Group #21426184 — subgroups

Subgroups — #21426184

Order 7552.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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×C₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic
2	#16837640	C₂	1	2	yes	maximal
3	#16837228	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837206	C₂	1	2	yes	maximal, complemented
5	C₂×Q₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
7	#14273703	—	2	2	no	—
8	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₁₆×D₅₉	—	2	2	no	—
10	#14273661	C₂²	1	2	yes	—
11	#14273651	—	2	2	no	—
12	C₂×Q₁₆×C₅₉	C₂²	1	2	yes	—
13	Q₃₂×C₅₉	—	2	2	no	—
14	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₅₉	—	2	2	no	—
16	C₂×C₄×D₅₉	D₄	1	1	yes	characteristic
17	Q₁₆×C₅₉	—	2	2	no	—
18	Q₁₆×C₅₉	—	2	2	no	—
19	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
20	(C₂×D₅₉)⋊C₄	—	4	2	no	—
21	C₄⋊Dic₅₉	—	2	2	no	—
22	Dic₅₉⋊C₄	—	4	2	no	—
23	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
24	C₈×D₅₉	—	2	1	no	—
25	C₈×D₅₉	—	2	1	no	—
26	C₁₆×C₅₉	D₄	1	2	yes	—
27	C₅₉⋊C₁₆	—	2	1	no	—
28	C₂²×D₅₉	D₈	1	1	yes	characteristic
29	Q₈×C₅₉	—	4	2	no	—
30	Q₈×C₅₉	—	4	2	no	—
31	C₂×C₄×C₅₉	—	4	2	no	—
32	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₅₉	—	4	2	no	—
34	C₂×Dic₅₉	D₈	1	1	yes	characteristic
35	C₄×D₅₉	—	2	1	no	—
36	C₄×D₅₉	—	2	1	no	—
37	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₅₉	#41	1	1	yes	characteristic
39	C₅₉⋊C₈	—	2	1	no	—
40	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
41	C₂×D₅₉	—	2	1	no	—
42	C₂×D₅₉	—	2	1	no	—
43	C₂×D₅₉	Q₃₂	1	2	yes	complemented
44	C₄×C₅₉	—	8	2	no	—
45	C₄×C₅₉	#121	1	1	yes	characteristic
46	C₄×C₅₉	#135	1	1	yes	characteristic
47	Dic₅₉	—	2	1	no	—
48	Dic₅₉	—	8	2	no	—
49	#2216	—	59	1	no	maximal, Sylow
50	C₂×C₅₉	#466	1	1	yes	characteristic
51	C₂×C₅₉	C₂×Q₃₂	1	1	yes	characteristic
52	C₂×C₅₉	#508	1	1	yes	characteristic
53	D₅₉	—	2	2	no	—
54	C₂×Q₃₂	D₅₉	1	1	yes	characteristic, complemented
55	C₂²×C₁₆	—	59	1	no	—
56	#467	—	59	2	no	—
57	#366	—	59	1	no	—
58	#358	—	59	2	no	—
59	C₅₉	#2216	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₁₆	C₂×D₅₉	1	2	yes	—
61	C₂²×C₈	—	59	1	no	—
62	C₂²⋊Q₈	—	118	2	no	—
63	Q₃₂	—	2	2	no	—
64	C₂×C₁₆	—	59	1	no	—
65	C₂×C₁₆	—	118	2	no	—
66	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
67	#107	—	59	2	no	—
68	#103	—	118	2	no	—
69	C₂×Q₈	—	2	2	no	—
70	C₂²×C₄	—	59	1	no	—
71	Q₁₆	—	2	2	no	—
72	Q₁₆	—	2	2	no	—
73	C₂×C₈	—	59	1	no	—
74	C₂×C₈	—	118	1	no	—
75	C₂×C₈	—	118	1	no	—
76	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
77	C₄⋊C₄	—	118	2	no	—
78	C₄⋊C₄	—	236	2	no	—
79	C₂²⋊C₄	—	236	2	no	—
80	C₁₆	—	118	1	no	—
81	C₁₆	C₂²⋊D₅₉	1	2	yes	—
82	C₂³	—	59	1	no	—
83	Q₈	—	4	2	no	—
84	Q₈	—	4	2	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	—	59	1	no	—
87	C₂×C₄	—	118	1	no	—
88	C₂×C₄	—	118	1	no	—
89	C₂×C₄	—	236	2	no	—
90	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
91	C₈	—	118	1	no	—
92	C₈	#11745687	1	1	yes	characteristic
93	C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
94	C₂²	—	59	2	no	—
95	C₂²	—	118	1	no	—
96	C₂²	—	118	1	no	—
97	C₂²	D₈×D₅₉	1	1	yes	characteristic
98	C₄	—	8	2	no	—
99	C₄	—	118	1	no	—
100	C₄	—	472	2	no	—
101	C₄	#14273698	1	1	yes	characteristic
102	C₄	#14273746	1	1	yes	characteristic
103	C₂	—	118	2	no	—
104	C₂	#16837635	1	1	yes	characteristic
105	C₂	Q₃₂×D₅₉	1	1	yes	characteristic
106	C₂	#16837835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₅₉

C₂

yes

maximal, characteristic

#16837640

C₂

yes

maximal

#16837228

C₂

yes

maximal, characteristic, complemented

#16837206

C₂

yes

maximal, complemented

C₂×Q₃₂×C₅₉

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₅₉

C₂²

yes

characteristic

#14273703

—

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₅₉

—

#14273661

C₂²

yes

—

#14273651

—

C₂×Q₁₆×C₅₉

C₂²

yes

—

Q₃₂×C₅₉

—

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

—

C₂×C₄×D₅₉

D₄

yes

characteristic

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₂×C₅₉⋊C₈

D₄

yes

characteristic

C₈×D₅₉

—

C₈×D₅₉

—

C₁₆×C₅₉

D₄

yes

—

C₅₉⋊C₁₆

—

C₂²×D₅₉

D₈

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

D₈

yes

characteristic

C₄×D₅₉

—

C₄×D₅₉

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

#41

yes

characteristic

C₅₉⋊C₈

—

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

Q₃₂

yes

complemented

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

Dic₅₉

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

C₂×Q₃₂

yes

characteristic

C₂×C₅₉

#508

yes

characteristic

D₅₉

—

C₂×Q₃₂

D₅₉

yes

characteristic, complemented

C₂²×C₁₆

—

#467

—

#366

—

#358

—

C₅₉

#2216

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₅₉

yes

—

C₂²×C₈

—

C₂²⋊Q₈

—

118

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

118

—

C₂×C₁₆

C₂×D₅₉

yes

characteristic

#107

—

#103

—

118

—

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

118

—

C₄⋊C₄

—

236

—

C₂²⋊C₄

—

236

—

C₁₆

—

118

—

C₁₆

C₂²⋊D₅₉

yes

—

C₂³

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

236

—

C₂×C₄

D₄×D₅₉

yes

characteristic

C₈

—

118

—

C₈

#11745687

yes

characteristic

C₈

C₂×C₂²⋊D₅₉

yes

characteristic

C₂²

—

C₂²

—

118

—

C₂²

—

118

—

C₂²

D₈×D₅₉

yes

characteristic

C₄

—

C₄

—

118

—

100

C₄

—

472

—

101

C₄

#14273698

yes

characteristic

102

C₄

#14273746

yes

characteristic

103

C₂

—

118

—

104

C₂

#16837635

yes

characteristic

105

C₂

Q₃₂×D₅₉

yes

characteristic

106

C₂

#16837835

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₅₉
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₂×Q₃₂×C₅₉	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	C₂×Q₃₂	D₅₉
hypocenter	C₅₉	#2216
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₅₉

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₂×Q₃₂×C₅₉

C₂

socle

C₂²×C₅₉

C₂×D₈

hypercenter

C₂×Q₃₂

D₅₉

hypocenter

C₅₉

#2216

LCS

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
3. #16837228	C₂	semidirect
4. #16837206	C₂	semidirect
5. C₂×Q₃₂×C₅₉	C₂	semidirect
43. C₂×D₅₉	Q₃₂	semidirect
54. C₂×Q₃₂	D₅₉	semidirect
59. C₅₉	#2216	semidirect

H ≅ G/N

type

3. #16837228

C₂

semidirect

4. #16837206

C₂

semidirect

5. C₂×Q₃₂×C₅₉

C₂

semidirect

43. C₂×D₅₉

Q₃₂

semidirect

54. C₂×Q₃₂

D₅₉

semidirect

59. C₅₉

#2216

semidirect

Subgroups — #21426184

Conjugacy classes of subgroups

Complements