Subgroups — C₄₇×#24303 #26064001

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2059	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2026	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1873	C₂	1	2	yes	maximal
10	C₄₇×#1854	C₂	1	2	yes	maximal
11	C₄₇×#1797	C₂	1	1	yes	maximal, characteristic
12	C₄₇×#533	—	2	4	no	—
13	C₄₇×#533	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#125×C₄₇	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
21	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
22	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₇	C₂²	1	2	yes	—
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#477	—	2	4	no	—
26	C₄₇×#475	—	2	4	no	—
27	C₂×#107×C₄₇	C₂²	1	2	yes	—
28	C₂×#106×C₄₇	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₇	C₂²	1	2	yes	—
32	C₂×#103×C₄₇	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
34	C₄₇×#391	C₂²	1	1	yes	characteristic
35	C₄₇×#389	C₂²	1	1	yes	characteristic
36	C₄₇×#387	—	2	1	no	—
37	C₄₇×#385	—	2	1	no	—
38	C₄₇×#380	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₄₇×#340	C₂²	1	2	yes	—
44	C₄₇×#340	C₂²	1	2	yes	—
45	C₄₇×#340	C₂²	1	2	yes	—
46	C₄₇×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₇	—	2	1	no	—
48	C₂²×Q₈×C₄₇	—	2	1	no	—
49	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₄₇	—	2	2	no	—
56	C₄⋊Q₈×C₄₇	—	2	2	no	—
57	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
58	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
59	#125×C₄₇	—	2	4	no	—
60	#125×C₄₇	—	2	4	no	—
61	C₂²⋊Q₈×C₄₇	—	2	8	no	—
62	C₂²⋊Q₈×C₄₇	—	2	8	no	—
63	C₂²⋊Q₈×C₄₇	—	2	2	no	—
64	C₂²⋊Q₈×C₄₇	Q₈	1	4	yes	complemented
65	C₄×Q₈×C₄₇	—	2	8	no	—
66	C₄×Q₈×C₄₇	—	2	8	no	—
67	C₄×Q₈×C₄₇	—	2	2	no	—
68	C₄×Q₈×C₄₇	—	2	2	no	—
69	#117×C₄₇	—	2	4	no	—
70	#117×C₄₇	—	2	4	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₄²×C₄₇	—	2	2	no	—
87	C₂×C₄²×C₄₇	—	2	2	no	—
88	C₂×C₄²×C₄₇	—	2	2	no	—
89	C₂×C₄²×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	#107×C₄₇	—	2	4	no	—
96	#106×C₄₇	—	2	4	no	—
97	C₄⋊C₈×C₄₇	—	2	2	no	—
98	C₄⋊C₈×C₄₇	—	2	2	no	—
99	#103×C₄₇	—	2	4	no	—
100	#103×C₄₇	—	2	4	no	—
101	C₂²⋊C₈×C₄₇	—	2	4	no	—
102	#95×C₄₇	—	2	1	no	—
103	#95×C₄₇	—	2	1	no	—
104	#95×C₄₇	—	2	1	no	—
105	#95×C₄₇	—	2	1	no	—
106	#95×C₄₇	—	2	1	no	—
107	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂×Q₈×C₄₇	—	2	4	no	—
109	C₂×Q₈×C₄₇	—	2	4	no	—
110	C₂×Q₈×C₄₇	—	2	1	no	—
111	C₂×Q₈×C₄₇	—	2	1	no	—
112	C₂×Q₈×C₄₇	—	2	1	no	—
113	C₂×Q₈×C₄₇	—	2	1	no	—
114	C₂×Q₈×C₄₇	—	2	1	no	—
115	C₂×Q₈×C₄₇	—	4	2	no	—
116	C₂×Q₈×C₄₇	—	4	2	no	—
117	C₂×Q₈×C₄₇	—	4	2	no	—
118	C₂×Q₈×C₄₇	—	4	2	no	—
119	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	1	no	—
127	C₂²×C₄×C₄₇	—	2	1	no	—
128	C₂²×C₄×C₄₇	—	2	2	no	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
132	C₂²×C₄×C₄₇	—	2	1	no	—
133	C₂²×C₄×C₄₇	—	2	1	no	—
134	C₂²×C₄×C₄₇	—	4	1	no	—
135	C₂²×C₄×C₄₇	—	4	1	no	—
136	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
142	C₂²×C₄×C₄₇	#41	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₄₇	—	2	2	no	—
145	C₂×C₈×C₄₇	—	2	2	no	—
146	C₂×C₈×C₄₇	—	2	2	no	—
147	C₂×C₈×C₄₇	—	2	2	no	—
148	C₂×C₈×C₄₇	—	2	2	no	—
149	C₂×C₈×C₄₇	—	2	2	no	—
150	C₄⋊C₄×C₄₇	—	2	8	no	—
151	C₄⋊C₄×C₄₇	—	2	8	no	—
152	C₄⋊C₄×C₄₇	—	2	4	no	—
153	C₄⋊C₄×C₄₇	—	2	4	no	—
154	C₄⋊C₄×C₄₇	—	2	4	no	—
155	C₄⋊C₄×C₄₇	—	2	2	no	—
156	C₄⋊C₄×C₄₇	—	2	2	no	—
157	C₄⋊C₄×C₄₇	—	2	1	no	—
158	C₄⋊C₄×C₄₇	—	2	1	no	—
159	C₄⋊C₄×C₄₇	—	2	1	no	—
160	C₄⋊C₄×C₄₇	—	2	1	no	—
161	C₄⋊C₄×C₄₇	—	2	1	no	—
162	C₄⋊C₄×C₄₇	—	4	2	no	—
163	C₄⋊C₄×C₄₇	—	4	2	no	—
164	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
165	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
166	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
167	C₂²⋊C₄×C₄₇	—	2	8	no	—
168	C₂²⋊C₄×C₄₇	—	2	4	no	—
169	C₂²⋊C₄×C₄₇	—	4	2	no	—
170	C₄²×C₄₇	—	2	8	no	—
171	C₄²×C₄₇	—	2	2	no	—
172	C₄²×C₄₇	—	2	2	no	—
173	C₄²×C₄₇	—	2	1	no	—
174	C₄²×C₄₇	—	2	1	no	—
175	C₄²×C₄₇	—	4	2	no	—
176	C₄²×C₄₇	—	4	2	no	—
177	C₄²×C₄₇	C₂×D₄	1	2	yes	—
178	C₄²×C₄₇	C₂×D₄	1	2	yes	—
179	C₂³×C₄₇	—	2	1	no	—
180	C₂³×C₄₇	—	2	1	no	—
181	C₂³×C₄₇	—	2	1	no	—
182	C₂³×C₄₇	—	2	1	no	—
183	C₂³×C₄₇	—	2	1	no	—
184	C₂³×C₄₇	—	2	1	no	—
185	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
186	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₄₇	—	2	2	no	—
188	Q₈×C₄₇	—	2	2	no	—
189	Q₈×C₄₇	—	4	8	no	—
190	Q₈×C₄₇	—	4	1	no	—
191	Q₈×C₄₇	—	4	1	no	—
192	Q₈×C₄₇	—	4	8	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	1	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	1	no	—
208	C₂×C₄×C₄₇	—	2	1	no	—
209	C₂×C₄×C₄₇	—	2	1	no	—
210	C₂×C₄×C₄₇	—	2	1	no	—
211	C₂×C₄×C₄₇	—	4	4	no	—
212	C₂×C₄×C₄₇	—	4	1	no	—
213	C₂×C₄×C₄₇	—	4	1	no	—
214	C₂×C₄×C₄₇	—	4	1	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	—	4	1	no	—
218	C₂×C₄×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	4	2	no	—
220	C₂×C₄×C₄₇	—	4	4	no	—
221	C₂×C₄×C₄₇	—	4	1	no	—
222	C₂×C₄×C₄₇	—	4	1	no	—
223	C₂×C₄×C₄₇	—	4	1	no	—
224	C₂×C₄×C₄₇	—	4	1	no	—
225	C₂×C₄×C₄₇	—	4	1	no	—
226	C₂×C₄×C₄₇	—	4	1	no	—
227	C₂×C₄×C₄₇	#120	1	2	yes	—
228	C₂×C₄×C₄₇	#120	1	2	yes	—
229	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
230	C₂×C₄×C₄₇	#135	1	2	yes	—
231	C₂×C₄×C₄₇	#137	1	2	yes	—
232	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
237	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
238	C₈×C₄₇	—	4	2	no	—
239	C₈×C₄₇	—	4	2	no	—
240	#24303	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂²×C₄₇	—	2	2	no	—
242	C₂²×C₄₇	—	2	2	no	—
243	C₂²×C₄₇	—	2	2	no	—
244	C₂²×C₄₇	—	4	1	no	—
245	C₂²×C₄₇	—	4	1	no	—
246	C₂²×C₄₇	—	4	1	no	—
247	C₂²×C₄₇	—	4	1	no	—
248	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
249	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
250	C₂²×C₄₇	#536	1	1	yes	characteristic
251	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
252	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
253	C₂²×C₄₇	#575	1	1	yes	characteristic
254	C₂²×C₄₇	#575	1	1	yes	characteristic
255	C₄×C₄₇	—	2	2	no	—
256	C₄×C₄₇	—	2	2	no	—
257	C₄×C₄₇	—	4	2	no	—
258	C₄×C₄₇	—	4	2	no	—
259	C₄×C₄₇	—	4	1	no	—
260	C₄×C₄₇	—	4	4	no	—
261	C₄×C₄₇	—	4	1	no	—
262	C₄×C₄₇	—	4	4	no	—
263	C₄×C₄₇	—	8	1	no	—
264	C₄×C₄₇	—	8	1	no	—
265	C₄×C₄₇	#452	1	4	yes	—
266	C₄×C₄₇	#548	1	1	yes	characteristic
267	C₄×C₄₇	#548	1	1	yes	characteristic
268	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
269	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
270	C₂×#533	C₂×C₄₇	1	1	yes	characteristic
271	C₂×#477	C₂×C₄₇	1	1	yes	characteristic, complemented
272	C₂×#475	C₂×C₄₇	1	1	yes	characteristic, complemented
273	C₄×C₂²⋊Q₈	C₂×C₄₇	1	1	yes	characteristic
274	#2059	C₂×C₄₇	1	2	yes	complemented
275	#2026	C₂×C₄₇	1	2	yes	complemented
276	#1988	C₂×C₄₇	1	1	yes	characteristic, complemented
277	#1987	C₂×C₄₇	1	1	yes	characteristic, complemented
278	#1873	C₂×C₄₇	1	2	yes	—
279	#1854	C₂×C₄₇	1	2	yes	—
280	#1797	C₂×C₄₇	1	1	yes	characteristic
281	C₂×C₄₇	—	4	2	no	—
282	C₂×C₄₇	#2409	1	1	yes	characteristic
283	C₂×C₄₇	C₂×#452	1	1	yes	characteristic
284	C₂×C₄₇	#3005	1	1	yes	characteristic
285	C₂×C₄₇	#3076	1	1	yes	characteristic
286	C₂×C₄₇	#3078	1	1	yes	characteristic
287	C₂×C₄₇	#3233	1	1	yes	characteristic
288	C₂×C₄₇	#3237	1	1	yes	characteristic
289	#533	—	2	4	no	—
290	#533	—	2	4	no	—
291	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
292	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
293	C₂×#125	C₂²×C₄₇	1	2	yes	—
294	C₂×C₂²⋊Q₈	—	2	1	no	—
295	C₂×C₂²⋊Q₈	—	2	1	no	—
296	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
297	C₂×C₄×Q₈	—	2	1	no	—
298	C₂×C₄×Q₈	—	2	1	no	—
299	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
300	C₂×#117	C₂²×C₄₇	1	2	yes	—
301	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
302	#477	—	2	4	no	—
303	#475	—	2	4	no	—
304	C₂×#107	C₂²×C₄₇	1	2	yes	—
305	C₂×#106	C₂²×C₄₇	1	2	yes	—
306	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
307	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
308	C₂×#103	C₂²×C₄₇	1	2	yes	—
309	C₂×#103	C₂²×C₄₇	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
311	#391	C₂²×C₄₇	1	1	yes	characteristic
312	#389	C₂²×C₄₇	1	1	yes	characteristic
313	#387	—	2	1	no	—
314	#385	—	2	1	no	—
315	#380	C₂²×C₄₇	1	1	yes	characteristic
316	C₄×C₄⋊C₄	—	2	1	no	—
317	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
318	C₄×C₂²⋊C₄	—	2	1	no	—
319	#340	C₂²×C₄₇	1	2	yes	—
320	#340	C₂²×C₄₇	1	2	yes	—
321	#340	C₂²×C₄₇	1	2	yes	—
322	#340	C₂²×C₄₇	1	2	yes	—
323	#336	C₂²×C₄₇	1	2	yes	—
324	C₄₇	#24303	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
328	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
329	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
331	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
332	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
336	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
337	#125	—	2	4	no	—
338	#125	—	2	4	no	—
339	C₂²⋊Q₈	—	2	8	no	—
340	C₂²⋊Q₈	—	2	8	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	Q₈×C₄₇	1	4	yes	complemented
343	C₄×Q₈	—	2	8	no	—
344	C₄×Q₈	—	2	8	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	#117	—	2	4	no	—
348	#117	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
370	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
373	#107	—	2	4	no	—
374	#106	—	2	4	no	—
375	C₄⋊C₈	—	2	2	no	—
376	C₄⋊C₈	—	2	2	no	—
377	#103	—	2	4	no	—
378	#103	—	2	4	no	—
379	C₂²⋊C₈	—	2	4	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	4	2	no	—
394	C₂×Q₈	—	4	2	no	—
395	C₂×Q₈	—	4	2	no	—
396	C₂×Q₈	—	4	2	no	—
397	C₂×Q₈	C₂×Q₈×C₄₇	1	2	yes	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	4	1	no	—
413	C₂²×C₄	—	4	1	no	—
414	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
419	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
420	C₂²×C₄	#41×C₄₇	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₄⋊C₄	—	4	2	no	—
442	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
443	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
444	C₄⋊C₄	C₂×Q₈×C₄₇	1	2	yes	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₄²	—	2	8	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	4	2	no	—
454	C₄²	—	4	2	no	—
455	C₄²	C₂×D₄×C₄₇	1	2	yes	—
456	C₄²	C₂×D₄×C₄₇	1	2	yes	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	C₂²⋊Q₈×C₄₇	1	2	yes	—
464	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
465	Q₈	—	2	2	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	4	8	no	—
468	Q₈	—	4	8	no	—
469	Q₈	—	4	1	no	—
470	Q₈	—	4	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	#120×C₄₇	1	2	yes	—
506	C₂×C₄	#120×C₄₇	1	2	yes	—
507	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
508	C₂×C₄	#135×C₄₇	1	2	yes	—
509	C₂×C₄	#137×C₄₇	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
512	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
513	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
514	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
515	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
516	C₈	—	4	2	no	—
517	C₈	—	4	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
526	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
527	C₂²	C₄₇×#536	1	1	yes	characteristic
528	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
529	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
530	C₂²	C₄₇×#575	1	1	yes	characteristic
531	C₂²	C₄₇×#575	1	1	yes	characteristic
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	4	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	4	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	1	no	—
542	C₄	C₄₇×#452	1	4	yes	—
543	C₄	C₄₇×#548	1	1	yes	characteristic
544	C₄	C₄₇×#548	1	1	yes	characteristic
545	C₄	D₄×Q₈×C₄₇	1	1	yes	characteristic
546	C₄	D₄×Q₈×C₄₇	1	1	yes	characteristic
547	C₂	—	4	2	no	—
548	C₂	C₄₇×#2409	1	1	yes	characteristic
549	C₂	C₂×C₄₇×#452	1	1	yes	characteristic
550	C₂	C₄₇×#3005	1	1	yes	characteristic
551	C₂	C₄₇×#3076	1	1	yes	characteristic
552	C₂	C₄₇×#3078	1	1	yes	characteristic
553	C₂	C₄₇×#3233	1	1	yes	characteristic
554	C₂	C₄₇×#3237	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂⁴×C₄₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#477	C₂	semidirect
3. C₂×C₄₇×#475	C₂	semidirect
5. C₄₇×#2059	C₂	semidirect
6. C₄₇×#2026	C₂	semidirect
7. C₄₇×#1988	C₂	semidirect
8. C₄₇×#1987	C₂	semidirect
64. C₂²⋊Q₈×C₄₇	Q₈	semidirect
240. #24303	C₄₇	direct (N × H)
271. C₂×#477	C₂×C₄₇	semidirect
272. C₂×#475	C₂×C₄₇	semidirect
274. #2059	C₂×C₄₇	semidirect
275. #2026	C₂×C₄₇	semidirect
276. #1988	C₂×C₄₇	semidirect
277. #1987	C₂×C₄₇	semidirect
324. C₄₇	#24303	direct (N × H)
342. C₂²⋊Q₈	Q₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#533	2
C₂×C₄₇×#477	2
C₂×C₄₇×#475	2
C₄×C₂²⋊Q₈×C₄₇	2
C₄₇×#2059	2
C₄₇×#2026	2
C₄₇×#1988	2
C₄₇×#1987	2
C₄₇×#1873	2
C₄₇×#1854	2
C₄₇×#1797	2
#24303	47

Subgroups — C47×#24303 #26064001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24303 #26064001