Group #21426269 — subgroups

Subgroups — #21426269

Order 7552.

120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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	#16837520	C₂	1	1	yes	maximal, characteristic
2	#16837224	C₂	1	2	yes	maximal, complemented
3	#16837223	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837211	C₂	1	2	yes	maximal
5	C₅₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
6	#14273749	C₂²	1	1	yes	characteristic
7	#14273733	—	2	1	no	—
8	#14273667	C₂²	1	2	yes	—
9	#14273663	C₂²	1	1	yes	characteristic
10	#14273655	—	2	1	no	—
11	#125×C₅₉	—	2	1	no	—
12	#107×C₅₉	—	2	1	no	—
13	#106×C₅₉	C₂²	1	2	yes	—
14	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
15	#11745685	—	2	1	no	—
16	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₅₉	—	2	2	no	—
19	C₄⋊C₄×C₅₉	—	4	2	no	—
20	C₄²×C₅₉	D₄	1	1	yes	characteristic
21	#11745664	—	2	1	no	—
22	Dic₂₃₆	Q₈	1	1	yes	characteristic
23	D₄₇₂	Q₈	1	1	yes	characteristic
24	#11745660	—	2	1	no	—
25	#11745659	—	4	1	no	—
26	C₈×D₅₉	—	4	1	no	—
27	C₅₉⋊C₁₆	—	2	2	no	—
28	C₂×C₄×C₅₉	—	2	1	no	—
29	C₂×C₄×C₅₉	—	4	2	no	—
30	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₅₉	—	4	1	no	—
32	D₂₃₆	—	2	1	no	—
33	C₄×D₅₉	—	4	1	no	—
34	Dic₁₁₈	—	2	1	no	—
35	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
36	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
37	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
38	C₈×C₅₉	#41	1	1	yes	characteristic
39	C₅₉⋊C₈	—	4	1	no	—
40	C₂²×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
41	C₂×D₅₉	—	4	1	no	—
42	C₄×C₅₉	—	4	1	no	—
43	C₄×C₅₉	—	8	2	no	—
44	C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
45	C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
46	Dic₅₉	—	4	1	no	—
47	#2231	—	59	1	no	maximal, Sylow
48	C₂×C₅₉	—	2	1	no	—
49	C₂×C₅₉	#476	1	1	yes	characteristic
50	D₅₉	—	8	1	no	—
51	#499	D₅₉	1	1	yes	characteristic, complemented
52	#443	—	59	1	no	—
53	#365	—	59	2	no	—
54	#364	—	59	1	no	—
55	#360	—	59	2	no	—
56	C₅₉	#2231	1	1	yes	characteristic, complemented, Sylow
57	#135	—	59	1	no	—
58	#131	—	118	1	no	—
59	#125	—	2	1	no	—
60	M₃₂	—	59	2	no	—
61	#108	—	59	1	no	—
62	#107	—	2	1	no	—
63	#106	C₂×D₅₉	1	2	yes	—
64	#104	—	118	1	no	—
65	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
66	#41	—	118	1	no	—
67	Q₁₆	—	59	1	no	—
68	SD₁₆	—	118	1	no	—
69	D₈	—	59	1	no	—
70	M₁₆	—	118	1	no	—
71	M₁₆	—	236	1	no	—
72	C₂×C₈	—	236	1	no	—
73	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	4	2	no	—
77	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
78	C₁₆	—	118	2	no	—
79	Q₈	—	118	1	no	—
80	D₄	—	118	1	no	—
81	D₄	—	236	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	—	236	1	no	—
85	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
86	C₈	—	236	1	no	—
87	C₈	#11745671	1	1	yes	characteristic
88	C₈	#11745671	1	1	yes	characteristic
89	C₈	Q₈×D₅₉	1	1	yes	characteristic
90	C₈	#11745689	1	1	yes	characteristic
91	C₂²	—	236	1	no	—
92	C₂²	#14273753	1	1	yes	characteristic
93	C₄	—	4	1	no	—
94	C₄	—	8	2	no	—
95	C₄	—	236	1	no	—
96	C₄	#14273703	1	1	yes	characteristic
97	C₄	C₂×#11745671	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	472	1	no	—
100	C₂	#16837689	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837520

C₂

yes

maximal, characteristic

#16837224

C₂

yes

maximal, complemented

#16837223

C₂

yes

maximal, characteristic, complemented

#16837211

C₂

yes

maximal

C₅₉×#499

C₂

yes

maximal, characteristic, complemented

#14273749

C₂²

yes

characteristic

#14273733

—

#14273667

C₂²

yes

—

#14273663

C₂²

yes

characteristic

#14273655

—

#125×C₅₉

—

#107×C₅₉

—

#106×C₅₉

C₂²

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

#11745685

—

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

D₄

yes

characteristic

#11745664

—

Dic₂₃₆

Q₈

yes

characteristic

D₄₇₂

Q₈

yes

characteristic

#11745660

—

#11745659

—

C₈×D₅₉

—

C₅₉⋊C₁₆

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²⋊D₅₉

—

D₂₃₆

—

C₄×D₅₉

—

Dic₁₁₈

—

C₈×C₅₉

SD₁₆

yes

characteristic

C₈×C₅₉

SD₁₆

yes

characteristic

C₈×C₅₉

C₂×Q₈

yes

characteristic

C₈×C₅₉

#41

yes

characteristic

C₅₉⋊C₈

—

C₂²×C₅₉

AGL(1,ℤ/8)

yes

characteristic

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₂²⋊Q₈

yes

characteristic

C₄×C₅₉

C₂×SD₁₆

yes

characteristic

Dic₅₉

—

#2231

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

#476

yes

characteristic

D₅₉

—

#499

D₅₉

yes

characteristic, complemented

—

—

—

—

C₅₉

#2231

yes

characteristic, complemented, Sylow

#135

—

#131

—

118

—

#125

—

M₃₂

—

#108

—

#107

—

#106

C₂×D₅₉

yes

—

#104

—

118

—

C₄×C₈

C₂×D₅₉

yes

characteristic

#41

—

118

—

Q₁₆

—

SD₁₆

—

118

—

D₈

—

M₁₆

—

118

—

M₁₆

—

236

—

C₂×C₈

—

236

—

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₅₉

yes

characteristic

C₁₆

—

118

—

Q₈

—

118

—

D₄

—

118

—

D₄

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

C₈

—

236

—

C₈

yes

C₈

yes

C₈

Q₈×D₅₉

yes

characteristic

C₈

#11745689

yes

characteristic

C₂²

—

236

—

C₂²

#14273753

yes

characteristic

C₄

—

C₄

—

C₄

—

236

—

C₄

yes

C₄

yes

C₂

—

C₂

—

472

—

100

C₂

#16837689

yes

characteristic

	subgroup	G/H
center	C₂	#16837689
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#499	C₂
socle	C₂×C₅₉	#476
hypercenter	#499	D₅₉
hypocenter	C₅₉	#2231
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #499

subgroup

G/H

center

C₂

#16837689

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#499

C₂

C₂×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #499

N	H ≅ G/N	type
2. #16837224	C₂	semidirect
3. #16837223	C₂	semidirect
5. C₅₉×#499	C₂	semidirect
51. #499	D₅₉	semidirect
56. C₅₉	#2231	semidirect

H ≅ G/N

type

2. #16837224

C₂

semidirect

3. #16837223

C₂

semidirect

5. C₅₉×#499

C₂

semidirect

51. #499

D₅₉

semidirect

56. C₅₉

#2231

semidirect

Subgroups — #21426269

Conjugacy classes of subgroups

Complements