Group #22625854 — subgroups

Subgroups — #22625854

Order 9344.

224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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	#17989533	C₂	1	1	yes	maximal, characteristic
2	#17989531	C₂	1	1	yes	maximal, characteristic
3	#17989461	C₂	1	4	yes	maximal
4	#97×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊#64408	—	2	2	no	—
6	C₂×C₄⋊#64408	C₂²	1	2	yes	—
7	C₂×C₄⋊#64408	C₂²	1	2	yes	—
8	(C₂×#64408)⋊C₄	—	2	2	no	—
9	C₂×C₈×D₇₃	C₂²	1	2	yes	—
10	C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	#14556502	C₄	1	1	yes	characteristic, complemented
12	#14556501	C₄	1	2	yes	complemented
13	#97×C₇₃	C₄	1	1	yes	characteristic, complemented
14	C₂²×#64408	—	2	2	no	—
15	C₂²×#64408	—	2	2	no	—
16	C₄⋊#64408	—	2	4	no	—
17	C₄⋊#64408	—	2	4	no	—
18	C₄⋊#64408	—	4	4	no	—
19	C₂×C₄×D₇₃	D₄	1	2	yes	—
20	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
21	C₂×#10596831	C₂×C₄	1	2	yes	—
22	C₈×D₇₃	—	2	2	no	—
23	C₈×D₇₃	—	2	2	no	—
24	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₇₃	Q₈	1	2	yes	—
26	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
27	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₇₃	C₂×D₄	1	1	yes	characteristic
29	C₂×#64408	—	4	2	no	—
30	C₂×#64408	—	4	2	no	—
31	C₂×#64408	—	4	4	no	—
32	C₂×#64408	—	4	2	no	—
33	C₂×#64408	—	4	2	no	—
34	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
37	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
38	C₄×D₇₃	—	2	2	no	—
39	C₄×D₇₃	—	2	2	no	—
40	C₄×D₇₃	#41	1	2	yes	—
41	C₄×D₇₃	#41	1	2	yes	—
42	C₈×C₇₃	—	2	2	no	—
43	#10596831	—	2	2	no	—
44	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×D₇₃	#124	1	1	yes	characteristic
46	C₂×D₇₃	#124	1	1	yes	characteristic
47	C₂×D₇₃	AGL(1,ℤ/8)	1	2	yes	—
48	C₂×D₇₃	#137	1	2	yes	—
49	#64408	—	8	2	no	—
50	#64408	—	8	2	no	—
51	C₄×C₇₃	—	2	2	no	—
52	C₄×C₇₃	#117	1	2	yes	—
53	Dic₇₃	—	2	2	no	—
54	Dic₇₃	#125	1	2	yes	—
55	C₂×C₇₃	#382	1	1	yes	characteristic
56	C₂×C₇₃	#428	1	2	yes	—
57	D₇₃	#489	1	2	yes	—
58	D₇₃	#490	1	1	yes	characteristic
59	D₇₃	#491	1	1	yes	characteristic
60	#1836	—	73	1	no	maximal, Sylow
61	C₇₃	#1836	1	1	yes	characteristic, complemented, Sylow
62	C₂×#97	—	73	1	no	—
63	#384	—	73	1	no	—
64	#382	—	73	1	no	—
65	#340	—	73	4	no	—
66	C₂²×C₈	—	73	2	no	—
67	C₂×C₄⋊C₄	—	73	2	no	—
68	C₂×C₄⋊C₄	—	73	2	no	—
69	C₂×C₄⋊C₄	—	146	2	no	—
70	C₂×C₄²	—	73	1	no	—
71	#97	—	73	2	no	—
72	#97	—	73	1	no	—
73	#97	#64408	1	1	yes	characteristic, complemented
74	#95	—	146	2	no	—
75	C₂²×C₄	—	73	1	no	—
76	C₂²×C₄	—	73	2	no	—
77	C₂²×C₄	—	146	2	no	—
78	C₂²×C₄	—	146	2	no	—
79	C₂×C₈	—	73	2	no	—
80	C₂×C₈	—	146	2	no	—
81	C₂×C₈	—	146	2	no	—
82	C₂×C₈	C₂×#64408	1	2	yes	—
83	C₄⋊C₄	—	292	4	no	—
84	C₄⋊C₄	—	146	4	no	—
85	C₄⋊C₄	—	146	4	no	—
86	C₄²	—	73	2	no	—
87	C₄²	—	73	1	no	—
88	C₄²	C₂×#64408	1	1	yes	characteristic
89	C₂³	—	73	1	no	—
90	C₂×C₄	—	292	4	no	—
91	C₂×C₄	—	292	2	no	—
92	C₂×C₄	—	292	2	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	—	73	2	no	—
99	C₂×C₄	—	146	2	no	—
100	C₂×C₄	—	146	2	no	—
101	C₂×C₄	C₄⋊#64408	1	2	yes	—
102	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
103	C₈	—	2	2	no	—
104	C₈	—	146	2	no	—
105	C₂²	—	73	1	no	—
106	C₂²	—	73	1	no	—
107	C₂²	—	73	2	no	—
108	C₂²	—	73	2	no	—
109	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
110	C₄	—	2	2	no	—
111	C₄	—	584	2	no	—
112	C₄	—	584	2	no	—
113	C₄	—	73	2	no	—
114	C₄	—	146	2	no	—
115	C₄	#14556670	1	2	yes	—
116	C₂	—	73	1	no	—
117	C₂	—	73	2	no	—
118	C₂	—	73	1	no	—
119	C₂	#17989531	1	1	yes	characteristic
120	C₂	#17989598	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989533

C₂

yes

maximal, characteristic

#17989531

C₂

yes

maximal, characteristic

#17989461

C₂

yes

maximal

#97×D₇₃

C₂

yes

maximal, characteristic

C₂×C₄⋊#64408

—

C₂×C₄⋊#64408

C₂²

yes

—

C₂×C₄⋊#64408

C₂²

yes

—

(C₂×#64408)⋊C₄

—

C₂×C₈×D₇₃

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#14556502

C₄

yes

characteristic, complemented

#14556501

C₄

yes

complemented

#97×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

C₂²×#64408

—

C₄⋊#64408

—

C₄⋊#64408

—

C₄⋊#64408

—

C₂×C₄×D₇₃

D₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

—

C₈×D₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂×D₄

yes

—

—

—

—

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂×Q₈

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

#41

yes

—

C₄×D₇₃

#41

yes

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

C₂×D₇₃

yes

C₂×D₇₃

yes

C₂×D₇₃

yes

—

C₂×D₇₃

#137

yes

—

#64408

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

#117

yes

—

Dic₇₃

—

Dic₇₃

#125

yes

—

C₂×C₇₃

#382

yes

characteristic

C₂×C₇₃

#428

yes

—

D₇₃

#489

yes

—

D₇₃

yes

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×#97

—

#384

—

#382

—

#340

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

#95

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

100

C₂×C₄

—

146

—

101

C₂×C₄

C₄⋊#64408

yes

—

102

C₂×C₄

C₂²×#64408

yes

characteristic

103

C₈

—

104

C₈

—

146

—

105

C₂²

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×C₄⋊#64408

yes

characteristic

110

C₄

—

111

C₄

—

584

—

112

C₄

—

584

—

113

C₄

—

114

C₄

—

146

—

115

C₄

#14556670

yes

—

116

C₂

—

117

C₂

—

118

C₂

—

119

C₂

#17989531

yes

characteristic

120

C₂

#17989598

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#97×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	#97	#64408
hypocenter	C₇₃	#1836
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#97×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
11. #14556502	C₄	semidirect
12. #14556501	C₄	semidirect
13. #97×C₇₃	C₄	semidirect
61. C₇₃	#1836	semidirect
73. #97	#64408	semidirect

H ≅ G/N

type

11. #14556502

C₄

semidirect

12. #14556501

C₄

semidirect

13. #97×C₇₃

C₄

semidirect

61. C₇₃

#1836

semidirect

73. #97

#64408

semidirect

Subgroups — #22625854

Conjugacy classes of subgroups

Complements