Group #21432472 — subgroups

Subgroups — #21432472

Order 7552.

504 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14273726	C₂	1	2	yes	maximal
2	#16837306	C₂	1	8	yes	maximal
3	#16837268	C₂	1	1	yes	maximal, characteristic
4	#16837267	C₂	1	2	yes	maximal
5	C₄²×Dic₅₉	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#382	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₁₁₈	C₂²	1	4	yes	—
8	#14273726	—	2	8	no	—
9	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
10	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
11	C₂×C₄×Dic₅₉	C₂²	1	4	yes	—
12	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
14	C₅₉⋊#95	C₂²	1	8	yes	—
15	C₅₉⋊#95	C₂²	1	4	yes	—
16	C₂×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
17	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
18	#95×C₅₉	C₂²	1	4	yes	—
19	C₂²×C₄×C₅₉	C₂³	1	4	yes	—
20	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
21	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₅₉	C₂³	1	4	yes	—
23	C₂²×Dic₅₉	C₂³	1	2	yes	—
24	C₂²×Dic₅₉	C₂³	1	2	yes	—
25	C₂×Dic₁₁₈	—	2	8	no	—
26	C₂×Dic₁₁₈	—	2	16	no	—
27	C₄⋊C₄×C₅₉	—	2	4	no	—
28	C₄²×C₅₉	Q₈	1	4	yes	complemented
29	C₄⋊Dic₅₉	—	2	4	no	—
30	Dic₅₉⋊C₄	—	2	8	no	—
31	C₄×Dic₅₉	—	2	8	no	—
32	C₄×Dic₅₉	D₄	1	4	yes	—
33	C₄×Dic₅₉	Q₈	1	4	yes	complemented
34	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
35	C₂×C₄×C₅₉	—	2	4	no	—
36	C₂×C₄×C₅₉	—	2	4	no	—
37	C₂×C₄×C₅₉	—	2	8	no	—
38	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₅₉	C₂×Q₈	1	4	yes	—
40	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
42	C₂×Dic₅₉	—	2	4	no	—
43	C₂×Dic₅₉	—	2	4	no	—
44	C₂×Dic₅₉	—	2	8	no	—
45	C₂×Dic₅₉	C₂×D₄	1	4	yes	—
46	C₂×Dic₅₉	C₂×Q₈	1	4	yes	—
47	C₂×Dic₅₉	#41	1	8	yes	—
48	Dic₁₁₈	—	4	16	no	—
49	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
50	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
51	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
52	C₂²×C₅₉	C₂×#41	1	4	yes	—
53	C₄×C₅₉	—	2	4	no	—
54	C₄×C₅₉	—	4	4	no	—
55	C₄×C₅₉	C₄⋊Q₈	1	4	yes	—
56	Dic₅₉	—	2	4	no	—
57	Dic₅₉	—	4	4	no	—
58	Dic₅₉	#124	1	8	yes	—
59	#2862	—	59	1	no	maximal, Sylow
60	C₂×C₅₉	C₂×#124	1	2	yes	—
61	C₂×C₅₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
62	C₂×C₅₉	#533	1	2	yes	—
63	C₂×C₅₉	#533	1	2	yes	—
64	C₂×C₄⋊Q₈	—	59	2	no	—
65	#391	—	59	8	no	—
66	#382	—	59	2	no	—
67	#382	—	59	1	no	—
68	#382	D₅₉	1	1	yes	characteristic
69	C₄³	—	59	1	no	—
70	C₅₉	#2862	1	1	yes	characteristic, complemented, Sylow
71	C₂²×Q₈	—	59	4	no	—
72	C₄⋊Q₈	—	118	8	no	—
73	C₂×C₄⋊C₄	—	59	2	no	—
74	C₂×C₄⋊C₄	—	59	4	no	—
75	C₂×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
76	C₂×C₄²	—	59	1	no	—
77	C₂×C₄²	—	59	1	no	—
78	C₂×C₄²	—	59	4	no	—
79	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
80	#95	—	59	8	no	—
81	#95	—	59	4	no	—
82	#95	C₂×D₅₉	1	4	yes	—
83	C₂×Q₈	—	118	8	no	—
84	C₂×Q₈	—	118	16	no	—
85	C₂²×C₄	—	59	2	no	—
86	C₂²×C₄	—	59	2	no	—
87	C₂²×C₄	—	59	4	no	—
88	C₂²×C₄	C₂²×D₅₉	1	4	yes	—
89	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
91	C₄⋊C₄	—	2	4	no	—
92	C₄⋊C₄	—	118	8	no	—
93	C₄⋊C₄	—	118	4	no	—
94	C₄²	—	59	4	no	—
95	C₄²	—	59	4	no	—
96	C₄²	—	118	8	no	—
97	C₄²	Dic₁₁₈	1	4	yes	complemented
98	C₂³	C₂³×D₅₉	1	1	yes	characteristic
99	Q₈	—	236	16	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	—	59	4	no	—
104	C₂×C₄	—	59	8	no	—
105	C₂×C₄	—	59	4	no	—
106	C₂×C₄	—	118	4	no	—
107	C₂×C₄	—	118	4	no	—
108	C₂×C₄	—	118	8	no	—
109	C₂×C₄	C₂×Dic₁₁₈	1	4	yes	—
110	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
111	C₂×C₄	D₄×D₅₉	1	2	yes	—
112	C₂×C₄	Q₈×D₅₉	1	2	yes	—
113	C₂²	C₂×D₄×D₅₉	1	1	yes	characteristic
114	C₂²	C₂×Q₈×D₅₉	1	1	yes	characteristic
115	C₂²	C₂²×Dic₁₁₈	1	1	yes	characteristic
116	C₂²	#41×D₅₉	1	4	yes	—
117	C₄	—	2	4	no	—
118	C₄	—	4	4	no	—
119	C₄	—	59	8	no	—
120	C₄	—	118	4	no	—
121	C₄	—	236	4	no	—
122	C₄	#14273726	1	4	yes	—
123	C₂	#124×D₅₉	1	2	yes	—
124	C₂	C₂×#14273726	1	1	yes	characteristic
125	C₂	#16837955	1	2	yes	—
126	C₂	#16837958	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273726

C₂

yes

maximal

#16837306

C₂

yes

maximal

#16837268

C₂

yes

maximal, characteristic

#16837267

C₂

yes

maximal

C₄²×Dic₅₉

C₂

yes

maximal, characteristic

C₅₉×#382

C₂

yes

maximal, characteristic

C₂²×Dic₁₁₈

C₂²

yes

—

#14273726

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₅₉⋊#95

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

#95×C₅₉

C₂²

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

Q₈

yes

complemented

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

D₄

yes

—

C₄×Dic₅₉

Q₈

yes

complemented

C₂³×C₅₉

C₂⁴

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

C₂×D₄

yes

—

C₂×Dic₅₉

C₂×Q₈

yes

—

C₂×Dic₅₉

#41

yes

—

Dic₁₁₈

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₂²×C₅₉

C₂²×Q₈

yes

characteristic

C₂²×C₅₉

C₂²×Q₈

yes

characteristic

C₂²×C₅₉

C₂×#41

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₄⋊Q₈

yes

—

Dic₅₉

—

Dic₅₉

—

Dic₅₉

#124

yes

—

#2862

—

maximal, Sylow

C₂×C₅₉

C₂×#124

yes

—

C₂×C₅₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₅₉

#533

yes

—

C₂×C₅₉

#533

yes

—

C₂×C₄⋊Q₈

—

—

—

—

D₅₉

yes

characteristic

C₄³

—

C₅₉

#2862

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₄⋊Q₈

—

118

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

—

—

C₂×D₅₉

yes

—

C₂×Q₈

—

118

—

C₂×Q₈

—

118

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄²

—

C₄²

—

C₄²

—

118

—

C₄²

Dic₁₁₈

yes

complemented

C₂³

C₂³×D₅₉

yes

characteristic

Q₈

—

236

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

118

—

107

C₂×C₄

—

118

—

108

C₂×C₄

—

118

—

109

C₂×C₄

C₂×Dic₁₁₈

yes

—

110

C₂×C₄

C₂×Dic₁₁₈

yes

—

111

C₂×C₄

D₄×D₅₉

yes

—

112

C₂×C₄

Q₈×D₅₉

yes

—

113

C₂²

C₂×D₄×D₅₉

yes

characteristic

114

C₂²

C₂×Q₈×D₅₉

yes

characteristic

115

C₂²

C₂²×Dic₁₁₈

yes

characteristic

116

C₂²

#41×D₅₉

yes

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

118

—

121

C₄

—

236

—

122

C₄

#14273726

yes

—

123

C₂

#124×D₅₉

yes

—

124

C₂

C₂×#14273726

yes

characteristic

125

C₂

#16837955

yes

—

126

C₂

#16837958

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₅₉×#382	C₂
hypercenter	#382	D₅₉
hypocenter	C₅₉	#2862
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₅₉×#382

C₂

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
28. C₄²×C₅₉	Q₈	semidirect
33. C₄×Dic₅₉	Q₈	semidirect
70. C₅₉	#2862	semidirect
97. C₄²	Dic₁₁₈	semidirect

H ≅ G/N

type

28. C₄²×C₅₉

Q₈

semidirect

33. C₄×Dic₅₉

Q₈

semidirect

70. C₅₉

#2862

semidirect

97. C₄²

Dic₁₁₈

semidirect

Subgroups — #21432472

Conjugacy classes of subgroups

Complements