Subgroups — C₄₇×#25340 #26065038

Order 12032.

874 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2563	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2538	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2076	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2036	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1892	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1808	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#477	—	2	4	no	—
18	C₈×D₄×C₄₇	—	2	4	no	—
19	C₂×#107×C₄₇	C₂²	1	2	yes	—
20	C₂×#107×C₄₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#396	—	2	2	no	—
28	C₄₇×#393	—	2	2	no	—
29	C₄₇×#390	—	2	1	no	—
30	C₄₇×#390	—	2	1	no	—
31	C₄₇×#389	—	2	1	no	—
32	C₄₇×#384	C₂²	1	1	yes	characteristic
33	C₄₇×#382	—	2	1	no	—
34	C₄₇×#380	C₂²	1	2	yes	—
35	C₄₇×#380	C₂²	1	2	yes	—
36	C₄₇×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#340	C₂²	1	1	yes	characteristic
39	C₄₇×#340	C₂²	1	1	yes	characteristic
40	C₄₇×#340	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₇	—	2	1	no	—
44	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₇	—	2	4	no	—
48	C₂²×C₈×C₄₇	—	2	4	no	—
49	C₂²×C₈×C₄₇	—	4	2	no	—
50	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₇	—	2	2	no	—
54	C₄⋊Q₈×C₄₇	—	2	2	no	—
55	C₂²⋊Q₈×C₄₇	—	2	4	no	—
56	C₂²⋊Q₈×C₄₇	—	4	2	no	—
57	C₄×Q₈×C₄₇	—	2	2	no	—
58	C₄×Q₈×C₄₇	—	2	2	no	—
59	C₄×D₄×C₄₇	—	2	2	no	—
60	C₄×D₄×C₄₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
77	C₂×C₄²×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	#107×C₄₇	—	2	4	no	—
81	#107×C₄₇	—	4	2	no	—
82	C₄⋊C₈×C₄₇	D₄	1	4	yes	—
83	#103×C₄₇	—	2	2	no	—
84	#103×C₄₇	—	2	4	no	—
85	#103×C₄₇	—	2	2	no	—
86	C₂²⋊C₈×C₄₇	—	2	4	no	—
87	C₄×C₈×C₄₇	—	2	2	no	—
88	#95×C₄₇	—	2	1	no	—
89	#95×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	—	4	2	no	—
99	C₂×Q₈×C₄₇	—	8	1	no	—
100	C₂×Q₈×C₄₇	—	8	1	no	—
101	C₂×Q₈×C₄₇	#41	1	2	yes	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	Q₁₆	1	4	yes	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	4	8	no	—
129	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
130	C₂×C₈×C₄₇	#41	1	2	yes	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	2	1	no	—
142	C₄⋊C₄×C₄₇	—	4	4	no	—
143	C₄⋊C₄×C₄₇	—	4	2	no	—
144	C₄⋊C₄×C₄₇	—	4	2	no	—
145	C₄⋊C₄×C₄₇	—	4	2	no	—
146	C₄⋊C₄×C₄₇	—	8	1	no	—
147	C₂²⋊C₄×C₄₇	—	2	4	no	—
148	C₂²⋊C₄×C₄₇	—	4	4	no	—
149	C₂²⋊C₄×C₄₇	—	8	2	no	—
150	C₂²⋊C₄×C₄₇	—	8	2	no	—
151	C₂²⋊C₄×C₄₇	—	8	2	no	—
152	C₄²×C₄₇	—	4	2	no	—
153	C₄²×C₄₇	—	4	2	no	—
154	C₄²×C₄₇	C₂×D₄	1	2	yes	—
155	C₄²×C₄₇	#41	1	2	yes	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	2	no	—
162	C₂³×C₄₇	C₂×Q₁₆	1	4	yes	—
163	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	—	2	2	no	—
166	Q₈×C₄₇	—	4	1	no	—
167	Q₈×C₄₇	—	4	1	no	—
168	Q₈×C₄₇	—	8	4	no	—
169	D₄×C₄₇	—	2	8	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	—	4	1	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	1	no	—
191	C₂×C₄×C₄₇	—	4	1	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	1	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	1	no	—
197	C₂×C₄×C₄₇	#121	1	2	yes	—
198	C₂×C₄×C₄₇	#121	1	2	yes	—
199	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
200	C₂×C₄×C₄₇	#135	1	2	yes	—
201	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
207	C₈×C₄₇	—	2	2	no	—
208	C₈×C₄₇	—	2	4	no	—
209	C₈×C₄₇	—	4	1	no	—
210	#25340	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₄₇	—	2	4	no	—
212	C₂²×C₄₇	—	2	4	no	—
213	C₂²×C₄₇	—	2	4	no	—
214	C₂²×C₄₇	—	4	2	no	—
215	C₂²×C₄₇	—	4	2	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	4	2	no	—
218	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
219	C₂²×C₄₇	#546	1	1	yes	characteristic
220	C₂²×C₄₇	#547	1	1	yes	characteristic
221	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
222	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
223	C₂²×C₄₇	#576	1	1	yes	characteristic
224	C₂²×C₄₇	#577	1	1	yes	characteristic
225	C₄×C₄₇	—	2	2	no	—
226	C₄×C₄₇	—	4	2	no	—
227	C₄×C₄₇	—	4	2	no	—
228	C₄×C₄₇	—	8	1	no	—
229	C₄×C₄₇	—	8	2	no	—
230	C₄×C₄₇	—	8	1	no	—
231	C₄×C₄₇	—	8	1	no	—
232	C₄×C₄₇	—	8	2	no	—
233	C₄×C₄₇	#467	1	4	yes	—
234	C₄×C₄₇	#529	1	1	yes	characteristic
235	C₄×C₄₇	#542	1	1	yes	characteristic
236	C₄×C₄₇	#546	1	1	yes	characteristic
237	C₄×C₄₇	#548	1	1	yes	characteristic
238	C₂×#477	C₂×C₄₇	1	1	yes	characteristic, complemented
239	C₂×C₈×D₄	C₂×C₄₇	1	1	yes	characteristic
240	#2563	C₂×C₄₇	1	1	yes	characteristic
241	#2538	C₂×C₄₇	1	1	yes	characteristic
242	#2076	C₂×C₄₇	1	2	yes	complemented
243	#2036	C₂×C₄₇	1	2	yes	complemented
244	#1990	C₂×C₄₇	1	1	yes	characteristic, complemented
245	#1947	C₂×C₄₇	1	1	yes	characteristic, complemented
246	#1892	C₂×C₄₇	1	2	yes	complemented
247	#1808	C₂×C₄₇	1	2	yes	complemented
248	C₄×#103	C₂×C₄₇	1	1	yes	characteristic, complemented
249	C₂×C₄₇	—	4	4	no	—
250	C₂×C₄₇	#2427	1	1	yes	characteristic
251	C₂×C₄₇	C₂×#467	1	1	yes	characteristic
252	C₂×C₄₇	#3062	1	1	yes	characteristic
253	C₂×C₄₇	#3299	1	1	yes	characteristic
254	C₂×C₄₇	#3305	1	1	yes	characteristic
255	C₂×C₄₇	#3338	1	1	yes	characteristic
256	C₂×C₄₇	#3340	1	1	yes	characteristic
257	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
258	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
259	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
260	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
262	#477	—	2	4	no	—
263	C₈×D₄	—	2	4	no	—
264	C₂×#107	C₂²×C₄₇	1	2	yes	—
265	C₂×#107	C₂²×C₄₇	1	2	yes	—
266	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
267	C₂×#103	C₂²×C₄₇	1	2	yes	—
268	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic
269	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
271	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
272	#396	—	2	2	no	—
273	#393	—	2	2	no	—
274	#390	—	2	1	no	—
275	#390	—	2	1	no	—
276	#389	—	2	1	no	—
277	#384	C₂²×C₄₇	1	1	yes	characteristic
278	#382	—	2	1	no	—
279	#380	C₂²×C₄₇	1	2	yes	—
280	#380	C₂²×C₄₇	1	2	yes	—
281	#380	C₂²×C₄₇	1	2	yes	—
282	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
283	#340	C₂²×C₄₇	1	1	yes	characteristic
284	#340	C₂²×C₄₇	1	2	yes	—
285	#340	C₂²×C₄₇	1	1	yes	characteristic
286	#340	C₂²×C₄₇	1	2	yes	—
287	#340	C₂²×C₄₇	1	2	yes	—
288	C₄₇	#25340	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
291	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
293	C₂²×C₈	—	2	4	no	—
294	C₂²×C₈	—	2	4	no	—
295	C₂²×C₈	—	4	2	no	—
296	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
298	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	C₂²⋊Q₈	—	4	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
326	#107	—	2	4	no	—
327	#107	—	4	2	no	—
328	C₄⋊C₈	D₄×C₄₇	1	4	yes	—
329	#103	—	2	2	no	—
330	#103	—	2	4	no	—
331	#103	—	2	2	no	—
332	C₂²⋊C₈	—	2	4	no	—
333	C₄×C₈	—	2	2	no	—
334	#95	—	2	1	no	—
335	#95	—	2	2	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	—	8	1	no	—
346	C₂×Q₈	—	8	1	no	—
347	C₂×Q₈	#41×C₄₇	1	2	yes	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	Q₁₆×C₄₇	1	4	yes	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	4	8	no	—
375	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
376	C₂×C₈	#41×C₄₇	1	2	yes	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	8	1	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	8	2	no	—
396	C₂²⋊C₄	—	8	2	no	—
397	C₂²⋊C₄	—	8	2	no	—
398	C₄²	—	4	2	no	—
399	C₄²	—	4	2	no	—
400	C₄²	C₂×D₄×C₄₇	1	2	yes	—
401	C₄²	#41×C₄₇	1	2	yes	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	C₂×Q₁₆×C₄₇	1	4	yes	—
409	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
410	Q₈	—	2	2	no	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	8	4	no	—
415	D₄	—	2	8	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	#121×C₄₇	1	2	yes	—
444	C₂×C₄	#121×C₄₇	1	2	yes	—
445	C₂×C₄	C₂×Q₁₆×C₄₇	1	2	yes	—
446	C₂×C₄	#135×C₄₇	1	2	yes	—
447	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
448	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
451	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
452	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	4	no	—
455	C₈	—	4	1	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
464	C₂²	C₄₇×#546	1	1	yes	characteristic
465	C₂²	C₄₇×#547	1	1	yes	characteristic
466	C₂²	C₂²×Q₁₆×C₄₇	1	1	yes	characteristic
467	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
468	C₂²	C₄₇×#576	1	1	yes	characteristic
469	C₂²	C₄₇×#577	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	8	2	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	2	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	C₄₇×#467	1	4	yes	—
479	C₄	C₄₇×#529	1	1	yes	characteristic
480	C₄	C₄₇×#542	1	1	yes	characteristic
481	C₄	C₄₇×#546	1	1	yes	characteristic
482	C₄	C₄₇×#548	1	1	yes	characteristic
483	C₂	—	4	4	no	—
484	C₂	C₄₇×#2427	1	1	yes	characteristic
485	C₂	C₂×C₄₇×#467	1	1	yes	characteristic
486	C₂	C₄₇×#3062	1	1	yes	characteristic
487	C₂	C₄₇×#3299	1	1	yes	characteristic
488	C₂	C₄₇×#3305	1	1	yes	characteristic
489	C₂	C₄₇×#3338	1	1	yes	characteristic
490	C₂	C₄₇×#3340	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×D₄×C₄₇	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#477	C₂	semidirect
5. C₄₇×#2076	C₂	semidirect
6. C₄₇×#2036	C₂	semidirect
7. C₄₇×#1990	C₂	semidirect
8. C₄₇×#1947	C₂	semidirect
9. C₄₇×#1892	C₂	semidirect
10. C₄₇×#1808	C₂	semidirect
11. C₄×#103×C₄₇	C₂	semidirect
210. #25340	C₄₇	direct (N × H)
238. C₂×#477	C₂×C₄₇	semidirect
242. #2076	C₂×C₄₇	semidirect
243. #2036	C₂×C₄₇	semidirect
244. #1990	C₂×C₄₇	semidirect
245. #1947	C₂×C₄₇	semidirect
246. #1892	C₂×C₄₇	semidirect
247. #1808	C₂×C₄₇	semidirect
248. C₄×#103	C₂×C₄₇	semidirect
288. C₄₇	#25340	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#477	2
C₂×C₈×D₄×C₄₇	2
C₄₇×#2563	2
C₄₇×#2538	2
C₄₇×#2076	2
C₄₇×#2036	2
C₄₇×#1990	2
C₄₇×#1947	2
C₄₇×#1892	2
C₄₇×#1808	2
C₄×#103×C₄₇	2
#25340	47

Subgroups — C47×#25340 #26065038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25340 #26065038