Subgroups — C₄₇×#20959 #26060657

Order 12032.

1974 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#525	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#410	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2280	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1890	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1889	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1740	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₄₇×#525	—	2	4	no	—
11	C₄₇×#525	C₄	1	8	yes	complemented
12	C₂×#123×C₄₇	C₂²	1	2	yes	—
13	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
14	C₂×#121×C₄₇	—	2	1	no	—
15	C₂×#120×C₄₇	C₂²	1	2	yes	—
16	C₄₇×#520	—	2	4	no	—
17	C₄₇×#519	—	2	1	no	—
18	C₄₇×#518	—	2	1	no	—
19	C₄₇×#518	C₂²	1	4	yes	—
20	C₄×#41×C₄₇	—	2	4	no	—
21	C₂×C₄×D₄×C₄₇	—	2	2	no	—
22	C₂×#117×C₄₇	—	2	2	no	—
23	C₂×#117×C₄₇	C₂²	1	2	yes	—
24	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#117×C₄₇	C₂²	1	2	yes	—
26	C₄₇×#410	—	2	4	no	—
27	C₂×#99×C₄₇	C₂²	1	4	yes	—
28	C₄₇×#381	C₂²	1	4	yes	—
29	C₄₇×#380	—	2	4	no	—
30	C₄₇×#379	C₂²	1	4	yes	—
31	C₄×C₂²⋊C₄×C₄₇	—	2	4	no	—
32	C₄₇×#342	C₂²	1	8	yes	—
33	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
34	C₂×#41×C₄₇	—	2	2	no	—
35	C₂×#41×C₄₇	—	2	2	no	—
36	C₂×#41×C₄₇	—	2	4	no	—
37	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
38	C₂×#41×C₄₇	D₄	1	4	yes	—
39	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₄₇	—	2	2	no	—
41	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₇	—	2	1	no	—
44	C₂³×C₄×C₄₇	—	2	1	no	—
45	C₂³×C₄×C₄₇	—	2	2	no	—
46	C₂³×C₄×C₄₇	—	2	2	no	—
47	C₂³×C₄×C₄₇	—	2	2	no	—
48	C₂³×C₄×C₄₇	—	2	4	no	—
49	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	complemented
50	C₂³×C₄×C₄₇	D₄	1	2	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	#123×C₄₇	—	2	4	no	—
54	#123×C₄₇	C₂×C₄	1	8	yes	complemented
55	C₂²⋊Q₈×C₄₇	—	2	8	no	—
56	#121×C₄₇	—	2	8	no	—
57	#120×C₄₇	—	2	4	no	—
58	#120×C₄₇	C₂×C₄	1	8	yes	complemented
59	C₄×Q₈×C₄₇	—	2	8	no	—
60	C₄×D₄×C₄₇	—	2	8	no	—
61	C₄×D₄×C₄₇	—	2	16	no	—
62	C₄×D₄×C₄₇	—	2	16	no	—
63	#117×C₄₇	—	2	4	no	—
64	#117×C₄₇	—	2	4	no	—
65	#117×C₄₇	—	2	2	no	—
66	#117×C₄₇	—	2	4	no	—
67	#117×C₄₇	—	2	2	no	—
68	#117×C₄₇	—	2	2	no	—
69	#117×C₄₇	—	2	2	no	—
70	#117×C₄₇	—	2	2	no	—
71	#117×C₄₇	—	2	4	no	—
72	#117×C₄₇	—	2	4	no	—
73	#117×C₄₇	C₂×C₄	1	4	yes	complemented
74	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	complemented
79	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	—	2	4	no	—
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	—	2	2	no	—
89	C₂×C₄²×C₄₇	D₄	1	4	yes	complemented
90	#99×C₄₇	—	2	8	no	—
91	#95×C₄₇	—	2	8	no	—
92	C₂⁴×C₄₇	—	2	2	no	—
93	C₂⁴×C₄₇	—	2	1	no	—
94	C₂⁴×C₄₇	—	2	1	no	—
95	C₂⁴×C₄₇	—	2	2	no	—
96	C₂⁴×C₄₇	—	4	4	no	—
97	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
99	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
100	#41×C₄₇	—	2	8	no	—
101	#41×C₄₇	—	2	8	no	—
102	#41×C₄₇	—	2	8	no	—
103	#41×C₄₇	—	2	8	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	complemented
107	C₂×D₄×C₄₇	—	2	4	no	—
108	C₂×D₄×C₄₇	—	2	4	no	—
109	C₂×D₄×C₄₇	—	2	8	no	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	4	8	no	—
113	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	complemented
114	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
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	2	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	8	no	—
125	C₂²×C₄×C₄₇	—	2	4	no	—
126	C₂²×C₄×C₄₇	—	2	4	no	—
127	C₂²×C₄×C₄₇	—	2	8	no	—
128	C₂²×C₄×C₄₇	—	2	8	no	—
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	—	4	2	no	—
131	C₂²×C₄×C₄₇	—	4	1	no	—
132	C₂²×C₄×C₄₇	—	4	1	no	—
133	C₂²×C₄×C₄₇	—	4	4	no	—
134	C₂²×C₄×C₄₇	—	4	4	no	—
135	C₂²×C₄×C₄₇	—	4	2	no	—
136	C₂²×C₄×C₄₇	—	4	2	no	—
137	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	complemented
138	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₄₇	#41	1	4	yes	—
148	C₄⋊C₄×C₄₇	—	2	8	no	—
149	C₄⋊C₄×C₄₇	—	2	4	no	—
150	C₄⋊C₄×C₄₇	—	2	8	no	—
151	C₄⋊C₄×C₄₇	—	2	4	no	—
152	C₄⋊C₄×C₄₇	—	2	4	no	—
153	C₄⋊C₄×C₄₇	—	4	4	no	—
154	C₂²⋊C₄×C₄₇	—	2	8	no	—
155	C₂²⋊C₄×C₄₇	—	2	8	no	—
156	C₂²⋊C₄×C₄₇	—	2	4	no	—
157	C₂²⋊C₄×C₄₇	—	2	4	no	—
158	C₂²⋊C₄×C₄₇	—	2	2	no	—
159	C₂²⋊C₄×C₄₇	—	2	8	no	—
160	C₂²⋊C₄×C₄₇	—	2	4	no	—
161	C₂²⋊C₄×C₄₇	—	2	4	no	—
162	C₂²⋊C₄×C₄₇	—	4	16	no	—
163	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
164	C₄²×C₄₇	—	2	8	no	—
165	C₄²×C₄₇	—	2	4	no	—
166	C₄²×C₄₇	—	2	4	no	—
167	C₄²×C₄₇	—	2	4	no	—
168	C₄²×C₄₇	—	4	4	no	—
169	C₂³×C₄₇	—	2	8	no	—
170	C₂³×C₄₇	—	2	4	no	—
171	C₂³×C₄₇	—	2	2	no	—
172	C₂³×C₄₇	—	2	4	no	—
173	C₂³×C₄₇	—	2	2	no	—
174	C₂³×C₄₇	—	2	2	no	—
175	C₂³×C₄₇	—	4	4	no	—
176	C₂³×C₄₇	—	4	2	no	—
177	C₂³×C₄₇	—	4	4	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	—	4	4	no	—
180	C₂³×C₄₇	—	4	8	no	—
181	C₂³×C₄₇	—	4	4	no	—
182	C₂³×C₄₇	—	4	1	no	—
183	C₂³×C₄₇	—	4	2	no	—
184	C₂³×C₄₇	—	4	1	no	—
185	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
186	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
189	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₂³×C₄₇	C₂×#41	1	2	yes	—
191	Q₈×C₄₇	—	2	8	no	—
192	D₄×C₄₇	—	2	8	no	—
193	D₄×C₄₇	—	2	8	no	—
194	D₄×C₄₇	—	2	8	no	—
195	D₄×C₄₇	—	4	16	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	8	no	—
199	C₂×C₄×C₄₇	—	2	8	no	—
200	C₂×C₄×C₄₇	—	2	4	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	4	no	—
203	C₂×C₄×C₄₇	—	2	8	no	—
204	C₂×C₄×C₄₇	—	4	4	no	—
205	C₂×C₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	4	no	—
209	C₂×C₄×C₄₇	—	4	4	no	—
210	C₂×C₄×C₄₇	—	4	8	no	—
211	C₂×C₄×C₄₇	—	4	8	no	—
212	C₂×C₄×C₄₇	—	4	8	no	—
213	C₂×C₄×C₄₇	—	4	4	no	—
214	C₂×C₄×C₄₇	—	8	8	no	—
215	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
216	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
219	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
220	C₂×C₄×C₄₇	#120	1	2	yes	—
221	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#121	1	4	yes	—
224	C₂×C₄×C₄₇	#121	1	4	yes	—
225	C₂×C₄×C₄₇	#123	1	2	yes	—
226	C₂×C₄×C₄₇	#123	1	2	yes	—
227	#20959	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₄₇	—	2	4	no	—
229	C₂²×C₄₇	—	2	2	no	—
230	C₂²×C₄₇	—	2	4	no	—
231	C₂²×C₄₇	—	2	8	no	—
232	C₂²×C₄₇	—	2	4	no	—
233	C₂²×C₄₇	—	4	1	no	—
234	C₂²×C₄₇	—	4	1	no	—
235	C₂²×C₄₇	—	4	2	no	—
236	C₂²×C₄₇	—	4	4	no	—
237	C₂²×C₄₇	—	4	2	no	—
238	C₂²×C₄₇	—	4	8	no	—
239	C₂²×C₄₇	—	4	4	no	—
240	C₂²×C₄₇	—	4	4	no	—
241	C₂²×C₄₇	—	4	4	no	—
242	C₂²×C₄₇	—	4	4	no	—
243	C₂²×C₄₇	—	4	2	no	—
244	C₂²×C₄₇	—	8	2	no	—
245	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
247	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
248	C₂²×C₄₇	C₂×#121	1	2	yes	—
249	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
250	C₄×C₄₇	—	2	4	no	—
251	C₄×C₄₇	—	4	4	no	—
252	C₄×C₄₇	—	4	8	no	—
253	C₄×C₄₇	—	4	2	no	—
254	C₄×C₄₇	—	8	4	no	—
255	C₄×C₄₇	#386	1	2	yes	—
256	C₄×C₄₇	#386	1	2	yes	—
257	C₄×C₄₇	#386	1	4	yes	—
258	C₂×#525	C₂×C₄₇	1	1	yes	characteristic
259	#3428	C₂×C₄₇	1	1	yes	characteristic, complemented
260	C₂×#410	C₂×C₄₇	1	1	yes	characteristic, complemented
261	#2280	C₂×C₄₇	1	2	yes	complemented
262	#1890	C₂×C₄₇	1	4	yes	complemented
263	#1889	C₂×C₄₇	1	4	yes	complemented
264	#1740	C₂×C₄₇	1	2	yes	complemented
265	C₂×C₄₇	—	2	1	no	—
266	C₂×C₄₇	—	2	2	no	—
267	C₂×C₄₇	—	2	2	no	—
268	C₂×C₄₇	—	2	1	no	—
269	C₂×C₄₇	—	4	4	no	—
270	C₂×C₄₇	—	4	4	no	—
271	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
272	C₂×C₄₇	#3025	1	2	yes	—
273	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
274	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
275	#525	—	2	4	no	—
276	#525	C₄×C₄₇	1	8	yes	complemented
277	C₂×#123	C₂²×C₄₇	1	2	yes	—
278	C₂×C₂²⋊Q₈	—	2	1	no	—
279	C₂×#121	—	2	1	no	—
280	C₂×#120	C₂²×C₄₇	1	2	yes	—
281	#520	—	2	4	no	—
282	#519	—	2	1	no	—
283	#518	—	2	1	no	—
284	#518	C₂²×C₄₇	1	4	yes	—
285	C₄×#41	—	2	4	no	—
286	C₂×C₄×D₄	—	2	2	no	—
287	C₂×#117	—	2	2	no	—
288	C₂×#117	C₂²×C₄₇	1	2	yes	—
289	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
290	C₂×#117	C₂²×C₄₇	1	2	yes	—
291	#410	—	2	4	no	—
292	C₂×#99	C₂²×C₄₇	1	4	yes	—
293	#381	C₂²×C₄₇	1	4	yes	—
294	#380	—	2	4	no	—
295	#379	C₂²×C₄₇	1	4	yes	—
296	C₄×C₂²⋊C₄	—	2	4	no	—
297	#342	C₂²×C₄₇	1	8	yes	—
298	C₄₇	#20959	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	4	no	—
303	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
304	C₂×#41	D₄×C₄₇	1	4	yes	—
305	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
308	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	—	2	2	no	—
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	—	2	2	no	—
314	C₂³×C₄	—	2	4	no	—
315	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	complemented
316	C₂³×C₄	D₄×C₄₇	1	2	yes	—
317	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
319	#123	—	2	4	no	—
320	#123	C₂×C₄×C₄₇	1	8	yes	complemented
321	C₂²⋊Q₈	—	2	8	no	—
322	#121	—	2	8	no	—
323	#120	—	2	4	no	—
324	#120	C₂×C₄×C₄₇	1	8	yes	complemented
325	C₄×Q₈	—	2	8	no	—
326	C₄×D₄	—	2	8	no	—
327	C₄×D₄	—	2	16	no	—
328	C₄×D₄	—	2	16	no	—
329	#117	—	2	4	no	—
330	#117	—	2	4	no	—
331	#117	—	2	2	no	—
332	#117	—	2	4	no	—
333	#117	—	2	2	no	—
334	#117	—	2	2	no	—
335	#117	—	2	2	no	—
336	#117	—	2	2	no	—
337	#117	—	2	4	no	—
338	#117	—	2	4	no	—
339	#117	C₂×C₄×C₄₇	1	4	yes	complemented
340	C₂×C₄⋊C₄	—	2	4	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	complemented
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	8	no	—
349	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
352	C₂×C₄²	—	2	4	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	D₄×C₄₇	1	4	yes	complemented
356	#99	—	2	8	no	—
357	#95	—	2	8	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	2	1	no	—
360	C₂⁴	—	2	1	no	—
361	C₂⁴	—	2	2	no	—
362	C₂⁴	—	4	4	no	—
363	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
364	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
365	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
366	#41	—	2	8	no	—
367	#41	—	2	8	no	—
368	#41	—	2	8	no	—
369	#41	—	2	8	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	C₂²⋊C₄×C₄₇	1	4	yes	complemented
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	4	8	no	—
379	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	complemented
380	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
381	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	C₂²⋊C₄×C₄₇	1	8	yes	complemented
404	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
405	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
408	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
413	C₂²×C₄	#41×C₄₇	1	4	yes	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	4	no	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	4	16	no	—
429	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
430	C₄²	—	2	8	no	—
431	C₄²	—	2	4	no	—
432	C₄²	—	2	4	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	4	4	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	8	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	1	no	—
451	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
452	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
453	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
454	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
455	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
456	C₂³	C₂×#41×C₄₇	1	2	yes	—
457	Q₈	—	2	8	no	—
458	D₄	—	2	8	no	—
459	D₄	—	2	8	no	—
460	D₄	—	2	8	no	—
461	D₄	—	4	16	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	8	8	no	—
481	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
482	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
483	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
484	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
485	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
486	C₂×C₄	#120×C₄₇	1	2	yes	—
487	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
488	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
489	C₂×C₄	#121×C₄₇	1	4	yes	—
490	C₂×C₄	#121×C₄₇	1	4	yes	—
491	C₂×C₄	#123×C₄₇	1	2	yes	—
492	C₂×C₄	#123×C₄₇	1	2	yes	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	8	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	8	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	8	2	no	—
510	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
511	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
512	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
513	C₂²	C₂×#121×C₄₇	1	2	yes	—
514	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
515	C₄	—	2	4	no	—
516	C₄	—	4	4	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	8	no	—
519	C₄	—	8	4	no	—
520	C₄	C₄₇×#386	1	2	yes	—
521	C₄	C₄₇×#386	1	2	yes	—
522	C₄	C₄₇×#386	1	4	yes	—
523	C₂	—	2	1	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	2	no	—
526	C₂	—	2	1	no	—
527	C₂	—	4	4	no	—
528	C₂	—	4	4	no	—
529	C₂	C₂×C₄₇×#386	1	1	yes	characteristic
530	C₂	C₄₇×#3025	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₇	#120
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×#120
prime radical	C₂×C₄₇×#525	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#3428	C₂	semidirect
3. C₂×C₄₇×#410	C₂	semidirect
4. C₄₇×#2280	C₂	semidirect
5. C₄₇×#1890	C₂	semidirect
6. C₄₇×#1889	C₂	semidirect
7. C₄₇×#1740	C₂	semidirect
11. C₄₇×#525	C₄	semidirect
49. C₂³×C₄×C₄₇	C₂×C₄	semidirect
54. #123×C₄₇	C₂×C₄	semidirect
58. #120×C₄₇	C₂×C₄	semidirect
73. #117×C₄₇	C₂×C₄	semidirect
78. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
89. C₂×C₄²×C₄₇	D₄	semidirect
106. C₂×Q₈×C₄₇	C₂²⋊C₄	semidirect
113. C₂×D₄×C₄₇	C₂²⋊C₄	semidirect
137. C₂²×C₄×C₄₇	C₂²⋊C₄	semidirect
227. #20959	C₄₇	direct (N × H)
259. #3428	C₂×C₄₇	semidirect
260. C₂×#410	C₂×C₄₇	semidirect
261. #2280	C₂×C₄₇	semidirect
262. #1890	C₂×C₄₇	semidirect
263. #1889	C₂×C₄₇	semidirect
264. #1740	C₂×C₄₇	semidirect
276. #525	C₄×C₄₇	semidirect
298. C₄₇	#20959	direct (N × H)
315. C₂³×C₄	C₂×C₄×C₄₇	semidirect
320. #123	C₂×C₄×C₄₇	semidirect
324. #120	C₂×C₄×C₄₇	semidirect
339. #117	C₂×C₄×C₄₇	semidirect
344. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
355. C₂×C₄²	D₄×C₄₇	semidirect
372. C₂×Q₈	C₂²⋊C₄×C₄₇	semidirect
379. C₂×D₄	C₂²⋊C₄×C₄₇	semidirect
403. C₂²×C₄	C₂²⋊C₄×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×#525	2
C₄₇×#3428	2
C₂×C₄₇×#410	2
C₄₇×#2280	2
C₄₇×#1890	2
C₄₇×#1889	2
C₄₇×#1740	2
#20959	47

Subgroups — C47×#20959 #26060657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20959 #26060657