Group #21447583 — subgroups

Subgroups — #21447583

Order 7808.

152 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 75 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	M₃₂×D₆₁	C₂	1	2	yes	maximal
2	#16839716	C₂	1	1	yes	maximal, characteristic
3	#16839583	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839582	C₂	1	2	yes	maximal, complemented
5	C₆₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758189	C₄	1	1	yes	characteristic
7	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
8	#14519734	C₄	1	1	yes	characteristic
9	#14519717	C₂²	1	2	yes	—
10	#14519716	—	2	2	no	—
11	C₁₆×D₆₁	—	2	2	no	—
12	#14519688	C₄	1	1	yes	characteristic
13	#14519687	C₄	1	1	yes	characteristic
14	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
15	M₃₂×C₆₁	C₂²	1	2	yes	—
16	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
20	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
21	#11758198	—	2	1	no	—
22	#11758196	—	2	1	no	—
23	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	C₂×C₄	1	1	yes	characteristic
25	C₂×#92418	C₂×C₄	1	1	yes	characteristic
26	#11758189	C₈	1	4	yes	—
27	C₈×D₆₁	D₄	1	2	yes	—
28	C₈×D₆₁	Q₈	1	2	yes	—
29	C₁₆×C₆₁	—	2	2	no	—
30	#11758185	—	2	2	no	—
31	C₂²×D₆₁	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₆₁	—	2	1	no	—
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	—	2	1	no	—
35	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
36	C₄×D₆₁	C₄⋊C₄	1	2	yes	—
37	C₄×D₆₁	C₂×C₈	1	2	yes	—
38	C₈×C₆₁	C₂×C₈	1	2	yes	—
39	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
40	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
41	#92418	C₄⋊C₄	1	2	yes	—
42	#92418	C₂×C₈	1	2	yes	—
43	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
44	C₂×D₆₁	—	4	1	no	—
45	C₂×D₆₁	C₄⋊C₈	1	2	yes	—
46	C₄×C₆₁	—	4	1	no	—
47	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
49	Dic₆₁	—	4	1	no	—
50	Dic₆₁	C₄⋊C₈	1	2	yes	—
51	#2153	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	—	2	1	no	—
53	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
54	D₆₁	—	2	2	no	—
55	C₂×M₃₂	—	61	2	no	—
56	#405	—	61	1	no	—
57	#364	—	61	2	no	—
58	#364	—	61	1	no	—
59	#364	D₆₁	1	1	yes	characteristic, complemented
60	C₆₁	#2153	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	61	1	no	—
62	C₂²×C₈	—	61	1	no	—
63	#117	—	61	1	no	—
64	M₃₂	—	61	2	no	—
65	M₃₂	—	122	2	no	—
66	M₃₂	C₂×D₆₁	1	2	yes	—
67	C₂×C₁₆	—	122	2	no	—
68	#97	—	61	1	no	—
69	#97	—	61	1	no	—
70	C₄×C₈	—	61	1	no	—
71	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
72	C₂²×C₄	—	61	1	no	—
73	M₁₆	—	61	4	no	—
74	C₂×C₈	—	61	1	no	—
75	C₂×C₈	—	61	1	no	—
76	C₂×C₈	—	61	2	no	—
77	C₂×C₈	—	61	2	no	—
78	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
79	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
80	C₄⋊C₄	—	122	1	no	—
81	C₂²⋊C₄	—	122	1	no	—
82	C₄²	—	61	1	no	—
83	C₄²	C₄×D₆₁	1	1	yes	characteristic
84	C₁₆	—	2	2	no	—
85	C₁₆	—	122	2	no	—
86	C₂³	—	61	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	61	1	no	—
89	C₂×C₄	—	61	2	no	—
90	C₂×C₄	—	61	2	no	—
91	C₂×C₄	—	122	1	no	—
92	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
93	C₈	—	61	2	no	—
94	C₈	—	61	2	no	—
95	C₈	C₈×D₆₁	1	2	yes	—
96	C₈	D₄×D₆₁	1	1	yes	characteristic
97	C₈	Q₈×D₆₁	1	1	yes	characteristic
98	C₂²	—	61	2	no	—
99	C₂²	—	244	1	no	—
100	C₂²	M₁₆×D₆₁	1	1	yes	characteristic
101	C₄	—	4	1	no	—
102	C₄	—	61	2	no	—
103	C₄	—	244	1	no	—
104	C₄	C₄⋊C₄×D₆₁	1	1	yes	characteristic
105	C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
106	C₂	—	2	1	no	—
107	C₂	—	122	2	no	—
108	C₂	C₄⋊C₈×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₃₂×D₆₁

C₂

yes

maximal

#16839716

C₂

yes

maximal, characteristic

#16839583

C₂

yes

maximal, characteristic, complemented

#16839582

C₂

yes

maximal, complemented

C₆₁×#364

C₂

yes

maximal, characteristic, complemented

C₂×#11758189

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519734

C₄

yes

characteristic

#14519717

C₂²

yes

—

#14519716

—

C₁₆×D₆₁

—

#14519688

C₄

yes

characteristic

#14519687

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

M₃₂×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

—

#11758196

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

C₈

yes

—

C₈×D₆₁

D₄

yes

—

C₈×D₆₁

Q₈

yes

—

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

M₁₆

yes

characteristic

C₄×D₆₁

C₄⋊C₄

yes

—

C₄×D₆₁

C₂×C₈

yes

—

C₈×C₆₁

C₂×C₈

yes

—

C₈×C₆₁

C₂×D₄

yes

characteristic

C₈×C₆₁

C₂×Q₈

yes

characteristic

#92418

C₄⋊C₄

yes

—

#92418

C₂×C₈

yes

—

C₂²×C₆₁

C₂×M₁₆

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₄⋊C₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

Dic₆₁

C₄⋊C₈

yes

—

#2153

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×C₄⋊C₈

yes

characteristic

D₆₁

—

C₂×M₃₂

—

—

—

—

D₆₁

yes

characteristic, complemented

C₆₁

#2153

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

122

—

M₃₂

C₂×D₆₁

yes

—

C₂×C₁₆

—

122

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

—

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

C₈

—

C₈

C₈×D₆₁

yes

—

C₈

D₄×D₆₁

yes

characteristic

C₈

Q₈×D₆₁

yes

characteristic

C₂²

—

C₂²

—

244

—

100

C₂²

M₁₆×D₆₁

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

244

—

104

C₄

C₄⋊C₄×D₆₁

yes

characteristic

105

C₄

C₂×C₈×D₆₁

yes

characteristic

106

C₂

—

107

C₂

—

122

—

108

C₂

C₄⋊C₈×D₆₁

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₆₁
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#364	C₂
socle	C₂×C₆₁	C₂×C₄⋊C₈
hypercenter	#364	D₆₁
hypocenter	C₆₁	#2153
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×D₆₁

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#364

C₂

socle

C₂×C₆₁

C₂×C₄⋊C₈

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
3. #16839583	C₂	semidirect
4. #16839582	C₂	semidirect
5. C₆₁×#364	C₂	semidirect
59. #364	D₆₁	semidirect
60. C₆₁	#2153	semidirect

H ≅ G/N

type

3. #16839583

C₂

semidirect

4. #16839582

C₂

semidirect

5. C₆₁×#364

C₂

semidirect

59. #364

D₆₁

semidirect

60. C₆₁

#2153

semidirect

Subgroups — #21447583

Conjugacy classes of subgroups

Complements