Group #21424252 — subgroups

Subgroups — #21424252

Order 7552.

280 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14273658	C₂	1	4	yes	maximal
2	C₂×C₄×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#16837272	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#384	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₅₉	—	2	2	no	—
7	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
8	#14273658	—	2	8	no	—
9	C₄×C₅₉⋊C₈	C₄	1	4	yes	complemented
10	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
11	C₂×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅₉	—	2	2	no	—
14	C₂²×C₄×C₅₉	D₄	1	2	yes	—
15	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₅₉	—	2	2	no	—
17	C₄⋊C₄×C₅₉	—	2	4	no	—
18	C₄⋊C₄×C₅₉	—	4	4	no	—
19	C₄²×C₅₉	C₂×C₄	1	2	yes	—
20	C₄²×C₅₉	Q₈	1	2	yes	—
21	C₄⋊Dic₅₉	—	2	4	no	—
22	C₄⋊Dic₅₉	—	4	4	no	—
23	C₂×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
24	C₂×C₅₉⋊C₈	D₄	1	4	yes	—
25	C₂×C₅₉⋊C₈	Q₈	1	4	yes	—
26	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₅₉	—	4	2	no	—
28	C₂×C₄×C₅₉	—	4	4	no	—
29	C₂×C₄×C₅₉	C₄⋊C₄	1	4	yes	—
30	C₂×C₄×C₅₉	SD₁₆	1	4	yes	—
31	C₂×C₄×C₅₉	SD₁₆	1	4	yes	—
32	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
36	C₂×Dic₅₉	—	4	2	no	—
37	C₂×Dic₅₉	—	4	4	no	—
38	C₅₉⋊C₈	C₄⋊C₄	1	8	yes	complemented
39	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₅₉	#127	1	1	yes	characteristic
41	C₂²×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₅₉	C₂×SD₁₆	1	2	yes	—
43	C₂²×C₅₉	C₂×SD₁₆	1	2	yes	—
44	C₄×C₅₉	—	8	2	no	—
45	C₄×C₅₉	#106	1	8	yes	complemented
46	C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
47	C₄×C₅₉	C₄⋊Q₈	1	2	yes	—
48	Dic₅₉	—	8	2	no	—
49	#1844	—	59	1	no	maximal, Sylow
50	C₂×C₅₉	#384	1	1	yes	characteristic
51	C₂×C₅₉	C₂×#106	1	2	yes	—
52	C₂×C₅₉	#492	1	1	yes	characteristic
53	C₂×C₅₉	#492	1	1	yes	characteristic
54	C₂×C₅₉	#498	1	2	yes	—
55	C₂×#106	—	59	4	no	—
56	C₂×C₄×C₈	—	59	1	no	—
57	#384	—	59	1	no	—
58	#384	D₅₉	1	1	yes	characteristic
59	C₅₉	#1844	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	59	2	no	—
61	C₂×C₄⋊C₄	—	2	2	no	—
62	C₂×C₄⋊C₄	—	59	2	no	—
63	C₂×C₄⋊C₄	—	118	2	no	—
64	C₂×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
65	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
66	#106	—	118	8	no	—
67	C₄×C₈	—	59	4	no	—
68	C₂²×C₄	—	2	2	no	—
69	C₂²×C₄	—	118	2	no	—
70	C₂²×C₄	C₂²⋊D₅₉	1	2	yes	—
71	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
72	C₂×C₈	—	59	4	no	—
73	C₂×C₈	—	59	4	no	—
74	C₂×C₈	—	59	4	no	—
75	C₄⋊C₄	—	2	4	no	—
76	C₄⋊C₄	—	4	4	no	—
77	C₄⋊C₄	—	118	4	no	—
78	C₄⋊C₄	—	236	4	no	—
79	C₄²	Dic₁₁₈	1	2	yes	—
80	C₄²	C₄×D₅₉	1	2	yes	—
81	C₂³	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	4	4	no	—
84	C₂×C₄	—	236	2	no	—
85	C₂×C₄	—	236	4	no	—
86	C₂×C₄	Dic₅₉⋊C₄	1	4	yes	—
87	C₂×C₄	#11745670	1	4	yes	—
88	C₂×C₄	#11745671	1	4	yes	—
89	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
91	C₂×C₄	D₄×D₅₉	1	2	yes	—
92	C₂×C₄	Q₈×D₅₉	1	2	yes	—
93	C₈	—	59	8	no	—
94	C₂²	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
95	C₂²	#14273723	1	1	yes	characteristic
96	C₂²	#14273725	1	1	yes	characteristic
97	C₂²	C₂×#11745671	1	2	yes	—
98	C₂²	C₂×#11745670	1	2	yes	—
99	C₄	—	8	2	no	—
100	C₄	—	472	2	no	—
101	C₄	#14273658	1	8	yes	complemented
102	C₄	C₄⋊C₄×D₅₉	1	2	yes	—
103	C₄	#14273726	1	2	yes	—
104	C₂	#16837271	1	1	yes	characteristic
105	C₂	C₂×#14273658	1	2	yes	—
106	C₂	#16837774	1	1	yes	characteristic
107	C₂	#16837776	1	1	yes	characteristic
108	C₂	#16837798	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273658

C₂

yes

maximal

C₂×C₄×C₅₉⋊C₈

C₂

yes

maximal, characteristic

#16837272

C₂

yes

maximal, characteristic

C₅₉×#384

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

#14273658

—

C₄×C₅₉⋊C₈

C₄

yes

complemented

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂×C₄

yes

—

C₄²×C₅₉

Q₈

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂×C₅₉⋊C₈

D₄

yes

—

C₂×C₅₉⋊C₈

Q₈

yes

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₄⋊C₄

yes

—

C₂×C₄×C₅₉

SD₁₆

yes

—

C₂×C₄×C₅₉

SD₁₆

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₅₉⋊C₈

C₄⋊C₄

yes

complemented

C₂²×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₅₉

#127

yes

characteristic

C₂²×C₅₉

C₄⋊Q₈

yes

characteristic

C₂²×C₅₉

C₂×SD₁₆

yes

—

C₂²×C₅₉

C₂×SD₁₆

yes

—

C₄×C₅₉

—

C₄×C₅₉

#106

yes

complemented

C₄×C₅₉

C₂×C₄⋊C₄

yes

—

C₄×C₅₉

C₄⋊Q₈

yes

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×#106

—

C₂×C₄×C₈

—

#384

—

#384

D₅₉

yes

characteristic

C₅₉

#1844

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

118

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#106

—

118

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

118

—

C₂²×C₄

C₂²⋊D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

236

—

C₄²

Dic₁₁₈

yes

—

C₄²

C₄×D₅₉

yes

—

C₂³

C₂×C₂²⋊D₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

—

236

—

C₂×C₄

Dic₅₉⋊C₄

yes

—

C₂×C₄

#11745670

yes

—

C₂×C₄

#11745671

yes

—

C₂×C₄

C₂×Dic₁₁₈

yes

characteristic

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

C₂×C₄

D₄×D₅₉

yes

—

C₂×C₄

Q₈×D₅₉

yes

—

C₈

—

C₂²

C₂×Dic₅₉⋊C₄

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

C₂×#11745670

yes

—

C₄

—

100

C₄

—

472

—

101

C₄

#14273658

yes

complemented

102

C₄

C₄⋊C₄×D₅₉

yes

—

103

C₄

#14273726

yes

—

104

C₂

#16837271

yes

characteristic

105

C₂

C₂×#14273658

yes

—

106

C₂

#16837774

yes

characteristic

107

C₂

#16837776

yes

characteristic

108

C₂

#16837798

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#384	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	#384	D₅₉
hypocenter	C₅₉	#1844
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₅₉×#384

C₂

socle

C₂³×C₅₉

C₂×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
9. C₄×C₅₉⋊C₈	C₄	semidirect
38. C₅₉⋊C₈	C₄⋊C₄	semidirect
45. C₄×C₅₉	#106	semidirect
59. C₅₉	#1844	semidirect
101. C₄	#14273658	semidirect

H ≅ G/N

type

9. C₄×C₅₉⋊C₈

C₄

semidirect

38. C₅₉⋊C₈

C₄⋊C₄

semidirect

45. C₄×C₅₉

#106

semidirect

59. C₅₉

#1844

semidirect

101. C₄

#14273658

semidirect

Subgroups — #21424252

Conjugacy classes of subgroups

Complements