Group #21444639 — subgroups

Subgroups — #21444639

Order 7808.

160 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₈×Dic₁₂₂	C₂	1	2	yes	maximal
2	C₄×Dic₂₄₄	C₂	1	1	yes	maximal, characteristic
3	#16839513	C₂	1	1	yes	maximal, characteristic
4	#16839494	C₂	1	2	yes	maximal
5	C₆₁×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₄₄	C₄	1	1	yes	characteristic
7	C₄×Dic₁₂₂	C₂²	1	2	yes	—
8	#14519711	C₄	1	1	yes	characteristic
9	C₄⋊#92418	C₂²	1	2	yes	—
10	#14519706	—	2	2	no	—
11	#14519702	C₄	1	2	yes	—
12	C₈×Dic₆₁	—	2	2	no	—
13	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₂₂	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₆₁	—	2	1	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	D₄	1	2	yes	—
21	C₄²×C₆₁	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
23	#11758196	—	2	2	no	—
24	C₄×Dic₆₁	—	2	2	no	—
25	C₂×#92418	—	2	2	no	—
26	Dic₂₄₄	C₈	1	4	yes	complemented
27	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
30	C₂×Dic₆₁	—	2	2	no	—
31	C₂×Dic₆₁	—	2	2	no	—
32	Dic₁₂₂	—	2	2	no	—
33	Dic₁₂₂	C₂×C₈	1	4	yes	—
34	C₈×C₆₁	—	2	1	no	—
35	C₈×C₆₁	—	2	2	no	—
36	C₈×C₆₁	—	4	1	no	—
37	C₈×C₆₁	C₂×C₈	1	2	yes	—
38	#92418	—	4	2	no	—
39	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
40	C₄×C₆₁	—	2	1	no	—
41	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₆₁	#131	1	1	yes	characteristic
43	C₄×C₆₁	#137	1	2	yes	—
44	Dic₆₁	—	2	4	no	—
45	Dic₆₁	—	4	2	no	—
46	#1579	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	C₈×D₄	1	1	yes	characteristic
48	C₂×C₆₁	#441	1	1	yes	characteristic
49	C₂×C₆₁	#444	1	1	yes	characteristic
50	C₈×Q₈	—	61	2	no	—
51	C₄×Q₁₆	—	61	1	no	—
52	#334	—	61	1	no	—
53	Q₈⋊C₈	—	61	2	no	—
54	#322	D₆₁	1	1	yes	characteristic
55	C₆₁	#1579	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₁₆	—	61	1	no	—
57	C₄×Q₈	—	61	2	no	—
58	#107	—	61	1	no	—
59	C₄⋊C₈	—	61	2	no	—
60	C₄⋊C₈	—	122	2	no	—
61	#103	—	61	2	no	—
62	C₄×C₈	—	122	2	no	—
63	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
64	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
65	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
66	C₂×Q₈	—	61	2	no	—
67	Q₁₆	—	61	4	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	122	2	no	—
70	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
71	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
72	C₂×C₈	D₂₄₄	1	2	yes	—
73	C₄⋊C₄	—	61	2	no	—
74	C₄⋊C₄	—	122	2	no	—
75	C₄²	—	122	2	no	—
76	C₄²	C₂²×D₆₁	1	1	yes	characteristic
77	Q₈	—	61	4	no	—
78	Q₈	—	122	2	no	—
79	C₂×C₄	—	122	2	no	—
80	C₂×C₄	—	122	2	no	—
81	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
82	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
83	C₂×C₄	#11758222	1	1	yes	characteristic
84	C₈	—	2	2	no	—
85	C₈	—	2	1	no	—
86	C₈	—	4	1	no	—
87	C₈	—	244	2	no	—
88	C₈	C₈×D₆₁	1	2	yes	—
89	C₂²	C₄×D₂₄₄	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	122	4	no	—
92	C₄	—	244	2	no	—
93	C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
94	C₄	#14519783	1	1	yes	characteristic
95	C₄	#14519810	1	2	yes	—
96	C₂	C₈×D₂₄₄	1	1	yes	characteristic
97	C₂	#16839870	1	1	yes	characteristic
98	C₂	#16839885	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₁₂₂

C₂

yes

maximal

C₄×Dic₂₄₄

C₂

yes

maximal, characteristic

#16839513

C₂

yes

maximal, characteristic

#16839494

C₂

yes

maximal

C₆₁×#322

C₂

yes

maximal, characteristic

C₂×Dic₂₄₄

C₄

yes

characteristic

C₄×Dic₁₂₂

C₂²

yes

—

#14519711

C₄

yes

characteristic

C₄⋊#92418

C₂²

yes

—

#14519706

—

#14519702

C₄

yes

—

C₈×Dic₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Dic₁₂₂

C₂×C₄

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

—

C₄²×C₆₁

C₂³

yes

characteristic

C₄⋊Dic₆₁

C₂×C₄

yes

—

#11758196

—

C₄×Dic₆₁

—

C₂×#92418

—

Dic₂₄₄

C₈

yes

complemented

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

C₂×C₈

yes

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

C₂×C₈

yes

—

#92418

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂²×C₈

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

Dic₆₁

—

Dic₆₁

—

#1579

—

maximal, Sylow

C₂×C₆₁

C₈×D₄

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

C₈×Q₈

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

D₆₁

yes

characteristic

C₆₁

#1579

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

#103

—

C₄×C₈

—

122

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₄×C₈

C₂×D₆₁

yes

characteristic

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

D₂₄₄

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄²

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

Q₈

—

Q₈

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

C₂×D₂₄₄

yes

characteristic

C₂×C₄

#11758222

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

244

—

C₈

C₈×D₆₁

yes

—

C₂²

C₄×D₂₄₄

yes

characteristic

C₄

—

C₄

—

122

—

C₄

—

244

—

C₄

C₂×C₈×D₆₁

yes

C₄

yes

C₄

yes

—

C₂

C₈×D₂₄₄

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₂₄₄
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#322	C₂
socle	C₂²×C₆₁	C₄×D₄
hypercenter	#322	D₆₁
hypocenter	C₆₁	#1579
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₂₄₄

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#322

C₂

socle

C₂²×C₆₁

C₄×D₄

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
26. Dic₂₄₄	C₈	semidirect
55. C₆₁	#1579	semidirect

H ≅ G/N

type

26. Dic₂₄₄

C₈

semidirect

55. C₆₁

#1579

semidirect

Subgroups — #21444639

Conjugacy classes of subgroups

Complements