Group #21426368 — subgroups

Subgroups — #21426368

Order 7552.

178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14273673	C₂	1	2	yes	maximal, complemented
2	C₂×#14273671	C₂	1	2	yes	maximal
3	#16837782	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837178	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#495	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₃₆	—	2	1	no	—
7	C₂×Dic₂₃₆	C₂²	1	2	yes	—
8	#14273727	—	2	1	no	—
9	#14273673	—	2	4	no	—
10	#14273671	—	2	4	no	—
11	C₂×C₅₉⋊C₁₆	C₂²	1	2	yes	—
12	C₂×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×SD₁₆×C₅₉	—	2	1	no	—
14	C₂×D₈×C₅₉	C₂²	1	1	yes	characteristic
15	#124×C₅₉	—	2	1	no	—
16	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₅₉	—	2	1	no	—
18	C₂×D₄×C₅₉	—	2	1	no	—
19	C₂×Dic₁₁₈	—	2	2	no	—
20	Q₁₆×C₅₉	—	2	2	no	—
21	SD₁₆×C₅₉	—	4	2	no	—
22	D₈×C₅₉	—	2	2	no	—
23	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
25	C₂²⋊C₄×C₅₉	—	4	2	no	—
26	C₄²×C₅₉	D₄	1	1	yes	characteristic
27	C₄⋊Dic₅₉	—	4	2	no	—
28	Dic₂₃₆	—	2	2	no	—
29	Dic₂₃₆	—	2	2	no	—
30	Dic₂₃₆	—	4	2	no	—
31	C₅₉⋊C₁₆	D₄	1	4	yes	—
32	C₂³×C₅₉	—	4	1	no	—
33	Q₈×C₅₉	—	4	1	no	—
34	Q₈×C₅₉	—	4	1	no	—
35	D₄×C₅₉	—	4	1	no	—
36	D₄×C₅₉	—	4	1	no	—
37	C₂×C₄×C₅₉	—	4	1	no	—
38	C₂×C₄×C₅₉	D₈	1	2	yes	—
39	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₅₉	—	4	2	no	—
41	Dic₁₁₈	—	4	2	no	—
42	Dic₁₁₈	—	4	2	no	—
43	C₈×C₅₉	D₈	1	2	yes	—
44	C₈×C₅₉	C₂×D₄	1	2	yes	—
45	C₂²×C₅₉	—	8	1	no	—
46	C₂²×C₅₉	—	8	2	no	—
47	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
48	C₄×C₅₉	—	2	2	no	—
49	C₄×C₅₉	—	8	1	no	—
50	C₄×C₅₉	#127	1	1	yes	characteristic
51	C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
52	Dic₅₉	—	8	2	no	—
53	#2251	—	59	1	no	maximal, Sylow
54	C₂×C₅₉	—	16	1	no	—
55	C₂×C₅₉	#493	1	1	yes	characteristic
56	C₂×C₅₉	#510	1	2	yes	—
57	C₂×Q₃₂	—	59	2	no	—
58	C₂×SD₃₂	—	59	2	no	—
59	#495	D₅₉	1	1	yes	characteristic
60	#494	—	59	1	no	—
61	#346	—	59	1	no	—
62	C₅₉	#2251	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₁₆	—	59	2	no	—
64	C₂×Q₁₆	—	118	1	no	—
65	C₂×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
66	C₂×SD₁₆	—	2	1	no	—
67	C₂×D₈	C₂×D₅₉	1	1	yes	characteristic
68	C₄⋊Q₈	—	118	1	no	—
69	#124	—	2	1	no	—
70	Q₃₂	—	118	4	no	—
71	SD₃₂	—	118	4	no	—
72	C₂×C₁₆	—	59	2	no	—
73	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
74	C₂×Q₈	—	2	1	no	—
75	C₂×Q₈	—	118	2	no	—
76	C₂×D₄	—	2	1	no	—
77	Q₁₆	—	2	2	no	—
78	Q₁₆	—	118	2	no	—
79	Q₁₆	—	118	2	no	—
80	Q₁₆	—	236	2	no	—
81	SD₁₆	—	4	2	no	—
82	D₈	—	2	2	no	—
83	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
85	C₄⋊C₄	—	236	2	no	—
86	C₂²⋊C₄	—	4	2	no	—
87	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
88	C₁₆	—	59	4	no	—
89	C₂³	—	4	1	no	—
90	Q₈	—	4	1	no	—
91	Q₈	—	4	1	no	—
92	Q₈	—	236	2	no	—
93	Q₈	—	236	2	no	—
94	D₄	—	4	1	no	—
95	D₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	236	2	no	—
98	C₂×C₄	#11745669	1	2	yes	—
99	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
100	C₈	#11745669	1	2	yes	—
101	C₈	D₄×D₅₉	1	2	yes	—
102	C₂²	—	8	1	no	—
103	C₂²	—	8	2	no	—
104	C₂²	C₂×#11745669	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	8	1	no	—
107	C₄	—	472	2	no	—
108	C₄	#14273723	1	1	yes	characteristic
109	C₄	C₂×#11745669	1	1	yes	characteristic
110	C₂	—	16	1	no	—
111	C₂	#16837778	1	1	yes	characteristic
112	C₂	#16837842	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273673

C₂

yes

maximal, complemented

C₂×#14273671

C₂

yes

maximal

#16837782

C₂

yes

maximal, characteristic, complemented

#16837178

C₂

yes

maximal, characteristic, complemented

C₅₉×#495

C₂

yes

maximal, characteristic

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

C₂²

yes

—

#14273727

—

#14273673

—

#14273671

—

C₂×C₅₉⋊C₁₆

C₂²

yes

—

C₂×Q₁₆×C₅₉

C₂²

yes

characteristic

C₂×SD₁₆×C₅₉

—

C₂×D₈×C₅₉

C₂²

yes

characteristic

#124×C₅₉

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

—

C₂×D₄×C₅₉

—

C₂×Dic₁₁₈

—

Q₁₆×C₅₉

—

SD₁₆×C₅₉

—

D₈×C₅₉

—

C₂×C₈×C₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

D₄

yes

characteristic

C₄⋊Dic₅₉

—

Dic₂₃₆

—

Dic₂₃₆

—

Dic₂₃₆

—

C₅₉⋊C₁₆

D₄

yes

—

C₂³×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

D₈

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

D₈

yes

—

C₈×C₅₉

C₂×D₄

yes

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#127

yes

characteristic

C₄×C₅₉

C₂×D₈

yes

characteristic

Dic₅₉

—

#2251

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

#493

yes

characteristic

C₂×C₅₉

#510

yes

—

C₂×Q₃₂

—

C₂×SD₃₂

—

#495

D₅₉

yes

characteristic

#494

—

#346

—

C₅₉

#2251

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

118

—

C₂×Q₁₆

C₂×D₅₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₅₉

yes

characteristic

C₄⋊Q₈

—

118

—

#124

—

Q₃₂

—

118

—

SD₃₂

—

118

—

C₂×C₁₆

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

118

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

118

—

Q₁₆

—

118

—

Q₁₆

—

236

—

SD₁₆

—

D₈

—

C₂×C₈

C₂²⋊D₅₉

yes

characteristic

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

236

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₅₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

Q₈

—

236

—

Q₈

—

236

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

#11745669

yes

—

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

100

C₈

#11745669

yes

—

101

C₈

D₄×D₅₉

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×#11745669

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

472

—

108

C₄

#14273723

yes

characteristic

109

C₄

C₂×#11745669

yes

characteristic

110

C₂

—

111

C₂

#16837778

yes

characteristic

112

C₂

#16837842

yes

—

	subgroup	G/H
center	C₂²	C₂×#11745669
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#495	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#495	D₅₉
hypocenter	C₅₉	#2251
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

C₂×#11745669

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#495

C₂

socle

C₂²×C₅₉

C₂×D₈

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. C₂×#14273673	C₂	semidirect
3. #16837782	C₂	semidirect
4. #16837178	C₂	semidirect
62. C₅₉	#2251	semidirect

H ≅ G/N

type

1. C₂×#14273673

C₂

semidirect

3. #16837782

C₂

semidirect

4. #16837178

C₂

semidirect

62. C₅₉

#2251

semidirect

Subgroups — #21426368

Conjugacy classes of subgroups

Complements