Group #21461734 — subgroups

Subgroups — #21461734

Order 7808.

260 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 118 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	#16840628	C₂	1	4	yes	maximal
3	C₄²×Dic₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#92420	C₂²	1	4	yes	—
5	C₄⋊#92420	—	2	4	no	—
6	C₂×C₄×Dic₆₁	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₄	1	2	yes	—
8	C₂×C₄×Dic₆₁	C₂²	1	2	yes	—
9	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₆₁	C₄	1	1	yes	characteristic
11	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
15	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
16	C₂×#92420	—	2	4	no	—
17	C₂×#92420	—	2	8	no	—
18	C₄²×C₆₁	C₈	1	4	yes	complemented
19	C₄×Dic₆₁	—	2	2	no	—
20	C₄×Dic₆₁	—	2	4	no	—
21	C₄×Dic₆₁	—	2	4	no	—
22	C₄×Dic₆₁	D₄	1	2	yes	—
23	C₄×Dic₆₁	Q₈	1	2	yes	—
24	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	—	2	2	no	—
26	C₂×C₄×C₆₁	—	2	2	no	—
27	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₆₁	C₂×C₈	1	4	yes	—
29	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
31	C₂×Dic₆₁	—	2	2	no	—
32	C₂×Dic₆₁	—	2	2	no	—
33	C₂×Dic₆₁	—	2	2	no	—
34	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₆₁	M₁₆	1	4	yes	—
36	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
38	C₂×Dic₆₁	#41	1	4	yes	—
39	#92420	—	4	4	no	—
40	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₆₁	#117	1	2	yes	—
42	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
43	C₂²×C₆₁	C₂×M₁₆	1	2	yes	—
44	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
45	C₄×C₆₁	—	2	4	no	—
46	C₄×C₆₁	C₄⋊C₈	1	4	yes	—
47	Dic₆₁	—	2	2	no	—
48	Dic₆₁	—	2	4	no	—
49	Dic₆₁	#124	1	2	yes	—
50	Dic₆₁	#125	1	2	yes	—
51	#1831	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	#382	1	1	yes	characteristic
53	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
54	C₂×C₆₁	#423	1	1	yes	characteristic
55	C₂×C₆₁	#431	1	2	yes	—
56	C₂×C₆₁	#432	1	2	yes	—
57	C₂×C₄⋊C₈	—	61	2	no	—
58	C₄³	—	61	1	no	—
59	#336	—	61	4	no	—
60	C₆₁	#1831	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₈	—	61	4	no	—
62	C₂×C₄²	—	61	1	no	—
63	C₂×C₄²	—	61	2	no	—
64	C₂×C₄²	—	61	2	no	—
65	C₂×C₄²	—	61	1	no	—
66	C₂×C₄²	#6923	1	1	yes	characteristic
67	C₄⋊C₈	—	122	4	no	—
68	C₂²×C₄	—	61	1	no	—
69	C₂²×C₄	—	61	1	no	—
70	C₂²×C₄	—	61	2	no	—
71	C₂²×C₄	C₂×#6923	1	2	yes	—
72	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
73	C₂×C₈	—	122	4	no	—
74	C₂×C₈	—	122	8	no	—
75	C₄²	—	61	2	no	—
76	C₄²	—	61	2	no	—
77	C₄²	—	122	4	no	—
78	C₄²	—	122	4	no	—
79	C₄²	—	122	2	no	—
80	C₄²	#92420	1	4	yes	complemented
81	C₂³	C₂²×#6923	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	61	1	no	—
85	C₂×C₄	—	61	1	no	—
86	C₂×C₄	—	61	4	no	—
87	C₂×C₄	—	61	2	no	—
88	C₂×C₄	—	61	4	no	—
89	C₂×C₄	—	122	2	no	—
90	C₂×C₄	—	122	2	no	—
91	C₂×C₄	—	122	2	no	—
92	C₂×C₄	#11758213	1	2	yes	—
93	C₂×C₄	C₄⋊#6923	1	2	yes	—
94	C₂×C₄	C₂×#92420	1	4	yes	—
95	C₂×C₄	C₂×#92420	1	2	yes	—
96	C₈	—	244	4	no	—
97	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
98	C₂²	#14519856	1	2	yes	—
99	C₂²	C₂²×#92420	1	1	yes	characteristic
100	C₂²	D₆₁⋊M₁₆	1	2	yes	—
101	C₂²	C₂×#11758213	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	61	2	no	—
104	C₄	—	61	2	no	—
105	C₄	—	122	2	no	—
106	C₄	—	122	4	no	—
107	C₄	C₄⋊#92420	1	4	yes	—
108	C₂	#16840706	1	1	yes	characteristic
109	C₂	C₂×C₄⋊#92420	1	1	yes	characteristic
110	C₂	#16840767	1	1	yes	characteristic
111	C₂	#16840778	1	2	yes	—
112	C₂	#16840784	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#92420

C₂

yes

maximal

#16840628

C₂

yes

maximal

C₄²×Dic₆₁

C₂

yes

maximal, characteristic

C₂²×#92420

C₂²

yes

—

C₄⋊#92420

—

C₂×C₄×Dic₆₁

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₄

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₂×C₄²×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

—

C₂²×Dic₆₁

C₂³

yes

characteristic

C₂×#92420

—

C₂×#92420

—

C₄²×C₆₁

C₈

yes

complemented

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

D₄

yes

—

C₄×Dic₆₁

Q₈

yes

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

C₂×Dic₆₁

M₁₆

yes

—

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

C₂×Q₈

yes

characteristic

C₂×Dic₆₁

#41

yes

—

#92420

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#117

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂²×C₆₁

C₂×M₁₆

yes

—

C₂²×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₄⋊C₈

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

#124

yes

—

Dic₆₁

#125

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₂×C₄⋊C₈

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#432

yes

—

C₂×C₄⋊C₈

—

C₄³

—

#336

—

C₆₁

#1831

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

#6923

yes

characteristic

C₄⋊C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

#92420

yes

complemented

C₂³

C₂²×#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

#11758213

yes

—

C₂×C₄

C₄⋊#6923

yes

—

C₂×C₄

C₂×#92420

yes

—

C₂×C₄

C₂×#92420

yes

—

C₈

—

244

—

C₂²

C₂×C₄⋊#6923

yes

characteristic

C₂²

#14519856

yes

—

C₂²

C₂²×#92420

yes

characteristic

100

C₂²

D₆₁⋊M₁₆

yes

—

101

C₂²

C₂×#11758213

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

122

—

106

C₄

—

122

—

107

C₄

C₄⋊#92420

yes

—

108

C₂

#16840706

yes

characteristic

109

C₂

C₂×C₄⋊#92420

yes

characteristic

110

C₂

#16840767

yes

characteristic

111

C₂

#16840778

yes

—

112

C₂

#16840784

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#6923
commutator	C₂²×C₆₁	C₂²×C₈
Fitting	C₂×C₄²×C₆₁	C₄
socle	C₂³×C₆₁	C₂²×C₄
hypercenter	C₂×C₄²	#6923
hypocenter	C₆₁	#1831
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

subgroup

G/H

center, Frattini

C₂³

C₂²×#6923

commutator

C₂²×C₆₁

C₂²×C₈

Fitting

C₂×C₄²×C₆₁

C₄

socle

C₂³×C₆₁

C₂²×C₄

C₂×C₄²

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂³ ◁ C₂×C₄²

N	H ≅ G/N	type
18. C₄²×C₆₁	C₈	semidirect
60. C₆₁	#1831	semidirect
80. C₄²	#92420	semidirect

H ≅ G/N

type

18. C₄²×C₆₁

C₈

semidirect

60. C₆₁

#1831

semidirect

80. C₄²

#92420

semidirect

Subgroups — #21461734

Conjugacy classes of subgroups

Complements