Group #20243549 — subgroups

Subgroups — #20243549

Order 6016.

248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13093957	C₂	1	2	yes	maximal
2	C₂×#13093956	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#15688988	C₂	1	2	yes	maximal
5	C₂×#106×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	#13093957	—	2	4	no	—
10	#13093956	—	2	2	no	—
11	C₈×Dic₄₇	C₄	1	4	yes	complemented
12	C₄₇⋊#95	—	2	4	no	—
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	#106×C₄₇	—	2	2	no	—
16	C₂²×C₄×C₄₇	—	2	2	no	—
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₇	—	2	2	no	—
19	C₂²×Dic₄₇	D₄	1	2	yes	—
20	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₄₇	D₄	1	2	yes	—
22	C₂×C₈×C₄₇	Q₈	1	2	yes	—
23	C₄⋊C₄×C₄₇	—	2	2	no	—
24	C₄⋊C₄×C₄₇	—	2	2	no	—
25	C₄⋊Dic₄₇	—	2	2	no	—
26	C₄⋊Dic₄₇	—	2	2	no	—
27	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
28	C₄×Dic₄₇	Q₈	1	2	yes	—
29	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
30	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
31	C₂×C₄₇⋊C₈	Q₈	1	2	yes	—
32	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	—	4	2	no	—
34	C₂×C₄×C₄₇	—	4	4	no	—
35	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
41	C₂×Dic₄₇	—	2	4	no	—
42	C₂×Dic₄₇	—	4	2	no	—
43	C₂×Dic₄₇	—	4	4	no	—
44	C₂×Dic₄₇	C₄⋊C₄	1	4	yes	—
45	C₈×C₄₇	C₄⋊C₄	1	4	yes	—
46	C₄₇⋊C₈	C₄⋊C₄	1	4	yes	—
47	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₄₇	#127	1	1	yes	characteristic
49	C₂²×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
50	C₂²×C₄₇	#135	1	4	yes	—
51	C₄×C₄₇	—	8	2	no	—
52	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
55	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
56	Dic₄₇	—	2	4	no	—
57	Dic₄₇	—	8	2	no	—
58	#1846	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	#384	1	1	yes	characteristic
60	C₂×C₄₇	#427	1	2	yes	—
61	C₂×C₄₇	#495	1	2	yes	—
62	C₂×C₄₇	#499	1	2	yes	—
63	C₂×#107	—	47	2	no	—
64	C₂×#106	—	47	1	no	—
65	C₂×#106	D₄₇	1	1	yes	characteristic
66	C₂×C₄×C₈	—	47	1	no	—
67	#382	—	47	2	no	—
68	C₄₇	#1846	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	47	1	no	—
70	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
71	C₂×C₄⋊C₄	—	47	2	no	—
72	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
73	C₂×C₄²	—	47	1	no	—
74	#107	—	94	4	no	—
75	#106	—	2	2	no	—
76	#106	—	94	2	no	—
77	C₄×C₈	—	47	4	no	—
78	#95	—	94	4	no	—
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	—	47	2	no	—
81	C₂²×C₄	—	94	2	no	—
82	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
83	C₂×C₈	—	47	2	no	—
84	C₂×C₈	—	47	2	no	—
85	C₂×C₈	—	47	2	no	—
86	C₂×C₈	Dic₉₄	1	2	yes	—
87	C₂×C₈	C₄×D₄₇	1	2	yes	—
88	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
89	C₄⋊C₄	—	2	2	no	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	94	2	no	—
92	C₄⋊C₄	—	94	2	no	—
93	C₄²	—	47	2	no	—
94	C₄²	—	47	2	no	—
95	C₂³	D₄×D₄₇	1	1	yes	characteristic
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	4	4	no	—
98	C₂×C₄	—	47	4	no	—
99	C₂×C₄	—	94	4	no	—
100	C₂×C₄	—	188	2	no	—
101	C₂×C₄	—	188	4	no	—
102	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
103	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
104	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
105	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
106	C₂×C₄	Q₈×D₄₇	1	1	yes	characteristic
107	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
108	C₈	—	47	4	no	—
109	C₈	Dic₄₇⋊C₄	1	4	yes	—
110	C₂²	C₄⋊C₄×D₄₇	1	1	yes	characteristic
111	C₂²	#13094020	1	1	yes	characteristic
112	C₂²	#13094023	1	1	yes	characteristic
113	C₂²	#13094045	1	4	yes	—
114	C₄	—	8	2	no	—
115	C₄	—	94	4	no	—
116	C₄	—	376	2	no	—
117	C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
118	C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
119	C₄	#13094022	1	1	yes	characteristic
120	C₄	#13094023	1	1	yes	characteristic
121	C₂	#15688992	1	1	yes	characteristic
122	C₂	#15689158	1	2	yes	—
123	C₂	#15689504	1	2	yes	—
124	C₂	#15689523	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093957

C₂

yes

maximal

C₂×#13093956

C₂

yes

maximal, characteristic

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic

#15688988

C₂

yes

maximal

C₂×#106×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093957

—

#13093956

—

C₈×Dic₄₇

C₄

yes

complemented

C₄₇⋊#95

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

#106×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

Q₈

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

Q₈

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

D₄

yes

—

C₂×C₄₇⋊C₈

Q₈

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₈×C₄₇

C₄⋊C₄

yes

—

C₄₇⋊C₈

C₄⋊C₄

yes

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

#127

yes

characteristic

C₂²×C₄₇

C₄⋊Q₈

yes

characteristic

C₂²×C₄₇

#135

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₇

C₄⋊Q₈

yes

characteristic

C₄×C₄₇

C₄⋊Q₈

yes

characteristic

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#495

yes

—

C₂×C₄₇

#499

yes

—

C₂×#107

—

C₂×#106

—

C₂×#106

D₄₇

yes

characteristic

C₂×C₄×C₈

—

#382

—

C₄₇

#1846

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

#107

—

#106

—

#106

—

C₄×C₈

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₉₄

yes

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₂²⋊D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₂³

D₄×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

188

—

101

C₂×C₄

—

188

—

102

C₂×C₄

C₂×Dic₉₄

yes

characteristic

103

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

104

C₂×C₄

D₄×D₄₇

yes

characteristic

105

C₂×C₄

Q₈×D₄₇

yes

characteristic

106

C₂×C₄

Q₈×D₄₇

yes

characteristic

107

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

108

C₈

—

109

C₈

Dic₄₇⋊C₄

yes

—

110

C₂²

C₄⋊C₄×D₄₇

yes

characteristic

111

C₂²

#13094020

yes

characteristic

112

C₂²

#13094023

yes

characteristic

113

C₂²

#13094045

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

376

—

117

C₄

C₄⋊C₄×D₄₇

yes

characteristic

118

C₄

C₂×Dic₄₇⋊C₄

yes

characteristic

119

C₄

#13094022

yes

characteristic

120

C₄

#13094023

yes

characteristic

121

C₂

#15688992

yes

characteristic

122

C₂

#15689158

yes

—

123

C₂

#15689504

yes

—

124

C₂

#15689523

yes

—

	subgroup	G/H
center	C₂³	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#106×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×#106	D₄₇
hypocenter	C₄₇	#1846
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂³

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#106×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
11. C₈×Dic₄₇	C₄	semidirect
68. C₄₇	#1846	semidirect

H ≅ G/N

type

11. C₈×Dic₄₇

C₄

semidirect

68. C₄₇

#1846

semidirect

Subgroups — #20243549

Conjugacy classes of subgroups

Complements