Group #21430046 — subgroups

Subgroups — #21430046

Order 7552.

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

normal subgroups only

This group has 416 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×#14273719	C₂	1	1	yes	maximal, characteristic
2	#16837340	C₂	1	8	yes	maximal
3	#16837309	C₂	1	4	yes	maximal
4	#16837248	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
6	#14273719	—	2	4	no	—
7	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
8	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
9	C₂×C₄×Dic₅₉	C₂²	1	2	yes	—
10	C₅₉⋊#95	C₂²	1	4	yes	—
11	C₅₉⋊#95	C₂²	1	16	yes	—
12	C₂²×Q₈×C₅₉	C₂²	1	2	yes	—
13	C₄⋊Q₈×C₅₉	—	2	4	no	—
14	C₂×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
15	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₅₉	—	2	4	no	—
17	C₂×Q₈×C₅₉	—	2	8	no	—
18	C₂²×C₄×C₅₉	C₂³	1	4	yes	—
19	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
20	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₅₉	C₂³	1	4	yes	—
22	C₂²×Dic₅₉	C₂³	1	4	yes	—
23	C₄⋊C₄×C₅₉	—	2	8	no	—
24	C₄²×C₅₉	D₄	1	4	yes	—
25	C₄⋊Dic₅₉	—	2	4	no	—
26	Dic₅₉⋊C₄	—	2	8	no	—
27	C₄×Dic₅₉	—	2	4	no	—
28	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
29	Q₈×C₅₉	—	4	8	no	—
30	C₂×C₄×C₅₉	—	2	4	no	—
31	C₂×C₄×C₅₉	—	2	4	no	—
32	C₂×C₄×C₅₉	—	2	8	no	—
33	C₂×C₄×C₅₉	C₂×D₄	1	4	yes	—
34	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₅₉	#41	1	4	yes	—
36	C₂×Dic₅₉	—	2	4	no	—
37	C₂×Dic₅₉	—	2	4	no	—
38	C₂×Dic₅₉	—	2	8	no	—
39	C₂×Dic₅₉	—	2	8	no	—
40	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
41	C₂²×C₅₉	C₂×#41	1	2	yes	—
42	C₂²×C₅₉	2₋¹⁺⁴	1	4	yes	—
43	C₄×C₅₉	—	2	4	no	—
44	C₄×C₅₉	—	4	4	no	—
45	C₄×C₅₉	#124	1	4	yes	—
46	Dic₅₉	—	4	4	no	—
47	Dic₅₉	—	4	4	no	—
48	#2642	—	59	1	no	maximal, Sylow
49	C₂×C₅₉	C₂×#124	1	1	yes	characteristic
50	C₂×C₅₉	#536	1	2	yes	—
51	C₂×C₅₉	#541	1	4	yes	—
52	C₂×C₄⋊Q₈	D₅₉	1	1	yes	characteristic
53	C₂×#125	—	59	1	no	—
54	#400	—	59	8	no	—
55	#391	—	59	4	no	—
56	#376	—	59	1	no	—
57	C₅₉	#2642	1	1	yes	characteristic, complemented, Sylow
58	C₂²×Q₈	C₂×D₅₉	1	2	yes	—
59	C₄⋊Q₈	—	2	4	no	—
60	#125	—	118	4	no	—
61	C₂×C₄⋊C₄	—	59	2	no	—
62	C₂×C₄⋊C₄	—	59	4	no	—
63	C₂×C₄⋊C₄	C₂×D₅₉	1	4	yes	—
64	C₂×C₄²	—	59	2	no	—
65	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
66	#95	—	59	4	no	—
67	#95	—	59	16	no	—
68	C₂×Q₈	—	2	8	no	—
69	C₂×Q₈	—	2	4	no	—
70	C₂²×C₄	—	59	4	no	—
71	C₂²×C₄	—	59	4	no	—
72	C₂²×C₄	C₂²×D₅₉	1	4	yes	—
73	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
74	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
75	C₄⋊C₄	—	2	8	no	—
76	C₄⋊C₄	—	118	8	no	—
77	C₄⋊C₄	—	118	4	no	—
78	C₄²	—	118	4	no	—
79	C₄²	C₂²⋊D₅₉	1	4	yes	—
80	C₂³	C₂³×D₅₉	1	1	yes	characteristic
81	Q₈	—	4	8	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	—	2	8	no	—
85	C₂×C₄	—	118	4	no	—
86	C₂×C₄	—	118	4	no	—
87	C₂×C₄	—	118	8	no	—
88	C₂×C₄	—	118	8	no	—
89	C₂×C₄	#11745687	1	4	yes	—
90	C₂×C₄	C₂×C₂²⋊D₅₉	1	4	yes	—
91	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
92	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
93	C₂²	C₂×#11745687	1	2	yes	—
94	C₂²	#14273775	1	4	yes	—
95	C₄	—	2	4	no	—
96	C₄	—	4	4	no	—
97	C₄	—	236	4	no	—
98	C₄	—	236	4	no	—
99	C₄	#14273714	1	4	yes	—
100	C₂	C₂×#14273714	1	1	yes	characteristic
101	C₂	#16837976	1	2	yes	—
102	C₂	#16838013	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273719

C₂

yes

maximal, characteristic

#16837340

C₂

yes

maximal

#16837309

C₂

yes

maximal

#16837248

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₅₉

C₂

yes

maximal, characteristic

#14273719

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₂²×Q₈×C₅₉

C₂²

yes

—

C₄⋊Q₈×C₅₉

—

C₂×C₄⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

D₄

yes

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₂³×C₅₉

C₂⁴

yes

characteristic

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₂²×C₅₉

C₂×#41

yes

—

C₂²×C₅₉

2₋¹⁺⁴

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#124

yes

—

Dic₅₉

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

#541

yes

—

C₂×C₄⋊Q₈

D₅₉

yes

—

—

—

—

C₅₉

#2642

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₅₉

yes

—

C₄⋊Q₈

—

#125

—

118

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#95

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄²

—

118

—

C₄²

C₂²⋊D₅₉

yes

—

C₂³

C₂³×D₅₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

#11745687

yes

—

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

C₂²

C₂×#11745687

yes

—

C₂²

#14273775

yes

—

C₄

—

C₄

—

C₄

—

236

—

C₄

—

236

—

C₄

#14273714

yes

—

100

C₂

C₂×#14273714

yes

characteristic

101

C₂

#16837976

yes

—

102

C₂

#16838013

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₂×C₄⋊Q₈×C₅₉	C₂
hypercenter	C₂×C₄⋊Q₈	D₅₉
hypocenter	C₅₉	#2642
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₂×C₄⋊Q₈×C₅₉

C₂

hypercenter

C₂×C₄⋊Q₈

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
57. C₅₉	#2642	semidirect

H ≅ G/N

type

57. C₅₉

#2642

semidirect

Subgroups — #21430046

Conjugacy classes of subgroups

Complements