Group #21423619 — subgroups

Subgroups — #21423619

Order 7552.

154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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	#16837807	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837692	C₂	1	2	yes	maximal
3	#16837153	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837150	C₂	1	2	yes	maximal, complemented
5	C₅₉×#436	C₂	1	1	yes	maximal, characteristic
6	#14273727	C₂²	1	2	yes	—
7	#14273661	—	2	1	no	—
8	#14273661	—	2	1	no	—
9	#14273658	—	2	2	no	—
10	C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
11	#14273648	—	2	2	no	—
12	C₂×M₁₆×C₅₉	—	2	1	no	—
13	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²⋊C₈×C₅₉	—	2	1	no	—
16	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₅₉	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₅₉	—	2	1	no	—
19	C₂×Dic₁₁₈	—	2	2	no	—
20	M₁₆×C₅₉	—	4	2	no	—
21	C₂×C₈×C₅₉	—	2	1	no	—
22	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
25	C₂²⋊C₄×C₅₉	—	2	1	no	—
26	C₄²×C₅₉	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₅₉	—	2	2	no	—
28	C₄⋊Dic₅₉	—	2	2	no	—
29	C₂×C₅₉⋊C₈	—	2	2	no	—
30	C₂³×C₅₉	—	2	1	no	—
31	D₄×C₅₉	—	2	2	no	—
32	C₂×C₄×C₅₉	—	2	1	no	—
33	C₂×C₄×C₅₉	—	4	1	no	—
34	C₂×C₄×C₅₉	—	4	1	no	—
35	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
38	C₂×Dic₅₉	—	4	2	no	—
39	Dic₁₁₈	—	8	2	no	—
40	C₈×C₅₉	—	2	1	no	—
41	C₈×C₅₉	—	4	1	no	—
42	C₈×C₅₉	SD₁₆	1	2	yes	—
43	C₅₉⋊C₈	—	4	2	no	—
44	C₂²×C₅₉	—	4	1	no	—
45	C₂²×C₅₉	—	4	1	no	—
46	C₂²×C₅₉	—	4	1	no	—
47	C₂²×C₅₉	#121	1	1	yes	characteristic
48	C₄×C₅₉	—	2	1	no	—
49	C₄×C₅₉	—	4	1	no	—
50	C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
51	C₄×C₅₉	#137	1	1	yes	characteristic
52	C₄×C₅₉	#137	1	2	yes	—
53	Dic₅₉	—	8	2	no	—
54	#1695	—	59	1	no	maximal, Sylow
55	C₂×C₅₉	—	8	1	no	—
56	C₂×C₅₉	#461	1	1	yes	characteristic
57	C₂×C₅₉	#470	1	1	yes	characteristic
58	C₂×C₅₉	#472	1	1	yes	characteristic
59	#500	—	59	1	no	—
60	#476	—	59	2	no	—
61	#436	D₅₉	1	1	yes	characteristic
62	#334	—	59	1	no	—
63	#333	—	59	2	no	—
64	C₅₉	#1695	1	1	yes	characteristic, complemented, Sylow
65	C₂×M₁₆	—	2	1	no	—
66	C₄⋊Q₈	—	59	2	no	—
67	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
68	#107	—	118	1	no	—
69	#107	—	118	1	no	—
70	#106	—	118	2	no	—
71	C₄⋊C₈	—	59	2	no	—
72	C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
73	#102	—	118	2	no	—
74	C₂²⋊C₈	—	2	1	no	—
75	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
76	C₂×Q₈	—	118	2	no	—
77	C₂×D₄	D₂₃₆	1	1	yes	characteristic
78	C₂²×C₄	—	2	1	no	—
79	M₁₆	—	4	2	no	—
80	C₂×C₈	—	2	1	no	—
81	C₂×C₈	—	118	2	no	—
82	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
84	C₄⋊C₄	—	118	2	no	—
85	C₄⋊C₄	—	118	2	no	—
86	C₄⋊C₄	D₂₃₆	1	1	yes	characteristic
87	C₂²⋊C₄	—	2	1	no	—
88	C₄²	C₂²×D₅₉	1	1	yes	characteristic
89	C₂³	—	2	1	no	—
90	Q₈	—	472	2	no	—
91	D₄	—	2	2	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	4	1	no	—
95	C₂×C₄	—	236	2	no	—
96	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
97	C₂×C₄	#11745685	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	4	1	no	—
101	C₈	—	236	2	no	—
102	C₈	#11745670	1	2	yes	—
103	C₂²	—	4	1	no	—
104	C₂²	—	4	1	no	—
105	C₂²	—	4	1	no	—
106	C₂²	#14273701	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	4	1	no	—
109	C₄	—	472	2	no	—
110	C₄	C₂×#11745670	1	1	yes	characteristic
111	C₄	#14273757	1	1	yes	characteristic
112	C₄	#14273760	1	2	yes	—
113	C₂	—	8	1	no	—
114	C₂	#16837607	1	1	yes	characteristic
115	C₂	#16837660	1	1	yes	characteristic
116	C₂	#16837672	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837807

C₂

yes

maximal, characteristic, complemented

#16837692

C₂

yes

maximal

#16837153

C₂

yes

maximal, characteristic, complemented

#16837150

C₂

yes

maximal, complemented

C₅₉×#436

C₂

yes

maximal, characteristic

#14273727

C₂²

yes

—

#14273661

—

#14273661

—

#14273658

—

C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

#14273648

—

C₂×M₁₆×C₅₉

—

C₄×D₄×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

C₂²

yes

characteristic

C₂²⋊C₈×C₅₉

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×D₄×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

—

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

D₄

yes

characteristic

C₄⋊C₄×C₅₉

D₄

yes

characteristic

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

#41

yes

characteristic

C₂×Dic₅₉

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

SD₁₆

yes

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

#121

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₂×SD₁₆

yes

C₄×C₅₉

yes

C₄×C₅₉

yes

—

Dic₅₉

—

#1695

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

—

D₅₉

yes

characteristic

#334

—

#333

—

C₅₉

#1695

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₅₉

yes

characteristic

#107

—

118

—

#107

—

118

—

#106

—

118

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₅₉

yes

characteristic

#102

—

118

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂×Q₈

—

118

—

C₂×D₄

D₂₃₆

yes

characteristic

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄⋊C₄

D₂₃₆

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂²×D₅₉

yes

characteristic

C₂³

—

Q₈

—

472

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

C₂×D₂₃₆

yes

characteristic

C₂×C₄

#11745685

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

236

—

102

C₈

#11745670

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

#14273701

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

472

—

110

C₄

C₂×#11745670

yes

characteristic

111

C₄

#14273757

yes

characteristic

112

C₄

#14273760

yes

—

113

C₂

—

114

C₂

#16837607

yes

characteristic

115

C₂

#16837660

yes

characteristic

116

C₂

#16837672

yes

characteristic

	subgroup	G/H
center	C₂²	#14273701
commutator	C₄²×C₅₉	C₂³
Frattini	C₄²	C₂²×D₅₉
Fitting	C₅₉×#436	C₂
socle	C₂²×C₅₉	#121
hypercenter	#436	D₅₉
hypocenter	C₅₉	#1695
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #436

subgroup

G/H

center

C₂²

#14273701

commutator

C₄²×C₅₉

C₂³

Frattini

C₄²

C₂²×D₅₉

Fitting

C₅₉×#436

C₂

C₂²×C₅₉

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #436

N	H ≅ G/N	type
1. #16837807	C₂	semidirect
3. #16837153	C₂	semidirect
4. #16837150	C₂	semidirect
64. C₅₉	#1695	semidirect

H ≅ G/N

type

1. #16837807

C₂

semidirect

3. #16837153

C₂

semidirect

4. #16837150

C₂

semidirect

64. C₅₉

#1695

semidirect

Subgroups — #21423619

Conjugacy classes of subgroups

Complements