Group #21445313 — subgroups

Subgroups — #21445313

Order 7808.

152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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	#16840142	C₂	1	1	yes	maximal, characteristic
2	#16840047	C₂	1	2	yes	maximal
3	#16839513	C₂	1	1	yes	maximal, characteristic
4	#16839509	C₂	1	2	yes	maximal
5	C₆₁×#446	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₄₄	—	2	1	no	—
7	C₂×Dic₂₄₄	—	2	1	no	—
8	#14519777	C₂²	1	2	yes	—
9	#14519708	—	2	2	no	—
10	C₄⋊#92418	C₂²	1	2	yes	—
11	#14519701	—	2	2	no	—
12	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₆₁	—	2	1	no	—
14	C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
15	#97×C₆₁	—	2	1	no	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₆₁	D₄	1	1	yes	characteristic
18	C₂×Dic₁₂₂	—	2	2	no	—
19	C₂×C₈×C₆₁	—	2	1	no	—
20	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₆₁	—	2	1	no	—
23	C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
24	C₄²×C₆₁	—	2	1	no	—
25	C₄²×C₆₁	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₆₁	—	2	2	no	—
27	C₄⋊Dic₆₁	—	2	2	no	—
28	C₂×#92418	—	2	2	no	—
29	Dic₂₄₄	—	4	2	no	—
30	Dic₂₄₄	—	4	2	no	—
31	Q₈×C₆₁	—	2	2	no	—
32	C₂×C₄×C₆₁	—	2	1	no	—
33	C₂×C₄×C₆₁	—	2	1	no	—
34	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
37	C₂×Dic₆₁	—	4	2	no	—
38	Dic₁₂₂	—	4	2	no	—
39	Dic₁₂₂	—	4	2	no	—
40	C₈×C₆₁	—	2	1	no	—
41	C₈×C₆₁	—	4	1	no	—
42	C₈×C₆₁	SD₁₆	1	2	yes	—
43	#92418	—	4	2	no	—
44	C₂²×C₆₁	#121	1	1	yes	characteristic
45	C₄×C₆₁	—	2	1	no	—
46	C₄×C₆₁	—	4	1	no	—
47	C₄×C₆₁	—	4	1	no	—
48	C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
49	C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
50	C₄×C₆₁	#137	1	2	yes	—
51	Dic₆₁	—	8	2	no	—
52	#1690	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	#460	1	1	yes	characteristic
54	C₂×C₆₁	#470	1	1	yes	characteristic
55	C₂×C₆₁	#473	1	1	yes	characteristic
56	#494	—	61	1	no	—
57	#475	—	61	2	no	—
58	#446	D₆₁	1	1	yes	characteristic
59	#334	—	61	1	no	—
60	#332	—	61	2	no	—
61	C₆₁	#1690	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₁₆	—	122	1	no	—
63	C₂×Q₁₆	—	122	1	no	—
64	C₄⋊Q₈	—	61	2	no	—
65	C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic
66	#106	—	122	2	no	—
67	C₄⋊C₈	—	2	1	no	—
68	C₄⋊C₈	—	61	2	no	—
69	C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
70	#103	—	122	2	no	—
71	#97	—	2	1	no	—
72	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
73	C₂×Q₈	—	122	2	no	—
74	C₂×Q₈	D₂₄₄	1	1	yes	characteristic
75	Q₁₆	—	244	2	no	—
76	Q₁₆	—	244	2	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	—	122	2	no	—
79	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₄⋊C₄	—	122	2	no	—
83	C₄⋊C₄	—	122	2	no	—
84	C₄⋊C₄	D₂₄₄	1	1	yes	characteristic
85	C₄²	—	2	1	no	—
86	C₄²	C₂²×D₆₁	1	1	yes	characteristic
87	Q₈	—	2	2	no	—
88	Q₈	—	244	2	no	—
89	Q₈	—	244	2	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	244	2	no	—
93	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
94	C₂×C₄	#11758222	1	1	yes	characteristic
95	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	4	1	no	—
98	C₈	—	244	2	no	—
99	C₈	#11758201	1	2	yes	—
100	C₂²	#14519751	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	4	1	no	—
103	C₄	—	4	1	no	—
104	C₄	—	488	2	no	—
105	C₄	C₂×#11758201	1	1	yes	characteristic
106	C₄	#14519802	1	1	yes	characteristic
107	C₄	#14519810	1	2	yes	—
108	C₂	#16839962	1	1	yes	characteristic
109	C₂	#16840020	1	1	yes	characteristic
110	C₂	#16840037	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840142

C₂

yes

maximal, characteristic

#16840047

C₂

yes

maximal

#16839513

C₂

yes

maximal, characteristic

#16839509

C₂

yes

maximal

C₆₁×#446

C₂

yes

maximal, characteristic

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

#14519777

C₂²

yes

—

#14519708

—

C₄⋊#92418

C₂²

yes

—

#14519701

—

C₄×Q₈×C₆₁

C₂²

yes

characteristic

C₄⋊C₈×C₆₁

—

C₄⋊C₈×C₆₁

C₂²

yes

characteristic

#97×C₆₁

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

D₄

yes

characteristic

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

D₄

yes

characteristic

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

D₄

yes

characteristic

C₄²×C₆₁

—

C₄²×C₆₁

C₂³

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂×#92418

—

Dic₂₄₄

—

Dic₂₄₄

—

Q₈×C₆₁

—

C₂×C₄×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

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

SD₁₆

yes

—

#92418

—

C₂²×C₆₁

#121

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₂×SD₁₆

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

D₆₁

yes

characteristic

#334

—

#332

—

C₆₁

#1690

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

122

—

C₂×Q₁₆

—

122

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₆₁

yes

characteristic

#106

—

122

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₆₁

yes

characteristic

#103

—

122

—

#97

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

122

—

C₂×Q₈

D₂₄₄

yes

characteristic

Q₁₆

—

244

—

Q₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

D₂₄₄

yes

characteristic

C₄²

—

C₄²

C₂²×D₆₁

yes

characteristic

Q₈

—

Q₈

—

244

—

Q₈

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

C₂×D₂₄₄

yes

characteristic

C₂×C₄

#11758222

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

C₈

—

244

—

C₈

#11758201

yes

—

100

C₂²

#14519751

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

488

—

105

C₄

C₂×#11758201

yes

characteristic

106

C₄

#14519802

yes

characteristic

107

C₄

#14519810

yes

—

108

C₂

#16839962

yes

characteristic

109

C₂

#16840020

yes

characteristic

110

C₂

#16840037

yes

characteristic

	subgroup	G/H
center	C₂²	#14519751
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#446	C₂
socle	C₂²×C₆₁	#121
hypercenter	#446	D₆₁
hypocenter	C₆₁	#1690
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#14519751

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#446

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
61. C₆₁	#1690	semidirect

H ≅ G/N

type

61. C₆₁

#1690

semidirect

Subgroups — #21445313

Conjugacy classes of subgroups

Complements