Group #21460869 — subgroups

Subgroups — #21460869

Order 7808.

132 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 62 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×#14519851	C₂	1	1	yes	maximal, characteristic
2	C₂×#14519851	C₂	1	1	yes	maximal, characteristic
3	#16839718	C₂	1	1	yes	maximal, characteristic
4	#14519851	—	2	1	no	—
5	#14519851	—	2	1	no	—
6	#14519851	—	2	1	no	—
7	#14519851	C₄	1	2	yes	complemented
8	C₂×#11758187	—	2	1	no	—
9	C₂×#11758187	C₄	1	2	yes	complemented
10	C₂×#11758194	C₄	1	1	yes	characteristic
11	C₂²×#92418	C₂²	1	1	yes	characteristic
12	#14519688	—	2	1	no	—
13	C₄×#92418	—	2	1	no	—
14	#117×C₆₁	C₄	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₄⋊C₄×C₆₁	—	2	1	no	—
17	C₂²⋊C₄×C₆₁	C₈	1	2	yes	—
18	C₄²×C₆₁	—	2	1	no	—
19	#11758194	—	2	1	no	—
20	#11758194	C₈	1	2	yes	—
21	C₂×#92418	—	2	1	no	—
22	C₂×#92418	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	D₄	1	1	yes	characteristic
25	C₂×#92418	D₄	1	1	yes	characteristic
26	C₂×#92418	D₄	1	1	yes	characteristic
27	C₂×#92418	Q₈	1	1	yes	characteristic
28	#11758187	—	2	2	no	—
29	#11758187	—	2	2	no	—
30	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₆₁	—	2	2	no	—
32	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
37	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
38	#92418	—	2	2	no	—
39	#92418	C₂²⋊C₄	1	1	yes	characteristic
40	#92418	C₂²⋊C₄	1	1	yes	characteristic
41	#92418	C₄⋊C₄	1	1	yes	characteristic
42	#92418	C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₆₁	—	4	1	no	—
44	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
45	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
46	C₂²×C₆₁	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₆₁	—	4	2	no	—
48	C₄×C₆₁	#95	1	1	yes	characteristic
49	C₄×C₆₁	#97	1	1	yes	characteristic
50	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
52	#1378	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	—	2	1	no	—
54	C₂×C₆₁	—	2	1	no	—
55	C₂×C₆₁	—	2	1	no	—
56	C₂×C₆₁	#336	1	1	yes	characteristic
57	C₂×M₃₂	—	61	1	no	—
58	C₂×M₃₂	—	61	1	no	—
59	#405	—	61	1	no	—
60	C₆₁	#1378	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	61	1	no	—
62	C₂²×C₈	—	61	1	no	—
63	#117	#6923	1	1	yes	characteristic
64	M₃₂	—	61	2	no	—
65	M₃₂	—	122	1	no	—
66	M₃₂	—	122	1	no	—
67	M₃₂	—	122	1	no	—
68	C₂×C₁₆	—	61	2	no	—
69	C₂×C₁₆	—	122	1	no	—
70	#97	—	122	1	no	—
71	C₄×C₈	—	122	1	no	—
72	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
73	M₁₆	—	61	2	no	—
74	M₁₆	—	122	1	no	—
75	C₂×C₈	—	61	1	no	—
76	C₂×C₈	—	61	1	no	—
77	C₂×C₈	—	61	1	no	—
78	C₂×C₈	—	61	1	no	—
79	C₂×C₈	—	61	1	no	—
80	C₂×C₈	—	61	1	no	—
81	C₂×C₈	—	122	1	no	—
82	C₄⋊C₄	—	2	1	no	—
83	C₂²⋊C₄	#92420	1	2	yes	—
84	C₄²	—	2	1	no	—
85	C₁₆	—	122	2	no	—
86	C₁₆	—	122	2	no	—
87	C₂³	C₂×#92420	1	1	yes	characteristic
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
90	C₂×C₄	#11758213	1	1	yes	characteristic
91	C₂×C₄	C₄×#6923	1	1	yes	characteristic
92	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
93	C₂×C₄	#11758217	1	1	yes	characteristic
94	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
95	C₈	—	61	1	no	—
96	C₈	—	61	1	no	—
97	C₈	—	61	1	no	—
98	C₈	—	61	1	no	—
99	C₈	—	122	2	no	—
100	C₂²	—	4	1	no	—
101	C₂²	C₄×#92420	1	1	yes	characteristic
102	C₂²	C₂²⋊#92420	1	1	yes	characteristic
103	C₂²	C₄⋊#92420	1	1	yes	characteristic
104	C₄	—	4	2	no	—
105	C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
106	C₄	#14519832	1	1	yes	characteristic
107	C₄	#14519834	1	1	yes	characteristic
108	C₄	#14519844	1	1	yes	characteristic
109	C₂	—	2	1	no	—
110	C₂	—	2	1	no	—
111	C₂	—	2	1	no	—
112	C₂	#16840628	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519851

C₂

yes

maximal, characteristic

C₂×#14519851

C₂

yes

maximal, characteristic

#16839718

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

complemented

C₂×#11758187

—

C₂×#11758187

C₄

yes

complemented

C₂×#11758194

C₄

yes

characteristic

C₂²×#92418

C₂²

yes

characteristic

#14519688

—

C₄×#92418

—

#117×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

C₈

yes

—

C₄²×C₆₁

—

#11758194

—

#11758194

C₈

yes

—

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

C₂×#92418

Q₈

yes

characteristic

#11758187

—

#11758187

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

#92418

—

#92418

C₂²⋊C₄

yes

characteristic

#92418

C₂²⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

C₄×C₈

yes

characteristic

C₂²×C₆₁

C₂²⋊C₈

yes

characteristic

C₂²×C₆₁

C₄⋊C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

C₂²⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

#1378

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#336

yes

characteristic

C₂×M₃₂

—

C₂×M₃₂

—

#405

—

C₆₁

#1378

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

#6923

yes

characteristic

M₃₂

—

M₃₂

—

122

—

M₃₂

—

122

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₂²⋊C₄

#92420

yes

—

C₄²

—

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

C₂×#92420

yes

characteristic

C₂×C₄

—

C₂×C₄

D₆₁⋊C₈

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

122

—

100

C₂²

—

101

C₂²

C₄×#92420

yes

characteristic

102

C₂²

C₂²⋊#92420

yes

characteristic

103

C₂²

C₄⋊#92420

yes

characteristic

104

C₄

—

105

C₄

(C₂×#6923)⋊C₄

yes

characteristic

106

C₄

#14519832

yes

characteristic

107

C₄

#14519834

yes

characteristic

108

C₄

#14519844

yes

characteristic

109

C₂

—

110

C₂

—

111

C₂

—

112

C₂

#16840628

yes

characteristic

	subgroup	G/H
center	C₄	(C₂×#6923)⋊C₄
commutator	C₂²×C₆₁	C₄×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	#117×C₆₁	C₄
socle	C₂×C₆₁	#336
hypercenter	#117	#6923
hypocenter	C₆₁	#1378
LCS	G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

subgroup

G/H

center

C₄

(C₂×#6923)⋊C₄

commutator

C₂²×C₆₁

C₄×C₈

Frattini

C₂²×C₄

C₂×#6923

Fitting

#117×C₆₁

C₄

C₂×C₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

N	H ≅ G/N	type
7. #14519851	C₄	semidirect
9. C₂×#11758187	C₄	semidirect
60. C₆₁	#1378	semidirect

H ≅ G/N

type

7. #14519851

C₄

semidirect

9. C₂×#11758187

C₄

semidirect

60. C₆₁

#1378

semidirect

Subgroups — #21460869

Conjugacy classes of subgroups

Complements