Subgroups — #44450010

Order 29824.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28416261	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₂₃₃	C₂	1	1	yes	maximal, characteristic
3	#21418469	—	2	2	no	—
4	C₂×C₁₆×C₂₃₃	C₂²	1	1	yes	characteristic
5	C₃₂×C₂₃₃	C₄	1	2	yes	complemented
6	C₄⋊Dic₂₃₃	—	4	2	no	—
7	C₂×C₈×C₂₃₃	D₄	1	1	yes	characteristic
8	C₁₆×C₂₃₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₃₃	Q₈	1	1	yes	characteristic
10	C₂×Dic₂₃₃	—	8	2	no	—
11	C₂×C₄×C₂₃₃	D₈	1	1	yes	characteristic
12	C₈×C₂₃₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₃₃	Q₁₆	1	1	yes	characteristic
14	C₂²×C₂₃₃	D₁₆	1	1	yes	characteristic
15	C₄×C₂₃₃	#107	1	1	yes	characteristic
16	C₄×C₂₃₃	Q₃₂	1	1	yes	characteristic
17	Dic₂₃₃	—	16	2	no	—
18	C₂×C₂₃₃	#366	1	1	yes	characteristic
19	C₂×C₂₃₃	D₃₂	1	1	yes	characteristic
20	C₂×C₂₃₃	Q₆₄	1	1	yes	characteristic
21	C₂₃₃	#1423	1	1	yes	characteristic, complemented, Sylow
22	#1423	—	233	1	no	maximal, Sylow
23	C₂×C₃₂	D₂₃₃	1	1	yes	characteristic
24	#366	—	233	2	no	—
25	C₂×C₁₆	C₂×D₂₃₃	1	1	yes	characteristic
26	#107	—	466	2	no	—
27	C₃₂	Dic₂₃₃	1	2	yes	complemented
28	C₂×C₈	D₉₃₂	1	1	yes	characteristic
29	C₄⋊C₄	—	932	2	no	—
30	C₁₆	C₂×Dic₂₃₃	1	1	yes	characteristic
31	C₁₆	Dic₄₆₆	1	1	yes	characteristic
32	C₂×C₄	—	1864	2	no	—
33	C₂×C₄	D₁₈₆₄	1	1	yes	characteristic
34	C₈	C₄⋊Dic₂₃₃	1	1	yes	characteristic
35	C₈	Dic₉₃₂	1	1	yes	characteristic
36	C₂²	D₃₇₂₈	1	1	yes	characteristic
37	C₄	—	3728	2	no	—
38	C₄	#21418469	1	1	yes	characteristic
39	C₄	Dic₁₈₆₄	1	1	yes	characteristic
40	C₂	#28416261	1	1	yes	characteristic
41	C₂	D₇₄₅₆	1	1	yes	characteristic
42	C₂	Dic₃₇₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₇₂₈
commutator	C₁₆×C₂₃₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₃₃
Fitting	C₂×C₃₂×C₂₃₃	C₂
socle, prime radical	C₂²×C₂₃₃	D₁₆
cosocle	C₂×C₁₆×C₂₃₃	C₂²
hypercenter	C₂×C₃₂	D₂₃₃
hypocenter	C₂₃₃	#1423
LCS	G ▷ C₁₆×C₂₃₃ ▷ C₈×C₂₃₃ ▷ C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₂₃₃	C₄	semidirect
21. C₂₃₃	#1423	semidirect
27. C₃₂	Dic₂₃₃	semidirect

Maximal subgroups

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

subgroup	index
#28416261	2
C₂×C₃₂×C₂₃₃	2
#1423	233