Group #21462155 — subgroups

Subgroups — #21462155

Order 7808.

160 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 76 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	1	yes	maximal, characteristic
2	C₂×D₆₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#16840683	C₂	1	2	yes	maximal, complemented
4	C₄⋊#11758187	C₂	1	2	yes	maximal, complemented
5	#16839719	C₂	1	1	yes	maximal, characteristic
6	#14519852	—	2	2	no	—
7	D₆₁⋊C₁₆	—	2	2	no	—
8	C₂×#11758187	C₂²	1	2	yes	—
9	C₂×#11758187	C₂²	1	2	yes	—
10	C₂×#11758189	C₄	1	1	yes	characteristic
11	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
12	#14519734	C₄	1	1	yes	characteristic
13	#14519687	C₄	1	1	yes	characteristic
14	C₄×#92418	C₂²	1	1	yes	characteristic
15	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
16	#97×C₆₁	C₄	1	1	yes	characteristic
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
21	#11758198	C₈	1	2	yes	—
22	#11758196	C₈	1	2	yes	—
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	C₂×C₄	1	1	yes	characteristic
25	C₂×#92418	C₂³	1	1	yes	characteristic
26	#11758189	—	2	2	no	—
27	C₈×D₆₁	D₄	1	2	yes	—
28	C₈×D₆₁	Q₈	1	2	yes	—
29	#11758187	—	2	2	no	—
30	#11758187	—	2	2	no	—
31	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
35	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
36	C₄×D₆₁	C₄⋊C₄	1	2	yes	—
37	C₄×D₆₁	M₁₆	1	2	yes	—
38	C₈×C₆₁	—	2	1	no	—
39	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
40	#92418	—	2	1	no	—
41	#92418	C₂×D₄	1	1	yes	characteristic
42	#92418	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
44	C₂×D₆₁	—	2	2	no	—
45	C₂×D₆₁	C₄⋊C₈	1	2	yes	—
46	C₄×C₆₁	—	2	2	no	—
47	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
49	Dic₆₁	—	2	2	no	—
50	Dic₆₁	C₄⋊C₈	1	2	yes	—
51	#2151	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
53	C₂×C₆₁	#504	1	2	yes	—
54	D₆₁	—	2	2	no	—
55	C₂×M₃₂	—	61	1	no	—
56	C₂²×C₁₆	—	61	1	no	—
57	#405	—	61	1	no	—
58	C₄⋊C₁₆	—	61	2	no	—
59	C₄⋊C₁₆	—	61	2	no	—
60	C₆₁	#2151	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	61	1	no	—
62	C₂²×C₈	—	61	1	no	—
63	#117	—	61	1	no	—
64	M₃₂	—	122	2	no	—
65	C₂×C₁₆	—	61	2	no	—
66	C₂×C₁₆	—	61	2	no	—
67	C₂×C₁₆	—	122	2	no	—
68	#97	—	61	1	no	—
69	#97	#6923	1	1	yes	characteristic
70	C₄×C₈	—	61	1	no	—
71	C₄×C₈	—	61	1	no	—
72	C₂²×C₄	—	61	1	no	—
73	M₁₆	—	122	2	no	—
74	C₂×C₈	—	61	1	no	—
75	C₂×C₈	—	61	2	no	—
76	C₂×C₈	—	61	2	no	—
77	C₂×C₈	—	61	1	no	—
78	C₂×C₈	C₂×#6923	1	1	yes	characteristic
79	C₂×C₈	C₂×#6923	1	1	yes	characteristic
80	C₄⋊C₄	—	61	2	no	—
81	C₂²⋊C₄	—	61	2	no	—
82	C₄²	—	61	1	no	—
83	C₄²	C₂×#6923	1	1	yes	characteristic
84	C₁₆	—	122	2	no	—
85	C₁₆	—	122	2	no	—
86	C₂³	—	61	1	no	—
87	C₂×C₄	—	61	1	no	—
88	C₂×C₄	—	61	2	no	—
89	C₂×C₄	—	61	2	no	—
90	C₂×C₄	—	61	2	no	—
91	C₂×C₄	D₆₁⋊C₈	1	2	yes	—
92	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	61	1	no	—
95	C₈	—	61	1	no	—
96	C₈	—	122	1	no	—
97	C₈	C₄⋊#6923	1	2	yes	—
98	C₂²	—	61	2	no	—
99	C₂²	—	122	2	no	—
100	C₂²	C₂×D₆₁⋊C₈	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	61	2	no	—
103	C₄	—	122	2	no	—
104	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
105	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
106	C₂	—	122	2	no	—
107	C₂	D₆₁⋊(C₄⋊C₈)	1	1	yes	characteristic
108	C₂	#16840821	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519852

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₁₆

C₂

yes

maximal, characteristic

#16840683

C₂

yes

maximal, complemented

C₄⋊#11758187

C₂

yes

maximal, complemented

#16839719

C₂

yes

maximal, characteristic

#14519852

—

D₆₁⋊C₁₆

—

C₂×#11758187

C₂²

yes

—

C₂×#11758187

C₂²

yes

—

C₂×#11758189

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519734

C₄

yes

characteristic

#14519687

C₄

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

#97×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

C₈

yes

—

#11758196

C₈

yes

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂³

yes

characteristic

#11758189

—

C₈×D₆₁

D₄

yes

—

C₈×D₆₁

Q₈

yes

—

#11758187

—

#11758187

—

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₄×D₆₁

C₄⋊C₄

yes

—

C₄×D₆₁

M₁₆

yes

—

C₈×C₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

—

#92418

—

#92418

C₂×D₄

yes

characteristic

#92418

C₂×Q₈

yes

characteristic

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₄⋊C₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

C₄⋊C₈

yes

—

#2151

—

maximal, Sylow

C₂×C₆₁

C₂×C₄⋊C₈

yes

characteristic

C₂×C₆₁

#504

yes

—

D₆₁

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₆₁

#2151

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₆₁⋊C₈

yes

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

122

—

C₈

C₄⋊#6923

yes

—

C₂²

—

C₂²

—

122

—

100

C₂²

C₂×D₆₁⋊C₈

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

122

—

104

C₄

C₂×C₄⋊#6923

yes

characteristic

105

C₄

D₆₁⋊M₁₆

yes

characteristic

106

C₂

—

122

—

107

C₂

D₆₁⋊(C₄⋊C₈)

yes

characteristic

108

C₂

#16840821

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	#97×C₆₁	C₄
hypercenter	#97	#6923
hypocenter	C₆₁	#2151
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

#97×C₆₁

C₄

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
3. #16840683	C₂	semidirect
4. C₄⋊#11758187	C₂	semidirect
60. C₆₁	#2151	semidirect

H ≅ G/N

type

3. #16840683

C₂

semidirect

4. C₄⋊#11758187

C₂

semidirect

60. C₆₁

#2151

semidirect

Subgroups — #21462155

Conjugacy classes of subgroups

Complements