Group #21460676 — subgroups

Subgroups — #21460676

Order 7808.

126 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 44 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	#16840784	C₂	1	1	yes	maximal, characteristic
2	#16840784	C₂	1	1	yes	maximal, characteristic
3	#16839813	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#92420	—	2	1	no	—
5	C₄⋊#92420	—	2	1	no	—
6	#14519834	—	2	1	no	—
7	#14519834	C₄	1	2	yes	—
8	#14519832	—	2	1	no	—
9	#14519832	C₄	1	2	yes	—
10	C₄²×D₆₁	C₂²	1	1	yes	characteristic
11	#14519706	—	2	1	no	—
12	#14519689	—	2	1	no	—
13	C₄×#92418	C₄	1	1	yes	characteristic
14	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
15	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
17	C₂×C₄×D₆₁	Q₈	1	1	yes	characteristic
18	C₂×#92420	—	2	2	no	—
19	C₂×#92420	—	2	2	no	—
20	C₂×C₈×C₆₁	—	2	1	no	—
21	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₆₁	D₄	1	1	yes	characteristic
24	C₄×Dic₆₁	D₄	1	1	yes	characteristic
25	C₂×#92418	—	2	1	no	—
26	C₂²×D₆₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
33	C₄×D₆₁	—	2	1	no	—
34	C₄×D₆₁	—	2	1	no	—
35	C₄×D₆₁	—	4	1	no	—
36	C₄×D₆₁	—	4	1	no	—
37	#92420	—	4	2	no	—
38	#92420	—	4	2	no	—
39	C₈×C₆₁	—	4	1	no	—
40	#92418	—	4	1	no	—
41	C₂²×C₆₁	#95	1	1	yes	characteristic
42	C₂×D₆₁	—	2	1	no	—
43	C₂×D₆₁	—	2	1	no	—
44	C₂×D₆₁	—	2	1	no	—
45	C₄×C₆₁	—	2	1	no	—
46	C₄×C₆₁	—	2	1	no	—
47	C₄×C₆₁	#108	1	1	yes	characteristic
48	C₄×C₆₁	#108	1	1	yes	characteristic
49	Dic₆₁	—	2	1	no	—
50	Dic₆₁	—	2	1	no	—
51	Dic₆₁	—	2	1	no	—
52	#1287	—	61	1	no	maximal, Sylow
53	C₂×C₆₁	H(3,ℤ/4)	1	1	yes	characteristic
54	C₂×C₆₁	#341	1	1	yes	characteristic
55	C₂×C₆₁	#344	1	1	yes	characteristic
56	D₆₁	—	4	1	no	—
57	#432	—	61	1	no	—
58	#432	—	61	1	no	—
59	#431	—	61	1	no	—
60	C₆₁	#1287	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₄²	—	61	1	no	—
62	C₄⋊C₈	—	122	1	no	—
63	C₄⋊C₈	—	122	1	no	—
64	C₄⋊C₈	—	122	1	no	—
65	C₂²⋊C₈	—	61	2	no	—
66	C₂²⋊C₈	—	122	1	no	—
67	C₂²⋊C₈	—	122	1	no	—
68	#97	—	61	2	no	—
69	#97	—	122	1	no	—
70	C₄×C₈	—	61	1	no	—
71	C₄×C₈	#6923	1	1	yes	characteristic
72	C₂²×C₄	—	61	1	no	—
73	C₂²×C₄	—	61	1	no	—
74	C₂²×C₄	—	61	1	no	—
75	C₂×C₈	—	2	1	no	—
76	C₂×C₈	—	122	2	no	—
77	C₂×C₈	—	122	2	no	—
78	C₂×C₈	—	122	1	no	—
79	C₄²	—	61	1	no	—
80	C₄²	—	61	1	no	—
81	C₄²	—	61	1	no	—
82	C₄²	C₂×#6923	1	1	yes	characteristic
83	C₂³	—	61	1	no	—
84	C₂×C₄	—	61	1	no	—
85	C₂×C₄	—	61	1	no	—
86	C₂×C₄	—	61	1	no	—
87	C₂×C₄	—	122	1	no	—
88	C₂×C₄	—	122	1	no	—
89	C₂×C₄	—	244	1	no	—
90	C₂×C₄	—	244	1	no	—
91	C₂×C₄	C₄×#6923	1	1	yes	characteristic
92	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
93	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
94	C₈	—	4	1	no	—
95	C₈	—	244	1	no	—
96	C₈	—	244	2	no	—
97	C₈	—	244	2	no	—
98	C₂²	—	122	1	no	—
99	C₂²	—	122	1	no	—
100	C₂²	—	122	1	no	—
101	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	2	1	no	—
104	C₄	—	122	1	no	—
105	C₄	—	122	1	no	—
106	C₄	—	122	1	no	—
107	C₄	#14519847	1	1	yes	characteristic
108	C₄	#14519848	1	1	yes	characteristic
109	C₂	—	244	1	no	—
110	C₂	#16840629	1	1	yes	characteristic
111	C₂	#16840638	1	1	yes	characteristic
112	C₂	#16840644	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840784

C₂

yes

maximal, characteristic

#16840784

C₂

yes

maximal, characteristic

#16839813

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

—

#14519832

—

#14519832

C₄

yes

—

C₄²×D₆₁

C₂²

yes

—

—

C₄

yes

characteristic

C₄×C₈×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

Q₈

yes

characteristic

C₂×#92420

—

C₂×#92420

—

C₂×C₈×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₂×#92418

—

C₂²×D₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

#92420

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#95

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#432

—

#432

—

#431

—

C₆₁

#1287

yes

characteristic, complemented, Sylow

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

C₂²⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

#97

—

#97

—

122

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

244

—

C₈

—

244

—

C₈

—

244

—

C₂²

—

122

—

C₂²

—

122

—

100

C₂²

—

122

—

101

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

122

—

105

C₄

—

122

—

106

C₄

—

122

—

107

C₄

#14519847

yes

characteristic

108

C₄

#14519848

yes

characteristic

109

C₂

—

244

—

110

C₂

#16840629

yes

characteristic

111

C₂

#16840638

yes

characteristic

112

C₂

#16840644

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#6923)⋊C₄
commutator	C₂×C₄×C₆₁	C₄²
Frattini	C₄²	C₂×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1287
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

(C₂×#6923)⋊C₄

commutator

C₂×C₄×C₆₁

C₄²

Frattini

C₄²

C₂×#6923

Fitting

C₄×C₈×C₆₁

C₄

C₂²×C₆₁

C₄×C₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
60. C₆₁	#1287	semidirect

H ≅ G/N

type

60. C₆₁

#1287

semidirect

Subgroups — #21460676

Conjugacy classes of subgroups

Complements