Group #21446573 — subgroups

Subgroups — #21446573

Order 7808.

200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14519713	C₂	1	1	yes	maximal, characteristic
2	#16839789	C₂	1	2	yes	maximal
3	C₂×#14519687	C₂	1	1	yes	maximal, characteristic
4	#16839521	C₂	1	2	yes	maximal
5	C₆₁×#427	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	2	yes	—
7	C₂²×#92418	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
9	#14519713	—	2	2	no	—
10	C₄⋊#92418	—	2	4	no	—
11	#14519687	—	2	2	no	—
12	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	#117×C₆₁	C₂²	1	2	yes	—
14	#107×C₆₁	C₄	1	2	yes	complemented
15	#106×C₆₁	C₄	1	2	yes	complemented
16	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
17	C₂²×Dic₆₁	—	2	1	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	D₄	1	2	yes	—
21	C₂×C₈×C₆₁	Q₈	1	2	yes	—
22	C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
23	C₂²⋊C₄×C₆₁	—	2	2	no	—
24	C₄²×C₆₁	—	2	2	no	—
25	C₄×Dic₆₁	—	2	1	no	—
26	C₄×Dic₆₁	Q₈	1	2	yes	—
27	#11758194	—	2	2	no	—
28	#11758194	—	2	2	no	—
29	C₂×#92418	—	2	1	no	—
30	C₂×#92418	—	2	1	no	—
31	C₂×#92418	—	2	2	no	—
32	C₂×#92418	D₄	1	2	yes	—
33	C₂³×C₆₁	#41	1	1	yes	characteristic
34	C₂×C₄×C₆₁	—	2	4	no	—
35	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
41	C₂×Dic₆₁	—	2	2	no	—
42	C₂×Dic₆₁	—	4	2	no	—
43	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
44	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
45	#92418	—	2	2	no	—
46	#92418	—	4	2	no	—
47	C₂²×C₆₁	—	2	2	no	—
48	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
49	C₂²×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₆₁	#125	1	1	yes	characteristic
51	C₄×C₆₁	—	4	4	no	—
52	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
54	C₄×C₆₁	#121	1	1	yes	characteristic
55	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
56	Dic₆₁	—	4	2	no	—
57	#1946	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	—	2	1	no	—
59	C₂×C₆₁	—	2	1	no	—
60	C₂×C₆₁	#389	1	1	yes	characteristic
61	C₂×C₆₁	#444	1	2	yes	—
62	C₂×#108	—	61	1	no	—
63	#427	D₆₁	1	1	yes	characteristic
64	#424	—	61	2	no	—
65	C₂×#97	—	61	1	no	—
66	#339	—	61	2	no	—
67	C₆₁	#1946	1	1	yes	characteristic, complemented, Sylow
68	C₂×M₁₆	—	61	2	no	—
69	C₂²×C₈	—	61	1	no	—
70	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
71	#117	C₂×D₆₁	1	2	yes	—
72	C₂×C₄²	—	61	1	no	—
73	#108	—	122	2	no	—
74	#107	Dic₆₁	1	2	yes	complemented
75	#106	Dic₆₁	1	2	yes	complemented
76	C₄⋊C₈	—	122	4	no	—
77	#97	—	122	2	no	—
78	C₂²×C₄	—	122	1	no	—
79	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
80	M₁₆	—	122	2	no	—
81	M₁₆	—	122	2	no	—
82	C₂×C₈	—	61	2	no	—
83	C₂×C₈	—	122	1	no	—
84	C₂×C₈	—	122	1	no	—
85	C₂×C₈	—	122	2	no	—
86	C₂×C₈	Dic₁₂₂	1	2	yes	—
87	C₂×C₈	D₂₄₄	1	2	yes	—
88	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
89	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
90	C₄⋊C₄	C₂×Dic₆₁	1	4	yes	—
91	C₂²⋊C₄	—	2	2	no	—
92	C₄²	—	2	2	no	—
93	C₄²	—	61	2	no	—
94	C₄²	—	122	1	no	—
95	C₂³	#11758224	1	1	yes	characteristic
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	122	2	no	—
98	C₂×C₄	—	244	2	no	—
99	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
100	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
101	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
102	C₂×C₄	Q₈×D₆₁	1	1	yes	characteristic
103	C₂×C₄	#11758226	1	1	yes	characteristic
104	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
105	C₈	—	122	2	no	—
106	C₈	—	244	2	no	—
107	C₈	C₄⋊Dic₆₁	1	2	yes	—
108	C₈	C₄⋊Dic₆₁	1	2	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	D₄×Dic₆₁	1	1	yes	characteristic
111	C₂²	#14519757	1	1	yes	characteristic
112	C₂²	#14519768	1	1	yes	characteristic
113	C₄	—	4	4	no	—
114	C₄	—	244	2	no	—
115	C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
116	C₄	Q₈×Dic₆₁	1	1	yes	characteristic
117	C₄	#14519752	1	1	yes	characteristic
118	C₄	#14519776	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	2	1	no	—
121	C₂	#16839661	1	1	yes	characteristic
122	C₂	#16839884	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519713

C₂

yes

maximal, characteristic

#16839789

C₂

yes

maximal

C₂×#14519687

C₂

yes

maximal, characteristic

#16839521

C₂

yes

maximal

C₆₁×#427

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

C₂²×#92418

C₂²

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

—

—

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#117×C₆₁

C₂²

yes

—

#107×C₆₁

C₄

yes

complemented

#106×C₆₁

C₄

yes

complemented

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

—

C₂×C₈×C₆₁

Q₈

yes

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

Q₈

yes

—

—

—

—

—

—

D₄

yes

—

C₂³×C₆₁

#41

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

C₄⋊C₄

yes

—

#92418

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₂²×C₆₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₆₁

#125

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₄×Q₈

yes

characteristic

C₄×C₆₁

#121

yes

characteristic

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

Dic₆₁

—

#1946

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#389

yes

characteristic

C₂×C₆₁

#444

yes

—

C₂×#108

—

#427

D₆₁

yes

characteristic

#424

—

C₂×#97

—

#339

—

C₆₁

#1946

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

C₂×D₆₁

yes

—

C₂×C₄²

—

#108

—

122

—

#107

Dic₆₁

yes

complemented

#106

Dic₆₁

yes

complemented

C₄⋊C₈

—

122

—

#97

—

122

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

D₂₄₄

yes

—

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₄⋊C₄

C₂×Dic₆₁

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₂³

#11758224

yes

characteristic

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

100

C₂×C₄

C₂×D₂₄₄

yes

characteristic

101

C₂×C₄

D₄×D₆₁

yes

characteristic

102

C₂×C₄

Q₈×D₆₁

yes

characteristic

103

C₂×C₄

#11758226

yes

characteristic

104

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

105

C₈

—

122

—

106

C₈

—

244

—

107

C₈

C₄⋊Dic₆₁

yes

—

108

C₈

C₄⋊Dic₆₁

yes

—

109

C₂²

—

110

C₂²

D₄×Dic₆₁

yes

characteristic

111

C₂²

#14519757

yes

characteristic

112

C₂²

#14519768

yes

characteristic

113

C₄

—

114

C₄

—

244

—

115

C₄

C₂×C₄⋊Dic₆₁

yes

characteristic

116

C₄

Q₈×Dic₆₁

yes

characteristic

117

C₄

#14519752

yes

characteristic

118

C₄

#14519776

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#16839661

yes

characteristic

122

C₂

#16839884

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#427	C₂
socle	C₂²×C₆₁	C₄×D₄
hypercenter	#427	D₆₁
hypocenter	C₆₁	#1946
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#427

C₂

socle

C₂²×C₆₁

C₄×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

N	H ≅ G/N	type
14. #107×C₆₁	C₄	semidirect
15. #106×C₆₁	C₄	semidirect
67. C₆₁	#1946	semidirect
74. #107	Dic₆₁	semidirect
75. #106	Dic₆₁	semidirect

H ≅ G/N

type

14. #107×C₆₁

C₄

semidirect

15. #106×C₆₁

C₄

semidirect

67. C₆₁

#1946

semidirect

74. #107

Dic₆₁

semidirect

75. #106

Dic₆₁

semidirect

Subgroups — #21446573

Conjugacy classes of subgroups

Complements