Group #21448103 — subgroups

Subgroups — #21448103

Order 7808.

120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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	#16840166	C₂	1	1	yes	maximal, characteristic
2	#16840163	C₂	1	1	yes	maximal, characteristic
3	#16839590	C₂	1	1	yes	maximal, characteristic
4	#16839589	C₂	1	1	yes	maximal, characteristic
5	#16839587	C₂	1	1	yes	maximal, characteristic
6	#16839537	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#366	C₂	1	1	yes	maximal, characteristic
8	#14519776	—	2	1	no	—
9	#14519768	—	2	1	no	—
10	C₂×#11758185	C₂²	1	1	yes	characteristic
11	#14519711	C₂²	1	1	yes	characteristic
12	#14519711	C₂²	1	1	yes	characteristic
13	#14519710	—	2	1	no	—
14	#14519708	—	2	1	no	—
15	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	#107×C₆₁	C₂²	1	1	yes	characteristic
18	#107×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₂₂	—	4	1	no	—
20	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₆₁	—	2	1	no	—
22	C₄⋊C₄×C₆₁	—	2	1	no	—
23	C₄⋊Dic₆₁	—	2	1	no	—
24	C₄⋊Dic₆₁	—	2	1	no	—
25	C₄⋊Dic₆₁	—	4	1	no	—
26	#11758196	—	4	1	no	—
27	#11758196	—	4	1	no	—
28	C₄×Dic₆₁	D₄	1	1	yes	characteristic
29	C₂×#92418	D₄	1	1	yes	characteristic
30	C₁₆×C₆₁	Q₈	1	2	yes	complemented
31	#11758185	Q₈	1	2	yes	complemented
32	C₂×C₄×C₆₁	—	4	1	no	—
33	C₂×C₄×C₆₁	—	4	1	no	—
34	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₆₁	—	4	1	no	—
36	C₂×Dic₆₁	—	4	1	no	—
37	C₂×Dic₆₁	D₈	1	1	yes	characteristic
38	C₂×Dic₆₁	D₈	1	1	yes	characteristic
39	Dic₁₂₂	—	8	2	no	—
40	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
41	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
42	#92418	Q₁₆	1	2	yes	—
43	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
44	C₄×C₆₁	—	8	1	no	—
45	C₄×C₆₁	—	8	1	no	—
46	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
47	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
48	Dic₆₁	—	2	1	no	—
49	Dic₆₁	—	2	1	no	—
50	Dic₆₁	—	8	1	no	—
51	Dic₆₁	—	8	1	no	—
52	#2255	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	#500	1	1	yes	characteristic
54	C₂×C₆₁	#509	1	1	yes	characteristic
55	C₂×C₆₁	#510	1	1	yes	characteristic
56	#500	—	61	1	no	—
57	#499	—	61	1	no	—
58	#367	—	61	1	no	—
59	#367	—	61	1	no	—
60	#366	—	61	1	no	—
61	#366	D₆₁	1	1	yes	characteristic
62	#346	—	61	1	no	—
63	C₆₁	#2255	1	1	yes	characteristic, complemented, Sylow
64	C₄⋊Q₈	—	122	1	no	—
65	#125	—	122	1	no	—
66	C₂×C₁₆	—	61	1	no	—
67	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
68	#107	—	61	1	no	—
69	#107	—	61	1	no	—
70	#107	—	122	1	no	—
71	#107	C₂×D₆₁	1	1	yes	characteristic
72	#107	C₂×D₆₁	1	1	yes	characteristic
73	#106	—	122	1	no	—
74	C₄×C₈	—	61	1	no	—
75	C₂×Q₈	—	244	1	no	—
76	C₂×C₈	—	61	1	no	—
77	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
78	C₄⋊C₄	—	2	1	no	—
79	C₄⋊C₄	—	2	1	no	—
80	C₄⋊C₄	—	122	1	no	—
81	C₄⋊C₄	—	122	1	no	—
82	C₄⋊C₄	—	244	1	no	—
83	C₄⋊C₄	—	244	1	no	—
84	C₄⋊C₄	—	244	1	no	—
85	C₄²	—	61	1	no	—
86	C₁₆	—	61	2	no	—
87	C₁₆	Dic₁₂₂	1	2	yes	complemented
88	Q₈	—	488	2	no	—
89	C₂×C₄	—	4	1	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	—	61	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	244	1	no	—
94	C₂×C₄	—	244	1	no	—
95	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
96	C₈	—	61	2	no	—
97	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
98	C₈	Q₈×D₆₁	1	1	yes	characteristic
99	C₂²	D₈×D₆₁	1	1	yes	characteristic
100	C₄	—	8	1	no	—
101	C₄	—	8	1	no	—
102	C₄	—	122	1	no	—
103	C₄	—	122	1	no	—
104	C₄	—	488	1	no	—
105	C₄	—	488	1	no	—
106	C₄	#14519776	1	1	yes	characteristic
107	C₄	Q₁₆×D₆₁	1	1	yes	characteristic
108	C₂	#16840166	1	1	yes	characteristic
109	C₂	#16840196	1	1	yes	characteristic
110	C₂	#16840204	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840166

C₂

yes

maximal, characteristic

#16840163

C₂

yes

maximal, characteristic

#16839590

C₂

yes

maximal, characteristic

#16839589

C₂

yes

maximal, characteristic

#16839587

C₂

yes

maximal, characteristic

#16839537

C₂

yes

maximal, characteristic

C₆₁×#366

C₂

yes

maximal, characteristic

#14519776

—

#14519768

—

C₂×#11758185

C₂²

yes

characteristic

#14519711

C₂²

yes

characteristic

#14519711

C₂²

yes

characteristic

#14519710

—

#14519708

—

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

#107×C₆₁

C₂²

yes

characteristic

#107×C₆₁

C₂²

yes

characteristic

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758196

—

#11758196

—

C₄×Dic₆₁

D₄

yes

characteristic

C₂×#92418

D₄

yes

characteristic

C₁₆×C₆₁

Q₈

yes

complemented

#11758185

Q₈

yes

complemented

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

D₈

yes

characteristic

C₂×Dic₆₁

D₈

yes

characteristic

Dic₁₂₂

—

C₈×C₆₁

C₂×Q₈

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

#92418

Q₁₆

yes

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

C₄×C₆₁

C₂×Q₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

—

—

—

D₆₁

yes

characteristic

#346

—

C₆₁

#2255

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

122

—

#125

—

122

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

—

—

—

122

—

#107

C₂×D₆₁

yes

characteristic

#107

C₂×D₆₁

yes

characteristic

#106

—

122

—

C₄×C₈

—

C₂×Q₈

—

244

—

C₂×C₈

—

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₄⋊C₄

—

244

—

C₄²

—

C₁₆

—

C₁₆

Dic₁₂₂

yes

complemented

Q₈

—

488

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

D₄×D₆₁

yes

characteristic

C₈

—

C₈

C₂×Dic₁₂₂

yes

characteristic

C₈

Q₈×D₆₁

yes

characteristic

C₂²

D₈×D₆₁

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

122

—

103

C₄

—

122

—

104

C₄

—

488

—

105

C₄

—

488

—

106

C₄

#14519776

yes

characteristic

107

C₄

Q₁₆×D₆₁

yes

characteristic

108

C₂

#16840166

yes

characteristic

109

C₂

#16840196

yes

characteristic

110

C₂

#16840204

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₆₁
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#366	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#366	D₆₁
hypocenter	C₆₁	#2255
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

subgroup

G/H

center

C₂²

D₈×D₆₁

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#366

C₂

socle

C₂²×C₆₁

C₂×D₈

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

N	H ≅ G/N	type
30. C₁₆×C₆₁	Q₈	semidirect
31. #11758185	Q₈	semidirect
63. C₆₁	#2255	semidirect
87. C₁₆	Dic₁₂₂	semidirect

H ≅ G/N

type

30. C₁₆×C₆₁

Q₈

semidirect

31. #11758185

Q₈

semidirect

63. C₆₁

#2255

semidirect

87. C₁₆

Dic₁₂₂

semidirect

Subgroups — #21448103

Conjugacy classes of subgroups

Complements