Group #20246108 — subgroups

Subgroups — #20246108

Order 6016.

516 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 237 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×Q₈×Dic₄₇	C₂	1	2	yes	maximal
2	#15689030	C₂	1	2	yes	maximal
3	#15689009	C₂	1	8	yes	maximal
4	#15688989	C₂	1	1	yes	maximal, characteristic
5	#15688969	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
7	Q₈×Dic₄₇	—	2	8	no	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
10	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
12	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₄₇⋊#95	C₂²	1	4	yes	—
14	C₄₇⋊#95	C₂²	1	4	yes	—
15	C₄₇⋊#95	C₂²	1	8	yes	—
16	C₂²×Q₈×C₄₇	C₂²	1	2	yes	—
17	C₄⋊Q₈×C₄₇	C₄	1	8	yes	complemented
18	C₂×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
19	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×Q₈×C₄₇	—	2	4	no	—
21	C₂×Q₈×C₄₇	—	2	4	no	—
22	C₂×Q₈×C₄₇	C₂×C₄	1	8	yes	—
23	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
24	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₇	C₂³	1	2	yes	—
27	C₂²×Dic₄₇	C₂³	1	4	yes	—
28	C₂²×Dic₄₇	C₂³	1	2	yes	—
29	C₄⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
30	C₄²×C₄₇	C₂×C₄	1	4	yes	—
31	C₄⋊Dic₄₇	—	2	4	no	—
32	C₄⋊Dic₄₇	—	2	8	no	—
33	C₄×Dic₄₇	—	2	2	no	—
34	C₄×Dic₄₇	—	2	8	no	—
35	C₄×Dic₄₇	D₄	1	4	yes	—
36	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
37	Q₈×C₄₇	—	2	16	no	—
38	C₂×C₄×C₄₇	—	2	4	no	—
39	C₂×C₄×C₄₇	—	2	4	no	—
40	C₂×C₄×C₄₇	—	2	4	no	—
41	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
42	C₂×C₄×C₄₇	C₂²×C₄	1	8	yes	—
43	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
44	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₄₇	#41	1	2	yes	—
46	C₂×Dic₄₇	—	2	4	no	—
47	C₂×Dic₄₇	—	2	4	no	—
48	C₂×Dic₄₇	—	2	2	no	—
49	C₂×Dic₄₇	—	2	8	no	—
50	C₂×Dic₄₇	—	2	4	no	—
51	C₂×Dic₄₇	C₂×D₄	1	4	yes	—
52	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
53	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
54	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
55	C₂²×C₄₇	2₋¹⁺⁴	1	4	yes	—
56	C₄×C₄₇	—	2	8	no	—
57	C₄×C₄₇	—	2	4	no	—
58	C₄×C₄₇	C₄×D₄	1	4	yes	—
59	Dic₄₇	—	2	4	no	—
60	Dic₄₇	—	4	4	no	—
61	Dic₄₇	—	4	2	no	—
62	#2327	—	47	1	no	maximal, Sylow
63	C₂×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
64	C₂×C₄₇	#519	1	2	yes	—
65	C₂×C₄₇	#536	1	2	yes	—
66	C₂×C₄₇	#541	1	2	yes	—
67	C₂×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
68	C₂×C₄×Q₈	—	47	2	no	—
69	#391	—	47	2	no	—
70	#387	—	47	8	no	—
71	#382	—	47	1	no	—
72	#376	—	47	1	no	—
73	C₄₇	#2327	1	1	yes	characteristic, complemented, Sylow
74	C₂²×Q₈	C₂×D₄₇	1	2	yes	—
75	C₄⋊Q₈	Dic₄₇	1	8	yes	complemented
76	C₄×Q₈	—	94	8	no	—
77	C₂×C₄⋊C₄	—	47	2	no	—
78	C₂×C₄⋊C₄	—	47	4	no	—
79	C₂×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
80	C₂×C₄²	—	47	1	no	—
81	C₂×C₄²	—	47	4	no	—
82	C₂×C₄²	—	47	1	no	—
83	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
84	#95	—	47	4	no	—
85	#95	—	47	4	no	—
86	#95	—	47	8	no	—
87	C₂×Q₈	—	2	4	no	—
88	C₂×Q₈	—	2	4	no	—
89	C₂×Q₈	C₂×Dic₄₇	1	8	yes	—
90	C₂²×C₄	—	47	2	no	—
91	C₂²×C₄	—	47	2	no	—
92	C₂²×C₄	—	47	4	no	—
93	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
94	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
95	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
96	C₄⋊C₄	—	94	8	no	—
97	C₄⋊C₄	—	94	4	no	—
98	C₄⋊C₄	C₂×Dic₄₇	1	16	yes	—
99	C₄²	—	47	4	no	—
100	C₄²	—	94	8	no	—
101	C₄²	—	94	2	no	—
102	C₄²	C₂×Dic₄₇	1	4	yes	—
103	C₂³	C₂³×D₄₇	1	1	yes	characteristic
104	Q₈	—	2	16	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	—	47	4	no	—
109	C₂×C₄	—	94	4	no	—
110	C₂×C₄	—	94	4	no	—
111	C₂×C₄	—	94	2	no	—
112	C₂×C₄	—	94	4	no	—
113	C₂×C₄	—	94	8	no	—
114	C₂×C₄	D₄×D₄₇	1	2	yes	—
115	C₂×C₄	#10625352	1	2	yes	—
116	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
117	C₂×C₄	C₂²×Dic₄₇	1	8	yes	—
118	C₂×C₄	C₂²×Dic₄₇	1	2	yes	—
119	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
120	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
121	C₂²	C₂×#10625352	1	1	yes	characteristic
122	C₂²	#13094072	1	4	yes	—
123	C₄	—	2	8	no	—
124	C₄	—	2	4	no	—
125	C₄	—	94	4	no	—
126	C₄	—	188	2	no	—
127	C₄	—	188	4	no	—
128	C₄	D₄×Dic₄₇	1	4	yes	—
129	C₂	C₂×D₄×Dic₄₇	1	1	yes	characteristic
130	C₂	#15689601	1	2	yes	—
131	C₂	#15689698	1	2	yes	—
132	C₂	#15689734	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₄₇

C₂

yes

maximal

#15689030

C₂

yes

maximal

#15689009

C₂

yes

maximal

#15688989

C₂

yes

maximal, characteristic

#15688969

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₄₇

C₂

yes

maximal, characteristic

Q₈×Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂×C₄

yes

—

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

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#2327

—

maximal, Sylow

C₂×C₄₇

C₂×C₄×D₄

yes

characteristic

C₂×C₄₇

#519

yes

—

C₂×C₄₇

#536

yes

—

C₂×C₄₇

#541

yes

—

C₂×C₄⋊Q₈

D₄₇

yes

characteristic

C₂×C₄×Q₈

—

—

—

—

—

C₄₇

#2327

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₇

yes

—

C₄⋊Q₈

Dic₄₇

yes

complemented

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₄₇

yes

—

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

C₂×Dic₄₇

yes

—

C₄²

—

100

C₄²

—

101

C₄²

—

102

C₄²

C₂×Dic₄₇

yes

—

103

C₂³

C₂³×D₄₇

yes

characteristic

104

Q₈

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

D₄×D₄₇

yes

—

115

C₂×C₄

#10625352

yes

—

116

C₂×C₄

C₂²×Dic₄₇

yes

—

117

C₂×C₄

C₂²×Dic₄₇

yes

—

118

C₂×C₄

C₂²×Dic₄₇

yes

—

119

C₂²

C₂³×Dic₄₇

yes

characteristic

120

C₂²

C₂×D₄×D₄₇

yes

characteristic

121

C₂²

C₂×#10625352

yes

characteristic

122

C₂²

#13094072

yes

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

188

—

127

C₄

—

188

—

128

C₄

D₄×Dic₄₇

yes

—

129

C₂

C₂×D₄×Dic₄₇

yes

characteristic

130

C₂

#15689601

yes

—

131

C₂

#15689698

yes

—

132

C₂

#15689734

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₂×C₄⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	#2327
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Fitting

C₂×C₄⋊Q₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂⁴

hypercenter

C₂×C₄⋊Q₈

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
17. C₄⋊Q₈×C₄₇	C₄	semidirect
73. C₄₇	#2327	semidirect
75. C₄⋊Q₈	Dic₄₇	semidirect

H ≅ G/N

type

17. C₄⋊Q₈×C₄₇

C₄

semidirect

73. C₄₇

#2327

semidirect

75. C₄⋊Q₈

Dic₄₇

semidirect

Subgroups — #20246108

Conjugacy classes of subgroups

Complements