Group #21426412 — subgroups

Subgroups — #21426412

Order 7552.

104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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	#16837831	C₂	1	1	yes	maximal, characteristic
2	Q₃₂×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₉₄₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837242	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837240	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837235	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×SD₆₄	C₂	1	1	yes	maximal, characteristic, complemented
8	#14273746	—	2	1	no	—
9	Q₁₆×D₅₉	—	2	1	no	—
10	Dic₄₇₂	C₂²	1	1	yes	characteristic
11	Dic₄₇₂	C₂²	1	1	yes	characteristic
12	#14273673	—	2	1	no	—
13	#14273671	—	2	1	no	—
14	C₁₆×D₅₉	C₂²	1	1	yes	characteristic
15	C₅₉⋊C₃₂	C₂²	1	1	yes	characteristic
16	Q₃₂×C₅₉	C₂²	1	1	yes	characteristic
17	D₁₆×C₅₉	C₂²	1	1	yes	characteristic
18	C₃₂×C₅₉	C₂²	1	1	yes	characteristic
19	Q₈×D₅₉	—	4	1	no	—
20	#11745687	—	4	1	no	—
21	Q₁₆×C₅₉	—	2	1	no	—
22	D₈×C₅₉	—	2	1	no	—
23	#11745672	—	4	1	no	—
24	#11745670	—	4	1	no	—
25	Dic₂₃₆	—	2	1	no	—
26	Dic₂₃₆	—	2	1	no	—
27	C₈×D₅₉	D₄	1	1	yes	characteristic
28	C₁₆×C₅₉	C₂³	1	1	yes	characteristic
29	C₅₉⋊C₁₆	D₄	1	1	yes	characteristic
30	Q₈×C₅₉	—	4	1	no	—
31	D₄×C₅₉	—	4	1	no	—
32	C₂²⋊D₅₉	—	8	1	no	—
33	C₂×Dic₅₉	—	8	1	no	—
34	C₄×D₅₉	—	8	1	no	—
35	C₄×D₅₉	D₈	1	1	yes	characteristic
36	Dic₁₁₈	—	4	1	no	—
37	Dic₁₁₈	—	4	1	no	—
38	Dic₁₁₈	—	8	1	no	—
39	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
40	C₅₉⋊C₈	D₈	1	1	yes	characteristic
41	C₂²×C₅₉	—	8	1	no	—
42	C₂×D₅₉	D₁₆	1	1	yes	characteristic
43	C₄×C₅₉	—	8	1	no	—
44	C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
45	Dic₅₉	—	8	1	no	—
46	Dic₅₉	—	8	1	no	—
47	Dic₅₉	D₁₆	1	1	yes	characteristic
48	#2264	—	59	1	no	maximal, Sylow
49	C₂×C₅₉	—	16	1	no	—
50	C₂×C₅₉	C₂×D₁₆	1	1	yes	characteristic
51	D₅₉	—	2	1	no	—
52	#508	—	59	1	no	—
53	C₂×Q₃₂	—	59	1	no	—
54	Q₆₄	—	59	1	no	—
55	Q₆₄	—	59	1	no	—
56	SD₆₄	—	59	1	no	—
57	SD₆₄	D₅₉	1	1	yes	characteristic, complemented
58	M₆₄	—	59	1	no	—
59	C₅₉	#2264	1	1	yes	characteristic, complemented, Sylow
60	#135	—	118	1	no	—
61	C₂×Q₁₆	—	118	1	no	—
62	Q₃₂	—	59	1	no	—
63	Q₃₂	—	59	1	no	—
64	Q₃₂	—	118	1	no	—
65	Q₃₂	C₂×D₅₉	1	1	yes	characteristic
66	SD₃₂	—	118	1	no	—
67	D₁₆	C₂×D₅₉	1	1	yes	characteristic
68	C₂×C₁₆	—	59	1	no	—
69	C₃₂	—	59	1	no	—
70	C₃₂	C₂×D₅₉	1	1	yes	characteristic
71	#41	—	236	1	no	—
72	C₂×Q₈	—	236	1	no	—
73	Q₁₆	—	2	1	no	—
74	Q₁₆	—	118	1	no	—
75	Q₁₆	—	118	1	no	—
76	Q₁₆	—	236	1	no	—
77	SD₁₆	—	236	1	no	—
78	D₈	—	2	1	no	—
79	C₂×C₈	—	59	1	no	—
80	C₁₆	—	59	1	no	—
81	C₁₆	C₂²×D₅₉	1	1	yes	characteristic
82	Q₈	—	4	1	no	—
83	Q₈	—	472	1	no	—
84	Q₈	—	236	1	no	—
85	Q₈	—	236	1	no	—
86	D₄	—	4	1	no	—
87	D₄	—	472	1	no	—
88	C₂×C₄	—	59	1	no	—
89	C₂×C₄	—	472	1	no	—
90	C₂×C₄	—	472	1	no	—
91	C₈	—	59	1	no	—
92	C₈	D₄×D₅₉	1	1	yes	characteristic
93	C₂²	—	8	1	no	—
94	C₂²	—	59	1	no	—
95	C₄	—	8	1	no	—
96	C₄	—	59	1	no	—
97	C₄	—	472	1	no	—
98	C₄	—	472	1	no	—
99	C₄	D₈×D₅₉	1	1	yes	characteristic
100	C₂	—	16	1	no	—
101	C₂	—	118	1	no	—
102	C₂	D₁₆×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837831

C₂

yes

maximal, characteristic

Q₃₂×D₅₉

C₂

yes

maximal, characteristic, complemented

Dic₉₄₄

C₂

yes

maximal, characteristic, complemented

#16837242

C₂

yes

maximal, characteristic, complemented

#16837240

C₂

yes

maximal, characteristic, complemented

#16837235

C₂

yes

maximal, characteristic, complemented

C₅₉×SD₆₄

C₂

yes

maximal, characteristic, complemented

#14273746

—

Q₁₆×D₅₉

—

Dic₄₇₂

C₂²

yes

characteristic

Dic₄₇₂

C₂²

yes

characteristic

#14273673

—

#14273671

—

C₁₆×D₅₉

C₂²

yes

characteristic

C₅₉⋊C₃₂

C₂²

yes

characteristic

Q₃₂×C₅₉

C₂²

yes

characteristic

D₁₆×C₅₉

C₂²

yes

characteristic

C₃₂×C₅₉

C₂²

yes

characteristic

Q₈×D₅₉

—

#11745687

—

Q₁₆×C₅₉

—

D₈×C₅₉

—

#11745672

—

#11745670

—

Dic₂₃₆

—

Dic₂₃₆

—

C₈×D₅₉

D₄

yes

characteristic

C₁₆×C₅₉

C₂³

yes

characteristic

C₅₉⋊C₁₆

D₄

yes

characteristic

Q₈×C₅₉

—

D₄×C₅₉

—

C₂²⋊D₅₉

—

C₂×Dic₅₉

—

C₄×D₅₉

—

C₄×D₅₉

D₈

yes

characteristic

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₅₉⋊C₈

D₈

yes

characteristic

C₂²×C₅₉

—

C₂×D₅₉

D₁₆

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

C₂×D₈

yes

characteristic

Dic₅₉

—

Dic₅₉

—

Dic₅₉

D₁₆

yes

characteristic

#2264

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

C₂×D₁₆

yes

characteristic

D₅₉

—

#508

—

C₂×Q₃₂

—

Q₆₄

—

Q₆₄

—

SD₆₄

—

SD₆₄

D₅₉

yes

characteristic, complemented

M₆₄

—

C₅₉

#2264

yes

characteristic, complemented, Sylow

#135

—

118

—

C₂×Q₁₆

—

118

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

118

—

Q₃₂

C₂×D₅₉

yes

characteristic

SD₃₂

—

118

—

D₁₆

C₂×D₅₉

yes

characteristic

C₂×C₁₆

—

C₃₂

—

C₃₂

C₂×D₅₉

yes

characteristic

#41

—

236

—

C₂×Q₈

—

236

—

Q₁₆

—

Q₁₆

—

118

—

Q₁₆

—

118

—

Q₁₆

—

236

—

SD₁₆

—

236

—

D₈

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂²×D₅₉

yes

characteristic

Q₈

—

Q₈

—

472

—

Q₈

—

236

—

Q₈

—

236

—

D₄

—

D₄

—

472

—

C₂×C₄

—

C₂×C₄

—

472

—

C₂×C₄

—

472

—

C₈

—

C₈

D₄×D₅₉

yes

characteristic

C₂²

—

C₂²

—

C₄

—

C₄

—

C₄

—

472

—

C₄

—

472

—

C₄

D₈×D₅₉

yes

characteristic

100

C₂

—

101

C₂

—

118

—

102

C₂

D₁₆×D₅₉

yes

characteristic

	subgroup	G/H
center	C₂	D₁₆×D₅₉
commutator	C₁₆×C₅₉	C₂³
Frattini	C₁₆	C₂²×D₅₉
Fitting	C₅₉×SD₆₄	C₂
socle	C₂×C₅₉	C₂×D₁₆
hypercenter	SD₆₄	D₅₉
hypocenter	C₅₉	#2264
LCS	G ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

subgroup

G/H

center

C₂

D₁₆×D₅₉

commutator

C₁₆×C₅₉

C₂³

Frattini

C₁₆

C₂²×D₅₉

Fitting

C₅₉×SD₆₄

C₂

socle

C₂×C₅₉

C₂×D₁₆

hypercenter

SD₆₄

D₅₉

hypocenter

C₅₉

#2264

LCS

G ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

N	H ≅ G/N	type
2. Q₃₂×D₅₉	C₂	semidirect
3. Dic₉₄₄	C₂	semidirect
4. #16837242	C₂	semidirect
5. #16837240	C₂	semidirect
6. #16837235	C₂	semidirect
7. C₅₉×SD₆₄	C₂	semidirect
57. SD₆₄	D₅₉	semidirect
59. C₅₉	#2264	semidirect

H ≅ G/N

type

2. Q₃₂×D₅₉

C₂

semidirect

3. Dic₉₄₄

C₂

semidirect

4. #16837242

C₂

semidirect

5. #16837240

C₂

semidirect

6. #16837235

C₂

semidirect

7. C₅₉×SD₆₄

C₂

semidirect

57. SD₆₄

D₅₉

semidirect

59. C₅₉

#2264

semidirect

Subgroups — #21426412

Conjugacy classes of subgroups

Complements