Group #21460894 — subgroups

Subgroups — #21460894

Order 7808.

136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 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	D₆₁⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519846	C₂	1	1	yes	maximal, characteristic
3	M₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic
4	D₆₁⋊M₁₆	—	2	1	no	—
5	C₂×C₄⋊#6923	—	2	1	no	—
6	#14519848	—	2	1	no	—
7	#14519847	C₄	1	2	yes	complemented
8	#14519846	—	2	1	no	—
9	#14519846	C₄	1	2	yes	—
10	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
11	#14519717	C₄	1	1	yes	characteristic, complemented
12	#14519716	—	2	1	no	—
13	C₁₆×D₆₁	—	2	1	no	—
14	M₃₂×C₆₁	C₄	1	1	yes	characteristic, complemented
15	C₂²×#6923	—	4	1	no	—
16	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
17	#11758217	—	4	1	no	—
18	C₄⋊#6923	—	2	2	no	—
19	C₄⋊#6923	—	4	1	no	—
20	#11758213	—	2	2	no	—
21	D₆₁⋊C₈	—	4	1	no	—
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	Q₈	1	1	yes	characteristic
24	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
25	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
26	C₈×D₆₁	D₄	1	1	yes	characteristic
27	C₈×D₆₁	D₄	1	1	yes	characteristic
28	C₁₆×C₆₁	—	2	1	no	—
29	#11758185	—	2	1	no	—
30	C₂²×D₆₁	SD₁₆	1	1	yes	characteristic
31	C₂×#6923	—	4	2	no	—
32	C₂×#6923	—	8	2	no	—
33	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
35	C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₄×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₄×D₆₁	D₈	1	1	yes	characteristic
38	C₄×D₆₁	Q₁₆	1	1	yes	characteristic
39	#92420	—	4	2	no	—
40	C₈×C₆₁	C₄²	1	1	yes	characteristic
41	C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
42	#92418	C₄⋊C₄	1	1	yes	characteristic
43	#92418	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₆₁	#106	1	1	yes	characteristic
45	C₂×D₆₁	—	2	1	no	—
46	C₂×D₆₁	—	2	1	no	—
47	C₂×D₆₁	#102	1	1	yes	characteristic
48	C₂×D₆₁	#103	1	1	yes	characteristic
49	#6923	—	8	2	no	—
50	C₄×C₆₁	#95	1	1	yes	characteristic
51	C₄×C₆₁	#107	1	1	yes	characteristic
52	Dic₆₁	#102	1	1	yes	characteristic
53	Dic₆₁	#103	1	1	yes	characteristic
54	#1387	—	61	1	no	maximal, Sylow
55	C₂×C₆₁	—	2	1	no	—
56	C₂×C₆₁	#340	1	1	yes	characteristic
57	D₆₁	—	2	1	no	—
58	D₆₁	#361	1	1	yes	characteristic
59	D₆₁	#362	1	1	yes	characteristic
60	C₂×M₃₂	—	61	1	no	—
61	C₂×#108	—	61	1	no	—
62	C₂×#107	—	61	1	no	—
63	C₆₁	#1387	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₁₆	—	122	1	no	—
65	C₂²×C₈	—	61	1	no	—
66	C₂×C₄⋊C₄	—	122	1	no	—
67	M₃₂	—	61	1	no	—
68	M₃₂	—	122	1	no	—
69	M₃₂	#6923	1	1	yes	characteristic, complemented
70	C₂×C₁₆	—	122	1	no	—
71	#108	—	61	2	no	—
72	#108	—	122	1	no	—
73	#107	—	61	2	no	—
74	#107	—	122	1	no	—
75	C₂²×C₄	—	61	1	no	—
76	C₂²×C₄	—	244	1	no	—
77	M₁₆	—	122	2	no	—
78	M₁₆	—	244	1	no	—
79	C₂×C₈	—	61	1	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	61	1	no	—
82	C₂×C₈	—	61	1	no	—
83	C₂×C₈	—	61	1	no	—
84	C₂×C₈	—	244	1	no	—
85	C₂×C₈	C₂×#6923	1	1	yes	characteristic
86	C₄⋊C₄	—	122	2	no	—
87	C₄⋊C₄	—	244	1	no	—
88	C₁₆	—	2	1	no	—
89	C₁₆	—	122	1	no	—
90	C₂³	—	61	1	no	—
91	C₂×C₄	—	61	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	61	1	no	—
94	C₂×C₄	—	61	1	no	—
95	C₂×C₄	—	61	1	no	—
96	C₂×C₄	—	488	2	no	—
97	C₂×C₄	—	244	2	no	—
98	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
99	C₈	—	61	1	no	—
100	C₈	—	61	1	no	—
101	C₈	—	244	2	no	—
102	C₈	C₄×#6923	1	1	yes	characteristic
103	C₈	C₂²⋊#6923	1	1	yes	characteristic
104	C₂²	—	61	1	no	—
105	C₂²	—	61	1	no	—
106	C₂²	—	122	1	no	—
107	C₂²	—	122	1	no	—
108	C₂²	#14519845	1	1	yes	characteristic
109	C₄	—	61	1	no	—
110	C₄	—	61	1	no	—
111	C₄	—	488	2	no	—
112	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
113	C₄	#14519846	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	61	1	no	—
116	C₂	—	61	1	no	—
117	C₂	—	122	1	no	—
118	C₂	#16840636	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₆₁⋊#108

C₂

yes

maximal, characteristic

C₂×#14519846

C₂

yes

maximal, characteristic

M₃₂×D₆₁

C₂

yes

maximal, characteristic

D₆₁⋊M₁₆

—

C₂×C₄⋊#6923

—

#14519848

—

#14519847

C₄

yes

complemented

#14519846

—

#14519846

C₄

yes

—

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519717

C₄

yes

characteristic, complemented

#14519716

—

C₁₆×D₆₁

—

M₃₂×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

—

C₂×C₄×D₆₁

D₄

yes

—

—

—

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×#92418

Q₈

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

SD₁₆

yes

characteristic

C₂×#6923

—

C₂×#6923

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

C₂²⋊C₄

yes

characteristic

C₄×D₆₁

C₂²⋊C₄

yes

characteristic

C₄×D₆₁

D₈

yes

characteristic

C₄×D₆₁

Q₁₆

yes

characteristic

#92420

—

C₈×C₆₁

C₄²

yes

characteristic

C₈×C₆₁

C₂²⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#106

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

yes

C₂×D₆₁

yes

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

#340

yes

characteristic

D₆₁

—

D₆₁

yes

D₆₁

yes

C₂×M₃₂

—

C₂×#108

—

C₂×#107

—

C₆₁

#1387

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

122

—

M₃₂

—

M₃₂

—

122

—

M₃₂

#6923

yes

characteristic, complemented

C₂×C₁₆

—

122

—

#108

—

#108

—

122

—

#107

—

#107

—

122

—

C₂²×C₄

—

C₂²×C₄

—

244

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

244

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₁₆

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

488

—

C₂×C₄

—

244

—

C₂×C₄

C₄⋊#6923

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

244

—

102

C₈

C₄×#6923

yes

characteristic

103

C₈

C₂²⋊#6923

yes

characteristic

104

C₂²

—

105

C₂²

—

106

C₂²

—

122

—

107

C₂²

—

122

—

108

C₂²

#14519845

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

488

—

112

C₄

(C₂×#6923)⋊C₄

yes

characteristic

113

C₄

#14519846

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

—

117

C₂

—

122

—

118

C₂

#16840636

yes

characteristic

	subgroup	G/H
center	C₂	#16840636
commutator	C₈×C₆₁	C₄²
Frattini	C₂×C₈	C₂×#6923
Fitting	M₃₂×C₆₁	C₄
socle	C₂×C₆₁	#340
hypercenter	M₃₂	#6923
hypocenter	C₆₁	#1387
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

subgroup

G/H

center

C₂

#16840636

commutator

C₈×C₆₁

C₄²

Frattini

C₂×C₈

C₂×#6923

Fitting

M₃₂×C₆₁

C₄

C₂×C₆₁

M₃₂

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

N	H ≅ G/N	type
7. #14519847	C₄	semidirect
11. #14519717	C₄	semidirect
14. M₃₂×C₆₁	C₄	semidirect
63. C₆₁	#1387	semidirect
69. M₃₂	#6923	semidirect

H ≅ G/N

type

7. #14519847

C₄

semidirect

11. #14519717

C₄

semidirect

14. M₃₂×C₆₁

C₄

semidirect

63. C₆₁

#1387

semidirect

69. M₃₂

#6923

semidirect

Subgroups — #21460894

Conjugacy classes of subgroups

Complements