Group #21462028 — subgroups

Subgroups — #21462028

Order 7808.

184 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 114 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	C₂²×#11758187	C₂	1	1	yes	maximal, characteristic
3	#16840650	C₂	1	2	yes	maximal, complemented
4	C₄×#11758187	C₂	1	2	yes	maximal, complemented
5	#16839718	C₂	1	1	yes	maximal, characteristic
6	#14519851	C₄	1	4	yes	complemented
7	C₂×#11758187	C₄	1	4	yes	complemented
8	C₂×#11758187	C₂²	1	1	yes	characteristic
9	C₂×#11758187	C₂²	1	1	yes	characteristic
10	C₂×#11758187	C₂²	1	2	yes	—
11	C₂×#11758194	C₄	1	1	yes	characteristic
12	C₂²×#92418	C₂²	1	1	yes	characteristic
13	#14519688	C₄	1	2	yes	—
14	C₄×#92418	C₂²	1	2	yes	—
15	#117×C₆₁	C₄	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄⋊C₄×C₆₁	C₈	1	2	yes	—
18	C₂²⋊C₄×C₆₁	C₈	1	2	yes	—
19	C₄²×C₆₁	C₂×C₄	1	2	yes	—
20	#11758194	C₈	1	4	yes	—
21	C₂×#92418	C₂×C₄	1	1	yes	characteristic
22	C₂×#92418	C₂×C₄	1	2	yes	—
23	C₂×#92418	C₂×C₄	1	2	yes	—
24	C₂×#92418	C₂×C₄	1	2	yes	—
25	C₂×#92418	C₂³	1	1	yes	characteristic
26	#11758187	C₂×C₄	1	2	yes	—
27	#11758187	C₂×C₄	1	2	yes	—
28	#11758187	C₂×C₄	1	4	yes	—
29	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₄²	1	2	yes	—
31	C₂×C₄×C₆₁	C₂×C₈	1	4	yes	—
32	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	#92418	C₄²	1	2	yes	—
36	#92418	C₂×C₈	1	4	yes	—
37	#92418	C₂²×C₄	1	1	yes	characteristic
38	#92418	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₆₁	—	2	2	no	—
40	C₂²×C₆₁	C₄×C₈	1	2	yes	—
41	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₆₁	—	2	4	no	—
43	C₄×C₆₁	C₄×C₈	1	2	yes	—
44	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
45	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
46	#2108	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	—	2	2	no	—
48	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
49	C₂×C₆₁	#504	1	2	yes	—
50	C₂×M₃₂	—	61	1	no	—
51	C₂²×C₁₆	—	61	1	no	—
52	#405	—	61	1	no	—
53	#346	—	61	2	no	—
54	C₄×C₁₆	—	61	2	no	—
55	C₆₁	#2108	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₁₆	—	61	1	no	—
57	C₂²×C₈	—	61	1	no	—
58	#117	#6923	1	1	yes	characteristic
59	M₃₂	—	61	4	no	—
60	C₂×C₁₆	—	61	4	no	—
61	C₂×C₁₆	—	61	1	no	—
62	C₂×C₁₆	—	61	2	no	—
63	C₂×C₁₆	—	61	1	no	—
64	#97	—	61	2	no	—
65	C₄×C₈	—	61	2	no	—
66	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
67	M₁₆	—	61	4	no	—
68	C₂×C₈	—	61	2	no	—
69	C₂×C₈	—	61	2	no	—
70	C₂×C₈	—	61	1	no	—
71	C₂×C₈	—	61	2	no	—
72	C₂×C₈	—	61	1	no	—
73	C₄⋊C₄	#92420	1	2	yes	—
74	C₂²⋊C₄	#92420	1	2	yes	—
75	C₄²	C₂×#6923	1	2	yes	—
76	C₁₆	—	61	2	no	—
77	C₁₆	—	61	2	no	—
78	C₁₆	—	61	4	no	—
79	C₂³	C₂×#92420	1	1	yes	characteristic
80	C₂×C₄	D₆₁⋊C₈	1	2	yes	—
81	C₂×C₄	C₄×#6923	1	2	yes	—
82	C₂×C₄	C₂×#92420	1	4	yes	—
83	C₂×C₄	C₂×#92420	1	1	yes	characteristic
84	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
85	C₈	—	61	2	no	—
86	C₈	—	61	1	no	—
87	C₈	—	61	1	no	—
88	C₈	—	61	4	no	—
89	C₂²	—	2	2	no	—
90	C₂²	C₄×#92420	1	2	yes	—
91	C₂²	C₂²×#92420	1	1	yes	characteristic
92	C₄	—	2	4	no	—
93	C₄	C₄×#92420	1	2	yes	—
94	C₄	C₂×C₄×#6923	1	1	yes	characteristic
95	C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
96	C₂	—	2	2	no	—
97	C₂	C₂×C₄×#92420	1	1	yes	characteristic
98	C₂	#16840820	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519851

C₂

yes

maximal, characteristic

C₂²×#11758187

C₂

yes

maximal, characteristic

#16840650

C₂

yes

maximal, complemented

C₄×#11758187

C₂

yes

maximal, complemented

#16839718

C₂

yes

maximal, characteristic

#14519851

C₄

yes

complemented

C₂×#11758187

C₄

yes

complemented

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758187

C₂²

yes

characteristic

C₂×#11758187

C₂²

yes

—

C₂×#11758194

C₄

yes

characteristic

C₂²×#92418

C₂²

yes

characteristic

#14519688

C₄

yes

—

C₄×#92418

C₂²

yes

—

#117×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

C₈

yes

—

C₂²⋊C₄×C₆₁

C₈

yes

—

C₄²×C₆₁

C₂×C₄

yes

—

#11758194

C₈

yes

—

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

C₂×C₄

yes

—

C₂×#92418

C₂³

yes

characteristic

#11758187

C₂×C₄

yes

—

#11758187

C₂×C₄

yes

—

#11758187

C₂×C₄

yes

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

#92418

C₄²

yes

—

#92418

C₂×C₈

yes

—

#92418

C₂²×C₄

yes

characteristic

#92418

C₂²×C₄

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

C₄×C₈

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₄×C₈

yes

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

#2108

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×C₄×C₈

yes

characteristic

C₂×C₆₁

#504

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

C₄×C₁₆

—

C₆₁

#2108

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

#6923

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₂²×C₄

C₂×#6923

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

#92420

yes

—

C₂²⋊C₄

#92420

yes

—

C₄²

C₂×#6923

yes

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

C₂×#92420

yes

characteristic

C₂×C₄

D₆₁⋊C₈

yes

—

C₂×C₄

C₄×#6923

yes

—

C₂×C₄

C₂×#92420

yes

—

C₂×C₄

C₂×#92420

yes

characteristic

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

C₄×#92420

yes

—

C₂²

C₂²×#92420

yes

characteristic

C₄

—

C₄

C₄×#92420

yes

—

C₄

C₂×C₄×#6923

yes

characteristic

C₄

C₂×D₆₁⋊C₈

yes

characteristic

C₂

—

C₂

C₂×C₄×#92420

yes

characteristic

C₂

#16840820

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator	C₂×C₆₁	C₂×C₄×C₈
Fitting	#117×C₆₁	C₄
socle	C₂²×C₆₁	C₂²×C₈
hypercenter	#117	#6923
hypocenter	C₆₁	#2108
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #117

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator

C₂×C₆₁

C₂×C₄×C₈

Fitting

#117×C₆₁

C₄

socle

C₂²×C₆₁

C₂²×C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ #117

N	H ≅ G/N	type
3. #16840650	C₂	semidirect
4. C₄×#11758187	C₂	semidirect
6. #14519851	C₄	semidirect
7. C₂×#11758187	C₄	semidirect
55. C₆₁	#2108	semidirect

H ≅ G/N

type

3. #16840650

C₂

semidirect

4. C₄×#11758187

C₂

semidirect

6. #14519851

C₄

semidirect

7. C₂×#11758187

C₄

semidirect

55. C₆₁

#2108

semidirect

Subgroups — #21462028

Conjugacy classes of subgroups

Complements