Group #21461761 — subgroups

Subgroups — #21461761

Order 7808.

212 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 86 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×#14519848	C₂	1	2	yes	maximal
2	C₂×#14519847	C₂	1	2	yes	maximal
3	#16840767	C₂	1	1	yes	maximal, characteristic
4	#16840766	C₂	1	1	yes	maximal, characteristic
5	#97×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	C₂²	1	2	yes	—
7	C₂×#11758213	C₂²	1	1	yes	characteristic
8	C₂×#11758213	C₂²	1	1	yes	characteristic
9	#14519848	—	2	4	no	—
10	#14519847	—	2	4	no	—
11	#14519844	—	2	2	no	—
12	C₄⋊#92420	—	2	2	no	—
13	C₂×C₈×D₆₁	C₂²	1	2	yes	—
14	C₄²×D₆₁	C₂²	1	1	yes	characteristic
15	#14519688	C₄	1	1	yes	characteristic
16	#14519687	C₄	1	2	yes	—
17	#97×C₆₁	C₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	Q₈	1	2	yes	—
19	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
20	C₂×#92420	—	2	2	no	—
21	C₂×#92420	—	2	1	no	—
22	C₂×#92420	—	2	1	no	—
23	#11758213	—	2	2	no	—
24	#11758213	—	2	2	no	—
25	#11758213	—	2	2	no	—
26	#11758213	—	2	2	no	—
27	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
28	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₆₁	D₄	1	2	yes	—
31	C₂×#92418	C₂×C₄	1	2	yes	—
32	C₈×D₆₁	D₄	1	4	yes	—
33	C₈×D₆₁	Q₈	1	4	yes	—
34	C₂²×D₆₁	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
38	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
39	C₄×D₆₁	—	4	2	no	—
40	C₄×D₆₁	C₂×D₄	1	2	yes	—
41	C₄×D₆₁	C₂×Q₈	1	2	yes	—
42	#92420	—	4	1	no	—
43	#92420	—	4	2	no	—
44	#92420	—	4	1	no	—
45	C₈×C₆₁	C₄⋊C₄	1	4	yes	—
46	#92418	C₄⋊C₄	1	4	yes	—
47	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×D₆₁	—	2	2	no	—
49	C₂×D₆₁	C₄⋊Q₈	1	2	yes	—
50	C₄×C₆₁	—	2	2	no	—
51	C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
52	Dic₆₁	—	2	2	no	—
53	Dic₆₁	#127	1	1	yes	characteristic
54	Dic₆₁	C₄⋊Q₈	1	1	yes	characteristic
55	#1849	—	61	1	no	maximal, Sylow
56	C₂×C₆₁	#384	1	1	yes	characteristic
57	C₂×C₆₁	#430	1	2	yes	—
58	D₆₁	—	2	2	no	—
59	C₂×#108	—	61	2	no	—
60	C₂×#108	—	61	2	no	—
61	#423	—	61	1	no	—
62	#423	—	61	1	no	—
63	C₂×#97	—	61	1	no	—
64	C₆₁	#1849	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₁₆	—	61	2	no	—
66	C₂×M₁₆	—	61	1	no	—
67	C₂×M₁₆	—	61	1	no	—
68	C₂²×C₈	—	61	2	no	—
69	C₂×C₄²	—	61	1	no	—
70	#108	—	122	4	no	—
71	#108	—	122	4	no	—
72	C₄⋊C₈	—	122	2	no	—
73	C₄⋊C₈	—	122	2	no	—
74	#97	—	61	2	no	—
75	#97	—	61	1	no	—
76	#97	#6923	1	1	yes	characteristic
77	C₂²×C₄	—	61	1	no	—
78	C₂²×C₄	—	61	2	no	—
79	M₁₆	—	122	2	no	—
80	M₁₆	—	122	2	no	—
81	M₁₆	—	122	2	no	—
82	M₁₆	—	122	2	no	—
83	C₂×C₈	—	61	2	no	—
84	C₂×C₈	—	61	4	no	—
85	C₂×C₈	—	61	4	no	—
86	C₂×C₈	—	122	2	no	—
87	C₂×C₈	—	122	1	no	—
88	C₂×C₈	—	122	1	no	—
89	C₂×C₈	C₂×#6923	1	2	yes	—
90	C₄²	—	61	2	no	—
91	C₄²	—	61	1	no	—
92	C₄²	C₂×#6923	1	1	yes	characteristic
93	C₂³	—	61	1	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	2	no	—
96	C₂×C₄	—	61	2	no	—
97	C₂×C₄	—	61	2	no	—
98	C₂×C₄	—	244	2	no	—
99	C₂×C₄	C₄⋊#6923	1	2	yes	—
100	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
101	C₈	—	61	4	no	—
102	C₈	—	244	1	no	—
103	C₈	—	244	2	no	—
104	C₈	—	244	1	no	—
105	C₈	C₄⋊#6923	1	4	yes	—
106	C₂²	—	61	2	no	—
107	C₂²	—	122	2	no	—
108	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	61	1	no	—
111	C₄	—	61	1	no	—
112	C₄	—	122	2	no	—
113	C₄	C₂×C₄⋊#6923	1	2	yes	—
114	C₂	—	122	2	no	—
115	C₂	#16840708	1	1	yes	characteristic
116	C₂	#16840777	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519848

C₂

yes

maximal

C₂×#14519847

C₂

yes

maximal

#16840767

C₂

yes

maximal, characteristic

#16840766

C₂

yes

maximal, characteristic

#97×D₆₁

C₂

yes

maximal, characteristic

C₂×#11758213

C₂²

yes

—

C₂×#11758213

C₂²

yes

characteristic

C₂×#11758213

C₂²

yes

—

—

—

—

C₂×C₈×D₆₁

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic

#14519687

C₄

yes

—

#97×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

—

C₂×C₄×D₆₁

C₂³

yes

—

—

—

—

—

—

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

D₄

yes

—

C₈×D₆₁

Q₈

yes

—

C₂²×D₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

C₂×D₄

yes

—

C₄×D₆₁

C₂×Q₈

yes

—

#92420

—

#92420

—

#92420

—

C₈×C₆₁

C₄⋊C₄

yes

—

#92418

C₄⋊C₄

yes

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₄⋊Q₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

—

Dic₆₁

—

Dic₆₁

#127

yes

characteristic

Dic₆₁

C₄⋊Q₈

yes

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

—

—

—

—

C₂×#97

—

C₆₁

#1849

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

#108

—

122

—

#108

—

122

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

C₄⋊#6923

yes

—

100

C₂×C₄

C₂²×#6923

yes

characteristic

101

C₈

—

102

C₈

—

244

—

103

C₈

—

244

—

104

C₈

—

244

—

105

C₈

C₄⋊#6923

yes

—

106

C₂²

—

107

C₂²

—

122

—

108

C₂²

C₂×C₄⋊#6923

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

122

—

113

C₄

C₂×C₄⋊#6923

yes

—

114

C₂

—

122

—

115

C₂

#16840708

yes

characteristic

116

C₂

#16840777

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#97×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#97	#6923
hypocenter	C₆₁	#1849
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#97×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
64. C₆₁	#1849	semidirect

H ≅ G/N

type

64. C₆₁

#1849

semidirect

Subgroups — #21461761

Conjugacy classes of subgroups

Complements