Group #20251748 — subgroups

Subgroups — #20251748

Order 6016.

472 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 181 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	C₂×#13094016	C₂	1	1	yes	maximal, characteristic
2	#15689018	C₂	1	8	yes	maximal
3	#15688992	C₂	1	2	yes	maximal
4	#15688988	C₂	1	2	yes	maximal
5	C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#125×C₄₇	C₂	1	1	yes	maximal, characteristic
7	#13094016	—	2	4	no	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×Dic₄₇⋊C₄	C₂²	1	8	yes	—
10	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
11	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
12	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
14	C₄₇⋊#95	C₂²	1	8	yes	—
15	#125×C₄₇	—	2	4	no	—
16	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
18	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₇	C₂³	1	4	yes	—
23	C₂²×Dic₄₇	C₂³	1	2	yes	—
24	C₂²×Dic₄₇	C₂³	1	2	yes	—
25	C₄⋊C₄×C₄₇	—	2	8	no	—
26	C₄⋊C₄×C₄₇	—	2	4	no	—
27	C₄²×C₄₇	D₄	1	4	yes	—
28	C₄⋊Dic₄₇	—	2	4	no	—
29	Dic₄₇⋊C₄	—	2	8	no	—
30	Dic₄₇⋊C₄	—	2	16	no	—
31	C₄×Dic₄₇	—	2	8	no	—
32	C₄×Dic₄₇	Q₈	1	4	yes	—
33	C₄×Dic₄₇	Q₈	1	4	yes	—
34	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
35	C₂×C₄×C₄₇	—	2	4	no	—
36	C₂×C₄×C₄₇	—	2	4	no	—
37	C₂×C₄×C₄₇	—	2	8	no	—
38	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
39	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
42	C₂×Dic₄₇	—	2	4	no	—
43	C₂×Dic₄₇	—	2	4	no	—
44	C₂×Dic₄₇	—	2	8	no	—
45	C₂×Dic₄₇	C₂×Q₈	1	4	yes	—
46	C₂×Dic₄₇	C₂×Q₈	1	4	yes	—
47	C₂×Dic₄₇	#41	1	8	yes	—
48	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
49	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
50	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
51	C₂²×C₄₇	C₂×#41	1	4	yes	—
52	C₄×C₄₇	—	2	4	no	—
53	C₄×C₄₇	—	4	4	no	—
54	C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
55	Dic₄₇	—	2	4	no	—
56	Dic₄₇	—	4	4	no	—
57	Dic₄₇	#125	1	8	yes	complemented
58	#2859	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	C₂×#125	1	2	yes	—
60	C₂×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
61	C₂×C₄₇	#532	1	2	yes	—
62	C₂×C₄₇	#533	1	2	yes	—
63	C₂×#125	—	47	1	no	—
64	C₂×#125	D₄₇	1	1	yes	characteristic
65	#389	—	47	8	no	—
66	#384	—	47	2	no	—
67	#382	—	47	2	no	—
68	C₄³	—	47	1	no	—
69	C₄₇	#2859	1	1	yes	characteristic, complemented, Sylow
70	#125	—	2	4	no	—
71	#125	—	94	4	no	—
72	C₂×C₄⋊C₄	—	47	4	no	—
73	C₂×C₄⋊C₄	—	47	2	no	—
74	C₂×C₄⋊C₄	—	47	8	no	—
75	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
76	C₂×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
77	C₂×C₄²	—	47	1	no	—
78	C₂×C₄²	—	47	1	no	—
79	C₂×C₄²	—	47	4	no	—
80	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
81	#95	—	47	8	no	—
82	C₂²×C₄	—	47	2	no	—
83	C₂²×C₄	—	47	2	no	—
84	C₂²×C₄	—	47	4	no	—
85	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
86	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
87	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
88	C₄⋊C₄	—	2	8	no	—
89	C₄⋊C₄	—	2	4	no	—
90	C₄⋊C₄	—	94	16	no	—
91	C₄⋊C₄	—	94	8	no	—
92	C₄⋊C₄	—	94	4	no	—
93	C₄²	—	47	4	no	—
94	C₄²	—	47	4	no	—
95	C₄²	—	94	8	no	—
96	C₄²	C₂²⋊D₄₇	1	4	yes	—
97	C₂³	C₂³×D₄₇	1	1	yes	characteristic
98	C₂×C₄	—	2	4	no	—
99	C₂×C₄	—	2	4	no	—
100	C₂×C₄	—	2	8	no	—
101	C₂×C₄	—	47	4	no	—
102	C₂×C₄	—	47	8	no	—
103	C₂×C₄	—	47	4	no	—
104	C₂×C₄	—	94	4	no	—
105	C₂×C₄	—	94	4	no	—
106	C₂×C₄	—	94	8	no	—
107	C₂×C₄	Q₈×D₄₇	1	2	yes	—
108	C₂×C₄	Q₈×D₄₇	1	2	yes	—
109	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
110	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
111	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
112	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
113	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
114	C₂²	#41×D₄₇	1	4	yes	—
115	C₄	—	2	4	no	—
116	C₄	—	4	4	no	—
117	C₄	—	47	8	no	—
118	C₄	—	94	4	no	—
119	C₄	—	188	4	no	—
120	C₄	#13094022	1	4	yes	—
121	C₂	#125×D₄₇	1	2	yes	—
122	C₂	C₂×#13094022	1	1	yes	characteristic
123	C₂	#15689669	1	2	yes	—
124	C₂	#15689679	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094016

C₂

yes

maximal, characteristic

#15689018

C₂

yes

maximal

#15688992

C₂

yes

maximal

#15688988

C₂

yes

maximal

C₄²×Dic₄₇

C₂

yes

maximal, characteristic

C₂×#125×C₄₇

C₂

yes

maximal, characteristic

#13094016

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₄₇⋊#95

C₂²

yes

—

#125×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

Q₈

yes

—

C₄×Dic₄₇

Q₈

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

#41

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄⋊Q₈

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

yes

—

C₂×C₄₇

yes

—

C₂×C₄₇

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₇

#532

yes

—

C₂×C₄₇

#533

yes

—

C₂×#125

—

C₂×#125

D₄₇

yes

—

—

—

C₄³

—

C₄₇

#2859

yes

characteristic, complemented, Sylow

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²⋊D₄₇

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

Q₈×D₄₇

yes

—

108

C₂×C₄

Q₈×D₄₇

yes

—

109

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

110

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

111

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

112

C₂²

C₂×Q₈×D₄₇

yes

characteristic

113

C₂²

C₂×Q₈×D₄₇

yes

characteristic

114

C₂²

#41×D₄₇

yes

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

188

—

120

C₄

#13094022

yes

—

121

C₂

#125×D₄₇

yes

—

122

C₂

C₂×#13094022

yes

characteristic

123

C₂

#15689669

yes

—

124

C₂

#15689679

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₂×#125×C₄₇	C₂
hypercenter	C₂×#125	D₄₇
hypocenter	C₄₇	#2859
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₂×#125×C₄₇

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
57. Dic₄₇	#125	semidirect
69. C₄₇	#2859	semidirect

H ≅ G/N

type

57. Dic₄₇

#125

semidirect

69. C₄₇

#2859

semidirect

Subgroups — #20251748

Conjugacy classes of subgroups

Complements