
199	C₂×C₄×C₄₇	—	2	4	no	—
200	C₂×C₄×C₄₇	—	2	4	no	—
201	C₂×C₄×C₄₇	—	2	4	no	—
202	C₂×C₄×C₄₇	—	2	4	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	—	4	8	no	—
209	C₂×C₄×C₄₇	—	4	4	no	—
210	C₂×C₄×C₄₇	—	4	8	no	—
211	C₂×C₄×C₄₇	—	4	4	no	—
212	C₂×C₄×C₄₇	—	4	8	no	—
213	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
214	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
215	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
217	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
218	C₂×#2611	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₄₇	—	2	4	no	—
220	C₂²×C₄₇	—	2	8	no	—
221	C₂²×C₄₇	—	4	16	no	—
222	C₂²×C₄₇	—	4	2	no	—
223	C₂²×C₄₇	—	4	2	no	—
224	C₂²×C₄₇	—	4	4	no	—
225	C₂²×C₄₇	#525	1	4	yes	—
226	C₂²×C₄₇	#532	1	4	yes	—
227	C₂²×C₄₇	#536	1	4	yes	—
228	C₂²×C₄₇	#552	1	8	yes	—
229	C₂²×C₄₇	#552	1	8	yes	—
230	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
231	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
232	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
233	C₂²×C₄₇	C₂²×#41	1	2	yes	—
234	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
235	C₄×C₄₇	—	2	4	no	—
236	C₄×C₄₇	—	2	4	no	—
237	C₄×C₄₇	—	2	4	no	—
238	C₄×C₄₇	—	2	4	no	—
239	C₄×C₄₇	—	2	8	no	—
240	C₄×C₄₇	—	4	4	no	—
241	C₄×C₄₇	—	4	2	no	—
242	C₄×C₄₇	—	4	4	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	—	4	4	no	—
245	C₂²×#125	C₂×C₄₇	1	1	yes	characteristic, complemented
246	C₂²×#117	C₂×C₄₇	1	1	yes	characteristic
247	#2611	C₂×C₄₇	1	16	yes	direct product factor
248	C₂×#400	C₂×C₄₇	1	1	yes	characteristic, complemented
249	C₂×#399	C₂×C₄₇	1	1	yes	characteristic
250	C₂×#398	C₂×C₄₇	1	1	yes	characteristic, complemented
251	C₂×#397	C₂×C₄₇	1	1	yes	characteristic
252	C₂×#389	C₂×C₄₇	1	2	yes	complemented
253	C₂×#388	C₂×C₄₇	1	2	yes	—
254	C₂×#387	C₂×C₄₇	1	2	yes	complemented
255	C₂×#385	C₂×C₄₇	1	2	yes	—
256	C₂×#376	C₂×C₄₇	1	1	yes	characteristic, complemented
257	C₂×C₄₇	—	4	4	no	—
258	C₂×C₄₇	#2611	1	8	yes	direct product factor
259	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
260	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
261	C₂×C₄₇	C₂×#536	1	1	yes	characteristic
262	C₂×C₄₇	C₂×#552	1	2	yes	—
263	C₂×C₄₇	C₂×#552	1	2	yes	—
264	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
265	C₂×#125	—	2	8	no	—
266	C₂×#125	C₂²×C₄₇	1	8	yes	complemented
267	C₂×#117	—	2	8	no	—
268	C₂×#117	C₂²×C₄₇	1	8	yes	—
269	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
272	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
274	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
276	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
277	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
278	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
279	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
280	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
281	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
282	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
283	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
284	#400	C₂²×C₄₇	1	8	yes	complemented
285	#399	C₂²×C₄₇	1	8	yes	—
286	#398	C₂²×C₄₇	1	8	yes	complemented
287	#397	C₂²×C₄₇	1	8	yes	—
288	#389	C₂²×C₄₇	1	16	yes	complemented
289	#388	C₂²×C₄₇	1	16	yes	—
290	#387	C₂²×C₄₇	1	16	yes	complemented
291	#385	C₂²×C₄₇	1	16	yes	—
292	#376	C₂²×C₄₇	1	8	yes	complemented
293	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
294	C₂×#95	C₂²×C₄₇	1	2	yes	—
295	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
296	C₂×#95	C₂²×C₄₇	1	2	yes	—
297	C₂×#95	C₂²×C₄₇	1	2	yes	—
298	C₂×#95	C₂²×C₄₇	1	2	yes	—
299	C₂×#95	C₂²×C₄₇	1	2	yes	—
300	C₄₇	C₂×#2611	1	1	yes	characteristic, direct product factor, Sylow
301	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
302	C₂³×C₄	—	2	4	no	—
303	C₂³×C₄	—	2	4	no	—
304	C₂³×C₄	—	2	4	no	—
305	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
306	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
307	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
310	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
311	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
315	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
316	#125	—	2	32	no	—
317	#117	—	2	32	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	8	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	8	no	—
324	C₂×C₄⋊C₄	—	2	8	no	—
325	C₂×C₄⋊C₄	—	2	8	no	—
326	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
329	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
330	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
333	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
334	C₂×C₂²⋊C₄	—	2	8	no	—
335	C₂×C₂²⋊C₄	—	2	4	no	—
336	C₂×C₂²⋊C₄	—	2	4	no	—
337	C₂×C₂²⋊C₄	—	2	8	no	—
338	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
342	C₂×C₄²	—	2	4	no	—
343	C₂×C₄²	—	2	8	no	—
344	C₂×C₄²	D₄×C₄₇	1	8	yes	—
345	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
346	C₂×C₄²	C₂³×C₄₇	1	8	yes	—
347	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
348	#95	C₂³×C₄₇	1	8	yes	—
349	#95	C₂³×C₄₇	1	4	yes	—
350	#95	C₂³×C₄₇	1	4	yes	—
351	#95	C₂³×C₄₇	1	8	yes	—
352	#95	C₂³×C₄₇	1	8	yes	—
353	#95	C₂³×C₄₇	1	8	yes	—
354	#95	C₂³×C₄₇	1	8	yes	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	—	2	4	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	4	no	—
359	C₂⁴	#41×C₄₇	1	4	yes	—
360	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
361	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
362	C₂²×C₄	—	2	32	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	8	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
388	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
389	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
390	C₂²×C₄	#41×C₄₇	1	8	yes	—
391	C₂²×C₄	#41×C₄₇	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
393	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
394	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	16	no	—
405	C₄⋊C₄	—	2	16	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	16	no	—
409	C₄⋊C₄	—	2	16	no	—
410	C₂²⋊C₄	—	2	16	no	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	16	no	—
414	C₄²	—	2	8	no	—
415	C₄²	—	2	16	no	—
416	C₄²	C₂×D₄×C₄₇	1	16	yes	—
417	C₂³	—	2	8	no	—
418	C₂³	—	2	16	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	4	4	no	—
424	C₂³	—	4	4	no	—
425	C₂³	—	4	8	no	—
426	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
427	C₂³	C₂×#41×C₄₇	1	4	yes	—
428	C₂³	C₂×#41×C₄₇	1	2	yes	—
429	C₂³	C₂×#41×C₄₇	1	2	yes	—
430	C₂³	C₂×#41×C₄₇	1	4	yes	—
431	C₂³	2₋¹⁺⁴×C₄₇	1	4	yes	—
432	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
433	C₂×C₄	—	2	32	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	16	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
466	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
467	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
468	C₂×C₄	C₂×#41×C₄₇	1	8	yes	—
469	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	4	16	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	C₄₇×#525	1	4	yes	—
477	C₂²	C₄₇×#532	1	4	yes	—
478	C₂²	C₄₇×#536	1	4	yes	—
479	C₂²	C₄₇×#552	1	8	yes	—
480	C₂²	C₄₇×#552	1	8	yes	—
481	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
482	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
483	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
484	C₂²	C₂²×#41×C₄₇	1	2	yes	—
485	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	2	yes	—
486	C₄	—	2	4	no	—
487	C₄	—	2	4	no	—
488	C₄	—	2	4	no	—
489	C₄	—	2	4	no	—
490	C₄	—	2	8	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₂	—	4	4	no	—
497	C₂	C₄₇×#2611	1	8	yes	direct product factor
498	C₂	C₂×C₄₇×#525	1	1	yes	characteristic
499	C₂	C₂×C₄₇×#532	1	1	yes	characteristic
500	C₂	C₂×C₄₇×#536	1	1	yes	characteristic
501	C₂	C₂×C₄₇×#552	1	2	yes	—
502	C₂	C₂×C₄₇×#552	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂⁵×C₄₇	C₂³
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×#125×C₄₇	C₂	semidirect
3. C₄₇×#2611	C₂	direct (N × H)
4. C₂×C₄₇×#400	C₂	semidirect
6. C₂×C₄₇×#398	C₂	semidirect
8. C₂×C₄₇×#389	C₂	semidirect
10. C₂×C₄₇×#387	C₂	semidirect
12. C₂×C₄₇×#376	C₂	semidirect
15. C₂×#125×C₄₇	C₂²	semidirect
33. C₄₇×#400	C₂²	semidirect
35. C₄₇×#398	C₂²	semidirect
37. C₄₇×#389	C₂²	semidirect
39. C₄₇×#387	C₂²	semidirect
41. C₄₇×#376	C₂²	semidirect
218. C₂×#2611	C₄₇	direct (N × H)
245. C₂²×#125	C₂×C₄₇	semidirect
247. #2611	C₂×C₄₇	direct (N × H)
248. C₂×#400	C₂×C₄₇	semidirect
250. C₂×#398	C₂×C₄₇	semidirect
252. C₂×#389	C₂×C₄₇	semidirect
254. C₂×#387	C₂×C₄₇	semidirect
256. C₂×#376	C₂×C₄₇	semidirect
258. C₂×C₄₇	#2611	direct (N × H)
266. C₂×#125	C₂²×C₄₇	semidirect
284. #400	C₂²×C₄₇	semidirect
286. #398	C₂²×C₄₇	semidirect
288. #389	C₂²×C₄₇	semidirect
290. #387	C₂²×C₄₇	semidirect
292. #376	C₂²×C₄₇	semidirect
300. C₄₇	C₂×#2611	direct (N × H)
497. C₂	C₄₇×#2611	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×#125×C₄₇	2
C₂²×#117×C₄₇	2
C₄₇×#2611	2
C₂×C₄₇×#400	2
C₂×C₄₇×#399	2
C₂×C₄₇×#398	2
C₂×C₄₇×#397	2
C₂×C₄₇×#389	2
C₂×C₄₇×#388	2
C₂×C₄₇×#387	2
C₂×C₄₇×#385	2
C₂×C₄₇×#376	2
C₂×#2611	47

Subgroups — C2×C47×#2611 #26074570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2611 #26074570