Group #22624996 — subgroups

Subgroups — #22624996

Order 9344.

136 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 52 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×#14556661	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556659	C₂	1	1	yes	maximal, characteristic
3	C₂×#14556530	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924038	—	2	1	no	—
5	C₂×C₄⋊#64408	—	2	1	no	—
6	#14556661	—	2	1	no	—
7	#14556661	C₄	1	2	yes	complemented
8	#14556659	—	2	1	no	—
9	#14556659	C₄	1	2	yes	—
10	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
11	#14556530	—	2	1	no	—
12	#14556530	—	2	1	no	—
13	C₂×#11924003	C₄	1	1	yes	characteristic, complemented
14	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
15	C₂²×#64408	—	4	1	no	—
16	#11924038	—	2	2	no	—
17	#11924038	—	4	1	no	—
18	C₂×#10596833	—	4	1	no	—
19	C₄⋊#64408	—	2	2	no	—
20	C₄⋊#64408	—	4	1	no	—
21	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
22	C₂×#10596831	Q₈	1	1	yes	characteristic
23	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
24	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
25	C₈×D₇₃	D₄	1	1	yes	characteristic
26	C₈×D₇₃	D₄	1	1	yes	characteristic
27	#11924003	—	2	1	no	—
28	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₁₆×C₇₃	—	2	1	no	—
30	C₂²×D₇₃	SD₁₆	1	1	yes	characteristic
31	C₂×#64408	—	4	2	no	—
32	C₂×#64408	—	8	1	no	—
33	C₂×#64408	—	8	1	no	—
34	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
36	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₄×D₇₃	D₈	1	1	yes	characteristic
39	C₄×D₇₃	Q₁₆	1	1	yes	characteristic
40	#10596833	—	4	2	no	—
41	C₈×C₇₃	C₄²	1	1	yes	characteristic
42	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
43	#10596831	C₄⋊C₄	1	1	yes	characteristic
44	#10596831	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₇₃	#106	1	1	yes	characteristic
46	C₂×D₇₃	—	2	1	no	—
47	C₂×D₇₃	—	2	1	no	—
48	C₂×D₇₃	#102	1	1	yes	characteristic
49	C₂×D₇₃	#103	1	1	yes	characteristic
50	#64408	—	8	2	no	—
51	C₄×C₇₃	#95	1	1	yes	characteristic
52	C₄×C₇₃	#107	1	1	yes	characteristic
53	Dic₇₃	#102	1	1	yes	characteristic
54	Dic₇₃	#103	1	1	yes	characteristic
55	C₂×C₇₃	#340	1	1	yes	characteristic
56	C₂×C₇₃	#365	1	1	yes	characteristic
57	C₂×C₇₃	#365	1	1	yes	characteristic
58	D₇₃	—	2	1	no	—
59	D₇₃	—	2	1	no	—
60	#1383	—	73	1	no	maximal, Sylow
61	C₇₃	#1383	1	1	yes	characteristic, complemented, Sylow
62	C₂×M₃₂	—	73	1	no	—
63	C₂×#108	—	73	1	no	—
64	C₂×#106	—	73	1	no	—
65	C₂×M₁₆	—	146	1	no	—
66	C₂²×C₈	—	73	1	no	—
67	C₂×C₄⋊C₄	—	146	1	no	—
68	M₃₂	—	146	1	no	—
69	M₃₂	—	146	1	no	—
70	C₂×C₁₆	—	73	1	no	—
71	C₂×C₁₆	#64408	1	1	yes	characteristic, complemented
72	#108	—	73	2	no	—
73	#108	—	146	1	no	—
74	#106	—	73	2	no	—
75	#106	—	146	1	no	—
76	C₂²×C₄	—	292	1	no	—
77	C₂²×C₄	—	73	1	no	—
78	M₁₆	—	292	1	no	—
79	M₁₆	—	146	2	no	—
80	C₂×C₈	—	292	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	—	73	1	no	—
83	C₂×C₈	—	73	1	no	—
84	C₂×C₈	—	73	1	no	—
85	C₂×C₈	—	73	1	no	—
86	C₂×C₈	C₂×#64408	1	1	yes	characteristic
87	C₄⋊C₄	—	292	1	no	—
88	C₄⋊C₄	—	146	2	no	—
89	C₁₆	—	2	1	no	—
90	C₁₆	—	146	1	no	—
91	C₂³	—	73	1	no	—
92	C₂×C₄	—	292	2	no	—
93	C₂×C₄	—	584	1	no	—
94	C₂×C₄	—	584	1	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	—	73	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
101	C₈	—	292	2	no	—
102	C₈	—	73	1	no	—
103	C₈	—	73	1	no	—
104	C₈	C₄×#64408	1	1	yes	characteristic
105	C₈	C₂²⋊#64408	1	1	yes	characteristic
106	C₂²	—	73	1	no	—
107	C₂²	—	73	1	no	—
108	C₂²	—	146	1	no	—
109	C₂²	—	146	1	no	—
110	C₂²	#14556659	1	1	yes	characteristic
111	C₄	—	584	2	no	—
112	C₄	—	73	1	no	—
113	C₄	—	73	1	no	—
114	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
115	C₄	#14556660	1	1	yes	characteristic
116	C₂	—	146	1	no	—
117	C₂	—	146	1	no	—
118	C₂	#17989461	1	1	yes	characteristic
119	C₂	#17989511	1	1	yes	characteristic
120	C₂	#17989512	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556661

C₂

yes

maximal, characteristic

C₂×#14556659

C₂

yes

maximal, characteristic

C₂×#14556530

C₂

yes

maximal, characteristic

C₂×#11924038

—

C₂×C₄⋊#64408

—

#14556661

—

#14556661

C₄

yes

complemented

#14556659

—

#14556659

C₄

yes

—

C₂×C₈×D₇₃

C₂²

yes

—

—

C₄

yes

characteristic, complemented

C₂×C₁₆×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

—

—

—

—

—

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×#10596831

Q₈

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

C₂×C₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

C₈×D₇₃

D₄

yes

characteristic

#11924003

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

—

C₂²×D₇₃

SD₁₆

yes

—

—

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

SD₁₆

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

D₈

yes

characteristic

C₄×D₇₃

Q₁₆

yes

characteristic

#10596833

—

C₈×C₇₃

C₄²

yes

characteristic

C₈×C₇₃

C₂²⋊C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

C₂²×C₇₃

#106

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

yes

C₂×D₇₃

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

yes

Dic₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

D₇₃

—

#1383

—

maximal, Sylow

C₇₃

#1383

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

—

C₂×#106

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

146

—

M₃₂

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

#64408

yes

characteristic, complemented

#108

—

#108

—

146

—

#106

—

#106

—

146

—

C₂²×C₄

—

292

—

C₂²×C₄

—

M₁₆

—

292

—

M₁₆

—

146

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#64408

yes

characteristic

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₁₆

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

584

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₄⋊#64408

yes

characteristic

101

C₈

—

292

—

102

C₈

—

103

C₈

—

104

C₈

C₄×#64408

yes

characteristic

105

C₈

C₂²⋊#64408

yes

characteristic

106

C₂²

—

107

C₂²

—

108

C₂²

—

146

—

109

C₂²

—

146

—

110

C₂²

#14556659

yes

characteristic

111

C₄

—

584

—

112

C₄

—

113

C₄

—

114

C₄

(C₂×#64408)⋊C₄

yes

characteristic

115

C₄

#14556660

yes

characteristic

116

C₂

—

146

—

117

C₂

—

146

—

118

C₂

#17989461

yes

characteristic

119

C₂

#17989511

yes

characteristic

120

C₂

#17989512

yes

characteristic

	subgroup	G/H
center	C₂²	#14556659
commutator	C₈×C₇₃	C₄²
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#106
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	#1383
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

subgroup

G/H

center

C₂²

#14556659

commutator

C₈×C₇₃

C₄²

Frattini

C₂×C₈

C₂×#64408

Fitting

C₂×C₁₆×C₇₃

C₄

C₂²×C₇₃

C₂×C₁₆

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

N	H ≅ G/N	type
7. #14556661	C₄	semidirect
13. C₂×#11924003	C₄	semidirect
14. C₂×C₁₆×C₇₃	C₄	semidirect
61. C₇₃	#1383	semidirect
71. C₂×C₁₆	#64408	semidirect

H ≅ G/N

type

7. #14556661

C₄

semidirect

13. C₂×#11924003

C₄

semidirect

14. C₂×C₁₆×C₇₃

C₄

semidirect

61. C₇₃

#1383

semidirect

71. C₂×C₁₆

#64408

semidirect

Subgroups — #22624996

Conjugacy classes of subgroups

Complements