Group #21426183 — subgroups

Subgroups — #21426183

Order 7552.

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

normal subgroups only

This group has 174 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×D₉₄₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837639	C₂	1	2	yes	maximal, complemented
4	#16837202	C₂	1	2	yes	maximal, complemented
5	C₅₉×#366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₇₂	C₂²	1	2	yes	—
7	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
8	#14273702	—	2	2	no	—
9	D₉₄₄	—	2	2	no	—
10	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₁₆×D₅₉	—	2	2	no	—
12	#14273647	—	2	2	no	—
13	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	#107×C₅₉	C₂²	1	2	yes	—
15	C₂×D₂₃₆	—	2	2	no	—
16	C₂×D₂₃₆	—	4	2	no	—
17	C₂×C₄×D₅₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₅₉	—	2	2	no	—
20	(C₂×D₅₉)⋊C₄	—	4	2	no	—
21	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
22	D₄₇₂	—	2	2	no	—
23	D₄₇₂	—	2	2	no	—
24	C₈×D₅₉	—	2	1	no	—
25	C₈×D₅₉	—	2	1	no	—
26	C₁₆×C₅₉	D₄	1	2	yes	complemented
27	C₅₉⋊C₁₆	—	2	1	no	—
28	C₂²×D₅₉	—	4	2	no	—
29	C₂²×D₅₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₅₉	—	4	2	no	—
31	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₅₉	D₈	1	1	yes	characteristic
33	D₂₃₆	—	4	2	no	—
34	D₂₃₆	—	4	2	no	—
35	D₂₃₆	—	8	4	no	—
36	C₄×D₅₉	—	2	1	no	—
37	C₄×D₅₉	—	2	1	no	—
38	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₅₉	#41	1	1	yes	characteristic
40	C₅₉⋊C₈	—	2	1	no	—
41	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
42	C₂×D₅₉	—	2	1	no	—
43	C₂×D₅₉	—	2	1	no	—
44	C₂×D₅₉	—	8	2	no	—
45	C₂×D₅₉	—	8	2	no	—
46	C₂×D₅₉	—	8	2	no	—
47	C₂×D₅₉	D₁₆	1	2	yes	complemented
48	C₄×C₅₉	—	8	2	no	—
49	C₄×C₅₉	#121	1	1	yes	characteristic
50	C₄×C₅₉	#135	1	1	yes	characteristic
51	Dic₅₉	—	2	1	no	—
52	#2215	—	59	1	no	maximal, Sylow
53	C₂×C₅₉	#466	1	1	yes	characteristic
54	C₂×C₅₉	C₂×D₁₆	1	1	yes	characteristic
55	C₂×C₅₉	#508	1	1	yes	characteristic
56	D₅₉	—	2	2	no	—
57	D₅₉	—	16	2	no	—
58	C₂×D₁₆	—	59	1	no	—
59	C₂²×C₁₆	—	59	1	no	—
60	#466	—	59	2	no	—
61	#366	D₅₉	1	1	yes	characteristic, complemented
62	#357	—	59	2	no	—
63	C₅₉	#2215	1	1	yes	characteristic, complemented, Sylow
64	C₂×D₈	—	59	2	no	—
65	C₂²×C₈	—	59	1	no	—
66	#121	—	118	2	no	—
67	D₁₆	—	118	2	no	—
68	C₂×C₁₆	—	59	1	no	—
69	C₂×C₁₆	—	118	2	no	—
70	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
71	#107	C₂×D₅₉	1	2	yes	—
72	#102	—	118	2	no	—
73	C₂×D₄	—	118	2	no	—
74	C₂×D₄	—	236	2	no	—
75	C₂²×C₄	—	59	1	no	—
76	D₈	—	118	2	no	—
77	D₈	—	118	2	no	—
78	C₂×C₈	—	59	1	no	—
79	C₂×C₈	—	118	1	no	—
80	C₂×C₈	—	118	1	no	—
81	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
82	C₄⋊C₄	—	2	2	no	—
83	C₂²⋊C₄	—	236	2	no	—
84	C₁₆	—	118	1	no	—
85	C₁₆	D₂₃₆	1	2	yes	complemented
86	C₂³	—	59	1	no	—
87	C₂³	—	236	2	no	—
88	D₄	—	472	4	no	—
89	D₄	—	236	2	no	—
90	D₄	—	236	2	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	—	59	1	no	—
93	C₂×C₄	—	118	1	no	—
94	C₂×C₄	—	118	1	no	—
95	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
96	C₈	—	118	1	no	—
97	C₈	C₂×D₂₃₆	1	1	yes	characteristic
98	C₈	#11745689	1	1	yes	characteristic
99	C₂²	—	59	2	no	—
100	C₂²	—	118	1	no	—
101	C₂²	—	118	1	no	—
102	C₂²	—	472	2	no	—
103	C₂²	—	472	2	no	—
104	C₂²	—	472	2	no	—
105	C₂²	D₈×D₅₉	1	1	yes	characteristic
106	C₄	—	8	2	no	—
107	C₄	—	118	1	no	—
108	C₄	#14273702	1	1	yes	characteristic
109	C₄	#14273750	1	1	yes	characteristic
110	C₂	—	118	2	no	—
111	C₂	—	944	2	no	—
112	C₂	#16837639	1	1	yes	characteristic
113	C₂	D₁₆×D₅₉	1	1	yes	characteristic
114	C₂	#16837835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₉₄₄

C₂

yes

maximal, characteristic, complemented

C₂×C₁₆×D₅₉

C₂

yes

maximal, characteristic, complemented

#16837639

C₂

yes

maximal, complemented

#16837202

C₂

yes

maximal, complemented

C₅₉×#366

C₂

yes

maximal, characteristic, complemented

C₂×D₄₇₂

C₂²

yes

—

C₂×C₈×D₅₉

C₂²

yes

characteristic

#14273702

—

D₉₄₄

—

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₅₉

—

#14273647

—

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

#107×C₅₉

C₂²

yes

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×C₄×D₅₉

D₄

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

—

(C₂×D₅₉)⋊C₄

—

C₂×C₅₉⋊C₈

D₄

yes

characteristic

D₄₇₂

—

D₄₇₂

—

C₈×D₅₉

—

C₈×D₅₉

—

C₁₆×C₅₉

D₄

yes

complemented

C₅₉⋊C₁₆

—

C₂²×D₅₉

—

C₂²×D₅₉

D₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×Dic₅₉

D₈

yes

characteristic

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

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

—

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

D₁₆

yes

complemented

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

C₂×D₁₆

yes

characteristic

C₂×C₅₉

#508

yes

characteristic

D₅₉

—

D₅₉

—

C₂×D₁₆

—

C₂²×C₁₆

—

#466

—

#366

D₅₉

yes

characteristic, complemented

#357

—

C₅₉

#2215

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂²×C₈

—

#121

—

118

—

D₁₆

—

118

—

C₂×C₁₆

—

C₂×C₁₆

—

118

—

C₂×C₁₆

C₂×D₅₉

yes

characteristic

#107

C₂×D₅₉

yes

—

#102

—

118

—

C₂×D₄

—

118

—

C₂×D₄

—

236

—

C₂²×C₄

—

D₈

—

118

—

D₈

—

118

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

236

—

C₁₆

—

118

—

C₁₆

D₂₃₆

yes

complemented

C₂³

—

C₂³

—

236

—

D₄

—

472

—

D₄

—

236

—

D₄

—

236

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

D₄×D₅₉

yes

characteristic

C₈

—

118

—

C₈

C₂×D₂₃₆

yes

characteristic

C₈

#11745689

yes

characteristic

C₂²

—

100

C₂²

—

118

—

101

C₂²

—

118

—

102

C₂²

—

472

—

103

C₂²

—

472

—

104

C₂²

—

472

—

105

C₂²

D₈×D₅₉

yes

characteristic

106

C₄

—

107

C₄

—

118

—

108

C₄

#14273702

yes

characteristic

109

C₄

#14273750

yes

characteristic

110

C₂

—

118

—

111

C₂

—

944

—

112

C₂

#16837639

yes

characteristic

113

C₂

D₁₆×D₅₉

yes

characteristic

114

C₂

#16837835

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₅₉
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#366	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#366	D₅₉
hypocenter	C₅₉	#2215
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

subgroup

G/H

center

C₂²

D₈×D₅₉

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#366

C₂

socle

C₂²×C₅₉

C₂×D₈

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

N	H ≅ G/N	type
1. C₂×D₉₄₄	C₂	semidirect
2. C₂×C₁₆×D₅₉	C₂	semidirect
3. #16837639	C₂	semidirect
4. #16837202	C₂	semidirect
5. C₅₉×#366	C₂	semidirect
26. C₁₆×C₅₉	D₄	semidirect
47. C₂×D₅₉	D₁₆	semidirect
61. #366	D₅₉	semidirect
63. C₅₉	#2215	semidirect
85. C₁₆	D₂₃₆	semidirect

H ≅ G/N

type

1. C₂×D₉₄₄

C₂

semidirect

2. C₂×C₁₆×D₅₉

C₂

semidirect

3. #16837639

C₂

semidirect

4. #16837202

C₂

semidirect

5. C₅₉×#366

C₂

semidirect

26. C₁₆×C₅₉

D₄

semidirect

47. C₂×D₅₉

D₁₆

semidirect

61. #366

D₅₉

semidirect

63. C₅₉

#2215

semidirect

85. C₁₆

D₂₃₆

semidirect

Subgroups — #21426183

Conjugacy classes of subgroups

Complements