Group #21421973 — subgroups

Subgroups — #21421973

Order 7552.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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	#16837366	C₂	1	2	yes	maximal
2	C₂×C₂²⋊C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11745664	—	2	2	no	—
4	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
5	C₂²⋊(C₅₉⋊C₈)	C₄	1	4	yes	—
6	C₂³×C₄×C₅₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₅₉	C₄	1	2	yes	—
8	C₂²⋊C₈×C₅₉	—	2	2	no	—
9	C₂⁴×C₅₉	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₅₉	—	4	2	no	—
11	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₅₉	D₄	1	2	yes	—
14	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₅₉	—	2	2	no	—
16	C₂×C₈×C₅₉	—	4	2	no	—
17	#11745664	—	4	4	no	—
18	C₂×C₅₉⋊C₈	—	2	4	no	—
19	C₂³×C₅₉	—	2	2	no	—
20	C₂³×C₅₉	—	4	1	no	—
21	C₂³×C₅₉	—	4	1	no	—
22	C₂³×C₅₉	C₄⋊C₄	1	2	yes	—
23	C₂³×C₅₉	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₅₉	—	2	4	no	—
25	C₂×C₄×C₅₉	—	2	2	no	—
26	C₂×C₄×C₅₉	—	4	2	no	—
27	C₂×C₄×C₅₉	—	4	1	no	—
28	C₂×C₄×C₅₉	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
30	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₈×C₅₉	—	4	2	no	—
32	C₅₉⋊C₈	—	4	4	no	—
33	C₂²×C₅₉	—	2	1	no	—
34	C₂²×C₅₉	—	2	1	no	—
35	C₂²×C₅₉	—	2	2	no	—
36	C₂²×C₅₉	—	2	2	no	—
37	C₂²×C₅₉	—	2	2	no	—
38	C₂²×C₅₉	—	4	4	no	—
39	C₂²×C₅₉	#95	1	1	yes	characteristic
40	C₂²×C₅₉	#108	1	2	yes	—
41	C₄×C₅₉	—	2	2	no	—
42	C₄×C₅₉	—	2	1	no	—
43	C₄×C₅₉	#99	1	2	yes	—
44	#1293	—	59	1	no	maximal, Sylow
45	C₂×C₅₉	—	2	2	no	—
46	C₂×C₅₉	—	4	2	no	—
47	C₂×C₅₉	#338	1	1	yes	characteristic
48	C₂×C₅₉	#341	1	1	yes	characteristic
49	C₂×C₅₉	#342	1	1	yes	characteristic
50	#407	—	59	2	no	—
51	C₂×C₂²⋊C₈	D₅₉	1	1	yes	characteristic
52	C₅₉	#1293	1	1	yes	characteristic, complemented, Sylow
53	C₂³×C₄	C₂×D₅₉	1	1	yes	characteristic
54	C₂×M₁₆	—	118	2	no	—
55	C₂²×C₈	Dic₅₉	1	2	yes	—
56	C₂²⋊C₈	—	2	2	no	—
57	C₂²⋊C₈	—	59	4	no	—
58	C₂²⋊C₈	—	118	2	no	—
59	C₂⁴	Dic₁₁₈	1	1	yes	characteristic
60	C₂²×C₄	—	4	2	no	—
61	C₂²×C₄	C₄×D₅₉	1	2	yes	—
62	C₂²×C₄	D₂₃₆	1	1	yes	characteristic
63	C₂²×C₄	C₂×Dic₅₉	1	1	yes	characteristic
64	C₂²×C₄	C₂²⋊D₅₉	1	2	yes	—
65	M₁₆	—	236	4	no	—
66	C₂×C₈	—	2	2	no	—
67	C₂×C₈	—	4	2	no	—
68	C₂×C₈	—	118	4	no	—
69	C₂³	—	2	2	no	—
70	C₂³	—	4	1	no	—
71	C₂³	—	4	1	no	—
72	C₂³	Dic₅₉⋊C₄	1	2	yes	—
73	C₂³	C₄⋊Dic₅₉	1	1	yes	characteristic
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	C₄×Dic₅₉	1	1	yes	characteristic
79	C₂×C₄	(C₂×D₅₉)⋊C₄	1	2	yes	—
80	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
81	C₈	—	4	2	no	—
82	C₈	—	236	4	no	—
83	C₂²	—	2	1	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	2	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	4	4	no	—
89	C₂²	C₅₉⋊#95	1	1	yes	characteristic
90	C₂²	#14273663	1	2	yes	—
91	C₄	—	2	2	no	—
92	C₄	—	2	1	no	—
93	C₄	#14273642	1	2	yes	—
94	C₂	—	2	2	no	—
95	C₂	—	4	2	no	—
96	C₂	C₅₉⋊#338	1	1	yes	characteristic
97	C₂	#16837167	1	1	yes	characteristic
98	C₂	#16837169	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837366

C₂

yes

maximal

C₂×C₂²⋊C₈×C₅₉

C₂

yes

maximal, characteristic

C₂×#11745664

—

C₂²⋊(C₅₉⋊C₈)

—

C₂²⋊(C₅₉⋊C₈)

C₄

yes

—

C₂³×C₄×C₅₉

C₂²

yes

characteristic

C₂²×C₈×C₅₉

C₄

yes

—

C₂²⋊C₈×C₅₉

—

C₂⁴×C₅₉

Q₈

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

—

C₂²×C₄×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

C₄⋊C₄

yes

—

C₂³×C₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₄²

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

#95

yes

characteristic

C₂²×C₅₉

#108

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#99

yes

—

#1293

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₂²⋊C₈

D₅₉

yes

characteristic

C₅₉

#1293

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₅₉

yes

characteristic

C₂×M₁₆

—

118

—

C₂²×C₈

Dic₅₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

118

—

C₂⁴

Dic₁₁₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄×D₅₉

yes

—

C₂²×C₄

D₂₃₆

yes

characteristic

C₂²×C₄

C₂×Dic₅₉

yes

characteristic

C₂²×C₄

C₂²⋊D₅₉

yes

—

M₁₆

—

236

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂³

—

C₂³

—

C₂³

—

C₂³

Dic₅₉⋊C₄

yes

—

C₂³

C₄⋊Dic₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₅₉

yes

characteristic

C₂×C₄

(C₂×D₅₉)⋊C₄

yes

—

C₂×C₄

C₂²⋊Dic₅₉

yes

characteristic

C₈

—

C₈

—

236

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₅₉⋊#95

yes

characteristic

C₂²

#14273663

yes

—

C₄

—

C₄

—

C₄

#14273642

yes

—

C₂

—

C₂

—

C₂

C₅₉⋊#338

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	C₅₉⋊#95
commutator	C₂×C₄×C₅₉	C₄²
Frattini	C₂³×C₄	C₂×D₅₉
Fitting	C₂×C₂²⋊C₈×C₅₉	C₂
socle	C₂²×C₅₉	#95
hypercenter	C₂×C₂²⋊C₈	D₅₉
hypocenter	C₅₉	#1293
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center

C₂²

C₅₉⋊#95

commutator

C₂×C₄×C₅₉

C₄²

Frattini

C₂³×C₄

C₂×D₅₉

Fitting

C₂×C₂²⋊C₈×C₅₉

C₂

socle

C₂²×C₅₉

#95

hypercenter

C₂×C₂²⋊C₈

D₅₉

hypocenter

C₅₉

#1293

LCS

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
52. C₅₉	#1293	semidirect

H ≅ G/N

type

52. C₅₉

#1293

semidirect

Subgroups — #21421973

Conjugacy classes of subgroups

Complements