Group #22625862 — subgroups

Subgroups — #22625862

Order 9344.

162 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 52 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	#17989469	C₂	1	2	yes	maximal
2	#17989458	C₂	1	2	yes	maximal
3	#17989456	C₂	1	1	yes	maximal, characteristic
4	#17989455	C₂	1	1	yes	maximal, characteristic
5	#17988539	C₂	1	1	yes	maximal, characteristic
6	D₇₃⋊M₁₆	C₂²	1	2	yes	—
7	#14556670	C₂²	1	2	yes	—
8	C₂×#11924011	C₂²	1	1	yes	characteristic
9	C₂×#11924011	C₂²	1	1	yes	characteristic
10	C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	#14556502	C₄	1	1	yes	characteristic, complemented
12	C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
13	C₈×Dic₇₃	C₄	1	1	yes	characteristic, complemented
14	#97×C₇₃	C₄	1	1	yes	characteristic, complemented
15	#11924038	—	2	2	no	—
16	#11924037	—	2	2	no	—
17	#11924036	—	2	2	no	—
18	C₄⋊#64408	—	2	2	no	—
19	C₂²⋊#64408	—	2	2	no	—
20	C₄×#64408	—	2	2	no	—
21	C₂×C₄×D₇₃	—	2	1	no	—
22	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
23	#11924011	—	2	2	no	—
24	#11924011	—	2	2	no	—
25	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
26	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₇₃	—	2	1	no	—
28	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
31	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₇₃	#41	1	1	yes	characteristic
33	C₂×#64408	—	4	2	no	—
34	C₂×C₄×C₇₃	—	2	1	no	—
35	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₇₃	—	2	1	no	—
37	C₂×Dic₇₃	#41	1	1	yes	characteristic
38	C₄×D₇₃	—	4	2	no	—
39	C₄×D₇₃	#41	1	2	yes	—
40	C₄×D₇₃	#41	1	2	yes	—
41	#10596833	—	4	2	no	—
42	C₈×C₇₃	—	2	1	no	—
43	C₈×C₇₃	—	2	1	no	—
44	#10596831	—	2	1	no	—
45	#10596831	—	2	1	no	—
46	C₂²×C₇₃	#117	1	1	yes	characteristic
47	C₂×D₇₃	—	4	1	no	—
48	C₂×D₇₃	#126	1	2	yes	—
49	#64408	—	8	2	no	—
50	C₄×C₇₃	—	4	1	no	—
51	C₄×C₇₃	#117	1	1	yes	characteristic
52	C₄×C₇₃	#117	1	1	yes	characteristic
53	Dic₇₃	—	2	2	no	—
54	Dic₇₃	#126	1	2	yes	—
55	C₂×C₇₃	—	2	1	no	—
56	C₂×C₇₃	#383	1	1	yes	characteristic
57	D₇₃	—	2	2	no	—
58	#1841	—	73	1	no	maximal, Sylow
59	C₇₃	#1841	1	1	yes	characteristic, complemented, Sylow
60	C₄×M₁₆	—	73	1	no	—
61	#344	—	73	2	no	—
62	#339	—	73	2	no	—
63	#338	—	73	1	no	—
64	H(3,ℤ/4)	—	73	1	no	—
65	C₂×M₁₆	—	73	1	no	—
66	C₂×M₁₆	—	73	1	no	—
67	C₂×M₁₆	—	73	2	no	—
68	#117	—	73	2	no	—
69	C₂×C₄²	—	73	1	no	—
70	#97	—	73	1	no	—
71	#97	#64408	1	1	yes	characteristic, complemented
72	C₄×C₈	—	73	1	no	—
73	C₄×C₈	—	73	1	no	—
74	C₂²×C₄	—	73	1	no	—
75	C₂²×C₄	—	146	1	no	—
76	M₁₆	—	146	2	no	—
77	M₁₆	—	146	2	no	—
78	M₁₆	—	146	2	no	—
79	M₁₆	—	146	2	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	146	2	no	—
83	C₂×C₈	C₂×#64408	1	1	yes	characteristic
84	C₂×C₈	C₂×#64408	1	1	yes	characteristic
85	C₄⋊C₄	—	146	2	no	—
86	C₂²⋊C₄	—	146	2	no	—
87	C₄²	—	73	1	no	—
88	C₄²	—	146	1	no	—
89	C₄²	—	146	2	no	—
90	C₄²	C₂×#64408	1	1	yes	characteristic
91	C₂³	—	73	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	292	2	no	—
94	C₂×C₄	—	292	2	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	2	no	—
97	C₂×C₄	—	73	2	no	—
98	C₂×C₄	—	146	1	no	—
99	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
100	C₈	—	2	1	no	—
101	C₈	—	2	1	no	—
102	C₈	—	292	2	no	—
103	C₈	—	146	1	no	—
104	C₈	—	146	1	no	—
105	C₂²	—	292	1	no	—
106	C₂²	—	73	2	no	—
107	C₂²	#14556670	1	1	yes	characteristic
108	C₄	—	4	1	no	—
109	C₄	—	584	2	no	—
110	C₄	—	73	2	no	—
111	C₄	—	146	2	no	—
112	C₄	#14556670	1	1	yes	characteristic
113	C₄	#14556670	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	146	2	no	—
116	C₂	#17989532	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989469

C₂

yes

maximal

#17989458

C₂

yes

maximal

#17989456

C₂

yes

maximal, characteristic

#17989455

C₂

yes

maximal, characteristic

#17988539

C₂

yes

maximal, characteristic

D₇₃⋊M₁₆

C₂²

yes

—

#14556670

C₂²

yes

—

C₂×#11924011

C₂²

yes

characteristic

C₂×#11924011

C₂²

yes

characteristic

C₄²×D₇₃

C₂²

yes

characteristic

#14556502

C₄

yes

characteristic, complemented

C₈×Dic₇₃

C₄

yes

characteristic, complemented

C₈×Dic₇₃

C₄

yes

characteristic, complemented

#97×C₇₃

C₄

yes

characteristic, complemented

—

—

—

—

—

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂³

yes

—

—

C₂×C₄

yes

characteristic

C₂×#10596831

C₂×C₄

yes

characteristic

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

C₂²×D₇₃

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

#41

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

#41

yes

—

C₄×D₇₃

#41

yes

—

#10596833

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

#117

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#126

yes

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

#126

yes

—

C₂×C₇₃

—

C₂×C₇₃

#383

yes

characteristic

D₇₃

—

#1841

—

maximal, Sylow

C₇₃

#1841

yes

characteristic, complemented, Sylow

C₄×M₁₆

—

—

—

—

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

#117

—

C₂×C₄²

—

#97

—

#97

#64408

yes

characteristic, complemented

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

—

146

—

C₄²

—

146

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂²×#64408

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

292

—

103

C₈

—

146

—

104

C₈

—

146

—

105

C₂²

—

292

—

106

C₂²

—

107

C₂²

#14556670

yes

characteristic

108

C₄

—

109

C₄

—

584

—

110

C₄

—

111

C₄

—

146

—

112

C₄

#14556670

yes

characteristic

113

C₄

#14556670

yes

characteristic

114

C₂

—

115

C₂

—

146

—

116

C₂

#17989532

yes

characteristic

	subgroup	G/H
center	C₄	#14556670
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#97×C₇₃	C₄
socle	C₂×C₇₃	#383
hypercenter	#97	#64408
hypocenter	C₇₃	#1841
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

subgroup

G/H

center

C₄

#14556670

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#97×C₇₃

C₄

C₂×C₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

N	H ≅ G/N	type
11. #14556502	C₄	semidirect
12. C₈×Dic₇₃	C₄	semidirect
13. C₈×Dic₇₃	C₄	semidirect
14. #97×C₇₃	C₄	semidirect
59. C₇₃	#1841	semidirect
71. #97	#64408	semidirect

H ≅ G/N

type

11. #14556502

C₄

semidirect

12. C₈×Dic₇₃

C₄

semidirect

13. C₈×Dic₇₃

C₄

semidirect

14. #97×C₇₃

C₄

semidirect

59. C₇₃

#1841

semidirect

71. #97

#64408

semidirect

Subgroups — #22625862

Conjugacy classes of subgroups

Complements