Group #21445727 — subgroups

Subgroups — #21445727

Order 7808.

220 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 117 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	M₁₆×Dic₆₁	C₂	1	2	yes	maximal
3	C₂×#14519687	C₂	1	1	yes	maximal, characteristic
4	#16839526	C₂	1	2	yes	maximal
5	C₂×#108×C₆₁	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	C₄	1	4	yes	complemented
10	#14519687	—	2	2	no	—
11	#14519687	C₄	1	4	yes	—
12	C₈×Dic₆₁	—	2	2	no	—
13	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	#108×C₆₁	C₄	1	4	yes	complemented
16	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
17	C₂²×Dic₆₁	Q₈	1	2	yes	—
18	M₁₆×C₆₁	—	2	2	no	—
19	M₁₆×C₆₁	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
24	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
25	C₄×Dic₆₁	D₄	1	2	yes	—
26	#11758194	—	2	2	no	—
27	#11758194	C₂×C₄	1	4	yes	—
28	C₂×#92418	—	2	2	no	—
29	C₂×#92418	—	2	1	no	—
30	C₂×#92418	—	2	1	no	—
31	C₂×#92418	C₂×C₄	1	2	yes	—
32	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
38	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
39	C₂×Dic₆₁	—	4	2	no	—
40	C₂×Dic₆₁	C₄⋊C₄	1	4	yes	—
41	C₈×C₆₁	—	2	4	no	—
42	C₈×C₆₁	C₄²	1	4	yes	—
43	#92418	—	2	2	no	—
44	#92418	—	2	4	no	—
45	C₂²×C₆₁	—	2	2	no	—
46	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₆₁	C₄×Q₈	1	1	yes	characteristic
48	C₂²×C₆₁	C₄×Q₈	1	1	yes	characteristic
49	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
50	C₄×C₆₁	#117	1	1	yes	characteristic
51	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
52	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
53	Dic₆₁	—	2	4	no	—
54	#1778	—	61	1	no	maximal, Sylow
55	C₂×C₆₁	—	2	1	no	—
56	C₂×C₆₁	—	2	1	no	—
57	C₂×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₆₁	#430	1	2	yes	—
59	C₂×#108	—	61	1	no	—
60	C₂×#108	D₆₁	1	1	yes	characteristic
61	C₄×M₁₆	—	61	2	no	—
62	C₂×#97	—	61	1	no	—
63	#341	—	61	2	no	—
64	C₆₁	#1778	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₁₆	—	61	2	no	—
66	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
67	C₂²×C₈	—	61	1	no	—
68	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
69	C₂×C₄²	—	61	1	no	—
70	#108	—	61	4	no	—
71	#108	Dic₆₁	1	4	yes	complemented
72	#97	—	61	4	no	—
73	#97	—	122	2	no	—
74	C₄×C₈	—	122	2	no	—
75	C₂²×C₄	—	61	2	no	—
76	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	61	4	no	—
79	M₁₆	—	122	2	no	—
80	M₁₆	C₂×Dic₆₁	1	4	yes	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	61	2	no	—
83	C₂×C₈	—	122	2	no	—
84	C₂×C₈	—	122	1	no	—
85	C₂×C₈	—	122	1	no	—
86	C₂×C₈	C₄×D₆₁	1	2	yes	—
87	C₂×C₈	C₄×D₆₁	1	2	yes	—
88	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
89	C₄²	—	61	2	no	—
90	C₄²	—	61	2	no	—
91	C₂³	Q₈×D₆₁	1	1	yes	characteristic
92	C₂×C₄	—	61	4	no	—
93	C₂×C₄	—	244	2	no	—
94	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
96	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
97	C₂×C₄	#11758224	1	1	yes	characteristic
98	C₂×C₄	#11758226	1	1	yes	characteristic
99	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
100	C₈	—	2	4	no	—
101	C₈	—	122	2	no	—
102	C₈	—	122	4	no	—
103	C₈	C₄×Dic₆₁	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	C₄⋊C₄×D₆₁	1	1	yes	characteristic
106	C₂²	#14519742	1	1	yes	characteristic
107	C₂²	Q₈×Dic₆₁	1	1	yes	characteristic
108	C₄	—	122	4	no	—
109	C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
110	C₄	#14519735	1	1	yes	characteristic
111	C₄	#14519739	1	1	yes	characteristic
112	C₄	D₄×Dic₆₁	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	C₄⋊C₄×Dic₆₁	1	1	yes	characteristic
116	C₂	#16839809	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519713

C₂

yes

maximal, characteristic

M₁₆×Dic₆₁

C₂

yes

maximal

C₂×#14519687

C₂

yes

maximal, characteristic

#16839526

C₂

yes

maximal

C₂×#108×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

C₂²×#92418

C₂²

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519713

C₄

yes

complemented

#14519687

—

#14519687

C₄

yes

—

C₈×Dic₆₁

—

C₂×M₁₆×C₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#108×C₆₁

C₄

yes

complemented

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

Q₈

yes

—

M₁₆×C₆₁

—

M₁₆×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

D₄

yes

—

#11758194

—

#11758194

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂³×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

—

C₈×C₆₁

C₄²

yes

—

#92418

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

C₄×Q₈

yes

characteristic

C₂²×C₆₁

C₄×Q₈

yes

characteristic

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

C₄×D₄

yes

characteristic

Dic₆₁

—

#1778

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₄×C₄⋊C₄

yes

characteristic

C₂×C₆₁

#430

yes

—

C₂×#108

—

C₂×#108

D₆₁

yes

characteristic

C₄×M₁₆

—

C₂×#97

—

#341

—

C₆₁

#1778

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄²

—

#108

—

#108

Dic₆₁

yes

complemented

#97

—

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

122

—

M₁₆

C₂×Dic₆₁

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₄²

—

C₄²

—

C₂³

Q₈×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

D₄×D₆₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

100

C₈

—

101

C₈

—

122

—

102

C₈

—

122

—

103

C₈

C₄×Dic₆₁

yes

—

104

C₂²

—

105

C₂²

C₄⋊C₄×D₆₁

yes

characteristic

106

C₂²

#14519742

yes

characteristic

107

C₂²

Q₈×Dic₆₁

yes

characteristic

108

C₄

—

122

—

109

C₄

C₂×C₄×Dic₆₁

yes

characteristic

110

C₄

#14519735

yes

characteristic

111

C₄

#14519739

yes

characteristic

112

C₄

D₄×Dic₆₁

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

C₄⋊C₄×Dic₆₁

yes

characteristic

116

C₂

#16839809

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#108×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₂×#108	D₆₁
hypocenter	C₆₁	#1778
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×#108×C₆₁

C₂

socle

C₂²×C₆₁

C₂×C₄⋊C₄

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
9. #14519713	C₄	semidirect
15. #108×C₆₁	C₄	semidirect
64. C₆₁	#1778	semidirect
71. #108	Dic₆₁	semidirect

H ≅ G/N

type

9. #14519713

C₄

semidirect

15. #108×C₆₁

C₄

semidirect

64. C₆₁

#1778

semidirect

71. #108

Dic₆₁

semidirect

Subgroups — #21445727

Conjugacy classes of subgroups

Complements