Group #22618331 — subgroups

Subgroups — C₂²×C₈×Dic₇₃ #22618331

Order 9344.

760 conjugacy classes of subgroups; only the 549 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 549 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	C₂³×#10596831	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×Dic₇₃	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₇₃	C₄	1	2	yes	—
6	C₂²×#10596831	C₄	1	8	yes	complemented
7	C₂²×#10596831	C₂²	1	6	yes	—
8	C₂×C₄×Dic₇₃	C₄	1	6	yes	—
9	C₂×C₄×Dic₇₃	C₂²	1	6	yes	—
10	C₈×Dic₇₃	C₂²	1	16	yes	direct product factor
11	C₂³×C₄×C₇₃	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₇₃	C₄	1	8	yes	complemented
13	C₂²×C₈×C₇₃	C₂²	1	6	yes	—
14	C₂²×Dic₇₃	C₈	1	16	yes	direct product factor
15	C₂²×Dic₇₃	C₂×C₄	1	12	yes	—
16	C₂×#10596831	C₂×C₄	1	24	yes	complemented
17	C₂×#10596831	C₂³	1	4	yes	—
18	C₄×Dic₇₃	C₂×C₄	1	12	yes	—
19	C₄×Dic₇₃	C₂³	1	4	yes	—
20	C₂⁴×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₇₃	C₂×C₄	1	3	yes	—
22	C₂²×C₄×C₇₃	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₇₃	C₂×C₄	1	4	yes	—
24	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
25	C₂×C₈×C₇₃	C₂×C₄	1	24	yes	complemented
26	C₂×C₈×C₇₃	C₂³	1	4	yes	—
27	C₂³×C₇₃	C₄²	1	4	yes	—
28	C₂³×C₇₃	C₂×C₈	1	8	yes	—
29	C₂³×C₇₃	C₂²×C₄	1	3	yes	—
30	C₂×C₄×C₇₃	C₄²	1	12	yes	—
31	C₂×C₄×C₇₃	C₂²×C₄	1	3	yes	—
32	C₂×C₄×C₇₃	C₂²×C₄	1	6	yes	—
33	C₂×C₄×C₇₃	C₂²×C₄	1	6	yes	—
34	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
35	C₂×Dic₇₃	C₂×C₈	1	48	yes	direct product factor
36	C₂×Dic₇₃	C₂²×C₄	1	8	yes	—
37	C₈×C₇₃	C₂²×C₄	1	8	yes	complemented
38	#10596831	C₂²×C₄	1	8	yes	complemented
39	C₂²×C₇₃	C₄×C₈	1	16	yes	complemented
40	C₂²×C₇₃	C₂×C₄²	1	6	yes	—
41	C₂²×C₇₃	C₂²×C₈	1	12	yes	—
42	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
43	C₄×C₇₃	C₂×C₄²	1	6	yes	—
44	C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
45	C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
46	Dic₇₃	C₂²×C₈	1	16	yes	direct product factor
47	C₂×C₇₃	C₂×C₄×C₈	1	12	yes	complemented
48	C₂×C₇₃	C₂²×C₄²	1	1	yes	characteristic
49	C₂×C₇₃	C₂³×C₈	1	2	yes	—
50	C₂²×C₄×C₈	—	73	1	no	maximal, Sylow
51	C₇₃	C₂²×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
52	C₂³×C₈	—	73	1	no	—
53	C₂³×C₈	D₇₃	1	1	yes	characteristic
54	C₂²×C₄²	—	73	1	no	—
55	C₂×C₄×C₈	—	73	12	no	—
56	C₂³×C₄	—	73	2	no	—
57	C₂³×C₄	C₂×D₇₃	1	1	yes	characteristic
58	C₂²×C₈	—	73	8	no	—
59	C₂²×C₈	—	73	6	no	—
60	C₂²×C₈	Dic₇₃	1	8	yes	direct product factor
61	C₂²×C₈	C₂×D₇₃	1	6	yes	—
62	C₂×C₄²	—	73	6	no	—
63	C₂×C₄²	—	73	6	no	—
64	C₄×C₈	—	73	16	no	—
65	C₂⁴	C₄×D₇₃	1	1	yes	characteristic
66	C₂²×C₄	—	73	16	no	—
67	C₂²×C₄	—	73	12	no	—
68	C₂²×C₄	C₄×D₇₃	1	3	yes	—
69	C₂²×C₄	C₄×D₇₃	1	4	yes	—
70	C₂²×C₄	C₂×Dic₇₃	1	4	yes	—
71	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
72	C₂×C₈	—	73	24	no	—
73	C₂×C₈	—	73	4	no	—
74	C₂×C₈	C₂×Dic₇₃	1	24	yes	direct product factor
75	C₂×C₈	C₂²×D₇₃	1	4	yes	—
76	C₄²	—	73	12	no	—
77	C₄²	—	73	4	no	—
78	C₂³	C₄×Dic₇₃	1	4	yes	—
79	C₂³	C₈×D₇₃	1	8	yes	—
80	C₂³	C₂×C₄×D₇₃	1	3	yes	—
81	C₂×C₄	—	73	48	no	—
82	C₂×C₄	—	73	8	no	—
83	C₂×C₄	C₄×Dic₇₃	1	12	yes	—
84	C₂×C₄	C₂×C₄×D₇₃	1	3	yes	—
85	C₂×C₄	C₂×C₄×D₇₃	1	6	yes	—
86	C₂×C₄	C₂²×Dic₇₃	1	6	yes	—
87	C₂×C₄	C₂³×D₇₃	1	1	yes	characteristic
88	C₈	—	73	8	no	—
89	C₈	C₂²×Dic₇₃	1	8	yes	direct product factor
90	C₂²	C₈×Dic₇₃	1	16	yes	direct product factor
91	C₂²	C₂×C₄×Dic₇₃	1	6	yes	—
92	C₂²	C₂×C₈×D₇₃	1	12	yes	—
93	C₂²	C₂²×C₄×D₇₃	1	1	yes	characteristic
94	C₄	—	73	16	no	—
95	C₄	C₂×C₄×Dic₇₃	1	6	yes	—
96	C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
97	C₄	C₂³×Dic₇₃	1	1	yes	characteristic
98	C₂	C₂×C₈×Dic₇₃	1	12	yes	direct product factor
99	C₂	C₂²×C₄×Dic₇₃	1	1	yes	characteristic
100	C₂	C₂²×C₈×D₇₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×#10596831

C₂

yes

maximal, characteristic

C₂²×C₄×Dic₇₃

C₂

yes

maximal, characteristic

C₂×C₈×Dic₇₃

C₂

yes

maximal, direct product factor

C₂³×C₈×C₇₃

C₂

yes

maximal, characteristic

C₂³×Dic₇₃

C₄

yes

—

C₂²×#10596831

C₄

yes

complemented

C₂²×#10596831

C₂²

yes

—

C₂×C₄×Dic₇₃

C₄

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₈×Dic₇₃

C₂²

yes

direct product factor

C₂³×C₄×C₇₃

C₂²

yes

characteristic

C₂²×C₈×C₇₃

C₄

yes

complemented

C₂²×C₈×C₇₃

C₂²

yes

—

C₂²×Dic₇₃

C₈

yes

direct product factor

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

complemented

C₂×#10596831

C₂³

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂³

yes

—

C₂⁴×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

complemented

C₂×C₈×C₇₃

C₂³

yes

—

C₂³×C₇₃

C₄²

yes

—

C₂³×C₇₃

C₂×C₈

yes

—

C₂³×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₄²

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

direct product factor

C₂×Dic₇₃

C₂²×C₄

yes

—

C₈×C₇₃

C₂²×C₄

yes

complemented

#10596831

C₂²×C₄

yes

complemented

C₂²×C₇₃

C₄×C₈

yes

complemented

C₂²×C₇₃

C₂×C₄²

yes

—

C₂²×C₇₃

C₂²×C₈

yes

—

C₂²×C₇₃

C₂³×C₄

yes

characteristic

C₄×C₇₃

C₂×C₄²

yes

—

C₄×C₇₃

C₂³×C₄

yes

characteristic

C₄×C₇₃

C₂³×C₄

yes

characteristic

Dic₇₃

C₂²×C₈

yes

direct product factor

C₂×C₇₃

C₂×C₄×C₈

yes

complemented

C₂×C₇₃

C₂²×C₄²

yes

characteristic

C₂×C₇₃

C₂³×C₈

yes

—

C₂²×C₄×C₈

—

maximal, Sylow

C₇₃

C₂²×C₄×C₈

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂³×C₈

D₇₃

yes

characteristic

C₂²×C₄²

—

C₂×C₄×C₈

—

C₂³×C₄

—

C₂³×C₄

C₂×D₇₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

Dic₇₃

yes

direct product factor

C₂²×C₈

C₂×D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₄×C₈

—

C₂⁴

C₄×D₇₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₇₃

yes

—

C₂²×C₄

C₄×D₇₃

yes

—

C₂²×C₄

C₂×Dic₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₇₃

yes

direct product factor

C₂×C₈

C₂²×D₇₃

yes

—

C₄²

—

C₄²

—

C₂³

C₄×Dic₇₃

yes

—

C₂³

C₈×D₇₃

yes

—

C₂³

C₂×C₄×D₇₃

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₇₃

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

—

C₂×C₄

C₂²×Dic₇₃

yes

—

C₂×C₄

C₂³×D₇₃

yes

characteristic

C₈

—

C₈

C₂²×Dic₇₃

yes

direct product factor

C₂²

C₈×Dic₇₃

yes

direct product factor

C₂²

C₂×C₄×Dic₇₃

yes

—

C₂²

C₂×C₈×D₇₃

yes

—

C₂²

C₂²×C₄×D₇₃

yes

characteristic

C₄

—

C₄

C₂×C₄×Dic₇₃

yes

—

C₄

C₂²×C₄×D₇₃

yes

characteristic

C₄

C₂³×Dic₇₃

yes

characteristic

C₂

C₂×C₈×Dic₇₃

yes

direct product factor

C₂

C₂²×C₄×Dic₇₃

yes

characteristic

100

C₂

C₂²×C₈×D₇₃

yes

—

	subgroup	G/H
center, hypercenter	C₂³×C₈	D₇₃
commutator, hypocenter	C₇₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×D₇₃
Fitting	C₂³×C₈×C₇₃	C₂
socle	C₂⁴×C₇₃	C₂×C₄
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂³×C₈

subgroup

G/H

center, hypercenter

C₂³×C₈

D₇₃

commutator, hypocenter

C₇₃

C₂²×C₄×C₈

Frattini

C₂×C₄

C₂³×D₇₃

Fitting

C₂³×C₈×C₇₃

C₂

socle

C₂⁴×C₇₃

C₂×C₄

LCS

G ▷ C₇₃

UCS

C₁ ◁ C₂³×C₈

N	H ≅ G/N	type
3. C₂×C₈×Dic₇₃	C₂	direct (N × H)
6. C₂²×#10596831	C₄	semidirect
10. C₈×Dic₇₃	C₂²	direct (N × H)
12. C₂²×C₈×C₇₃	C₄	semidirect
14. C₂²×Dic₇₃	C₈	direct (N × H)
16. C₂×#10596831	C₂×C₄	semidirect
25. C₂×C₈×C₇₃	C₂×C₄	semidirect
35. C₂×Dic₇₃	C₂×C₈	direct (N × H)
37. C₈×C₇₃	C₂²×C₄	semidirect
38. #10596831	C₂²×C₄	semidirect
39. C₂²×C₇₃	C₄×C₈	semidirect
46. Dic₇₃	C₂²×C₈	direct (N × H)
47. C₂×C₇₃	C₂×C₄×C₈	semidirect
51. C₇₃	C₂²×C₄×C₈	semidirect
60. C₂²×C₈	Dic₇₃	direct (N × H)
74. C₂×C₈	C₂×Dic₇₃	direct (N × H)
89. C₈	C₂²×Dic₇₃	direct (N × H)
90. C₂²	C₈×Dic₇₃	direct (N × H)
98. C₂	C₂×C₈×Dic₇₃	direct (N × H)

H ≅ G/N

type

3. C₂×C₈×Dic₇₃

C₂

direct (N × H)

6. C₂²×#10596831

C₄

semidirect

10. C₈×Dic₇₃

C₂²

direct (N × H)

12. C₂²×C₈×C₇₃

C₄

semidirect

14. C₂²×Dic₇₃

C₈

direct (N × H)

16. C₂×#10596831

C₂×C₄

semidirect

25. C₂×C₈×C₇₃

C₂×C₄

semidirect

35. C₂×Dic₇₃

C₂×C₈

direct (N × H)

37. C₈×C₇₃

C₂²×C₄

semidirect

38. #10596831

C₂²×C₄

semidirect

39. C₂²×C₇₃

C₄×C₈

semidirect

46. Dic₇₃

C₂²×C₈

direct (N × H)

47. C₂×C₇₃

C₂×C₄×C₈

semidirect

51. C₇₃

C₂²×C₄×C₈

semidirect

60. C₂²×C₈

Dic₇₃

direct (N × H)

74. C₂×C₈

C₂×Dic₇₃

direct (N × H)

89. C₈

C₂²×Dic₇₃

direct (N × H)

90. C₂²

C₈×Dic₇₃

direct (N × H)

98. C₂

C₂×C₈×Dic₇₃

direct (N × H)

Subgroups — C₂²×C₈×Dic₇₃ #22618331

Conjugacy classes of subgroups

Complements

Subgroups — C22×C8×Dic73 #22618331

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₈×Dic₇₃ #22618331