Subgroups — #20255791

Order 6016.

366 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689819	C₂	1	2	yes	maximal, complemented
2	#15689525	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689448	C₂	1	2	yes	maximal, complemented
4	#15689442	C₂	1	2	yes	maximal, complemented
5	#15689424	C₂	1	2	yes	maximal, complemented
6	#15689359	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689359	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689161	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
13	#13094019	—	2	2	no	—
14	#13094016	C₂²	1	2	yes	—
15	#13094006	—	2	2	no	—
16	#13093998	C₂²	1	2	yes	—
17	#13093998	C₂²	1	2	yes	—
18	#13093996	—	2	2	no	—
19	C₄×D₁₈₈	C₂²	1	2	yes	—
20	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
21	#13093983	C₂²	1	2	yes	—
22	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
23	#13093958	C₂²	1	1	yes	characteristic
24	#13093958	C₂²	1	1	yes	characteristic
25	#13093958	C₂²	1	1	yes	characteristic
26	#13093958	C₂²	1	2	yes	—
27	#13093956	C₂²	1	2	yes	—
28	#13093956	C₂²	1	2	yes	—
29	#13093946	C₂²	1	2	yes	—
30	#13093946	C₂²	1	2	yes	—
31	#13093946	C₂²	1	2	yes	—
32	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×D₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×C₂²⋊D₄₇	—	2	2	no	—
43	C₂×C₂²⋊D₄₇	—	2	2	no	—
44	C₂²×Dic₄₇	—	2	2	no	—
45	C₂×D₁₈₈	C₂³	1	2	yes	—
46	C₂×C₄×D₄₇	—	2	2	no	—
47	C₂×C₈×C₄₇	—	2	2	no	—
48	C₂×C₈×C₄₇	—	2	2	no	—
49	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
51	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
53	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
55	C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
56	C₄²×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²⋊Dic₄₇	—	2	2	no	—
58	(C₂×D₄₇)⋊C₄	—	2	2	no	—
59	(C₂×D₄₇)⋊C₄	—	2	2	no	—
60	(C₂×D₄₇)⋊C₄	—	2	2	no	—
61	C₄⋊Dic₄₇	—	2	2	no	—
62	C₄⋊Dic₄₇	C₂³	1	2	yes	—
63	C₄⋊Dic₄₇	C₂³	1	2	yes	—
64	C₄⋊Dic₄₇	C₂³	1	2	yes	—
65	Dic₄₇⋊C₄	—	2	2	no	—
66	Dic₄₇⋊C₄	—	2	2	no	—
67	C₄×Dic₄₇	—	2	2	no	—
68	D₃₇₆	—	2	2	no	—
69	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×D₄₇	—	2	2	no	—
72	D₄×C₄₇	—	2	2	no	—
73	C₂×C₄×C₄₇	—	2	1	no	—
74	C₂×C₄×C₄₇	—	2	1	no	—
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	2	1	no	—
77	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
82	C₂²⋊D₄₇	—	4	4	no	—
83	C₂²⋊D₄₇	—	8	2	no	—
84	C₂×Dic₄₇	—	2	2	no	—
85	C₂×Dic₄₇	—	2	2	no	—
86	C₂×Dic₄₇	—	2	2	no	—
87	C₂×Dic₄₇	—	8	2	no	—
88	D₁₈₈	—	2	2	no	—
89	D₁₈₈	—	2	2	no	—
90	C₄×D₄₇	—	8	2	no	—
91	C₈×C₄₇	—	2	1	no	—
92	C₈×C₄₇	—	2	1	no	—
93	C₈×C₄₇	—	2	1	no	—
94	C₈×C₄₇	#41	1	2	yes	—
95	C₂²×C₄₇	—	2	1	no	—
96	C₂²×C₄₇	—	2	1	no	—
97	C₂²×C₄₇	—	2	1	no	—
98	C₂²×C₄₇	—	2	1	no	—
99	C₂²×C₄₇	—	2	1	no	—
100	C₂²×C₄₇	#135	1	2	yes	—
101	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
102	C₂×D₄₇	—	4	2	no	—
103	C₂×D₄₇	—	4	2	no	—
104	C₂×D₄₇	—	4	2	no	—
105	C₄×C₄₇	—	2	1	no	—
106	C₄×C₄₇	—	2	1	no	—
107	C₄×C₄₇	—	2	1	no	—
108	C₄×C₄₇	—	2	1	no	—
109	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
110	C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
111	Dic₄₇	—	4	2	no	—
112	Dic₄₇	—	4	2	no	—
113	Dic₄₇	—	4	2	no	—
114	#3339	—	47	1	no	maximal, Sylow
115	C₂×C₄₇	—	2	2	no	—
116	C₂×C₄₇	—	4	1	no	—
117	C₂×C₄₇	#547	1	1	yes	characteristic
118	C₂×C₄₇	C₂×#135	1	1	yes	characteristic
119	C₂×C₄₇	#576	1	1	yes	characteristic
120	D₄₇	—	8	2	no	—
121	#553	—	47	2	no	—
122	#499	—	47	1	no	—
123	#482	—	47	2	no	—
124	#481	—	47	2	no	—
125	#478	—	47	2	no	—
126	#466	—	47	1	no	—
127	#466	—	47	1	no	—
128	C₄×D₈	—	47	1	no	—
129	C₈×D₄	D₄₇	1	1	yes	characteristic, complemented
130	#427	—	47	1	no	—
131	C₂×#107	—	47	1	no	—
132	C₄₇	#3339	1	1	yes	characteristic, complemented, Sylow
133	C₂×D₈	—	47	1	no	—
134	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
135	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
136	#126	—	94	2	no	—
137	#125	—	47	2	no	—
138	#123	—	94	2	no	—
139	#121	—	47	2	no	—
140	#121	—	47	2	no	—
141	#121	—	94	2	no	—
142	C₄×D₄	—	47	2	no	—
143	C₄×D₄	—	94	2	no	—
144	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
145	#117	—	47	2	no	—
146	C₂×C₄⋊C₄	—	47	2	no	—
147	#107	—	47	1	no	—
148	#107	—	47	1	no	—
149	#107	—	47	2	no	—
150	#107	—	47	1	no	—
151	#106	—	47	2	no	—
152	#106	—	47	2	no	—
153	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
154	#102	—	47	2	no	—
155	#102	—	47	2	no	—
156	#102	—	47	2	no	—
157	C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
158	C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
159	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
160	C₂×D₄	—	47	2	no	—
161	C₂×D₄	—	94	2	no	—
162	C₂×D₄	—	94	2	no	—
163	C₂×D₄	D₁₈₈	1	1	yes	characteristic
164	C₂²×C₄	—	94	2	no	—
165	C₂²×C₄	—	94	2	no	—
166	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
167	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
168	D₈	—	94	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
172	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
173	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
174	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
175	C₄⋊C₄	—	47	2	no	—
176	C₄⋊C₄	—	47	2	no	—
177	C₄⋊C₄	—	47	2	no	—
178	C₄⋊C₄	—	94	2	no	—
179	C₄⋊C₄	—	94	2	no	—
180	C₄⋊C₄	—	94	2	no	—
181	C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
182	C₂²⋊C₄	—	94	2	no	—
183	C₂²⋊C₄	—	94	2	no	—
184	C₂²⋊C₄	—	94	2	no	—
185	C₂²⋊C₄	—	94	2	no	—
186	C₂²⋊C₄	D₁₈₈	1	1	yes	characteristic
187	C₂²⋊C₄	D₁₈₈	1	1	yes	characteristic
188	C₄²	—	94	2	no	—
189	C₄²	C₂²×D₄₇	1	1	yes	characteristic
190	C₂³	—	94	2	no	—
191	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
192	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
193	D₄	—	2	2	no	—
194	D₄	—	94	2	no	—
195	D₄	—	94	2	no	—
196	D₄	—	376	2	no	—
197	D₄	—	188	4	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	94	2	no	—
203	C₂×C₄	—	94	2	no	—
204	C₂×C₄	—	94	2	no	—
205	C₂×C₄	—	376	2	no	—
206	C₂×C₄	—	376	2	no	—
207	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
208	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
209	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
210	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
211	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
212	C₈	—	2	1	no	—
213	C₈	—	2	1	no	—
214	C₈	—	2	1	no	—
215	C₈	#10625352	1	2	yes	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	188	2	no	—
222	C₂²	—	188	2	no	—
223	C₂²	—	188	2	no	—
224	C₂²	#13094046	1	2	yes	—
225	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	1	no	—
229	C₄	—	2	1	no	—
230	C₄	—	188	2	no	—
231	C₄	—	188	2	no	—
232	C₄	—	188	2	no	—
233	C₄	C₂×#10625352	1	1	yes	characteristic
234	C₄	#13094071	1	1	yes	characteristic
235	C₂	—	2	2	no	—
236	C₂	—	4	1	no	—
237	C₂	—	376	2	no	—
238	C₂	#15689777	1	1	yes	characteristic
239	C₂	C₂×#13094046	1	1	yes	characteristic
240	C₂	#15689928	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₈×D₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	C₈×D₄	D₄₇
hypocenter	C₄₇	#3339
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. #15689819	C₂	semidirect
2. #15689525	C₂	semidirect
3. #15689448	C₂	semidirect
4. #15689442	C₂	semidirect
5. #15689424	C₂	semidirect
6. #15689359	C₂	semidirect
7. #15689359	C₂	semidirect
8. C₄×D₃₇₆	C₂	semidirect
9. #15689161	C₂	semidirect
10. C₂×#13093958	C₂	semidirect
11. C₈×D₄×C₄₇	C₂	semidirect
129. C₈×D₄	D₄₇	semidirect
132. C₄₇	#3339	semidirect