Group #22626841 — subgroups

Subgroups — #22626841

Order 9344.

330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 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	#17989639	C₂	1	4	yes	maximal, complemented
2	#17989636	C₂	1	4	yes	maximal, complemented
3	#17989612	C₂	1	4	yes	maximal
4	#17989605	C₂	1	2	yes	maximal
5	#17989143	C₂	1	1	yes	maximal, characteristic
6	#14556658	C₂²	1	2	yes	—
7	#14556658	C₂²	1	4	yes	—
8	#14556658	C₂²	1	2	yes	—
9	C₄⋊#10596833	C₂²	1	4	yes	—
10	#14556648	C₂²	1	4	yes	—
11	#14556646	C₂²	1	4	yes	—
12	C₄×#10596833	C₂²	1	4	yes	—
13	C₄×#10596833	C₂²	1	4	yes	—
14	#14556590	C₄	1	2	yes	—
15	#14556583	C₄	1	1	yes	characteristic
16	#14556569	C₄	1	4	yes	—
17	#14556556	C₂²	1	4	yes	—
18	#14556549	C₂²	1	2	yes	—
19	C₄²×D₇₃	C₂²	1	1	yes	characteristic
20	#125×C₇₃	C₄	1	1	yes	characteristic
21	C₂×#10596833	C₂³	1	4	yes	—
22	C₂×#10596833	C₂³	1	4	yes	—
23	C₂×Dic₁₄₆	C₂×C₄	1	4	yes	—
24	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
27	#11924007	C₂×C₄	1	4	yes	—
28	#11924007	C₂×C₄	1	4	yes	—
29	#11924005	C₂×C₄	1	4	yes	—
30	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₇₃	C₂³	1	2	yes	—
32	C₄×Dic₇₃	C₂³	1	4	yes	—
33	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
34	C₄⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
35	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×D₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
39	C₂×C₄×C₇₃	C₂²×C₄	1	4	yes	—
40	C₂×Dic₇₃	C₂²×C₄	1	4	yes	—
41	C₂×Dic₇₃	C₂²×C₄	1	2	yes	—
42	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
43	C₄×D₇₃	—	2	4	no	—
44	C₄×D₇₃	—	2	2	no	—
45	Dic₁₄₆	—	2	8	no	—
46	#10596833	—	2	4	no	—
47	#10596833	—	2	4	no	—
48	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
49	C₂×D₇₃	—	2	1	no	—
50	C₂×D₇₃	—	2	2	no	—
51	C₄×C₇₃	—	2	1	no	—
52	C₄×C₇₃	—	2	4	no	—
53	C₄×C₇₃	—	2	2	no	—
54	Dic₇₃	—	2	4	no	—
55	Dic₇₃	#131	1	4	yes	—
56	Dic₇₃	2₋¹⁺⁴	1	2	yes	—
57	C₂×C₇₃	#519	1	1	yes	characteristic
58	C₂×C₇₃	C₂×#131	1	2	yes	—
59	D₇₃	—	4	1	no	—
60	#2986	—	73	1	no	maximal, Sylow
61	C₇₃	#2986	1	1	yes	characteristic, complemented, Sylow
62	#533	—	73	1	no	—
63	#446	—	73	4	no	—
64	C₈×Q₈	—	73	4	no	—
65	#433	—	73	4	no	—
66	#431	—	73	2	no	—
67	C₄⋊Q₈	—	73	2	no	—
68	#125	—	73	1	no	—
69	#125	#64408	1	1	yes	characteristic
70	C₂²⋊Q₈	—	73	4	no	—
71	C₄×Q₈	—	73	4	no	—
72	#117	—	73	2	no	—
73	C₂×C₄²	—	73	1	no	—
74	C₄⋊C₈	—	73	2	no	—
75	C₄⋊C₈	—	73	2	no	—
76	C₄⋊C₈	—	73	4	no	—
77	C₄⋊C₈	—	73	4	no	—
78	C₂²⋊C₈	—	73	4	no	—
79	#97	—	73	4	no	—
80	C₄×C₈	—	73	4	no	—
81	C₄×C₈	—	73	4	no	—
82	C₂×Q₈	—	73	4	no	—
83	C₂²×C₄	—	73	2	no	—
84	C₂²×C₄	—	73	1	no	—
85	C₂×C₈	—	73	4	no	—
86	C₂×C₈	—	73	4	no	—
87	C₄⋊C₄	—	73	4	no	—
88	C₄⋊C₄	—	73	4	no	—
89	C₄⋊C₄	—	73	2	no	—
90	C₄⋊C₄	C₂×#64408	1	2	yes	—
91	C₄⋊C₄	C₂×#64408	1	4	yes	—
92	C₂²⋊C₄	—	73	4	no	—
93	C₄²	—	73	1	no	—
94	C₄²	—	73	2	no	—
95	C₄²	—	73	4	no	—
96	C₄²	C₂×#64408	1	1	yes	characteristic
97	C₂³	—	73	1	no	—
98	Q₈	—	146	8	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	2	no	—
101	C₂×C₄	—	73	4	no	—
102	C₂×C₄	—	146	2	no	—
103	C₂×C₄	—	146	4	no	—
104	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
105	C₂×C₄	C₂²×#64408	1	2	yes	—
106	C₂×C₄	C₂²×#64408	1	4	yes	—
107	C₈	—	146	4	no	—
108	C₈	—	146	4	no	—
109	C₂²	—	146	1	no	—
110	C₂²	—	146	2	no	—
111	C₂²	C₂³×#64408	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	2	2	no	—
114	C₄	—	2	4	no	—
115	C₄	—	73	2	no	—
116	C₄	—	73	4	no	—
117	C₄	—	146	4	no	—
118	C₂	—	292	1	no	—
119	C₂	#17989655	1	1	yes	characteristic
120	C₂	D₇₃⋊#131	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989639

C₂

yes

maximal, complemented

#17989636

C₂

yes

maximal, complemented

#17989612

C₂

yes

maximal

#17989605

C₂

yes

maximal

#17989143

C₂

yes

maximal, characteristic

#14556658

C₂²

yes

—

#14556658

C₂²

yes

—

#14556658

C₂²

yes

—

C₄⋊#10596833

C₂²

yes

—

#14556648

C₂²

yes

—

#14556646

C₂²

yes

—

C₄×#10596833

C₂²

yes

—

C₄×#10596833

C₂²

yes

—

#14556590

C₄

yes

—

#14556583

C₄

yes

characteristic

#14556569

C₄

yes

—

#14556556

C₂²

yes

—

#14556549

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#125×C₇₃

C₄

yes

characteristic

C₂×#10596833

C₂³

yes

—

C₂×#10596833

C₂³

yes

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

C₂×C₄

yes

—

#11924007

C₂×C₄

yes

—

#11924005

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂³

yes

—

C₄×Dic₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂⁴

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

Dic₁₄₆

—

#10596833

—

#10596833

—

C₂²×C₇₃

C₂³×C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

#131

yes

—

Dic₇₃

2₋¹⁺⁴

yes

—

C₂×C₇₃

#519

yes

characteristic

C₂×C₇₃

C₂×#131

yes

—

D₇₃

—

#2986

—

maximal, Sylow

C₇₃

#2986

yes

characteristic, complemented, Sylow

#533

—

#446

—

C₈×Q₈

—

#433

—

#431

—

C₄⋊Q₈

—

—

yes

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#64408

yes

—

C₄⋊C₄

C₂×#64408

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

Q₈

—

146

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

146

—

103

C₂×C₄

—

146

—

104

C₂×C₄

C₂²×#64408

yes

characteristic

105

C₂×C₄

C₂²×#64408

yes

—

106

C₂×C₄

C₂²×#64408

yes

—

107

C₈

—

146

—

108

C₈

—

146

—

109

C₂²

—

146

—

110

C₂²

—

146

—

111

C₂²

C₂³×#64408

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

146

—

118

C₂

—

292

—

119

C₂

#17989655

yes

characteristic

120

C₂

D₇₃⋊#131

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂³×C₄
Fitting	#125×C₇₃	C₄
hypercenter	#125	#64408
hypocenter	C₇₃	#2986
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×#64408

commutator, socle

C₂²×C₇₃

C₂³×C₄

Fitting

#125×C₇₃

C₄

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
1. #17989639	C₂	semidirect
2. #17989636	C₂	semidirect
61. C₇₃	#2986	semidirect

H ≅ G/N

type

1. #17989639

C₂

semidirect

2. #17989636

C₂

semidirect

61. C₇₃

#2986

semidirect

Subgroups — #22626841

Conjugacy classes of subgroups

Complements