Group #21445679 — subgroups

Subgroups — #21445679

Order 7808.

260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14519706	C₂	1	2	yes	maximal
2	C₂×C₄×#92418	C₂	1	1	yes	maximal, characteristic
3	#16839608	C₂	1	1	yes	maximal, characteristic
4	#16839516	C₂	1	2	yes	maximal
5	C₂×#97×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×#92418	C₂²	1	2	yes	—
7	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
9	#14519706	C₄	1	8	yes	complemented
10	C₄×#92418	—	2	2	no	—
11	#14519684	C₄	1	4	yes	—
12	C₂²×C₈×C₆₁	C₂²	1	2	yes	—
13	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
14	#97×C₆₁	—	2	2	no	—
15	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
17	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
18	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₆₁	—	2	2	no	—
20	C₂×C₈×C₆₁	—	2	2	no	—
21	C₂×C₈×C₆₁	C₂×C₄	1	4	yes	—
22	C₄²×C₆₁	D₄	1	2	yes	—
23	C₄²×C₆₁	Q₈	1	2	yes	—
24	C₄×Dic₆₁	—	2	2	no	—
25	C₄×Dic₆₁	C₂×C₄	1	4	yes	—
26	C₂×#92418	—	2	2	no	—
27	C₂×#92418	—	2	2	no	—
28	C₂×#92418	C₂×C₄	1	4	yes	—
29	C₂³×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	—	2	4	no	—
31	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
32	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
33	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₆₁	#41	1	2	yes	—
36	C₂×Dic₆₁	—	2	4	no	—
37	C₂×Dic₆₁	—	2	2	no	—
38	C₂×Dic₆₁	—	2	4	no	—
39	C₂×Dic₆₁	C₄²	1	4	yes	—
40	C₈×C₆₁	—	2	4	no	—
41	#92418	—	2	4	no	—
42	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
43	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₆₁	#117	1	1	yes	characteristic
45	C₂²×C₆₁	#131	1	4	yes	—
46	C₄×C₆₁	—	2	4	no	—
47	C₄×C₆₁	C₄×D₄	1	2	yes	—
48	C₄×C₆₁	C₄×Q₈	1	2	yes	—
49	Dic₆₁	—	2	4	no	—
50	Dic₆₁	—	4	2	no	—
51	#1768	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₆₁	#405	1	2	yes	—
54	C₂×C₆₁	#424	1	2	yes	—
55	C₂×C₆₁	#433	1	2	yes	—
56	C₂×C₄⋊C₈	—	61	2	no	—
57	C₂×#97	D₆₁	1	1	yes	characteristic
58	C₂×C₄×C₈	—	61	1	no	—
59	#376	—	61	1	no	—
60	#336	—	61	2	no	—
61	C₆₁	#1768	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	61	2	no	—
63	C₂²×C₈	C₂×D₆₁	1	2	yes	—
64	C₂×C₄²	—	61	1	no	—
65	C₂×C₄²	—	61	1	no	—
66	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
67	C₄⋊C₈	—	61	8	no	—
68	#97	—	2	2	no	—
69	C₄×C₈	—	122	2	no	—
70	#95	—	61	4	no	—
71	C₂²×C₄	—	61	2	no	—
72	C₂²×C₄	—	61	2	no	—
73	C₂²×C₄	C₄×D₆₁	1	2	yes	—
74	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	61	4	no	—
78	C₂×C₈	—	122	2	no	—
79	C₂×C₈	—	122	2	no	—
80	C₂×C₈	C₄×D₆₁	1	4	yes	—
81	C₄²	—	61	4	no	—
82	C₄²	—	122	2	no	—
83	C₄²	Dic₁₂₂	1	2	yes	—
84	C₄²	C₂²⋊D₆₁	1	2	yes	—
85	C₂³	C₂×C₄×D₆₁	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	61	4	no	—
88	C₂×C₄	—	122	4	no	—
89	C₂×C₄	—	122	2	no	—
90	C₂×C₄	—	122	4	no	—
91	C₂×C₄	#11758196	1	4	yes	—
92	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
93	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
94	C₂×C₄	#11758222	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
96	C₈	—	2	4	no	—
97	C₈	—	122	4	no	—
98	C₂²	C₄²×D₆₁	1	1	yes	characteristic
99	C₂²	C₂×#11758196	1	1	yes	characteristic
100	C₂²	#14519734	1	1	yes	characteristic
101	C₂²	#14519785	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	122	4	no	—
104	C₄	—	244	2	no	—
105	C₄	C₄×C₂²⋊D₆₁	1	2	yes	—
106	C₄	C₄×Dic₁₂₂	1	2	yes	—
107	C₂	C₄×#11758196	1	1	yes	characteristic
108	C₂	#16839719	1	2	yes	—
109	C₂	#16839790	1	2	yes	—
110	C₂	#16839824	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519706

C₂

yes

maximal

C₂×C₄×#92418

C₂

yes

maximal, characteristic

#16839608

C₂

yes

maximal, characteristic

#16839516

C₂

yes

maximal

C₂×#97×C₆₁

C₂

yes

maximal, characteristic

C₂²×#92418

C₂²

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519706

C₄

yes

complemented

C₄×#92418

—

#14519684

C₄

yes

—

C₂²×C₈×C₆₁

C₂²

yes

—

C₂×C₄²×C₆₁

C₂²

yes

characteristic

#97×C₆₁

—

C₂²×C₄×C₆₁

C₂×C₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

—

C₂²×Dic₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

D₄

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

—

C₂×#92418

—

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄²

yes

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂²×C₆₁

C₂×C₄⋊C₄

yes

C₂²×C₆₁

yes

C₂²×C₆₁

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₄×D₄

yes

—

C₄×C₆₁

C₄×Q₈

yes

—

Dic₆₁

—

Dic₆₁

—

#1768

—

maximal, Sylow

C₂×C₆₁

C₄×C₄⋊C₄

yes

characteristic

C₂×C₆₁

#405

yes

—

C₂×C₆₁

#424

yes

—

C₂×C₆₁

#433

yes

—

C₂×C₄⋊C₈

—

C₂×#97

D₆₁

yes

characteristic

C₂×C₄×C₈

—

#376

—

#336

—

C₆₁

#1768

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₆₁

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

122

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₆₁

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

—

C₄²

—

C₄²

—

122

—

C₄²

Dic₁₂₂

yes

—

C₄²

C₂²⋊D₆₁

yes

—

C₂³

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

#11758196

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

C₂×C₄×D₆₁

yes

—

C₂×C₄

#11758222

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

122

—

C₂²

C₄²×D₆₁

yes

characteristic

C₂²

C₂×#11758196

yes

characteristic

100

C₂²

#14519734

yes

characteristic

101

C₂²

#14519785

yes

—

102

C₄

—

103

C₄

—

122

—

104

C₄

—

244

—

105

C₄

C₄×C₂²⋊D₆₁

yes

—

106

C₄

C₄×Dic₁₂₂

yes

—

107

C₂

C₄×#11758196

yes

characteristic

108

C₂

#16839719

yes

—

109

C₂

#16839790

yes

—

110

C₂

#16839824

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₆₁
commutator	C₂²×C₆₁	C₂×C₄²
Fitting	C₂×#97×C₆₁	C₂
socle	C₂³×C₆₁	C₂²×C₄
hypercenter	C₂×#97	D₆₁
hypocenter	C₆₁	#1768
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₆₁

commutator

C₂²×C₆₁

C₂×C₄²

Fitting

C₂×#97×C₆₁

C₂

socle

C₂³×C₆₁

C₂²×C₄

hypercenter

C₂×#97

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
9. #14519706	C₄	semidirect
61. C₆₁	#1768	semidirect

H ≅ G/N

type

9. #14519706

C₄

semidirect

61. C₆₁

#1768

semidirect

Subgroups — #21445679

Conjugacy classes of subgroups

Complements