Group #21432459 — subgroups

Subgroups — #21432459

Order 7552.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 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×#14273719	C₂	1	2	yes	maximal
2	#16837300	C₂	1	8	yes	maximal
3	#16837272	C₂	1	2	yes	maximal
4	#16837268	C₂	1	2	yes	maximal
5	C₄³×C₅₉	C₂	1	1	yes	maximal, characteristic
6	#14273719	—	2	8	no	—
7	C₂×C₄⋊Dic₅₉	C₂²	1	4	yes	—
8	C₂×C₄⋊Dic₅₉	C₂²	1	8	yes	—
9	C₂×Dic₅₉⋊C₄	C₂²	1	8	yes	—
10	C₅₉⋊#95	C₂²	1	8	yes	—
11	C₂×C₄²×C₅₉	C₂²	1	4	yes	—
12	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
16	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
17	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
19	C₂²×Dic₅₉	C₂³	1	8	yes	—
20	C₄²×C₅₉	—	2	8	no	—
21	C₄²×C₅₉	D₄	1	4	yes	—
22	C₄²×C₅₉	Q₈	1	4	yes	—
23	C₄²×C₅₉	Q₈	1	4	yes	—
24	C₄⋊Dic₅₉	—	2	8	no	—
25	C₄⋊Dic₅₉	—	2	16	no	—
26	Dic₅₉⋊C₄	—	2	16	no	—
27	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₅₉	—	2	4	no	—
29	C₂×C₄×C₅₉	—	2	4	no	—
30	C₂×C₄×C₅₉	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₅₉	C₂×Q₈	1	4	yes	—
33	C₂×C₄×C₅₉	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₅₉	#41	1	8	yes	—
37	C₂×Dic₅₉	—	2	8	no	—
38	C₂×Dic₅₉	—	2	16	no	—
39	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
40	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
41	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₅₉	C₂×#41	1	4	yes	—
43	C₄×C₅₉	—	2	4	no	—
44	C₄×C₅₉	—	2	4	no	—
45	C₄×C₅₉	#125	1	8	yes	complemented
46	C₄×C₅₉	C₄⋊Q₈	1	4	yes	—
47	Dic₅₉	—	4	8	no	—
48	#2859	—	59	1	no	maximal, Sylow
49	C₂×C₅₉	C₂×#125	1	2	yes	—
50	C₂×C₅₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
51	C₂×C₅₉	#532	1	2	yes	—
52	C₂×C₅₉	#533	1	2	yes	—
53	C₂×#125	—	59	2	no	—
54	#389	—	59	8	no	—
55	#384	—	59	2	no	—
56	#382	—	59	2	no	—
57	C₄³	D₅₉	1	1	yes	characteristic
58	C₅₉	#2859	1	1	yes	characteristic, complemented, Sylow
59	#125	—	118	8	no	—
60	C₂×C₄⋊C₄	—	59	4	no	—
61	C₂×C₄⋊C₄	—	59	8	no	—
62	C₂×C₄⋊C₄	—	59	8	no	—
63	C₂×C₄²	C₂×D₅₉	1	4	yes	—
64	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
66	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
67	#95	—	59	8	no	—
68	C₂²×C₄	—	59	8	no	—
69	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
70	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
71	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
73	C₄⋊C₄	—	118	16	no	—
74	C₄⋊C₄	—	118	8	no	—
75	C₄⋊C₄	—	118	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	Dic₁₁₈	1	4	yes	—
78	C₄²	Dic₁₁₈	1	4	yes	—
79	C₄²	D₂₃₆	1	4	yes	—
80	C₂³	C₂³×D₅₉	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	118	8	no	—
84	C₂×C₄	—	118	16	no	—
85	C₂×C₄	C₂×Dic₁₁₈	1	4	yes	—
86	C₂×C₄	C₂×Dic₁₁₈	1	4	yes	—
87	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
88	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
89	C₂×C₄	C₂×D₂₃₆	1	4	yes	—
90	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
91	C₂×C₄	#11745685	1	8	yes	—
92	C₂²	C₂²×D₂₃₆	1	1	yes	characteristic
93	C₂²	C₂²×Dic₁₁₈	1	1	yes	characteristic
94	C₂²	C₂²×Dic₁₁₈	1	1	yes	characteristic
95	C₂²	C₂×#11745685	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	236	8	no	—
99	C₄	#14273719	1	8	yes	complemented
100	C₄	#14273727	1	4	yes	—
101	C₂	C₂×#14273719	1	2	yes	—
102	C₂	C₂×#14273727	1	1	yes	characteristic
103	C₂	#16837952	1	2	yes	—
104	C₂	#16837959	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273719

C₂

yes

maximal

#16837300

C₂

yes

maximal

#16837272

C₂

yes

maximal

#16837268

C₂

yes

maximal

C₄³×C₅₉

C₂

yes

maximal, characteristic

#14273719

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₄²×C₅₉

—

C₄²×C₅₉

D₄

yes

—

C₄²×C₅₉

Q₈

yes

—

C₄²×C₅₉

Q₈

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₂³×C₅₉

C₂⁴

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

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×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

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

#125

yes

complemented

C₄×C₅₉

C₄⋊Q₈

yes

—

Dic₅₉

—

#2859

—

maximal, Sylow

C₂×C₅₉

C₂×#125

yes

—

C₂×C₅₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₅₉

#532

yes

—

C₂×C₅₉

#533

yes

—

—

—

—

—

C₄³

D₅₉

yes

characteristic

C₅₉

#2859

yes

characteristic, complemented, Sylow

#125

—

118

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₅₉

yes

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₂×C₄²

C₂×D₅₉

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂²×C₄

C₂²×D₅₉

yes

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄²

—

C₄²

Dic₁₁₈

yes

—

C₄²

Dic₁₁₈

yes

—

C₄²

D₂₃₆

yes

—

C₂³

C₂³×D₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

C₂×Dic₁₁₈

yes

—

C₂×C₄

C₂×Dic₁₁₈

yes

—

C₂×C₄

C₂×Dic₁₁₈

yes

—

C₂×C₄

C₂×Dic₁₁₈

yes

—

C₂×C₄

C₂×D₂₃₆

yes

—

C₂×C₄

C₂×D₂₃₆

yes

—

C₂×C₄

#11745685

yes

—

C₂²

C₂²×D₂₃₆

yes

characteristic

C₂²

C₂²×Dic₁₁₈

yes

characteristic

C₂²

C₂²×Dic₁₁₈

yes

characteristic

C₂²

C₂×#11745685

yes

—

C₄

—

C₄

—

C₄

—

236

—

C₄

#14273719

yes

complemented

100

C₄

#14273727

yes

—

101

C₂

C₂×#14273719

yes

—

102

C₂

C₂×#14273727

yes

characteristic

103

C₂

#16837952

yes

—

104

C₂

#16837959

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₄³×C₅₉	C₂
hypercenter	C₄³	D₅₉
hypocenter	C₅₉	#2859
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₄³×C₅₉

C₂

hypercenter

C₄³

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
45. C₄×C₅₉	#125	semidirect
58. C₅₉	#2859	semidirect
99. C₄	#14273719	semidirect

H ≅ G/N

type

45. C₄×C₅₉

#125

semidirect

58. C₅₉

#2859

semidirect

99. C₄

#14273719

semidirect

Subgroups — #21432459

Conjugacy classes of subgroups

Complements