Group #21425606 — subgroups

Subgroups — #21425606

Order 7552.

176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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	#16837445	C₂	1	2	yes	maximal
2	C₂×#14273659	C₂	1	1	yes	maximal, characteristic
3	#16837170	C₂	1	2	yes	maximal
4	#16837167	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#424	C₂	1	1	yes	maximal, characteristic
6	C₂×#11745664	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
8	#14273660	—	2	2	no	—
9	#14273659	—	2	2	no	—
10	#14273658	—	2	2	no	—
11	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	#117×C₅₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₅₉	—	2	2	no	—
15	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₅₉	—	2	2	no	—
17	M₁₆×C₅₉	—	2	2	no	—
18	C₂×C₈×C₅₉	—	2	2	no	—
19	C₂×C₈×C₅₉	—	2	1	no	—
20	C₂×C₈×C₅₉	D₄	1	2	yes	—
21	C₄⋊C₄×C₅₉	D₄	1	2	yes	—
22	C₂²⋊C₄×C₅₉	—	2	1	no	—
23	C₄²×C₅₉	—	2	1	no	—
24	C₄⋊Dic₅₉	—	2	2	no	—
25	C₄⋊Dic₅₉	—	2	2	no	—
26	#11745664	—	2	2	no	—
27	#11745664	Q₈	1	4	yes	—
28	C₂×C₅₉⋊C₈	—	2	2	no	—
29	C₂³×C₅₉	#41	1	1	yes	characteristic
30	C₂×C₄×C₅₉	—	2	2	no	—
31	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₅₉	#41	1	2	yes	—
35	C₂×Dic₅₉	—	4	2	no	—
36	C₂×Dic₅₉	—	8	2	no	—
37	C₈×C₅₉	—	2	2	no	—
38	C₈×C₅₉	—	4	1	no	—
39	C₅₉⋊C₈	—	2	4	no	—
40	C₂²×C₅₉	—	2	2	no	—
41	C₂²×C₅₉	#121	1	1	yes	characteristic
42	C₂²×C₅₉	#125	1	2	yes	—
43	C₄×C₅₉	—	4	2	no	—
44	C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
45	C₄×C₅₉	#123	1	1	yes	characteristic
46	C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
47	Dic₅₉	—	8	2	no	—
48	#2090	—	59	1	no	maximal, Sylow
49	C₂×C₅₉	—	2	2	no	—
50	C₂×C₅₉	#398	1	1	yes	characteristic
51	C₂×C₅₉	#471	1	2	yes	—
52	#428	—	59	2	no	—
53	C₂×#106	—	59	1	no	—
54	#424	D₅₉	1	1	yes	characteristic
55	#343	—	59	2	no	—
56	#341	—	59	1	no	—
57	C₅₉	#2090	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₁₆	—	59	2	no	—
59	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
60	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
61	#117	C₂×D₅₉	1	1	yes	characteristic
62	C₂×C₄⋊C₄	—	59	2	no	—
63	#107	—	118	2	no	—
64	#106	—	118	2	no	—
65	#106	—	118	2	no	—
66	C₄⋊C₈	—	2	2	no	—
67	C₂²×C₄	—	118	2	no	—
68	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	59	4	no	—
71	M₁₆	—	118	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	118	2	no	—
75	C₂×C₈	C₂²⋊D₅₉	1	2	yes	—
76	C₄⋊C₄	—	118	2	no	—
77	C₄⋊C₄	—	118	2	no	—
78	C₄⋊C₄	D₂₃₆	1	2	yes	—
79	C₂²⋊C₄	—	2	1	no	—
80	C₄²	—	2	1	no	—
81	C₂³	#11745685	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	472	2	no	—
84	C₂×C₄	—	236	2	no	—
85	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
86	C₂×C₄	#11745687	1	2	yes	—
87	C₂×C₄	Q₈×D₅₉	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
89	C₈	—	2	2	no	—
90	C₈	—	4	1	no	—
91	C₈	—	118	4	no	—
92	C₂²	—	2	2	no	—
93	C₂²	#14273701	1	1	yes	characteristic
94	C₂²	#14273717	1	2	yes	—
95	C₄	—	4	2	no	—
96	C₄	—	472	2	no	—
97	C₄	#14273707	1	2	yes	—
98	C₄	#14273708	1	1	yes	characteristic
99	C₄	#14273725	1	1	yes	characteristic
100	C₂	—	2	2	no	—
101	C₂	#16837332	1	1	yes	characteristic
102	C₂	#16837665	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16837445

C₂

yes

maximal

C₂×#14273659

C₂

yes

maximal, characteristic

#16837170

C₂

yes

maximal

#16837167

C₂

yes

maximal, characteristic

C₅₉×#424

C₂

yes

maximal, characteristic

C₂×#11745664

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

#14273660

—

#14273659

—

#14273658

—

C₂×M₁₆×C₅₉

C₂²

yes

characteristic

C₂²×C₈×C₅₉

C₂²

yes

characteristic

#117×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

D₄

yes

—

C₄⋊C₄×C₅₉

D₄

yes

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

#11745664

—

#11745664

Q₈

yes

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#41

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

#121

yes

characteristic

C₂²×C₅₉

#125

yes

—

C₄×C₅₉

—

C₄×C₅₉

C₂²⋊Q₈

yes

—

C₄×C₅₉

#123

yes

characteristic

C₄×C₅₉

C₄⋊Q₈

yes

characteristic

Dic₅₉

—

#2090

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

#398

yes

characteristic

C₂×C₅₉

#471

yes

—

#428

—

C₂×#106

—

#424

D₅₉

yes

characteristic

#343

—

#341

—

C₅₉

#2090

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₅₉

yes

characteristic

C₂²×C₈

C₂×D₅₉

yes

characteristic

#117

C₂×D₅₉

yes

characteristic

C₂×C₄⋊C₄

—

#107

—

118

—

#106

—

118

—

#106

—

118

—

C₄⋊C₈

—

C₂²×C₄

—

118

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

118

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

C₂²⋊D₅₉

yes

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄⋊C₄

D₂₃₆

yes

—

C₂²⋊C₄

—

C₄²

—

C₂³

#11745685

yes

characteristic

C₂×C₄

—

C₂×C₄

—

472

—

C₂×C₄

—

236

—

C₂×C₄

C₂×D₂₃₆

yes

characteristic

C₂×C₄

#11745687

yes

—

C₂×C₄

Q₈×D₅₉

yes

—

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

C₈

—

C₈

—

C₈

—

118

—

C₂²

—

C₂²

#14273701

yes

characteristic

C₂²

#14273717

yes

—

C₄

—

C₄

—

472

—

C₄

#14273707

yes

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#16837332

yes

characteristic

102

C₂

#16837665

yes

—

	subgroup	G/H
center	C₂²	#14273701
commutator	C₂²×C₄×C₅₉	C₂³
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#424	C₂
socle	C₂²×C₅₉	#121
hypercenter	#424	D₅₉
hypocenter	C₅₉	#2090
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#14273701

commutator

C₂²×C₄×C₅₉

C₂³

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₅₉×#424

C₂

C₂²×C₅₉

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
57. C₅₉	#2090	semidirect

H ≅ G/N

type

57. C₅₉

#2090

semidirect

Subgroups — #21425606

Conjugacy classes of subgroups

Complements