Group #21460789 — subgroups

Subgroups — #21460789

Order 7808.

114 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 26 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	#16840659	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840630	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840012	C₂	1	1	yes	maximal, characteristic
4	#14519856	—	2	1	no	—
5	#14519851	—	2	1	no	—
6	C₂×#11758189	C₂²	1	1	yes	characteristic
7	#14519748	—	2	1	no	—
8	#14519709	C₄	1	1	yes	characteristic, complemented
9	#14519698	—	2	1	no	—
10	C₂×D₈×C₆₁	C₄	1	1	yes	characteristic, complemented
11	C₂×D₄×C₆₁	—	2	1	no	—
12	C₂×C₂²⋊D₆₁	—	4	1	no	—
13	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
14	C₂²⋊#6923	—	4	1	no	—
15	C₄⋊#6923	—	4	1	no	—
16	C₄×#6923	—	2	2	no	—
17	D₈×C₆₁	—	4	1	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊Dic₆₁	—	4	1	no	—
20	C₄⋊Dic₆₁	—	2	1	no	—
21	C₂×#92418	D₄	1	1	yes	characteristic
22	#11758189	—	4	1	no	—
23	#11758187	—	4	1	no	—
24	C₂³×C₆₁	—	4	1	no	—
25	C₂²×D₆₁	D₈	1	1	yes	characteristic
26	C₂×#6923	—	4	2	no	—
27	D₄×C₆₁	—	4	1	no	—
28	D₄×C₆₁	—	4	1	no	—
29	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²⋊D₆₁	—	8	2	no	—
31	C₂×Dic₆₁	—	4	1	no	—
32	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
33	C₄×D₆₁	—	2	1	no	—
34	C₄×D₆₁	—	2	1	no	—
35	C₈×C₆₁	—	2	1	no	—
36	#92418	—	2	1	no	—
37	C₂²×C₆₁	—	8	1	no	—
38	C₂²×C₆₁	—	8	1	no	—
39	C₂²×C₆₁	—	8	1	no	—
40	C₂²×C₆₁	#102	1	1	yes	characteristic
41	C₂×D₆₁	—	2	1	no	—
42	C₂×D₆₁	—	4	1	no	—
43	#6923	—	8	2	no	—
44	C₄×C₆₁	#99	1	1	yes	characteristic
45	C₄×C₆₁	#104	1	1	yes	characteristic
46	Dic₆₁	—	2	1	no	—
47	Dic₆₁	—	8	1	no	—
48	#1339	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	—	2	1	no	—
50	C₂×C₆₁	—	16	1	no	—
51	C₂×C₆₁	#327	1	1	yes	characteristic
52	D₆₁	—	4	1	no	—
53	#469	—	61	1	no	—
54	#349	—	61	1	no	—
55	H(3,ℤ/4)	—	61	1	no	—
56	C₆₁	#1339	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₈	#6923	1	1	yes	characteristic, complemented
58	C₂×M₁₆	—	61	1	no	—
59	#121	—	122	1	no	—
60	#117	—	122	1	no	—
61	M₃₂	—	122	1	no	—
62	#106	—	61	1	no	—
63	#102	—	122	1	no	—
64	C₂×D₄	—	2	1	no	—
65	C₂×D₄	—	244	1	no	—
66	C₂²×C₄	—	61	1	no	—
67	D₈	—	4	1	no	—
68	M₁₆	—	244	1	no	—
69	C₂×C₈	—	61	1	no	—
70	C₂×C₈	C₂×#6923	1	1	yes	characteristic
71	C₄⋊C₄	—	122	1	no	—
72	C₄⋊C₄	—	244	1	no	—
73	C₂²⋊C₄	—	244	1	no	—
74	C₂²⋊C₄	—	244	1	no	—
75	C₄²	—	122	2	no	—
76	C₁₆	—	244	1	no	—
77	C₂³	—	4	1	no	—
78	C₂³	—	61	1	no	—
79	D₄	—	4	1	no	—
80	D₄	—	4	1	no	—
81	D₄	—	488	2	no	—
82	C₂×C₄	—	61	1	no	—
83	C₂×C₄	—	122	1	no	—
84	C₂×C₄	—	122	1	no	—
85	C₂×C₄	—	244	2	no	—
86	C₂×C₄	—	244	1	no	—
87	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	122	1	no	—
90	C₂²	—	8	1	no	—
91	C₂²	—	8	1	no	—
92	C₂²	—	8	1	no	—
93	C₂²	—	122	1	no	—
94	C₂²	—	244	1	no	—
95	C₂²	#14519839	1	1	yes	characteristic
96	C₄	—	122	1	no	—
97	C₄	—	488	1	no	—
98	C₄	—	488	2	no	—
99	C₄	#14519835	1	1	yes	characteristic
100	C₄	#14519841	1	1	yes	characteristic
101	C₂	—	2	1	no	—
102	C₂	—	16	1	no	—
103	C₂	—	244	1	no	—
104	C₂	#16840613	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840659

C₂

yes

maximal, characteristic, complemented

#16840630

C₂

yes

maximal, characteristic, complemented

#16840012

C₂

yes

maximal, characteristic

#14519856

—

#14519851

—

C₂×#11758189

C₂²

yes

characteristic

#14519748

—

#14519709

C₄

yes

characteristic, complemented

#14519698

—

C₂×D₈×C₆₁

C₄

yes

characteristic, complemented

C₂×D₄×C₆₁

—

C₂×C₂²⋊D₆₁

—

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂²⋊#6923

—

C₄⋊#6923

—

C₄×#6923

—

D₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂×#92418

D₄

yes

characteristic

#11758189

—

#11758187

—

C₂³×C₆₁

—

C₂²×D₆₁

D₈

yes

characteristic

C₂×#6923

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂²⋊D₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#102

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

#6923

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

—

#1339

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#327

yes

characteristic

D₆₁

—

#469

—

#349

—

H(3,ℤ/4)

—

C₆₁

#1339

yes

characteristic, complemented, Sylow

C₂×D₈

#6923

yes

characteristic, complemented

C₂×M₁₆

—

#121

—

122

—

#117

—

122

—

M₃₂

—

122

—

#106

—

#102

—

122

—

C₂×D₄

—

C₂×D₄

—

244

—

C₂²×C₄

—

D₈

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

C₂²⋊C₄

—

244

—

C₄²

—

122

—

C₁₆

—

244

—

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

488

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

122

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

122

—

C₂²

—

244

—

C₂²

#14519839

yes

characteristic

C₄

—

122

—

C₄

—

488

—

C₄

—

488

—

C₄

#14519835

yes

characteristic

100

C₄

#14519841

yes

characteristic

101

C₂

—

102

C₂

—

103

C₂

—

244

—

104

C₂

#16840613

yes

characteristic

	subgroup	G/H
center	C₂	#16840613
commutator	C₂×C₈×C₆₁	C₂×C₄
Frattini	C₂×C₈	C₂×#6923
Fitting	C₂×D₈×C₆₁	C₄
socle	C₂×C₆₁	#327
hypercenter	C₂×D₈	#6923
hypocenter	C₆₁	#1339
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂

#16840613

commutator

C₂×C₈×C₆₁

C₂×C₄

Frattini

C₂×C₈

C₂×#6923

Fitting

C₂×D₈×C₆₁

C₄

C₂×C₆₁

C₂×D₈

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. #16840659	C₂	semidirect
2. #16840630	C₂	semidirect
8. #14519709	C₄	semidirect
10. C₂×D₈×C₆₁	C₄	semidirect
56. C₆₁	#1339	semidirect
57. C₂×D₈	#6923	semidirect

H ≅ G/N

type

1. #16840659

C₂

semidirect

2. #16840630

C₂

semidirect

8. #14519709

C₄

semidirect

10. C₂×D₈×C₆₁

C₄

semidirect

56. C₆₁

#1339

semidirect

57. C₂×D₈

#6923

semidirect

Subgroups — #21460789

Conjugacy classes of subgroups

Complements