Group #20256790 — subgroups

Subgroups — #20256790

Order 6016.

996 conjugacy classes of subgroups; only the 509 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689752	C₂	1	12	yes	maximal, complemented
2	#15689749	C₂	1	3	yes	maximal
3	#15689675	C₂	1	12	yes	maximal, complemented
4	C₂×#13093980	C₂	1	3	yes	maximal
5	C₄₇×#543	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
7	#13094023	C₂²	1	12	yes	complemented
8	#13094022	C₂²	1	12	yes	complemented
9	#13094014	C₂²	1	24	yes	complemented
10	#13094003	C₂²	1	12	yes	—
11	#13094001	C₂²	1	24	yes	—
12	Q₈×Dic₄₇	C₂²	1	4	yes	complemented
13	#13093989	C₂²	1	12	yes	complemented
14	#13093980	C₂²	1	12	yes	—
15	#13093980	C₂²	1	12	yes	—
16	C₂×Dic₄₇⋊C₄	C₂²	1	6	yes	—
17	C₂×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
18	C₂×C₄×Dic₄₇	C₂²	1	6	yes	—
19	C₂²⋊Q₈×C₄₇	C₂²	1	12	yes	—
20	C₂×C₂²⋊C₄×C₄₇	C₂²	1	3	yes	—
21	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
22	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
23	C₂²×C₄×C₄₇	C₂³	1	6	yes	—
24	C₂²×Dic₄₇	Q₈	1	8	yes	complemented
25	C₂²×Dic₄₇	C₂³	1	6	yes	—
26	C₂²×Dic₄₇	C₂³	1	3	yes	—
27	C₂²×Dic₄₇	C₂³	1	3	yes	—
28	C₂×Dic₉₄	C₂³	1	12	yes	—
29	C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
30	C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
31	C₂²⋊Dic₄₇	C₂³	1	12	yes	—
32	C₄⋊Dic₄₇	C₂³	1	12	yes	—
33	Dic₄₇⋊C₄	C₂³	1	24	yes	—
34	Dic₄₇⋊C₄	C₂³	1	24	yes	—
35	C₄×Dic₄₇	C₂³	1	12	yes	—
36	C₄×Dic₄₇	C₂³	1	12	yes	—
37	C₂³×C₄₇	—	4	2	no	—
38	C₂³×C₄₇	C₂×Q₈	1	4	yes	—
39	C₂³×C₄₇	C₂⁴	1	3	yes	—
40	Q₈×C₄₇	—	4	4	no	—
41	C₂×C₄×C₄₇	—	4	6	no	—
42	C₂×C₄×C₄₇	C₂⁴	1	12	yes	—
43	C₂×Dic₄₇	—	4	6	no	—
44	C₂×Dic₄₇	C₂×Q₈	1	12	yes	—
45	C₂×Dic₄₇	C₂×Q₈	1	12	yes	—
46	C₂×Dic₄₇	C₂⁴	1	12	yes	—
47	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₄₇	C₂⁴	1	3	yes	—
49	Dic₉₄	—	4	12	no	—
50	C₂²×C₄₇	—	2	6	no	—
51	C₂²×C₄₇	—	4	4	no	—
52	C₂²×C₄₇	C₂²×Q₈	1	6	yes	—
53	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
54	C₄×C₄₇	—	2	12	no	—
55	Dic₄₇	—	2	12	no	—
56	Dic₄₇	C₂²×Q₈	1	2	yes	—
57	Dic₄₇	C₂²×Q₈	1	6	yes	—
58	#3458	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	—	2	6	no	—
60	C₂×C₄₇	C₂³×Q₈	1	1	yes	characteristic
61	C₂×C₄₇	#585	1	2	yes	—
62	#544	—	47	12	no	—
63	#543	—	47	3	no	—
64	#543	D₄₇	1	1	yes	characteristic
65	#533	—	47	12	no	—
66	C₂×#117	—	47	3	no	—
67	C₄₇	#3458	1	1	yes	characteristic, complemented, Sylow
68	C₂³×C₄	—	47	1	no	—
69	C₄⋊Q₈	—	47	12	no	—
70	C₄⋊Q₈	—	47	12	no	—
71	#125	—	47	24	no	—
72	C₂²⋊Q₈	—	47	12	no	—
73	C₂²⋊Q₈	—	47	24	no	—
74	C₂²⋊Q₈	C₂×D₄₇	1	12	yes	—
75	C₄×Q₈	—	47	4	no	—
76	C₄×Q₈	—	47	12	no	—
77	#117	—	47	12	no	—
78	#117	—	47	12	no	—
79	C₂×C₄⋊C₄	—	47	6	no	—
80	C₂×C₂²⋊C₄	—	47	3	no	—
81	C₂×C₂²⋊C₄	C₂×D₄₇	1	3	yes	—
82	C₂×C₄²	—	47	6	no	—
83	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
84	C₂×Q₈	—	47	12	no	—
85	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
86	C₂²×C₄	—	47	8	no	—
87	C₂²×C₄	—	47	3	no	—
88	C₂²×C₄	—	47	3	no	—
89	C₂²×C₄	—	47	6	no	—
90	C₂²×C₄	C₂²×D₄₇	1	6	yes	—
91	C₄⋊C₄	—	47	24	no	—
92	C₄⋊C₄	—	47	24	no	—
93	C₄⋊C₄	—	47	12	no	—
94	C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
95	C₂²⋊C₄	—	47	12	no	—
96	C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
97	C₄²	—	47	12	no	—
98	C₄²	—	47	12	no	—
99	C₂³	—	4	2	no	—
100	C₂³	Q₈×D₄₇	1	4	yes	—
101	C₂³	C₂³×D₄₇	1	3	yes	—
102	Q₈	—	4	4	no	—
103	Q₈	—	188	12	no	—
104	C₂×C₄	—	4	6	no	—
105	C₂×C₄	—	47	12	no	—
106	C₂×C₄	—	47	12	no	—
107	C₂×C₄	—	47	1	no	—
108	C₂×C₄	—	47	3	no	—
109	C₂×C₄	—	47	12	no	—
110	C₂×C₄	—	188	6	no	—
111	C₂×C₄	C₂³×D₄₇	1	12	yes	—
112	C₂²	—	2	6	no	—
113	C₂²	—	4	4	no	—
114	C₂²	C₂×Q₈×D₄₇	1	6	yes	—
115	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
116	C₄	—	2	12	no	—
117	C₄	—	47	2	no	—
118	C₄	—	47	6	no	—
119	C₄	—	94	12	no	—
120	C₂	—	2	6	no	—
121	C₂	C₂²×Q₈×D₄₇	1	1	yes	characteristic
122	C₂	#15689958	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689752

C₂

yes

maximal, complemented

#15689749

C₂

yes

maximal

#15689675

C₂

yes

maximal, complemented

C₂×#13093980

C₂

yes

maximal

C₄₇×#543

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

#13094023

C₂²

yes

complemented

#13094022

C₂²

yes

complemented

#13094014

C₂²

yes

complemented

#13094003

C₂²

yes

—

#13094001

C₂²

yes

—

Q₈×Dic₄₇

C₂²

yes

complemented

#13093989

C₂²

yes

complemented

#13093980

C₂²

yes

—

#13093980

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂²⋊Q₈×C₄₇

C₂²

yes

—

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×Q₈×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

Q₈

yes

complemented

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×Dic₉₄

C₂³

yes

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₂²⋊C₄×C₄₇

C₂³

yes

—

C₂²⋊Dic₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

C₂³

yes

—

Dic₄₇⋊C₄

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

C₂⁴

yes

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂⁴

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

C₂⁴

yes

—

C₂×Dic₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

C₂⁴

yes

—

Dic₉₄

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×Q₈

yes

—

C₂²×C₄₇

C₂⁵

yes

characteristic

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

C₂²×Q₈

yes

—

Dic₄₇

C₂²×Q₈

yes

—

#3458

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂³×Q₈

yes

characteristic

C₂×C₄₇

#585

yes

—

#544

—

#543

—

#543

D₄₇

yes

characteristic

#533

—

C₂×#117

—

C₄₇

#3458

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂²⋊Q₈

C₂×D₄₇

yes

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

C₂²×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₇

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂²×D₄₇

yes

—

C₄²

—

C₄²

—

C₂³

—

100

C₂³

Q₈×D₄₇

yes

—

101

C₂³

C₂³×D₄₇

yes

—

102

Q₈

—

103

Q₈

—

188

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

188

—

111

C₂×C₄

C₂³×D₄₇

yes

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₂×Q₈×D₄₇

yes

—

115

C₂²

C₂⁴×D₄₇

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₂

—

121

C₂

C₂²×Q₈×D₄₇

yes

characteristic

122

C₂

#15689958

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#543	C₂
hypercenter	#543	D₄₇
hypocenter	C₄₇	#3458
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #543

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₄₇

commutator, socle

C₂²×C₄₇

C₂⁵

Fitting

C₄₇×#543

C₂

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂² ◁ #543

N	H ≅ G/N	type
1. #15689752	C₂	semidirect
3. #15689675	C₂	semidirect
7. #13094023	C₂²	semidirect
8. #13094022	C₂²	semidirect
9. #13094014	C₂²	semidirect
12. Q₈×Dic₄₇	C₂²	semidirect
13. #13093989	C₂²	semidirect
24. C₂²×Dic₄₇	Q₈	semidirect
67. C₄₇	#3458	semidirect

H ≅ G/N

type

1. #15689752

C₂

semidirect

3. #15689675

C₂

semidirect

7. #13094023

C₂²

semidirect

8. #13094022

C₂²

semidirect

9. #13094014

C₂²

semidirect

12. Q₈×Dic₄₇

C₂²

semidirect

13. #13093989

C₂²

semidirect

24. C₂²×Dic₄₇

Q₈

semidirect

67. C₄₇

#3458

semidirect

Subgroups — #20256790

Conjugacy classes of subgroups

Complements