Group #21444715 — subgroups

Subgroups — #21444715

Order 7808.

152 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 65 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	#16839889	C₂	1	2	yes	maximal
2	C₄×Dic₂₄₄	C₂	1	1	yes	maximal, characteristic
3	#16839492	C₂	1	2	yes	maximal
4	C₈×#92418	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#335	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	#14519706	—	2	2	no	—
10	#14519702	C₄	1	2	yes	—
11	#14519687	—	2	2	no	—
12	C₄×#92418	C₂²	1	1	yes	characteristic
13	C₄×#92418	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
15	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₂₂	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₆₁	C₂³	1	1	yes	characteristic
21	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
22	#11758196	—	2	2	no	—
23	C₄×Dic₆₁	—	2	2	no	—
24	C₂×#92418	—	2	1	no	—
25	C₂×#92418	D₄	1	1	yes	characteristic
26	C₂×#92418	D₄	1	1	yes	characteristic
27	Dic₂₄₄	—	2	2	no	—
28	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
31	C₂×Dic₆₁	—	2	2	no	—
32	C₂×Dic₆₁	—	2	2	no	—
33	Dic₁₂₂	—	2	2	no	—
34	Dic₁₂₂	—	2	2	no	—
35	C₈×C₆₁	—	2	1	no	—
36	C₈×C₆₁	—	4	2	no	—
37	C₈×C₆₁	M₁₆	1	2	yes	—
38	#92418	—	2	2	no	—
39	#92418	—	2	1	no	—
40	#92418	Q₁₆	1	2	yes	complemented
41	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
42	C₄×C₆₁	—	2	1	no	—
43	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₆₁	#131	1	1	yes	characteristic
45	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₆₁	#135	1	1	yes	characteristic
47	Dic₆₁	—	4	2	no	—
48	Dic₆₁	—	4	2	no	—
49	#1591	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	#436	1	1	yes	characteristic
51	C₂×C₆₁	C₄×Q₁₆	1	1	yes	characteristic
52	C₂×C₆₁	#443	1	1	yes	characteristic
53	#446	—	61	2	no	—
54	C₄×Q₁₆	—	61	1	no	—
55	#335	D₆₁	1	1	yes	characteristic
56	Q₈⋊C₈	—	61	2	no	—
57	C₈²	—	61	1	no	—
58	C₆₁	#1591	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	—	61	1	no	—
60	C₄×Q₈	—	61	2	no	—
61	#107	—	61	1	no	—
62	C₄⋊C₈	—	122	2	no	—
63	C₄⋊C₈	C₂×D₆₁	1	2	yes	—
64	#103	—	61	2	no	—
65	#97	—	122	2	no	—
66	C₄×C₈	—	61	1	no	—
67	C₄×C₈	—	61	1	no	—
68	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
69	C₂×Q₈	—	61	2	no	—
70	Q₁₆	—	122	2	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	61	1	no	—
73	C₂×C₈	—	61	1	no	—
74	C₂×C₈	—	122	1	no	—
75	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
76	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
77	C₄⋊C₄	—	61	2	no	—
78	C₄⋊C₄	—	122	2	no	—
79	C₄²	—	122	2	no	—
80	C₄²	C₂²×D₆₁	1	1	yes	characteristic
81	Q₈	—	122	2	no	—
82	Q₈	—	122	2	no	—
83	C₂×C₄	—	122	2	no	—
84	C₂×C₄	—	122	2	no	—
85	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
86	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
87	C₂×C₄	#11758226	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	4	2	no	—
90	C₈	—	61	2	no	—
91	C₈	—	122	2	no	—
92	C₈	—	122	1	no	—
93	C₈	#11758189	1	2	yes	—
94	C₂²	#14519739	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	244	2	no	—
97	C₄	—	244	2	no	—
98	C₄	C₂×#11758189	1	1	yes	characteristic
99	C₄	#14519785	1	1	yes	characteristic
100	C₄	Q₁₆×D₆₁	1	1	yes	characteristic
101	C₄	#14519796	1	1	yes	characteristic
102	C₂	#16839839	1	1	yes	characteristic
103	C₂	#16839856	1	1	yes	characteristic
104	C₂	#16839878	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839889

C₂

yes

maximal

C₄×Dic₂₄₄

C₂

yes

maximal, characteristic

#16839492

C₂

yes

maximal

C₈×#92418

C₂

yes

maximal, characteristic

C₆₁×#335

C₂

yes

maximal, characteristic

C₂×Dic₂₄₄

C₄

yes

characteristic

C₄×Dic₁₂₂

C₂²

yes

—

#14519711

C₄

yes

characteristic

#14519706

—

#14519702

C₄

yes

—

#14519687

—

C₄×#92418

C₂²

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

C₂²

yes

—

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

C₄²×C₆₁

C₂³

yes

characteristic

C₄⋊Dic₆₁

C₂×C₄

yes

—

#11758196

—

C₄×Dic₆₁

—

C₂×#92418

—

C₂×#92418

D₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

Dic₂₄₄

—

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

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

—

#92418

—

#92418

—

#92418

Q₁₆

yes

complemented

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

#131

yes

characteristic

C₄×C₆₁

C₂×Q₁₆

yes

characteristic

C₄×C₆₁

#135

yes

characteristic

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₄×Q₁₆

yes

C₂×C₆₁

yes

—

C₄×Q₁₆

—

#335

D₆₁

yes

characteristic

Q₈⋊C₈

—

C₈²

—

C₆₁

#1591

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

122

—

C₄⋊C₈

C₂×D₆₁

yes

—

#103

—

#97

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

Q₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄²

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

Q₈

—

122

—

Q₈

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

D₄×D₆₁

yes

characteristic

C₂×C₄

#11758226

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

122

—

C₈

—

122

—

C₈

#11758189

yes

—

C₂²

#14519739

yes

characteristic

C₄

—

C₄

—

244

—

C₄

—

244

—

C₄

yes

C₄

yes

100

C₄

Q₁₆×D₆₁

yes

characteristic

101

C₄

#14519796

yes

characteristic

102

C₂

#16839839

yes

characteristic

103

C₂

#16839856

yes

characteristic

104

C₂

#16839878

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#335	C₂
socle	C₂²×C₆₁	C₄×D₄
hypercenter	#335	D₆₁
hypocenter	C₆₁	#1591
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

subgroup

G/H

center

C₂×C₄

D₄×D₆₁

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#335

C₂

socle

C₂²×C₆₁

C₄×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

N	H ≅ G/N	type
40. #92418	Q₁₆	semidirect
58. C₆₁	#1591	semidirect

H ≅ G/N

type

40. #92418

Q₁₆

semidirect

58. C₆₁

#1591

semidirect

Subgroups — #21444715

Conjugacy classes of subgroups

Complements