Group #22609441 — subgroups

Subgroups — #22609441

Order 9344.

166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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	#17988789	C₂	1	2	yes	maximal
2	#17988666	C₂	1	1	yes	maximal, characteristic
3	#17988338	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988333	C₂	1	2	yes	maximal, complemented
5	#500×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924015	—	2	2	no	—
7	C₂×#11924011	—	2	1	no	—
8	C₄×D₂₉₂	C₂²	1	1	yes	characteristic
9	C₄⋊#10596831	C₂²	1	1	yes	characteristic
10	C₄⋊#10596831	C₂²	1	2	yes	—
11	#14556515	—	2	2	no	—
12	#14556503	—	2	1	no	—
13	C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
14	#107×C₇₃	—	2	1	no	—
15	#107×C₇₃	—	2	1	no	—
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×D₂₉₂	D₄	1	1	yes	characteristic
18	C₂×C₄×D₇₃	—	2	1	no	—
19	#11924015	—	4	4	no	—
20	#11924011	—	4	2	no	—
21	C₂×#10596831	—	2	1	no	—
22	C₂×#10596831	—	2	2	no	—
23	C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
24	#11924005	—	2	1	no	—
25	C₂×Q₈×C₇₃	—	2	2	no	—
26	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
27	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
28	C₄⋊C₄×C₇₃	—	2	2	no	—
29	C₄⋊C₄×C₇₃	—	2	2	no	—
30	C₄²×C₇₃	C₂³	1	1	yes	characteristic
31	C₂²×D₇₃	—	2	1	no	—
32	Q₈×C₇₃	—	4	2	no	—
33	Q₈×C₇₃	—	4	2	no	—
34	C₂×C₄×C₇₃	—	4	2	no	—
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₃	#41	1	1	yes	characteristic
38	C₂×Dic₇₃	—	2	1	no	—
39	D₂₉₂	—	2	2	no	—
40	C₄×D₇₃	—	4	1	no	—
41	C₄×D₇₃	—	4	1	no	—
42	C₈×C₇₃	—	2	1	no	—
43	C₈×C₇₃	SD₁₆	1	2	yes	complemented
44	#10596831	—	4	1	no	—
45	#10596831	—	4	2	no	—
46	C₂²×C₇₃	#121	1	1	yes	characteristic
47	C₂×D₇₃	—	4	1	no	—
48	C₂×D₇₃	—	4	1	no	—
49	C₂×D₇₃	—	4	1	no	—
50	C₄×C₇₃	—	2	1	no	—
51	C₄×C₇₃	—	8	2	no	—
52	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
53	C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
54	C₄×C₇₃	#137	1	1	yes	characteristic
55	Dic₇₃	—	4	1	no	—
56	C₂×C₇₃	#461	1	1	yes	characteristic
57	C₂×C₇₃	#469	1	1	yes	characteristic
58	C₂×C₇₃	#473	1	1	yes	characteristic
59	D₇₃	—	8	1	no	—
60	#1693	—	73	1	no	maximal, Sylow
61	C₇₃	#1693	1	1	yes	characteristic, complemented, Sylow
62	#500	D₇₃	1	1	yes	characteristic, complemented
63	#461	—	73	2	no	—
64	#436	—	73	1	no	—
65	#334	—	73	1	no	—
66	#332	—	73	2	no	—
67	C₂×SD₁₆	—	146	2	no	—
68	C₂×M₁₆	—	146	1	no	—
69	C₄⋊Q₈	C₂×D₇₃	1	2	yes	—
70	C₄×D₄	—	73	1	no	—
71	#107	—	2	1	no	—
72	#107	—	2	1	no	—
73	C₄⋊C₈	—	73	1	no	—
74	C₄⋊C₈	—	73	2	no	—
75	#103	—	146	2	no	—
76	C₂²⋊C₈	—	146	1	no	—
77	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
78	C₂×Q₈	—	2	2	no	—
79	C₂×D₄	—	73	1	no	—
80	C₂²×C₄	—	146	1	no	—
81	SD₁₆	—	292	4	no	—
82	M₁₆	—	292	2	no	—
83	C₂×C₈	—	146	2	no	—
84	C₂×C₈	—	146	1	no	—
85	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
86	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	73	1	no	—
90	C₂²⋊C₄	—	146	1	no	—
91	C₄²	C₂²×D₇₃	1	1	yes	characteristic
92	C₂³	—	146	1	no	—
93	Q₈	—	4	2	no	—
94	Q₈	—	4	2	no	—
95	D₄	—	146	2	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	292	1	no	—
98	C₂×C₄	—	292	1	no	—
99	C₂×C₄	—	146	1	no	—
100	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
101	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
102	C₂×C₄	#11924027	1	1	yes	characteristic
103	C₈	—	2	1	no	—
104	C₈	—	292	1	no	—
105	C₈	—	292	2	no	—
106	C₈	#11924015	1	2	yes	complemented
107	C₂²	—	292	1	no	—
108	C₂²	—	292	1	no	—
109	C₂²	—	292	1	no	—
110	C₂²	#14556562	1	1	yes	characteristic
111	C₄	—	2	1	no	—
112	C₄	—	8	2	no	—
113	C₄	—	292	1	no	—
114	C₄	C₂×#11924015	1	1	yes	characteristic
115	C₄	#14556615	1	2	yes	—
116	C₄	#14556622	1	1	yes	characteristic
117	C₂	—	584	1	no	—
118	C₂	#17988789	1	1	yes	characteristic
119	C₂	#17988837	1	1	yes	characteristic
120	C₂	#17988859	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988789

C₂

yes

maximal

#17988666

C₂

yes

maximal, characteristic

#17988338

C₂

yes

maximal, characteristic, complemented

#17988333

C₂

yes

maximal, complemented

#500×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924015

—

C₂×#11924011

—

C₄×D₂₉₂

C₂²

yes

characteristic

C₄⋊#10596831

C₂²

yes

characteristic

C₄⋊#10596831

C₂²

yes

—

#14556515

—

#14556503

—

C₄⋊Q₈×C₇₃

C₂²

yes

—

#107×C₇₃

—

#107×C₇₃

—

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×D₂₉₂

D₄

yes

characteristic

C₂×C₄×D₇₃

—

—

—

—

—

C₄⋊Dic₇₃

D₄

yes

characteristic

#11924005

—

C₂×Q₈×C₇₃

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

—

Q₈×C₇₃

—

Q₈×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

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

C₈×C₇₃

SD₁₆

yes

complemented

#10596831

—

#10596831

—

C₂²×C₇₃

#121

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₄×C₇₃

#137

yes

characteristic

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1693

—

maximal, Sylow

C₇₃

#1693

yes

characteristic, complemented, Sylow

#500

D₇₃

yes

characteristic, complemented

—

—

—

—

C₂×SD₁₆

—

146

—

C₂×M₁₆

—

146

—

C₄⋊Q₈

C₂×D₇₃

yes

—

C₄×D₄

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

146

—

C₂²⋊C₈

—

146

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

146

—

SD₁₆

—

292

—

M₁₆

—

292

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

146

—

Q₈

—

Q₈

—

D₄

—

146

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

100

C₂×C₄

D₄×D₇₃

yes

characteristic

101

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

102

C₂×C₄

#11924027

yes

characteristic

103

C₈

—

104

C₈

—

292

—

105

C₈

—

292

—

106

C₈

#11924015

yes

complemented

107

C₂²

—

292

—

108

C₂²

—

292

—

109

C₂²

—

292

—

110

C₂²

#14556562

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

292

—

114

C₄

C₂×#11924015

yes

characteristic

115

C₄

#14556615

yes

—

116

C₄

#14556622

yes

characteristic

117

C₂

—

584

—

118

C₂

#17988789

yes

characteristic

119

C₂

#17988837

yes

characteristic

120

C₂

#17988859

yes

characteristic

	subgroup	G/H
center	C₂²	#14556562
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#500×C₇₃	C₂
socle	C₂²×C₇₃	#121
hypercenter	#500	D₇₃
hypocenter	C₇₃	#1693
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#14556562

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#500×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
3. #17988338	C₂	semidirect
4. #17988333	C₂	semidirect
5. #500×C₇₃	C₂	semidirect
43. C₈×C₇₃	SD₁₆	semidirect
61. C₇₃	#1693	semidirect
62. #500	D₇₃	semidirect
106. C₈	#11924015	semidirect

H ≅ G/N

type

3. #17988338

C₂

semidirect

4. #17988333

C₂

semidirect

5. #500×C₇₃

C₂

semidirect

43. C₈×C₇₃

SD₁₆

semidirect

61. C₇₃

#1693

semidirect

62. #500

D₇₃

semidirect

106. C₈

#11924015

semidirect

Subgroups — #22609441

Conjugacy classes of subgroups

Complements