Group #21425858 — subgroups

Subgroups — C₂×#16837222 #21425858

Order 7552.

168 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14273667	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₅₉	C₂	1	1	yes	maximal, characteristic
3	#16837222	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅₉⋊C₈	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₅₉	C₄	1	1	yes	characteristic
7	#14273667	—	2	1	no	—
8	#14273667	C₂²	1	2	yes	—
9	C₂×C₅₉⋊C₁₆	—	2	1	no	—
10	C₈×Dic₅₉	C₄	1	2	yes	—
11	C₈×Dic₅₉	C₂²	1	2	yes	—
12	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	M₃₂×C₅₉	—	2	1	no	—
14	M₃₂×C₅₉	C₂²	1	2	yes	—
15	C₂×C₁₆×C₅₉	—	2	1	no	—
16	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₅₉	—	2	1	no	—
18	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₅₉	Q₈	1	1	yes	characteristic
22	C₂×C₈×C₅₉	Q₈	1	1	yes	characteristic
23	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
24	C₄×Dic₅₉	—	2	1	no	—
25	C₄×Dic₅₉	C₂×C₄	1	2	yes	—
26	C₂×C₅₉⋊C₈	C₈	1	2	yes	—
27	C₂×C₅₉⋊C₈	C₈	1	2	yes	—
28	C₂×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
29	C₁₆×C₅₉	—	2	2	no	—
30	C₅₉⋊C₁₆	—	2	2	no	—
31	C₂³×C₅₉	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₅₉	M₁₆	1	1	yes	characteristic
37	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₅₉	—	2	4	no	—
39	C₂×Dic₅₉	—	2	2	no	—
40	C₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
43	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
44	C₅₉⋊C₈	C₂×C₈	1	4	yes	—
45	C₂²×C₅₉	—	2	2	no	—
46	C₂²×C₅₉	C₄⋊C₈	1	1	yes	characteristic
47	C₂²×C₅₉	C₄⋊C₈	1	1	yes	characteristic
48	C₂²×C₅₉	C₂×M₁₆	1	1	yes	characteristic
49	C₄×C₅₉	C₄⋊C₈	1	1	yes	characteristic
50	C₄×C₅₉	C₄⋊C₈	1	1	yes	characteristic
51	C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
53	Dic₅₉	—	2	4	no	—
54	C₂×#364	—	59	1	no	maximal, Sylow
55	C₂×C₅₉	—	2	1	no	—
56	C₂×C₅₉	—	2	1	no	—
57	C₂×C₅₉	#364	1	2	yes	complemented
58	C₂×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
59	C₂×M₃₂	—	59	1	no	—
60	C₂×M₃₂	D₅₉	1	1	yes	characteristic
61	C₂×C₄×C₈	—	59	1	no	—
62	#364	—	59	4	no	—
63	C₅₉	C₂×#364	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₈	—	59	1	no	—
65	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
66	C₂×C₄²	—	59	1	no	—
67	M₃₂	—	2	1	no	—
68	M₃₂	—	59	2	no	—
69	M₃₂	—	118	1	no	—
70	M₃₂	C₂×D₅₉	1	2	yes	—
71	C₂×C₁₆	—	2	1	no	—
72	C₂×C₁₆	—	118	1	no	—
73	C₄×C₈	—	59	2	no	—
74	C₄×C₈	—	59	2	no	—
75	C₂²×C₄	—	118	1	no	—
76	C₂²×C₄	C₄×D₅₉	1	1	yes	characteristic
77	C₂×C₈	—	59	2	no	—
78	C₂×C₈	—	59	2	no	—
79	C₂×C₈	—	59	2	no	—
80	C₂×C₈	Dic₁₁₈	1	1	yes	characteristic
81	C₂×C₈	Dic₁₁₈	1	1	yes	characteristic
82	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
84	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
85	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
86	C₄²	—	59	2	no	—
87	C₄²	—	118	1	no	—
88	C₁₆	—	2	2	no	—
89	C₁₆	—	118	2	no	—
90	C₂³	#11745659	1	1	yes	characteristic
91	C₂×C₄	—	118	4	no	—
92	C₂×C₄	—	118	2	no	—
93	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
94	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
95	C₂×C₄	#11745659	1	1	yes	characteristic
96	C₂×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
97	C₂×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
98	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
99	C₈	—	59	4	no	—
100	C₈	Dic₅₉⋊C₄	1	1	yes	characteristic
101	C₈	Dic₅₉⋊C₄	1	1	yes	characteristic
102	C₈	C₂×Dic₁₁₈	1	1	yes	characteristic
103	C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
104	C₂²	—	2	2	no	—
105	C₂²	Dic₅₉⋊C₈	1	1	yes	characteristic
106	C₂²	Dic₅₉⋊C₈	1	1	yes	characteristic
107	C₂²	C₂×#11745659	1	1	yes	characteristic
108	C₄	—	118	4	no	—
109	C₄	Dic₅₉⋊C₈	1	1	yes	characteristic
110	C₄	Dic₅₉⋊C₈	1	1	yes	characteristic
111	C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
112	C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#16837222	1	2	yes	direct product factor
116	C₂	C₂×Dic₅₉⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273667

C₂

yes

maximal, characteristic

C₂×C₈×Dic₅₉

C₂

yes

maximal, characteristic

#16837222

C₂

yes

maximal, direct product factor

C₂×M₃₂×C₅₉

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₅₉

C₄

yes

characteristic

#14273667

—

#14273667

C₂²

yes

—

C₂×C₅₉⋊C₁₆

—

C₈×Dic₅₉

C₄

yes

—

C₈×Dic₅₉

C₂²

yes

—

C₂²×C₈×C₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

—

M₃₂×C₅₉

C₂²

yes

—

C₂×C₁₆×C₅₉

—

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×Dic₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

Q₈

yes

characteristic

C₂×C₈×C₅₉

Q₈

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄×Dic₅₉

—

C₄×Dic₅₉

C₂×C₄

yes

—

C₂×C₅₉⋊C₈

C₈

yes

—

C₂×C₅₉⋊C₈

C₈

yes

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

M₁₆

yes

characteristic

C₂×C₄×C₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

M₁₆

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

C₄⋊C₄

yes

characteristic

C₈×C₅₉

C₄⋊C₄

yes

characteristic

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

C₂×Q₈

yes

characteristic

C₅₉⋊C₈

C₂×C₈

yes

—

C₂²×C₅₉

—

C₂²×C₅₉

C₄⋊C₈

yes

characteristic

C₂²×C₅₉

C₄⋊C₈

yes

characteristic

C₂²×C₅₉

C₂×M₁₆

yes

characteristic

C₄×C₅₉

C₄⋊C₈

yes

characteristic

C₄×C₅₉

C₄⋊C₈

yes

characteristic

C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₅₉

C₂²×C₈

yes

characteristic

Dic₅₉

—

C₂×#364

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

#364

yes

complemented

C₂×C₅₉

C₂×C₄⋊C₈

yes

characteristic

C₂×M₃₂

—

C₂×M₃₂

D₅₉

yes

characteristic

C₂×C₄×C₈

—

#364

—

C₅₉

C₂×#364

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₅₉

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

118

—

M₃₂

C₂×D₅₉

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

118

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

118

—

C₂²×C₄

C₄×D₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₁₁₈

yes

characteristic

C₂×C₈

Dic₁₁₈

yes

characteristic

C₂×C₈

C₄×D₅₉

yes

characteristic

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄²

—

C₄²

—

118

—

C₁₆

—

C₁₆

—

118

—

C₂³

#11745659

yes

characteristic

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

C₈×D₅₉

yes

characteristic

C₂×C₄

C₈×D₅₉

yes

characteristic

C₂×C₄

#11745659

yes

characteristic

C₂×C₄

Dic₅₉⋊C₄

yes

characteristic

C₂×C₄

Dic₅₉⋊C₄

yes

characteristic

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

C₈

—

100

C₈

Dic₅₉⋊C₄

yes

characteristic

101

C₈

Dic₅₉⋊C₄

yes

characteristic

102

C₈

C₂×Dic₁₁₈

yes

characteristic

103

C₈

C₂×C₂²⋊D₅₉

yes

characteristic

104

C₂²

—

105

C₂²

Dic₅₉⋊C₈

yes

characteristic

106

C₂²

Dic₅₉⋊C₈

yes

characteristic

107

C₂²

C₂×#11745659

yes

characteristic

108

C₄

—

118

—

109

C₄

Dic₅₉⋊C₈

yes

characteristic

110

C₄

Dic₅₉⋊C₈

yes

characteristic

111

C₄

C₂×Dic₅₉⋊C₄

yes

characteristic

112

C₄

C₂×C₈×D₅₉

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#16837222

yes

direct product factor

116

C₂

C₂×Dic₅₉⋊C₈

yes

characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₅₉
commutator	C₄×C₅₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₂×M₃₂×C₅₉	C₂
socle	C₂²×C₅₉	C₄⋊C₈
hypercenter	C₂×M₃₂	D₅₉
hypocenter	C₅₉	C₂×#364
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₈

C₂²⋊D₅₉

commutator

C₄×C₅₉

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₂×M₃₂×C₅₉

C₂

socle

C₂²×C₅₉

C₄⋊C₈

hypercenter

C₂×M₃₂

D₅₉

hypocenter

C₅₉

C₂×#364

LCS

G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #16837222	C₂	direct (N × H)
57. C₂×C₅₉	#364	semidirect
63. C₅₉	C₂×#364	semidirect
115. C₂	#16837222	direct (N × H)

H ≅ G/N

type

3. #16837222

C₂

direct (N × H)

57. C₂×C₅₉

#364

semidirect

63. C₅₉

C₂×#364

semidirect

115. C₂

#16837222

direct (N × H)

Subgroups — C₂×#16837222 #21425858

Conjugacy classes of subgroups

Complements

Subgroups — C2×#16837222 #21425858

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16837222 #21425858