Group #21445983 — subgroups

Subgroups — #21445983

Order 7808.

248 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519711	C₂	1	2	yes	maximal
2	C₂×#14519709	C₂	1	2	yes	maximal
3	#16839628	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₆₁	C₂²	1	4	yes	—
6	#14519711	—	2	4	no	—
7	#14519709	—	2	4	no	—
8	#14519684	—	2	4	no	—
9	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₆₁	C₄	1	4	yes	complemented
13	C₂²×C₄×C₆₁	D₄	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
15	C₂²×Dic₆₁	—	2	4	no	—
16	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₆₁	D₄	1	2	yes	—
19	C₂×C₈×C₆₁	D₄	1	2	yes	—
20	C₂×C₈×C₆₁	Q₈	1	2	yes	—
21	C₂×C₈×C₆₁	Q₈	1	2	yes	—
22	C₄²×C₆₁	C₂×C₄	1	2	yes	—
23	C₄²×C₆₁	Q₈	1	2	yes	—
24	C₄⋊Dic₆₁	—	2	4	no	—
25	C₄⋊Dic₆₁	—	2	4	no	—
26	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₆₁	—	2	4	no	—
28	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
29	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
35	C₂×Dic₆₁	—	4	4	no	—
36	C₂×Dic₆₁	—	4	8	no	—
37	C₈×C₆₁	C₄⋊C₄	1	4	yes	—
38	C₈×C₆₁	C₄⋊C₄	1	4	yes	—
39	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₆₁	#127	1	1	yes	characteristic
41	C₂²×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₆₁	#135	1	4	yes	—
43	C₄×C₆₁	—	2	4	no	—
44	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
47	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
48	Dic₆₁	—	8	4	no	—
49	#1846	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	#384	1	1	yes	characteristic
51	C₂×C₆₁	#427	1	2	yes	—
52	C₂×C₆₁	#495	1	2	yes	—
53	C₂×C₆₁	#499	1	2	yes	—
54	C₂×#107	—	61	2	no	—
55	C₂×#106	—	61	2	no	—
56	C₂×C₄×C₈	D₆₁	1	1	yes	characteristic
57	#382	—	61	2	no	—
58	C₆₁	#1846	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
60	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
61	C₂×C₄⋊C₄	—	61	4	no	—
62	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
63	#107	—	122	4	no	—
64	#106	—	122	4	no	—
65	C₄×C₈	Dic₆₁	1	4	yes	complemented
66	#95	—	122	4	no	—
67	C₂²×C₄	—	122	4	no	—
68	C₂²×C₄	D₂₄₄	1	2	yes	—
69	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
70	C₂×C₈	Dic₁₂₂	1	2	yes	—
71	C₂×C₈	Dic₁₂₂	1	2	yes	—
72	C₂×C₈	D₂₄₄	1	2	yes	—
73	C₂×C₈	D₂₄₄	1	2	yes	—
74	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
75	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
76	C₄⋊C₄	—	122	4	no	—
77	C₄⋊C₄	—	122	4	no	—
78	C₄²	Dic₁₂₂	1	2	yes	—
79	C₄²	C₂×Dic₆₁	1	2	yes	—
80	C₂³	C₂×D₂₄₄	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	244	4	no	—
83	C₂×C₄	—	244	8	no	—
84	C₂×C₄	C₄⋊Dic₆₁	1	4	yes	—
85	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
86	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
87	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
88	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
89	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
90	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
91	C₈	C₄⋊Dic₆₁	1	4	yes	—
92	C₈	C₄⋊Dic₆₁	1	4	yes	—
93	C₂²	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
94	C₂²	#14519774	1	1	yes	characteristic
95	C₂²	#14519777	1	1	yes	characteristic
96	C₂²	#14519799	1	4	yes	—
97	C₄	—	2	4	no	—
98	C₄	—	488	4	no	—
99	C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
100	C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
101	C₄	#14519777	1	1	yes	characteristic
102	C₄	#14519777	1	1	yes	characteristic
103	C₂	#16839632	1	1	yes	characteristic
104	C₂	#16839800	1	2	yes	—
105	C₂	#16840146	1	2	yes	—
106	C₂	#16840164	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519711

C₂

yes

maximal

C₂×#14519709

C₂

yes

maximal

#16839628

C₂

yes

maximal

C₂×C₄×C₈×C₆₁

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₆₁

C₂²

yes

—

#14519711

—

#14519709

—

#14519684

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄²×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₄

yes

complemented

C₂²×C₄×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

D₄

yes

—

C₂×C₈×C₆₁

D₄

yes

—

C₂×C₈×C₆₁

Q₈

yes

—

C₂×C₈×C₆₁

Q₈

yes

—

C₄²×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

Q₈

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₂³×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₈

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

C₄⋊C₄

yes

—

C₈×C₆₁

C₄⋊C₄

yes

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₆₁

#127

yes

characteristic

C₂²×C₆₁

C₄⋊Q₈

yes

characteristic

C₂²×C₆₁

#135

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

C₄×C₆₁

C₄⋊Q₈

yes

characteristic

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

C₂×C₆₁

#495

yes

—

C₂×C₆₁

#499

yes

—

C₂×#107

—

C₂×#106

—

C₂×C₄×C₈

D₆₁

yes

characteristic

#382

—

C₆₁

#1846

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₆₁

yes

characteristic

#107

—

122

—

#106

—

122

—

C₄×C₈

Dic₆₁

yes

complemented

#95

—

122

—

C₂²×C₄

—

122

—

C₂²×C₄

D₂₄₄

yes

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

Dic₁₂₂

yes

—

C₂×C₈

D₂₄₄

yes

—

C₂×C₈

D₂₄₄

yes

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄²

Dic₁₂₂

yes

—

C₄²

C₂×Dic₆₁

yes

—

C₂³

C₂×D₂₄₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₄⋊Dic₆₁

yes

—

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

C₂×Dic₁₂₂

yes

characteristic

C₂×C₄

C₂×D₂₄₄

yes

characteristic

C₂×C₄

C₂×D₂₄₄

yes

characteristic

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₈

C₄⋊Dic₆₁

yes

—

C₈

C₄⋊Dic₆₁

yes

—

C₂²

C₂×C₄⋊Dic₆₁

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₄

—

C₄

—

488

—

C₄

C₂×C₄⋊Dic₆₁

yes

characteristic

100

C₄

C₂×C₄⋊Dic₆₁

yes

characteristic

101

C₄

#14519777

yes

characteristic

102

C₄

#14519777

yes

characteristic

103

C₂

#16839632

yes

characteristic

104

C₂

#16839800

yes

—

105

C₂

#16840146

yes

—

106

C₂

#16840164

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₄₄
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×C₄×C₈×C₆₁	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	C₂×C₄×C₈	D₆₁
hypocenter	C₆₁	#1846
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₂₄₄

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₂×C₄×C₈×C₆₁

C₂

socle

C₂³×C₆₁

C₂×D₄

hypercenter

C₂×C₄×C₈

D₆₁

hypocenter

C₆₁

#1846

LCS

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
12. C₄×C₈×C₆₁	C₄	semidirect
58. C₆₁	#1846	semidirect
65. C₄×C₈	Dic₆₁	semidirect

H ≅ G/N

type

12. C₄×C₈×C₆₁

C₄

semidirect

58. C₆₁

#1846

semidirect

65. C₄×C₈

Dic₆₁

semidirect

Subgroups — #21445983

Conjugacy classes of subgroups

Complements