Subgroups — C₄₇×#14822 #26054520

Order 12032.

2046 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#400	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1442	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1441	C₂	1	2	yes	maximal, complemented
6	C₄₇×C₂²⋊#95	C₂	1	2	yes	maximal
7	C₄₇×C₂²⋊#95	C₂	1	2	yes	maximal
8	C₄₇×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₇	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₄₇	—	2	8	no	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#400	—	2	8	no	—
21	C₄₇×#380	—	2	4	no	—
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	4	yes	—
25	C₂×#95×C₄₇	C₂²	1	4	yes	—
26	C₂×#95×C₄₇	C₂²	1	4	yes	—
27	C₂×#95×C₄₇	C₂²	1	4	yes	—
28	C₂×#95×C₄₇	C₂²	1	2	yes	—
29	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₄₇	—	2	2	no	—
31	C₂³×C₄×C₄₇	—	2	2	no	—
32	C₂³×C₄×C₄₇	—	2	4	no	—
33	C₂³×C₄×C₄₇	—	2	4	no	—
34	C₂³×C₄×C₄₇	—	2	2	no	—
35	C₂³×C₄×C₄₇	—	2	4	no	—
36	C₂³×C₄×C₄₇	—	2	4	no	—
37	C₂³×C₄×C₄₇	—	2	4	no	—
38	C₂³×C₄×C₄₇	—	2	4	no	—
39	C₂³×C₄×C₄₇	—	4	2	no	—
40	C₂³×C₄×C₄₇	—	4	2	no	—
41	C₂³×C₄×C₄₇	D₄	1	4	yes	—
42	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
43	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₇	—	2	32	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
60	C₂×C₄⋊C₄×C₄₇	D₄	1	8	yes	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
66	#95×C₄₇	—	2	4	no	—
67	#95×C₄₇	—	2	8	no	—
68	#95×C₄₇	—	2	8	no	—
69	#95×C₄₇	—	2	4	no	—
70	#95×C₄₇	—	2	8	no	—
71	#95×C₄₇	—	4	4	no	—
72	#95×C₄₇	—	4	2	no	—
73	C₂⁴×C₄₇	—	2	2	no	—
74	C₂⁴×C₄₇	—	2	2	no	—
75	C₂⁴×C₄₇	—	2	2	no	—
76	C₂⁴×C₄₇	—	2	2	no	—
77	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
78	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
79	C₂⁴×C₄₇	#41	1	2	yes	—
80	C₂⁴×C₄₇	#41	1	4	yes	—
81	C₂⁴×C₄₇	#41	1	4	yes	—
82	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	—	2	8	no	—
84	C₂²×C₄×C₄₇	—	2	16	no	—
85	C₂²×C₄×C₄₇	—	2	8	no	—
86	C₂²×C₄×C₄₇	—	2	8	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	16	no	—
94	C₂²×C₄×C₄₇	—	2	8	no	—
95	C₂²×C₄×C₄₇	—	2	8	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	8	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	4	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	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	4	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	—	4	4	no	—
120	C₂²×C₄×C₄₇	—	4	16	no	—
121	C₂²×C₄×C₄₇	—	4	16	no	—
122	C₂²×C₄×C₄₇	—	4	4	no	—
123	C₂²×C₄×C₄₇	—	4	4	no	—
124	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
130	C₂²×C₄×C₄₇	#41	1	4	yes	—
131	C₄⋊C₄×C₄₇	—	2	16	no	—
132	C₄⋊C₄×C₄₇	—	2	16	no	—
133	C₄⋊C₄×C₄₇	—	4	4	no	—
134	C₄⋊C₄×C₄₇	—	4	4	no	—
135	C₂²⋊C₄×C₄₇	—	4	8	no	—
136	C₂²⋊C₄×C₄₇	—	4	8	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	4	no	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	2	4	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	4	no	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	—	2	8	no	—
146	C₂³×C₄₇	—	2	8	no	—
147	C₂³×C₄₇	—	2	8	no	—
148	C₂³×C₄₇	—	2	8	no	—
149	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
150	C₂³×C₄₇	#123	1	4	yes	—
151	C₂³×C₄₇	#124	1	4	yes	—
152	C₂³×C₄₇	#125	1	8	yes	—
153	C₂³×C₄₇	#126	1	8	yes	—
154	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
156	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
157	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂³×C₄₇	C₂×#41	1	2	yes	—
159	C₂³×C₄₇	C₂×#41	1	2	yes	—
160	C₂³×C₄₇	C₂×#41	1	2	yes	—
161	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
162	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
163	C₂×C₄×C₄₇	—	2	32	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	8	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	8	no	—
178	C₂×C₄×C₄₇	—	4	16	no	—
179	C₂×C₄×C₄₇	—	4	16	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	4	no	—
183	C₂×C₄×C₄₇	—	4	4	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	4	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	4	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	4	no	—
193	C₂×C₄×C₄₇	—	4	4	no	—
194	C₂×C₄×C₄₇	—	4	8	no	—
195	C₂×C₄×C₄₇	—	4	4	no	—
196	C₂×C₄×C₄₇	—	4	4	no	—
197	C₂×C₄×C₄₇	—	4	8	no	—
198	C₂×C₄×C₄₇	—	4	4	no	—
199	C₂×C₄×C₄₇	#120	1	4	yes	—
200	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
201	#14822	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	2	4	no	—
204	C₂²×C₄₇	—	2	4	no	—
205	C₂²×C₄₇	—	2	4	no	—
206	C₂²×C₄₇	—	2	4	no	—
207	C₂²×C₄₇	—	2	16	no	—
208	C₂²×C₄₇	—	2	16	no	—
209	C₂²×C₄₇	—	2	4	no	—
210	C₂²×C₄₇	#400	1	8	yes	complemented
211	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
214	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
215	C₂²×C₄₇	#525	1	1	yes	characteristic
216	C₂²×C₄₇	#525	1	2	yes	—
217	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#125	1	2	yes	—
219	C₂²×C₄₇	C₂×#126	1	2	yes	—
220	C₂²×C₄₇	#534	1	1	yes	characteristic
221	C₂²×C₄₇	#536	1	1	yes	characteristic
222	C₂²×C₄₇	#539	1	2	yes	—
223	C₂²×C₄₇	#544	1	2	yes	—
224	C₂²×C₄₇	#546	1	4	yes	—
225	C₂²×C₄₇	#548	1	4	yes	—
226	C₂²×C₄₇	#552	1	4	yes	—
227	C₂²×C₄₇	#553	1	4	yes	—
228	C₄×C₄₇	—	2	8	no	—
229	C₄×C₄₇	—	2	4	no	—
230	C₄×C₄₇	—	4	2	no	—
231	C₄×C₄₇	—	4	4	no	—
232	C₄×C₄₇	—	8	2	no	—
233	C₄×C₄₇	—	8	2	no	—
234	C₄×C₄₇	—	8	4	no	—
235	C₂³×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
236	C₂×#400	C₂×C₄₇	1	2	yes	complemented
237	C₂×#380	C₂×C₄₇	1	1	yes	characteristic
238	#1442	C₂×C₄₇	1	4	yes	complemented
239	#1441	C₂×C₄₇	1	2	yes	complemented
240	C₂²⋊#95	C₂×C₄₇	1	1	yes	characteristic
241	C₂²⋊#95	C₂×C₄₇	1	2	yes	—
242	C₂²⋊#95	C₂×C₄₇	1	2	yes	—
243	C₂×C₄₇	—	2	8	no	—
244	C₂×C₄₇	C₂×#400	1	1	yes	characteristic
245	C₂×C₄₇	#2405	1	1	yes	characteristic
246	C₂×C₄₇	#2436	1	1	yes	characteristic
247	C₂×C₄₇	#2442	1	4	yes	—
248	C₂×C₄₇	#2481	1	4	yes	—
249	C₂×C₄₇	#2484	1	1	yes	characteristic
250	C₂×C₄₇	#2591	1	1	yes	characteristic
251	C₂×C₄₇	#2627	1	1	yes	characteristic
252	C₂×C₄₇	#2848	1	1	yes	characteristic
253	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
254	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
255	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	—	2	4	no	—
257	C₂²×C₄⋊C₄	—	2	8	no	—
258	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
261	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
263	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
264	#400	—	2	8	no	—
265	#380	—	2	4	no	—
266	C₂×#95	C₂²×C₄₇	1	2	yes	—
267	C₂×#95	C₂²×C₄₇	1	4	yes	—
268	C₂×#95	C₂²×C₄₇	1	4	yes	—
269	C₂×#95	C₂²×C₄₇	1	4	yes	—
270	C₂×#95	C₂²×C₄₇	1	2	yes	—
271	C₂×#95	C₂²×C₄₇	1	4	yes	—
272	C₂×#95	C₂²×C₄₇	1	2	yes	—
273	C₄₇	#14822	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	—	2	4	no	—
278	C₂³×C₄	—	2	4	no	—
279	C₂³×C₄	—	2	2	no	—
280	C₂³×C₄	—	2	4	no	—
281	C₂³×C₄	—	2	4	no	—
282	C₂³×C₄	—	2	4	no	—
283	C₂³×C₄	—	2	4	no	—
284	C₂³×C₄	—	4	2	no	—
285	C₂³×C₄	—	4	2	no	—
286	C₂³×C₄	D₄×C₄₇	1	4	yes	—
287	C₂³×C₄	Q₈×C₄₇	1	4	yes	—
288	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
289	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
290	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
291	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
293	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
295	C₂×C₄⋊C₄	—	2	32	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	—	4	2	no	—
305	C₂×C₄⋊C₄	D₄×C₄₇	1	8	yes	—
306	C₂×C₂²⋊C₄	—	2	4	no	—
307	C₂×C₂²⋊C₄	—	2	8	no	—
308	C₂×C₂²⋊C₄	—	2	4	no	—
309	C₂×C₂²⋊C₄	—	2	4	no	—
310	C₂×C₂²⋊C₄	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	2	4	no	—
313	#95	—	2	8	no	—
314	#95	—	2	8	no	—
315	#95	—	2	8	no	—
316	#95	—	4	2	no	—
317	#95	—	4	4	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	2	2	no	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
323	C₂⁴	C₂×Q₈×C₄₇	1	2	yes	—
324	C₂⁴	#41×C₄₇	1	2	yes	—
325	C₂⁴	#41×C₄₇	1	4	yes	—
326	C₂⁴	#41×C₄₇	1	4	yes	—
327	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	16	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	—	2	8	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	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	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	16	no	—
366	C₂²×C₄	—	4	16	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
372	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
374	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
375	C₂²×C₄	#41×C₄₇	1	4	yes	—
376	C₄⋊C₄	—	2	16	no	—
377	C₄⋊C₄	—	2	16	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	8	no	—
381	C₂²⋊C₄	—	4	8	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	8	no	—
391	C₂³	—	2	8	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	2	8	no	—
394	C₂³	C₂²⋊Q₈×C₄₇	1	4	yes	—
395	C₂³	#123×C₄₇	1	4	yes	—
396	C₂³	#124×C₄₇	1	4	yes	—
397	C₂³	#125×C₄₇	1	8	yes	—
398	C₂³	#126×C₄₇	1	8	yes	—
399	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
400	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
401	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
402	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
403	C₂³	C₂×#41×C₄₇	1	2	yes	—
404	C₂³	C₂×#41×C₄₇	1	2	yes	—
405	C₂³	C₂×#41×C₄₇	1	2	yes	—
406	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
407	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
408	C₂×C₄	—	2	32	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	4	16	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	8	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	8	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	#120×C₄₇	1	4	yes	—
445	C₂×C₄	C₂²⋊Q₈×C₄₇	1	8	yes	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	16	no	—
452	C₂²	—	2	16	no	—
453	C₂²	—	2	4	no	—
454	C₂²	C₄₇×#400	1	8	yes	complemented
455	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
456	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
457	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
458	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
459	C₂²	C₄₇×#525	1	1	yes	characteristic
460	C₂²	C₄₇×#525	1	2	yes	—
461	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
462	C₂²	C₂×#125×C₄₇	1	2	yes	—
463	C₂²	C₂×#126×C₄₇	1	2	yes	—
464	C₂²	C₄₇×#534	1	1	yes	characteristic
465	C₂²	C₄₇×#536	1	1	yes	characteristic
466	C₂²	C₄₇×#539	1	2	yes	—
467	C₂²	C₄₇×#544	1	2	yes	—
468	C₂²	C₄₇×#546	1	4	yes	—
469	C₂²	C₄₇×#548	1	4	yes	—
470	C₂²	C₄₇×#552	1	4	yes	—
471	C₂²	C₄₇×#553	1	4	yes	—
472	C₄	—	2	8	no	—
473	C₄	—	2	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	4	no	—
476	C₄	—	8	2	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	4	no	—
479	C₂	—	2	8	no	—
480	C₂	C₂×C₄₇×#400	1	1	yes	characteristic
481	C₂	C₄₇×#2405	1	1	yes	characteristic
482	C₂	C₄₇×#2436	1	1	yes	characteristic
483	C₂	C₄₇×#2442	1	4	yes	—
484	C₂	C₄₇×#2481	1	4	yes	—
485	C₂	C₄₇×#2484	1	1	yes	characteristic
486	C₂	C₄₇×#2591	1	1	yes	characteristic
487	C₂	C₄₇×#2627	1	1	yes	characteristic
488	C₂	C₄₇×#2848	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂⁵×C₄₇	C₂³
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₄₇×#400	C₂	semidirect
4. C₄₇×#1442	C₂	semidirect
5. C₄₇×#1441	C₂	semidirect
201. #14822	C₄₇	direct (N × H)
210. C₂²×C₄₇	#400	semidirect
236. C₂×#400	C₂×C₄₇	semidirect
238. #1442	C₂×C₄₇	semidirect
239. #1441	C₂×C₄₇	semidirect
273. C₄₇	#14822	direct (N × H)
454. C₂²	C₄₇×#400	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₄₇	2
C₂×C₄₇×#400	2
C₂×C₄₇×#380	2
C₄₇×#1442	2
C₄₇×#1441	2
C₄₇×C₂²⋊#95	2
#14822	47

Subgroups — C47×#14822 #26054520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#14822 #26054520