Group #21462205 — subgroups

Subgroups — #21462205

Order 7808.

162 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 66 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×#14519852	C₂	1	2	yes	maximal, complemented
2	C₄⋊#11758187	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840657	C₂	1	2	yes	maximal, complemented
4	C₄×#11758187	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839827	C₂	1	1	yes	maximal, characteristic
6	#14519852	—	2	4	no	—
7	C₂×#11758187	C₂²	1	2	yes	—
8	C₂×#11758187	C₂²	1	1	yes	characteristic
9	C₂×#11758187	C₂²	1	1	yes	characteristic
10	C₂×C₈×D₆₁	C₂²	1	2	yes	—
11	C₄×D₂₄₄	C₄	1	1	yes	characteristic
12	#14519689	C₄	1	2	yes	—
13	C₄×#92418	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic
15	C₂×D₂₄₄	C₈	1	1	yes	characteristic
16	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
18	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
19	#11758198	C₈	1	2	yes	—
20	C₄⋊Dic₆₁	C₈	1	1	yes	characteristic
21	C₂×#92418	C₂×C₄	1	1	yes	characteristic
22	C₂×#92418	C₂³	1	1	yes	characteristic
23	C₈×D₆₁	—	2	2	no	—
24	C₈×D₆₁	—	2	2	no	—
25	#11758187	—	2	2	no	—
26	#11758187	—	2	1	no	—
27	#11758187	D₄	1	2	yes	complemented
28	C₂²×D₆₁	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
33	D₂₄₄	—	2	2	no	—
34	C₄×D₆₁	—	2	2	no	—
35	C₄×D₆₁	—	2	2	no	—
36	C₈×C₆₁	—	2	2	no	—
37	#92418	—	2	1	no	—
38	#92418	C₂×D₄	1	1	yes	characteristic
39	#92418	#41	1	1	yes	characteristic
40	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
41	C₂×D₆₁	—	2	2	no	—
42	C₂×D₆₁	—	2	2	no	—
43	C₂×D₆₁	—	2	2	no	—
44	C₄×C₆₁	—	2	1	no	—
45	C₄×C₆₁	M₃₂	1	2	yes	complemented
46	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
47	C₄×C₆₁	#131	1	1	yes	characteristic
48	Dic₆₁	—	2	2	no	—
49	#2169	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	C₈×D₄	1	1	yes	characteristic
51	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
52	C₂×C₆₁	#504	1	1	yes	characteristic
53	D₆₁	—	4	2	no	—
54	C₂×M₃₂	—	61	2	no	—
55	C₈×D₄	—	61	1	no	—
56	C₄⋊C₁₆	—	61	1	no	—
57	C₂²⋊C₁₆	—	61	2	no	—
58	C₄×C₁₆	—	61	1	no	—
59	C₆₁	#2169	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	61	2	no	—
61	C₄×D₄	—	61	1	no	—
62	M₃₂	—	122	4	no	—
63	C₂×C₁₆	—	61	1	no	—
64	C₂×C₁₆	—	61	1	no	—
65	C₂×C₁₆	—	61	2	no	—
66	C₄⋊C₈	#6923	1	1	yes	characteristic
67	C₂²⋊C₈	—	61	2	no	—
68	C₄×C₈	—	61	1	no	—
69	C₂×D₄	—	61	1	no	—
70	C₂²×C₄	—	61	2	no	—
71	C₂×C₈	—	61	1	no	—
72	C₂×C₈	—	61	1	no	—
73	C₂×C₈	—	122	2	no	—
74	C₂×C₈	—	122	2	no	—
75	C₂×C₈	C₂×#6923	1	2	yes	—
76	C₄⋊C₄	—	61	1	no	—
77	C₂²⋊C₄	—	61	2	no	—
78	C₄²	C₂×#6923	1	1	yes	characteristic
79	C₁₆	—	61	2	no	—
80	C₁₆	—	122	1	no	—
81	C₁₆	—	122	2	no	—
82	C₂³	—	61	2	no	—
83	D₄	—	122	2	no	—
84	C₂×C₄	—	61	2	no	—
85	C₂×C₄	—	122	2	no	—
86	C₂×C₄	—	122	2	no	—
87	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
88	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
89	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	61	1	no	—
92	C₈	—	61	1	no	—
93	C₈	—	122	1	no	—
94	C₂²	—	122	2	no	—
95	C₂²	—	122	2	no	—
96	C₂²	—	122	2	no	—
97	C₂²	C₂×D₆₁⋊C₈	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	122	2	no	—
100	C₄	#14519852	1	2	yes	complemented
101	C₄	D₄×#6923	1	1	yes	characteristic
102	C₄	#14519865	1	1	yes	characteristic
103	C₂	—	244	2	no	—
104	C₂	#16840790	1	1	yes	characteristic
105	C₂	C₂×#14519852	1	1	yes	characteristic
106	C₂	#16840821	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519852

C₂

yes

maximal, complemented

C₄⋊#11758187

C₂

yes

maximal, characteristic, complemented

#16840657

C₂

yes

maximal, complemented

C₄×#11758187

C₂

yes

maximal, characteristic, complemented

#16839827

C₂

yes

maximal, characteristic

#14519852

—

C₂×#11758187

C₂²

yes

—

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758187

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

—

C₄×D₂₄₄

C₄

yes

characteristic

#14519689

C₄

yes

—

C₄×#92418

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

C₄

yes

characteristic

C₂×D₂₄₄

C₈

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

C₈

yes

—

C₄⋊Dic₆₁

C₈

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂³

yes

characteristic

C₈×D₆₁

—

C₈×D₆₁

—

#11758187

—

#11758187

—

#11758187

D₄

yes

complemented

C₂²×D₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

—

D₂₄₄

—

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

#92418

—

#92418

C₂×D₄

yes

yes

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

M₃₂

yes

complemented

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

#131

yes

characteristic

Dic₆₁

—

#2169

—

maximal, Sylow

C₂×C₆₁

C₈×D₄

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

C₂×C₆₁

#504

yes

characteristic

D₆₁

—

C₂×M₃₂

—

C₈×D₄

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₆₁

#2169

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₄×D₄

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

#6923

yes

characteristic

C₂²⋊C₈

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂×#6923

yes

characteristic

C₁₆

—

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

—

D₄

—

122

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

D₆₁⋊C₈

yes

characteristic

C₂×C₄

D₆₁⋊C₈

yes

characteristic

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

122

—

C₂²

—

122

—

C₂²

—

122

—

C₂²

—

122

—

C₂²

C₂×D₆₁⋊C₈

yes

characteristic

C₄

—

C₄

—

122

—

100

C₄

#14519852

yes

complemented

101

C₄

D₄×#6923

yes

characteristic

102

C₄

#14519865

yes

characteristic

103

C₂

—

244

—

104

C₂

#16840790

yes

characteristic

105

C₂

C₂×#14519852

yes

characteristic

106

C₂

#16840821

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₄⋊C₈×C₆₁	C₄
hypercenter	C₄⋊C₈	#6923
hypocenter	C₆₁	#2169
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₄⋊C₈×C₆₁

C₄

C₄⋊C₈

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

N	H ≅ G/N	type
1. C₂×#14519852	C₂	semidirect
2. C₄⋊#11758187	C₂	semidirect
3. #16840657	C₂	semidirect
4. C₄×#11758187	C₂	semidirect
27. #11758187	D₄	semidirect
45. C₄×C₆₁	M₃₂	semidirect
59. C₆₁	#2169	semidirect
100. C₄	#14519852	semidirect

H ≅ G/N

type

1. C₂×#14519852

C₂

semidirect

2. C₄⋊#11758187

C₂

semidirect

3. #16840657

C₂

semidirect

4. C₄×#11758187

C₂

semidirect

27. #11758187

D₄

semidirect

45. C₄×C₆₁

M₃₂

semidirect

59. C₆₁

#2169

semidirect

100. C₄

#14519852

semidirect

Subgroups — #21462205

Conjugacy classes of subgroups

Complements