Group #22609330 — subgroups

Subgroups — #22609330

Order 9344.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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	#17988992	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988877	C₂	1	2	yes	maximal
3	#17988340	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988335	C₂	1	2	yes	maximal, complemented
5	C₈×D₄×C₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556591	C₂²	1	2	yes	—
7	#14556525	—	2	1	no	—
8	#14556525	—	2	1	no	—
9	#14556522	—	2	2	no	—
10	C₄⋊#10596831	C₂²	1	2	yes	—
11	#14556512	—	2	2	no	—
12	C₂²×C₈×C₇₃	—	2	1	no	—
13	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²⋊C₈×C₇₃	—	2	1	no	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×#10596831	—	2	2	no	—
19	C₄⋊Dic₇₃	—	2	2	no	—
20	C₄⋊Dic₇₃	—	2	2	no	—
21	C₂×D₄×C₇₃	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₇₃	—	2	1	no	—
23	C₂×C₈×C₇₃	—	2	1	no	—
24	C₂×C₈×C₇₃	—	4	2	no	—
25	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
26	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
27	C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
28	C₂²⋊C₄×C₇₃	—	2	1	no	—
29	C₄²×C₇₃	C₂³	1	1	yes	characteristic
30	C₂³×C₇₃	—	2	1	no	—
31	D₄×C₇₃	—	2	1	no	—
32	D₄×C₇₃	Q₁₆	1	2	yes	—
33	C₂×C₄×C₇₃	—	2	1	no	—
34	C₂×C₄×C₇₃	—	4	1	no	—
35	C₂×C₄×C₇₃	—	4	1	no	—
36	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
39	C₂×Dic₇₃	—	4	2	no	—
40	Dic₁₄₆	—	8	2	no	—
41	C₈×C₇₃	—	2	1	no	—
42	C₈×C₇₃	—	4	1	no	—
43	C₈×C₇₃	SD₁₆	1	2	yes	—
44	#10596831	—	4	2	no	—
45	C₂²×C₇₃	—	2	2	no	—
46	C₂²×C₇₃	—	4	1	no	—
47	C₂²×C₇₃	—	4	1	no	—
48	C₂²×C₇₃	#121	1	1	yes	characteristic
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	—	4	1	no	—
51	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
52	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
53	C₄×C₇₃	#135	1	1	yes	characteristic
54	C₄×C₇₃	#137	1	1	yes	characteristic
55	Dic₇₃	—	8	2	no	—
56	C₂×C₇₃	—	4	2	no	—
57	C₂×C₇₃	#461	1	1	yes	characteristic
58	C₂×C₇₃	#467	1	1	yes	characteristic
59	C₂×C₇₃	#472	1	1	yes	characteristic
60	#1675	—	73	1	no	maximal, Sylow
61	C₇₃	#1675	1	1	yes	characteristic, complemented, Sylow
62	#500	—	73	1	no	—
63	#476	—	73	2	no	—
64	C₈×D₄	D₇₃	1	1	yes	characteristic
65	#335	—	73	1	no	—
66	#333	—	73	2	no	—
67	C₂²×C₈	—	2	1	no	—
68	C₄⋊Q₈	—	73	2	no	—
69	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
70	#107	—	146	1	no	—
71	#107	—	146	1	no	—
72	#106	—	146	2	no	—
73	C₄⋊C₈	—	73	2	no	—
74	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
75	#102	—	146	2	no	—
76	C₂²⋊C₈	—	2	1	no	—
77	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
78	C₂×Q₈	—	146	2	no	—
79	C₂×D₄	D₂₉₂	1	1	yes	characteristic
80	C₂²×C₄	—	2	1	no	—
81	C₂×C₈	—	2	1	no	—
82	C₂×C₈	—	4	2	no	—
83	C₂×C₈	—	146	2	no	—
84	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
85	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
86	C₄⋊C₄	—	146	2	no	—
87	C₄⋊C₄	—	146	2	no	—
88	C₄⋊C₄	D₂₉₂	1	1	yes	characteristic
89	C₂²⋊C₄	—	2	1	no	—
90	C₄²	C₂²×D₇₃	1	1	yes	characteristic
91	C₂³	—	2	1	no	—
92	Q₈	—	584	2	no	—
93	D₄	—	2	1	no	—
94	D₄	Dic₂₉₂	1	2	yes	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	292	2	no	—
99	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
100	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
101	C₂×C₄	#11924028	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	4	1	no	—
104	C₈	—	292	2	no	—
105	C₈	#11924016	1	2	yes	—
106	C₂²	—	2	2	no	—
107	C₂²	—	4	1	no	—
108	C₂²	—	4	1	no	—
109	C₂²	#14556565	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	4	1	no	—
112	C₄	—	584	2	no	—
113	C₄	C₂×#11924016	1	1	yes	characteristic
114	C₄	C₂×Dic₂₉₂	1	1	yes	characteristic
115	C₄	#14556613	1	1	yes	characteristic
116	C₄	#14556621	1	1	yes	characteristic
117	C₂	—	4	2	no	—
118	C₂	#17988792	1	1	yes	characteristic
119	C₂	#17988828	1	1	yes	characteristic
120	C₂	#17988857	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988992

C₂

yes

maximal, characteristic, complemented

#17988877

C₂

yes

maximal

#17988340

C₂

yes

maximal, characteristic, complemented

#17988335

C₂

yes

maximal, complemented

C₈×D₄×C₇₃

C₂

yes

maximal, characteristic

#14556591

C₂²

yes

—

—

—

—

C₂²

yes

—

#14556512

—

C₂²×C₈×C₇₃

—

C₄×D₄×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

C₂²⋊C₈×C₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂×D₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

Q₁₆

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

#41

yes

characteristic

C₂×Dic₇₃

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

SD₁₆

yes

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#121

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₄×C₇₃

C₂×Q₁₆

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#500

—

#476

—

C₈×D₄

D₇₃

yes

characteristic

#335

—

#333

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₇₃

yes

characteristic

#107

—

146

—

#107

—

146

—

#106

—

146

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₇₃

yes

characteristic

#102

—

146

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

146

—

C₂×D₄

D₂₉₂

yes

characteristic

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

D₂₉₂

yes

characteristic

C₂²⋊C₄

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

Q₈

—

584

—

D₄

—

D₄

Dic₂₉₂

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

100

C₂×C₄

C₂×D₂₉₂

yes

characteristic

101

C₂×C₄

#11924028

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

292

—

105

C₈

#11924016

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

#14556565

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

584

—

113

C₄

C₂×#11924016

yes

characteristic

114

C₄

C₂×Dic₂₉₂

yes

characteristic

115

C₄

#14556613

yes

characteristic

116

C₄

#14556621

yes

characteristic

117

C₂

—

118

C₂

#17988792

yes

characteristic

119

C₂

#17988828

yes

characteristic

120

C₂

#17988857

yes

characteristic

	subgroup	G/H
center	C₂²	#14556565
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	C₈×D₄×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	C₈×D₄	D₇₃
hypocenter	C₇₃	#1675
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

subgroup

G/H

center

C₂²

#14556565

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

C₈×D₄×C₇₃

C₂

socle

C₂²×C₇₃

#121

hypercenter

C₈×D₄

D₇₃

hypocenter

C₇₃

#1675

LCS

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×D₄

N	H ≅ G/N	type
1. #17988992	C₂	semidirect
3. #17988340	C₂	semidirect
4. #17988335	C₂	semidirect
61. C₇₃	#1675	semidirect

H ≅ G/N

type

1. #17988992

C₂

semidirect

3. #17988340

C₂

semidirect

4. #17988335

C₂

semidirect

61. C₇₃

#1675

semidirect

Subgroups — #22609330

Conjugacy classes of subgroups

Complements