Group #21432705 — subgroups

Subgroups — #21432705

Order 7552.

440 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 249 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	#16838169	C₂	1	1	yes	maximal, characteristic
2	C₂×#14273734	C₂	1	1	yes	maximal, characteristic
3	#16837450	C₂	1	6	yes	maximal, complemented
4	C₂×#14273662	C₂	1	6	yes	maximal, complemented
5	C₅₉×#568	C₂	1	1	yes	maximal, characteristic
6	#14273734	—	2	4	no	—
7	#14273734	C₄	1	8	yes	—
8	C₂×#11745664	C₂²	1	6	yes	—
9	C₂×#11745664	C₂²	1	3	yes	—
10	C₂²×C₅₉⋊C₈	C₂²	1	3	yes	—
11	#14273662	C₂²	1	4	yes	—
12	#14273662	C₂²	1	12	yes	—
13	C₂×#41×C₅₉	C₂²	1	1	yes	characteristic
14	#131×C₅₉	—	2	4	no	—
15	C₂×M₁₆×C₅₉	C₂²	1	6	yes	—
16	#41×C₅₉	C₂×C₄	1	4	yes	—
17	#41×C₅₉	D₄	1	4	yes	—
18	C₂×Q₈×C₅₉	Q₈	1	1	yes	characteristic
19	C₂×D₄×C₅₉	Q₈	1	3	yes	—
20	C₂²×C₄×C₅₉	C₂³	1	3	yes	—
21	M₁₆×C₅₉	—	2	6	no	—
22	M₁₆×C₅₉	C₂³	1	4	yes	—
23	C₂×C₈×C₅₉	—	2	6	no	—
24	#11745664	—	2	6	no	—
25	#11745664	C₂×C₄	1	12	yes	—
26	#11745664	C₂³	1	4	yes	—
27	C₂×C₅₉⋊C₈	—	2	6	no	—
28	C₂×C₅₉⋊C₈	C₂×C₄	1	12	yes	—
29	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
30	C₂×C₅₉⋊C₈	C₂³	1	3	yes	—
31	C₂³×C₅₉	C₂×Q₈	1	3	yes	—
32	Q₈×C₅₉	C₄⋊C₄	1	4	yes	—
33	D₄×C₅₉	C₄⋊C₄	1	12	yes	—
34	C₂×C₄×C₅₉	C₂²×C₄	1	6	yes	—
35	C₂×C₄×C₅₉	C₂×D₄	1	6	yes	—
36	C₂×C₄×C₅₉	C₂×Q₈	1	3	yes	—
37	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
38	C₈×C₅₉	—	2	4	no	—
39	C₅₉⋊C₈	—	2	4	no	—
40	C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
41	C₅₉⋊C₈	C₂²×C₄	1	6	yes	—
42	C₂²×C₅₉	—	4	3	no	—
43	C₂²×C₅₉	C₂×C₄⋊C₄	1	6	yes	—
44	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
45	C₄×C₅₉	C₂×C₄⋊C₄	1	6	yes	—
46	C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
47	C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
48	#2916	—	59	1	no	maximal, Sylow
49	C₂×C₅₉	—	2	1	no	—
50	C₂×C₅₉	—	2	6	no	—
51	C₂×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
52	#568	—	59	1	no	—
53	#568	D₅₉	1	1	yes	characteristic
54	C₂×#131	—	59	1	no	—
55	#430	—	59	6	no	—
56	C₂×#108	—	59	6	no	—
57	C₅₉	#2916	1	1	yes	characteristic, complemented, Sylow
58	C₂×#41	C₂×D₅₉	1	1	yes	characteristic
59	#131	—	2	4	no	—
60	#131	—	59	8	no	—
61	#131	—	118	4	no	—
62	C₂×M₁₆	—	59	3	no	—
63	C₂×M₁₆	—	59	6	no	—
64	C₂×M₁₆	C₂×D₅₉	1	6	yes	—
65	C₂²×C₈	—	59	3	no	—
66	#108	—	59	4	no	—
67	#108	—	59	12	no	—
68	#41	C₄×D₅₉	1	4	yes	—
69	#41	C₂²⋊D₅₉	1	4	yes	—
70	C₂×Q₈	Dic₁₁₈	1	1	yes	characteristic
71	C₂×D₄	Dic₁₁₈	1	3	yes	—
72	C₂²×C₄	C₂²×D₅₉	1	3	yes	—
73	M₁₆	—	2	6	no	—
74	M₁₆	—	59	12	no	—
75	M₁₆	—	59	4	no	—
76	M₁₆	—	118	6	no	—
77	M₁₆	C₂²×D₅₉	1	4	yes	—
78	C₂×C₈	—	2	6	no	—
79	C₂×C₈	—	59	12	no	—
80	C₂×C₈	—	59	1	no	—
81	C₂×C₈	—	59	3	no	—
82	C₂×C₈	—	118	6	no	—
83	C₂³	C₂×Dic₁₁₈	1	3	yes	—
84	Q₈	Dic₅₉⋊C₄	1	4	yes	—
85	D₄	Dic₅₉⋊C₄	1	12	yes	—
86	C₂×C₄	C₂×Dic₁₁₈	1	3	yes	—
87	C₂×C₄	C₂×C₄×D₅₉	1	6	yes	—
88	C₂×C₄	C₂×C₂²⋊D₅₉	1	6	yes	—
89	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	59	2	no	—
92	C₈	—	59	6	no	—
93	C₈	—	118	4	no	—
94	C₂²	—	4	3	no	—
95	C₂²	C₂×Dic₅₉⋊C₄	1	6	yes	—
96	C₂²	C₂²×Dic₁₁₈	1	1	yes	characteristic
97	C₄	C₂×Dic₅₉⋊C₄	1	6	yes	—
98	C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
99	C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	2	6	no	—
102	C₂	C₂²×Dic₅₉⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16838169

C₂

yes

maximal, characteristic

C₂×#14273734

C₂

yes

maximal, characteristic

#16837450

C₂

yes

maximal, complemented

C₂×#14273662

C₂

yes

maximal, complemented

C₅₉×#568

C₂

yes

maximal, characteristic

#14273734

—

#14273734

C₄

yes

—

C₂×#11745664

C₂²

yes

—

C₂×#11745664

C₂²

yes

—

C₂²×C₅₉⋊C₈

C₂²

yes

—

#14273662

C₂²

yes

—

#14273662

C₂²

yes

—

C₂×#41×C₅₉

C₂²

yes

characteristic

#131×C₅₉

—

C₂×M₁₆×C₅₉

C₂²

yes

—

#41×C₅₉

C₂×C₄

yes

—

#41×C₅₉

D₄

yes

—

C₂×Q₈×C₅₉

Q₈

yes

characteristic

C₂×D₄×C₅₉

Q₈

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

M₁₆×C₅₉

—

M₁₆×C₅₉

C₂³

yes

—

C₂×C₈×C₅₉

—

#11745664

—

#11745664

C₂×C₄

yes

—

#11745664

C₂³

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂×C₅₉⋊C₈

C₂³

yes

characteristic

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂³×C₅₉

C₂×Q₈

yes

—

Q₈×C₅₉

C₄⋊C₄

yes

—

D₄×C₅₉

C₄⋊C₄

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

C₂²×C₄

yes

—

C₅₉⋊C₈

C₂²×C₄

yes

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×C₄⋊C₄

yes

—

C₂²×C₅₉

C₂²×Q₈

yes

characteristic

C₄×C₅₉

C₂×C₄⋊C₄

yes

—

C₄×C₅₉

C₂³×C₄

yes

characteristic

C₄×C₅₉

C₂²×D₄

yes

characteristic

#2916

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

C₂²×C₄⋊C₄

yes

characteristic

#568

—

#568

D₅₉

yes

—

—

—

C₅₉

#2916

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₅₉

yes

—

—

—

118

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₅₉

yes

—

C₂²×C₈

—

#108

—

#108

—

#41

C₄×D₅₉

yes

—

#41

C₂²⋊D₅₉

yes

—

C₂×Q₈

Dic₁₁₈

yes

characteristic

C₂×D₄

Dic₁₁₈

yes

—

C₂²×C₄

C₂²×D₅₉

yes

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

118

—

M₁₆

C₂²×D₅₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂³

C₂×Dic₁₁₈

yes

—

Q₈

Dic₅₉⋊C₄

yes

—

D₄

Dic₅₉⋊C₄

yes

—

C₂×C₄

C₂×Dic₁₁₈

yes

—

C₂×C₄

C₂×C₄×D₅₉

yes

—

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

C₂×C₄

C₂³×D₅₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

118

—

C₂²

—

C₂²

C₂×Dic₅₉⋊C₄

yes

—

C₂²

C₂²×Dic₁₁₈

yes

characteristic

C₄

C₂×Dic₅₉⋊C₄

yes

—

C₄

C₂²×C₄×D₅₉

yes

characteristic

C₄

C₂²×C₂²⋊D₅₉

yes

characteristic

100

C₂

—

101

C₂

—

102

C₂

C₂²×Dic₅₉⋊C₄

yes

characteristic

	subgroup	G/H
center	C₄	C₂²×C₂²⋊D₅₉
commutator	C₄×C₅₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#568	C₂
socle	C₂×C₅₉	C₂²×C₄⋊C₄
hypercenter	#568	D₅₉
hypocenter	C₅₉	#2916
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ #568

subgroup

G/H

center

C₄

C₂²×C₂²⋊D₅₉

commutator

C₄×C₅₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#568

C₂

socle

C₂×C₅₉

C₂²×C₄⋊C₄

D₅₉

C₅₉

G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₄ ◁ C₂×#41 ◁ #568

N	H ≅ G/N	type
3. #16837450	C₂	semidirect
4. C₂×#14273662	C₂	semidirect
57. C₅₉	#2916	semidirect

H ≅ G/N

type

3. #16837450

C₂

semidirect

4. C₂×#14273662

C₂

semidirect

57. C₅₉

#2916

semidirect

Subgroups — #21432705

Conjugacy classes of subgroups

Complements