Subgroups — #20241647

Order 6016.

520 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊#95	C₂	1	2	yes	maximal
2	C₂×C₄₇⋊#95	C₂	1	2	yes	maximal
3	C₂×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₄₇	C₂²	1	2	yes	—
7	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₄₇⋊#95	—	2	4	no	—
10	C₄₇⋊#95	—	2	2	no	—
11	C₄₇⋊#95	—	2	4	no	—
12	C₄₇⋊#95	C₄	1	4	yes	complemented
13	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
14	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
16	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
17	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	—	2	2	no	—
19	C₂²×C₄×C₄₇	—	2	2	no	—
20	C₂²×C₄×C₄₇	—	2	2	no	—
21	C₂²×C₄×C₄₇	—	2	2	no	—
22	C₂²×C₄×C₄₇	—	2	2	no	—
23	C₂²×C₄×C₄₇	—	2	2	no	—
24	C₂²×C₄×C₄₇	—	2	2	no	—
25	C₂²×C₄×C₄₇	—	2	2	no	—
26	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₄₇	D₄	1	4	yes	—
28	C₂²×C₄×C₄₇	D₄	1	2	yes	—
29	C₂²×C₄×C₄₇	Q₈	1	2	yes	—
30	C₂²×Dic₄₇	—	2	2	no	—
31	C₂²×Dic₄₇	—	2	2	no	—
32	C₂²×Dic₄₇	—	2	1	no	—
33	C₂²×Dic₄₇	—	2	1	no	—
34	C₂²×Dic₄₇	—	2	2	no	—
35	C₂²×Dic₄₇	—	2	2	no	—
36	C₂²×Dic₄₇	—	2	2	no	—
37	C₂²×Dic₄₇	—	2	2	no	—
38	C₂²×Dic₄₇	—	2	2	no	—
39	C₂²×Dic₄₇	—	2	1	no	—
40	C₂²×Dic₄₇	—	2	2	no	—
41	C₂²×Dic₄₇	—	2	1	no	—
42	C₂²×Dic₄₇	—	2	2	no	—
43	C₂²×Dic₄₇	—	2	2	no	—
44	C₂²×Dic₄₇	C₂×C₄	1	4	yes	—
45	C₂²×Dic₄₇	D₄	1	2	yes	—
46	C₂²×Dic₄₇	Q₈	1	2	yes	—
47	C₄⋊C₄×C₄₇	—	2	8	no	—
48	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
49	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂³×C₄₇	C₂×D₄	1	2	yes	—
52	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
53	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
54	C₂³×C₄₇	#41	1	2	yes	—
55	C₂³×C₄₇	#41	1	2	yes	—
56	C₂³×C₄₇	#41	1	1	yes	characteristic
57	C₂³×C₄₇	#41	1	2	yes	—
58	C₂³×C₄₇	#41	1	1	yes	characteristic
59	C₂×C₄×C₄₇	—	2	4	no	—
60	C₂×C₄×C₄₇	—	2	2	no	—
61	C₂×C₄×C₄₇	—	2	4	no	—
62	C₂×C₄×C₄₇	—	2	2	no	—
63	C₂×C₄×C₄₇	—	2	4	no	—
64	C₂×C₄×C₄₇	—	2	4	no	—
65	C₂×C₄×C₄₇	—	2	4	no	—
66	C₂×C₄×C₄₇	—	4	2	no	—
67	C₂×C₄×C₄₇	—	4	2	no	—
68	C₂×C₄×C₄₇	—	4	2	no	—
69	C₂×C₄×C₄₇	—	4	2	no	—
70	C₂×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
71	C₂×Dic₄₇	—	2	4	no	—
72	C₂×Dic₄₇	—	2	4	no	—
73	C₂×Dic₄₇	—	2	4	no	—
74	C₂×Dic₄₇	—	2	2	no	—
75	C₂×Dic₄₇	—	2	4	no	—
76	C₂×Dic₄₇	—	2	2	no	—
77	C₂×Dic₄₇	—	2	4	no	—
78	C₂×Dic₄₇	—	4	1	no	—
79	C₂×Dic₄₇	—	4	2	no	—
80	C₂×Dic₄₇	—	4	1	no	—
81	C₂×Dic₄₇	—	4	2	no	—
82	C₂×Dic₄₇	—	4	2	no	—
83	C₂×Dic₄₇	—	4	1	no	—
84	C₂×Dic₄₇	—	4	2	no	—
85	C₂×Dic₄₇	—	4	1	no	—
86	C₂×Dic₄₇	—	4	2	no	—
87	C₂×Dic₄₇	—	4	2	no	—
88	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄₇	#117	1	2	yes	—
90	C₂²×C₄₇	C₄×D₄	1	2	yes	—
91	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
92	C₂²×C₄₇	C₄×Q₈	1	1	yes	characteristic
93	C₂²×C₄₇	#120	1	1	yes	characteristic
94	C₂²×C₄₇	#121	1	1	yes	characteristic
95	C₂²×C₄₇	#121	1	2	yes	—
96	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
97	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
98	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
99	C₂²×C₄₇	#123	1	2	yes	—
100	C₂²×C₄₇	#123	1	1	yes	characteristic
101	C₂²×C₄₇	#123	1	2	yes	—
102	C₂²×C₄₇	#124	1	1	yes	characteristic
103	C₂²×C₄₇	#124	1	1	yes	characteristic
104	C₂²×C₄₇	#124	1	2	yes	—
105	C₂²×C₄₇	#125	1	2	yes	—
106	C₂²×C₄₇	#125	1	2	yes	—
107	C₂²×C₄₇	#125	1	1	yes	characteristic
108	C₂²×C₄₇	#126	1	2	yes	—
109	C₂²×C₄₇	#126	1	2	yes	—
110	C₂²×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
111	C₄×C₄₇	—	2	4	no	—
112	C₄×C₄₇	—	4	4	no	—
113	Dic₄₇	—	4	4	no	—
114	Dic₄₇	—	4	2	no	—
115	Dic₄₇	—	4	2	no	—
116	#1442	—	47	1	no	maximal, Sylow
117	C₂×C₄₇	#382	1	1	yes	characteristic
118	C₂×C₄₇	#385	1	1	yes	characteristic
119	C₂×C₄₇	#387	1	2	yes	—
120	C₂×C₄₇	#388	1	2	yes	—
121	C₂×C₄₇	#389	1	1	yes	characteristic
122	C₂×C₄₇	#393	1	1	yes	characteristic
123	C₂×C₄₇	#394	1	1	yes	characteristic
124	C₂×C₄₇	#397	1	1	yes	characteristic
125	C₂×C₄₇	#398	1	2	yes	—
126	C₂×C₄₇	#400	1	1	yes	characteristic
127	C₂×C₄₇	#400	1	2	yes	—
128	C₂²×C₄⋊C₄	D₄₇	1	1	yes	characteristic
129	C₂×#95	—	47	1	no	—
130	C₂×#95	—	47	2	no	—
131	C₂×#95	—	47	2	no	—
132	C₂×#95	—	47	1	no	—
133	C₄₇	#1442	1	1	yes	characteristic, complemented, Sylow
134	C₂³×C₄	—	47	2	no	—
135	C₂³×C₄	—	47	1	no	—
136	C₂³×C₄	—	47	1	no	—
137	C₂³×C₄	C₂×D₄₇	1	2	yes	—
138	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
139	C₂×C₄⋊C₄	—	2	4	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	#95	—	47	4	no	—
142	#95	—	94	4	no	—
143	#95	—	94	4	no	—
144	#95	—	94	2	no	—
145	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	2	2	no	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	47	4	no	—
155	C₂²×C₄	—	47	2	no	—
156	C₂²×C₄	—	47	2	no	—
157	C₂²×C₄	—	94	2	no	—
158	C₂²×C₄	—	94	2	no	—
159	C₂²×C₄	—	94	2	no	—
160	C₂²×C₄	—	94	2	no	—
161	C₂²×C₄	—	94	1	no	—
162	C₂²×C₄	—	94	2	no	—
163	C₂²×C₄	—	94	2	no	—
164	C₂²×C₄	—	94	2	no	—
165	C₂²×C₄	—	94	1	no	—
166	C₂²×C₄	—	94	2	no	—
167	C₂²×C₄	—	94	2	no	—
168	C₂²×C₄	—	94	1	no	—
169	C₂²×C₄	—	94	1	no	—
170	C₂²×C₄	—	94	2	no	—
171	C₂²×C₄	Dic₉₄	1	2	yes	—
172	C₂²×C₄	C₄×D₄₇	1	2	yes	—
173	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
174	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
175	C₄⋊C₄	—	2	8	no	—
176	C₂³	C₂×Dic₉₄	1	1	yes	characteristic
177	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
178	C₂³	#10625350	1	2	yes	—
179	C₂³	D₄×D₄₇	1	1	yes	characteristic
180	C₂³	#10625352	1	2	yes	—
181	C₂³	#10625352	1	1	yes	characteristic
182	C₂³	Q₈×D₄₇	1	1	yes	characteristic
183	C₂³	#10625354	1	2	yes	—
184	C₂³	#10625354	1	1	yes	characteristic
185	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
186	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	4	no	—
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	94	4	no	—
199	C₂×C₄	—	94	4	no	—
200	C₂×C₄	—	94	4	no	—
201	C₂×C₄	—	94	2	no	—
202	C₂×C₄	—	94	4	no	—
203	C₂×C₄	—	94	2	no	—
204	C₂×C₄	—	94	4	no	—
205	C₂×C₄	—	188	1	no	—
206	C₂×C₄	—	188	2	no	—
207	C₂×C₄	—	188	1	no	—
208	C₂×C₄	—	188	2	no	—
209	C₂×C₄	—	188	2	no	—
210	C₂×C₄	—	188	1	no	—
211	C₂×C₄	—	188	2	no	—
212	C₂×C₄	—	188	1	no	—
213	C₂×C₄	—	188	2	no	—
214	C₂×C₄	—	188	2	no	—
215	C₂×C₄	Dic₄₇⋊C₄	1	4	yes	—
216	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
217	C₂²	#13093982	1	2	yes	—
218	C₂²	C₄×C₂²⋊D₄₇	1	2	yes	—
219	C₂²	#13093986	1	1	yes	characteristic
220	C₂²	#13093989	1	1	yes	characteristic
221	C₂²	#13093993	1	1	yes	characteristic
222	C₂²	#13093995	1	1	yes	characteristic
223	C₂²	#13093996	1	2	yes	—
224	C₂²	#13094000	1	2	yes	—
225	C₂²	#13094000	1	1	yes	characteristic
226	C₂²	#13094003	1	2	yes	—
227	C₂²	#13094005	1	2	yes	—
228	C₂²	#13094007	1	1	yes	characteristic
229	C₂²	#13094009	1	2	yes	—
230	C₂²	#13094011	1	1	yes	characteristic
231	C₂²	#13094013	1	1	yes	characteristic
232	C₂²	#13094013	1	2	yes	—
233	C₂²	#13094014	1	2	yes	—
234	C₂²	#13094015	1	2	yes	—
235	C₂²	#13094015	1	1	yes	characteristic
236	C₂²	#13094019	1	2	yes	—
237	C₂²	#13094019	1	2	yes	—
238	C₂²	#13094023	1	1	yes	characteristic
239	C₄	—	2	4	no	—
240	C₄	—	4	4	no	—
241	C₄	—	188	4	no	—
242	C₄	—	188	2	no	—
243	C₄	—	188	2	no	—
244	C₂	#15688988	1	1	yes	characteristic
245	C₂	#15688996	1	1	yes	characteristic
246	C₂	#15689004	1	2	yes	—
247	C₂	#15689013	1	2	yes	—
248	C₂	#15689019	1	1	yes	characteristic
249	C₂	#15689034	1	1	yes	characteristic
250	C₂	#15689037	1	1	yes	characteristic
251	C₂	#15689049	1	1	yes	characteristic
252	C₂	#15689056	1	2	yes	—
253	C₂	#15689061	1	1	yes	characteristic
254	C₂	#15689062	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂²×C₄
Fitting	C₂²×C₄⋊C₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂²×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#1442
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
12. C₄₇⋊#95	C₄	semidirect
133. C₄₇	#1442	semidirect