Group #21445334 — subgroups

Subgroups — #21445334

Order 7808.

152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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	#16839969	C₂	1	2	yes	maximal
2	#16839892	C₂	1	1	yes	maximal, characteristic
3	#16839513	C₂	1	1	yes	maximal, characteristic
4	#16839508	C₂	1	2	yes	maximal
5	C₆₁×#500	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758202	—	2	2	no	—
7	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic
8	C₄⋊#92418	C₂²	1	2	yes	—
9	C₄⋊#92418	C₂²	1	1	yes	characteristic
10	#14519706	—	2	1	no	—
11	#14519701	—	2	2	no	—
12	#14519687	—	2	1	no	—
13	C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
14	#107×C₆₁	—	2	1	no	—
15	#107×C₆₁	—	2	1	no	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₆₁	—	2	2	no	—
18	C₂×Dic₁₂₂	D₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
21	C₄⋊C₄×C₆₁	—	2	2	no	—
22	C₄⋊C₄×C₆₁	—	2	2	no	—
23	C₄²×C₆₁	C₂³	1	1	yes	characteristic
24	#11758202	—	4	4	no	—
25	C₄⋊Dic₆₁	D₄	1	1	yes	characteristic
26	#11758196	—	2	1	no	—
27	C₄×Dic₆₁	—	2	1	no	—
28	C₂×#92418	—	2	1	no	—
29	C₂×#92418	—	2	2	no	—
30	Q₈×C₆₁	—	4	2	no	—
31	Q₈×C₆₁	—	4	2	no	—
32	C₂×C₄×C₆₁	—	4	2	no	—
33	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
36	C₂×Dic₆₁	—	2	1	no	—
37	C₂×Dic₆₁	—	2	1	no	—
38	Dic₁₂₂	—	2	2	no	—
39	C₈×C₆₁	—	2	1	no	—
40	C₈×C₆₁	Q₁₆	1	2	yes	complemented
41	#92418	—	4	2	no	—
42	#92418	—	4	1	no	—
43	C₂²×C₆₁	#121	1	1	yes	characteristic
44	C₄×C₆₁	—	2	1	no	—
45	C₄×C₆₁	—	8	2	no	—
46	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
47	C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
48	C₄×C₆₁	#137	1	1	yes	characteristic
49	Dic₆₁	—	4	1	no	—
50	Dic₆₁	—	4	1	no	—
51	#1694	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	#462	1	1	yes	characteristic
53	C₂×C₆₁	#469	1	1	yes	characteristic
54	C₂×C₆₁	#473	1	1	yes	characteristic
55	#500	D₆₁	1	1	yes	characteristic
56	#462	—	61	2	no	—
57	#446	—	61	1	no	—
58	#334	—	61	1	no	—
59	#332	—	61	2	no	—
60	C₆₁	#1694	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₁₆	—	122	2	no	—
62	C₄⋊Q₈	C₂×D₆₁	1	2	yes	—
63	C₄×Q₈	—	61	1	no	—
64	#107	—	2	1	no	—
65	#107	—	2	1	no	—
66	C₄⋊C₈	—	61	1	no	—
67	C₄⋊C₈	—	61	2	no	—
68	C₄⋊C₈	—	122	1	no	—
69	#103	—	122	2	no	—
70	#97	—	122	1	no	—
71	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
72	C₂×Q₈	—	2	2	no	—
73	C₂×Q₈	—	61	1	no	—
74	Q₁₆	—	244	4	no	—
75	C₂×C₈	—	122	2	no	—
76	C₂×C₈	—	122	1	no	—
77	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	61	1	no	—
82	C₄⋊C₄	—	122	1	no	—
83	C₄²	—	122	1	no	—
84	C₄²	C₂²×D₆₁	1	1	yes	characteristic
85	Q₈	—	4	2	no	—
86	Q₈	—	4	2	no	—
87	Q₈	—	122	2	no	—
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	122	1	no	—
90	C₂×C₄	—	122	1	no	—
91	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
92	C₂×C₄	#11758224	1	1	yes	characteristic
93	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	244	1	no	—
96	C₈	—	244	2	no	—
97	C₈	#11758202	1	2	yes	complemented
98	C₂²	#14519748	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	8	2	no	—
101	C₄	—	244	1	no	—
102	C₄	—	244	1	no	—
103	C₄	C₂×#11758202	1	1	yes	characteristic
104	C₄	#14519801	1	2	yes	—
105	C₄	#14519808	1	1	yes	characteristic
106	C₂	#16839969	1	1	yes	characteristic
107	C₂	#16840012	1	1	yes	characteristic
108	C₂	#16840034	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839969

C₂

yes

maximal

#16839892

C₂

yes

maximal, characteristic

#16839513

C₂

yes

maximal, characteristic

#16839508

C₂

yes

maximal

C₆₁×#500

C₂

yes

maximal, characteristic

C₂×#11758202

—

C₄×Dic₁₂₂

C₂²

yes

characteristic

C₄⋊#92418

C₂²

yes

—

C₄⋊#92418

C₂²

yes

—

—

—

C₄⋊Q₈×C₆₁

C₂²

yes

—

#107×C₆₁

—

#107×C₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×Dic₁₂₂

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

C₂³

yes

characteristic

#11758202

—

C₄⋊Dic₆₁

D₄

yes

characteristic

#11758196

—

C₄×Dic₆₁

—

C₂×#92418

—

C₂×#92418

—

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

Q₁₆

yes

complemented

#92418

—

#92418

—

C₂²×C₆₁

#121

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×Q₁₆

yes

characteristic

C₄×C₆₁

AGL(1,ℤ/8)

yes

—

C₄×C₆₁

#137

yes

characteristic

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

yes

—

—

—

—

C₆₁

#1694

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

122

—

C₄⋊Q₈

C₂×D₆₁

yes

—

C₄×Q₈

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

#103

—

122

—

#97

—

122

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

244

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄²

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

122

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

D₄×D₆₁

yes

characteristic

C₂×C₄

#11758224

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

244

—

C₈

—

244

—

C₈

yes

C₂²

yes

C₄

—

100

C₄

—

101

C₄

—

244

—

102

C₄

—

244

—

103

C₄

C₂×#11758202

yes

characteristic

104

C₄

#14519801

yes

—

105

C₄

#14519808

yes

characteristic

106

C₂

#16839969

yes

characteristic

107

C₂

#16840012

yes

characteristic

108

C₂

#16840034

yes

characteristic

	subgroup	G/H
center	C₂²	#14519748
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#500	C₂
socle	C₂²×C₆₁	#121
hypercenter	#500	D₆₁
hypocenter	C₆₁	#1694
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#14519748

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#500

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
40. C₈×C₆₁	Q₁₆	semidirect
60. C₆₁	#1694	semidirect
97. C₈	#11758202	semidirect

H ≅ G/N

type

40. C₈×C₆₁

Q₁₆

semidirect

60. C₆₁

#1694

semidirect

97. C₈

#11758202

semidirect

Subgroups — #21445334

Conjugacy classes of subgroups

Complements