Group #21425860 — subgroups

Subgroups — #21425860

Order 7552.

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×D₅₉	C₂	1	2	yes	maximal
2	#16837356	C₂	1	1	yes	maximal, characteristic
3	#16837223	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837222	C₂	1	2	yes	maximal, complemented
5	C₅₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11745659	C₄	1	1	yes	characteristic
7	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
8	#14273684	C₄	1	1	yes	characteristic
9	#14273667	C₂²	1	2	yes	—
10	#14273666	—	2	2	no	—
11	C₁₆×D₅₉	—	2	2	no	—
12	#14273638	C₄	1	1	yes	characteristic
13	#14273637	C₄	1	1	yes	characteristic
14	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
15	M₃₂×C₅₉	C₂²	1	2	yes	—
16	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
20	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
21	(C₂×D₅₉)⋊C₄	—	2	1	no	—
22	Dic₅₉⋊C₄	—	2	1	no	—
23	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	#11745659	C₈	1	4	yes	—
27	C₈×D₅₉	D₄	1	2	yes	—
28	C₈×D₅₉	Q₈	1	2	yes	—
29	C₁₆×C₅₉	—	2	2	no	—
30	C₅₉⋊C₁₆	—	2	2	no	—
31	C₂²×D₅₉	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₅₉	—	2	1	no	—
33	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₅₉	—	2	1	no	—
35	C₂×Dic₅₉	M₁₆	1	1	yes	characteristic
36	C₄×D₅₉	C₄⋊C₄	1	2	yes	—
37	C₄×D₅₉	C₂×C₈	1	2	yes	—
38	C₈×C₅₉	C₂×C₈	1	2	yes	—
39	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
40	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
41	C₅₉⋊C₈	C₄⋊C₄	1	2	yes	—
42	C₅₉⋊C₈	C₂×C₈	1	2	yes	—
43	C₂²×C₅₉	C₂×M₁₆	1	1	yes	characteristic
44	C₂×D₅₉	—	4	1	no	—
45	C₂×D₅₉	C₄⋊C₈	1	2	yes	—
46	C₄×C₅₉	—	4	1	no	—
47	C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
49	Dic₅₉	—	4	1	no	—
50	Dic₅₉	C₄⋊C₈	1	2	yes	—
51	#2153	—	59	1	no	maximal, Sylow
52	C₂×C₅₉	—	2	1	no	—
53	C₂×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
54	D₅₉	—	2	2	no	—
55	C₂×M₃₂	—	59	2	no	—
56	#405	—	59	1	no	—
57	#364	—	59	2	no	—
58	#364	—	59	1	no	—
59	#364	D₅₉	1	1	yes	characteristic, complemented
60	C₅₉	#2153	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	59	1	no	—
62	C₂²×C₈	—	59	1	no	—
63	#117	—	59	1	no	—
64	M₃₂	—	59	2	no	—
65	M₃₂	—	118	2	no	—
66	M₃₂	C₂×D₅₉	1	2	yes	—
67	C₂×C₁₆	—	118	2	no	—
68	#97	—	59	1	no	—
69	#97	—	59	1	no	—
70	C₄×C₈	—	59	1	no	—
71	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
72	C₂²×C₄	—	59	1	no	—
73	M₁₆	—	59	4	no	—
74	C₂×C₈	—	59	1	no	—
75	C₂×C₈	—	59	1	no	—
76	C₂×C₈	—	59	2	no	—
77	C₂×C₈	—	59	2	no	—
78	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
79	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
80	C₄⋊C₄	—	118	1	no	—
81	C₂²⋊C₄	—	118	1	no	—
82	C₄²	—	59	1	no	—
83	C₄²	C₄×D₅₉	1	1	yes	characteristic
84	C₁₆	—	2	2	no	—
85	C₁₆	—	118	2	no	—
86	C₂³	—	59	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	59	1	no	—
89	C₂×C₄	—	59	2	no	—
90	C₂×C₄	—	59	2	no	—
91	C₂×C₄	—	118	1	no	—
92	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
93	C₈	—	59	2	no	—
94	C₈	—	59	2	no	—
95	C₈	C₈×D₅₉	1	2	yes	—
96	C₈	D₄×D₅₉	1	1	yes	characteristic
97	C₈	Q₈×D₅₉	1	1	yes	characteristic
98	C₂²	—	59	2	no	—
99	C₂²	—	236	1	no	—
100	C₂²	M₁₆×D₅₉	1	1	yes	characteristic
101	C₄	—	4	1	no	—
102	C₄	—	59	2	no	—
103	C₄	—	236	1	no	—
104	C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
105	C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
106	C₂	—	2	1	no	—
107	C₂	—	118	2	no	—
108	C₂	C₄⋊C₈×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₃₂×D₅₉

C₂

yes

maximal

#16837356

C₂

yes

maximal, characteristic

#16837223

C₂

yes

maximal, characteristic, complemented

#16837222

C₂

yes

maximal, complemented

C₅₉×#364

C₂

yes

maximal, characteristic, complemented

C₂×#11745659

C₄

yes

characteristic

C₂×C₈×D₅₉

C₂²

yes

characteristic

#14273684

C₄

yes

characteristic

#14273667

C₂²

yes

—

#14273666

—

C₁₆×D₅₉

—

#14273638

C₄

yes

characteristic

#14273637

C₄

yes

characteristic

C₈×Dic₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

C₂²

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄×D₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

C₂×C₄

yes

characteristic

(C₂×D₅₉)⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

#11745659

C₈

yes

—

C₈×D₅₉

D₄

yes

—

C₈×D₅₉

Q₈

yes

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂²×D₅₉

M₁₆

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

M₁₆

yes

characteristic

C₄×D₅₉

C₄⋊C₄

yes

—

C₄×D₅₉

C₂×C₈

yes

—

C₈×C₅₉

C₂×C₈

yes

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

C₂×Q₈

yes

characteristic

C₅₉⋊C₈

C₄⋊C₄

yes

—

C₅₉⋊C₈

C₂×C₈

yes

—

C₂²×C₅₉

C₂×M₁₆

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

C₄⋊C₈

yes

—

C₄×C₅₉

—

C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₅₉

C₂²×C₈

yes

characteristic

Dic₅₉

—

Dic₅₉

C₄⋊C₈

yes

—

#2153

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

C₂×C₄⋊C₈

yes

characteristic

D₅₉

—

C₂×M₃₂

—

—

—

—

D₅₉

yes

characteristic, complemented

C₅₉

#2153

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

118

—

M₃₂

C₂×D₅₉

yes

—

C₂×C₁₆

—

118

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

118

—

C₂²⋊C₄

—

118

—

C₄²

—

C₄²

C₄×D₅₉

yes

characteristic

C₁₆

—

C₁₆

—

118

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

C₈

—

C₈

—

C₈

C₈×D₅₉

yes

—

C₈

D₄×D₅₉

yes

characteristic

C₈

Q₈×D₅₉

yes

characteristic

C₂²

—

C₂²

—

236

—

100

C₂²

M₁₆×D₅₉

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

236

—

104

C₄

C₄⋊C₄×D₅₉

yes

characteristic

105

C₄

C₂×C₈×D₅₉

yes

characteristic

106

C₂

—

107

C₂

—

118

—

108

C₂

C₄⋊C₈×D₅₉

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₅₉
commutator	C₄×C₅₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#364	C₂
socle	C₂×C₅₉	C₂×C₄⋊C₈
hypercenter	#364	D₅₉
hypocenter	C₅₉	#2153
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×D₅₉

commutator

C₄×C₅₉

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#364

C₂

socle

C₂×C₅₉

C₂×C₄⋊C₈

D₅₉

C₅₉

G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
3. #16837223	C₂	semidirect
4. #16837222	C₂	semidirect
5. C₅₉×#364	C₂	semidirect
59. #364	D₅₉	semidirect
60. C₅₉	#2153	semidirect

H ≅ G/N

type

3. #16837223

C₂

semidirect

4. #16837222

C₂

semidirect

5. C₅₉×#364

C₂

semidirect

59. #364

D₅₉

semidirect

60. C₅₉

#2153

semidirect

Subgroups — #21425860

Conjugacy classes of subgroups

Complements