Group #21425906 — subgroups

Subgroups — #21425906

Order 7552.

128 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 53 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	#16837354	C₂	1	1	yes	maximal, characteristic
2	#16837222	C₂	1	2	yes	maximal, complemented
3	#16837183	C₂	1	2	yes	maximal
4	#16837180	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#347	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11745659	C₄	1	1	yes	characteristic
7	C₂×#11745659	C₂²	1	1	yes	characteristic
8	C₄²×D₅₉	C₄	1	1	yes	characteristic
9	#14273667	C₂²	1	2	yes	—
10	#14273638	C₄	1	1	yes	characteristic
11	C₈×Dic₅₉	C₄	1	1	yes	characteristic
12	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
13	M₃₂×C₅₉	C₂²	1	2	yes	—
14	#97×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₅₉	—	2	1	no	—
16	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
19	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₅₉	—	2	1	no	—
21	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	#11745659	—	2	2	no	—
25	#11745659	—	2	2	no	—
26	C₁₆×C₅₉	—	2	2	no	—
27	C₅₉⋊C₁₆	—	2	2	no	—
28	C₂²×D₅₉	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₅₉	—	2	1	no	—
30	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₅₉	—	2	1	no	—
32	C₂×Dic₅₉	M₁₆	1	1	yes	characteristic
33	C₄×D₅₉	—	2	1	no	—
34	C₄×D₅₉	—	2	1	no	—
35	C₄×D₅₉	—	4	2	no	—
36	C₈×C₅₉	—	2	1	no	—
37	C₈×C₅₉	#41	1	2	yes	—
38	C₅₉⋊C₈	—	2	1	no	—
39	C₅₉⋊C₈	M₁₆	1	2	yes	—
40	C₂²×C₅₉	C₂×M₁₆	1	1	yes	characteristic
41	C₂×D₅₉	—	2	1	no	—
42	C₂×D₅₉	—	4	1	no	—
43	C₄×C₅₉	—	4	1	no	—
44	C₄×C₅₉	#117	1	1	yes	characteristic
45	C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
46	Dic₅₉	—	2	2	no	—
47	Dic₅₉	—	2	1	no	—
48	#2165	—	59	1	no	maximal, Sylow
49	C₂×C₅₉	—	2	1	no	—
50	C₂×C₅₉	#432	1	1	yes	characteristic
51	D₅₉	—	4	1	no	—
52	C₄×M₁₆	—	59	1	no	—
53	#364	—	59	2	no	—
54	#349	—	59	2	no	—
55	#347	—	59	1	no	—
56	#347	D₅₉	1	1	yes	characteristic, complemented
57	C₅₉	#2165	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₁₆	—	59	1	no	—
59	C₂×M₁₆	—	59	1	no	—
60	C₂×C₄²	—	59	1	no	—
61	M₃₂	—	59	2	no	—
62	M₃₂	C₂×D₅₉	1	2	yes	—
63	#97	—	59	1	no	—
64	#97	C₂×D₅₉	1	1	yes	characteristic
65	C₄×C₈	—	59	1	no	—
66	C₄×C₈	—	59	1	no	—
67	C₂²×C₄	—	59	1	no	—
68	C₂²×C₄	—	118	1	no	—
69	M₁₆	—	118	2	no	—
70	M₁₆	—	118	2	no	—
71	C₂×C₈	—	59	1	no	—
72	C₂×C₈	—	59	1	no	—
73	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
75	C₄²	—	59	1	no	—
76	C₄²	—	118	1	no	—
77	C₄²	C₄×D₅₉	1	1	yes	characteristic
78	C₁₆	—	2	2	no	—
79	C₁₆	—	118	2	no	—
80	C₂³	—	59	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	59	1	no	—
83	C₂×C₄	—	118	1	no	—
84	C₂×C₄	—	118	1	no	—
85	C₂×C₄	—	118	1	no	—
86	C₂×C₄	—	236	2	no	—
87	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	59	2	no	—
90	C₈	—	118	1	no	—
91	C₈	#11745685	1	2	yes	—
92	C₂²	—	118	1	no	—
93	C₂²	—	236	1	no	—
94	C₂²	M₁₆×D₅₉	1	1	yes	characteristic
95	C₄	—	4	1	no	—
96	C₄	—	118	2	no	—
97	C₄	—	118	1	no	—
98	C₄	#14273684	1	1	yes	characteristic
99	C₄	M₁₆×D₅₉	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	236	1	no	—
102	C₂	#16837457	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837354

C₂

yes

maximal, characteristic

#16837222

C₂

yes

maximal, complemented

#16837183

C₂

yes

maximal

#16837180

C₂

yes

maximal, characteristic, complemented

C₅₉×#347

C₂

yes

maximal, characteristic, complemented

C₂×#11745659

C₄

yes

characteristic

C₂×#11745659

C₂²

yes

characteristic

C₄²×D₅₉

C₄

yes

characteristic

#14273667

C₂²

yes

—

#14273638

C₄

yes

characteristic

C₈×Dic₅₉

C₄

yes

characteristic

C₈×Dic₅₉

C₂²

yes

characteristic

M₃₂×C₅₉

C₂²

yes

—

#97×C₅₉

C₂²

yes

characteristic

C₂×C₄×D₅₉

—

C₂×C₄×D₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

C₂×C₄

yes

characteristic

C₄×Dic₅₉

—

C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

#11745659

—

#11745659

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂²×D₅₉

M₁₆

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

M₁₆

yes

characteristic

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

C₈×C₅₉

—

C₈×C₅₉

#41

yes

—

C₅₉⋊C₈

—

C₅₉⋊C₈

M₁₆

yes

—

C₂²×C₅₉

C₂×M₁₆

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#117

yes

characteristic

C₄×C₅₉

C₂×M₁₆

yes

characteristic

Dic₅₉

—

Dic₅₉

—

#2165

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

#432

yes

characteristic

D₅₉

—

C₄×M₁₆

—

—

—

—

D₅₉

yes

characteristic, complemented

C₅₉

#2165

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×C₄²

—

M₃₂

—

M₃₂

C₂×D₅₉

yes

—

#97

—

#97

C₂×D₅₉

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

118

—

M₁₆

—

118

—

M₁₆

—

118

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄²

—

C₄²

—

118

—

C₄²

C₄×D₅₉

yes

characteristic

C₁₆

—

C₁₆

—

118

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

236

—

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

C₈

—

C₈

—

C₈

—

118

—

C₈

#11745685

yes

—

C₂²

—

118

—

C₂²

—

236

—

C₂²

M₁₆×D₅₉

yes

characteristic

C₄

—

C₄

—

118

—

C₄

—

118

—

C₄

#14273684

yes

characteristic

C₄

M₁₆×D₅₉

yes

characteristic

100

C₂

—

101

C₂

—

236

—

102

C₂

#16837457

yes

characteristic

	subgroup	G/H
center	C₄	#14273684
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#347	C₂
socle	C₂×C₅₉	#432
hypercenter	#347	D₅₉
hypocenter	C₅₉	#2165
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ #97 ◁ #347

subgroup

G/H

center

C₄

#14273684

commutator

C₂×C₄×C₅₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#347

C₂

C₂×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₄ ◁ #97 ◁ #347

N	H ≅ G/N	type
2. #16837222	C₂	semidirect
4. #16837180	C₂	semidirect
5. C₅₉×#347	C₂	semidirect
56. #347	D₅₉	semidirect
57. C₅₉	#2165	semidirect

H ≅ G/N

type

2. #16837222

C₂

semidirect

4. #16837180

C₂

semidirect

5. C₅₉×#347

C₂

semidirect

56. #347

D₅₉

semidirect

57. C₅₉

#2165

semidirect

Subgroups — #21425906

Conjugacy classes of subgroups

Complements