Group #21426358 — subgroups

Subgroups — #21426358

Order 7552.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14273670	C₂	1	2	yes	maximal, complemented
2	C₂×D₉₄₄	C₂	1	1	yes	maximal, characteristic
3	#16837787	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11745671	—	2	2	no	—
7	C₂×D₄₇₂	C₂²	1	2	yes	—
8	#14273716	—	2	2	no	—
9	#14273670	—	2	4	no	—
10	D₉₄₄	—	2	2	no	—
11	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
13	C₂×Q₁₆×C₅₉	C₂²	1	2	yes	—
14	Q₃₂×C₅₉	—	2	2	no	—
15	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₅₉	—	2	2	no	—
17	C₂×D₂₃₆	—	2	2	no	—
18	Q₁₆×C₅₉	—	2	2	no	—
19	Q₁₆×C₅₉	—	2	2	no	—
20	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
21	#11745671	—	4	4	no	—
22	(C₂×D₅₉)⋊C₄	—	4	4	no	—
23	C₄×Dic₅₉	D₄	1	1	yes	characteristic
24	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
25	D₄₇₂	—	2	2	no	—
26	D₄₇₂	—	2	2	no	—
27	C₁₆×C₅₉	D₄	1	2	yes	—
28	C₅₉⋊C₁₆	D₄	1	2	yes	—
29	C₂²×D₅₉	—	4	2	no	—
30	Q₈×C₅₉	—	4	2	no	—
31	Q₈×C₅₉	—	4	2	no	—
32	C₂×C₄×C₅₉	—	4	2	no	—
33	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₅₉	D₈	1	2	yes	—
35	D₂₃₆	—	4	2	no	—
36	D₂₃₆	—	4	2	no	—
37	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
39	C₅₉⋊C₈	D₈	1	2	yes	—
40	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
41	C₂×D₅₉	—	8	2	no	—
42	C₂×D₅₉	—	8	4	no	—
43	C₄×C₅₉	—	8	2	no	—
44	C₄×C₅₉	#127	1	1	yes	characteristic
45	C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
46	Dic₅₉	—	2	2	no	—
47	#2249	—	59	1	no	maximal, Sylow
48	C₂×C₅₉	#493	1	1	yes	characteristic
49	C₂×C₅₉	#508	1	2	yes	—
50	D₅₉	—	16	2	no	—
51	C₂×Q₃₂	D₅₉	1	1	yes	characteristic, complemented
52	C₂×SD₃₂	—	59	2	no	—
53	C₂×D₁₆	—	59	1	no	—
54	#495	—	59	2	no	—
55	C₄×C₁₆	—	59	1	no	—
56	C₅₉	#2249	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₁₆	C₂×D₅₉	1	2	yes	—
58	C₂×SD₁₆	—	118	2	no	—
59	C₂×D₈	—	59	2	no	—
60	#124	—	118	2	no	—
61	Q₃₂	—	2	2	no	—
62	SD₃₂	—	118	4	no	—
63	D₁₆	—	118	2	no	—
64	C₂×C₁₆	—	59	1	no	—
65	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
66	C₄×C₈	—	59	1	no	—
67	C₂×Q₈	—	2	2	no	—
68	C₂×D₄	—	118	2	no	—
69	Q₁₆	—	2	2	no	—
70	Q₁₆	—	2	2	no	—
71	SD₁₆	—	236	4	no	—
72	D₈	—	118	2	no	—
73	D₈	—	118	2	no	—
74	C₂×C₈	—	59	1	no	—
75	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
76	C₂²⋊C₄	—	236	4	no	—
77	C₄²	—	59	1	no	—
78	C₁₆	—	59	2	no	—
79	C₁₆	C₂²⋊D₅₉	1	2	yes	—
80	C₂³	—	236	2	no	—
81	Q₈	—	4	2	no	—
82	Q₈	—	4	2	no	—
83	D₄	—	236	2	no	—
84	D₄	—	236	2	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	—	59	2	no	—
87	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
88	C₈	—	59	2	no	—
89	C₈	D₄×D₅₉	1	1	yes	characteristic
90	C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
91	C₂²	—	472	2	no	—
92	C₂²	—	472	4	no	—
93	C₂²	D₈×D₅₉	1	1	yes	characteristic
94	C₄	—	8	2	no	—
95	C₄	—	118	2	no	—
96	C₄	#14273723	1	1	yes	characteristic
97	C₄	D₈×D₅₉	1	1	yes	characteristic
98	C₂	—	944	2	no	—
99	C₂	#16837777	1	1	yes	characteristic
100	C₂	#16837835	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273670

C₂

yes

maximal, complemented

C₂×D₉₄₄

C₂

yes

maximal, characteristic

#16837787

C₂

yes

maximal, complemented

C₁₆×Dic₅₉

C₂

yes

maximal, characteristic, complemented

C₂×Q₃₂×C₅₉

C₂

yes

maximal, characteristic, complemented

C₂×#11745671

—

C₂×D₄₇₂

C₂²

yes

—

#14273716

—

#14273670

—

D₉₄₄

—

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

C₈×Dic₅₉

C₂²

yes

characteristic

C₂×Q₁₆×C₅₉

C₂²

yes

—

Q₃₂×C₅₉

—

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

—

C₂×D₂₃₆

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

#11745671

—

(C₂×D₅₉)⋊C₄

—

C₄×Dic₅₉

D₄

yes

characteristic

C₂×C₅₉⋊C₈

D₄

yes

characteristic

D₄₇₂

—

D₄₇₂

—

C₁₆×C₅₉

D₄

yes

—

C₅₉⋊C₁₆

D₄

yes

—

C₂²×D₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

D₈

yes

—

D₂₃₆

—

D₂₃₆

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

C₂×D₄

yes

characteristic

C₅₉⋊C₈

D₈

yes

—

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#127

yes

characteristic

C₄×C₅₉

C₂×D₈

yes

characteristic

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

D₅₉

—

C₂×Q₃₂

D₅₉

yes

characteristic, complemented

C₂×SD₃₂

—

C₂×D₁₆

—

#495

—

C₄×C₁₆

—

C₅₉

#2249

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₅₉

yes

—

C₂×SD₁₆

—

118

—

C₂×D₈

—

#124

—

118

—

Q₃₂

—

SD₃₂

—

118

—

D₁₆

—

118

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₅₉

yes

characteristic

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

118

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

236

—

D₈

—

118

—

D₈

—

118

—

C₂×C₈

—

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₂²⋊C₄

—

236

—

C₄²

—

C₁₆

—

C₁₆

C₂²⋊D₅₉

yes

—

C₂³

—

236

—

Q₈

—

Q₈

—

D₄

—

236

—

D₄

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₅₉

yes

characteristic

C₈

—

C₈

D₄×D₅₉

yes

characteristic

C₈

C₂×C₂²⋊D₅₉

yes

characteristic

C₂²

—

472

—

C₂²

—

472

—

C₂²

D₈×D₅₉

yes

characteristic

C₄

—

C₄

—

118

—

C₄

#14273723

yes

characteristic

C₄

D₈×D₅₉

yes

characteristic

C₂

—

944

—

C₂

#16837777

yes

characteristic

100

C₂

#16837835

yes

—

	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	#2249
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

#2249

LCS

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
1. C₂×#14273670	C₂	semidirect
3. #16837787	C₂	semidirect
4. C₁₆×Dic₅₉	C₂	semidirect
5. C₂×Q₃₂×C₅₉	C₂	semidirect
51. C₂×Q₃₂	D₅₉	semidirect
56. C₅₉	#2249	semidirect

H ≅ G/N

type

1. C₂×#14273670

C₂

semidirect

3. #16837787

C₂

semidirect

4. C₁₆×Dic₅₉

C₂

semidirect

5. C₂×Q₃₂×C₅₉

C₂

semidirect

51. C₂×Q₃₂

D₅₉

semidirect

56. C₅₉

#2249

semidirect

Subgroups — #21426358

Conjugacy classes of subgroups

Complements