Group #22625650 — subgroups

Subgroups — #22625650

Order 9344.

240 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 98 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×#14556646	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10596833	C₂	1	1	yes	maximal, characteristic
3	#17989453	C₂	1	4	yes	maximal
4	#17988432	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10596833	C₂²	1	2	yes	—
6	C₂²×#10596833	C₂²	1	2	yes	—
7	#14556646	C₄	1	4	yes	complemented
8	C₄×#10596833	C₄	1	4	yes	complemented
9	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
10	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
11	#14556498	C₄	1	2	yes	—
12	#14556498	C₄	1	1	yes	characteristic
13	#95×C₇₃	C₄	1	1	yes	characteristic
14	C₂×#10596833	—	2	4	no	—
15	C₂×#10596833	—	2	4	no	—
16	C₂×#10596833	C₂×C₄	1	4	yes	—
17	C₂×#10596833	C₂×C₄	1	4	yes	—
18	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
19	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
21	C₄×Dic₇₃	—	2	4	no	—
22	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
23	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₃	—	2	2	no	—
28	C₂×C₄×C₇₃	—	2	2	no	—
29	C₂×C₄×C₇₃	—	2	2	no	—
30	C₂×C₄×C₇₃	—	2	2	no	—
31	C₂×C₄×C₇₃	C₄²	1	2	yes	—
32	C₂×Dic₇₃	—	2	1	no	—
33	C₂×Dic₇₃	—	2	1	no	—
34	C₂×Dic₇₃	—	2	2	no	—
35	C₂×Dic₇₃	—	2	2	no	—
36	C₂×Dic₇₃	—	2	2	no	—
37	C₂×Dic₇₃	C₄²	1	2	yes	—
38	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₇₃	#41	1	4	yes	—
41	#10596833	—	2	4	no	—
42	#10596833	—	2	4	no	—
43	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₇₃	#117	1	2	yes	—
45	C₂²×C₇₃	#131	1	2	yes	—
46	C₂²×C₇₃	#131	1	1	yes	characteristic
47	C₂²×C₇₃	#131	1	1	yes	characteristic
48	C₄×C₇₃	—	2	2	no	—
49	C₄×C₇₃	—	4	2	no	—
50	Dic₇₃	—	2	2	no	—
51	Dic₇₃	—	4	2	no	—
52	Dic₇₃	#117	1	2	yes	—
53	Dic₇₃	#117	1	2	yes	—
54	C₂×C₇₃	#376	1	1	yes	characteristic
55	C₂×C₇₃	#405	1	1	yes	characteristic
56	C₂×C₇₃	#405	1	1	yes	characteristic
57	C₂×C₇₃	#433	1	2	yes	—
58	C₂×C₇₃	#433	1	2	yes	—
59	#1746	—	73	1	no	maximal, Sylow
60	C₇₃	#1746	1	1	yes	characteristic, complemented, Sylow
61	C₂×#97	—	73	1	no	—
62	C₂×C₄×C₈	—	73	1	no	—
63	#376	—	73	1	no	—
64	#336	—	73	4	no	—
65	C₂²×C₈	—	73	2	no	—
66	C₂²×C₈	—	73	2	no	—
67	C₂×C₄²	—	73	1	no	—
68	C₂×C₄²	—	73	2	no	—
69	#97	—	73	4	no	—
70	C₄×C₈	—	73	4	no	—
71	#95	—	73	2	no	—
72	#95	—	73	1	no	—
73	#95	#64408	1	1	yes	characteristic
74	C₂²×C₄	—	73	1	no	—
75	C₂²×C₄	—	73	1	no	—
76	C₂²×C₄	—	73	2	no	—
77	C₂²×C₄	C₂×#64408	1	2	yes	—
78	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
79	C₂×C₈	—	73	4	no	—
80	C₂×C₈	—	73	4	no	—
81	C₂×C₈	—	146	4	no	—
82	C₂×C₈	—	146	4	no	—
83	C₄²	—	73	2	no	—
84	C₄²	—	73	2	no	—
85	C₄²	—	146	4	no	—
86	C₂³	C₂²×#64408	1	1	yes	characteristic
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	—	73	4	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	146	2	no	—
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	—	146	2	no	—
98	C₂×C₄	—	146	1	no	—
99	C₂×C₄	—	146	1	no	—
100	C₂×C₄	C₄×#64408	1	2	yes	—
101	C₈	—	146	4	no	—
102	C₈	—	146	4	no	—
103	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
104	C₂²	#14556670	1	2	yes	—
105	C₂²	#14556678	1	2	yes	—
106	C₂²	#14556678	1	1	yes	characteristic
107	C₂²	#14556679	1	1	yes	characteristic
108	C₄	—	2	2	no	—
109	C₄	—	4	2	no	—
110	C₄	—	292	2	no	—
111	C₄	—	73	2	no	—
112	C₄	—	73	2	no	—
113	C₄	—	146	2	no	—
114	C₂	#17989523	1	1	yes	characteristic
115	C₂	#17989551	1	1	yes	characteristic
116	C₂	#17989552	1	1	yes	characteristic
117	C₂	#17989611	1	2	yes	—
118	C₂	#17989612	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556646

C₂

yes

maximal, characteristic

C₂×C₄×#10596833

C₂

yes

maximal, characteristic

#17989453

C₂

yes

maximal

#17988432

C₂

yes

maximal, characteristic

C₂²×#10596833

C₂²

yes

—

C₂²×#10596833

C₂²

yes

—

#14556646

C₄

yes

complemented

C₄×#10596833

C₄

yes

complemented

C₂×C₄×Dic₇₃

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556498

C₄

yes

—

#14556498

C₄

yes

characteristic

#95×C₇₃

C₄

yes

—

—

C₂×C₄

yes

—

C₂×#10596833

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

characteristic

C₂²×Dic₇₃

C₂³

yes

characteristic

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄²

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

#41

yes

—

#10596833

—

#10596833

—

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₂²×C₇₃

#117

yes

—

C₂²×C₇₃

#131

yes

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#117

yes

—

Dic₇₃

#117

yes

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₂×C₇₃

#433

yes

—

#1746

—

maximal, Sylow

C₇₃

#1746

yes

characteristic, complemented, Sylow

C₂×#97

—

C₂×C₄×C₈

—

#376

—

#336

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

#97

—

C₄×C₈

—

—

—

yes

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₂³

C₂²×#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

100

C₂×C₄

C₄×#64408

yes

—

101

C₈

—

146

—

102

C₈

—

146

—

103

C₂²

C₂×C₄×#64408

yes

characteristic

104

C₂²

#14556670

yes

—

105

C₂²

#14556678

yes

—

106

C₂²

#14556678

yes

characteristic

107

C₂²

#14556679

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

292

—

111

C₄

—

112

C₄

—

113

C₄

—

146

—

114

C₂

#17989523

yes

characteristic

115

C₂

#17989551

yes

characteristic

116

C₂

#17989552

yes

characteristic

117

C₂

#17989611

yes

—

118

C₂

#17989612

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#64408
commutator	C₂²×C₇₃	C₂×C₄²
Fitting	#95×C₇₃	C₄
socle	C₂³×C₇₃	C₂²×C₄
hypercenter	#95	#64408
hypocenter	C₇₃	#1746
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#64408

commutator

C₂²×C₇₃

C₂×C₄²

Fitting

#95×C₇₃

C₄

socle

C₂³×C₇₃

C₂²×C₄

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
7. #14556646	C₄	semidirect
8. C₄×#10596833	C₄	semidirect
60. C₇₃	#1746	semidirect

H ≅ G/N

type

7. #14556646

C₄

semidirect

8. C₄×#10596833

C₄

semidirect

60. C₇₃

#1746

semidirect

Subgroups — #22625650

Conjugacy classes of subgroups

Complements