Group #21447622 — subgroups

Subgroups — #21447622

Order 7808.

152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 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	C₄⋊#11758185	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11758185	C₂	1	2	yes	maximal
3	#16839538	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758185	C₂²	1	4	yes	—
6	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₆₁	C₄	1	1	yes	characteristic
9	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
10	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
11	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₆₁	C₈	1	1	yes	characteristic
14	C₂²×C₄×C₆₁	C₈	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	—	2	2	no	—
17	C₂×C₈×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
22	C₄²×C₆₁	C₈	1	1	yes	characteristic
23	C₄²×C₆₁	C₈	1	1	yes	characteristic
24	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
26	#11758185	—	2	4	no	—
27	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₆₁	—	2	2	no	—
29	C₂×C₄×C₆₁	—	2	2	no	—
30	C₂×C₄×C₆₁	—	2	1	no	—
31	C₂×C₄×C₆₁	—	2	1	no	—
32	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₆₁	—	2	1	no	—
39	C₈×C₆₁	—	2	1	no	—
40	C₈×C₆₁	M₁₆	1	2	yes	—
41	C₈×C₆₁	#41	1	2	yes	—
42	C₂²×C₆₁	—	2	1	no	—
43	C₂²×C₆₁	—	2	1	no	—
44	C₂²×C₆₁	M₃₂	1	2	yes	—
45	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
46	C₄×C₆₁	—	2	1	no	—
47	C₄×C₆₁	—	2	1	no	—
48	C₄×C₆₁	—	2	1	no	—
49	C₄×C₆₁	—	2	1	no	—
50	C₄×C₆₁	M₃₂	1	2	yes	—
51	C₄×C₆₁	#117	1	1	yes	characteristic
52	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
53	#2163	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	—	2	2	no	—
55	C₂×C₆₁	#431	1	1	yes	characteristic
56	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
57	C₂×C₆₁	C₂×M₃₂	1	1	yes	characteristic
58	C₂×C₄×C₈	D₆₁	1	1	yes	characteristic
59	C₄⋊C₁₆	—	61	2	no	—
60	C₂²⋊C₁₆	—	61	2	no	—
61	#346	—	61	2	no	—
62	C₆₁	#2163	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₈	Dic₆₁	1	1	yes	characteristic
64	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
65	C₂×C₄²	Dic₆₁	1	1	yes	characteristic
66	C₂×C₁₆	—	61	4	no	—
67	C₄×C₈	Dic₆₁	1	1	yes	characteristic
68	C₄×C₈	Dic₆₁	1	1	yes	characteristic
69	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
70	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
71	C₂²×C₄	#92418	1	1	yes	characteristic
72	C₂²×C₄	#92418	1	1	yes	characteristic
73	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
77	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
78	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
79	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
80	C₄²	#92418	1	1	yes	characteristic
81	C₄²	#92418	1	1	yes	characteristic
82	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
83	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
84	C₁₆	—	122	4	no	—
85	C₂³	C₂×#92418	1	1	yes	characteristic
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	C₂×#92418	1	1	yes	characteristic
91	C₂×C₄	C₂×#92418	1	1	yes	characteristic
92	C₂×C₄	C₂×#92418	1	1	yes	characteristic
93	C₂×C₄	C₂×#92418	1	1	yes	characteristic
94	C₂×C₄	C₂×#92418	1	1	yes	characteristic
95	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	2	1	no	—
98	C₈	#11758194	1	2	yes	—
99	C₈	#11758222	1	2	yes	—
100	C₂²	—	2	1	no	—
101	C₂²	—	2	1	no	—
102	C₂²	#14519717	1	2	yes	—
103	C₂²	C₂²×#92418	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	#14519717	1	2	yes	—
109	C₄	#14519736	1	1	yes	characteristic
110	C₄	C₂×#11758194	1	1	yes	characteristic
111	C₂	—	2	2	no	—
112	C₂	#16839815	1	1	yes	characteristic
113	C₂	C₂×#14519717	1	1	yes	characteristic
114	C₂	C₂×#14519717	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#11758185

C₂

yes

maximal, complemented

C₂²⋊#11758185

C₂

yes

maximal

#16839538

C₂

yes

maximal, complemented

C₂×C₄×C₈×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758185

C₂²

yes

—

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄²×C₆₁

C₄

yes

characteristic

C₄×C₈×C₆₁

C₄

yes

characteristic

C₄×C₈×C₆₁

C₄

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

C₈

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₈

yes

characteristic

C₄²×C₆₁

C₈

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758185

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

—

C₈×C₆₁

#41

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

M₃₂

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

M₃₂

yes

—

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

#2163

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#431

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

characteristic

C₂×C₄×C₈

D₆₁

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₆₁

#2163

yes

characteristic, complemented, Sylow

C₂²×C₈

Dic₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄²

Dic₆₁

yes

characteristic

C₂×C₁₆

—

C₄×C₈

Dic₆₁

yes

characteristic

C₄×C₈

Dic₆₁

yes

characteristic

C₄×C₈

C₂×D₆₁

yes

characteristic

C₄×C₈

C₂×D₆₁

yes

C₂²×C₄

yes

C₂²×C₄

yes

C₂²×C₄

C₂×Dic₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

C₄²

yes

C₄²

yes

C₄²

C₂×Dic₆₁

yes

characteristic

C₄²

C₂×Dic₆₁

yes

characteristic

C₁₆

—

122

—

C₂³

C₂×#92418

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₈

—

C₈

—

C₈

#11758194

yes

—

C₈

#11758222

yes

—

100

C₂²

—

101

C₂²

—

102

C₂²

#14519717

yes

—

103

C₂²

C₂²×#92418

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

#14519717

yes

—

109

C₄

#14519736

yes

characteristic

110

C₄

C₂×#11758194

yes

characteristic

111

C₂

—

112

C₂

#16839815

yes

characteristic

113

C₂

C₂×#14519717

yes

characteristic

114

C₂

C₂×#14519717

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₂×C₄×C₈×C₆₁	C₂
hypercenter	C₂×C₄×C₈	D₆₁
hypocenter	C₆₁	#2163
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₆₁

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₂×C₄×C₈×C₆₁

C₂

hypercenter

C₂×C₄×C₈

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
1. C₄⋊#11758185	C₂	semidirect
3. #16839538	C₂	semidirect
62. C₆₁	#2163	semidirect

H ≅ G/N

type

1. C₄⋊#11758185

C₂

semidirect

3. #16839538

C₂

semidirect

62. C₆₁

#2163

semidirect

Subgroups — #21447622

Conjugacy classes of subgroups

Complements