Group #22609007 — subgroups

Subgroups — #22609007

Order 9344.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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	#17989317	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988784	C₂	1	2	yes	maximal
3	#17988336	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988319	C₂	1	2	yes	maximal, complemented
5	#492×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924016	—	2	2	no	—
7	#14556590	—	2	2	no	—
8	#14556589	—	2	2	no	—
9	C₄×Dic₁₄₆	C₂²	1	2	yes	—
10	#14556556	—	2	2	no	—
11	C₄⋊#10596831	C₂²	1	2	yes	—
12	#14556512	—	2	2	no	—
13	C₂×SD₁₆×C₇₃	—	2	2	no	—
14	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	#127×C₇₃	C₂²	1	1	yes	characteristic
16	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×Dic₁₄₆	D₄	1	2	yes	—
19	#11924016	—	4	4	no	—
20	C₂×#10596831	—	2	2	no	—
21	C₄⋊Dic₇₃	D₄	1	2	yes	—
22	#11924007	—	2	4	no	—
23	#11924007	—	2	2	no	—
24	C₄×Dic₇₃	—	2	2	no	—
25	C₄×Dic₇₃	—	2	2	no	—
26	C₂×Q₈×C₇₃	D₄	1	2	yes	—
27	C₂×D₄×C₇₃	—	2	1	no	—
28	C₂×D₄×C₇₃	—	2	2	no	—
29	SD₁₆×C₇₃	—	4	4	no	—
30	C₂×C₈×C₇₃	—	2	1	no	—
31	C₄⋊C₄×C₇₃	—	2	2	no	—
32	C₄²×C₇₃	C₂³	1	1	yes	characteristic
33	C₂³×C₇₃	—	4	1	no	—
34	Q₈×C₇₃	—	4	2	no	—
35	D₄×C₇₃	—	4	2	no	—
36	D₄×C₇₃	—	4	2	no	—
37	D₄×C₇₃	—	4	2	no	—
38	C₂×C₄×C₇₃	—	2	2	no	—
39	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₇₃	—	2	2	no	—
42	C₂×Dic₇₃	—	2	2	no	—
43	Dic₁₄₆	—	2	2	no	—
44	Dic₁₄₆	—	8	2	no	—
45	Dic₁₄₆	SD₁₆	1	4	yes	complemented
46	C₈×C₇₃	—	2	2	no	—
47	#10596831	—	4	2	no	—
48	C₂²×C₇₃	—	8	2	no	—
49	C₂²×C₇₃	—	8	1	no	—
50	C₂²×C₇₃	#120	1	1	yes	characteristic
51	C₄×C₇₃	—	2	1	no	—
52	C₄×C₇₃	—	4	2	no	—
53	C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
54	C₄×C₇₃	#137	1	2	yes	—
55	Dic₇₃	—	2	4	no	—
56	Dic₇₃	—	4	2	no	—
57	C₂×C₇₃	—	16	1	no	—
58	C₂×C₇₃	#448	1	2	yes	—
59	C₂×C₇₃	#453	1	1	yes	characteristic
60	#1623	—	73	1	no	maximal, Sylow
61	C₇₃	#1623	1	1	yes	characteristic, complemented, Sylow
62	Q₈²	—	73	1	no	—
63	#492	D₇₃	1	1	yes	characteristic
64	#460	—	73	2	no	—
65	#333	—	73	1	no	—
66	Q₈⋊C₈	—	73	2	no	—
67	C₂×SD₁₆	—	2	2	no	—
68	C₂×SD₁₆	—	146	2	no	—
69	C₄⋊Q₈	—	146	2	no	—
70	C₄⋊Q₈	—	146	2	no	—
71	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
72	#127	C₂×D₇₃	1	1	yes	characteristic
73	C₄×Q₈	—	73	2	no	—
74	C₄×Q₈	—	146	2	no	—
75	C₄⋊C₈	—	73	2	no	—
76	#102	—	146	2	no	—
77	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
78	C₂×Q₈	—	73	2	no	—
79	C₂×Q₈	—	146	2	no	—
80	C₂×Q₈	C₂²⋊D₇₃	1	2	yes	—
81	C₂×D₄	—	2	2	no	—
82	C₂×D₄	—	2	1	no	—
83	SD₁₆	—	4	4	no	—
84	SD₁₆	—	292	4	no	—
85	C₂×C₈	—	2	1	no	—
86	C₂×C₈	—	146	2	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	73	2	no	—
89	C₄⋊C₄	—	146	4	no	—
90	C₄⋊C₄	—	146	2	no	—
91	C₄²	—	146	2	no	—
92	C₄²	—	146	2	no	—
93	C₄²	C₂²×D₇₃	1	1	yes	characteristic
94	C₂³	—	4	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	584	2	no	—
97	Q₈	—	73	4	no	—
98	Q₈	—	146	2	no	—
99	D₄	—	4	2	no	—
100	D₄	—	4	2	no	—
101	D₄	—	4	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	146	2	no	—
104	C₂×C₄	—	146	2	no	—
105	C₂×C₄	D₄×D₇₃	1	2	yes	—
106	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
107	C₈	—	2	2	no	—
108	C₈	—	292	2	no	—
109	C₂²	—	8	2	no	—
110	C₂²	—	8	1	no	—
111	C₂²	#14556559	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	4	2	no	—
114	C₄	—	292	2	no	—
115	C₄	—	146	4	no	—
116	C₄	SD₁₆×D₇₃	1	2	yes	—
117	C₄	#14556620	1	2	yes	—
118	C₂	—	16	1	no	—
119	C₂	#17988724	1	2	yes	—
120	C₂	#17988754	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989317

C₂

yes

maximal, characteristic, complemented

#17988784

C₂

yes

maximal

#17988336

C₂

yes

maximal, characteristic, complemented

#17988319

C₂

yes

maximal, complemented

#492×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924016

—

#14556590

—

#14556589

—

C₄×Dic₁₄₆

C₂²

yes

—

#14556556

—

C₄⋊#10596831

C₂²

yes

—

#14556512

—

C₂×SD₁₆×C₇₃

—

C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

#127×C₇₃

C₂²

yes

characteristic

C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

#11924016

—

C₂×#10596831

—

C₄⋊Dic₇₃

D₄

yes

—

#11924007

—

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

SD₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

SD₁₆

yes

complemented

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#120

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×SD₁₆

yes

—

C₄×C₇₃

#137

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#448

yes

—

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

Q₈²

—

#492

D₇₃

yes

characteristic

#460

—

#333

—

Q₈⋊C₈

—

C₂×SD₁₆

—

C₂×SD₁₆

—

146

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

C₂×D₇₃

yes

characteristic

#127

C₂×D₇₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

146

—

C₄⋊C₈

—

#102

—

146

—

C₄×C₈

C₂×D₇₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

C₂²⋊D₇₃

yes

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

SD₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

146

—

C₄²

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

584

—

Q₈

—

Q₈

—

146

—

D₄

—

100

D₄

—

101

D₄

—

102

C₂×C₄

—

103

C₂×C₄

—

146

—

104

C₂×C₄

—

146

—

105

C₂×C₄

D₄×D₇₃

yes

—

106

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

107

C₈

—

108

C₈

—

292

—

109

C₂²

—

110

C₂²

—

111

C₂²

#14556559

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

292

—

115

C₄

—

146

—

116

C₄

SD₁₆×D₇₃

yes

—

117

C₄

#14556620

yes

—

118

C₂

—

119

C₂

#17988724

yes

—

120

C₂

#17988754

yes

characteristic

	subgroup	G/H
center	C₂²	#14556559
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#492×C₇₃	C₂
socle	C₂²×C₇₃	#120
hypercenter	#492	D₇₃
hypocenter	C₇₃	#1623
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#14556559

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#492×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
1. #17989317	C₂	semidirect
3. #17988336	C₂	semidirect
4. #17988319	C₂	semidirect
45. Dic₁₄₆	SD₁₆	semidirect
61. C₇₃	#1623	semidirect

H ≅ G/N

type

1. #17989317

C₂

semidirect

3. #17988336

C₂

semidirect

4. #17988319

C₂

semidirect

45. Dic₁₄₆

SD₁₆

semidirect

61. C₇₃

#1623

semidirect

Subgroups — #22609007

Conjugacy classes of subgroups

Complements