Group #21443902 — subgroups

Subgroups — #21443902

Order 7808.

140 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14519717	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519687	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#92418	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
6	#14519717	—	2	1	no	—
7	#14519717	C₄	1	2	yes	complemented
8	C₂×#11758185	—	2	1	no	—
9	#14519687	—	2	1	no	—
10	#14519687	—	2	1	no	—
11	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	M₃₂×C₆₁	—	2	1	no	—
13	M₃₂×C₆₁	C₄	1	2	yes	complemented
14	C₂×C₁₆×C₆₁	—	2	1	no	—
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₆₁	C₈	1	2	yes	—
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	Q₈	1	1	yes	characteristic
23	C₄×Dic₆₁	—	2	1	no	—
24	C₄×Dic₆₁	—	2	1	no	—
25	C₂×#92418	—	2	1	no	—
26	C₂×#92418	—	2	1	no	—
27	C₂×#92418	C₈	1	2	yes	—
28	C₁₆×C₆₁	—	2	2	no	—
29	#11758185	—	2	2	no	—
30	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
36	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
37	C₂×Dic₆₁	—	2	2	no	—
38	C₂×Dic₆₁	—	4	2	no	—
39	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
41	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
43	#92418	—	2	2	no	—
44	C₂²×C₆₁	—	2	2	no	—
45	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
46	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
47	C₂²×C₆₁	C₄⋊C₈	1	1	yes	characteristic
48	C₄×C₆₁	#95	1	1	yes	characteristic
49	C₄×C₆₁	#97	1	1	yes	characteristic
50	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
52	Dic₆₁	—	4	2	no	—
53	#1377	—	61	1	no	maximal, Sylow
54	C₂×C₆₁	—	2	1	no	—
55	C₂×C₆₁	—	2	1	no	—
56	C₂×C₆₁	#336	1	1	yes	characteristic
57	C₂×C₆₁	#349	1	2	yes	—
58	C₂×M₃₂	—	61	1	no	—
59	C₂×M₃₂	D₆₁	1	1	yes	characteristic
60	C₂×#97	—	61	1	no	—
61	C₆₁	#1377	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	61	1	no	—
63	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
64	C₂×C₄²	—	61	1	no	—
65	M₃₂	—	2	1	no	—
66	M₃₂	—	61	2	no	—
67	M₃₂	—	122	1	no	—
68	M₃₂	Dic₆₁	1	2	yes	complemented
69	C₂×C₁₆	—	2	1	no	—
70	C₂×C₁₆	—	122	1	no	—
71	#97	—	122	1	no	—
72	#97	—	122	1	no	—
73	C₂²×C₄	—	61	2	no	—
74	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
75	C₂×C₈	—	61	2	no	—
76	C₂×C₈	—	122	1	no	—
77	C₂×C₈	—	122	1	no	—
78	C₂×C₈	Dic₁₂₂	1	1	yes	characteristic
79	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
80	C₂×C₈	D₂₄₄	1	1	yes	characteristic
81	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
84	C₄²	—	122	1	no	—
85	C₄²	—	122	1	no	—
86	C₁₆	—	2	2	no	—
87	C₁₆	—	122	2	no	—
88	C₂³	C₈×D₆₁	1	1	yes	characteristic
89	C₂×C₄	—	122	2	no	—
90	C₂×C₄	—	244	2	no	—
91	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
92	C₂×C₄	#11758189	1	1	yes	characteristic
93	C₂×C₄	#11758189	1	1	yes	characteristic
94	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
95	C₂×C₄	#11758196	1	1	yes	characteristic
96	C₂×C₄	#11758198	1	1	yes	characteristic
97	C₈	—	122	2	no	—
98	C₈	#11758196	1	1	yes	characteristic
99	C₈	C₄⋊Dic₆₁	1	1	yes	characteristic
100	C₈	#11758198	1	1	yes	characteristic
101	C₈	C₂²⋊Dic₆₁	1	1	yes	characteristic
102	C₂²	—	2	2	no	—
103	C₂²	C₈×Dic₆₁	1	1	yes	characteristic
104	C₂²	#14519689	1	1	yes	characteristic
105	C₂²	#14519706	1	1	yes	characteristic
106	C₄	—	244	2	no	—
107	C₄	#14519684	1	1	yes	characteristic
108	C₄	#14519687	1	1	yes	characteristic
109	C₄	#14519689	1	1	yes	characteristic
110	C₄	#14519706	1	1	yes	characteristic
111	C₂	—	2	1	no	—
112	C₂	—	2	1	no	—
113	C₂	#16839516	1	1	yes	characteristic
114	C₂	#16839543	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, characteristic

C₂×#14519687

C₂

yes

maximal, characteristic

C₂×M₃₂×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₄

yes

characteristic

#14519717

—

#14519717

C₄

yes

—

—

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

M₃₂×C₆₁

—

M₃₂×C₆₁

C₄

yes

complemented

C₂×C₁₆×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₈

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

characteristic

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₂×#92418

—

C₂×#92418

—

C₂×#92418

C₈

yes

—

C₁₆×C₆₁

—

#11758185

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

C₂²⋊C₄

yes

characteristic

C₈×C₆₁

C₂²⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₄⋊C₄

yes

characteristic

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄×C₈

yes

characteristic

C₂²×C₆₁

C₂²⋊C₈

yes

characteristic

C₂²×C₆₁

C₄⋊C₈

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

C₂²⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

Dic₆₁

—

#1377

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#336

yes

characteristic

C₂×C₆₁

#349

yes

—

C₂×M₃₂

—

C₂×M₃₂

D₆₁

yes

characteristic

C₂×#97

—

C₆₁

#1377

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

122

—

M₃₂

Dic₆₁

yes

complemented

C₂×C₁₆

—

C₂×C₁₆

—

122

—

#97

—

122

—

#97

—

122

—

C₂²×C₄

—

C₂²×C₄

C₄×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

Dic₁₂₂

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

D₂₄₄

yes

characteristic

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄²

—

122

—

C₄²

—

122

—

C₁₆

—

C₁₆

—

122

—

C₂³

C₈×D₆₁

yes

characteristic

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

C₈×D₆₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₄×Dic₆₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

122

—

C₈

#11758196

yes

characteristic

C₈

C₄⋊Dic₆₁

yes

characteristic

100

C₈

#11758198

yes

characteristic

101

C₈

C₂²⋊Dic₆₁

yes

characteristic

102

C₂²

—

103

C₂²

C₈×Dic₆₁

yes

characteristic

104

C₂²

#14519689

yes

characteristic

105

C₂²

#14519706

yes

characteristic

106

C₄

—

244

—

107

C₄

#14519684

yes

characteristic

108

C₄

#14519687

yes

characteristic

109

C₄

#14519689

yes

characteristic

110

C₄

#14519706

yes

characteristic

111

C₂

—

112

C₂

—

113

C₂

#16839516

yes

characteristic

114

C₂

#16839543

yes

—

	subgroup	G/H
center	C₂×C₄	#11758198
commutator	C₂²×C₆₁	C₄×C₈
Frattini	C₂²×C₈	C₂×D₆₁
Fitting	C₂×M₃₂×C₆₁	C₂
socle	C₂²×C₆₁	C₂²⋊C₈
hypercenter	C₂×M₃₂	D₆₁
hypocenter	C₆₁	#1377
LCS	G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₄

#11758198

commutator

C₂²×C₆₁

C₄×C₈

Frattini

C₂²×C₈

C₂×D₆₁

Fitting

C₂×M₃₂×C₆₁

C₂

socle

C₂²×C₆₁

C₂²⋊C₈

hypercenter

C₂×M₃₂

D₆₁

hypocenter

C₆₁

#1377

LCS

G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
7. #14519717	C₄	semidirect
13. M₃₂×C₆₁	C₄	semidirect
61. C₆₁	#1377	semidirect
68. M₃₂	Dic₆₁	semidirect

H ≅ G/N

type

7. #14519717

C₄

semidirect

13. M₃₂×C₆₁

C₄

semidirect

61. C₆₁

#1377

semidirect

68. M₃₂

Dic₆₁

semidirect

Subgroups — #21443902

Conjugacy classes of subgroups

Complements