Group #21432360 — subgroups

Subgroups — #21432360

Order 7552.

548 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 133 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	#16837338	C₂	1	4	yes	maximal, complemented
2	#16837325	C₂	1	8	yes	maximal, complemented
3	#16837258	C₂	1	2	yes	maximal
4	C₅₉×#379	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₅₉	C₂²	1	4	yes	complemented
6	C₂×Dic₅₉⋊C₄	C₂²	1	8	yes	complemented
7	C₂×C₂²⋊Dic₅₉	C₂²	1	4	yes	—
8	C₂×C₂²⋊Dic₅₉	C₂²	1	4	yes	—
9	C₂×C₂²⋊Dic₅₉	C₂²	1	4	yes	—
10	C₅₉⋊#95	C₂²	1	4	yes	complemented
11	C₂⁵×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
13	C₂×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
14	C₂⁴×C₅₉	—	4	4	no	—
15	C₂⁴×C₅₉	—	4	2	no	—
16	C₂⁴×C₅₉	Q₈	1	4	yes	—
17	C₂⁴×C₅₉	C₂³	1	2	yes	—
18	C₂⁴×C₅₉	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₅₉	C₂³	1	4	yes	—
20	C₂²×Dic₅₉	C₂³	1	8	yes	—
21	C₂²⋊C₄×C₅₉	—	4	4	no	—
22	C₂²⋊C₄×C₅₉	—	4	2	no	—
23	C₂²⋊Dic₅₉	—	4	4	no	—
24	C₂²⋊Dic₅₉	—	4	4	no	—
25	C₂²⋊Dic₅₉	—	4	4	no	—
26	C₄⋊Dic₅₉	—	4	4	no	—
27	Dic₅₉⋊C₄	—	4	8	no	—
28	C₂³×C₅₉	—	2	4	no	—
29	C₂³×C₅₉	—	2	4	no	—
30	C₂³×C₅₉	—	2	4	no	—
31	C₂³×C₅₉	—	2	4	no	—
32	C₂³×C₅₉	—	2	2	no	—
33	C₂³×C₅₉	—	4	8	no	—
34	C₂³×C₅₉	—	4	4	no	—
35	C₂³×C₅₉	—	4	16	no	—
36	C₂³×C₅₉	C₂×Q₈	1	4	yes	—
37	C₂³×C₅₉	C₂×Q₈	1	2	yes	—
38	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
39	C₂×C₄×C₅₉	—	2	8	no	—
40	C₂×C₄×C₅₉	—	2	4	no	—
41	C₂×Dic₅₉	—	2	8	no	—
42	C₂×Dic₅₉	—	2	8	no	—
43	C₂×Dic₅₉	—	2	8	no	—
44	C₂²×C₅₉	—	2	4	no	—
45	C₂²×C₅₉	—	2	4	no	—
46	C₂²×C₅₉	—	2	4	no	—
47	C₂²×C₅₉	—	2	4	no	—
48	C₂²×C₅₉	—	2	2	no	—
49	C₂²×C₅₉	—	4	16	no	—
50	C₂²×C₅₉	—	4	8	no	—
51	C₂²×C₅₉	—	4	4	no	—
52	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
53	C₂²×C₅₉	H(5,𝔽₂)	1	4	yes	—
54	C₂²×C₅₉	H(5,𝔽₂)	1	2	yes	—
55	C₄×C₅₉	—	4	4	no	—
56	Dic₅₉	—	4	8	no	—
57	#2842	—	59	1	no	maximal, Sylow
58	C₂×C₅₉	—	4	4	no	—
59	C₂×C₅₉	—	4	2	no	—
60	C₂×C₅₉	#543	1	2	yes	—
61	C₂×C₅₉	#543	1	1	yes	characteristic
62	C₂×C₅₉	#560	1	4	yes	—
63	#399	—	59	4	no	—
64	#396	—	59	8	no	—
65	#379	—	59	2	no	—
66	#379	D₅₉	1	1	yes	characteristic
67	C₅₉	#2842	1	1	yes	characteristic, complemented, Sylow
68	C₂⁵	C₂×D₅₉	1	1	yes	characteristic
69	C₂×C₄⋊C₄	—	59	8	no	—
70	C₂×C₄⋊C₄	—	59	4	no	—
71	C₂×C₂²⋊C₄	—	59	4	no	—
72	C₂×C₂²⋊C₄	—	59	4	no	—
73	C₂×C₂²⋊C₄	—	59	4	no	—
74	C₂×C₂²⋊C₄	C₂×D₅₉	1	4	yes	—
75	C₂×C₂²⋊C₄	C₂×D₅₉	1	2	yes	—
76	#95	—	59	4	no	—
77	C₂⁴	—	4	4	no	—
78	C₂⁴	—	4	2	no	—
79	C₂⁴	Dic₁₁₈	1	4	yes	—
80	C₂⁴	C₂²×D₅₉	1	2	yes	—
81	C₂⁴	C₂²×D₅₉	1	1	yes	characteristic
82	C₂²×C₄	—	59	8	no	—
83	C₂²×C₄	C₂²×D₅₉	1	4	yes	—
84	C₄⋊C₄	—	236	8	no	—
85	C₄⋊C₄	—	236	4	no	—
86	C₂²⋊C₄	—	4	4	no	—
87	C₂²⋊C₄	—	4	2	no	—
88	C₂²⋊C₄	—	236	4	no	—
89	C₂²⋊C₄	—	236	4	no	—
90	C₂²⋊C₄	—	236	4	no	—
91	C₂³	—	2	4	no	—
92	C₂³	—	2	2	no	—
93	C₂³	—	2	4	no	—
94	C₂³	—	2	4	no	—
95	C₂³	—	2	4	no	—
96	C₂³	—	4	8	no	—
97	C₂³	—	4	4	no	—
98	C₂³	—	4	16	no	—
99	C₂³	C₂×Dic₁₁₈	1	4	yes	—
100	C₂³	C₂×Dic₁₁₈	1	2	yes	—
101	C₂³	C₂³×D₅₉	1	1	yes	characteristic
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	118	8	no	—
105	C₂×C₄	—	118	8	no	—
106	C₂×C₄	—	118	8	no	—
107	C₂²	—	2	4	no	—
108	C₂²	—	2	2	no	—
109	C₂²	—	2	4	no	—
110	C₂²	—	2	4	no	—
111	C₂²	—	2	4	no	—
112	C₂²	—	4	16	no	—
113	C₂²	—	4	8	no	—
114	C₂²	—	4	4	no	—
115	C₂²	C₂²×Dic₁₁₈	1	1	yes	characteristic
116	C₂²	#14273772	1	4	yes	—
117	C₂²	#14273772	1	2	yes	—
118	C₄	—	4	4	no	—
119	C₄	—	236	8	no	—
120	C₂	—	4	4	no	—
121	C₂	—	4	2	no	—
122	C₂	#16838028	1	2	yes	—
123	C₂	#16838028	1	1	yes	characteristic
124	C₂	#16838141	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16837338

C₂

yes

maximal, complemented

#16837325

C₂

yes

maximal, complemented

#16837258

C₂

yes

maximal

C₅₉×#379

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₅₉

C₂²

yes

complemented

C₂×Dic₅₉⋊C₄

C₂²

yes

complemented

C₂×C₂²⋊Dic₅₉

C₂²

yes

—

C₂×C₂²⋊Dic₅₉

C₂²

yes

—

C₂×C₂²⋊Dic₅₉

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

complemented

C₂⁵×C₅₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₅₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₅₉

C₂²

yes

—

C₂⁴×C₅₉

—

C₂⁴×C₅₉

—

C₂⁴×C₅₉

Q₈

yes

—

C₂⁴×C₅₉

C₂³

yes

—

C₂⁴×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₂²⋊Dic₅₉

—

C₂²⋊Dic₅₉

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

C₂×Q₈

yes

—

C₂³×C₅₉

C₂×Q₈

yes

—

C₂³×C₅₉

C₂⁴

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂²×Q₈

yes

characteristic

C₂²×C₅₉

H(5,𝔽₂)

yes

—

C₂²×C₅₉

H(5,𝔽₂)

yes

—

C₄×C₅₉

—

Dic₅₉

—

#2842

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

#543

yes

—

C₂×C₅₉

#543

yes

characteristic

C₂×C₅₉

#560

yes

—

—

—

—

D₅₉

yes

characteristic

C₅₉

#2842

yes

characteristic, complemented, Sylow

C₂⁵

C₂×D₅₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₅₉

yes

—

C₂×C₂²⋊C₄

C₂×D₅₉

yes

—

#95

—

C₂⁴

—

C₂⁴

—

C₂⁴

Dic₁₁₈

yes

—

C₂⁴

C₂²×D₅₉

yes

—

C₂⁴

C₂²×D₅₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₄⋊C₄

—

236

—

C₄⋊C₄

—

236

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

236

—

C₂²⋊C₄

—

236

—

C₂²⋊C₄

—

236

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×Dic₁₁₈

yes

—

100

C₂³

C₂×Dic₁₁₈

yes

—

101

C₂³

C₂³×D₅₉

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

118

—

105

C₂×C₄

—

118

—

106

C₂×C₄

—

118

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂²×Dic₁₁₈

yes

characteristic

116

C₂²

#14273772

yes

—

117

C₂²

#14273772

yes

—

118

C₄

—

119

C₄

—

236

—

120

C₂

—

121

C₂

—

122

C₂

#16838028

yes

—

123

C₂

#16838028

yes

characteristic

124

C₂

#16838141

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₅₉×#379	C₂
hypercenter	#379	D₅₉
hypocenter	C₅₉	#2842
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ #379

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₅₉×#379

C₂

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ #379

N	H ≅ G/N	type
1. #16837338	C₂	semidirect
2. #16837325	C₂	semidirect
5. C₂×C₄⋊Dic₅₉	C₂²	semidirect
6. C₂×Dic₅₉⋊C₄	C₂²	semidirect
10. C₅₉⋊#95	C₂²	semidirect
67. C₅₉	#2842	semidirect

H ≅ G/N

type

1. #16837338

C₂

semidirect

2. #16837325

C₂

semidirect

5. C₂×C₄⋊Dic₅₉

C₂²

semidirect

6. C₂×Dic₅₉⋊C₄

C₂²

semidirect

10. C₅₉⋊#95

C₂²

semidirect

67. C₅₉

#2842

semidirect

Subgroups — #21432360

Conjugacy classes of subgroups

Complements