Subgroups — C₂×C₄₇×#2572 #26074541

Order 12032.

2614 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2572	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₄₇×#400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#394	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#393	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇×#388	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#386	C₂	1	2	yes	maximal
8	C₂×C₄₇×#383	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#381	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	2	yes	maximal, complemented
11	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#400	C₂²	1	8	yes	complemented
24	C₄₇×#394	C₂²	1	8	yes	—
25	C₄₇×#393	C₂²	1	16	yes	complemented
26	C₄₇×#391	C₂²	1	8	yes	complemented
27	C₄₇×#388	C₂²	1	16	yes	complemented
28	C₄₇×#386	C₂²	1	16	yes	—
29	C₄₇×#383	C₂²	1	16	yes	complemented
30	C₄₇×#381	C₂²	1	16	yes	complemented
31	C₄×C₂²⋊C₄×C₄₇	C₂²	1	16	yes	complemented
32	C₂×#95×C₄₇	C₂²	1	2	yes	—
33	C₂×#95×C₄₇	C₂²	1	2	yes	—
34	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#95×C₄₇	C₂²	1	2	yes	—
36	C₂×#95×C₄₇	C₂²	1	2	yes	—
37	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#95×C₄₇	C₂²	1	2	yes	—
39	C₂×#95×C₄₇	C₂²	1	2	yes	—
40	C₂×#95×C₄₇	C₂²	1	2	yes	—
41	C₂⁵×C₄₇	C₂³	1	2	yes	—
42	C₂²×Q₈×C₄₇	—	2	4	no	—
43	C₂²×Q₈×C₄₇	—	4	2	no	—
44	C₂²×Q₈×C₄₇	—	4	2	no	—
45	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
46	C₂²×D₄×C₄₇	—	2	8	no	—
47	C₂²×D₄×C₄₇	—	4	2	no	—
48	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
49	C₂³×C₄×C₄₇	—	2	8	no	—
50	C₂³×C₄×C₄₇	—	2	8	no	—
51	C₂³×C₄×C₄₇	—	4	4	no	—
52	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
60	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
62	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
63	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
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	—	4	4	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	4	4	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	8	yes	—
75	C₂×C₄²×C₄₇	—	2	8	no	—
76	C₂×C₄²×C₄₇	—	4	2	no	—
77	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
79	#95×C₄₇	C₂³	1	8	yes	—
80	#95×C₄₇	C₂³	1	8	yes	—
81	#95×C₄₇	C₂³	1	4	yes	—
82	#95×C₄₇	C₂³	1	8	yes	—
83	#95×C₄₇	C₂³	1	8	yes	—
84	#95×C₄₇	C₂³	1	4	yes	—
85	#95×C₄₇	C₂³	1	8	yes	—
86	#95×C₄₇	C₂³	1	8	yes	—
87	#95×C₄₇	C₂³	1	8	yes	—
88	C₂⁴×C₄₇	—	2	4	no	—
89	C₂⁴×C₄₇	—	2	4	no	—
90	C₂⁴×C₄₇	—	2	4	no	—
91	C₂⁴×C₄₇	—	2	4	no	—
92	C₂⁴×C₄₇	—	2	4	no	—
93	C₂⁴×C₄₇	—	2	4	no	—
94	C₂⁴×C₄₇	#41	1	8	yes	—
95	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
96	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂×Q₈×C₄₇	—	2	8	no	—
98	C₂×Q₈×C₄₇	—	4	4	no	—
99	C₂×Q₈×C₄₇	—	4	4	no	—
100	C₂×Q₈×C₄₇	—	4	16	no	—
101	C₂×D₄×C₄₇	—	2	16	no	—
102	C₂×D₄×C₄₇	—	4	4	no	—
103	C₂×D₄×C₄₇	—	4	16	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	4	no	—
114	C₂²×C₄×C₄₇	—	2	16	no	—
115	C₂²×C₄×C₄₇	—	2	4	no	—
116	C₂²×C₄×C₄₇	—	2	4	no	—
117	C₂²×C₄×C₄₇	—	2	4	no	—
118	C₂²×C₄×C₄₇	—	2	4	no	—
119	C₂²×C₄×C₄₇	—	2	4	no	—
120	C₂²×C₄×C₄₇	—	2	4	no	—
121	C₂²×C₄×C₄₇	—	2	4	no	—
122	C₂²×C₄×C₄₇	—	2	4	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	16	no	—
126	C₂²×C₄×C₄₇	—	4	8	no	—
127	C₂²×C₄×C₄₇	—	4	32	no	—
128	C₂²×C₄×C₄₇	#41	1	8	yes	—
129	C₂²×C₄×C₄₇	#41	1	4	yes	—
130	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
138	C₄⋊C₄×C₄₇	—	4	4	no	—
139	C₄⋊C₄×C₄₇	—	4	4	no	—
140	C₂²⋊C₄×C₄₇	—	2	16	no	—
141	C₂²⋊C₄×C₄₇	—	2	16	no	—
142	C₂²⋊C₄×C₄₇	—	2	16	no	—
143	C₂²⋊C₄×C₄₇	—	4	8	no	—
144	C₂²⋊C₄×C₄₇	—	4	8	no	—
145	C₄²×C₄₇	—	2	16	no	—
146	C₄²×C₄₇	—	4	4	no	—
147	C₂³×C₄₇	—	2	16	no	—
148	C₂³×C₄₇	—	2	16	no	—
149	C₂³×C₄₇	—	2	16	no	—
150	C₂³×C₄₇	—	2	4	no	—
151	C₂³×C₄₇	—	2	4	no	—
152	C₂³×C₄₇	—	2	4	no	—
153	C₂³×C₄₇	—	2	4	no	—
154	C₂³×C₄₇	—	2	4	no	—
155	C₂³×C₄₇	—	2	4	no	—
156	C₂³×C₄₇	—	4	8	no	—
157	C₂³×C₄₇	—	4	8	no	—
158	C₂³×C₄₇	—	4	8	no	—
159	C₂³×C₄₇	—	4	8	no	—
160	C₂³×C₄₇	C₂×#41	1	8	yes	—
161	C₂³×C₄₇	C₂×#41	1	2	yes	—
162	C₂³×C₄₇	C₂×#41	1	4	yes	—
163	C₂³×C₄₇	C₂×#41	1	4	yes	—
164	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
165	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
166	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
167	Q₈×C₄₇	—	4	16	no	—
168	D₄×C₄₇	—	4	16	no	—
169	C₂×C₄×C₄₇	—	2	8	no	—
170	C₂×C₄×C₄₇	—	2	16	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	4	no	—
183	C₂×C₄×C₄₇	—	2	4	no	—
184	C₂×C₄×C₄₇	—	2	4	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	2	4	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	4	32	no	—
192	C₂×C₄×C₄₇	—	4	8	no	—
193	C₂×C₄×C₄₇	—	4	8	no	—
194	C₂×C₄×C₄₇	—	4	4	no	—
195	C₂×C₄×C₄₇	—	4	8	no	—
196	C₂×C₄×C₄₇	—	4	4	no	—
197	C₂×C₄×C₄₇	—	4	8	no	—
198	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
199	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
200	C₂×#2572	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₄₇	—	2	8	no	—
202	C₂²×C₄₇	—	2	8	no	—
203	C₂²×C₄₇	—	2	8	no	—
204	C₂²×C₄₇	—	4	32	no	—
205	C₂²×C₄₇	—	4	4	no	—
206	C₂²×C₄₇	—	4	4	no	—
207	C₂²×C₄₇	—	4	4	no	—
208	C₂²×C₄₇	—	4	4	no	—
209	C₂²×C₄₇	#529	1	8	yes	—
210	C₂²×C₄₇	#538	1	4	yes	—
211	C₂²×C₄₇	#551	1	8	yes	—
212	C₂²×C₄₇	#551	1	4	yes	—
213	C₂²×C₄₇	#555	1	4	yes	—
214	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
215	C₂²×C₄₇	C₂²×#41	1	2	yes	—
216	C₂²×C₄₇	C₂²×#41	1	2	yes	—
217	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
219	C₄×C₄₇	—	2	4	no	—
220	C₄×C₄₇	—	2	8	no	—
221	C₄×C₄₇	—	4	4	no	—
222	C₄×C₄₇	—	4	4	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	—	4	4	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	4	4	no	—
227	#2572	C₂×C₄₇	1	16	yes	direct product factor
228	C₂×#400	C₂×C₄₇	1	1	yes	characteristic, complemented
229	C₂×#394	C₂×C₄₇	1	1	yes	characteristic
230	C₂×#393	C₂×C₄₇	1	2	yes	complemented
231	C₂×#391	C₂×C₄₇	1	1	yes	characteristic, complemented
232	C₂×#388	C₂×C₄₇	1	2	yes	complemented
233	C₂×#386	C₂×C₄₇	1	2	yes	—
234	C₂×#383	C₂×C₄₇	1	2	yes	complemented
235	C₂×#381	C₂×C₄₇	1	2	yes	complemented
236	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	2	yes	complemented
237	C₂×C₄₇	—	4	8	no	—
238	C₂×C₄₇	#2572	1	8	yes	direct product factor
239	C₂×C₄₇	C₂×#529	1	2	yes	—
240	C₂×C₄₇	C₂×#538	1	1	yes	characteristic
241	C₂×C₄₇	C₂×#551	1	2	yes	—
242	C₂×C₄₇	C₂×#551	1	1	yes	characteristic
243	C₂×C₄₇	C₂×#555	1	1	yes	characteristic
244	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
245	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
246	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
247	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
250	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
251	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
252	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
253	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
254	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
255	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
256	#400	C₂²×C₄₇	1	8	yes	complemented
257	#394	C₂²×C₄₇	1	8	yes	—
258	#393	C₂²×C₄₇	1	16	yes	complemented
259	#391	C₂²×C₄₇	1	8	yes	complemented
260	#388	C₂²×C₄₇	1	16	yes	complemented
261	#386	C₂²×C₄₇	1	16	yes	—
262	#383	C₂²×C₄₇	1	16	yes	complemented
263	#381	C₂²×C₄₇	1	16	yes	complemented
264	C₄×C₂²⋊C₄	C₂²×C₄₇	1	16	yes	complemented
265	C₂×#95	C₂²×C₄₇	1	2	yes	—
266	C₂×#95	C₂²×C₄₇	1	2	yes	—
267	C₂×#95	C₂²×C₄₇	1	2	yes	—
268	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
269	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
270	C₂×#95	C₂²×C₄₇	1	2	yes	—
271	C₂×#95	C₂²×C₄₇	1	2	yes	—
272	C₂×#95	C₂²×C₄₇	1	2	yes	—
273	C₂×#95	C₂²×C₄₇	1	2	yes	—
274	C₄₇	C₂×#2572	1	1	yes	characteristic, direct product factor, Sylow
275	C₂⁵	C₂³×C₄₇	1	2	yes	—
276	C₂²×Q₈	—	2	4	no	—
277	C₂²×Q₈	—	4	2	no	—
278	C₂²×Q₈	—	4	2	no	—
279	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
280	C₂²×D₄	—	2	8	no	—
281	C₂²×D₄	—	4	2	no	—
282	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
283	C₂³×C₄	—	2	8	no	—
284	C₂³×C₄	—	2	8	no	—
285	C₂³×C₄	—	4	4	no	—
286	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
288	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
289	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
290	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
291	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₄₇	1	8	yes	—
293	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
295	C₂×C₄⋊C₄	—	4	2	no	—
296	C₂×C₄⋊C₄	—	4	2	no	—
297	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
298	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
299	C₂×C₂²⋊C₄	—	2	8	no	—
300	C₂×C₂²⋊C₄	—	2	8	no	—
301	C₂×C₂²⋊C₄	—	2	8	no	—
302	C₂×C₂²⋊C₄	—	4	4	no	—
303	C₂×C₂²⋊C₄	—	4	4	no	—
304	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
309	C₂×C₄²	—	2	8	no	—
310	C₂×C₄²	—	4	2	no	—
311	C₂×C₄²	C₂³×C₄₇	1	8	yes	—
312	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
313	#95	C₂³×C₄₇	1	8	yes	—
314	#95	C₂³×C₄₇	1	8	yes	—
315	#95	C₂³×C₄₇	1	4	yes	—
316	#95	C₂³×C₄₇	1	8	yes	—
317	#95	C₂³×C₄₇	1	8	yes	—
318	#95	C₂³×C₄₇	1	4	yes	—
319	#95	C₂³×C₄₇	1	8	yes	—
320	#95	C₂³×C₄₇	1	8	yes	—
321	#95	C₂³×C₄₇	1	8	yes	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	2	4	no	—
328	C₂⁴	#41×C₄₇	1	8	yes	—
329	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
330	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
331	C₂×Q₈	—	2	8	no	—
332	C₂×Q₈	—	4	4	no	—
333	C₂×Q₈	—	4	4	no	—
334	C₂×Q₈	—	4	16	no	—
335	C₂×D₄	—	2	16	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	16	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	16	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	16	no	—
360	C₂²×C₄	—	4	8	no	—
361	C₂²×C₄	—	4	32	no	—
362	C₂²×C₄	#41×C₄₇	1	8	yes	—
363	C₂²×C₄	#41×C₄₇	1	4	yes	—
364	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
372	C₄⋊C₄	—	4	4	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	2	16	no	—
375	C₂²⋊C₄	—	2	16	no	—
376	C₂²⋊C₄	—	2	16	no	—
377	C₂²⋊C₄	—	4	8	no	—
378	C₂²⋊C₄	—	4	8	no	—
379	C₄²	—	2	16	no	—
380	C₄²	—	4	4	no	—
381	C₂³	—	2	16	no	—
382	C₂³	—	2	16	no	—
383	C₂³	—	2	16	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	4	8	no	—
392	C₂³	—	4	8	no	—
393	C₂³	—	4	8	no	—
394	C₂³	C₂×#41×C₄₇	1	8	yes	—
395	C₂³	C₂×#41×C₄₇	1	2	yes	—
396	C₂³	C₂×#41×C₄₇	1	4	yes	—
397	C₂³	C₂×#41×C₄₇	1	4	yes	—
398	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
399	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
400	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
401	Q₈	—	4	16	no	—
402	D₄	—	4	16	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	16	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	32	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	C₂×#41×C₄₇	1	8	yes	—
433	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
434	C₂²	—	2	8	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	4	32	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	C₄₇×#529	1	8	yes	—
443	C₂²	C₄₇×#538	1	4	yes	—
444	C₂²	C₄₇×#551	1	8	yes	—
445	C₂²	C₄₇×#551	1	4	yes	—
446	C₂²	C₄₇×#555	1	4	yes	—
447	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
448	C₂²	C₂²×#41×C₄₇	1	2	yes	—
449	C₂²	C₂²×#41×C₄₇	1	2	yes	—
450	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
451	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
452	C₄	—	2	4	no	—
453	C₄	—	2	8	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₂	—	4	8	no	—
461	C₂	C₄₇×#2572	1	8	yes	direct product factor
462	C₂	C₂×C₄₇×#529	1	2	yes	—
463	C₂	C₂×C₄₇×#538	1	1	yes	characteristic
464	C₂	C₂×C₄₇×#551	1	2	yes	—
465	C₂	C₂×C₄₇×#551	1	1	yes	characteristic
466	C₂	C₂×C₄₇×#555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×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
1. C₄₇×#2572	C₂	direct (N × H)
2. C₂×C₄₇×#400	C₂	semidirect
4. C₂×C₄₇×#393	C₂	semidirect
5. C₂×C₄₇×#391	C₂	semidirect
6. C₂×C₄₇×#388	C₂	semidirect
8. C₂×C₄₇×#383	C₂	semidirect
9. C₂×C₄₇×#381	C₂	semidirect
10. C₂×C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
23. C₄₇×#400	C₂²	semidirect
25. C₄₇×#393	C₂²	semidirect
26. C₄₇×#391	C₂²	semidirect
27. C₄₇×#388	C₂²	semidirect
29. C₄₇×#383	C₂²	semidirect
30. C₄₇×#381	C₂²	semidirect
31. C₄×C₂²⋊C₄×C₄₇	C₂²	semidirect
200. C₂×#2572	C₄₇	direct (N × H)
227. #2572	C₂×C₄₇	direct (N × H)
228. C₂×#400	C₂×C₄₇	semidirect
230. C₂×#393	C₂×C₄₇	semidirect
231. C₂×#391	C₂×C₄₇	semidirect
232. C₂×#388	C₂×C₄₇	semidirect
234. C₂×#383	C₂×C₄₇	semidirect
235. C₂×#381	C₂×C₄₇	semidirect
236. C₂×C₄×C₂²⋊C₄	C₂×C₄₇	semidirect
238. C₂×C₄₇	#2572	direct (N × H)
256. #400	C₂²×C₄₇	semidirect
258. #393	C₂²×C₄₇	semidirect
259. #391	C₂²×C₄₇	semidirect
260. #388	C₂²×C₄₇	semidirect
262. #383	C₂²×C₄₇	semidirect
263. #381	C₂²×C₄₇	semidirect
264. C₄×C₂²⋊C₄	C₂²×C₄₇	semidirect
274. C₄₇	C₂×#2572	direct (N × H)
461. C₂	C₄₇×#2572	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#2572	2
C₂×C₄₇×#400	2
C₂×C₄₇×#394	2
C₂×C₄₇×#393	2
C₂×C₄₇×#391	2
C₂×C₄₇×#388	2
C₂×C₄₇×#386	2
C₂×C₄₇×#383	2
C₂×C₄₇×#381	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₂×#2572	47

Subgroups — C2×C47×#2572 #26074541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2572 #26074541