Group #22612093 — subgroups

Subgroups — #22612093

Order 9344.

124 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 49 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	#17988988	C₂	1	1	yes	maximal, characteristic
2	Q₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	#17988415	C₂	1	1	yes	maximal, characteristic
4	#17988412	C₂	1	1	yes	maximal, characteristic
5	#17988405	C₂	1	1	yes	maximal, characteristic
6	#17988391	C₂	1	1	yes	maximal, characteristic
7	#358×C₇₃	C₂	1	1	yes	maximal, characteristic
8	#14556582	—	2	1	no	—
9	Q₈×Dic₇₃	—	2	1	no	—
10	C₂×#11924003	C₂²	1	1	yes	characteristic
11	#14556525	C₂²	1	1	yes	characteristic
12	#14556525	C₂²	1	1	yes	characteristic
13	#14556522	—	2	1	no	—
14	#14556515	—	2	1	no	—
15	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
18	#107×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#10596831	D₄	1	1	yes	characteristic
20	C₄⋊Dic₇₃	—	2	1	no	—
21	C₄⋊Dic₇₃	—	2	1	no	—
22	C₄⋊Dic₇₃	—	4	1	no	—
23	C₄⋊Dic₇₃	—	4	1	no	—
24	#11924007	—	4	1	no	—
25	C₄×Dic₇₃	—	4	1	no	—
26	C₄×Dic₇₃	D₄	1	1	yes	characteristic
27	#11924003	—	2	1	no	—
28	C₂×Q₈×C₇₃	—	2	1	no	—
29	Q₁₆×C₇₃	—	2	1	no	—
30	Q₁₆×C₇₃	Q₈	1	2	yes	—
31	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
32	C₄⋊C₄×C₇₃	—	2	1	no	—
33	C₁₆×C₇₃	—	2	1	no	—
34	Q₈×C₇₃	—	2	2	no	—
35	Q₈×C₇₃	—	4	1	no	—
36	C₂×C₄×C₇₃	—	4	1	no	—
37	C₂×C₄×C₇₃	—	4	1	no	—
38	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₇₃	—	4	1	no	—
40	C₂×Dic₇₃	—	4	1	no	—
41	C₂×Dic₇₃	D₈	1	1	yes	characteristic
42	C₂×Dic₇₃	D₈	1	1	yes	characteristic
43	C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
44	C₈×C₇₃	#41	1	1	yes	characteristic
45	#10596831	—	2	1	no	—
46	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
47	C₄×C₇₃	—	4	2	no	—
48	C₄×C₇₃	—	8	1	no	—
49	C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
50	C₄×C₇₃	#137	1	1	yes	characteristic
51	Dic₇₃	—	2	1	no	—
52	Dic₇₃	—	2	1	no	—
53	Dic₇₃	—	8	1	no	—
54	Dic₇₃	—	8	1	no	—
55	C₂×C₇₃	#474	1	1	yes	characteristic
56	C₂×C₇₃	#508	1	1	yes	characteristic
57	C₂×C₇₃	#510	1	1	yes	characteristic
58	#2229	—	73	1	no	maximal, Sylow
59	C₇₃	#2229	1	1	yes	characteristic, complemented, Sylow
60	#499	—	73	1	no	—
61	C₄×Q₁₆	—	73	1	no	—
62	#367	—	73	1	no	—
63	#366	—	73	1	no	—
64	C₄⋊C₁₆	—	73	1	no	—
65	#358	—	73	1	no	—
66	#358	D₇₃	1	1	yes	characteristic
67	C₂×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
68	#125	—	146	1	no	—
69	C₄×Q₈	—	146	1	no	—
70	C₂×C₁₆	—	73	1	no	—
71	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
72	#107	—	73	1	no	—
73	#107	—	73	1	no	—
74	#107	C₂×D₇₃	1	1	yes	characteristic
75	#106	—	146	1	no	—
76	#103	—	146	1	no	—
77	C₄×C₈	—	73	1	no	—
78	C₂×Q₈	—	2	1	no	—
79	Q₁₆	—	2	1	no	—
80	Q₁₆	Dic₁₄₆	1	2	yes	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	292	1	no	—
85	C₄⋊C₄	—	292	1	no	—
86	C₄⋊C₄	—	292	1	no	—
87	C₄⋊C₄	—	146	1	no	—
88	C₄⋊C₄	—	146	1	no	—
89	C₄²	—	292	1	no	—
90	C₄²	—	73	1	no	—
91	C₁₆	—	2	1	no	—
92	C₁₆	—	146	1	no	—
93	Q₈	—	2	2	no	—
94	Q₈	—	4	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	292	1	no	—
98	C₂×C₄	—	292	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
102	C₈	—	146	1	no	—
103	C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
104	C₈	#11924027	1	1	yes	characteristic
105	C₂²	D₈×D₇₃	1	1	yes	characteristic
106	C₄	—	4	2	no	—
107	C₄	—	8	1	no	—
108	C₄	—	584	1	no	—
109	C₄	—	584	1	no	—
110	C₄	—	146	1	no	—
111	C₄	—	146	1	no	—
112	C₄	#14556568	1	1	yes	characteristic
113	C₄	#14556620	1	1	yes	characteristic
114	C₂	#17988865	1	1	yes	characteristic
115	C₂	#17989018	1	1	yes	characteristic
116	C₂	#17989029	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988988

C₂

yes

maximal, characteristic

Q₁₆×Dic₇₃

C₂

yes

maximal, characteristic

#17988415

C₂

yes

maximal, characteristic

#17988412

C₂

yes

maximal, characteristic

#17988405

C₂

yes

maximal, characteristic

#17988391

C₂

yes

maximal, characteristic

#358×C₇₃

C₂

yes

maximal, characteristic

#14556582

—

Q₈×Dic₇₃

—

C₂×#11924003

C₂²

yes

characteristic

#14556525

C₂²

yes

characteristic

#14556525

C₂²

yes

characteristic

#14556522

—

#14556515

—

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×Q₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

#107×C₇₃

C₂²

yes

characteristic

C₂×#10596831

D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

characteristic

#11924003

—

C₂×Q₈×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

Q₈

yes

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₁₆×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₂×Dic₇₃

D₈

yes

characteristic

C₈×C₇₃

C₂×Q₈

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

C₄×C₇₃

#137

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#499

—

C₄×Q₁₆

—

#367

—

#366

—

C₄⋊C₁₆

—

#358

—

#358

D₇₃

yes

characteristic

C₂×Q₁₆

C₂×D₇₃

yes

characteristic

#125

—

146

—

C₄×Q₈

—

146

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

—

—

C₂×D₇₃

yes

characteristic

#106

—

146

—

#103

—

146

—

C₄×C₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

Dic₁₄₆

yes

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄²

—

292

—

C₄²

—

C₁₆

—

C₁₆

—

146

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

D₄×D₇₃

yes

characteristic

102

C₈

—

146

—

103

C₈

C₂×Dic₁₄₆

yes

characteristic

104

C₈

#11924027

yes

characteristic

105

C₂²

D₈×D₇₃

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

584

—

109

C₄

—

584

—

110

C₄

—

146

—

111

C₄

—

146

—

112

C₄

#14556568

yes

characteristic

113

C₄

#14556620

yes

characteristic

114

C₂

#17988865

yes

characteristic

115

C₂

#17989018

yes

characteristic

116

C₂

#17989029

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₃
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#358×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#358	D₇₃
hypocenter	C₇₃	#2229
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₇₃

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#358×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
59. C₇₃	#2229	semidirect

H ≅ G/N

type

59. C₇₃

#2229

semidirect

Subgroups — #22612093

Conjugacy classes of subgroups

Complements