Group #21447574 — subgroups

Subgroups — #21447574

Order 7808.

172 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14519717	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	#16839580	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
7	#14519717	—	2	2	no	—
8	C₂×#11758185	C₂²	1	2	yes	—
9	C₈×Dic₆₁	C₄	1	2	yes	—
10	C₈×Dic₆₁	C₂²	1	2	yes	—
11	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	M₃₂×C₆₁	—	2	2	no	—
13	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₆₁	C₈	1	2	yes	—
16	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	D₄	1	2	yes	—
18	C₂×C₈×C₆₁	Q₈	1	2	yes	—
19	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
20	C₄×Dic₆₁	C₈	1	1	yes	characteristic
21	C₄×Dic₆₁	C₈	1	1	yes	characteristic
22	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
23	C₂×#92418	—	2	2	no	—
24	C₂×#92418	C₂×C₄	1	2	yes	—
25	C₁₆×C₆₁	—	2	2	no	—
26	#11758185	—	2	2	no	—
27	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₆₁	—	2	4	no	—
33	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
34	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
35	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
36	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
37	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
38	#92418	—	2	2	no	—
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	C₄⋊C₈	1	2	yes	—
43	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
45	Dic₆₁	—	2	2	no	—
46	Dic₆₁	M₃₂	1	4	yes	complemented
47	#2150	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	2	2	no	—
49	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
50	C₂×C₆₁	C₂×M₃₂	1	2	yes	—
51	C₂×M₃₂	—	61	1	no	—
52	C₂×M₃₂	D₆₁	1	1	yes	characteristic
53	C₂×C₄×C₈	—	61	1	no	—
54	C₄⋊C₁₆	—	61	4	no	—
55	C₆₁	#2150	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₈	—	61	1	no	—
57	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
58	C₂×C₄²	—	61	1	no	—
59	M₃₂	—	2	2	no	—
60	M₃₂	—	122	2	no	—
61	C₂×C₁₆	—	61	2	no	—
62	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
63	C₄×C₈	—	61	2	no	—
64	C₄×C₈	—	61	2	no	—
65	C₂²×C₄	—	61	2	no	—
66	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
67	C₂×C₈	—	61	2	no	—
68	C₂×C₈	—	122	2	no	—
69	C₂×C₈	Dic₁₂₂	1	2	yes	—
70	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
71	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
72	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
73	C₄²	—	61	1	no	—
74	C₄²	—	61	1	no	—
75	C₄²	—	61	2	no	—
76	C₁₆	—	2	2	no	—
77	C₁₆	—	122	2	no	—
78	C₂³	C₈×D₆₁	1	1	yes	characteristic
79	C₂×C₄	—	61	2	no	—
80	C₂×C₄	—	61	2	no	—
81	C₂×C₄	—	122	4	no	—
82	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
83	C₂×C₄	#11758189	1	2	yes	—
84	C₂×C₄	#11758196	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
86	C₈	—	122	2	no	—
87	C₈	#11758196	1	2	yes	—
88	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
89	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#14519706	1	2	yes	—
92	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
93	C₄	—	61	4	no	—
94	C₄	—	122	2	no	—
95	C₄	#14519706	1	2	yes	—
96	C₄	C₂×#11758196	1	1	yes	characteristic
97	C₄	C₂×#11758189	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×#14519706	1	1	yes	characteristic
100	C₂	M₃₂×D₆₁	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, characteristic

C₂×C₈×Dic₆₁

C₂

yes

maximal, characteristic

#16839580

C₂

yes

maximal, complemented

C₂×M₃₂×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₄

yes

characteristic

#14519717

—

C₂×#11758185

C₂²

yes

—

C₈×Dic₆₁

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

M₃₂×C₆₁

—

C₂×C₁₆×C₆₁

C₂²

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₈

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

—

C₂×C₈×C₆₁

Q₈

yes

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄×Dic₆₁

C₈

yes

characteristic

C₄×Dic₆₁

C₈

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

—

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

—

C₁₆×C₆₁

—

#11758185

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

C₂×C₈

yes

—

C₈×C₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄⋊C₈

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

M₃₂

yes

complemented

#2150

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×C₄⋊C₈

yes

characteristic

C₂×C₆₁

C₂×M₃₂

yes

—

C₂×M₃₂

—

C₂×M₃₂

D₆₁

yes

characteristic

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₆₁

#2150

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

122

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₄×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

—

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

122

—

C₂³

C₈×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₈×D₆₁

yes

characteristic

C₂×C₄

#11758189

yes

—

C₂×C₄

#11758196

yes

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

122

—

C₈

#11758196

yes

—

C₈

C₂×Dic₁₂₂

yes

characteristic

C₈

C₂×C₂²⋊D₆₁

yes

characteristic

C₂²

—

C₂²

#14519706

yes

—

C₂²

C₂×C₈×D₆₁

yes

characteristic

C₄

—

C₄

—

122

—

C₄

#14519706

yes

—

C₄

yes

C₄

yes

C₂

—

C₂

C₂×#14519706

yes

characteristic

100

C₂

M₃₂×D₆₁

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₂×M₃₂×C₆₁	C₂
hypercenter	C₂×M₃₂	D₆₁
hypocenter	C₆₁	#2150
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₆₁

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₂×M₃₂×C₆₁

C₂

hypercenter

C₂×M₃₂

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #16839580	C₂	semidirect
46. Dic₆₁	M₃₂	semidirect
55. C₆₁	#2150	semidirect

H ≅ G/N

type

3. #16839580

C₂

semidirect

46. Dic₆₁

M₃₂

semidirect

55. C₆₁

#2150

semidirect

Subgroups — #21447574

Conjugacy classes of subgroups

Complements