Group #20246587 — subgroups

Subgroups — C₂×#15689034 #20246587

Order 6016.

1036 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 269 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	C₂²×(C₂×D₄₇)⋊C₄	C₂	1	3	yes	maximal
2	#15689034	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄₇⋊#95	C₂	1	3	yes	maximal, complemented
4	C₂³×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₄₇	C₂²	1	1	yes	characteristic
6	C₂³×Dic₄₇	C₂²	1	3	yes	—
7	C₂×(C₂×D₄₇)⋊C₄	—	2	12	no	—
8	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	12	yes	—
9	C₄₇⋊#95	C₂²	1	12	yes	complemented
10	C₂²×Q₈×C₄₇	—	2	12	no	—
11	C₂²×Q₈×C₄₇	C₂²	1	4	yes	complemented
12	C₂³×C₄×C₄₇	C₂²	1	3	yes	—
13	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
14	C₂³×D₄₇	—	2	6	no	—
15	C₂³×D₄₇	—	2	6	no	—
16	C₂³×D₄₇	Q₈	1	4	yes	complemented
17	C₂³×D₄₇	C₂³	1	2	yes	—
18	C₂×Q₈×C₄₇	—	2	32	no	—
19	C₂×Q₈×C₄₇	—	2	24	no	—
20	C₂²×C₄×C₄₇	—	2	12	no	—
21	C₂²×C₄×C₄₇	D₄	1	12	yes	—
22	C₂²×C₄×C₄₇	C₂³	1	6	yes	—
23	C₂²×Dic₄₇	—	2	6	no	—
24	C₂²×Dic₄₇	—	2	12	no	—
25	C₂²×Dic₄₇	C₂³	1	6	yes	—
26	(C₂×D₄₇)⋊C₄	—	2	24	no	—
27	C₂³×C₄₇	C₂×D₄	1	6	yes	—
28	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
29	C₂³×C₄₇	#41	1	6	yes	—
30	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
31	C₂²×D₄₇	—	2	24	no	—
32	C₂²×D₄₇	—	2	6	no	—
33	C₂²×D₄₇	—	2	6	no	—
34	C₂²×D₄₇	—	4	4	no	—
35	C₂²×D₄₇	—	4	12	no	—
36	C₂²×D₄₇	C₂×Q₈	1	4	yes	complemented
37	Q₈×C₄₇	—	2	32	no	—
38	C₂×C₄×C₄₇	—	2	24	no	—
39	C₂×C₄×C₄₇	—	2	12	no	—
40	C₂×C₄×C₄₇	C₂×D₄	1	12	yes	—
41	C₂×Dic₄₇	—	2	6	no	—
42	C₂×Dic₄₇	—	2	12	no	—
43	C₂×Dic₄₇	—	4	12	no	—
44	C₂²×C₄₇	#120	1	4	yes	—
45	C₂²×C₄₇	C₂²⋊Q₈	1	12	yes	—
46	C₂²×C₄₇	#124	1	12	yes	—
47	C₂²×C₄₇	C₂²×D₄	1	3	yes	—
48	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
49	C₂²×C₄₇	C₂×#41	1	3	yes	—
50	C₂×D₄₇	—	2	12	no	—
51	C₂×D₄₇	—	4	2	no	—
52	C₂×D₄₇	—	4	6	no	—
53	C₂×D₄₇	—	4	16	no	—
54	C₄×C₄₇	—	2	12	no	—
55	Dic₄₇	—	4	6	no	—
56	C₂×#393	—	47	1	no	maximal, Sylow
57	C₂×C₄₇	#393	1	8	yes	complemented
58	C₂×C₄₇	C₂×#120	1	1	yes	characteristic
59	C₂×C₄₇	C₂×C₂²⋊Q₈	1	3	yes	—
60	C₂×C₄₇	C₂×#124	1	3	yes	—
61	D₄₇	—	4	4	no	—
62	C₂³×Q₈	D₄₇	1	1	yes	characteristic, complemented
63	C₂²×C₂²⋊C₄	—	47	3	no	—
64	#393	—	47	8	no	—
65	C₂×#95	—	47	3	no	—
66	C₄₇	C₂×#393	1	1	yes	characteristic, complemented, Sylow
67	C₂⁵	—	47	1	no	—
68	C₂²×Q₈	—	2	12	no	—
69	C₂²×Q₈	C₂×D₄₇	1	4	yes	complemented
70	C₂³×C₄	—	47	3	no	—
71	C₂³×C₄	C₂×D₄₇	1	3	yes	—
72	C₂×C₂²⋊C₄	—	47	12	no	—
73	C₂×C₂²⋊C₄	—	94	12	no	—
74	#95	—	47	12	no	—
75	C₂⁴	—	47	4	no	—
76	C₂⁴	—	47	2	no	—
77	C₂⁴	—	94	6	no	—
78	C₂⁴	—	94	6	no	—
79	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
80	C₂×Q₈	—	2	32	no	—
81	C₂×Q₈	—	2	24	no	—
82	C₂²×C₄	—	2	12	no	—
83	C₂²×C₄	—	47	6	no	—
84	C₂²×C₄	—	94	12	no	—
85	C₂²×C₄	—	94	6	no	—
86	C₂²×C₄	C₂²⋊D₄₇	1	12	yes	—
87	C₂²×C₄	C₂²×D₄₇	1	6	yes	—
88	C₂²⋊C₄	—	94	24	no	—
89	C₂³	—	47	4	no	—
90	C₂³	—	94	24	no	—
91	C₂³	—	94	6	no	—
92	C₂³	—	94	6	no	—
93	C₂³	—	188	4	no	—
94	C₂³	—	188	12	no	—
95	C₂³	Q₈×D₄₇	1	2	yes	—
96	C₂³	#10625354	1	6	yes	—
97	C₂³	C₂×C₂²⋊D₄₇	1	6	yes	—
98	C₂³	C₂³×D₄₇	1	1	yes	characteristic
99	Q₈	—	2	32	no	—
100	C₂×C₄	—	2	24	no	—
101	C₂×C₄	—	2	12	no	—
102	C₂×C₄	—	94	6	no	—
103	C₂×C₄	—	94	12	no	—
104	C₂×C₄	—	188	12	no	—
105	C₂×C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
106	C₂²	—	94	12	no	—
107	C₂²	—	188	16	no	—
108	C₂²	—	188	2	no	—
109	C₂²	—	188	6	no	—
110	C₂²	#13093993	1	4	yes	—
111	C₂²	#13094000	1	12	yes	—
112	C₂²	#13094013	1	12	yes	—
113	C₂²	C₂²×C₂²⋊D₄₇	1	3	yes	—
114	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
115	C₂²	C₂×#10625354	1	3	yes	—
116	C₄	—	2	12	no	—
117	C₄	—	188	6	no	—
118	C₂	—	188	4	no	—
119	C₂	#15689034	1	8	yes	direct product factor
120	C₂	C₂×#13093993	1	1	yes	characteristic
121	C₂	C₂×#13094000	1	3	yes	—
122	C₂	C₂×#13094013	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×(C₂×D₄₇)⋊C₄

C₂

yes

maximal

#15689034

C₂

yes

maximal, direct product factor

C₂×C₄₇⋊#95

C₂

yes

maximal, complemented

C₂³×Q₈×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂⁴×D₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

complemented

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

C₂²

yes

complemented

C₂³×C₄×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂³×D₄₇

—

C₂³×D₄₇

—

C₂³×D₄₇

Q₈

yes

complemented

C₂³×D₄₇

C₂³

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

(C₂×D₄₇)⋊C₄

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂×Q₈

yes

complemented

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

#120

yes

—

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

#124

yes

—

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

C₂×C₂²⋊Q₈

yes

—

C₂×C₄₇

C₂×#124

yes

—

D₄₇

—

C₂³×Q₈

D₄₇

yes

characteristic, complemented

C₂²×C₂²⋊C₄

—

#393

—

C₂×#95

—

C₄₇

C₂×#393

yes

characteristic, complemented, Sylow

C₂⁵

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₇

yes

complemented

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

188

—

C₂³

—

188

—

C₂³

Q₈×D₄₇

yes

—

C₂³

#10625354

yes

—

C₂³

C₂×C₂²⋊D₄₇

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

188

—

105

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

106

C₂²

—

107

C₂²

—

188

—

108

C₂²

—

188

—

109

C₂²

—

188

—

110

C₂²

#13093993

yes

—

111

C₂²

#13094000

yes

—

112

C₂²

#13094013

yes

—

113

C₂²

C₂²×C₂²⋊D₄₇

yes

—

114

C₂²

C₂×Q₈×D₄₇

yes

characteristic

115

C₂²

C₂×#10625354

yes

—

116

C₄

—

117

C₄

—

188

—

118

C₂

—

188

—

119

C₂

#15689034

yes

direct product factor

120

C₂

C₂×#13093993

yes

characteristic

121

C₂

C₂×#13094000

yes

—

122

C₂

C₂×#13094013

yes

—

	subgroup	G/H
center	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂⁴
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂³×Q₈×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂³×Q₈	D₄₇
hypocenter	C₄₇	C₂×#393
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×Q₈

subgroup

G/H

center

C₂⁴

C₂²×D₄₇

commutator

C₂³×C₄₇

C₂⁴

Frattini

C₂³

C₂³×D₄₇

Fitting

C₂³×Q₈×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂³×Q₈

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂³×Q₈

N	H ≅ G/N	type
2. #15689034	C₂	direct (N × H)
3. C₂×C₄₇⋊#95	C₂	semidirect
4. C₂³×Q₈×C₄₇	C₂	semidirect
9. C₄₇⋊#95	C₂²	semidirect
11. C₂²×Q₈×C₄₇	C₂²	semidirect
16. C₂³×D₄₇	Q₈	semidirect
36. C₂²×D₄₇	C₂×Q₈	semidirect
57. C₂×C₄₇	#393	semidirect
62. C₂³×Q₈	D₄₇	semidirect
66. C₄₇	C₂×#393	semidirect
69. C₂²×Q₈	C₂×D₄₇	semidirect
119. C₂	#15689034	direct (N × H)

H ≅ G/N

type

2. #15689034

C₂

direct (N × H)

3. C₂×C₄₇⋊#95

C₂

semidirect

4. C₂³×Q₈×C₄₇

C₂

semidirect

9. C₄₇⋊#95

C₂²

semidirect

11. C₂²×Q₈×C₄₇

C₂²

semidirect

16. C₂³×D₄₇

Q₈

semidirect

36. C₂²×D₄₇

C₂×Q₈

semidirect

57. C₂×C₄₇

#393

semidirect

62. C₂³×Q₈

D₄₇

semidirect

66. C₄₇

C₂×#393

semidirect

69. C₂²×Q₈

C₂×D₄₇

semidirect

119. C₂

#15689034

direct (N × H)

Subgroups — C₂×#15689034 #20246587

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689034 #20246587

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689034 #20246587