Subgroups — C₂²⋊C₄×D₇₃₃ #37553124

Order 23456.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₇₃₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₇₃₃	C₂	1	2	yes	maximal, complemented
3	C₂²⋊Dic₇₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#26043990	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₄×C₇₃₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₃₃	—	2	4	no	—
7	C₂²×D₇₃₃	C₄	1	4	yes	complemented
8	C₂²×D₇₃₃	C₂²	1	1	yes	characteristic
9	C₂²×D₇₃₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₇₃₃	C₂²	1	2	yes	complemented
11	C₄×D₇₃₃	—	2	4	no	—
12	C₂³×C₇₃₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇₃₃	C₂²	1	2	yes	complemented
14	C₂²×C₇₃₃	—	2	2	no	—
15	C₂²×C₇₃₃	C₂×C₄	1	2	yes	complemented
16	C₂²×C₇₃₃	C₂³	1	1	yes	characteristic
17	C₂×D₇₃₃	—	2	2	no	—
18	C₂×D₇₃₃	—	2	8	no	—
19	C₂×D₇₃₃	C₂×C₄	1	2	yes	—
20	C₂×D₇₃₃	C₂×C₄	1	2	yes	complemented
21	C₂×D₇₃₃	D₄	1	4	yes	—
22	C₄×C₇₃₃	—	2	2	no	—
23	Dic₇₃₃	—	2	2	no	—
24	C₂×C₇₃₃	—	2	2	no	—
25	C₂×C₇₃₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₇₃₃	C₂×D₄	1	2	yes	—
27	D₇₃₃	—	2	2	no	—
28	D₇₃₃	C₂²⋊C₄	1	4	yes	direct product factor
29	C₇₃₃	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₂²⋊C₄	—	733	1	no	maximal, Sylow
31	C₂⁴	—	733	1	no	—
32	C₂²×C₄	—	733	2	no	—
33	C₂²⋊C₄	—	733	1	no	—
34	C₂²⋊C₄	—	733	2	no	—
35	C₂²⋊C₄	D₇₃₃	1	1	yes	characteristic, direct product factor
36	C₂³	—	1466	4	no	—
37	C₂³	—	733	4	no	—
38	C₂³	—	733	1	no	—
39	C₂³	—	733	1	no	—
40	C₂³	C₂×D₇₃₃	1	1	yes	characteristic
41	C₂×C₄	—	1466	4	no	—
42	C₂×C₄	—	733	2	no	—
43	C₂×C₄	C₂×D₇₃₃	1	2	yes	complemented
44	C₂²	—	2	2	no	—
45	C₂²	—	1466	8	no	—
46	C₂²	—	1466	2	no	—
47	C₂²	—	733	2	no	—
48	C₂²	—	733	2	no	—
49	C₂²	—	733	4	no	—
50	C₂²	C₄×D₇₃₃	1	2	yes	complemented
51	C₂²	C₂²×D₇₃₃	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	—	1466	2	no	—
54	C₂	—	2	2	no	—
55	C₂	—	1466	2	no	—
56	C₂	—	733	4	no	—
57	C₂	C₂×C₄×D₇₃₃	1	1	yes	characteristic
58	C₂	D₄×D₇₃₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₇₃₃
commutator	C₂×C₇₃₃	C₂²×C₄
Fitting	C₂²⋊C₄×C₇₃₃	C₂
socle, cosocle	C₂²×C₇₃₃	C₂³
prime radical	C₂³×D₇₃₃	C₂
hypercenter	C₂²⋊C₄	D₇₃₃
hypocenter	C₇₃₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂×C₇₃₃ ▷ C₇₃₃
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₄×D₇₃₃	C₂	semidirect
3. C₂²⋊Dic₇₃₃	C₂	semidirect
4. #26043990	C₂	semidirect
5. C₂²⋊C₄×C₇₃₃	C₂	semidirect
7. C₂²×D₇₃₃	C₄	semidirect
10. C₂×Dic₇₃₃	C₂²	semidirect
13. C₂×C₄×C₇₃₃	C₂²	semidirect
15. C₂²×C₇₃₃	C₂×C₄	semidirect
20. C₂×D₇₃₃	C₂×C₄	semidirect
28. D₇₃₃	C₂²⋊C₄	direct (N × H)
29. C₇₃₃	C₂×C₂²⋊C₄	semidirect
35. C₂²⋊C₄	D₇₃₃	direct (N × H)
43. C₂×C₄	C₂×D₇₃₃	semidirect
50. C₂²	C₄×D₇₃₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×D₇₃₃	2
C₂×C₄×D₇₃₃	2
C₂²⋊Dic₇₃₃	2
#26043990	2
C₂²⋊C₄×C₇₃₃	2
C₂×C₂²⋊C₄	733

Subgroups — C22⋊C4×D733 #37553124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊C₄×D₇₃₃ #37553124