Group #21446599 — subgroups

Subgroups — #21446599

Order 7808.

196 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 93 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	#16839805	C₂	1	2	yes	maximal
3	C₂×#14519709	C₂	1	1	yes	maximal, characteristic
4	#16839530	C₂	1	2	yes	maximal
5	C₆₁×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
8	#14519713	C₄	1	4	yes	complemented
9	#14519710	—	2	2	no	—
10	#14519709	—	2	1	no	—
11	#14519709	—	2	1	no	—
12	#14519708	—	2	2	no	—
13	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	#117×C₆₁	C₂²	1	1	yes	characteristic
16	#97×C₆₁	—	2	1	no	—
17	C₄×C₈×C₆₁	—	2	1	no	—
18	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
19	C₂²×Dic₆₁	—	2	2	no	—
20	M₁₆×C₆₁	—	2	1	no	—
21	M₁₆×C₆₁	Q₈	1	2	yes	—
22	C₂×C₈×C₆₁	—	2	1	no	—
23	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
25	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
26	C₂×C₈×C₆₁	Q₈	1	2	yes	—
27	C₄⋊C₄×C₆₁	D₄	1	2	yes	—
28	C₂²⋊C₄×C₆₁	—	2	1	no	—
29	C₄²×C₆₁	—	2	1	no	—
30	C₄⋊Dic₆₁	—	2	2	no	—
31	C₄⋊Dic₆₁	—	2	2	no	—
32	#11758194	—	2	2	no	—
33	#11758194	C₂×C₄	1	4	yes	—
34	C₂×#92418	—	2	2	no	—
35	C₂³×C₆₁	#41	1	1	yes	characteristic
36	C₂×C₄×C₆₁	—	2	2	no	—
37	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
43	C₂×Dic₆₁	—	4	2	no	—
44	C₂×Dic₆₁	—	8	2	no	—
45	C₈×C₆₁	—	2	2	no	—
46	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
47	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
48	#92418	—	2	4	no	—
49	C₂²×C₆₁	—	2	2	no	—
50	C₂²×C₆₁	C₄×Q₈	1	1	yes	characteristic
51	C₂²×C₆₁	#121	1	1	yes	characteristic
52	C₂²×C₆₁	#125	1	1	yes	characteristic
53	C₄×C₆₁	—	4	2	no	—
54	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
56	C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
57	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
58	Dic₆₁	—	8	2	no	—
59	#1951	—	61	1	no	maximal, Sylow
60	C₂×C₆₁	—	2	1	no	—
61	C₂×C₆₁	—	2	1	no	—
62	C₂×C₆₁	#389	1	1	yes	characteristic
63	C₂×C₆₁	#471	1	2	yes	—
64	C₂×#108	—	61	1	no	—
65	#428	—	61	2	no	—
66	C₂×#106	—	61	1	no	—
67	#405	D₆₁	1	1	yes	characteristic
68	#343	—	61	2	no	—
69	C₆₁	#1951	1	1	yes	characteristic, complemented, Sylow
70	C₂×M₁₆	—	61	2	no	—
71	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
72	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
73	#117	C₂×D₆₁	1	1	yes	characteristic
74	C₂×C₄⋊C₄	—	61	2	no	—
75	#108	—	61	4	no	—
76	#107	—	122	2	no	—
77	#106	—	122	1	no	—
78	#106	—	122	1	no	—
79	#106	—	122	2	no	—
80	#97	—	2	1	no	—
81	C₄×C₈	—	2	1	no	—
82	C₂²×C₄	—	122	2	no	—
83	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
84	M₁₆	—	2	1	no	—
85	M₁₆	—	61	4	no	—
86	M₁₆	—	122	2	no	—
87	M₁₆	Dic₁₂₂	1	2	yes	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	122	2	no	—
90	C₂×C₈	Dic₁₂₂	1	2	yes	—
91	C₂×C₈	C₄×D₆₁	1	2	yes	—
92	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
93	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
94	C₄⋊C₄	—	122	2	no	—
95	C₄⋊C₄	—	122	2	no	—
96	C₄⋊C₄	D₂₄₄	1	2	yes	—
97	C₂²⋊C₄	—	2	1	no	—
98	C₄²	—	2	1	no	—
99	C₂³	#11758222	1	1	yes	characteristic
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	488	2	no	—
102	C₂×C₄	—	244	2	no	—
103	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
104	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
105	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
106	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
107	C₂×C₄	#11758222	1	1	yes	characteristic
108	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
109	C₈	—	2	2	no	—
110	C₈	—	122	4	no	—
111	C₈	#11758196	1	2	yes	—
112	C₈	#11758196	1	2	yes	—
113	C₂²	—	2	2	no	—
114	C₂²	C₄×Dic₁₂₂	1	1	yes	characteristic
115	C₂²	#14519751	1	1	yes	characteristic
116	C₂²	#14519769	1	1	yes	characteristic
117	C₄	—	4	2	no	—
118	C₄	—	488	2	no	—
119	C₄	C₂×#11758196	1	1	yes	characteristic
120	C₄	C₄×D₂₄₄	1	1	yes	characteristic
121	C₄	#14519756	1	1	yes	characteristic
122	C₄	#14519777	1	1	yes	characteristic
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	#16839660	1	1	yes	characteristic
126	C₂	#16840025	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519713

C₂

yes

maximal, characteristic

#16839805

C₂

yes

maximal

C₂×#14519709

C₂

yes

maximal, characteristic

#16839530

C₂

yes

maximal

C₆₁×#405

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

C₂×C₄⋊Dic₆₁

C₂²

yes

—

#14519713

C₄

yes

—

—

—

—

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#117×C₆₁

C₂²

yes

characteristic

#97×C₆₁

—

C₄×C₈×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

Q₈

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

Q₈

yes

—

C₄⋊C₄×C₆₁

D₄

yes

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758194

—

#11758194

C₂×C₄

yes

—

C₂×#92418

—

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

—

C₈×C₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

C₄⋊C₄

yes

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄×Q₈

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

C₂²⋊Q₈

yes

characteristic

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

Dic₆₁

—

#1951

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#389

yes

characteristic

C₂×C₆₁

#471

yes

—

—

—

—

D₆₁

yes

characteristic

#343

—

C₆₁

#1951

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

C₂×D₆₁

yes

characteristic

C₂×C₄⋊C₄

—

#108

—

#107

—

122

—

#106

—

122

—

#106

—

122

—

#106

—

122

—

#97

—

C₄×C₈

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

Dic₁₂₂

yes

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

D₂₄₄

yes

—

C₂²⋊C₄

—

C₄²

—

C₂³

#11758222

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

488

—

102

C₂×C₄

—

244

—

103

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

104

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

105

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

106

C₂×C₄

C₂×D₂₄₄

yes

characteristic

107

C₂×C₄

#11758222

yes

characteristic

108

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

109

C₈

—

110

C₈

—

122

—

111

C₈

#11758196

yes

—

112

C₈

#11758196

yes

—

113

C₂²

—

114

C₂²

C₄×Dic₁₂₂

yes

characteristic

115

C₂²

#14519751

yes

characteristic

116

C₂²

#14519769

yes

characteristic

117

C₄

—

118

C₄

—

488

—

119

C₄

C₂×#11758196

yes

characteristic

120

C₄

C₄×D₂₄₄

yes

characteristic

121

C₄

#14519756

yes

characteristic

122

C₄

#14519777

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

#16839660

yes

characteristic

126

C₂

#16840025

yes

—

	subgroup	G/H
center	C₂²	#14519751
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#405	C₂
socle	C₂²×C₆₁	#121
hypercenter	#405	D₆₁
hypocenter	C₆₁	#1951
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405

subgroup

G/H

center

C₂²

#14519751

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#405

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405

N	H ≅ G/N	type
8. #14519713	C₄	semidirect
69. C₆₁	#1951	semidirect

H ≅ G/N

type

8. #14519713

C₄

semidirect

69. C₆₁

#1951

semidirect

Subgroups — #21446599

Conjugacy classes of subgroups

Complements