Group #21424173 — subgroups

Subgroups — #21424173

Order 7552.

300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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	#16837265	C₂	1	2	yes	maximal
2	#16837169	C₂	1	4	yes	maximal
3	C₂×#117×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊Dic₅₉	C₂²	1	4	yes	—
5	C₅₉⋊#95	—	2	4	no	—
6	C₂³×C₄×C₅₉	C₂²	1	1	yes	characteristic
7	#117×C₅₉	—	2	4	no	—
8	C₂×C₄⋊C₄×C₅₉	C₄	1	2	yes	complemented
9	C₂×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₅₉	C₄	1	2	yes	complemented
11	C₂⁴×C₅₉	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₅₉	—	2	4	no	—
13	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₅₉	C₂×C₄	1	4	yes	—
16	C₂²×C₄×C₅₉	D₄	1	4	yes	—
17	C₂²×Dic₅₉	—	2	4	no	—
18	C₄⋊C₄×C₅₉	—	2	4	no	—
19	C₂²⋊C₄×C₅₉	—	2	4	no	—
20	C₄²×C₅₉	—	2	4	no	—
21	C₂²⋊Dic₅₉	—	2	8	no	—
22	C₂³×C₅₉	—	4	2	no	—
23	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
24	C₂³×C₅₉	C₂×D₄	1	2	yes	—
25	C₂³×C₅₉	#41	1	4	yes	—
26	C₂×C₄×C₅₉	—	2	2	no	—
27	C₂×C₄×C₅₉	—	2	2	no	—
28	C₂×C₄×C₅₉	—	2	8	no	—
29	C₂×C₄×C₅₉	—	2	4	no	—
30	C₂×C₄×C₅₉	—	4	4	no	—
31	C₂×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
33	C₂×Dic₅₉	—	4	8	no	—
34	C₂×Dic₅₉	—	4	4	no	—
35	C₂²×C₅₉	—	2	4	no	—
36	C₂²×C₅₉	—	2	2	no	—
37	C₂²×C₅₉	—	4	4	no	—
38	C₂²×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₅₉	#117	1	2	yes	—
40	C₂²×C₅₉	#123	1	4	yes	—
41	C₄×C₅₉	—	2	2	no	—
42	C₄×C₅₉	—	2	2	no	—
43	C₄×C₅₉	—	4	4	no	—
44	Dic₅₉	—	8	4	no	—
45	#1820	—	59	1	no	maximal, Sylow
46	C₂×C₅₉	—	2	4	no	—
47	C₂×C₅₉	—	2	2	no	—
48	C₂×C₅₉	#381	1	1	yes	characteristic
49	C₂×C₅₉	#410	1	2	yes	—
50	C₂×#117	D₅₉	1	1	yes	characteristic
51	#381	—	59	2	no	—
52	#342	—	59	4	no	—
53	C₅₉	#1820	1	1	yes	characteristic, complemented, Sylow
54	C₂³×C₄	C₂×D₅₉	1	1	yes	characteristic
55	#117	—	2	4	no	—
56	C₂×C₄⋊C₄	Dic₅₉	1	2	yes	complemented
57	C₂×C₂²⋊C₄	—	59	4	no	—
58	C₂×C₂²⋊C₄	C₂×D₅₉	1	2	yes	—
59	C₂×C₄²	Dic₅₉	1	2	yes	complemented
60	#95	—	118	4	no	—
61	C₂⁴	C₂²×D₅₉	1	1	yes	characteristic
62	C₂²×C₄	—	2	4	no	—
63	C₂²×C₄	—	118	4	no	—
64	C₂²×C₄	C₂×Dic₅₉	1	1	yes	characteristic
65	C₂²×C₄	C₂×Dic₅₉	1	1	yes	characteristic
66	C₂²×C₄	C₂×Dic₅₉	1	4	yes	—
67	C₂²×C₄	C₂²⋊D₅₉	1	4	yes	—
68	C₄⋊C₄	—	2	4	no	—
69	C₂²⋊C₄	—	2	4	no	—
70	C₂²⋊C₄	—	118	8	no	—
71	C₄²	—	2	4	no	—
72	C₂³	—	4	2	no	—
73	C₂³	#11745685	1	4	yes	—
74	C₂³	C₂²×Dic₅₉	1	1	yes	characteristic
75	C₂³	C₂×C₂²⋊D₅₉	1	2	yes	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	2	2	no	—
78	C₂×C₄	—	2	8	no	—
79	C₂×C₄	—	2	4	no	—
80	C₂×C₄	—	4	4	no	—
81	C₂×C₄	—	236	8	no	—
82	C₂×C₄	—	236	4	no	—
83	C₂×C₄	C₂²⋊Dic₅₉	1	2	yes	—
84	C₂×C₄	C₂²⋊Dic₅₉	1	2	yes	—
85	C₂²	—	2	2	no	—
86	C₂²	—	2	4	no	—
87	C₂²	—	4	4	no	—
88	C₂²	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
89	C₂²	#14273686	1	2	yes	—
90	C₂²	#14273710	1	4	yes	—
91	C₄	—	2	2	no	—
92	C₄	—	2	2	no	—
93	C₄	—	4	4	no	—
94	C₄	—	472	4	no	—
95	C₂	—	2	4	no	—
96	C₂	—	2	2	no	—
97	C₂	#16837265	1	1	yes	characteristic
98	C₂	#16837376	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16837265

C₂

yes

maximal

#16837169

C₂

yes

maximal

C₂×#117×C₅₉

C₂

yes

maximal, characteristic

C₂×C₂²⋊Dic₅₉

C₂²

yes

—

C₅₉⋊#95

—

C₂³×C₄×C₅₉

C₂²

yes

characteristic

#117×C₅₉

—

C₂×C₄⋊C₄×C₅₉

C₄

yes

complemented

C₂×C₂²⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₄

yes

complemented

C₂⁴×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

—

C₂²×C₄×C₅₉

D₄

yes

—

C₂²×Dic₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₂²⋊Dic₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

C₂²×C₄

yes

characteristic

C₂³×C₅₉

C₂×D₄

yes

—

C₂³×C₅₉

#41

yes

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₅₉

#117

yes

—

C₂²×C₅₉

#123

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

Dic₅₉

—

#1820

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

#381

yes

characteristic

C₂×C₅₉

#410

yes

—

C₂×#117

D₅₉

yes

characteristic

#381

—

#342

—

C₅₉

#1820

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₅₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

Dic₅₉

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₅₉

yes

—

C₂×C₄²

Dic₅₉

yes

complemented

#95

—

118

—

C₂⁴

C₂²×D₅₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

118

—

C₂²×C₄

C₂×Dic₅₉

yes

characteristic

C₂²×C₄

C₂×Dic₅₉

yes

characteristic

C₂²×C₄

C₂×Dic₅₉

yes

—

C₂²×C₄

C₂²⋊D₅₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

118

—

C₄²

—

C₂³

—

C₂³

#11745685

yes

—

C₂³

C₂²×Dic₅₉

yes

characteristic

C₂³

C₂×C₂²⋊D₅₉

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

—

236

—

C₂×C₄

C₂²⋊Dic₅₉

yes

—

C₂×C₄

C₂²⋊Dic₅₉

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊Dic₅₉

yes

characteristic

C₂²

#14273686

yes

—

C₂²

#14273710

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

472

—

C₂

—

C₂

—

C₂

#16837265

yes

characteristic

C₂

#16837376

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₅₉
commutator	C₂³×C₅₉	C₂²×C₄
Frattini	C₂⁴	C₂²×D₅₉
Fitting	C₂×#117×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₂²⋊C₄
hypercenter	C₂×#117	D₅₉
hypocenter	C₅₉	#1820
LCS	G ▷ C₂³×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#117

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₅₉

commutator

C₂³×C₅₉

C₂²×C₄

Frattini

C₂⁴

C₂²×D₅₉

Fitting

C₂×#117×C₅₉

C₂

socle

C₂²×C₅₉

C₂×C₂²⋊C₄

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#117

N	H ≅ G/N	type
8. C₂×C₄⋊C₄×C₅₉	C₄	semidirect
10. C₂×C₄²×C₅₉	C₄	semidirect
53. C₅₉	#1820	semidirect
56. C₂×C₄⋊C₄	Dic₅₉	semidirect
59. C₂×C₄²	Dic₅₉	semidirect

H ≅ G/N

type

8. C₂×C₄⋊C₄×C₅₉

C₄

semidirect

10. C₂×C₄²×C₅₉

C₄

semidirect

53. C₅₉

#1820

semidirect

56. C₂×C₄⋊C₄

Dic₅₉

semidirect

59. C₂×C₄²

Dic₅₉

semidirect

Subgroups — #21424173

Conjugacy classes of subgroups

Complements