Group #21444895 — subgroups

Subgroups — #21444895

Order 7808.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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	#16840492	C₂	1	1	yes	maximal, characteristic, complemented
2	#16839959	C₂	1	2	yes	maximal
3	#16839511	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839494	C₂	1	2	yes	maximal, complemented
5	C₆₁×#492	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758200	—	2	2	no	—
7	#14519776	—	2	2	no	—
8	#14519775	—	2	2	no	—
9	C₄×Dic₁₂₂	C₂²	1	2	yes	—
10	#14519742	—	2	2	no	—
11	C₄⋊#92418	C₂²	1	2	yes	—
12	#14519698	—	2	2	no	—
13	C₂×SD₁₆×C₆₁	—	2	2	no	—
14	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	#127×C₆₁	C₂²	1	1	yes	characteristic
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₆₁	D₄	1	2	yes	—
18	C₂×D₄×C₆₁	—	2	1	no	—
19	C₂×D₄×C₆₁	—	2	2	no	—
20	C₂×Dic₁₂₂	—	2	2	no	—
21	C₂×Dic₁₂₂	D₄	1	2	yes	—
22	SD₁₆×C₆₁	—	4	4	no	—
23	C₂×C₈×C₆₁	—	2	1	no	—
24	C₄⋊C₄×C₆₁	—	2	2	no	—
25	C₄²×C₆₁	C₂³	1	1	yes	characteristic
26	#11758200	—	4	4	no	—
27	C₄⋊Dic₆₁	D₄	1	2	yes	—
28	#11758196	—	2	4	no	—
29	#11758196	—	2	2	no	—
30	C₄×Dic₆₁	—	2	2	no	—
31	C₄×Dic₆₁	—	2	2	no	—
32	C₂×#92418	—	2	2	no	—
33	C₂³×C₆₁	—	4	1	no	—
34	Q₈×C₆₁	—	4	2	no	—
35	D₄×C₆₁	—	4	2	no	—
36	D₄×C₆₁	—	4	2	no	—
37	D₄×C₆₁	—	4	2	no	—
38	C₂×C₄×C₆₁	—	2	2	no	—
39	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
41	C₂×Dic₆₁	—	2	2	no	—
42	C₂×Dic₆₁	—	2	2	no	—
43	Dic₁₂₂	—	2	2	no	—
44	Dic₁₂₂	—	8	2	no	—
45	Dic₁₂₂	SD₁₆	1	4	yes	complemented
46	C₈×C₆₁	—	2	2	no	—
47	#92418	—	4	2	no	—
48	C₂²×C₆₁	—	8	2	no	—
49	C₂²×C₆₁	—	8	1	no	—
50	C₂²×C₆₁	#120	1	1	yes	characteristic
51	C₄×C₆₁	—	2	1	no	—
52	C₄×C₆₁	—	4	2	no	—
53	C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
54	C₄×C₆₁	#137	1	2	yes	—
55	Dic₆₁	—	2	4	no	—
56	Dic₆₁	—	4	2	no	—
57	#1623	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	—	16	1	no	—
59	C₂×C₆₁	#448	1	2	yes	—
60	C₂×C₆₁	#453	1	1	yes	characteristic
61	Q₈²	—	61	1	no	—
62	#492	D₆₁	1	1	yes	characteristic
63	#460	—	61	2	no	—
64	#333	—	61	1	no	—
65	Q₈⋊C₈	—	61	2	no	—
66	C₆₁	#1623	1	1	yes	characteristic, complemented, Sylow
67	C₂×SD₁₆	—	2	2	no	—
68	C₂×SD₁₆	—	122	2	no	—
69	C₄⋊Q₈	—	122	2	no	—
70	C₄⋊Q₈	—	122	2	no	—
71	C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
72	#127	C₂×D₆₁	1	1	yes	characteristic
73	C₄×Q₈	—	61	2	no	—
74	C₄×Q₈	—	122	2	no	—
75	C₄⋊C₈	—	61	2	no	—
76	#102	—	122	2	no	—
77	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
78	C₂×Q₈	—	61	2	no	—
79	C₂×Q₈	—	122	2	no	—
80	C₂×Q₈	C₂²⋊D₆₁	1	2	yes	—
81	C₂×D₄	—	2	2	no	—
82	C₂×D₄	—	2	1	no	—
83	SD₁₆	—	4	4	no	—
84	SD₁₆	—	244	4	no	—
85	C₂×C₈	—	2	1	no	—
86	C₂×C₈	—	122	2	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	61	2	no	—
89	C₄⋊C₄	—	122	4	no	—
90	C₄⋊C₄	—	122	2	no	—
91	C₄²	—	122	2	no	—
92	C₄²	—	122	2	no	—
93	C₄²	C₂²×D₆₁	1	1	yes	characteristic
94	C₂³	—	4	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	61	4	no	—
97	Q₈	—	122	2	no	—
98	Q₈	—	488	2	no	—
99	D₄	—	4	2	no	—
100	D₄	—	4	2	no	—
101	D₄	—	4	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	122	2	no	—
104	C₂×C₄	—	122	2	no	—
105	C₂×C₄	D₄×D₆₁	1	2	yes	—
106	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
107	C₈	—	2	2	no	—
108	C₈	—	244	2	no	—
109	C₂²	—	8	2	no	—
110	C₂²	—	8	1	no	—
111	C₂²	#14519745	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	4	2	no	—
114	C₄	—	122	4	no	—
115	C₄	—	244	2	no	—
116	C₄	SD₁₆×D₆₁	1	2	yes	—
117	C₄	#14519806	1	2	yes	—
118	C₂	—	16	1	no	—
119	C₂	#16839899	1	2	yes	—
120	C₂	#16839929	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840492

C₂

yes

maximal, characteristic, complemented

#16839959

C₂

yes

maximal

#16839511

C₂

yes

maximal, characteristic, complemented

#16839494

C₂

yes

maximal, complemented

C₆₁×#492

C₂

yes

maximal, characteristic

C₂×#11758200

—

#14519776

—

#14519775

—

C₄×Dic₁₂₂

C₂²

yes

—

#14519742

—

C₄⋊#92418

C₂²

yes

—

#14519698

—

C₂×SD₁₆×C₆₁

—

C₄⋊Q₈×C₆₁

C₂²

yes

characteristic

#127×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

D₄

yes

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

D₄

yes

—

SD₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

C₂³

yes

characteristic

#11758200

—

C₄⋊Dic₆₁

D₄

yes

—

#11758196

—

#11758196

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₂×#92418

—

C₂³×C₆₁

—

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

Dic₁₂₂

SD₁₆

yes

complemented

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#120

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×SD₁₆

yes

—

C₄×C₆₁

#137

yes

—

Dic₆₁

—

Dic₆₁

—

#1623

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#448

yes

—

C₂×C₆₁

#453

yes

characteristic

Q₈²

—

#492

D₆₁

yes

characteristic

#460

—

#333

—

Q₈⋊C₈

—

C₆₁

#1623

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×SD₁₆

—

122

—

C₄⋊Q₈

—

122

—

C₄⋊Q₈

—

122

—

C₄⋊Q₈

C₂×D₆₁

yes

characteristic

#127

C₂×D₆₁

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

122

—

C₄⋊C₈

—

#102

—

122

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

122

—

C₂×Q₈

C₂²⋊D₆₁

yes

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

SD₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

Q₈

—

122

—

Q₈

—

488

—

D₄

—

100

D₄

—

101

D₄

—

102

C₂×C₄

—

103

C₂×C₄

—

122

—

104

C₂×C₄

—

122

—

105

C₂×C₄

D₄×D₆₁

yes

—

106

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

107

C₈

—

108

C₈

—

244

—

109

C₂²

—

110

C₂²

—

111

C₂²

#14519745

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

122

—

115

C₄

—

244

—

116

C₄

SD₁₆×D₆₁

yes

—

117

C₄

#14519806

yes

—

118

C₂

—

119

C₂

#16839899

yes

—

120

C₂

#16839929

yes

characteristic

	subgroup	G/H
center	C₂²	#14519745
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#492	C₂
socle	C₂²×C₆₁	#120
hypercenter	#492	D₆₁
hypocenter	C₆₁	#1623
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#14519745

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#492

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
1. #16840492	C₂	semidirect
3. #16839511	C₂	semidirect
4. #16839494	C₂	semidirect
45. Dic₁₂₂	SD₁₆	semidirect
66. C₆₁	#1623	semidirect

H ≅ G/N

type

1. #16840492

C₂

semidirect

3. #16839511

C₂

semidirect

4. #16839494

C₂

semidirect

45. Dic₁₂₂

SD₁₆

semidirect

66. C₆₁

#1623

semidirect

Subgroups — #21444895

Conjugacy classes of subgroups

Complements