Group #22625491 — subgroups

Subgroups — #22625491

Order 9344.

168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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	2	yes	maximal
2	#17989451	C₂	1	2	yes	maximal, complemented
3	#17989448	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊#10596833	C₂²	1	4	yes	—
6	C₂²⋊#10596833	—	2	2	no	—
7	#14556646	—	2	2	no	—
8	C₂²×#10596831	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
10	C₈×Dic₇₃	C₄	1	1	yes	characteristic
11	C₈×Dic₇₃	C₄	1	1	yes	characteristic
12	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
13	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
15	C₂×#10596833	—	2	4	no	—
16	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
17	C₂²×Dic₇₃	Q₈	1	1	yes	characteristic
18	C₂×#10596831	—	2	2	no	—
19	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
20	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₇₃	D₄	1	1	yes	characteristic
23	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
24	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	—	2	2	no	—
27	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₃	—	2	1	no	—
31	C₂×C₄×C₇₃	—	2	1	no	—
32	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₇₃	—	2	2	no	—
35	C₂×Dic₇₃	—	2	2	no	—
36	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
40	#10596833	—	4	4	no	—
41	C₈×C₇₃	—	2	1	no	—
42	C₈×C₇₃	M₁₆	1	2	yes	—
43	#10596831	—	2	1	no	—
44	#10596831	M₁₆	1	2	yes	—
45	C₂²×C₇₃	—	2	1	no	—
46	C₂²×C₇₃	—	2	1	no	—
47	C₂²×C₇₃	#108	1	2	yes	—
48	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
51	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
52	Dic₇₃	—	2	1	no	—
53	Dic₇₃	—	2	1	no	—
54	Dic₇₃	—	2	1	no	—
55	Dic₇₃	#135	1	2	yes	—
56	C₂×C₇₃	—	2	2	no	—
57	C₂×C₇₃	#423	1	1	yes	characteristic
58	C₂×C₇₃	#427	1	1	yes	characteristic
59	C₂×C₇₃	C₂×#108	1	1	yes	characteristic
60	#1568	—	73	1	no	maximal, Sylow
61	C₇₃	#1568	1	1	yes	characteristic, complemented, Sylow
62	#432	—	73	2	no	—
63	C₂×C₄×C₈	—	73	1	no	—
64	#335	—	73	2	no	—
65	#334	—	73	2	no	—
66	C₂²×C₈	—	73	1	no	—
67	C₂²×C₈	#64408	1	1	yes	characteristic
68	C₂×C₄²	—	73	1	no	—
69	C₄⋊C₈	—	73	4	no	—
70	C₂²⋊C₈	—	146	2	no	—
71	#97	—	146	2	no	—
72	C₄×C₈	—	73	1	no	—
73	C₄×C₈	—	73	1	no	—
74	C₄×C₈	—	73	1	no	—
75	C₄×C₈	—	73	1	no	—
76	C₂²×C₄	—	73	1	no	—
77	C₂²×C₄	—	73	1	no	—
78	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	146	4	no	—
83	C₂×C₈	—	146	2	no	—
84	C₂×C₈	C₂×#64408	1	1	yes	characteristic
85	C₂×C₈	C₂×#64408	1	1	yes	characteristic
86	C₄²	—	73	1	no	—
87	C₄²	—	73	1	no	—
88	C₄²	—	73	1	no	—
89	C₄²	—	73	1	no	—
90	C₂³	C₄⋊#64408	1	1	yes	characteristic
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	73	1	no	—
94	C₂×C₄	—	73	1	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	146	2	no	—
98	C₂×C₄	—	146	2	no	—
99	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
100	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
101	C₈	—	2	1	no	—
102	C₈	—	292	4	no	—
103	C₈	—	73	2	no	—
104	C₈	—	146	1	no	—
105	C₈	#11924037	1	2	yes	—
106	C₂²	—	2	1	no	—
107	C₂²	—	2	1	no	—
108	C₂²	#14556661	1	2	yes	—
109	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	73	2	no	—
112	C₄	—	146	1	no	—
113	C₄	—	146	1	no	—
114	C₄	—	146	1	no	—
115	C₄	C₂×#11924037	1	1	yes	characteristic
116	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
117	C₂	—	2	2	no	—
118	C₂	#17989590	1	1	yes	characteristic
119	C₂	#17989597	1	1	yes	characteristic
120	C₂	C₂×#14556661	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989608

C₂

yes

maximal

#17989451

C₂

yes

maximal, complemented

#17989448

C₂

yes

maximal, complemented

C₂×C₈×Dic₇₃

C₂

yes

maximal, characteristic

C₄⋊#10596833

C₂²

yes

—

C₂²⋊#10596833

—

#14556646

—

C₂²×#10596831

C₄

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

C₄

yes

characteristic

C₈×Dic₇₃

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

C₂²×C₈×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

Q₈

yes

characteristic

C₂×#10596831

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₄×Dic₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

#10596833

—

C₈×C₇₃

—

C₈×C₇₃

M₁₆

yes

—

#10596831

—

#10596831

M₁₆

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#108

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#135

yes

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#432

—

C₂×C₄×C₈

—

#335

—

#334

—

C₂²×C₈

—

C₂²×C₈

#64408

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

146

—

#97

—

146

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄⋊#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₄⋊#64408

yes

characteristic

100

C₂×C₄

C₂²×#64408

yes

characteristic

101

C₈

—

102

C₈

—

292

—

103

C₈

—

104

C₈

—

146

—

105

C₈

#11924037

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

#14556661

yes

—

109

C₂²

C₂×C₄⋊#64408

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

146

—

113

C₄

—

146

—

114

C₄

—

146

—

115

C₄

C₂×#11924037

yes

characteristic

116

C₄

D₇₃⋊M₁₆

yes

characteristic

117

C₂

—

118

C₂

#17989590

yes

characteristic

119

C₂

#17989597

yes

characteristic

120

C₂

C₂×#14556661

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	C₂²×C₈	#64408
hypocenter	C₇₃	#1568
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₂²×C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₂²×C₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. #17989451	C₂	semidirect
3. #17989448	C₂	semidirect
61. C₇₃	#1568	semidirect

H ≅ G/N

type

2. #17989451

C₂

semidirect

3. #17989448

C₂

semidirect

61. C₇₃

#1568

semidirect

Subgroups — #22625491

Conjugacy classes of subgroups

Complements