Group #22626276 — subgroups

Subgroups — C₂×#17989512 #22626276

Order 9344.

152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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	#17989512	C₂	1	4	yes	maximal, direct product factor
4	C₂×#14556530	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924038	—	2	1	no	—
6	C₂×C₄⋊#64408	—	2	1	no	—
7	#14556661	—	2	1	no	—
8	#14556661	C₂²	1	2	yes	—
9	#14556659	—	2	1	no	—
10	#14556659	C₂²	1	2	yes	—
11	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
12	#14556530	C₄	1	2	yes	complemented
13	#14556530	C₂²	1	2	yes	—
14	C₂×#11924003	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
16	C₂²×#64408	—	4	1	no	—
17	#11924038	—	2	2	no	—
18	#11924038	—	4	1	no	—
19	C₂×#10596833	—	4	1	no	—
20	C₄⋊#64408	—	2	2	no	—
21	C₄⋊#64408	—	4	1	no	—
22	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
23	C₂×#10596831	Q₈	1	1	yes	characteristic
24	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
25	C₈×D₇₃	D₄	1	1	yes	characteristic
26	C₈×D₇₃	Q₈	1	1	yes	characteristic
27	C₈×D₇₃	C₂³	1	1	yes	characteristic
28	#11924003	C₂×C₄	1	2	yes	complemented
29	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₁₆×C₇₃	C₂×C₄	1	2	yes	complemented
31	C₂²×D₇₃	SD₁₆	1	1	yes	characteristic
32	C₂×#64408	—	4	2	no	—
33	C₂×#64408	—	8	2	no	—
34	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
36	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
37	C₄×D₇₃	SD₁₆	1	1	yes	characteristic
38	C₄×D₇₃	SD₁₆	1	1	yes	characteristic
39	C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
40	#10596833	—	4	2	no	—
41	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
43	#10596831	C₄⋊C₄	1	1	yes	characteristic
44	#10596831	C₂×Q₈	1	1	yes	characteristic
45	C₂²×C₇₃	#106	1	1	yes	characteristic
46	C₂×D₇₃	—	2	2	no	—
47	C₂×D₇₃	#106	1	1	yes	characteristic
48	C₂×D₇₃	C₂×SD₁₆	1	1	yes	characteristic
49	#64408	—	8	2	no	—
50	C₄×C₇₃	#106	1	1	yes	characteristic
51	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
52	Dic₇₃	#106	1	1	yes	characteristic
53	Dic₇₃	C₂×SD₁₆	1	1	yes	characteristic
54	C₂×C₇₃	#365	1	2	yes	complemented
55	C₂×C₇₃	C₂×#106	1	1	yes	characteristic
56	D₇₃	—	2	1	no	—
57	D₇₃	—	2	1	no	—
58	C₂×#365	—	73	1	no	maximal, Sylow
59	C₇₃	C₂×#365	1	1	yes	characteristic, complemented, Sylow
60	C₂×M₃₂	—	73	1	no	—
61	C₂×#108	—	73	1	no	—
62	C₂×#106	—	73	1	no	—
63	#365	—	73	4	no	—
64	C₂×M₁₆	—	146	1	no	—
65	C₂²×C₈	—	73	1	no	—
66	C₂×C₄⋊C₄	—	146	1	no	—
67	M₃₂	—	73	2	no	—
68	M₃₂	—	73	2	no	—
69	C₂×C₁₆	—	73	1	no	—
70	C₂×C₁₆	#64408	1	1	yes	characteristic, complemented
71	#108	—	73	2	no	—
72	#108	—	146	1	no	—
73	#106	—	73	2	no	—
74	#106	—	146	1	no	—
75	C₂²×C₄	—	292	1	no	—
76	C₂²×C₄	—	73	1	no	—
77	M₁₆	—	292	1	no	—
78	M₁₆	—	146	2	no	—
79	C₂×C₈	—	292	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	—	73	1	no	—
85	C₂×C₈	C₂×#64408	1	1	yes	characteristic
86	C₄⋊C₄	—	292	1	no	—
87	C₄⋊C₄	—	146	2	no	—
88	C₁₆	—	73	2	no	—
89	C₁₆	C₂×#64408	1	2	yes	complemented
90	C₂³	—	73	1	no	—
91	C₂×C₄	—	292	2	no	—
92	C₂×C₄	—	584	2	no	—
93	C₂×C₄	—	73	1	no	—
94	C₂×C₄	—	73	1	no	—
95	C₂×C₄	—	73	1	no	—
96	C₂×C₄	—	73	1	no	—
97	C₂×C₄	—	73	1	no	—
98	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
99	C₈	—	292	2	no	—
100	C₈	—	73	1	no	—
101	C₈	—	73	1	no	—
102	C₈	C₄⋊#64408	1	1	yes	characteristic
103	C₈	C₂²×#64408	1	1	yes	characteristic
104	C₂²	—	73	1	no	—
105	C₂²	—	73	1	no	—
106	C₂²	—	146	2	no	—
107	C₂²	#14556659	1	1	yes	characteristic
108	C₄	—	584	2	no	—
109	C₄	—	73	1	no	—
110	C₄	—	73	1	no	—
111	C₄	#14556659	1	1	yes	characteristic
112	C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
113	C₂	—	146	1	no	—
114	C₂	—	146	1	no	—
115	C₂	#17989512	1	2	yes	direct product factor
116	C₂	C₂×#14556659	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556661

C₂

yes

maximal, characteristic

C₂×#14556659

C₂

yes

maximal, characteristic

#17989512

C₂

yes

maximal, direct product factor

C₂×#14556530

C₂

yes

maximal, characteristic

C₂×#11924038

—

C₂×C₄⋊#64408

—

#14556661

—

#14556661

C₂²

yes

—

#14556659

—

#14556659

C₂²

yes

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556530

C₄

yes

complemented

#14556530

C₂²

yes

—

C₂×#11924003

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

D₄

yes

characteristic

C₈×D₇₃

Q₈

yes

characteristic

C₈×D₇₃

C₂³

yes

characteristic

#11924003

C₂×C₄

yes

complemented

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₁₆×C₇₃

C₂×C₄

yes

complemented

C₂²×D₇₃

SD₁₆

yes

characteristic

C₂×#64408

—

C₂×#64408

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

SD₁₆

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

SD₁₆

yes

characteristic

C₄×D₇₃

SD₁₆

yes

characteristic

C₄×D₇₃

C₂×D₄

yes

characteristic

#10596833

—

C₈×C₇₃

C₄⋊C₄

yes

characteristic

C₈×C₇₃

C₂²×C₄

yes

characteristic

#10596831

C₄⋊C₄

yes

characteristic

#10596831

C₂×Q₈

yes

characteristic

C₂²×C₇₃

#106

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#106

yes

characteristic

C₂×D₇₃

C₂×SD₁₆

yes

characteristic

#64408

—

C₄×C₇₃

#106

yes

characteristic

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

Dic₇₃

#106

yes

characteristic

Dic₇₃

C₂×SD₁₆

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

D₇₃

—

C₂×#365

—

maximal, Sylow

C₇₃

C₂×#365

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×#108

—

C₂×#106

—

#365

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

146

—

M₃₂

—

M₃₂

—

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

C₂×#64408

yes

complemented

C₂³

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊#64408

yes

characteristic

C₈

—

292

—

100

C₈

—

101

C₈

—

102

C₈

C₄⋊#64408

yes

characteristic

103

C₈

C₂²×#64408

yes

characteristic

104

C₂²

—

105

C₂²

—

106

C₂²

—

146

—

107

C₂²

#14556659

yes

characteristic

108

C₄

—

584

—

109

C₄

—

110

C₄

—

111

C₄

#14556659

yes

characteristic

112

C₄

C₂×C₄⋊#64408

yes

characteristic

113

C₂

—

146

—

114

C₂

—

146

—

115

C₂

#17989512

yes

direct product factor

116

C₂

C₂×#14556659

yes

characteristic

	subgroup	G/H
center	C₂²	#14556659
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₈	C₂²×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#106
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	C₂×#365
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

C₂²×C₄

Frattini

C₈

C₂²×#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
3. #17989512	C₂	direct (N × H)
12. #14556530	C₄	semidirect
14. C₂×#11924003	C₄	semidirect
15. C₂×C₁₆×C₇₃	C₄	semidirect
28. #11924003	C₂×C₄	semidirect
30. C₁₆×C₇₃	C₂×C₄	semidirect
54. C₂×C₇₃	#365	semidirect
59. C₇₃	C₂×#365	semidirect
70. C₂×C₁₆	#64408	semidirect
89. C₁₆	C₂×#64408	semidirect
115. C₂	#17989512	direct (N × H)

H ≅ G/N

type

3. #17989512

C₂

direct (N × H)

12. #14556530

C₄

semidirect

14. C₂×#11924003

C₄

semidirect

15. C₂×C₁₆×C₇₃

C₄

semidirect

28. #11924003

C₂×C₄

semidirect

30. C₁₆×C₇₃

C₂×C₄

semidirect

54. C₂×C₇₃

#365

semidirect

59. C₇₃

C₂×#365

semidirect

70. C₂×C₁₆

#64408

semidirect

89. C₁₆

C₂×#64408

semidirect

115. C₂

#17989512

direct (N × H)

Subgroups — C₂×#17989512 #22626276

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17989512 #22626276

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989512 #22626276