Group #22626563 — subgroups

Subgroups — C₂²×C₄⋊#10596833 #22626563

Order 9344.

640 conjugacy classes of subgroups; only the 378 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 378 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×#10596833	C₂	1	2	yes	maximal
2	C₂×C₄⋊#10596833	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄×Dic₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10596833	—	2	8	no	—
5	C₂²×#10596833	C₂²	1	12	yes	—
6	C₄⋊#10596833	C₂²	1	16	yes	direct product factor
7	C₂³×Dic₇₃	C₄	1	1	yes	characteristic
8	C₂³×Dic₇₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₇₃	C₄	1	6	yes	—
10	C₂×C₄×Dic₇₃	C₂²	1	6	yes	—
11	C₂³×C₄×C₇₃	C₄	1	1	yes	characteristic
12	C₂×#10596833	—	2	24	no	—
13	C₂×#10596833	C₂³	1	8	yes	—
14	C₂²×Dic₇₃	—	2	4	no	—
15	C₂²×Dic₇₃	C₂×C₄	1	6	yes	—
16	C₂²×Dic₇₃	C₂×C₄	1	3	yes	—
17	C₂²×Dic₇₃	D₄	1	4	yes	—
18	C₂²×Dic₇₃	Q₈	1	4	yes	—
19	C₂²×Dic₇₃	C₂³	1	3	yes	—
20	C₄×Dic₇₃	C₂×C₄	1	12	yes	—
21	C₄×Dic₇₃	C₂³	1	4	yes	—
22	C₂⁴×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₇₃	C₈	1	8	yes	complemented
24	C₂²×C₄×C₇₃	C₂×C₄	1	6	yes	—
25	C₂³×C₇₃	C₄⋊C₄	1	4	yes	—
26	C₂³×C₇₃	C₂×C₈	1	4	yes	—
27	C₂³×C₇₃	M₁₆	1	4	yes	—
28	C₂³×C₇₃	C₂²×C₄	1	3	yes	—
29	C₂×C₄×C₇₃	C₂×C₈	1	24	yes	complemented
30	C₂×C₄×C₇₃	C₂²×C₄	1	4	yes	—
31	C₂×Dic₇₃	—	2	12	no	—
32	C₂×Dic₇₃	C₄⋊C₄	1	12	yes	—
33	C₂×Dic₇₃	C₂²×C₄	1	4	yes	—
34	C₂×Dic₇₃	C₂²×C₄	1	3	yes	—
35	C₂×Dic₇₃	C₂×D₄	1	6	yes	—
36	C₂×Dic₇₃	C₂×Q₈	1	6	yes	—
37	C₂×Dic₇₃	C₂⁴	1	1	yes	characteristic
38	#10596833	—	2	8	no	—
39	C₂²×C₇₃	C₄⋊C₈	1	16	yes	complemented
40	C₂²×C₇₃	C₂×C₄⋊C₄	1	6	yes	—
41	C₂²×C₇₃	C₂²×C₈	1	6	yes	—
42	C₂²×C₇₃	C₂×M₁₆	1	6	yes	—
43	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
44	C₄×C₇₃	C₂²×C₈	1	8	yes	complemented
45	Dic₇₃	—	2	4	no	—
46	Dic₇₃	C₂×C₄⋊C₄	1	6	yes	—
47	Dic₇₃	C₂²×D₄	1	1	yes	characteristic
48	Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
49	C₂×C₇₃	C₂×C₄⋊C₈	1	12	yes	complemented
50	C₂×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₇₃	C₂³×C₈	1	1	yes	characteristic
52	C₂×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
53	C₂²×C₄⋊C₈	—	73	1	no	maximal, Sylow
54	C₇₃	C₂²×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
55	C₂³×C₈	—	73	2	no	—
56	C₂²×C₄²	—	73	1	no	—
57	C₂×C₄⋊C₈	—	73	12	no	—
58	C₂³×C₄	—	73	1	no	—
59	C₂³×C₄	—	73	1	no	—
60	C₂³×C₄	#64408	1	1	yes	characteristic
61	C₂²×C₈	—	73	12	no	—
62	C₂²×C₈	—	146	8	no	—
63	C₂×C₄²	—	73	6	no	—
64	C₂×C₄²	—	73	6	no	—
65	C₄⋊C₈	—	73	16	no	—
66	C₂⁴	C₂×#64408	1	1	yes	characteristic
67	C₂²×C₄	—	73	4	no	—
68	C₂²×C₄	—	73	4	no	—
69	C₂²×C₄	—	73	3	no	—
70	C₂²×C₄	—	73	3	no	—
71	C₂²×C₄	—	73	6	no	—
72	C₂²×C₄	—	146	4	no	—
73	C₂²×C₄	#10596833	1	8	yes	complemented
74	C₂²×C₄	C₂×#64408	1	6	yes	—
75	C₂×C₈	—	73	8	no	—
76	C₂×C₈	—	146	24	no	—
77	C₄²	—	73	12	no	—
78	C₄²	—	73	4	no	—
79	C₂³	C₄⋊#64408	1	4	yes	—
80	C₂³	C₂×#10596833	1	4	yes	—
81	C₂³	#11924038	1	4	yes	—
82	C₂³	C₂²×#64408	1	3	yes	—
83	C₂×C₄	—	73	1	no	—
84	C₂×C₄	—	73	3	no	—
85	C₂×C₄	—	73	6	no	—
86	C₂×C₄	—	73	12	no	—
87	C₂×C₄	—	73	6	no	—
88	C₂×C₄	—	73	4	no	—
89	C₂×C₄	—	146	12	no	—
90	C₂×C₄	C₂×#10596833	1	24	yes	complemented
91	C₂×C₄	C₂²×#64408	1	4	yes	—
92	C₈	—	146	8	no	—
93	C₂²	C₄⋊#10596833	1	16	yes	direct product factor
94	C₂²	C₂×C₄⋊#64408	1	6	yes	—
95	C₂²	C₂²×#10596833	1	6	yes	—
96	C₂²	C₂×#11924038	1	6	yes	—
97	C₂²	C₂³×#64408	1	1	yes	characteristic
98	C₄	—	73	1	no	—
99	C₄	—	73	6	no	—
100	C₄	—	73	1	no	—
101	C₄	—	146	4	no	—
102	C₄	C₂²×#10596833	1	8	yes	complemented
103	C₂	C₂×C₄⋊#10596833	1	12	yes	direct product factor
104	C₂	C₂²×C₄⋊#64408	1	1	yes	characteristic
105	C₂	C₂³×#10596833	1	1	yes	characteristic
106	C₂	C₂²×#11924038	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×#10596833

C₂

yes

maximal

C₂×C₄⋊#10596833

C₂

yes

maximal, direct product factor

C₂²×C₄×Dic₇₃

C₂

yes

maximal, characteristic

C₂²×#10596833

—

C₂²×#10596833

C₂²

yes

—

C₄⋊#10596833

C₂²

yes

direct product factor

C₂³×Dic₇₃

C₄

yes

characteristic

C₂³×Dic₇₃

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₄

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₂³×C₄×C₇₃

C₄

yes

characteristic

C₂×#10596833

—

C₂×#10596833

C₂³

yes

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

C₂×C₄

yes

—

C₂²×Dic₇₃

D₄

yes

—

C₂²×Dic₇₃

Q₈

yes

—

C₂²×Dic₇₃

C₂³

yes

—

C₄×Dic₇₃

C₂×C₄

yes

—

C₄×Dic₇₃

C₂³

yes

—

C₂⁴×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₈

yes

complemented

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₄⋊C₄

yes

—

C₂³×C₇₃

C₂×C₈

yes

—

C₂³×C₇₃

M₁₆

yes

—

C₂³×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

complemented

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

—

C₂×Dic₇₃

C₂×Q₈

yes

—

C₂×Dic₇₃

C₂⁴

yes

characteristic

#10596833

—

C₂²×C₇₃

C₄⋊C₈

yes

complemented

C₂²×C₇₃

C₂×C₄⋊C₄

yes

—

C₂²×C₇₃

C₂²×C₈

yes

—

C₂²×C₇₃

C₂×M₁₆

yes

—

C₂²×C₇₃

C₂³×C₄

yes

characteristic

C₄×C₇₃

C₂²×C₈

yes

complemented

Dic₇₃

—

Dic₇₃

C₂×C₄⋊C₄

yes

—

Dic₇₃

C₂²×D₄

yes

characteristic

Dic₇₃

C₂²×Q₈

yes

characteristic

C₂×C₇₃

C₂×C₄⋊C₈

yes

complemented

C₂×C₇₃

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₇₃

C₂³×C₈

yes

characteristic

C₂×C₇₃

C₂²×M₁₆

yes

characteristic

C₂²×C₄⋊C₈

—

maximal, Sylow

C₇₃

C₂²×C₄⋊C₈

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂²×C₄²

—

C₂×C₄⋊C₈

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

#64408

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

146

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₂⁴

C₂×#64408

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂²×C₄

#10596833

yes

complemented

C₂²×C₄

C₂×#64408

yes

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

C₂³

C₄⋊#64408

yes

—

C₂³

C₂×#10596833

yes

—

C₂³

#11924038

yes

—

C₂³

C₂²×#64408

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

C₂×#10596833

yes

complemented

C₂×C₄

C₂²×#64408

yes

—

C₈

—

146

—

C₂²

C₄⋊#10596833

yes

direct product factor

C₂²

C₂×C₄⋊#64408

yes

—

C₂²

C₂²×#10596833

yes

—

C₂²

C₂×#11924038

yes

—

C₂²

C₂³×#64408

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

—

146

—

102

C₄

C₂²×#10596833

yes

complemented

103

C₂

C₂×C₄⋊#10596833

yes

direct product factor

104

C₂

C₂²×C₄⋊#64408

yes

characteristic

105

C₂

C₂³×#10596833

yes

characteristic

106

C₂

C₂²×#11924038

yes

characteristic

	subgroup	G/H
center	C₂⁴	C₂×#64408
commutator	C₂×C₇₃	C₂³×C₈
Frattini	C₂²	C₂³×#64408
Fitting	C₂³×C₄×C₇₃	C₄
socle	C₂⁴×C₇₃	C₂×C₄
hypercenter	C₂³×C₄	#64408
hypocenter	C₇₃	C₂²×C₄⋊C₈
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

subgroup

G/H

center

C₂⁴

C₂×#64408

commutator

C₂×C₇₃

C₂³×C₈

Frattini

C₂²

C₂³×#64408

Fitting

C₂³×C₄×C₇₃

C₄

socle

C₂⁴×C₇₃

C₂×C₄

hypercenter

C₂³×C₄

#64408

hypocenter

C₇₃

C₂²×C₄⋊C₈

LCS

G ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂⁴ ◁ C₂³×C₄

N	H ≅ G/N	type
2. C₂×C₄⋊#10596833	C₂	direct (N × H)
6. C₄⋊#10596833	C₂²	direct (N × H)
23. C₂²×C₄×C₇₃	C₈	semidirect
29. C₂×C₄×C₇₃	C₂×C₈	semidirect
39. C₂²×C₇₃	C₄⋊C₈	semidirect
44. C₄×C₇₃	C₂²×C₈	semidirect
49. C₂×C₇₃	C₂×C₄⋊C₈	semidirect
54. C₇₃	C₂²×C₄⋊C₈	semidirect
73. C₂²×C₄	#10596833	semidirect
90. C₂×C₄	C₂×#10596833	semidirect
93. C₂²	C₄⋊#10596833	direct (N × H)
102. C₄	C₂²×#10596833	semidirect
103. C₂	C₂×C₄⋊#10596833	direct (N × H)

H ≅ G/N

type

2. C₂×C₄⋊#10596833

C₂

direct (N × H)

6. C₄⋊#10596833

C₂²

direct (N × H)

23. C₂²×C₄×C₇₃

C₈

semidirect

29. C₂×C₄×C₇₃

C₂×C₈

semidirect

39. C₂²×C₇₃

C₄⋊C₈

semidirect

44. C₄×C₇₃

C₂²×C₈

semidirect

49. C₂×C₇₃

C₂×C₄⋊C₈

semidirect

54. C₇₃

C₂²×C₄⋊C₈

semidirect

73. C₂²×C₄

#10596833

semidirect

90. C₂×C₄

C₂×#10596833

semidirect

93. C₂²

C₄⋊#10596833

direct (N × H)

102. C₄

C₂²×#10596833

semidirect

103. C₂

C₂×C₄⋊#10596833

direct (N × H)

Subgroups — C₂²×C₄⋊#10596833 #22626563

Conjugacy classes of subgroups

Complements

Subgroups — C22×C4⋊#10596833 #22626563

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×C₄⋊#10596833 #22626563