Group #21425878 — subgroups

Subgroups — #21425878

Order 7552.

152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#16837440	C₂	1	1	yes	maximal, characteristic
3	#16837229	C₂	1	2	yes	maximal, complemented
4	#16837227	C₂	1	2	yes	maximal, complemented
5	C₅₉×#427	C₂	1	1	yes	maximal, characteristic
6	#14273686	—	2	1	no	—
7	C₂×C₅₉⋊C₁₆	C₄	1	4	yes	complemented
8	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
10	#14273661	C₂²	1	2	yes	—
11	#14273659	—	2	1	no	—
12	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	#117×C₅₉	—	2	1	no	—
14	#107×C₅₉	C₂²	1	2	yes	—
15	#106×C₅₉	—	2	1	no	—
16	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₅₉	Q₈	1	2	yes	—
20	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₅₉	—	2	2	no	—
22	C₂²⋊C₄×C₅₉	—	4	1	no	—
23	C₄²×C₅₉	—	4	1	no	—
24	C₂²⋊Dic₅₉	—	4	1	no	—
25	C₄⋊Dic₅₉	—	2	2	no	—
26	C₄×Dic₅₉	—	4	1	no	—
27	C₅₉⋊C₁₆	C₂×C₄	1	2	yes	—
28	C₅₉⋊C₁₆	C₂×C₄	1	2	yes	—
29	C₂³×C₅₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₅₉	—	4	2	no	—
31	C₂×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
32	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
33	C₂×C₄×C₅₉	Q₁₆	1	2	yes	—
34	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₅₉	—	4	2	no	—
36	C₈×C₅₉	C₄⋊C₄	1	2	yes	—
37	C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₅₉	—	2	2	no	—
40	C₂²×C₅₉	#107	1	2	yes	—
41	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
42	C₄×C₅₉	—	8	2	no	—
43	C₄×C₅₉	#107	1	2	yes	—
44	C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
46	Dic₅₉	—	8	2	no	—
47	#2158	—	59	1	no	maximal, Sylow
48	C₂×C₅₉	—	2	2	no	—
49	C₂×C₅₉	C₂×#107	1	1	yes	characteristic
50	C₂×C₅₉	#508	1	2	yes	—
51	C₂²×C₁₆	—	59	1	no	—
52	#427	—	59	1	no	—
53	#427	D₅₉	1	1	yes	characteristic
54	#367	—	59	2	no	—
55	#366	—	59	2	no	—
56	C₅₉	#2158	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
58	#117	—	2	1	no	—
59	#117	—	118	1	no	—
60	C₂×C₁₆	—	59	4	no	—
61	C₂×C₁₆	—	59	1	no	—
62	C₂×C₁₆	—	59	1	no	—
63	#107	—	59	2	no	—
64	#107	C₂×D₅₉	1	2	yes	—
65	#106	—	2	1	no	—
66	#106	—	118	1	no	—
67	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
68	C₂×C₈	Dic₁₁₈	1	2	yes	—
69	C₂×C₈	C₄×D₅₉	1	2	yes	—
70	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	118	2	no	—
74	C₂²⋊C₄	—	4	1	no	—
75	C₂²⋊C₄	—	236	1	no	—
76	C₄²	—	4	1	no	—
77	C₄²	—	236	1	no	—
78	C₁₆	—	59	2	no	—
79	C₁₆	—	59	2	no	—
80	C₂³	#11745669	1	1	yes	characteristic
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	236	2	no	—
83	C₂×C₄	Dic₅₉⋊C₄	1	2	yes	—
84	C₂×C₄	#11745669	1	1	yes	characteristic
85	C₂×C₄	#11745672	1	2	yes	—
86	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
87	C₈	Dic₅₉⋊C₄	1	2	yes	—
88	C₈	C₂×Dic₁₁₈	1	1	yes	characteristic
89	C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#14273660	1	2	yes	—
92	C₂²	C₂×#11745669	1	1	yes	characteristic
93	C₄	—	8	2	no	—
94	C₄	—	472	2	no	—
95	C₄	#14273660	1	2	yes	—
96	C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
97	C₄	C₂×#11745672	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×#14273660	1	1	yes	characteristic
100	C₂	#16837832	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₅₉⋊C₁₆

C₂

yes

maximal, characteristic

#16837440

C₂

yes

maximal, characteristic

#16837229

C₂

yes

maximal, complemented

#16837227

C₂

yes

maximal, complemented

C₅₉×#427

C₂

yes

maximal, characteristic

#14273686

—

C₂×C₅₉⋊C₁₆

C₄

yes

complemented

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

#14273661

C₂²

yes

—

#14273659

—

C₂²×C₈×C₅₉

C₂²

yes

characteristic

#117×C₅₉

—

#107×C₅₉

C₂²

yes

—

#106×C₅₉

—

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

Q₈

yes

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

—

C₅₉⋊C₁₆

C₂×C₄

yes

—

C₅₉⋊C₁₆

C₂×C₄

yes

—

C₂³×C₅₉

D₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₄⋊C₄

yes

—

C₂×C₄×C₅₉

D₈

yes

characteristic

C₂×C₄×C₅₉

Q₁₆

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

—

C₈×C₅₉

C₄⋊C₄

yes

—

C₈×C₅₉

C₂²×C₄

yes

characteristic

C₈×C₅₉

C₂×Q₈

yes

characteristic

C₂²×C₅₉

—

C₂²×C₅₉

#107

yes

—

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

#107

yes

—

C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₅₉

C₂×Q₁₆

yes

characteristic

Dic₅₉

—

#2158

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

C₂×#107

yes

characteristic

C₂×C₅₉

#508

yes

—

C₂²×C₁₆

—

#427

—

#427

D₅₉

yes

characteristic

#367

—

#366

—

C₅₉

#2158

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₅₉

yes

characteristic

#117

—

#117

—

118

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₅₉

yes

—

#106

—

#106

—

118

—

C₂²×C₄

C₂²⋊D₅₉

yes

characteristic

C₂×C₈

Dic₁₁₈

yes

—

C₂×C₈

C₄×D₅₉

yes

—

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

118

—

C₂²⋊C₄

—

C₂²⋊C₄

—

236

—

C₄²

—

C₄²

—

236

—

C₁₆

—

C₁₆

—

C₂³

#11745669

yes

characteristic

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

Dic₅₉⋊C₄

yes

—

C₂×C₄

#11745669

yes

characteristic

C₂×C₄

#11745672

yes

—

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

C₈

Dic₅₉⋊C₄

yes

—

C₈

C₂×Dic₁₁₈

yes

characteristic

C₈

C₂×C₄×D₅₉

yes

characteristic

C₂²

—

C₂²

#14273660

yes

—

C₂²

C₂×#11745669

yes

characteristic

C₄

—

C₄

—

472

—

C₄

#14273660

yes

—

C₄

C₂×Dic₅₉⋊C₄

yes

characteristic

C₄

C₂×#11745672

yes

characteristic

C₂

—

C₂

C₂×#14273660

yes

characteristic

100

C₂

#16837832

yes

—

	subgroup	G/H
center	C₂×C₄	#11745669
commutator	C₈×C₅₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#427	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#427	D₅₉
hypocenter	C₅₉	#2158
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

subgroup

G/H

center

C₂×C₄

#11745669

commutator

C₈×C₅₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#427

C₂

socle

C₂²×C₅₉

C₂×D₈

D₅₉

C₅₉

G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

N	H ≅ G/N	type
3. #16837229	C₂	semidirect
4. #16837227	C₂	semidirect
7. C₂×C₅₉⋊C₁₆	C₄	semidirect
56. C₅₉	#2158	semidirect

H ≅ G/N

type

3. #16837229

C₂

semidirect

4. #16837227

C₂

semidirect

7. C₂×C₅₉⋊C₁₆

C₄

semidirect

56. C₅₉

#2158

semidirect

Subgroups — #21425878

Conjugacy classes of subgroups

Complements