Group #22610012 — subgroups

Subgroups — #22610012

Order 9344.

272 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14556550	C₂	1	1	yes	maximal, characteristic
2	#17988551	C₂	1	1	yes	maximal, characteristic
3	#17988355	C₂	1	4	yes	maximal, complemented
4	#407×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924012	C₂²	1	2	yes	—
6	#14556550	—	2	2	no	—
7	#14556550	—	2	2	no	—
8	C₂×C₄⋊Dic₇₃	C₂²	1	2	yes	—
9	C₂×C₂²⋊Dic₇₃	C₄	1	2	yes	—
10	C₂×C₄×Dic₇₃	C₄	1	2	yes	—
11	C₂²⋊#10596831	—	2	2	no	—
12	C₂³×C₄×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²⋊C₈×C₇₃	—	2	2	no	—
15	C₂²×Dic₇₃	C₂×C₄	1	4	yes	—
16	#11924012	—	2	4	no	—
17	C₂×#10596831	—	2	2	no	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	—	2	2	no	—
20	C₂²⋊Dic₇₃	—	2	4	no	—
21	C₄×Dic₇₃	—	2	4	no	—
22	C₂⁴×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₇₃	—	2	4	no	—
24	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₇₃	D₄	1	2	yes	—
26	C₂²×C₄×C₇₃	D₄	1	2	yes	—
27	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
28	M₁₆×C₇₃	—	2	4	no	—
29	C₂×C₈×C₇₃	—	2	2	no	—
30	C₂³×C₇₃	—	2	2	no	—
31	C₂³×C₇₃	—	4	2	no	—
32	C₂³×C₇₃	C₂²⋊C₄	1	2	yes	—
33	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₃	—	2	2	no	—
35	C₂×C₄×C₇₃	—	2	4	no	—
36	C₂×C₄×C₇₃	—	2	4	no	—
37	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
38	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₇₃	#41	1	4	yes	—
41	C₂×Dic₇₃	—	2	4	no	—
42	C₂×Dic₇₃	—	4	4	no	—
43	C₈×C₇₃	—	4	2	no	—
44	#10596831	—	4	2	no	—
45	C₂²×C₇₃	—	2	2	no	—
46	C₂²×C₇₃	—	2	2	no	—
47	C₂²×C₇₃	—	2	4	no	—
48	C₂²×C₇₃	—	4	4	no	—
49	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₇₃	#117	1	2	yes	—
51	C₄×C₇₃	—	2	2	no	—
52	C₄×C₇₃	#123	1	2	yes	—
53	C₄×C₇₃	#123	1	2	yes	—
54	Dic₇₃	—	4	4	no	—
55	C₂×C₇₃	—	2	2	no	—
56	C₂×C₇₃	—	4	2	no	—
57	C₂×C₇₃	#381	1	1	yes	characteristic
58	C₂×C₇₃	#413	1	2	yes	—
59	#1822	—	73	1	no	maximal, Sylow
60	C₇₃	#1822	1	1	yes	characteristic, complemented, Sylow
61	C₂×#117	—	73	1	no	—
62	#407	—	73	1	no	—
63	#407	D₇₃	1	1	yes	characteristic
64	#343	—	73	4	no	—
65	C₂³×C₄	C₂×D₇₃	1	1	yes	characteristic
66	C₂×M₁₆	—	73	2	no	—
67	C₂×M₁₆	C₂×D₇₃	1	2	yes	—
68	#117	—	146	2	no	—
69	#117	—	146	2	no	—
70	C₂×C₄⋊C₄	—	73	2	no	—
71	C₂×C₂²⋊C₄	—	73	2	no	—
72	C₂×C₄²	—	73	2	no	—
73	C₂²⋊C₈	—	2	2	no	—
74	C₂²⋊C₈	—	146	2	no	—
75	C₂⁴	C₄×D₇₃	1	1	yes	characteristic
76	C₂²×C₄	—	2	4	no	—
77	C₂²×C₄	—	73	4	no	—
78	C₂²×C₄	C₄×D₇₃	1	1	yes	characteristic
79	C₂²×C₄	D₂₉₂	1	2	yes	—
80	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
81	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
82	M₁₆	—	2	4	no	—
83	M₁₆	—	146	4	no	—
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	146	2	no	—
86	C₄⋊C₄	—	146	2	no	—
87	C₄⋊C₄	—	146	2	no	—
88	C₂²⋊C₄	—	146	4	no	—
89	C₄²	—	146	4	no	—
90	C₂³	—	2	2	no	—
91	C₂³	—	4	2	no	—
92	C₂³	#11924005	1	2	yes	—
93	C₂³	C₂×C₄×D₇₃	1	1	yes	characteristic
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	292	4	no	—
98	C₂×C₄	—	146	4	no	—
99	C₂×C₄	#11924005	1	2	yes	—
100	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
101	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
102	C₂×C₄	#11924027	1	4	yes	—
103	C₈	—	4	2	no	—
104	C₈	—	292	2	no	—
105	C₂²	—	2	2	no	—
106	C₂²	—	2	2	no	—
107	C₂²	—	2	4	no	—
108	C₂²	—	4	4	no	—
109	C₂²	C₂×#11924005	1	1	yes	characteristic
110	C₂²	#14556547	1	2	yes	—
111	C₄	—	2	2	no	—
112	C₄	—	292	4	no	—
113	C₄	#14556572	1	2	yes	—
114	C₄	#14556575	1	2	yes	—
115	C₂	—	2	2	no	—
116	C₂	—	4	2	no	—
117	C₂	#17988448	1	1	yes	characteristic
118	C₂	#17988569	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556550

C₂

yes

maximal, characteristic

#17988551

C₂

yes

maximal, characteristic

#17988355

C₂

yes

maximal, complemented

#407×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

#14556550

—

#14556550

—

C₂×C₄⋊Dic₇₃

C₂²

yes

—

C₂×C₂²⋊Dic₇₃

C₄

yes

—

C₂×C₄×Dic₇₃

C₄

yes

—

C₂²⋊#10596831

—

C₂³×C₄×C₇₃

C₂²

yes

characteristic

C₂×M₁₆×C₇₃

C₂²

yes

—

C₂²⋊C₈×C₇₃

—

C₂²×Dic₇₃

C₂×C₄

yes

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂⁴×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

#117

yes

—

C₄×C₇₃

—

C₄×C₇₃

#123

yes

—

C₄×C₇₃

#123

yes

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#381

yes

characteristic

C₂×C₇₃

#413

yes

—

#1822

—

maximal, Sylow

C₇₃

#1822

yes

characteristic, complemented, Sylow

C₂×#117

—

#407

—

#407

D₇₃

yes

characteristic

#343

—

C₂³×C₄

C₂×D₇₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₇₃

yes

—

#117

—

146

—

#117

—

146

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂²⋊C₈

—

C₂²⋊C₈

—

146

—

C₂⁴

C₄×D₇₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₃

yes

characteristic

C₂²×C₄

D₂₉₂

yes

—

C₂²×C₄

C₂²⋊D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

—

146

—

C₂³

—

C₂³

—

C₂³

#11924005

yes

—

C₂³

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

#11924005

yes

—

100

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

101

C₂×C₄

C₂×D₂₉₂

yes

characteristic

102

C₂×C₄

#11924027

yes

—

103

C₈

—

104

C₈

—

292

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×#11924005

yes

characteristic

110

C₂²

#14556547

yes

—

111

C₄

—

112

C₄

—

292

—

113

C₄

#14556572

yes

—

114

C₄

#14556575

yes

—

115

C₂

—

116

C₂

—

117

C₂

#17988448

yes

characteristic

118

C₂

#17988569

yes

—

	subgroup	G/H
center	C₂²	C₂×#11924005
commutator	C₂³×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#407×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#407	D₇₃
hypocenter	C₇₃	#1822
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂²

C₂×#11924005

commutator

C₂³×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#407×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
3. #17988355	C₂	semidirect
60. C₇₃	#1822	semidirect

H ≅ G/N

type

3. #17988355

C₂

semidirect

60. C₇₃

#1822

semidirect

Subgroups — #22610012

Conjugacy classes of subgroups

Complements