Group #21422992 — subgroups

Subgroups — #21422992

Order 7552.

152 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 65 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	#16837529	C₂	1	2	yes	maximal
2	C₄×Dic₂₃₆	C₂	1	1	yes	maximal, characteristic
3	#16837132	C₂	1	2	yes	maximal
4	C₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₃₆	C₄	1	1	yes	characteristic
7	C₄×Dic₁₁₈	C₂²	1	2	yes	—
8	#14273661	C₄	1	1	yes	characteristic
9	Dic₅₉⋊C₈	—	2	2	no	—
10	#14273652	C₄	1	2	yes	—
11	#14273637	—	2	2	no	—
12	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
15	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₁₈	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₅₉	—	2	2	no	—
18	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₅₉	C₂³	1	1	yes	characteristic
21	C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
22	Dic₅₉⋊C₄	—	2	2	no	—
23	C₄×Dic₅₉	—	2	2	no	—
24	C₂×C₅₉⋊C₈	—	2	1	no	—
25	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
26	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
27	Dic₂₃₆	—	2	2	no	—
28	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
31	C₂×Dic₅₉	—	2	2	no	—
32	C₂×Dic₅₉	—	2	2	no	—
33	Dic₁₁₈	—	2	2	no	—
34	Dic₁₁₈	—	2	2	no	—
35	C₈×C₅₉	—	2	1	no	—
36	C₈×C₅₉	—	4	2	no	—
37	C₈×C₅₉	M₁₆	1	2	yes	—
38	C₅₉⋊C₈	—	2	2	no	—
39	C₅₉⋊C₈	—	2	1	no	—
40	C₅₉⋊C₈	Q₁₆	1	2	yes	complemented
41	C₂²×C₅₉	C₄×D₄	1	1	yes	characteristic
42	C₄×C₅₉	—	2	1	no	—
43	C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₅₉	#131	1	1	yes	characteristic
45	C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₅₉	#135	1	1	yes	characteristic
47	Dic₅₉	—	4	2	no	—
48	Dic₅₉	—	4	2	no	—
49	#1591	—	59	1	no	maximal, Sylow
50	C₂×C₅₉	#436	1	1	yes	characteristic
51	C₂×C₅₉	C₄×Q₁₆	1	1	yes	characteristic
52	C₂×C₅₉	#443	1	1	yes	characteristic
53	#446	—	59	2	no	—
54	C₄×Q₁₆	—	59	1	no	—
55	#335	D₅₉	1	1	yes	characteristic
56	Q₈⋊C₈	—	59	2	no	—
57	C₈²	—	59	1	no	—
58	C₅₉	#1591	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	—	59	1	no	—
60	C₄×Q₈	—	59	2	no	—
61	#107	—	59	1	no	—
62	C₄⋊C₈	—	118	2	no	—
63	C₄⋊C₈	C₂×D₅₉	1	2	yes	—
64	#103	—	59	2	no	—
65	#97	—	118	2	no	—
66	C₄×C₈	—	59	1	no	—
67	C₄×C₈	—	59	1	no	—
68	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
69	C₂×Q₈	—	59	2	no	—
70	Q₁₆	—	118	2	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	59	1	no	—
73	C₂×C₈	—	59	1	no	—
74	C₂×C₈	—	118	1	no	—
75	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
76	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
77	C₄⋊C₄	—	59	2	no	—
78	C₄⋊C₄	—	118	2	no	—
79	C₄²	—	118	2	no	—
80	C₄²	C₂²×D₅₉	1	1	yes	characteristic
81	Q₈	—	118	2	no	—
82	Q₈	—	118	2	no	—
83	C₂×C₄	—	118	2	no	—
84	C₂×C₄	—	118	2	no	—
85	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
86	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
87	C₂×C₄	#11745689	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	4	2	no	—
90	C₈	—	59	2	no	—
91	C₈	—	118	2	no	—
92	C₈	—	118	1	no	—
93	C₈	#11745659	1	2	yes	—
94	C₂²	#14273689	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	236	2	no	—
97	C₄	—	236	2	no	—
98	C₄	C₂×#11745659	1	1	yes	characteristic
99	C₄	#14273735	1	1	yes	characteristic
100	C₄	Q₁₆×D₅₉	1	1	yes	characteristic
101	C₄	#14273746	1	1	yes	characteristic
102	C₂	#16837479	1	1	yes	characteristic
103	C₂	#16837496	1	1	yes	characteristic
104	C₂	#16837518	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837529

C₂

yes

maximal

C₄×Dic₂₃₆

C₂

yes

maximal, characteristic

#16837132

C₂

yes

maximal

C₈×C₅₉⋊C₈

C₂

yes

maximal, characteristic

C₅₉×#335

C₂

yes

maximal, characteristic

C₂×Dic₂₃₆

C₄

yes

characteristic

C₄×Dic₁₁₈

C₂²

yes

—

#14273661

C₄

yes

characteristic

Dic₅₉⋊C₈

—

#14273652

C₄

yes

—

#14273637

—

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

C₂²

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×Dic₁₁₈

C₂×C₄

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊Dic₅₉

C₂×C₄

yes

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

D₄

yes

characteristic

C₂×C₅₉⋊C₈

D₄

yes

characteristic

Dic₂₃₆

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

#41

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

M₁₆

yes

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

Q₁₆

yes

complemented

C₂²×C₅₉

C₄×D₄

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

C₂×M₁₆

yes

characteristic

C₄×C₅₉

#131

yes

characteristic

C₄×C₅₉

C₂×Q₁₆

yes

characteristic

C₄×C₅₉

#135

yes

characteristic

Dic₅₉

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

C₄×Q₁₆

yes

C₂×C₅₉

yes

—

C₄×Q₁₆

—

#335

D₅₉

yes

characteristic

Q₈⋊C₈

—

C₈²

—

C₅₉

#1591

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

118

—

C₄⋊C₈

C₂×D₅₉

yes

—

#103

—

#97

—

118

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂×Q₈

—

Q₁₆

—

118

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

C₄×D₅₉

yes

characteristic

C₂×C₈

C₄×D₅₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

118

—

C₄²

—

118

—

C₄²

C₂²×D₅₉

yes

characteristic

Q₈

—

118

—

Q₈

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

C₂×C₄

D₄×D₅₉

yes

characteristic

C₂×C₄

#11745689

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

118

—

C₈

—

118

—

C₈

#11745659

yes

—

C₂²

#14273689

yes

characteristic

C₄

—

C₄

—

236

—

C₄

—

236

—

C₄

yes

C₄

yes

100

C₄

Q₁₆×D₅₉

yes

characteristic

101

C₄

#14273746

yes

characteristic

102

C₂

#16837479

yes

characteristic

103

C₂

#16837496

yes

characteristic

104

C₂

#16837518

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₄²	C₂²×D₅₉
Fitting	C₅₉×#335	C₂
socle	C₂²×C₅₉	C₄×D₄
hypercenter	#335	D₅₉
hypocenter	C₅₉	#1591
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

subgroup

G/H

center

C₂×C₄

D₄×D₅₉

commutator

C₂×C₄×C₅₉

C₂²×C₄

Frattini

C₄²

C₂²×D₅₉

Fitting

C₅₉×#335

C₂

socle

C₂²×C₅₉

C₄×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #335

N	H ≅ G/N	type
40. C₅₉⋊C₈	Q₁₆	semidirect
58. C₅₉	#1591	semidirect

H ≅ G/N

type

40. C₅₉⋊C₈

Q₁₆

semidirect

58. C₅₉

#1591

semidirect

Subgroups — #21422992

Conjugacy classes of subgroups

Complements