Group #22627010 — subgroups

Subgroups — #22627010

Order 9344.

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

normal subgroups only

This group has 132 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	C₂×#14556688	C₂	1	1	yes	maximal, characteristic
2	#17989706	C₂	1	1	yes	maximal, characteristic
3	#17989553	C₂	1	1	yes	maximal, characteristic
4	#14556688	—	2	1	no	—
5	#14556688	—	2	1	no	—
6	#14556688	—	2	1	no	—
7	#14556687	C₄	1	2	yes	complemented
8	#14556686	—	2	1	no	—
9	C₂×#11924040	C₄	1	2	yes	complemented
10	C₂×#11924036	C₂²	1	1	yes	characteristic
11	#14556670	C₄	1	1	yes	characteristic
12	#14556645	—	2	1	no	—
13	C₈×#64408	—	2	1	no	—
14	M₁₆×D₇₃	C₄	1	1	yes	characteristic
15	#11924040	—	2	2	no	—
16	#11924040	—	2	2	no	—
17	#11924036	D₄	1	1	yes	characteristic
18	#11924036	D₄	1	1	yes	characteristic
19	#11924036	D₄	1	1	yes	characteristic
20	#11924036	Q₈	1	1	yes	characteristic
21	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
22	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
23	C₄⋊#64408	—	2	1	no	—
24	C₂²⋊#64408	C₈	1	2	yes	—
25	C₄×#64408	—	2	1	no	—
26	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
27	#11924012	C₈	1	1	yes	characteristic
28	#11924011	—	2	1	no	—
29	C₈×D₇₃	—	2	1	no	—
30	M₁₆×C₇₃	C₈	1	1	yes	characteristic
31	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
32	C₂×#64408	—	2	2	no	—
33	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
34	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
35	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₄×D₇₃	M₁₆	1	1	yes	characteristic
38	C₄×D₇₃	M₁₆	1	1	yes	characteristic
39	#10596833	C₂²⋊C₄	1	1	yes	characteristic
40	#10596833	C₂²⋊C₄	1	1	yes	characteristic
41	#10596833	C₄⋊C₄	1	1	yes	characteristic
42	#10596833	C₄⋊C₄	1	1	yes	characteristic
43	C₈×C₇₃	—	2	1	no	—
44	#10596831	—	2	1	no	—
45	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
46	C₂×D₇₃	—	4	1	no	—
47	C₂×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
48	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
49	#64408	—	4	2	no	—
50	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
52	Dic₇₃	#95	1	1	yes	characteristic
53	Dic₇₃	#97	1	1	yes	characteristic
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	#336	1	1	yes	characteristic
56	D₇₃	—	2	1	no	—
57	D₇₃	—	2	1	no	—
58	#1378	—	73	1	no	maximal, Sylow
59	C₇₃	#1378	1	1	yes	characteristic, complemented, Sylow
60	C₂×M₃₂	—	73	1	no	—
61	C₂×M₃₂	—	73	1	no	—
62	#405	—	73	1	no	—
63	C₂×M₁₆	—	73	1	no	—
64	C₂²×C₈	—	73	1	no	—
65	#117	—	73	1	no	—
66	M₃₂	—	73	2	no	—
67	M₃₂	—	146	1	no	—
68	M₃₂	—	146	1	no	—
69	M₃₂	—	146	1	no	—
70	C₂×C₁₆	—	73	2	no	—
71	C₂×C₁₆	—	146	1	no	—
72	#97	—	146	1	no	—
73	C₄×C₈	—	146	1	no	—
74	C₂²×C₄	—	73	1	no	—
75	M₁₆	—	73	1	no	—
76	M₁₆	—	146	1	no	—
77	M₁₆	#10596842	1	1	yes	characteristic
78	C₂×C₈	—	73	1	no	—
79	C₂×C₈	—	73	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	146	1	no	—
85	C₄⋊C₄	—	146	1	no	—
86	C₂²⋊C₄	—	73	2	no	—
87	C₄²	—	146	1	no	—
88	C₁₆	—	146	2	no	—
89	C₁₆	—	146	2	no	—
90	C₂³	—	73	1	no	—
91	C₂×C₄	—	73	1	no	—
92	C₂×C₄	—	73	1	no	—
93	C₂×C₄	—	73	1	no	—
94	C₂×C₄	—	73	1	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
98	C₈	—	2	1	no	—
99	C₈	—	73	1	no	—
100	C₈	—	73	1	no	—
101	C₈	—	73	1	no	—
102	C₈	—	73	1	no	—
103	C₈	—	146	1	no	—
104	C₂²	—	292	1	no	—
105	C₂²	—	73	1	no	—
106	C₂²	—	73	1	no	—
107	C₂²	C₄×#10596842	1	1	yes	characteristic
108	C₄	—	292	2	no	—
109	C₄	—	73	1	no	—
110	C₄	—	73	1	no	—
111	C₄	C₂²⋊#10596842	1	1	yes	characteristic
112	C₄	C₄⋊#10596842	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	146	1	no	—
115	C₂	—	146	1	no	—
116	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556688

C₂

yes

maximal, characteristic

#17989706

C₂

yes

maximal, characteristic

#17989553

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

complemented

#14556686

—

C₂×#11924040

C₄

yes

complemented

C₂×#11924036

C₂²

yes

characteristic

#14556670

C₄

yes

characteristic

#14556645

—

C₈×#64408

—

M₁₆×D₇₃

C₄

yes

—

—

D₄

yes

characteristic

#11924036

D₄

yes

characteristic

#11924036

D₄

yes

characteristic

#11924036

Q₈

yes

characteristic

C₂×#10596833

C₂×C₄

yes

characteristic

C₂×#10596833

C₂×C₄

yes

characteristic

C₄⋊#64408

—

C₂²⋊#64408

C₈

yes

—

C₄×#64408

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

#11924012

C₈

yes

characteristic

#11924011

—

C₈×D₇₃

—

M₁₆×C₇₃

C₈

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂×#64408

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

#10596833

C₂²⋊C₄

yes

characteristic

#10596833

C₂²⋊C₄

yes

characteristic

#10596833

C₄⋊C₄

yes

characteristic

#10596833

C₄⋊C₄

yes

characteristic

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

characteristic

#64408

—

C₄×C₇₃

C₂²⋊C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

—

C₂×C₇₃

#336

yes

characteristic

D₇₃

—

D₇₃

—

#1378

—

maximal, Sylow

C₇₃

#1378

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

—

#405

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

146

—

M₃₂

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

#97

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

146

—

M₁₆

#10596842

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

C₄²

—

146

—

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

C₈

—

100

C₈

—

101

C₈

—

102

C₈

—

103

C₈

—

146

—

104

C₂²

—

292

—

105

C₂²

—

106

C₂²

—

107

C₂²

C₄×#10596842

yes

characteristic

108

C₄

—

292

—

109

C₄

—

110

C₄

—

111

C₄

C₂²⋊#10596842

yes

characteristic

112

C₄

C₄⋊#10596842

yes

characteristic

113

C₂

—

114

C₂

—

146

—

115

C₂

—

146

—

116

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₂	(C₂×#10596842)⋊C₄
commutator	C₂²×C₇₃	C₄×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	M₁₆×C₇₃	C₈
socle	C₂×C₇₃	#336
hypercenter	M₁₆	#10596842
hypocenter	C₇₃	#1378
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

subgroup

G/H

center

C₂

(C₂×#10596842)⋊C₄

commutator

C₂²×C₇₃

C₄×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

M₁₆×C₇₃

C₈

C₂×C₇₃

M₁₆

C₇₃

G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

N	H ≅ G/N	type
7. #14556687	C₄	semidirect
9. C₂×#11924040	C₄	semidirect
59. C₇₃	#1378	semidirect

H ≅ G/N

type

7. #14556687

C₄

semidirect

9. C₂×#11924040

C₄

semidirect

59. C₇₃

#1378

semidirect

Subgroups — #22627010

Conjugacy classes of subgroups

Complements