Group #22624809 — subgroups

Subgroups — #22624809

Order 9344.

188 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 76 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×#14556658	C₂	1	2	yes	maximal
2	#17988456	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10596833	—	2	2	no	—
4	#14556658	—	2	2	no	—
5	#14556658	C₄	1	4	yes	complemented
6	C₂×C₄⋊Dic₇₃	C₄	1	1	yes	characteristic
7	C₂×#11924007	—	2	2	no	—
8	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₇₃	C₄	1	1	yes	characteristic
10	C₂×#10596833	—	2	4	no	—
11	C₂×#10596833	—	4	2	no	—
12	C₂×#10596833	—	4	2	no	—
13	C₂²×Dic₇₃	—	2	1	no	—
14	C₂²×Dic₇₃	D₄	1	2	yes	—
15	C₄⋊Dic₇₃	—	4	1	no	—
16	#11924007	—	4	2	no	—
17	#11924007	—	4	2	no	—
18	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
19	C₄×Dic₇₃	D₄	1	1	yes	characteristic
20	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
21	C₂²×C₄×C₇₃	—	2	1	no	—
22	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄⋊C₄×C₇₃	—	4	1	no	—
24	C₂³×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₃	—	2	1	no	—
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	—	4	2	no	—
29	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×Dic₇₃	—	4	1	no	—
32	C₂×Dic₇₃	—	4	2	no	—
33	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
34	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₇₃	D₈	1	2	yes	—
36	C₂×Dic₇₃	SD₁₆	1	2	yes	—
37	C₂×Dic₇₃	SD₁₆	1	2	yes	—
38	C₂×Dic₇₃	Q₁₆	1	2	yes	—
39	#10596833	—	4	4	no	—
40	C₂²×C₇₃	#95	1	1	yes	characteristic
41	C₂²×C₇₃	#100	1	1	yes	characteristic
42	C₂²×C₇₃	#101	1	1	yes	characteristic
43	C₂²×C₇₃	#102	1	2	yes	—
44	C₂²×C₇₃	#103	1	2	yes	—
45	C₄×C₇₃	—	2	1	no	—
46	C₄×C₇₃	—	2	1	no	—
47	C₄×C₇₃	—	8	1	no	—
48	Dic₇₃	—	8	1	no	—
49	Dic₇₃	#102	1	2	yes	—
50	Dic₇₃	#103	1	2	yes	—
51	Dic₇₃	#106	1	2	yes	—
52	Dic₇₃	#107	1	2	yes	—
53	C₂×C₇₃	#331	1	1	yes	characteristic
54	C₂×C₇₃	#332	1	2	yes	—
55	C₂×C₇₃	#333	1	1	yes	characteristic
56	C₂×C₇₃	#340	1	2	yes	—
57	C₂×C₇₃	#343	1	1	yes	characteristic
58	#1296	—	73	1	no	maximal, Sylow
59	C₇₃	#1296	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₄⋊C₈	—	73	2	no	—
61	#384	—	73	1	no	—
62	C₂²×C₈	—	146	2	no	—
63	C₂×C₄⋊C₄	—	73	1	no	—
64	C₂×C₄⋊C₄	—	146	2	no	—
65	C₂×C₄⋊C₄	#64408	1	1	yes	characteristic
66	C₂×C₄²	—	73	1	no	—
67	C₄⋊C₈	—	73	4	no	—
68	C₄⋊C₈	—	146	2	no	—
69	C₂²×C₄	—	2	1	no	—
70	C₂²×C₄	—	73	2	no	—
71	C₂²×C₄	—	146	1	no	—
72	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
73	C₂×C₈	—	292	2	no	—
74	C₂×C₈	—	292	2	no	—
75	C₂×C₈	—	146	4	no	—
76	C₄⋊C₄	—	4	1	no	—
77	C₄⋊C₄	—	292	1	no	—
78	C₄⋊C₄	—	292	2	no	—
79	C₄⋊C₄	—	292	2	no	—
80	C₄²	—	73	2	no	—
81	C₄²	—	73	1	no	—
82	C₄²	—	73	1	no	—
83	C₂³	C₂²⋊#64408	1	1	yes	characteristic
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	—	4	2	no	—
88	C₂×C₄	—	292	1	no	—
89	C₂×C₄	—	292	2	no	—
90	C₂×C₄	—	73	2	no	—
91	C₂×C₄	—	73	2	no	—
92	C₂×C₄	—	73	2	no	—
93	C₂×C₄	—	73	2	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	73	2	no	—
96	C₂×C₄	C₄×#64408	1	1	yes	characteristic
97	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
98	C₈	—	292	4	no	—
99	C₂²	(C₂×#64408)⋊C₄	1	1	yes	characteristic
100	C₂²	#14556651	1	1	yes	characteristic
101	C₂²	#14556652	1	1	yes	characteristic
102	C₂²	#14556653	1	2	yes	—
103	C₂²	#14556654	1	2	yes	—
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	8	1	no	—
107	C₄	—	584	1	no	—
108	C₄	—	73	2	no	—
109	C₄	—	73	2	no	—
110	C₄	—	73	2	no	—
111	C₄	—	73	2	no	—
112	C₂	#17989445	1	1	yes	characteristic
113	C₂	#17989446	1	2	yes	—
114	C₂	#17989447	1	1	yes	characteristic
115	C₂	#17989460	1	2	yes	—
116	C₂	#17989467	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556658

C₂

yes

maximal

#17988456

C₂

yes

maximal, characteristic

C₂²×#10596833

—

#14556658

—

#14556658

C₄

yes

complemented

C₂×C₄⋊Dic₇₃

C₄

yes

characteristic

C₂×#11924007

—

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

C₄

yes

—

—

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

D₄

yes

—

C₄⋊Dic₇₃

—

#11924007

—

#11924007

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

D₈

yes

—

C₂×Dic₇₃

SD₁₆

yes

—

C₂×Dic₇₃

SD₁₆

yes

—

C₂×Dic₇₃

Q₁₆

yes

—

#10596833

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₂²×C₇₃

#103

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

#102

yes

—

Dic₇₃

#103

yes

—

Dic₇₃

#106

yes

—

Dic₇₃

#107

yes

—

C₂×C₇₃

#331

yes

characteristic

C₂×C₇₃

#332

yes

—

C₂×C₇₃

#333

yes

characteristic

C₂×C₇₃

#340

yes

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

#384

—

C₂²×C₈

—

146

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄⋊C₄

#64408

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²⋊#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

292

—

C₂²

(C₂×#64408)⋊C₄

yes

characteristic

100

C₂²

#14556651

yes

characteristic

101

C₂²

#14556652

yes

characteristic

102

C₂²

#14556653

yes

—

103

C₂²

#14556654

yes

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

584

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₂

#17989445

yes

characteristic

113

C₂

#17989446

yes

—

114

C₂

#17989447

yes

characteristic

115

C₂

#17989460

yes

—

116

C₂

#17989467

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₄²
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂×C₄⋊C₄×C₇₃	C₄
socle	C₂³×C₇₃	C₂²⋊C₄
hypercenter	C₂×C₄⋊C₄	#64408
hypocenter	C₇₃	#1296
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₄²

Frattini

C₂²×C₄

C₂×#64408

Fitting

C₂×C₄⋊C₄×C₇₃

C₄

socle

C₂³×C₇₃

C₂²⋊C₄

C₂×C₄⋊C₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
5. #14556658	C₄	semidirect
59. C₇₃	#1296	semidirect

H ≅ G/N

type

5. #14556658

C₄

semidirect

59. C₇₃

#1296

semidirect

Subgroups — #22624809

Conjugacy classes of subgroups

Complements