Group #22624826 — subgroups

Subgroups — #22624826

Order 9344.

144 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 46 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	#17989608	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556646	C₂	1	1	yes	maximal, characteristic
3	#17988637	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10596833	—	2	1	no	—
5	C₄⋊#10596833	C₄	1	2	yes	—
6	C₂²⋊#10596833	—	2	1	no	—
7	#14556646	—	2	1	no	—
8	#14556646	—	2	1	no	—
9	#14556646	C₄	1	2	yes	—
10	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
11	#14556520	—	2	1	no	—
12	C₂²⋊#10596831	C₄	1	1	yes	characteristic
13	C₈×Dic₇₃	—	2	1	no	—
14	C₂²⋊C₈×C₇₃	C₄	1	1	yes	characteristic
15	C₂×#10596833	—	2	4	no	—
16	C₂×#10596833	—	2	2	no	—
17	C₂×#10596833	—	2	2	no	—
18	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
19	C₂²×Dic₇₃	Q₈	1	1	yes	characteristic
20	C₂×#10596831	—	2	1	no	—
21	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₇₃	D₄	1	1	yes	characteristic
24	C₄×Dic₇₃	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	—	2	1	no	—
27	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₇₃	—	4	1	no	—
29	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×Dic₇₃	—	2	1	no	—
32	C₂×Dic₇₃	—	2	1	no	—
33	C₂×Dic₇₃	—	2	2	no	—
34	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
38	#10596833	—	2	4	no	—
39	#10596833	—	4	2	no	—
40	C₈×C₇₃	—	4	1	no	—
41	#10596831	—	4	1	no	—
42	C₂²×C₇₃	—	2	1	no	—
43	C₂²×C₇₃	—	2	1	no	—
44	C₂²×C₇₃	#95	1	1	yes	characteristic
45	C₂²×C₇₃	#108	1	1	yes	characteristic
46	C₂²×C₇₃	#108	1	1	yes	characteristic
47	C₄×C₇₃	—	2	1	no	—
48	C₄×C₇₃	—	2	1	no	—
49	Dic₇₃	—	2	1	no	—
50	Dic₇₃	—	2	1	no	—
51	Dic₇₃	—	2	1	no	—
52	Dic₇₃	#104	1	2	yes	—
53	C₂×C₇₃	—	2	1	no	—
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	#339	1	1	yes	characteristic
56	C₂×C₇₃	#341	1	1	yes	characteristic
57	C₂×C₇₃	#344	1	1	yes	characteristic
58	#1302	—	73	1	no	maximal, Sylow
59	C₇₃	#1302	1	1	yes	characteristic, complemented, Sylow
60	#432	—	73	1	no	—
61	#431	—	73	1	no	—
62	C₂×#97	—	73	1	no	—
63	C₂²×C₈	—	146	1	no	—
64	C₂×C₄²	—	73	1	no	—
65	C₄⋊C₈	—	73	2	no	—
66	C₄⋊C₈	—	146	1	no	—
67	C₂²⋊C₈	—	73	1	no	—
68	C₂²⋊C₈	—	146	1	no	—
69	C₂²⋊C₈	#64408	1	1	yes	characteristic
70	#97	—	73	2	no	—
71	#97	—	146	1	no	—
72	#97	—	146	1	no	—
73	C₄×C₈	—	146	1	no	—
74	C₂²×C₄	—	73	1	no	—
75	C₂²×C₄	—	73	1	no	—
76	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	—	146	2	no	—
79	C₂×C₈	—	146	1	no	—
80	C₂×C₈	—	146	2	no	—
81	C₂×C₈	—	146	4	no	—
82	C₄²	—	73	1	no	—
83	C₄²	—	73	1	no	—
84	C₄²	—	73	1	no	—
85	C₄²	—	73	1	no	—
86	C₂³	C₄⋊#64408	1	1	yes	characteristic
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	73	1	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	146	2	no	—
93	C₂×C₄	—	146	1	no	—
94	C₂×C₄	—	146	1	no	—
95	C₂×C₄	C₄×#64408	1	1	yes	characteristic
96	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
97	C₈	—	4	1	no	—
98	C₈	—	292	1	no	—
99	C₈	—	292	2	no	—
100	C₈	—	146	4	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	2	1	no	—
103	C₂²	(C₂×#64408)⋊C₄	1	1	yes	characteristic
104	C₂²	#14556661	1	1	yes	characteristic
105	C₂²	#14556662	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	73	2	no	—
109	C₄	—	146	1	no	—
110	C₄	—	146	1	no	—
111	C₄	—	146	1	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	1	no	—
114	C₂	#17989459	1	1	yes	characteristic
115	C₂	#17989463	1	1	yes	characteristic
116	C₂	#17989468	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989608

C₂

yes

maximal, characteristic

C₂×#14556646

C₂

yes

maximal, characteristic

#17988637

C₂

yes

maximal, characteristic

C₂²×#10596833

—

C₄⋊#10596833

C₄

yes

—

—

—

—

C₄

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556520

—

C₂²⋊#10596831

C₄

yes

characteristic

C₈×Dic₇₃

—

C₂²⋊C₈×C₇₃

C₄

yes

—

—

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

Q₈

yes

characteristic

C₂×#10596831

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

#10596833

—

#10596833

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#104

yes

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#432

—

#431

—

C₂×#97

—

C₂²×C₈

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

C₂²⋊C₈

—

146

—

C₂²⋊C₈

yes

—

—

146

—

#97

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄⋊#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

292

—

C₈

—

292

—

100

C₈

—

146

—

101

C₂²

—

102

C₂²

—

103

C₂²

(C₂×#64408)⋊C₄

yes

characteristic

104

C₂²

#14556661

yes

characteristic

105

C₂²

#14556662

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

146

—

110

C₄

—

146

—

111

C₄

—

146

—

112

C₂

—

113

C₂

—

114

C₂

#17989459

yes

characteristic

115

C₂

#17989463

yes

characteristic

116

C₂

#17989468

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#64408)⋊C₄
commutator	C₂×C₄×C₇₃	C₄²
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂²⋊C₈×C₇₃	C₄
socle	C₂²×C₇₃	#95
hypercenter	C₂²⋊C₈	#64408
hypocenter	C₇₃	#1302
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

subgroup

G/H

center

C₂²

(C₂×#64408)⋊C₄

commutator

C₂×C₄×C₇₃

C₄²

Frattini

C₂²×C₄

C₂×#64408

Fitting

C₂²⋊C₈×C₇₃

C₄

C₂²×C₇₃

C₂²⋊C₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
59. C₇₃	#1302	semidirect

H ≅ G/N

type

59. C₇₃

#1302

semidirect

Subgroups — #22624826

Conjugacy classes of subgroups

Complements