Group #21460641 — subgroups

Subgroups — #21460641

Order 7808.

212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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	C₂×C₄×#92420	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#92420	C₄	1	4	yes	—
4	C₄×#92420	—	2	2	no	—
5	C₄×#92420	—	2	2	no	—
6	C₂²×#92418	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
8	C₈×Dic₆₁	—	2	2	no	—
9	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
12	C₂×#92420	—	2	4	no	—
13	C₂×#92420	—	2	4	no	—
14	C₂×#92420	C₈	1	8	yes	complemented
15	C₂×C₈×C₆₁	—	2	1	no	—
16	C₂×C₈×C₆₁	—	2	1	no	—
17	C₂×C₈×C₆₁	C₈	1	2	yes	complemented
18	C₄×Dic₆₁	D₄	1	1	yes	characteristic
19	C₄×Dic₆₁	D₄	1	2	yes	—
20	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
21	C₂×#92418	—	2	1	no	—
22	C₂×#92418	—	2	1	no	—
23	C₂×#92418	C₈	1	2	yes	complemented
24	C₂³×C₆₁	C₄²	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
31	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
32	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
33	C₂×Dic₆₁	C₂×C₈	1	4	yes	—
34	C₂×Dic₆₁	M₁₆	1	4	yes	—
35	#92420	—	2	8	no	—
36	C₈×C₆₁	—	2	2	no	—
37	#92418	—	2	2	no	—
38	C₂²×C₆₁	#95	1	1	yes	characteristic
39	C₂²×C₆₁	C₄×C₈	1	2	yes	—
40	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
41	C₂²×C₆₁	#97	1	2	yes	—
42	C₂²×C₆₁	#97	1	1	yes	characteristic
43	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
44	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
45	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
46	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
47	Dic₆₁	C₂²⋊C₈	1	4	yes	—
48	Dic₆₁	C₄⋊C₈	1	4	yes	—
49	#1273	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	C₈²	1	1	yes	characteristic
51	C₂×C₆₁	#322	1	1	yes	characteristic
52	C₂×C₆₁	#322	1	2	yes	—
53	C₂×C₆₁	#336	1	2	yes	—
54	C₂×C₆₁	#336	1	1	yes	characteristic
55	C₂×C₄×C₈	—	61	2	no	—
56	C₂×C₄×C₈	—	61	1	no	—
57	C₆₁	#1273	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₈	—	61	4	no	—
59	C₂²×C₈	—	61	1	no	—
60	C₂²×C₈	#6923	1	1	yes	characteristic
61	C₂×C₄²	—	61	1	no	—
62	C₄×C₈	—	122	2	no	—
63	C₄×C₈	—	122	2	no	—
64	C₄×C₈	—	122	2	no	—
65	C₂²×C₄	—	61	2	no	—
66	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	61	8	no	—
70	C₂×C₈	—	61	2	no	—
71	C₂×C₈	—	122	4	no	—
72	C₂×C₈	—	122	4	no	—
73	C₂×C₈	—	122	1	no	—
74	C₂×C₈	—	122	1	no	—
75	C₂×C₈	#92420	1	2	yes	complemented
76	C₄²	—	61	1	no	—
77	C₄²	—	61	1	no	—
78	C₄²	—	61	2	no	—
79	C₂³	C₄×#6923	1	1	yes	characteristic
80	C₂×C₄	—	61	2	no	—
81	C₂×C₄	—	61	2	no	—
82	C₂×C₄	—	61	4	no	—
83	C₂×C₄	—	61	4	no	—
84	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
85	C₂×C₄	#11758213	1	1	yes	characteristic
86	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
87	C₂×C₄	C₂×#92420	1	1	yes	characteristic
88	C₂×C₄	#11758217	1	1	yes	characteristic
89	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	122	8	no	—
92	C₈	—	122	2	no	—
93	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
94	C₂²	C₈×#6923	1	2	yes	—
95	C₂²	C₄×#92420	1	1	yes	characteristic
96	C₂²	#14519831	1	2	yes	—
97	C₂²	#14519832	1	1	yes	characteristic
98	C₄	—	61	4	no	—
99	C₄	—	61	4	no	—
100	C₄	C₂²⋊#92420	1	1	yes	characteristic
101	C₄	#14519834	1	1	yes	characteristic
102	C₄	C₄⋊#92420	1	1	yes	characteristic
103	C₄	#14519844	1	1	yes	characteristic
104	C₂	C₈×#92420	1	1	yes	characteristic
105	C₂	#16840603	1	1	yes	characteristic
106	C₂	#92420⋊C₈	1	2	yes	—
107	C₂	(C₂×#6923)⋊C₈	1	2	yes	—
108	C₂	#16840628	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×#92420

C₂

yes

maximal

C₂×C₈×Dic₆₁

C₂

yes

maximal, characteristic

C₂²×#92420

C₄

yes

—

C₄×#92420

—

C₄×#92420

—

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

—

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

—

C₂×#92420

—

C₂×#92420

—

C₂×#92420

C₈

yes

complemented

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₈

yes

complemented

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

—

C₄×Dic₆₁

Q₈

yes

—

—

C₈

yes

complemented

C₂³×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

M₁₆

yes

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#95

yes

characteristic

C₂²×C₆₁

C₄×C₈

yes

—

C₂²×C₆₁

C₄×C₈

yes

characteristic

C₂²×C₆₁

#97

yes

—

C₂²×C₆₁

#97

yes

characteristic

C₄×C₆₁

C₂²⋊C₈

yes

characteristic

C₄×C₆₁

C₂²⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

Dic₆₁

C₂²⋊C₈

yes

—

Dic₆₁

C₄⋊C₈

yes

—

#1273

—

maximal, Sylow

C₂×C₆₁

C₈²

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#336

yes

—

C₂×C₆₁

#336

yes

characteristic

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₆₁

#1273

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

#6923

yes

characteristic

C₂×C₄²

—

C₄×C₈

—

122

—

C₄×C₈

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

#92420

yes

complemented

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₆₁⋊C₈

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

122

—

C₈

—

122

—

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

C₂²

C₈×#6923

yes

—

C₂²

C₄×#92420

yes

characteristic

C₂²

#14519831

yes

—

C₂²

#14519832

yes

characteristic

C₄

—

C₄

—

100

C₄

C₂²⋊#92420

yes

characteristic

101

C₄

#14519834

yes

characteristic

102

C₄

C₄⋊#92420

yes

characteristic

103

C₄

#14519844

yes

characteristic

104

C₂

C₈×#92420

yes

characteristic

105

C₂

#16840603

yes

characteristic

106

C₂

#92420⋊C₈

yes

—

107

C₂

(C₂×#6923)⋊C₈

yes

—

108

C₂

#16840628

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×#6923
commutator	C₂×C₆₁	C₈²
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂³×C₆₁	C₄²
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	#1273
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂×#6923

commutator

C₂×C₆₁

C₈²

Fitting

C₂²×C₈×C₆₁

C₄

socle

C₂³×C₆₁

C₄²

C₂²×C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
14. C₂×#92420	C₈	semidirect
17. C₂×C₈×C₆₁	C₈	semidirect
23. C₂×#92418	C₈	semidirect
57. C₆₁	#1273	semidirect
75. C₂×C₈	#92420	semidirect

H ≅ G/N

type

14. C₂×#92420

C₈

semidirect

17. C₂×C₈×C₆₁

C₈

semidirect

23. C₂×#92418

C₈

semidirect

57. C₆₁

#1273

semidirect

75. C₂×C₈

#92420

semidirect

Subgroups — #21460641

Conjugacy classes of subgroups

Complements