Group #21461535 — subgroups

Subgroups — #21461535

Order 7808.

272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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	#16840721	C₂	1	1	yes	maximal, characteristic
2	C₄²×#6923	C₂	1	1	yes	maximal, characteristic
3	(C₂×#6923)⋊C₈	C₂	1	4	yes	maximal
4	#97×D₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×D₆₁⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄×#6923	C₄	1	4	yes	—
7	C₂×C₄×#6923	C₂²	1	2	yes	—
8	#14519832	C₄	1	4	yes	complemented
9	C₂×C₈×D₆₁	C₂²	1	2	yes	—
10	C₄²×D₆₁	C₂²	1	1	yes	characteristic
11	#14519688	C₄	1	1	yes	characteristic, complemented
12	#14519687	C₄	1	2	yes	complemented
13	#97×C₆₁	C₄	1	1	yes	characteristic, complemented
14	C₂²×#6923	C₂×C₄	1	4	yes	—
15	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
17	C₂×#92420	C₂×C₄	1	4	yes	—
18	C₄×#6923	—	2	8	no	—
19	C₄×#6923	—	2	4	no	—
20	D₆₁⋊C₈	—	2	4	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
22	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
25	C₂×#92418	C₂×C₄	1	2	yes	—
26	C₈×D₆₁	—	2	4	no	—
27	C₂²×D₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×#6923	—	2	4	no	—
29	C₂×#6923	—	2	4	no	—
30	C₂×#6923	M₁₆	1	8	yes	—
31	C₂×C₄×C₆₁	C₄²	1	2	yes	—
32	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₆₁	C₄²	1	2	yes	—
34	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₄×D₆₁	—	2	4	no	—
36	C₄×D₆₁	#41	1	4	yes	—
37	#92420	—	2	4	no	—
38	C₈×C₆₁	—	2	2	no	—
39	#92418	—	2	2	no	—
40	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
41	C₂×D₆₁	#117	1	2	yes	—
42	C₂×D₆₁	C₂×M₁₆	1	4	yes	—
43	#6923	—	2	8	no	—
44	C₄×C₆₁	—	2	2	no	—
45	C₄×C₆₁	#117	1	2	yes	—
46	Dic₆₁	—	2	2	no	—
47	Dic₆₁	#117	1	2	yes	—
48	#1745	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	#376	1	1	yes	characteristic
50	C₂×C₆₁	C₄×M₁₆	1	2	yes	—
51	D₆₁	#432	1	4	yes	—
52	C₂×#97	—	61	1	no	—
53	C₂×#97	—	61	1	no	—
54	C₄³	—	61	1	no	—
55	#336	—	61	4	no	—
56	C₆₁	#1745	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	—	61	2	no	—
58	C₂²×C₈	—	61	2	no	—
59	C₂×C₄²	—	61	1	no	—
60	C₂×C₄²	—	61	4	no	—
61	C₂×C₄²	—	61	2	no	—
62	#97	—	61	4	no	—
63	#97	—	61	2	no	—
64	#97	—	61	1	no	—
65	#97	#6923	1	1	yes	characteristic, complemented
66	C₂²×C₄	—	61	1	no	—
67	C₂²×C₄	—	61	4	no	—
68	C₂²×C₄	—	61	2	no	—
69	C₂×C₈	—	61	4	no	—
70	C₂×C₈	—	61	2	no	—
71	C₂×C₈	—	122	4	no	—
72	C₂×C₈	—	122	4	no	—
73	C₂×C₈	C₂×#6923	1	2	yes	—
74	C₄²	—	61	2	no	—
75	C₄²	—	61	1	no	—
76	C₄²	—	122	4	no	—
77	C₄²	—	122	8	no	—
78	C₄²	C₂×#6923	1	1	yes	characteristic
79	C₂³	—	61	1	no	—
80	C₂×C₄	—	61	1	no	—
81	C₂×C₄	—	61	4	no	—
82	C₂×C₄	—	61	8	no	—
83	C₂×C₄	—	61	2	no	—
84	C₂×C₄	—	122	4	no	—
85	C₂×C₄	—	122	4	no	—
86	C₂×C₄	—	122	4	no	—
87	C₂×C₄	C₄×#6923	1	2	yes	—
88	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
89	C₈	—	2	2	no	—
90	C₈	—	122	4	no	—
91	C₈	—	122	2	no	—
92	C₂²	—	61	4	no	—
93	C₂²	—	61	2	no	—
94	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	61	2	no	—
97	C₄	—	122	8	no	—
98	C₄	—	122	2	no	—
99	C₄	#14519856	1	2	yes	—
100	C₂	—	61	4	no	—
101	C₂	#16840698	1	1	yes	characteristic
102	C₂	M₁₆×#6923	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840721

C₂

yes

maximal, characteristic

C₄²×#6923

C₂

yes

maximal, characteristic

(C₂×#6923)⋊C₈

C₂

yes

maximal

#97×D₆₁

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

C₂²

yes

—

C₂×C₄×#6923

C₄

yes

—

C₂×C₄×#6923

C₂²

yes

—

#14519832

C₄

yes

complemented

C₂×C₈×D₆₁

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#14519688

C₄

yes

characteristic, complemented

#14519687

C₄

yes

complemented

#97×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₂³

yes

characteristic

C₂×#92420

C₂×C₄

yes

—

C₄×#6923

—

C₄×#6923

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

—

C₂²×D₆₁

C₂²×C₄

yes

—

—

M₁₆

yes

—

C₂×C₄×C₆₁

C₄²

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄²

yes

—

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

#41

yes

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

#117

yes

—

C₂×D₆₁

C₂×M₁₆

yes

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

#117

yes

—

Dic₆₁

—

Dic₆₁

#117

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₄×M₁₆

yes

—

D₆₁

#432

yes

—

C₂×#97

—

C₂×#97

—

C₄³

—

#336

—

C₆₁

#1745

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₄×#6923

yes

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

122

—

C₈

—

122

—

C₂²

—

C₂²

—

C₂²

C₂×C₄×#6923

yes

characteristic

C₄

—

C₄

—

C₄

—

122

—

C₄

—

122

—

C₄

#14519856

yes

—

100

C₂

—

101

C₂

#16840698

yes

characteristic

102

C₂

M₁₆×#6923

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂×C₄²
Fitting	#97×C₆₁	C₄
hypercenter	#97	#6923
hypocenter	C₆₁	#1745
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂×C₄²

Fitting

#97×C₆₁

C₄

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
8. #14519832	C₄	semidirect
11. #14519688	C₄	semidirect
12. #14519687	C₄	semidirect
13. #97×C₆₁	C₄	semidirect
56. C₆₁	#1745	semidirect
65. #97	#6923	semidirect

H ≅ G/N

type

8. #14519832

C₄

semidirect

11. #14519688

C₄

semidirect

12. #14519687

C₄

semidirect

13. #97×C₆₁

C₄

semidirect

56. C₆₁

#1745

semidirect

65. #97

#6923

semidirect

Subgroups — #21461535

Conjugacy classes of subgroups

Complements