Group #22627038 — subgroups

Subgroups — C₂×#17989671 #22627038

Order 9344.

248 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 119 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×C₄×#10596842	C₂	1	2	yes	maximal
2	#17989671	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×#64408	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10596842	C₄	1	4	yes	—
5	C₄×#10596842	C₄	1	4	yes	—
6	C₄×#10596842	C₂²	1	4	yes	—
7	C₂×#11924036	C₄	1	1	yes	characteristic
8	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
9	C₈×#64408	C₄	1	2	yes	—
10	C₈×#64408	C₂²	1	2	yes	—
11	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
12	C₂×#10596842	—	2	8	no	—
13	C₂×#10596842	C₂×C₄	1	8	yes	—
14	C₂²×#64408	C₂×C₄	1	2	yes	—
15	#11924036	C₈	1	2	yes	complemented
16	#11924036	C₂×C₄	1	2	yes	—
17	C₂×#10596833	C₈	1	2	yes	complemented
18	C₄×#64408	C₂×C₄	1	2	yes	—
19	C₄×#64408	C₂×C₄	1	1	yes	characteristic
20	C₄×#64408	C₂³	1	1	yes	characteristic
21	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×#10596831	C₈	1	1	yes	characteristic, complemented
23	C₈×D₇₃	C₈	1	2	yes	complemented
24	C₈×D₇₃	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic, complemented
26	C₂²×D₇₃	C₄²	1	1	yes	characteristic
27	C₂×#64408	C₄²	1	2	yes	—
28	C₂×#64408	M₁₆	1	8	yes	—
29	C₂×#64408	C₂²×C₄	1	2	yes	—
30	#10596842	—	2	8	no	—
31	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
32	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
33	C₄×D₇₃	C₄²	1	1	yes	characteristic
34	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
35	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
36	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
37	#10596833	C₂×C₈	1	4	yes	complemented
38	C₈×C₇₃	C₂×C₈	1	2	yes	complemented
39	#10596831	C₂×C₈	1	2	yes	complemented
40	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
41	C₂×D₇₃	C₄×C₈	1	1	yes	characteristic
42	C₂×D₇₃	#97	1	4	yes	—
43	C₂×D₇₃	C₂×C₄²	1	1	yes	characteristic
44	#64408	#97	1	4	yes	—
45	#64408	C₂×M₁₆	1	4	yes	—
46	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
47	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
48	Dic₇₃	C₄×C₈	1	1	yes	characteristic
49	Dic₇₃	C₂²×C₈	1	1	yes	characteristic
50	C₂×C₇₃	#322	1	2	yes	complemented
51	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
52	D₇₃	#322	1	2	yes	complemented
53	D₇₃	C₂×#97	1	2	yes	—
54	C₂×#322	—	73	1	no	maximal, Sylow
55	C₇₃	C₂×#322	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₄×C₈	—	73	2	no	—
57	C₂×C₄×C₈	—	73	1	no	—
58	#322	—	73	4	no	—
59	C₂²×C₈	—	73	1	no	—
60	C₂²×C₈	—	73	1	no	—
61	C₂²×C₈	—	73	4	no	—
62	C₂×C₄²	—	73	1	no	—
63	C₄×C₈	—	73	4	no	—
64	C₄×C₈	—	73	4	no	—
65	C₄×C₈	—	73	2	no	—
66	C₄×C₈	—	73	2	no	—
67	C₂²×C₄	—	73	2	no	—
68	C₂²×C₄	—	73	1	no	—
69	C₂×C₈	—	73	2	no	—
70	C₂×C₈	—	73	2	no	—
71	C₂×C₈	—	73	2	no	—
72	C₂×C₈	—	73	1	no	—
73	C₂×C₈	—	73	2	no	—
74	C₂×C₈	—	73	2	no	—
75	C₂×C₈	—	73	8	no	—
76	C₂×C₈	—	146	8	no	—
77	C₂×C₈	#10596842	1	1	yes	characteristic, complemented
78	C₄²	—	73	2	no	—
79	C₄²	—	73	1	no	—
80	C₄²	—	73	1	no	—
81	C₂³	—	73	1	no	—
82	C₂×C₄	—	73	2	no	—
83	C₂×C₄	—	73	2	no	—
84	C₂×C₄	—	73	8	no	—
85	C₂×C₄	—	73	1	no	—
86	C₂×C₄	—	73	1	no	—
87	C₂×C₄	—	73	1	no	—
88	C₂×C₄	—	73	1	no	—
89	C₂×C₄	—	73	1	no	—
90	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
91	C₈	—	73	4	no	—
92	C₈	—	73	2	no	—
93	C₈	—	146	8	no	—
94	C₈	C₂×#10596842	1	2	yes	complemented
95	C₂²	—	73	4	no	—
96	C₂²	—	73	1	no	—
97	C₂²	—	73	1	no	—
98	C₂²	C₄×#10596842	1	1	yes	characteristic
99	C₄	—	73	4	no	—
100	C₄	—	73	4	no	—
101	C₄	—	73	1	no	—
102	C₄	—	73	1	no	—
103	C₄	C₄×#10596842	1	1	yes	characteristic
104	C₄	C₂²×#10596842	1	1	yes	characteristic
105	C₂	—	73	2	no	—
106	C₂	—	73	2	no	—
107	C₂	#17989671	1	2	yes	direct product factor
108	C₂	C₂×C₄×#10596842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×#10596842

C₂

yes

maximal

#17989671

C₂

yes

maximal, direct product factor

C₂×C₈×#64408

C₂

yes

maximal, characteristic

C₂²×#10596842

C₄

yes

—

C₄×#10596842

C₄

yes

—

C₄×#10596842

C₂²

yes

—

C₂×#11924036

C₄

yes

characteristic

C₂×C₄×#64408

C₂²

yes

characteristic

C₈×#64408

C₄

yes

—

C₈×#64408

C₂²

yes

—

C₂×C₈×D₇₃

C₄

yes

characteristic

C₂×#10596842

—

C₂×#10596842

C₂×C₄

yes

—

C₂²×#64408

C₂×C₄

yes

—

#11924036

C₈

yes

complemented

#11924036

C₂×C₄

yes

—

C₂×#10596833

C₈

yes

complemented

C₄×#64408

C₂×C₄

yes

—

C₄×#64408

C₂×C₄

yes

characteristic

C₄×#64408

C₂³

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#10596831

C₈

yes

characteristic, complemented

C₈×D₇₃

C₈

yes

complemented

C₈×D₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₈

yes

characteristic, complemented

C₂²×D₇₃

C₄²

yes

characteristic

C₂×#64408

C₄²

yes

—

C₂×#64408

M₁₆

yes

—

C₂×#64408

C₂²×C₄

yes

—

#10596842

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

characteristic

#10596833

C₂×C₈

yes

complemented

C₈×C₇₃

C₂×C₈

yes

complemented

#10596831

C₂×C₈

yes

complemented

C₂²×C₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

C₄×C₈

yes

characteristic

C₂×D₇₃

#97

yes

—

C₂×D₇₃

C₂×C₄²

yes

characteristic

#64408

#97

yes

—

#64408

C₂×M₁₆

yes

—

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

characteristic

Dic₇₃

C₄×C₈

yes

characteristic

Dic₇₃

C₂²×C₈

yes

characteristic

C₂×C₇₃

#322

yes

complemented

C₂×C₇₃

C₂×C₄×C₈

yes

characteristic

D₇₃

#322

yes

complemented

D₇₃

C₂×#97

yes

—

C₂×#322

—

maximal, Sylow

C₇₃

C₂×#322

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#322

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

#10596842

yes

characteristic, complemented

C₄²

—

C₄²

—

C₄²

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

C₈

—

C₈

—

146

—

C₈

C₂×#10596842

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

C₄×#10596842

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

C₄×#10596842

yes

characteristic

104

C₄

C₂²×#10596842

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

#17989671

yes

direct product factor

108

C₂

C₂×C₄×#10596842

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#10596842
commutator	C₂×C₇₃	C₂×C₄×C₈
Frattini	C₄	C₂²×#10596842
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂²×C₇₃	C₄×C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	C₂×#322
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

subgroup

G/H

center

C₂×C₄

C₂×#10596842

commutator

C₂×C₇₃

C₂×C₄×C₈

Frattini

C₄

C₂²×#10596842

Fitting

C₂×C₈×C₇₃

C₈

socle

C₂²×C₇₃

C₄×C₈

C₂×C₈

C₇₃

G ▷ C₂×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₂×C₈

N	H ≅ G/N	type
2. #17989671	C₂	direct (N × H)
15. #11924036	C₈	semidirect
17. C₂×#10596833	C₈	semidirect
22. C₂×#10596831	C₈	semidirect
23. C₈×D₇₃	C₈	semidirect
25. C₂×C₈×C₇₃	C₈	semidirect
37. #10596833	C₂×C₈	semidirect
38. C₈×C₇₃	C₂×C₈	semidirect
39. #10596831	C₂×C₈	semidirect
50. C₂×C₇₃	#322	semidirect
52. D₇₃	#322	semidirect
55. C₇₃	C₂×#322	semidirect
77. C₂×C₈	#10596842	semidirect
94. C₈	C₂×#10596842	semidirect
107. C₂	#17989671	direct (N × H)

H ≅ G/N

type

2. #17989671

C₂

direct (N × H)

15. #11924036

C₈

semidirect

17. C₂×#10596833

C₈

semidirect

22. C₂×#10596831

C₈

semidirect

23. C₈×D₇₃

C₈

semidirect

25. C₂×C₈×C₇₃

C₈

semidirect

37. #10596833

C₂×C₈

semidirect

38. C₈×C₇₃

C₂×C₈

semidirect

39. #10596831

C₂×C₈

semidirect

50. C₂×C₇₃

#322

semidirect

52. D₇₃

#322

semidirect

55. C₇₃

C₂×#322

semidirect

77. C₂×C₈

#10596842

semidirect

94. C₈

C₂×#10596842

semidirect

107. C₂

#17989671

direct (N × H)

Subgroups — C₂×#17989671 #22627038

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17989671 #22627038

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989671 #22627038