Group #20243034 — subgroups

Subgroups — #20243034

Order 6016.

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

normal subgroups only

This group has 164 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
2	#15689521	C₂	1	1	yes	maximal, characteristic
3	#15689474	C₂	1	1	yes	maximal, characteristic
4	#15689474	C₂	1	1	yes	maximal, characteristic
5	#15689474	C₂	1	1	yes	maximal, characteristic
6	#15689474	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#322	C₂	1	1	yes	maximal, characteristic
8	#13094024	C₂²	1	1	yes	characteristic
9	#13094024	C₂²	1	1	yes	characteristic
10	#13094024	C₂²	1	1	yes	characteristic
11	#13094024	C₂²	1	1	yes	characteristic
12	#13093958	—	2	2	no	—
13	#13093956	—	2	2	no	—
14	#13093949	—	2	2	no	—
15	#13093949	—	2	2	no	—
16	#13093949	—	2	2	no	—
17	#13093949	—	2	2	no	—
18	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×Dic₉₄	—	2	1	no	—
22	C₂×Dic₉₄	—	2	1	no	—
23	C₂×Dic₉₄	—	2	1	no	—
24	C₂×Dic₉₄	—	2	1	no	—
25	C₂×C₈×C₄₇	D₄	1	2	yes	—
26	C₂×C₈×C₄₇	D₄	1	2	yes	—
27	C₂×C₈×C₄₇	D₄	1	2	yes	—
28	C₄²×C₄₇	C₂³	1	1	yes	characteristic
29	C₄⋊Dic₄₇	—	2	1	no	—
30	C₄⋊Dic₄₇	—	2	1	no	—
31	C₄⋊Dic₄₇	—	2	1	no	—
32	C₄⋊Dic₄₇	—	2	1	no	—
33	C₄⋊Dic₄₇	—	2	1	no	—
34	C₄⋊Dic₄₇	—	2	1	no	—
35	C₄⋊Dic₄₇	—	2	1	no	—
36	C₄⋊Dic₄₇	—	2	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	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₄₇	—	4	1	no	—
41	C₂×Dic₄₇	—	4	1	no	—
42	C₂×Dic₄₇	—	4	1	no	—
43	C₂×Dic₄₇	—	4	1	no	—
44	Dic₉₄	—	4	2	no	—
45	Dic₉₄	—	4	2	no	—
46	Dic₉₄	—	4	2	no	—
47	Dic₉₄	—	4	2	no	—
48	C₈×C₄₇	—	2	2	no	—
49	C₈×C₄₇	—	2	2	no	—
50	C₈×C₄₇	—	2	2	no	—
51	C₂²×C₄₇	#127	1	1	yes	characteristic
52	C₄×C₄₇	#135	1	2	yes	—
53	C₄×C₄₇	#137	1	2	yes	—
54	C₄×C₄₇	#137	1	2	yes	—
55	Dic₄₇	—	8	1	no	—
56	Dic₄₇	—	8	1	no	—
57	Dic₄₇	—	8	1	no	—
58	Dic₄₇	—	8	1	no	—
59	#1718	—	47	1	no	maximal, Sylow
60	C₂×C₄₇	#495	1	1	yes	characteristic
61	C₂×C₄₇	#497	1	1	yes	characteristic
62	C₂×C₄₇	#497	1	1	yes	characteristic
63	#500	—	47	1	no	—
64	#498	—	47	1	no	—
65	#487	—	47	1	no	—
66	#487	—	47	1	no	—
67	#487	—	47	1	no	—
68	#487	—	47	1	no	—
69	#322	D₄₇	1	1	yes	characteristic
70	C₄₇	#1718	1	1	yes	characteristic, complemented, Sylow
71	C₄⋊Q₈	—	47	1	no	—
72	C₄⋊Q₈	—	47	1	no	—
73	C₄⋊Q₈	—	47	1	no	—
74	C₄⋊Q₈	—	47	1	no	—
75	#107	—	94	2	no	—
76	#106	—	94	2	no	—
77	#103	—	94	2	no	—
78	#103	—	94	2	no	—
79	#103	—	94	2	no	—
80	#103	—	94	2	no	—
81	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
82	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
83	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
84	C₂×Q₈	—	94	1	no	—
85	C₂×Q₈	—	94	1	no	—
86	C₂×Q₈	—	94	1	no	—
87	C₂×Q₈	—	94	1	no	—
88	C₂×C₈	D₁₈₈	1	2	yes	—
89	C₂×C₈	D₁₈₈	1	2	yes	—
90	C₂×C₈	D₁₈₈	1	2	yes	—
91	C₄⋊C₄	—	94	1	no	—
92	C₄⋊C₄	—	94	1	no	—
93	C₄⋊C₄	—	94	1	no	—
94	C₄⋊C₄	—	94	1	no	—
95	C₄⋊C₄	—	94	1	no	—
96	C₄⋊C₄	—	94	1	no	—
97	C₄⋊C₄	—	94	1	no	—
98	C₄⋊C₄	—	94	1	no	—
99	C₄²	C₂²×D₄₇	1	1	yes	characteristic
100	Q₈	—	188	2	no	—
101	Q₈	—	188	2	no	—
102	Q₈	—	188	2	no	—
103	Q₈	—	188	2	no	—
104	C₂×C₄	—	188	1	no	—
105	C₂×C₄	—	188	1	no	—
106	C₂×C₄	—	188	1	no	—
107	C₂×C₄	—	188	1	no	—
108	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
109	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
110	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	2	2	no	—
113	C₈	—	2	2	no	—
114	C₂²	#13094021	1	1	yes	characteristic
115	C₄	—	376	1	no	—
116	C₄	—	376	1	no	—
117	C₄	—	376	1	no	—
118	C₄	—	376	1	no	—
119	C₄	#13094046	1	2	yes	—
120	C₄	#13094057	1	2	yes	—
121	C₄	#13094057	1	2	yes	—
122	C₂	#15689507	1	1	yes	characteristic
123	C₂	#15689517	1	1	yes	characteristic
124	C₂	#15689517	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689528

C₂

yes

maximal, characteristic

#15689521

C₂

yes

maximal, characteristic

#15689474

C₂

yes

maximal, characteristic

#15689474

C₂

yes

maximal, characteristic

#15689474

C₂

yes

maximal, characteristic

#15689474

C₂

yes

maximal, characteristic

C₄₇×#322

C₂

yes

maximal, characteristic

#13094024

C₂²

yes

characteristic

#13094024

C₂²

yes

characteristic

#13094024

C₂²

yes

characteristic

#13094024

C₂²

yes

—

—

—

—

—

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₂²×C₄₇

#127

yes

characteristic

C₄×C₄₇

#135

yes

—

C₄×C₄₇

#137

yes

—

C₄×C₄₇

#137

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#1718

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

—

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₄×C₈

C₂×D₄₇

yes

characteristic

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×C₈

D₁₈₈

yes

—

C₂×C₈

D₁₈₈

yes

—

C₂×C₈

D₁₈₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

100

Q₈

—

188

—

101

Q₈

—

188

—

102

Q₈

—

188

—

103

Q₈

—

188

—

104

C₂×C₄

—

188

—

105

C₂×C₄

—

188

—

106

C₂×C₄

—

188

—

107

C₂×C₄

—

188

—

108

C₂×C₄

C₂×D₁₈₈

yes

characteristic

109

C₂×C₄

C₂×D₁₈₈

yes

characteristic

110

C₂×C₄

C₂×D₁₈₈

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

#13094021

yes

characteristic

115

C₄

—

376

—

116

C₄

—

376

—

117

C₄

—

376

—

118

C₄

—

376

—

119

C₄

#13094046

yes

—

120

C₄

#13094057

yes

—

121

C₄

#13094057

yes

—

122

C₂

#15689507

yes

characteristic

123

C₂

#15689517

yes

characteristic

124

C₂

#15689517

yes

characteristic

	subgroup	G/H
center	C₂²	#13094021
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#322	C₂
socle	C₂²×C₄₇	#127
hypercenter	#322	D₄₇
hypocenter	C₄₇	#1718
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#13094021

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#322

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
70. C₄₇	#1718	semidirect

H ≅ G/N

type

70. C₄₇

#1718

semidirect

Subgroups — #20243034

Conjugacy classes of subgroups

Complements