Group #21425909 — subgroups

Subgroups — #21425909

Order 7552.

122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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	#16837360	C₂	1	1	yes	maximal, characteristic
2	#16837222	C₂	1	2	yes	maximal, complemented
3	#16837184	C₂	1	1	yes	maximal, characteristic
4	#16837179	C₂	1	2	yes	maximal, complemented
5	C₅₉×#349	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅₉⋊C₈	C₄	1	1	yes	characteristic
7	#14273686	C₄	1	1	yes	characteristic
8	#14273667	C₂²	1	2	yes	—
9	#14273637	C₄	1	1	yes	characteristic
10	#14273637	C₂²	1	1	yes	characteristic
11	C₈×Dic₅₉	C₄	1	1	yes	characteristic
12	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	M₃₂×C₅₉	C₂²	1	2	yes	—
15	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
16	M₁₆×C₅₉	—	2	2	no	—
17	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
19	C₂²⋊Dic₅₉	—	2	1	no	—
20	C₄⋊Dic₅₉	—	2	1	no	—
21	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₅₉⋊C₈	—	2	2	no	—
24	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₁₆×C₅₉	—	2	2	no	—
27	C₅₉⋊C₁₆	—	2	2	no	—
28	C₂³×C₅₉	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₅₉	—	2	1	no	—
30	C₂×C₄×C₅₉	—	2	1	no	—
31	C₂×C₄×C₅₉	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₅₉	—	2	1	no	—
34	C₂×Dic₅₉	—	2	1	no	—
35	C₈×C₅₉	—	2	1	no	—
36	C₈×C₅₉	#41	1	2	yes	—
37	C₅₉⋊C₈	—	2	1	no	—
38	C₅₉⋊C₈	M₁₆	1	2	yes	—
39	C₂²×C₅₉	—	2	1	no	—
40	C₂²×C₅₉	—	4	1	no	—
41	C₂²×C₅₉	C₂×M₁₆	1	1	yes	characteristic
42	C₄×C₅₉	—	2	1	no	—
43	C₄×C₅₉	#117	1	1	yes	characteristic
44	C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
45	Dic₅₉	—	4	1	no	—
46	Dic₅₉	—	4	1	no	—
47	#2166	—	59	1	no	maximal, Sylow
48	C₂×C₅₉	—	2	1	no	—
49	C₂×C₅₉	—	4	1	no	—
50	C₂×C₅₉	#432	1	1	yes	characteristic
51	#405	—	59	1	no	—
52	#364	—	59	2	no	—
53	#349	—	59	1	no	—
54	#349	D₅₉	1	1	yes	characteristic
55	#347	—	59	2	no	—
56	C₅₉	#2166	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
58	C₂²×C₈	—	59	1	no	—
59	#117	—	59	1	no	—
60	M₃₂	—	59	2	no	—
61	M₃₂	C₂×D₅₉	1	2	yes	—
62	#97	—	59	1	no	—
63	#97	—	59	1	no	—
64	C₄×C₈	—	59	1	no	—
65	C₄×C₈	—	59	1	no	—
66	C₂²×C₄	C₄×D₅₉	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	C₂×C₈	—	59	1	no	—
69	C₂×C₈	—	59	1	no	—
70	C₂×C₈	—	118	2	no	—
71	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
73	C₄⋊C₄	—	118	1	no	—
74	C₂²⋊C₄	—	118	1	no	—
75	C₄²	—	59	1	no	—
76	C₄²	—	59	1	no	—
77	C₁₆	—	2	2	no	—
78	C₁₆	—	118	2	no	—
79	C₂³	#11745659	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	118	1	no	—
83	C₂×C₄	—	118	1	no	—
84	C₂×C₄	#11745659	1	1	yes	characteristic
85	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	59	2	no	—
88	C₈	—	118	1	no	—
89	C₈	#11745687	1	2	yes	—
90	C₂²	—	2	1	no	—
91	C₂²	—	4	1	no	—
92	C₂²	C₂×#11745659	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	236	1	no	—
95	C₄	—	236	1	no	—
96	C₄	#14273683	1	1	yes	characteristic
97	C₄	M₁₆×D₅₉	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	4	1	no	—
100	C₂	#16837456	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837360

C₂

yes

maximal, characteristic

#16837222

C₂

yes

maximal, complemented

#16837184

C₂

yes

maximal, characteristic

#16837179

C₂

yes

maximal, complemented

C₅₉×#349

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₄

yes

characteristic

#14273686

C₄

yes

characteristic

#14273667

C₂²

yes

—

#14273637

C₄

yes

characteristic

#14273637

C₂²

yes

characteristic

C₈×Dic₅₉

C₄

yes

characteristic

C₈×Dic₅₉

C₂²

yes

characteristic

C₂×M₁₆×C₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

C₂²

yes

—

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

M₁₆×C₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

M₁₆

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

M₁₆

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

#41

yes

—

C₅₉⋊C₈

—

C₅₉⋊C₈

M₁₆

yes

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×M₁₆

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

#117

yes

characteristic

C₄×C₅₉

C₂×M₁₆

yes

characteristic

Dic₅₉

—

Dic₅₉

—

#2166

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

yes

—

—

—

D₅₉

yes

characteristic

#347

—

C₅₉

#2166

yes

characteristic, complemented, Sylow

C₂×M₁₆

C₂×D₅₉

yes

characteristic

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

C₂×D₅₉

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₄×D₅₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

C₄×D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

118

—

C₂²⋊C₄

—

118

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

118

—

C₂³

#11745659

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

#11745659

yes

characteristic

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

C₈

—

C₈

—

C₈

—

118

—

C₈

#11745687

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#11745659

yes

characteristic

C₄

—

C₄

—

236

—

C₄

—

236

—

C₄

#14273683

yes

characteristic

C₄

M₁₆×D₅₉

yes

characteristic

C₂

—

C₂

—

100

C₂

#16837456

yes

characteristic

	subgroup	G/H
center	C₄	#14273683
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#349	C₂
socle	C₂×C₅₉	#432
hypercenter	#349	D₅₉
hypocenter	C₅₉	#2166
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #349

subgroup

G/H

center

C₄

#14273683

commutator

C₂×C₄×C₅₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#349

C₂

C₂×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #349

N	H ≅ G/N	type
2. #16837222	C₂	semidirect
4. #16837179	C₂	semidirect
56. C₅₉	#2166	semidirect

H ≅ G/N

type

2. #16837222

C₂

semidirect

4. #16837179

C₂

semidirect

56. C₅₉

#2166

semidirect

Subgroups — #21425909

Conjugacy classes of subgroups

Complements