Group #22610039 — subgroups

Subgroups — #22610039

Order 9344.

296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556506	C₂	1	2	yes	maximal
2	#17988353	C₂	1	4	yes	maximal, complemented
3	#518×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊Dic₇₃	C₂²	1	4	yes	—
5	#14556506	—	2	4	no	—
6	C₂²×D₄×C₇₃	C₂²	1	1	yes	characteristic
7	C₄×D₄×C₇₃	—	2	4	no	—
8	#117×C₇₃	C₄	1	2	yes	complemented
9	C₂×C₂²⋊C₄×C₇₃	C₄	1	2	yes	complemented
10	C₂×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
11	C₂²×Dic₇₃	—	2	4	no	—
12	C₂²⋊Dic₇₃	—	2	4	no	—
13	C₂²⋊Dic₇₃	—	2	4	no	—
14	C₂⁴×C₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂⁴×C₇₃	C₂³	1	1	yes	characteristic
16	C₂×D₄×C₇₃	—	2	4	no	—
17	C₂×D₄×C₇₃	D₄	1	4	yes	—
18	C₂²×C₄×C₇₃	—	2	2	no	—
19	C₂²×C₄×C₇₃	—	2	2	no	—
20	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₇₃	—	2	2	no	—
22	C₂²⋊C₄×C₇₃	—	2	2	no	—
23	C₂²⋊C₄×C₇₃	—	2	2	no	—
24	C₂²⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
25	C₄²×C₇₃	—	2	2	no	—
26	C₂³×C₇₃	—	2	2	no	—
27	C₂³×C₇₃	—	8	1	no	—
28	C₂³×C₇₃	—	8	1	no	—
29	C₂³×C₇₃	C₂²⋊C₄	1	2	yes	—
30	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	C₂³×C₇₃	C₂×D₄	1	2	yes	—
32	C₂³×C₇₃	#41	1	4	yes	—
33	D₄×C₇₃	—	2	8	no	—
34	C₂×C₄×C₇₃	—	2	2	no	—
35	C₂×C₄×C₇₃	—	2	4	no	—
36	C₂×C₄×C₇₃	—	8	2	no	—
37	C₂×C₄×C₇₃	—	8	2	no	—
38	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₇₃	—	4	4	no	—
40	C₂×Dic₇₃	—	8	4	no	—
41	C₂²×C₇₃	—	2	2	no	—
42	C₂²×C₇₃	—	4	4	no	—
43	C₂²×C₇₃	—	4	2	no	—
44	C₂²×C₇₃	—	4	1	no	—
45	C₂²×C₇₃	—	4	2	no	—
46	C₂²×C₇₃	—	8	2	no	—
47	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₇₃	#117	1	2	yes	—
49	C₂²×C₇₃	#123	1	4	yes	—
50	C₄×C₇₃	—	2	2	no	—
51	C₄×C₇₃	—	4	4	no	—
52	Dic₇₃	—	8	4	no	—
53	C₂×C₇₃	—	2	4	no	—
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	—	2	2	no	—
56	C₂×C₇₃	—	4	2	no	—
57	C₂×C₇₃	#381	1	1	yes	characteristic
58	#1828	—	73	1	no	maximal, Sylow
59	C₇₃	#1828	1	1	yes	characteristic, complemented, Sylow
60	#518	D₇₃	1	1	yes	characteristic
61	C₂×#99	—	73	2	no	—
62	#342	—	73	4	no	—
63	C₂²×D₄	C₂×D₇₃	1	1	yes	characteristic
64	C₄×D₄	—	2	4	no	—
65	#117	Dic₇₃	1	2	yes	complemented
66	C₂×C₂²⋊C₄	—	73	4	no	—
67	C₂×C₂²⋊C₄	Dic₇₃	1	2	yes	complemented
68	C₂×C₂²⋊C₄	C₂×D₇₃	1	2	yes	—
69	#99	—	146	4	no	—
70	C₂⁴	C₂×Dic₇₃	1	1	yes	characteristic
71	C₂⁴	C₂²×D₇₃	1	1	yes	characteristic
72	C₂×D₄	—	2	4	no	—
73	C₂×D₄	C₂²⋊D₇₃	1	4	yes	—
74	C₂²×C₄	—	2	2	no	—
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	—	146	4	no	—
77	C₂²×C₄	C₂×Dic₇₃	1	1	yes	characteristic
78	C₄⋊C₄	—	2	2	no	—
79	C₂²⋊C₄	—	2	2	no	—
80	C₂²⋊C₄	—	2	2	no	—
81	C₂²⋊C₄	—	146	4	no	—
82	C₂²⋊C₄	—	146	4	no	—
83	C₂²⋊C₄	C₂×Dic₇₃	1	4	yes	—
84	C₄²	—	2	2	no	—
85	C₂³	—	2	2	no	—
86	C₂³	—	8	1	no	—
87	C₂³	—	8	1	no	—
88	C₂³	C₂²⋊Dic₇₃	1	2	yes	—
89	C₂³	C₂²×Dic₇₃	1	1	yes	characteristic
90	C₂³	C₂×C₂²⋊D₇₃	1	2	yes	—
91	C₂³	#11924028	1	4	yes	—
92	D₄	—	2	8	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	8	2	no	—
96	C₂×C₄	—	8	2	no	—
97	C₂×C₄	—	292	4	no	—
98	C₂×C₄	—	584	4	no	—
99	C₂×C₄	C₂²⋊Dic₇₃	1	2	yes	—
100	C₂²	—	2	2	no	—
101	C₂²	—	4	2	no	—
102	C₂²	—	4	4	no	—
103	C₂²	—	4	1	no	—
104	C₂²	—	4	2	no	—
105	C₂²	—	8	2	no	—
106	C₂²	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
107	C₂²	#14556550	1	2	yes	—
108	C₂²	#14556574	1	4	yes	—
109	C₄	—	2	2	no	—
110	C₄	—	4	4	no	—
111	C₄	—	584	4	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	4	no	—
114	C₂	—	2	2	no	—
115	C₂	—	4	2	no	—
116	C₂	#17988450	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556506

C₂

yes

maximal

#17988353

C₂

yes

maximal, complemented

#518×C₇₃

C₂

yes

maximal, characteristic

C₂×C₂²⋊Dic₇₃

C₂²

yes

—

#14556506

—

C₂²×D₄×C₇₃

C₂²

yes

characteristic

C₄×D₄×C₇₃

—

#117×C₇₃

C₄

yes

complemented

C₂×C₂²⋊C₄×C₇₃

C₄

yes

complemented

C₂×C₂²⋊C₄×C₇₃

C₂²

yes

—

C₂²×Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₂⁴×C₇₃

C₂×C₄

yes

characteristic

C₂⁴×C₇₃

C₂³

yes

characteristic

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂²⋊C₄

yes

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂³×C₇₃

C₂×D₄

yes

—

C₂³×C₇₃

#41

yes

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

#117

yes

—

C₂²×C₇₃

#123

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#518

D₇₃

yes

characteristic

C₂×#99

—

#342

—

C₂²×D₄

C₂×D₇₃

yes

characteristic

C₄×D₄

—

#117

Dic₇₃

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

Dic₇₃

yes

complemented

C₂×C₂²⋊C₄

C₂×D₇₃

yes

—

#99

—

146

—

C₂⁴

C₂×Dic₇₃

yes

characteristic

C₂⁴

C₂²×D₇₃

yes

characteristic

C₂×D₄

—

C₂×D₄

C₂²⋊D₇₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂×Dic₇₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₂²⋊C₄

C₂×Dic₇₃

yes

—

C₄²

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊Dic₇₃

yes

—

C₂³

C₂²×Dic₇₃

yes

characteristic

C₂³

C₂×C₂²⋊D₇₃

yes

—

C₂³

#11924028

yes

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

C₂²⋊Dic₇₃

yes

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂×C₂²⋊Dic₇₃

yes

characteristic

107

C₂²

#14556550

yes

—

108

C₂²

#14556574

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

584

—

112

C₂

—

113

C₂

—

114

C₂

—

115

C₂

—

116

C₂

#17988450

yes

characteristic

	subgroup	G/H
center	C₂	#17988450
commutator	C₂³×C₇₃	C₂²×C₄
Frattini	C₂⁴	C₂²×D₇₃
Fitting	#518×C₇₃	C₂
socle	C₂×C₇₃	#381
hypercenter	#518	D₇₃
hypocenter	C₇₃	#1828
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #518

subgroup

G/H

center

C₂

#17988450

commutator

C₂³×C₇₃

C₂²×C₄

Frattini

C₂⁴

C₂²×D₇₃

Fitting

#518×C₇₃

C₂

C₂×C₇₃

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂⁴ ◁ #518

N	H ≅ G/N	type
2. #17988353	C₂	semidirect
8. #117×C₇₃	C₄	semidirect
9. C₂×C₂²⋊C₄×C₇₃	C₄	semidirect
59. C₇₃	#1828	semidirect
65. #117	Dic₇₃	semidirect
67. C₂×C₂²⋊C₄	Dic₇₃	semidirect

H ≅ G/N

type

2. #17988353

C₂

semidirect

8. #117×C₇₃

C₄

semidirect

9. C₂×C₂²⋊C₄×C₇₃

C₄

semidirect

59. C₇₃

#1828

semidirect

65. #117

Dic₇₃

semidirect

67. C₂×C₂²⋊C₄

Dic₇₃

semidirect

Subgroups — #22610039

Conjugacy classes of subgroups

Complements