Group #21425942 — subgroups

Subgroups — #21425942

Order 7552.

174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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	C₂×D₉₄₄	C₂	1	1	yes	maximal, characteristic
2	#16837484	C₂	1	2	yes	maximal, complemented
3	#16837202	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₇₂	C₂²	1	2	yes	—
7	#14273689	—	2	2	no	—
8	D₉₄₄	C₄	1	4	yes	complemented
9	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
10	#14273647	—	2	2	no	—
11	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
13	#107×C₅₉	C₂²	1	2	yes	—
14	C₂×D₂₃₆	—	2	2	no	—
15	C₂×C₄×D₅₉	—	4	2	no	—
16	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₅₉	—	2	2	no	—
18	(C₂×D₅₉)⋊C₄	—	4	2	no	—
19	C₄×Dic₅₉	D₄	1	1	yes	characteristic
20	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
21	D₄₇₂	—	2	2	no	—
22	D₄₇₂	C₂×C₄	1	4	yes	complemented
23	C₁₆×C₅₉	C₂×C₄	1	2	yes	complemented
24	C₅₉⋊C₁₆	—	2	1	no	—
25	C₂²×D₅₉	—	4	2	no	—
26	C₂×C₄×C₅₉	—	4	2	no	—
27	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₅₉	D₈	1	1	yes	characteristic
29	C₂×Dic₅₉	D₈	1	1	yes	characteristic
30	D₂₃₆	—	2	4	no	—
31	D₂₃₆	—	4	2	no	—
32	C₄×D₅₉	—	8	4	no	—
33	C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₅₉	#41	1	1	yes	characteristic
35	C₅₉⋊C₈	—	2	1	no	—
36	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
37	C₂×D₅₉	—	4	4	no	—
38	C₂×D₅₉	—	8	2	no	—
39	C₂×D₅₉	—	8	2	no	—
40	C₄×C₅₉	—	8	2	no	—
41	C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
42	C₄×C₅₉	#135	1	1	yes	characteristic
43	Dic₅₉	—	2	1	no	—
44	Dic₅₉	D₁₆	1	2	yes	complemented
45	C₄×D₁₆	—	59	1	no	maximal, Sylow
46	C₂×C₅₉	C₄×D₈	1	1	yes	characteristic
47	C₂×C₅₉	C₂×D₁₆	1	1	yes	characteristic
48	C₂×C₅₉	#508	1	1	yes	characteristic
49	D₅₉	—	8	4	no	—
50	C₂×D₁₆	—	59	1	no	—
51	C₄×D₈	—	59	2	no	—
52	#366	D₅₉	1	1	yes	characteristic, complemented
53	#357	—	59	2	no	—
54	C₄×C₁₆	—	59	1	no	—
55	C₅₉	C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	59	2	no	—
57	C₄×D₄	—	118	2	no	—
58	D₁₆	—	59	4	no	—
59	C₂×C₁₆	—	59	1	no	—
60	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
61	#107	C₂×D₅₉	1	2	yes	—
62	#102	—	118	2	no	—
63	C₄×C₈	—	59	1	no	—
64	C₂×D₄	—	118	2	no	—
65	C₂²×C₄	—	236	2	no	—
66	D₈	—	59	4	no	—
67	D₈	—	118	2	no	—
68	C₂×C₈	—	59	1	no	—
69	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
70	C₄⋊C₄	—	2	2	no	—
71	C₂²⋊C₄	—	236	2	no	—
72	C₄²	—	59	1	no	—
73	C₁₆	—	118	1	no	—
74	C₁₆	C₄×D₅₉	1	2	yes	complemented
75	C₂³	—	236	2	no	—
76	D₄	—	118	4	no	—
77	D₄	—	236	2	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	—	59	1	no	—
80	C₂×C₄	—	59	1	no	—
81	C₂×C₄	—	472	4	no	—
82	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
83	C₈	—	118	1	no	—
84	C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
85	C₈	#11745689	1	1	yes	characteristic
86	C₂²	—	472	2	no	—
87	C₂²	—	472	2	no	—
88	C₂²	—	236	4	no	—
89	C₂²	D₈×D₅₉	1	1	yes	characteristic
90	C₄	—	8	2	no	—
91	C₄	—	59	2	no	—
92	C₄	—	118	1	no	—
93	C₄	#14273689	1	1	yes	characteristic
94	C₄	#14273750	1	1	yes	characteristic
95	C₂	—	472	4	no	—
96	C₂	#16837484	1	1	yes	characteristic
97	C₂	D₁₆×D₅₉	1	1	yes	characteristic
98	C₂	#16837835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₉₄₄

C₂

yes

maximal, characteristic

#16837484

C₂

yes

maximal, complemented

#16837202

C₂

yes

maximal, complemented

C₁₆×Dic₅₉

C₂

yes

maximal, characteristic, complemented

C₅₉×#366

C₂

yes

maximal, characteristic, complemented

C₂×D₄₇₂

C₂²

yes

—

#14273689

—

D₉₄₄

C₄

yes

complemented

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

#14273647

—

C₈×Dic₅₉

C₂²

yes

characteristic

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

#107×C₅₉

C₂²

yes

—

C₂×D₂₃₆

—

C₂×C₄×D₅₉

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

—

(C₂×D₅₉)⋊C₄

—

C₄×Dic₅₉

D₄

yes

characteristic

C₂×C₅₉⋊C₈

D₄

yes

characteristic

D₄₇₂

—

D₄₇₂

C₂×C₄

yes

complemented

C₁₆×C₅₉

C₂×C₄

yes

complemented

C₅₉⋊C₁₆

—

C₂²×D₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

D₈

yes

characteristic

C₂×Dic₅₉

D₈

yes

characteristic

D₂₃₆

—

D₂₃₆

—

C₄×D₅₉

—

C₈×C₅₉

C₂²×C₄

yes

characteristic

C₈×C₅₉

#41

yes

characteristic

C₅₉⋊C₈

—

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₄×D₄

yes

characteristic

C₄×C₅₉

#135

yes

characteristic

Dic₅₉

—

Dic₅₉

D₁₆

yes

complemented

C₄×D₁₆

—

maximal, Sylow

C₂×C₅₉

C₄×D₈

yes

characteristic

C₂×C₅₉

C₂×D₁₆

yes

characteristic

C₂×C₅₉

#508

yes

characteristic

D₅₉

—

C₂×D₁₆

—

C₄×D₈

—

#366

D₅₉

yes

characteristic, complemented

#357

—

C₄×C₁₆

—

C₅₉

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₄×D₄

—

118

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₅₉

yes

characteristic

#107

C₂×D₅₉

yes

—

#102

—

118

—

C₄×C₈

—

C₂×D₄

—

118

—

C₂²×C₄

—

236

—

D₈

—

D₈

—

118

—

C₂×C₈

—

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

236

—

C₄²

—

C₁₆

—

118

—

C₁₆

C₄×D₅₉

yes

complemented

C₂³

—

236

—

D₄

—

118

—

D₄

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

472

—

C₂×C₄

D₄×D₅₉

yes

characteristic

C₈

—

118

—

C₈

C₂×C₄×D₅₉

yes

characteristic

C₈

#11745689

yes

characteristic

C₂²

—

472

—

C₂²

—

472

—

C₂²

—

236

—

C₂²

D₈×D₅₉

yes

characteristic

C₄

—

C₄

—

C₄

—

118

—

C₄

yes

C₄

yes

C₂

—

472

—

C₂

#16837484

yes

characteristic

C₂

D₁₆×D₅₉

yes

characteristic

C₂

#16837835

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₅₉
commutator	C₈×C₅₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#366	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#366	D₅₉
hypocenter	C₅₉	C₄×D₁₆
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

subgroup

G/H

center

C₂²

D₈×D₅₉

commutator

C₈×C₅₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#366

C₂

socle

C₂²×C₅₉

C₂×D₈

hypercenter

#366

D₅₉

hypocenter

C₅₉

C₄×D₁₆

LCS

G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

N	H ≅ G/N	type
2. #16837484	C₂	semidirect
3. #16837202	C₂	semidirect
4. C₁₆×Dic₅₉	C₂	semidirect
5. C₅₉×#366	C₂	semidirect
8. D₉₄₄	C₄	semidirect
22. D₄₇₂	C₂×C₄	semidirect
23. C₁₆×C₅₉	C₂×C₄	semidirect
44. Dic₅₉	D₁₆	semidirect
52. #366	D₅₉	semidirect
55. C₅₉	C₄×D₁₆	semidirect
74. C₁₆	C₄×D₅₉	semidirect

H ≅ G/N

type

2. #16837484

C₂

semidirect

3. #16837202

C₂

semidirect

4. C₁₆×Dic₅₉

C₂

semidirect

5. C₅₉×#366

C₂

semidirect

8. D₉₄₄

C₄

semidirect

22. D₄₇₂

C₂×C₄

semidirect

23. C₁₆×C₅₉

C₂×C₄

semidirect

44. Dic₅₉

D₁₆

semidirect

52. #366

D₅₉

semidirect

55. C₅₉

C₄×D₁₆

semidirect

74. C₁₆

C₄×D₅₉

semidirect

Subgroups — #21425942

Conjugacy classes of subgroups

Complements