Group #22609010 — subgroups

Subgroups — #22609010

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	#17988961	C₂	1	1	yes	maximal, characteristic
3	#17988788	C₂	1	2	yes	maximal
4	#17988317	C₂	1	2	yes	maximal, complemented
5	#333×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924017	—	2	2	no	—
7	C₂×#11924015	—	2	2	no	—
8	#14556590	—	2	2	no	—
9	#14556589	—	2	2	no	—
10	#14556588	C₂²	1	1	yes	characteristic
11	C₄×Dic₁₄₆	C₂²	1	2	yes	—
12	#14556556	—	2	2	no	—
13	#14556513	—	2	2	no	—
14	C₄×#10596831	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×Dic₁₄₆	D₄	1	2	yes	—
19	C₂×D₂₉₂	—	2	2	no	—
20	C₂×D₂₉₂	—	2	1	no	—
21	#11924017	—	4	4	no	—
22	#11924015	—	4	4	no	—
23	C₂×#10596831	—	2	1	no	—
24	C₄⋊Dic₇₃	D₄	1	2	yes	—
25	#11924007	—	2	4	no	—
26	#11924007	—	2	2	no	—
27	C₄×Dic₇₃	—	2	2	no	—
28	C₄×Dic₇₃	—	2	2	no	—
29	C₂×Q₈×C₇₃	D₄	1	2	yes	—
30	C₂×C₈×C₇₃	—	2	2	no	—
31	C₄⋊C₄×C₇₃	—	2	2	no	—
32	C₄²×C₇₃	C₂³	1	1	yes	characteristic
33	C₂²×D₇₃	—	4	1	no	—
34	Q₈×C₇₃	—	4	2	no	—
35	C₂×C₄×C₇₃	—	2	2	no	—
36	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₇₃	—	2	2	no	—
39	C₂×Dic₇₃	—	2	2	no	—
40	D₂₉₂	—	4	2	no	—
41	D₂₉₂	—	4	2	no	—
42	D₂₉₂	—	4	2	no	—
43	Dic₁₄₆	—	2	2	no	—
44	Dic₁₄₆	—	8	2	no	—
45	Dic₁₄₆	SD₁₆	1	4	yes	complemented
46	C₈×C₇₃	—	4	2	no	—
47	#10596831	—	2	2	no	—
48	C₂²×C₇₃	#120	1	1	yes	characteristic
49	C₂×D₇₃	—	8	2	no	—
50	C₂×D₇₃	—	8	1	no	—
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	#448	1	2	yes	—
58	C₂×C₇₃	#453	1	1	yes	characteristic
59	D₇₃	—	16	1	no	—
60	#1623	—	73	1	no	maximal, Sylow
61	C₇₃	#1623	1	1	yes	characteristic, complemented, Sylow
62	Q₈²	—	73	1	no	—
63	#492	—	73	1	no	—
64	#460	—	73	2	no	—
65	#333	D₇₃	1	1	yes	characteristic, complemented
66	Q₈⋊C₈	—	73	2	no	—
67	C₂×SD₁₆	—	146	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	—	73	1	no	—
73	C₄×Q₈	—	73	2	no	—
74	C₄×Q₈	—	146	2	no	—
75	C₄⋊C₈	C₂×D₇₃	1	2	yes	—
76	#102	—	146	2	no	—
77	C₄×C₈	—	73	1	no	—
78	C₂×Q₈	—	73	2	no	—
79	C₂×Q₈	—	146	2	no	—
80	C₂×Q₈	D₂₉₂	1	2	yes	—
81	C₂×D₄	—	146	2	no	—
82	C₂×D₄	—	146	1	no	—
83	SD₁₆	—	292	4	no	—
84	SD₁₆	—	292	4	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	146	1	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	—	292	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	584	2	no	—
97	Q₈	—	73	4	no	—
98	Q₈	—	146	2	no	—
99	D₄	—	292	2	no	—
100	D₄	—	292	2	no	—
101	D₄	—	292	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×D₂₉₂	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	146	2	no	—
109	C₂²	—	584	2	no	—
110	C₂²	—	584	1	no	—
111	C₂²	#14556561	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	#14556623	1	2	yes	—
118	C₂	—	1168	1	no	—
119	C₂	#17988727	1	2	yes	—
120	C₂	#17988757	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989317

C₂

yes

maximal, characteristic, complemented

#17988961

C₂

yes

maximal, characteristic

#17988788

C₂

yes

maximal

#17988317

C₂

yes

maximal, complemented

#333×C₇₃

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

characteristic

C₄×Dic₁₄₆

C₂²

yes

—

#14556556

—

#14556513

—

C₄×#10596831

C₂²

yes

characteristic

C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

#11924017

—

#11924015

—

C₂×#10596831

—

C₄⋊Dic₇₃

D₄

yes

—

#11924007

—

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

SD₁₆

yes

complemented

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#120

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×SD₁₆

yes

—

C₄×C₇₃

#137

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#448

yes

—

C₂×C₇₃

#453

yes

characteristic

D₇₃

—

#1623

—

maximal, Sylow

C₇₃

#1623

yes

characteristic, complemented, Sylow

Q₈²

—

#492

—

#460

—

#333

D₇₃

yes

characteristic, complemented

Q₈⋊C₈

—

C₂×SD₁₆

—

146

—

C₂×SD₁₆

—

146

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

—

146

—

C₄⋊Q₈

C₂×D₇₃

yes

characteristic

#127

—

C₄×Q₈

—

C₄×Q₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

—

#102

—

146

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

D₂₉₂

yes

—

C₂×D₄

—

146

—

C₂×D₄

—

146

—

SD₁₆

—

292

—

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

—

292

—

Q₈

—

Q₈

—

584

—

Q₈

—

Q₈

—

146

—

D₄

—

292

—

100

D₄

—

292

—

101

D₄

—

292

—

102

C₂×C₄

—

103

C₂×C₄

—

146

—

104

C₂×C₄

—

146

—

105

C₂×C₄

D₄×D₇₃

yes

—

106

C₂×C₄

C₂×D₂₉₂

yes

characteristic

107

C₈

—

108

C₈

—

146

—

109

C₂²

—

584

—

110

C₂²

—

584

—

111

C₂²

#14556561

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

292

—

115

C₄

—

146

—

116

C₄

SD₁₆×D₇₃

yes

—

117

C₄

#14556623

yes

—

118

C₂

—

1168

—

119

C₂

#17988727

yes

—

120

C₂

#17988757

yes

characteristic

	subgroup	G/H
center	C₂²	#14556561
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#333×C₇₃	C₂
socle	C₂²×C₇₃	#120
hypercenter	#333	D₇₃
hypocenter	C₇₃	#1623
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#14556561

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#333×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
1. #17989317	C₂	semidirect
4. #17988317	C₂	semidirect
5. #333×C₇₃	C₂	semidirect
45. Dic₁₄₆	SD₁₆	semidirect
61. C₇₃	#1623	semidirect
65. #333	D₇₃	semidirect

H ≅ G/N

type

1. #17989317

C₂

semidirect

4. #17988317

C₂

semidirect

5. #333×C₇₃

C₂

semidirect

45. Dic₁₄₆

SD₁₆

semidirect

61. C₇₃

#1623

semidirect

65. #333

D₇₃

semidirect

Subgroups — #22609010

Conjugacy classes of subgroups

Complements