Group #21461459 — subgroups

Subgroups — #21461459

Order 7808.

152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 58 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	#16840813	C₂	1	2	yes	maximal
2	#16840625	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊#92420	C₂	1	2	yes	maximal
4	C₈×#92420	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
6	#14519844	—	2	2	no	—
7	C₄⋊#92420	C₂²	1	2	yes	—
8	#14519832	—	2	2	no	—
9	C₄×#92420	C₂²	1	1	yes	characteristic
10	C₄×#92420	C₂²	1	1	yes	characteristic
11	Q₈×Dic₆₁	C₂²	1	2	yes	—
12	#14519711	C₄	1	1	yes	characteristic
13	#14519701	C₄	1	2	yes	—
14	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
15	C₂×Q₁₆×C₆₁	C₄	1	1	yes	characteristic
16	C₂×Q₈×C₆₁	C₂×C₄	1	2	yes	—
17	C₂×#92420	—	2	1	no	—
18	C₂×#92420	—	2	2	no	—
19	C₂×#92420	D₄	1	1	yes	characteristic
20	C₂×#92420	D₄	1	1	yes	characteristic
21	Q₁₆×C₆₁	—	2	2	no	—
22	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄⋊Dic₆₁	—	2	2	no	—
24	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
25	C₄×Dic₆₁	—	2	2	no	—
26	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
27	C₂×#92418	C₂×C₄	1	1	yes	characteristic
28	Q₈×C₆₁	—	2	2	no	—
29	Q₈×C₆₁	—	2	2	no	—
30	C₂×C₄×C₆₁	—	2	2	no	—
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₆₁	—	2	2	no	—
33	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₆₁	#41	1	1	yes	characteristic
35	#92420	—	2	2	no	—
36	#92420	—	2	1	no	—
37	#92420	—	4	2	no	—
38	#92420	Q₁₆	1	2	yes	complemented
39	C₈×C₆₁	M₁₆	1	2	yes	—
40	#92418	—	2	1	no	—
41	C₂²×C₆₁	C₄×D₄	1	1	yes	characteristic
42	C₄×C₆₁	—	4	2	no	—
43	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₆₁	#131	1	1	yes	characteristic
45	Dic₆₁	—	2	1	no	—
46	Dic₆₁	—	4	2	no	—
47	Dic₆₁	C₂×Q₁₆	1	1	yes	characteristic
48	Dic₆₁	#135	1	1	yes	characteristic
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	—	61	1	no	—
56	Q₈⋊C₈	—	61	2	no	—
57	C₈²	—	61	1	no	—
58	C₆₁	#1591	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	#6923	1	1	yes	characteristic
60	C₄×Q₈	—	61	2	no	—
61	#107	—	61	1	no	—
62	C₄⋊C₈	—	61	2	no	—
63	C₄⋊C₈	—	122	2	no	—
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	—	61	1	no	—
69	C₂×Q₈	C₂×#6923	1	2	yes	—
70	Q₁₆	—	2	2	no	—
71	C₂×C₈	—	61	1	no	—
72	C₂×C₈	—	61	1	no	—
73	C₂×C₈	—	61	1	no	—
74	C₂×C₈	—	122	1	no	—
75	C₂×C₈	—	122	2	no	—
76	C₂×C₈	C₂×#6923	1	1	yes	characteristic
77	C₄⋊C₄	—	61	2	no	—
78	C₄⋊C₄	—	122	2	no	—
79	C₄²	—	61	1	no	—
80	C₄²	—	122	2	no	—
81	Q₈	—	2	2	no	—
82	Q₈	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	61	1	no	—
85	C₂×C₄	—	61	1	no	—
86	C₂×C₄	—	122	2	no	—
87	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
88	C₈	—	61	2	no	—
89	C₈	—	122	1	no	—
90	C₈	—	122	2	no	—
91	C₈	—	122	1	no	—
92	C₈	—	244	2	no	—
93	C₈	#11758217	1	2	yes	—
94	C₂²	D₄×#6923	1	1	yes	characteristic
95	C₄	—	4	2	no	—
96	C₄	—	61	1	no	—
97	C₄	—	61	1	no	—
98	C₄	—	122	1	no	—
99	C₄	—	244	2	no	—
100	C₄	C₂×#11758217	1	1	yes	characteristic
101	C₄	#14519864	1	1	yes	characteristic
102	C₂	#16840797	1	1	yes	characteristic
103	C₂	Q₁₆×#6923	1	1	yes	characteristic
104	C₂	#16840806	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840813

C₂

yes

maximal

#16840625

C₂

yes

maximal, characteristic

Q₈⋊#92420

C₂

yes

maximal

C₈×#92420

C₂

yes

maximal, characteristic

Q₁₆×Dic₆₁

C₂

yes

maximal, characteristic

#14519844

—

C₄⋊#92420

C₂²

yes

—

#14519832

—

C₄×#92420

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

characteristic

Q₈×Dic₆₁

C₂²

yes

—

#14519711

C₄

yes

characteristic

#14519701

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×Q₁₆×C₆₁

C₄

yes

characteristic

C₂×Q₈×C₆₁

C₂×C₄

yes

—

C₂×#92420

—

C₂×#92420

—

C₂×#92420

D₄

yes

characteristic

C₂×#92420

D₄

yes

characteristic

Q₁₆×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂×D₄

yes

C₂×Dic₆₁

yes

—

—

—

Q₁₆

yes

complemented

C₈×C₆₁

M₁₆

yes

—

#92418

—

C₂²×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

#131

yes

characteristic

Dic₆₁

—

Dic₆₁

—

Dic₆₁

C₂×Q₁₆

yes

Dic₆₁

yes

—

C₂×C₆₁

yes

C₂×C₆₁

C₄×Q₁₆

yes

C₂×C₆₁

yes

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

—

C₆₁

#1591

yes

characteristic, complemented, Sylow

C₂×Q₁₆

#6923

yes

characteristic

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

#103

—

#97

—

122

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

C₂×#6923

yes

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄²

—

C₄²

—

122

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

122

—

C₈

—

122

—

C₈

—

122

—

C₈

—

244

—

C₈

#11758217

yes

—

C₂²

D₄×#6923

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

122

—

C₄

—

244

—

100

C₄

C₂×#11758217

yes

characteristic

101

C₄

#14519864

yes

characteristic

102

C₂

#16840797

yes

characteristic

103

C₂

Q₁₆×#6923

yes

characteristic

104

C₂

#16840806

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂×Q₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₄×D₄
hypercenter	C₂×Q₁₆	#6923
hypocenter	C₆₁	#1591
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

subgroup

G/H

center

C₂²

D₄×#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₂×Q₁₆×C₆₁

C₄

socle

C₂²×C₆₁

C₄×D₄

C₂×Q₁₆

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

N	H ≅ G/N	type
38. #92420	Q₁₆	semidirect
58. C₆₁	#1591	semidirect

H ≅ G/N

type

38. #92420

Q₁₆

semidirect

58. C₆₁

#1591

semidirect

Subgroups — #21461459

Conjugacy classes of subgroups

Complements