Group #21447922 — subgroups

Subgroups — #21447922

Order 7808.

170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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×D₉₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#16839998	C₂	1	2	yes	maximal, complemented
3	#16839590	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839564	C₂	1	2	yes	maximal, complemented
5	C₂×M₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₈₈	C₂²	1	2	yes	—
7	#14519751	—	2	2	no	—
8	D₉₇₆	—	2	2	no	—
9	#14519711	C₂²	1	2	yes	—
10	#14519699	—	2	2	no	—
11	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	M₃₂×C₆₁	—	2	2	no	—
13	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
16	C₂×C₂²⋊D₆₁	—	4	2	no	—
17	C₂×D₂₄₄	—	2	2	no	—
18	C₂×C₈×C₆₁	—	2	1	no	—
19	C₂×C₈×C₆₁	—	2	1	no	—
20	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
22	#11758198	—	4	2	no	—
23	C₄⋊Dic₆₁	—	2	2	no	—
24	D₄₈₈	—	2	2	no	—
25	D₄₈₈	—	2	2	no	—
26	C₁₆×C₆₁	—	2	1	no	—
27	C₁₆×C₆₁	D₄	1	2	yes	complemented
28	C₂³×C₆₁	D₈	1	1	yes	characteristic
29	C₂²×D₆₁	—	4	2	no	—
30	C₂×C₄×C₆₁	—	2	1	no	—
31	C₂×C₄×C₆₁	—	2	1	no	—
32	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₂²⋊D₆₁	—	8	4	no	—
35	C₂×Dic₆₁	—	4	2	no	—
36	D₂₄₄	—	4	2	no	—
37	D₂₄₄	—	4	2	no	—
38	C₈×C₆₁	—	2	1	no	—
39	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
40	C₈×C₆₁	#41	1	1	yes	characteristic
41	C₂²×C₆₁	—	2	1	no	—
42	C₂²×C₆₁	—	2	2	no	—
43	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
44	C₂×D₆₁	—	8	2	no	—
45	C₂×D₆₁	—	8	2	no	—
46	C₂×D₆₁	—	8	2	no	—
47	C₄×C₆₁	—	2	1	no	—
48	C₄×C₆₁	#121	1	1	yes	characteristic
49	C₄×C₆₁	#135	1	1	yes	characteristic
50	Dic₆₁	—	8	2	no	—
51	#2218	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	—	4	1	no	—
53	C₂×C₆₁	#466	1	1	yes	characteristic
54	C₂×C₆₁	#509	1	2	yes	—
55	D₆₁	—	16	2	no	—
56	C₂×D₁₆	—	61	1	no	—
57	C₂×M₃₂	D₆₁	1	1	yes	characteristic, complemented
58	#466	—	61	2	no	—
59	#367	—	61	1	no	—
60	#357	—	61	2	no	—
61	C₆₁	#2218	1	1	yes	characteristic, complemented, Sylow
62	C₂×D₈	—	61	2	no	—
63	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
64	#121	—	122	2	no	—
65	D₁₆	—	122	2	no	—
66	M₃₂	—	2	2	no	—
67	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
68	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
69	#107	—	61	2	no	—
70	#102	—	122	2	no	—
71	C₂×D₄	—	122	2	no	—
72	C₂×D₄	—	244	2	no	—
73	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
74	D₈	—	122	2	no	—
75	D₈	—	122	2	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	D₂₄₄	1	1	yes	characteristic
79	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
80	C₄⋊C₄	—	122	2	no	—
81	C₂²⋊C₄	—	244	2	no	—
82	C₁₆	—	2	1	no	—
83	C₁₆	C₂²⋊D₆₁	1	2	yes	complemented
84	C₂³	—	244	2	no	—
85	C₂³	D₄₈₈	1	1	yes	characteristic
86	D₄	—	488	4	no	—
87	D₄	—	244	2	no	—
88	D₄	—	244	2	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	244	2	no	—
92	C₂×C₄	D₄₈₈	1	1	yes	characteristic
93	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	#11758222	1	1	yes	characteristic
96	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
97	C₂²	—	2	2	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	488	2	no	—
100	C₂²	—	488	2	no	—
101	C₂²	—	488	2	no	—
102	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	488	2	no	—
105	C₄	#14519751	1	1	yes	characteristic
106	C₄	#14519799	1	1	yes	characteristic
107	C₂	—	4	1	no	—
108	C₂	—	976	2	no	—
109	C₂	#16839998	1	1	yes	characteristic
110	C₂	#16840200	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₉₇₆

C₂

yes

maximal, characteristic, complemented

#16839998

C₂

yes

maximal, complemented

#16839590

C₂

yes

maximal, characteristic, complemented

#16839564

C₂

yes

maximal, complemented

C₂×M₃₂×C₆₁

C₂

yes

maximal, characteristic, complemented

C₂×D₄₈₈

C₂²

yes

—

#14519751

—

D₉₇₆

—

#14519711

C₂²

yes

—

#14519699

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

M₃₂×C₆₁

—

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

D₄

yes

characteristic

C₂×C₂²⋊D₆₁

—

C₂×D₂₄₄

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

#11758198

—

C₄⋊Dic₆₁

—

D₄₈₈

—

D₄₈₈

—

C₁₆×C₆₁

—

C₁₆×C₆₁

D₄

yes

complemented

C₂³×C₆₁

D₈

yes

characteristic

C₂²×D₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²⋊D₆₁

—

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

C₈×C₆₁

—

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

#41

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

#2218

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#466

yes

characteristic

C₂×C₆₁

#509

yes

—

D₆₁

—

C₂×D₁₆

—

C₂×M₃₂

D₆₁

yes

characteristic, complemented

#466

—

#367

—

#357

—

C₆₁

#2218

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

#121

—

122

—

D₁₆

—

122

—

M₃₂

—

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₂×C₁₆

C₂×D₆₁

yes

characteristic

#107

—

#102

—

122

—

C₂×D₄

—

122

—

C₂×D₄

—

244

—

C₂²×C₄

D₂₄₄

yes

characteristic

D₈

—

122

—

D₈

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₂₄₄

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

244

—

C₁₆

—

C₁₆

C₂²⋊D₆₁

yes

complemented

C₂³

—

244

—

C₂³

D₄₈₈

yes

characteristic

D₄

—

488

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

D₄₈₈

yes

characteristic

C₂×C₄

C₂×D₂₄₄

yes

characteristic

C₈

—

C₈

#11758222

yes

characteristic

C₈

C₂×C₂²⋊D₆₁

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

488

—

100

C₂²

—

488

—

101

C₂²

—

488

—

102

C₂²

C₂×D₄₈₈

yes

characteristic

103

C₄

—

104

C₄

—

488

—

105

C₄

#14519751

yes

characteristic

106

C₄

#14519799

yes

characteristic

107

C₂

—

108

C₂

—

976

—

109

C₂

#16839998

yes

characteristic

110

C₂

#16840200

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄₈₈
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂×M₃₂×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₂×M₃₂	D₆₁
hypocenter	C₆₁	#2218
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

C₂×D₄₈₈

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂×M₃₂×C₆₁

C₂

socle

C₂²×C₆₁

C₂×D₈

hypercenter

C₂×M₃₂

D₆₁

hypocenter

C₆₁

#2218

LCS

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
1. C₂×D₉₇₆	C₂	semidirect
2. #16839998	C₂	semidirect
3. #16839590	C₂	semidirect
4. #16839564	C₂	semidirect
5. C₂×M₃₂×C₆₁	C₂	semidirect
27. C₁₆×C₆₁	D₄	semidirect
57. C₂×M₃₂	D₆₁	semidirect
61. C₆₁	#2218	semidirect
83. C₁₆	C₂²⋊D₆₁	semidirect

H ≅ G/N

type

1. C₂×D₉₇₆

C₂

semidirect

2. #16839998

C₂

semidirect

3. #16839590

C₂

semidirect

4. #16839564

C₂

semidirect

5. C₂×M₃₂×C₆₁

C₂

semidirect

27. C₁₆×C₆₁

D₄

semidirect

57. C₂×M₃₂

D₆₁

semidirect

61. C₆₁

#2218

semidirect

83. C₁₆

C₂²⋊D₆₁

semidirect

Subgroups — #21447922

Conjugacy classes of subgroups

Complements