Group #21423954 — subgroups

Subgroups — #21423954

Order 7552.

260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 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×Dic₅₉⋊C₈	C₂	1	2	yes	maximal
2	C₂×#14273638	C₂	1	1	yes	maximal, characteristic
3	#16837248	C₂	1	1	yes	maximal, characteristic
4	#16837156	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
9	Dic₅₉⋊C₈	C₄	1	8	yes	complemented
10	#14273638	—	2	2	no	—
11	C₅₉⋊#95	C₄	1	4	yes	—
12	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₅₉	—	2	2	no	—
15	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
17	C₂²×Dic₅₉	C₂×C₄	1	2	yes	—
18	C₂²×Dic₅₉	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₅₉	—	2	2	no	—
20	C₂×C₈×C₅₉	—	2	2	no	—
21	C₂×C₈×C₅₉	C₂×C₄	1	4	yes	—
22	C₄²×C₅₉	D₄	1	2	yes	—
23	C₄²×C₅₉	Q₈	1	2	yes	—
24	C₄×Dic₅₉	—	2	2	no	—
25	C₄×Dic₅₉	C₂×C₄	1	4	yes	—
26	C₂×C₅₉⋊C₈	—	2	2	no	—
27	C₂×C₅₉⋊C₈	—	2	2	no	—
28	C₂×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
29	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₅₉	—	2	4	no	—
31	C₂×C₄×C₅₉	C₄⋊C₄	1	4	yes	—
32	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
33	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₅₉	#41	1	2	yes	—
36	C₂×Dic₅₉	—	2	4	no	—
37	C₂×Dic₅₉	—	2	2	no	—
38	C₂×Dic₅₉	—	2	4	no	—
39	C₂×Dic₅₉	C₄²	1	4	yes	—
40	C₈×C₅₉	—	2	4	no	—
41	C₅₉⋊C₈	—	2	4	no	—
42	C₂²×C₅₉	C₂×C₄²	1	1	yes	characteristic
43	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₅₉	#117	1	1	yes	characteristic
45	C₂²×C₅₉	#131	1	4	yes	—
46	C₄×C₅₉	—	2	4	no	—
47	C₄×C₅₉	C₄×D₄	1	2	yes	—
48	C₄×C₅₉	C₄×Q₈	1	2	yes	—
49	Dic₅₉	—	2	4	no	—
50	Dic₅₉	—	4	2	no	—
51	#1768	—	59	1	no	maximal, Sylow
52	C₂×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₅₉	#405	1	2	yes	—
54	C₂×C₅₉	#424	1	2	yes	—
55	C₂×C₅₉	#433	1	2	yes	—
56	C₂×C₄⋊C₈	—	59	2	no	—
57	C₂×#97	—	59	1	no	—
58	C₂×C₄×C₈	D₅₉	1	1	yes	characteristic
59	#376	—	59	1	no	—
60	#336	—	59	2	no	—
61	C₅₉	#1768	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	59	2	no	—
63	C₂²×C₈	C₂×D₅₉	1	2	yes	—
64	C₂×C₄²	—	59	1	no	—
65	C₂×C₄²	—	59	1	no	—
66	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
67	C₄⋊C₈	—	59	8	no	—
68	#97	—	118	2	no	—
69	C₄×C₈	—	2	2	no	—
70	#95	—	59	4	no	—
71	C₂²×C₄	—	59	2	no	—
72	C₂²×C₄	—	59	2	no	—
73	C₂²×C₄	C₄×D₅₉	1	2	yes	—
74	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	59	4	no	—
78	C₂×C₈	—	118	2	no	—
79	C₂×C₈	—	118	2	no	—
80	C₂×C₈	C₄×D₅₉	1	4	yes	—
81	C₄²	—	59	4	no	—
82	C₄²	—	118	2	no	—
83	C₄²	Dic₁₁₈	1	2	yes	—
84	C₄²	C₂²⋊D₅₉	1	2	yes	—
85	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	59	4	no	—
88	C₂×C₄	—	118	4	no	—
89	C₂×C₄	—	118	2	no	—
90	C₂×C₄	—	118	4	no	—
91	C₂×C₄	Dic₅₉⋊C₄	1	4	yes	—
92	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
93	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
94	C₂×C₄	#11745685	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
96	C₈	—	2	4	no	—
97	C₈	—	118	4	no	—
98	C₂²	C₄²×D₅₉	1	1	yes	characteristic
99	C₂²	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
100	C₂²	#14273684	1	1	yes	characteristic
101	C₂²	#14273733	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	118	4	no	—
104	C₄	—	236	2	no	—
105	C₄	C₄×C₂²⋊D₅₉	1	2	yes	—
106	C₄	C₄×Dic₁₁₈	1	2	yes	—
107	C₂	C₄×Dic₅₉⋊C₄	1	1	yes	characteristic
108	C₂	#16837356	1	2	yes	—
109	C₂	#16837428	1	2	yes	—
110	C₂	#16837461	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₉⋊C₈

C₂

yes

maximal

C₂×#14273638

C₂

yes

maximal, characteristic

#16837248

C₂

yes

maximal, characteristic

#16837156

C₂

yes

maximal

C₂×C₄×C₈×C₅₉

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

Dic₅₉⋊C₈

C₄

yes

complemented

#14273638

—

C₅₉⋊#95

C₄

yes

—

C₂²×C₈×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₄×C₈×C₅₉

—

C₂²×C₄×C₅₉

C₂×C₄

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂×C₄

yes

—

C₂²×Dic₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₄²×C₅₉

D₄

yes

—

C₄²×C₅₉

Q₈

yes

—

C₄×Dic₅₉

—

C₄×Dic₅₉

C₂×C₄

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂³×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₄⋊C₄

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

C₄²

yes

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

C₂×C₄²

yes

characteristic

C₂²×C₅₉

C₂×C₄⋊C₄

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

—

C₄×C₅₉

—

C₄×C₅₉

C₄×D₄

yes

—

C₄×C₅₉

C₄×Q₈

yes

—

Dic₅₉

—

Dic₅₉

—

#1768

—

maximal, Sylow

C₂×C₅₉

C₄×C₄⋊C₄

yes

characteristic

C₂×C₅₉

#405

yes

—

C₂×C₅₉

#424

yes

—

C₂×C₅₉

#433

yes

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×C₄×C₈

D₅₉

yes

characteristic

#376

—

#336

—

C₅₉

#1768

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₄⋊C₈

—

#97

—

118

—

C₄×C₈

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₂×C₈

C₄×D₅₉

yes

—

C₄²

—

C₄²

—

118

—

C₄²

Dic₁₁₈

yes

—

C₄²

C₂²⋊D₅₉

yes

—

C₂³

C₂×C₄×D₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

Dic₅₉⋊C₄

yes

—

C₂×C₄

C₂×Dic₁₁₈

yes

characteristic

C₂×C₄

C₂×C₄×D₅₉

yes

—

C₂×C₄

#11745685

yes

—

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

C₈

—

C₈

—

118

—

C₂²

C₄²×D₅₉

yes

characteristic

C₂²

C₂×Dic₅₉⋊C₄

yes

characteristic

100

C₂²

#14273684

yes

characteristic

101

C₂²

#14273733

yes

—

102

C₄

—

103

C₄

—

118

—

104

C₄

—

236

—

105

C₄

C₄×C₂²⋊D₅₉

yes

—

106

C₄

C₄×Dic₁₁₈

yes

—

107

C₂

C₄×Dic₅₉⋊C₄

yes

characteristic

108

C₂

#16837356

yes

—

109

C₂

#16837428

yes

—

110

C₂

#16837461

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅₉
commutator	C₂²×C₅₉	C₂×C₄²
Fitting	C₂×C₄×C₈×C₅₉	C₂
socle	C₂³×C₅₉	C₂²×C₄
hypercenter	C₂×C₄×C₈	D₅₉
hypocenter	C₅₉	#1768
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₅₉

commutator

C₂²×C₅₉

C₂×C₄²

Fitting

C₂×C₄×C₈×C₅₉

C₂

socle

C₂³×C₅₉

C₂²×C₄

hypercenter

C₂×C₄×C₈

D₅₉

C₅₉

G ▷ C₂²×C₅₉ ▷ C₅₉

C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. Dic₅₉⋊C₈	C₄	semidirect
61. C₅₉	#1768	semidirect

H ≅ G/N

type

9. Dic₅₉⋊C₈

C₄

semidirect

61. C₅₉

#1768

semidirect

Subgroups — #21423954

Conjugacy classes of subgroups

Complements