Group #20256963 — subgroups

Subgroups — C₂×#15689853 #20256963

Order 6016.

1112 conjugacy classes of subgroups; only the 581 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 581 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	#15689853	C₂	1	16	yes	maximal, direct product factor
2	C₂×#13094023	C₂	1	4	yes	maximal
3	C₂×#13094022	C₂	1	4	yes	maximal
4	C₂×C₄×Dic₉₄	C₂	1	2	yes	maximal
5	C₂×#13093989	C₂	1	4	yes	maximal
6	C₂×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₉₄	C₂²	1	4	yes	—
8	C₂²×Dic₉₄	C₂²	1	2	yes	—
9	#13094023	C₂²	1	32	yes	—
10	#13094022	C₂²	1	32	yes	—
11	C₄×Dic₉₄	C₂²	1	16	yes	—
12	#13093989	C₂²	1	32	yes	—
13	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	C₂×Dic₄₇⋊C₄	C₂²	1	8	yes	—
15	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
16	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
17	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
18	C₂²×Q₈×C₄₇	C₂²	1	2	yes	—
19	C₄⋊Q₈×C₄₇	C₂²	1	8	yes	—
20	C₂×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
21	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×Q₈×C₄₇	—	4	4	no	—
23	C₂×Q₈×C₄₇	C₂³	1	8	yes	—
24	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
26	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
27	C₂²×Dic₄₇	C₂³	1	4	yes	—
28	C₂²×Dic₄₇	C₂³	1	4	yes	—
29	C₂×Dic₉₄	—	4	8	no	—
30	C₂×Dic₉₄	Q₈	1	16	yes	complemented
31	C₂×Dic₉₄	C₂³	1	16	yes	—
32	C₂×Dic₉₄	C₂³	1	8	yes	—
33	C₄⋊C₄×C₄₇	C₂³	1	16	yes	—
34	C₄²×C₄₇	C₂³	1	4	yes	—
35	C₄⋊Dic₄₇	C₂³	1	8	yes	—
36	Dic₄₇⋊C₄	C₂³	1	32	yes	—
37	Dic₄₇⋊C₄	C₂³	1	16	yes	—
38	C₄×Dic₄₇	C₂³	1	16	yes	—
39	C₄×Dic₄₇	C₂³	1	16	yes	—
40	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
41	Q₈×C₄₇	—	4	8	no	—
42	C₂×C₄×C₄₇	—	2	8	no	—
43	C₂×C₄×C₄₇	—	2	2	no	—
44	C₂×C₄×C₄₇	C₂×Q₈	1	8	yes	—
45	C₂×C₄×C₄₇	C₂⁴	1	8	yes	—
46	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
47	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
48	C₂×Dic₄₇	—	2	8	no	—
49	C₂×Dic₄₇	C₂×Q₈	1	16	yes	—
50	C₂×Dic₄₇	C₂⁴	1	8	yes	—
51	C₂×Dic₄₇	C₂⁴	1	8	yes	—
52	Dic₉₄	—	4	16	no	—
53	Dic₉₄	C₂×Q₈	1	32	yes	complemented
54	C₂²×C₄₇	C₂²×Q₈	1	4	yes	—
55	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
56	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
57	C₄×C₄₇	—	2	8	no	—
58	C₄×C₄₇	—	2	2	no	—
59	C₄×C₄₇	C₂²×Q₈	1	8	yes	—
60	Dic₄₇	—	2	8	no	—
61	Dic₄₇	C₂²×Q₈	1	16	yes	—
62	C₂×Q₈²	—	47	1	no	maximal, Sylow
63	C₂×C₄₇	Q₈²	1	4	yes	complemented
64	C₂×C₄₇	C₂³×Q₈	1	2	yes	—
65	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
66	Q₈²	—	47	16	no	—
67	C₂×C₄⋊Q₈	—	47	4	no	—
68	C₂×C₄⋊Q₈	—	47	4	no	—
69	C₂×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
70	C₂×C₄×Q₈	—	47	4	no	—
71	C₂×C₄×Q₈	—	47	2	no	—
72	C₄₇	C₂×Q₈²	1	1	yes	characteristic, complemented, Sylow
73	C₂²×Q₈	—	47	2	no	—
74	C₂²×Q₈	—	47	4	no	—
75	C₂²×Q₈	C₂×D₄₇	1	2	yes	—
76	C₄⋊Q₈	—	47	32	no	—
77	C₄⋊Q₈	—	47	32	no	—
78	C₄⋊Q₈	C₂×D₄₇	1	8	yes	—
79	C₄×Q₈	—	47	32	no	—
80	C₄×Q₈	—	47	16	no	—
81	C₂×C₄⋊C₄	—	47	8	no	—
82	C₂×C₄⋊C₄	—	47	4	no	—
83	C₂×C₄⋊C₄	—	47	2	no	—
84	C₂×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
85	C₂×C₄²	—	47	4	no	—
86	C₂×C₄²	—	47	4	no	—
87	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
88	C₂×Q₈	—	4	4	no	—
89	C₂×Q₈	—	47	16	no	—
90	C₂×Q₈	—	47	8	no	—
91	C₂×Q₈	—	47	16	no	—
92	C₂×Q₈	—	188	8	no	—
93	C₂×Q₈	C₂²×D₄₇	1	8	yes	—
94	C₂²×C₄	—	47	4	no	—
95	C₂²×C₄	—	47	4	no	—
96	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
97	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
99	C₄⋊C₄	—	47	32	no	—
100	C₄⋊C₄	—	47	16	no	—
101	C₄⋊C₄	—	47	8	no	—
102	C₄⋊C₄	C₂²×D₄₇	1	16	yes	—
103	C₄²	—	47	16	no	—
104	C₄²	—	47	16	no	—
105	C₄²	C₂²×D₄₇	1	4	yes	—
106	C₂³	C₂³×D₄₇	1	1	yes	characteristic
107	Q₈	—	4	8	no	—
108	Q₈	—	47	32	no	—
109	Q₈	—	188	16	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	2	8	no	—
112	C₂×C₄	—	47	16	no	—
113	C₂×C₄	—	47	8	no	—
114	C₂×C₄	—	47	8	no	—
115	C₂×C₄	—	94	8	no	—
116	C₂×C₄	Q₈×D₄₇	1	8	yes	—
117	C₂×C₄	C₂³×D₄₇	1	8	yes	—
118	C₂×C₄	C₂³×D₄₇	1	2	yes	—
119	C₂×C₄	C₂³×D₄₇	1	4	yes	—
120	C₂²	C₂×Q₈×D₄₇	1	4	yes	—
121	C₂²	#13094069	1	2	yes	—
122	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
123	C₄	—	2	2	no	—
124	C₄	—	2	8	no	—
125	C₄	—	47	16	no	—
126	C₄	—	94	8	no	—
127	C₄	C₂×Q₈×D₄₇	1	8	yes	—
128	C₂	#15689853	1	4	yes	direct product factor
129	C₂	C₂²×Q₈×D₄₇	1	2	yes	—
130	C₂	C₂×#13094069	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689853

C₂

yes

maximal, direct product factor

C₂×#13094023

C₂

yes

maximal

C₂×#13094022

C₂

yes

maximal

C₂×C₄×Dic₉₄

C₂

yes

maximal

C₂×#13093989

C₂

yes

maximal

C₂×C₄⋊Q₈×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

—

C₂²×Dic₉₄

C₂²

yes

—

#13094023

C₂²

yes

—

#13094022

C₂²

yes

—

C₄×Dic₉₄

C₂²

yes

—

#13093989

C₂²

yes

—

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

—

C₂²×Q₈×C₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

Q₈

yes

complemented

C₂×Dic₉₄

C₂³

yes

—

C₂×Dic₉₄

C₂³

yes

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₄²×C₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

C₂³

yes

—

Dic₄₇⋊C₄

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

C₂⁴

yes

—

C₂×Dic₄₇

C₂⁴

yes

—

Dic₉₄

—

Dic₉₄

C₂×Q₈

yes

complemented

C₂²×C₄₇

C₂²×Q₈

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

C₂⁵

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²×Q₈

yes

—

Dic₄₇

—

Dic₄₇

C₂²×Q₈

yes

—

C₂×Q₈²

—

maximal, Sylow

C₂×C₄₇

Q₈²

yes

complemented

C₂×C₄₇

C₂³×Q₈

yes

—

C₂×C₄₇

C₂×H(5,𝔽₂)

yes

characteristic

Q₈²

—

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

D₄₇

yes

characteristic

C₂×C₄×Q₈

—

C₂×C₄×Q₈

—

C₄₇

C₂×Q₈²

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₇

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₇

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

188

—

C₂×Q₈

C₂²×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

C₂²×D₄₇

yes

—

103

C₄²

—

104

C₄²

—

105

C₄²

C₂²×D₄₇

yes

—

106

C₂³

C₂³×D₄₇

yes

characteristic

107

Q₈

—

108

Q₈

—

109

Q₈

—

188

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

Q₈×D₄₇

yes

—

117

C₂×C₄

C₂³×D₄₇

yes

—

118

C₂×C₄

C₂³×D₄₇

yes

—

119

C₂×C₄

C₂³×D₄₇

yes

—

120

C₂²

C₂×Q₈×D₄₇

yes

—

121

C₂²

#13094069

yes

—

122

C₂²

C₂⁴×D₄₇

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

C₂×Q₈×D₄₇

yes

—

128

C₂

#15689853

yes

direct product factor

129

C₂

C₂²×Q₈×D₄₇

yes

—

130

C₂

C₂×#13094069

yes

characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁵
Frattini	C₂²	C₂⁴×D₄₇
Fitting	C₂×C₄⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	C₂×Q₈²
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂³×D₄₇

commutator

C₂²×C₄₇

C₂⁵

Frattini

C₂²

C₂⁴×D₄₇

Fitting

C₂×C₄⋊Q₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂⁴

hypercenter

C₂×C₄⋊Q₈

D₄₇

hypocenter

C₄₇

C₂×Q₈²

LCS

G ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
1. #15689853	C₂	direct (N × H)
30. C₂×Dic₉₄	Q₈	semidirect
53. Dic₉₄	C₂×Q₈	semidirect
63. C₂×C₄₇	Q₈²	semidirect
72. C₄₇	C₂×Q₈²	semidirect
128. C₂	#15689853	direct (N × H)

H ≅ G/N

type

1. #15689853

C₂

direct (N × H)

30. C₂×Dic₉₄

Q₈

semidirect

53. Dic₉₄

C₂×Q₈

semidirect

63. C₂×C₄₇

Q₈²

semidirect

72. C₄₇

C₂×Q₈²

semidirect

128. C₂

#15689853

direct (N × H)

Subgroups — C₂×#15689853 #20256963

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689853 #20256963

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689853 #20256963