Group #21422113 — subgroups

Subgroups — #21422113

Order 7552.

104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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	#16837643	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₅₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#341	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₃₆	C₄	1	1	yes	characteristic
5	#14273706	—	2	1	no	—
6	C₂×C₅₉⋊C₁₆	—	2	1	no	—
7	#14273661	C₄	1	1	yes	characteristic
8	#14273652	—	2	1	no	—
9	C₂×M₁₆×C₅₉	—	2	1	no	—
10	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
12	C₂×Dic₁₁₈	—	2	1	no	—
13	M₁₆×C₅₉	—	2	2	no	—
14	M₁₆×C₅₉	—	4	1	no	—
15	C₂×C₈×C₅₉	—	4	1	no	—
16	C₂×C₈×C₅₉	—	4	1	no	—
17	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
19	C₂²⋊Dic₅₉	—	4	1	no	—
20	C₄⋊Dic₅₉	—	2	1	no	—
21	Dic₅₉⋊C₄	—	4	1	no	—
22	Dic₂₃₆	—	4	1	no	—
23	C₅₉⋊C₁₆	—	4	1	no	—
24	C₂³×C₅₉	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₅₉	—	2	1	no	—
26	C₂×C₄×C₅₉	—	2	1	no	—
27	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
29	C₂×Dic₅₉	—	4	1	no	—
30	C₂×Dic₅₉	—	4	1	no	—
31	Dic₁₁₈	—	4	1	no	—
32	Dic₁₁₈	—	4	1	no	—
33	C₈×C₅₉	—	2	1	no	—
34	C₈×C₅₉	—	2	1	no	—
35	C₈×C₅₉	—	4	2	no	—
36	C₂²×C₅₉	—	2	1	no	—
37	C₂²×C₅₉	—	2	1	no	—
38	C₂²×C₅₉	—	2	1	no	—
39	C₂²×C₅₉	#102	1	1	yes	characteristic
40	C₄×C₅₉	—	2	1	no	—
41	C₄×C₅₉	#99	1	1	yes	characteristic
42	C₄×C₅₉	#104	1	1	yes	characteristic
43	Dic₅₉	—	8	1	no	—
44	Dic₅₉	—	8	1	no	—
45	#1350	—	59	1	no	maximal, Sylow
46	C₂×C₅₉	—	4	1	no	—
47	C₂×C₅₉	#327	1	1	yes	characteristic
48	C₂×C₅₉	#359	1	1	yes	characteristic
49	C₂×C₅₉	#362	1	1	yes	characteristic
50	#467	—	59	1	no	—
51	C₂²⋊C₁₆	—	59	1	no	—
52	#341	D₅₉	1	1	yes	characteristic
53	C₅₉	#1350	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₁₆	—	59	1	no	—
55	C₂×M₁₆	—	2	1	no	—
56	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
57	C₂²⋊Q₈	—	118	1	no	—
58	C₂×C₁₆	—	118	1	no	—
59	#107	—	59	1	no	—
60	#103	—	118	1	no	—
61	C₂×Q₈	—	118	1	no	—
62	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
63	Q₁₆	—	236	1	no	—
64	M₁₆	—	2	2	no	—
65	M₁₆	—	4	1	no	—
66	C₂×C₈	—	4	1	no	—
67	C₂×C₈	—	4	1	no	—
68	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
69	C₂×C₈	D₂₃₆	1	1	yes	characteristic
70	C₄⋊C₄	—	118	1	no	—
71	C₄⋊C₄	—	236	1	no	—
72	C₂²⋊C₄	—	236	1	no	—
73	C₁₆	—	236	1	no	—
74	C₂³	#11745671	1	1	yes	characteristic
75	Q₈	—	236	1	no	—
76	Q₈	—	236	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	236	1	no	—
80	C₂×C₄	—	236	1	no	—
81	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
82	C₂×C₄	#11745669	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₈	—	4	2	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	2	1	no	—
88	C₂²	—	2	1	no	—
89	C₂²	#14273647	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	472	1	no	—
92	C₄	—	472	1	no	—
93	C₄	#14273641	1	1	yes	characteristic
94	C₄	#14273655	1	1	yes	characteristic
95	C₂	—	4	1	no	—
96	C₂	#16837135	1	1	yes	characteristic
97	C₂	#16837208	1	1	yes	characteristic
98	C₂	#16837217	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837643

C₂

yes

maximal, characteristic

C₂²⋊(C₅₉⋊C₁₆)

C₂

yes

maximal, characteristic

C₅₉×#341

C₂

yes

maximal, characteristic

C₂×Dic₂₃₆

C₄

yes

characteristic

#14273706

—

C₂×C₅₉⋊C₁₆

—

#14273661

C₄

yes

characteristic

#14273652

—

C₂×M₁₆×C₅₉

—

C₂²×C₈×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

Dic₂₃₆

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

SD₁₆

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

D₈

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

#102

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

Dic₅₉

—

Dic₅₉

—

#1350

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂²⋊C₁₆

—

#341

D₅₉

yes

characteristic

C₅₉

#1350

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₅₉

yes

characteristic

C₂²⋊Q₈

—

118

—

C₂×C₁₆

—

118

—

#107

—

#103

—

118

—

C₂×Q₈

—

118

—

C₂²×C₄

C₂²⋊D₅₉

yes

characteristic

Q₁₆

—

236

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₅₉

yes

characteristic

C₂×C₈

D₂₃₆

yes

characteristic

C₄⋊C₄

—

118

—

C₄⋊C₄

—

236

—

C₂²⋊C₄

—

236

—

C₁₆

—

236

—

C₂³

#11745671

yes

characteristic

Q₈

—

236

—

Q₈

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

—

236

—

C₂×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

C₂×C₄

#11745669

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#14273647

yes

characteristic

C₄

—

C₄

—

472

—

C₄

—

472

—

C₄

yes

C₄

yes

C₂

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	#14273647
commutator	C₂×C₈×C₅₉	C₂×C₄
Frattini	C₂²×C₈	C₂×D₅₉
Fitting	C₅₉×#341	C₂
socle	C₂²×C₅₉	#102
hypercenter	#341	D₅₉
hypocenter	C₅₉	#1350
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #341

subgroup

G/H

center

C₂²

#14273647

commutator

C₂×C₈×C₅₉

C₂×C₄

Frattini

C₂²×C₈

C₂×D₅₉

Fitting

C₅₉×#341

C₂

C₂²×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #341

N	H ≅ G/N	type
53. C₅₉	#1350	semidirect

H ≅ G/N

type

53. C₅₉

#1350

semidirect

Subgroups — #21422113

Conjugacy classes of subgroups

Complements