Group #21445309 — subgroups

Subgroups — #21445309

Order 7808.

166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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	#16840142	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840043	C₂	1	2	yes	maximal
3	#16839841	C₂	1	1	yes	maximal, characteristic
4	#16839507	C₂	1	2	yes	maximal, complemented
5	C₆₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₄₄	—	2	1	no	—
7	C₂×Dic₂₄₄	—	2	1	no	—
8	C₂×#11758189	—	2	1	no	—
9	#14519777	C₂²	1	2	yes	—
10	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
11	#14519711	—	2	2	no	—
12	C₄⋊#92418	C₂²	1	1	yes	characteristic
13	#14519699	—	2	2	no	—
14	#14519689	—	2	1	no	—
15	C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×D₂₄₄	D₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	—	2	1	no	—
19	C₂×Dic₁₂₂	—	2	2	no	—
20	C₂×C₈×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
23	C₄²×C₆₁	C₂³	1	1	yes	characteristic
24	#11758198	—	2	1	no	—
25	C₄⋊Dic₆₁	—	2	2	no	—
26	C₄⋊Dic₆₁	—	2	2	no	—
27	C₄⋊Dic₆₁	D₄	1	1	yes	characteristic
28	C₂×#92418	—	2	1	no	—
29	Dic₂₄₄	—	4	2	no	—
30	Dic₂₄₄	—	4	2	no	—
31	#11758189	—	4	2	no	—
32	C₂²×D₆₁	—	2	1	no	—
33	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
36	C₂×Dic₆₁	—	2	1	no	—
37	C₂×Dic₆₁	—	4	2	no	—
38	D₂₄₄	—	2	2	no	—
39	C₄×D₆₁	—	4	1	no	—
40	C₄×D₆₁	—	4	1	no	—
41	Dic₁₂₂	—	4	2	no	—
42	Dic₁₂₂	—	4	2	no	—
43	C₈×C₆₁	—	2	1	no	—
44	C₈×C₆₁	—	4	2	no	—
45	C₈×C₆₁	D₈	1	2	yes	—
46	#92418	—	4	1	no	—
47	C₂²×C₆₁	#121	1	1	yes	characteristic
48	C₂×D₆₁	—	4	1	no	—
49	C₂×D₆₁	—	4	1	no	—
50	C₂×D₆₁	—	4	1	no	—
51	C₄×C₆₁	—	2	1	no	—
52	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
53	C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
54	C₄×C₆₁	#137	1	2	yes	—
55	Dic₆₁	—	4	1	no	—
56	Dic₆₁	—	8	2	no	—
57	#1689	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	#459	1	1	yes	characteristic
59	C₂×C₆₁	#470	1	1	yes	characteristic
60	C₂×C₆₁	#473	1	1	yes	characteristic
61	D₆₁	—	8	1	no	—
62	#494	—	61	1	no	—
63	#474	—	61	2	no	—
64	#436	—	61	1	no	—
65	#334	D₆₁	1	1	yes	characteristic, complemented
66	#332	—	61	2	no	—
67	C₆₁	#1689	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₁₆	—	122	1	no	—
69	C₂×Q₁₆	—	122	1	no	—
70	C₂×M₁₆	—	122	1	no	—
71	C₄⋊Q₈	—	61	2	no	—
72	C₄×D₄	—	61	1	no	—
73	#107	—	122	2	no	—
74	C₄⋊C₈	—	61	1	no	—
75	C₄⋊C₈	C₂×D₆₁	1	2	yes	—
76	#102	—	122	2	no	—
77	C₂²⋊C₈	—	122	1	no	—
78	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
79	C₂×Q₈	—	122	2	no	—
80	C₂×D₄	—	61	1	no	—
81	C₂²×C₄	—	122	1	no	—
82	Q₁₆	—	244	2	no	—
83	Q₁₆	—	244	2	no	—
84	M₁₆	—	244	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	122	1	no	—
87	C₂×C₈	D₂₄₄	1	1	yes	characteristic
88	C₂×C₈	D₂₄₄	1	1	yes	characteristic
89	C₄⋊C₄	—	61	1	no	—
90	C₄⋊C₄	—	122	2	no	—
91	C₄⋊C₄	—	122	2	no	—
92	C₂²⋊C₄	—	122	1	no	—
93	C₄²	C₂²×D₆₁	1	1	yes	characteristic
94	C₂³	—	122	1	no	—
95	Q₈	—	244	2	no	—
96	Q₈	—	244	2	no	—
97	D₄	—	122	2	no	—
98	C₂×C₄	—	122	1	no	—
99	C₂×C₄	—	244	2	no	—
100	C₂×C₄	—	244	1	no	—
101	C₂×C₄	—	244	1	no	—
102	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
103	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
104	C₂×C₄	#11758226	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	4	2	no	—
107	C₈	—	244	1	no	—
108	C₈	D₄₈₈	1	2	yes	—
109	C₂²	—	244	1	no	—
110	C₂²	—	244	1	no	—
111	C₂²	—	244	1	no	—
112	C₂²	#14519752	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	488	2	no	—
115	C₄	—	244	1	no	—
116	C₄	C₂×D₄₈₈	1	1	yes	characteristic
117	C₄	#14519805	1	1	yes	characteristic
118	C₄	#14519806	1	2	yes	—
119	C₂	—	488	1	no	—
120	C₂	#16839958	1	1	yes	characteristic
121	C₂	#16840021	1	1	yes	characteristic
122	C₂	#16840038	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840142

C₂

yes

maximal, characteristic, complemented

#16840043

C₂

yes

maximal

#16839841

C₂

yes

maximal, characteristic

#16839507

C₂

yes

maximal, complemented

C₆₁×#334

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×#11758189

—

#14519777

C₂²

yes

—

C₄×D₂₄₄

C₂²

yes

characteristic

#14519711

—

C₄⋊#92418

C₂²

yes

characteristic

#14519699

—

#14519689

—

C₄⋊C₈×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×D₂₄₄

D₄

yes

characteristic

C₂×C₄×D₆₁

—

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₄²×C₆₁

C₂³

yes

characteristic

#11758198

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

D₄

yes

characteristic

C₂×#92418

—

Dic₂₄₄

—

Dic₂₄₄

—

#11758189

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

D₂₄₄

—

C₄×D₆₁

—

C₄×D₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

D₈

yes

—

#92418

—

C₂²×C₆₁

#121

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×D₈

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

—

—

—

D₆₁

yes

characteristic, complemented

#332

—

C₆₁

#1689

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

122

—

C₂×Q₁₆

—

122

—

C₂×M₁₆

—

122

—

C₄⋊Q₈

—

C₄×D₄

—

#107

—

122

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₆₁

yes

—

#102

—

122

—

C₂²⋊C₈

—

122

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×D₄

—

C₂²×C₄

—

122

—

Q₁₆

—

244

—

Q₁₆

—

244

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

D₂₄₄

yes

characteristic

C₂×C₈

D₂₄₄

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

122

—

Q₈

—

244

—

Q₈

—

244

—

D₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

100

C₂×C₄

—

244

—

101

C₂×C₄

—

244

—

102

C₂×C₄

C₂×D₂₄₄

yes

characteristic

103

C₂×C₄

D₄×D₆₁

yes

characteristic

104

C₂×C₄

#11758226

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

244

—

108

C₈

D₄₈₈

yes

—

109

C₂²

—

244

—

110

C₂²

—

244

—

111

C₂²

—

244

—

112

C₂²

#14519752

yes

characteristic

113

C₄

—

114

C₄

—

488

—

115

C₄

—

244

—

116

C₄

C₂×D₄₈₈

yes

characteristic

117

C₄

#14519805

yes

characteristic

118

C₄

#14519806

yes

—

119

C₂

—

488

—

120

C₂

#16839958

yes

characteristic

121

C₂

#16840021

yes

characteristic

122

C₂

#16840038

yes

characteristic

	subgroup	G/H
center	C₂²	#14519752
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#334	C₂
socle	C₂²×C₆₁	#121
hypercenter	#334	D₆₁
hypocenter	C₆₁	#1689
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#14519752

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#334

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
1. #16840142	C₂	semidirect
4. #16839507	C₂	semidirect
5. C₆₁×#334	C₂	semidirect
65. #334	D₆₁	semidirect
67. C₆₁	#1689	semidirect

H ≅ G/N

type

1. #16840142

C₂

semidirect

4. #16839507

C₂

semidirect

5. C₆₁×#334

C₂

semidirect

65. #334

D₆₁

semidirect

67. C₆₁

#1689

semidirect

Subgroups — #21445309

Conjugacy classes of subgroups

Complements