Group #20242777 — subgroups

Subgroups — #20242777

Order 6016.

172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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	#15689528	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689328	C₂	1	2	yes	maximal
3	#15688876	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688868	C₂	1	2	yes	maximal, complemented
5	C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625335	—	2	2	no	—
7	#13094024	C₂²	1	2	yes	—
8	#13093958	—	2	1	no	—
9	#13093958	—	2	1	no	—
10	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	#13093947	—	2	2	no	—
12	C₂²×C₈×C₄₇	—	2	1	no	—
13	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²⋊C₈×C₄₇	—	2	1	no	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₄₇	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	—	2	1	no	—
19	C₂×Dic₉₄	—	2	2	no	—
20	C₂×C₈×C₄₇	—	2	1	no	—
21	C₂×C₈×C₄₇	—	4	2	no	—
22	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
25	C₂²⋊C₄×C₄₇	—	2	1	no	—
26	C₄²×C₄₇	C₂³	1	1	yes	characteristic
27	#10625335	—	4	4	no	—
28	C₄⋊Dic₄₇	—	2	2	no	—
29	C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄₇⋊C₈	—	2	2	no	—
31	C₂³×C₄₇	—	2	1	no	—
32	D₄×C₄₇	—	2	1	no	—
33	D₄×C₄₇	D₈	1	2	yes	—
34	C₂×C₄×C₄₇	—	2	1	no	—
35	C₂×C₄×C₄₇	—	4	1	no	—
36	C₂×C₄×C₄₇	—	4	1	no	—
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
40	C₂×Dic₄₇	—	4	2	no	—
41	Dic₉₄	—	4	2	no	—
42	Dic₉₄	—	4	2	no	—
43	C₈×C₄₇	—	2	1	no	—
44	C₈×C₄₇	—	4	1	no	—
45	C₈×C₄₇	SD₁₆	1	2	yes	complemented
46	C₄₇⋊C₈	—	4	2	no	—
47	C₂²×C₄₇	—	2	2	no	—
48	C₂²×C₄₇	—	4	1	no	—
49	C₂²×C₄₇	—	4	1	no	—
50	C₂²×C₄₇	#121	1	1	yes	characteristic
51	C₄×C₄₇	—	2	1	no	—
52	C₄×C₄₇	—	4	1	no	—
53	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
54	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
55	C₄×C₄₇	#135	1	1	yes	characteristic
56	C₄×C₄₇	#137	1	1	yes	characteristic
57	Dic₄₇	—	8	2	no	—
58	#1673	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	—	4	2	no	—
60	C₂×C₄₇	#461	1	1	yes	characteristic
61	C₂×C₄₇	#466	1	1	yes	characteristic
62	C₂×C₄₇	#473	1	1	yes	characteristic
63	#500	—	47	1	no	—
64	#461	—	47	2	no	—
65	C₈×D₄	D₄₇	1	1	yes	characteristic
66	#335	—	47	1	no	—
67	#332	—	47	2	no	—
68	C₄₇	#1673	1	1	yes	characteristic, complemented, Sylow
69	C₂×SD₁₆	—	94	2	no	—
70	C₂²×C₈	—	2	1	no	—
71	C₄⋊Q₈	—	47	2	no	—
72	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
73	#107	—	94	1	no	—
74	#107	—	94	1	no	—
75	C₄⋊C₈	—	47	2	no	—
76	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
77	#103	—	94	2	no	—
78	C₂²⋊C₈	—	2	1	no	—
79	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
80	C₂×Q₈	—	94	2	no	—
81	C₂×D₄	D₁₈₈	1	1	yes	characteristic
82	C₂²×C₄	—	2	1	no	—
83	SD₁₆	—	188	4	no	—
84	C₂×C₈	—	2	1	no	—
85	C₂×C₈	—	4	2	no	—
86	C₂×C₈	—	94	2	no	—
87	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
88	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
89	C₄⋊C₄	—	94	2	no	—
90	C₄⋊C₄	—	94	2	no	—
91	C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
92	C₂²⋊C₄	—	2	1	no	—
93	C₄²	C₂²×D₄₇	1	1	yes	characteristic
94	C₂³	—	2	1	no	—
95	Q₈	—	188	2	no	—
96	Q₈	—	188	2	no	—
97	D₄	—	2	1	no	—
98	D₄	D₃₇₆	1	2	yes	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	188	2	no	—
103	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
104	C₂×C₄	#10625350	1	1	yes	characteristic
105	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	—	4	1	no	—
108	C₈	—	188	2	no	—
109	C₈	#10625335	1	2	yes	complemented
110	C₂²	—	2	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	4	1	no	—
113	C₂²	#13093998	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	4	1	no	—
116	C₄	—	376	2	no	—
117	C₄	C₂×D₃₇₆	1	1	yes	characteristic
118	C₄	C₂×#10625335	1	1	yes	characteristic
119	C₄	#13094046	1	1	yes	characteristic
120	C₄	#13094054	1	1	yes	characteristic
121	C₂	—	4	2	no	—
122	C₂	#15689328	1	1	yes	characteristic
123	C₂	#15689359	1	1	yes	characteristic
124	C₂	#15689398	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689528

C₂

yes

maximal, characteristic, complemented

#15689328

C₂

yes

maximal

#15688876

C₂

yes

maximal, characteristic, complemented

#15688868

C₂

yes

maximal, complemented

C₈×D₄×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625335

—

#13094024

C₂²

yes

—

#13093958

—

#13093958

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093947

—

C₂²×C₈×C₄₇

—

C₄×D₄×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

C₂²

yes

characteristic

C₂²⋊C₈×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625335

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

SD₁₆

yes

complemented

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#121

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1673

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

C₈×D₄

D₄₇

yes

characteristic

#335

—

#332

—

C₄₇

#1673

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₄₇

yes

characteristic

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

characteristic

#103

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

D₁₈₈

yes

characteristic

C₂²×C₄

—

SD₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₈₈

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

Q₈

—

188

—

Q₈

—

188

—

D₄

—

D₄

D₃₇₆

yes

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

188

—

103

C₂×C₄

C₂×D₁₈₈

yes

characteristic

104

C₂×C₄

#10625350

yes

characteristic

105

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

106

C₈

—

107

C₈

—

108

C₈

—

188

—

109

C₈

#10625335

yes

complemented

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

#13093998

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

376

—

117

C₄

C₂×D₃₇₆

yes

characteristic

118

C₄

C₂×#10625335

yes

characteristic

119

C₄

#13094046

yes

characteristic

120

C₄

#13094054

yes

characteristic

121

C₂

—

122

C₂

#15689328

yes

characteristic

123

C₂

#15689359

yes

characteristic

124

C₂

#15689398

yes

characteristic

	subgroup	G/H
center	C₂²	#13093998
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₈×D₄×C₄₇	C₂
socle	C₂²×C₄₇	#121
hypercenter	C₈×D₄	D₄₇
hypocenter	C₄₇	#1673
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

subgroup

G/H

center

C₂²

#13093998

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₈×D₄×C₄₇

C₂

socle

C₂²×C₄₇

#121

hypercenter

C₈×D₄

D₄₇

hypocenter

C₄₇

#1673

LCS

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

N	H ≅ G/N	type
1. #15689528	C₂	semidirect
3. #15688876	C₂	semidirect
4. #15688868	C₂	semidirect
45. C₈×C₄₇	SD₁₆	semidirect
68. C₄₇	#1673	semidirect
109. C₈	#10625335	semidirect

H ≅ G/N

type

1. #15689528

C₂

semidirect

3. #15688876

C₂

semidirect

4. #15688868

C₂

semidirect

45. C₈×C₄₇

SD₁₆

semidirect

68. C₄₇

#1673

semidirect

109. C₈

#10625335

semidirect

Subgroups — #20242777

Conjugacy classes of subgroups

Complements