Group #22624916 — subgroups

Subgroups — #22624916

Order 9344.

124 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 30 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	#17989467	C₂	1	1	yes	maximal, characteristic
2	#17989433	C₂	1	1	yes	maximal, characteristic
3	#17988519	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924037	—	2	1	no	—
5	C₂²⋊#10596833	—	2	1	no	—
6	C₂×C₄⋊Dic₇₃	—	2	1	no	—
7	C₂×C₄⋊Dic₇₃	C₄	1	1	yes	characteristic
8	C₂×#11924007	C₂²	1	1	yes	characteristic
9	#14556498	—	2	1	no	—
10	#95×C₇₃	C₄	1	1	yes	characteristic
11	#11924037	—	2	2	no	—
12	#11924037	—	4	1	no	—
13	C₂×#10596833	—	4	1	no	—
14	C₂×#10596833	—	4	1	no	—
15	C₂²×Dic₇₃	—	2	1	no	—
16	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
17	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
18	C₄⋊Dic₇₃	—	4	1	no	—
19	C₄⋊Dic₇₃	—	4	1	no	—
20	C₄⋊Dic₇₃	—	4	1	no	—
21	#11924007	—	4	1	no	—
22	C₂²×C₄×C₇₃	—	2	1	no	—
23	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₃	—	2	2	no	—
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	—	4	1	no	—
29	C₂×C₄×C₇₃	—	4	1	no	—
30	C₂×Dic₇₃	—	2	1	no	—
31	C₂×Dic₇₃	—	2	1	no	—
32	C₂×Dic₇₃	—	2	1	no	—
33	C₂×Dic₇₃	—	4	1	no	—
34	C₂×Dic₇₃	—	4	1	no	—
35	C₂×Dic₇₃	—	4	1	no	—
36	C₂×Dic₇₃	—	4	1	no	—
37	C₂×Dic₇₃	D₈	1	1	yes	characteristic
38	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
39	#10596833	—	4	2	no	—
40	#10596833	—	8	1	no	—
41	C₂²×C₇₃	—	2	1	no	—
42	C₂²×C₇₃	—	2	1	no	—
43	C₂²×C₇₃	#99	1	1	yes	characteristic
44	C₂²×C₇₃	#102	1	1	yes	characteristic
45	C₂²×C₇₃	#104	1	1	yes	characteristic
46	C₄×C₇₃	—	4	2	no	—
47	C₄×C₇₃	—	4	1	no	—
48	Dic₇₃	—	2	1	no	—
49	Dic₇₃	—	2	1	no	—
50	Dic₇₃	—	4	1	no	—
51	Dic₇₃	—	8	1	no	—
52	C₂×C₇₃	—	2	1	no	—
53	C₂×C₇₃	—	2	1	no	—
54	C₂×C₇₃	#327	1	1	yes	characteristic
55	C₂×C₇₃	#352	1	1	yes	characteristic
56	C₂×C₇₃	#356	1	1	yes	characteristic
57	#1346	—	73	1	no	maximal, Sylow
58	C₇₃	#1346	1	1	yes	characteristic, complemented, Sylow
59	#398	—	73	1	no	—
60	#343	—	73	1	no	—
61	#324	—	73	1	no	—
62	C₂×M₁₆	—	146	1	no	—
63	C₂×C₄⋊C₄	—	73	1	no	—
64	C₂×C₄⋊C₄	—	73	1	no	—
65	C₂×C₄⋊C₄	—	146	1	no	—
66	C₂²⋊C₈	—	146	1	no	—
67	#95	—	146	1	no	—
68	#95	#64408	1	1	yes	characteristic
69	C₂²×C₄	—	2	1	no	—
70	C₂²×C₄	—	73	1	no	—
71	C₂²×C₄	—	73	1	no	—
72	C₂²×C₄	—	146	1	no	—
73	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
74	M₁₆	—	292	1	no	—
75	M₁₆	—	146	2	no	—
76	C₂×C₈	—	292	1	no	—
77	C₂×C₈	—	292	1	no	—
78	C₄⋊C₄	—	292	1	no	—
79	C₄⋊C₄	—	292	1	no	—
80	C₄⋊C₄	—	292	1	no	—
81	C₄⋊C₄	—	292	1	no	—
82	C₂³	C₂²⋊#64408	1	1	yes	characteristic
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	292	1	no	—
89	C₂×C₄	—	292	1	no	—
90	C₂×C₄	—	292	1	no	—
91	C₂×C₄	—	292	1	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	—	73	1	no	—
94	C₂×C₄	—	146	1	no	—
95	C₂×C₄	—	146	1	no	—
96	C₂×C₄	—	146	1	no	—
97	C₈	—	292	2	no	—
98	C₈	—	584	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#14556650	1	1	yes	characteristic
102	C₂²	#14556653	1	1	yes	characteristic
103	C₂²	#14556656	1	1	yes	characteristic
104	C₄	—	4	2	no	—
105	C₄	—	4	1	no	—
106	C₄	—	292	1	no	—
107	C₄	—	584	1	no	—
108	C₄	—	146	1	no	—
109	C₄	—	146	1	no	—
110	C₂	—	2	1	no	—
111	C₂	—	2	1	no	—
112	C₂	#17989439	1	1	yes	characteristic
113	C₂	#17989490	1	1	yes	characteristic
114	C₂	#17989498	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989467

C₂

yes

maximal, characteristic

#17989433

C₂

yes

maximal, characteristic

#17988519

C₂

yes

maximal, characteristic

C₂×#11924037

—

C₂²⋊#10596833

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

C₄

yes

characteristic

C₂×#11924007

C₂²

yes

characteristic

#14556498

—

#95×C₇₃

C₄

yes

—

—

—

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²×C₄×C₇₃

—

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

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₂×Dic₇₃

SD₁₆

yes

characteristic

#10596833

—

#10596833

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#398

—

#343

—

#324

—

C₂×M₁₆

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂²⋊C₈

—

146

—

#95

—

146

—

#95

#64408

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₂³

C₂²⋊#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₈

—

292

—

C₈

—

584

—

C₂²

—

100

C₂²

—

101

C₂²

#14556650

yes

characteristic

102

C₂²

#14556653

yes

characteristic

103

C₂²

#14556656

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

292

—

107

C₄

—

584

—

108

C₄

—

146

—

109

C₄

—

146

—

110

C₂

—

111

C₂

—

112

C₂

#17989439

yes

characteristic

113

C₂

#17989490

yes

characteristic

114

C₂

#17989498

yes

characteristic

	subgroup	G/H
center	C₂²	#14556650
commutator	C₂²×C₄×C₇₃	C₂×C₄
Frattini	C₂²×C₄	C₂×#64408
Fitting	#95×C₇₃	C₄
socle	C₂²×C₇₃	#99
hypercenter	#95	#64408
hypocenter	C₇₃	#1346
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #95

subgroup

G/H

center

C₂²

#14556650

commutator

C₂²×C₄×C₇₃

C₂×C₄

Frattini

C₂²×C₄

C₂×#64408

Fitting

#95×C₇₃

C₄

C₂²×C₇₃

C₇₃

G ▷ C₂²×C₄×C₇₃ ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #95

N	H ≅ G/N	type
58. C₇₃	#1346	semidirect

H ≅ G/N

type

58. C₇₃

#1346

semidirect

Subgroups — #22624916

Conjugacy classes of subgroups

Complements