Subgroups — #42122728

Order 27712.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357295	C₂	1	1	yes	maximal, characteristic, complemented
2	#28357288	C₂	1	1	yes	maximal, characteristic, complemented
3	#28357243	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#13181884	—	2	1	no	—
5	#20294100	—	2	1	no	—
6	#20294098	—	2	1	no	—
7	#20294084	—	2	1	no	—
8	D₃₄₆₄	C₄	1	1	yes	characteristic, complemented
9	C₈×D₄₃₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₄₃₃	C₄	1	1	yes	characteristic, complemented
11	C₂×#13181884	—	4	1	no	—
12	D₁₇₃₂	—	2	1	no	—
13	D₁₇₃₂	—	4	1	no	—
14	C₄×D₄₃₃	—	4	1	no	—
15	C₄×D₄₃₃	D₄	1	1	yes	characteristic
16	#16812358	D₄	1	1	yes	characteristic
17	Q₈×C₄₃₃	—	2	1	no	—
18	C₈×C₄₃₃	C₂×C₄	1	1	yes	characteristic
19	C₂×D₄₃₃	—	4	1	no	—
20	C₂×D₄₃₃	D₈	1	1	yes	characteristic
21	#13181884	—	8	1	no	—
22	C₄×C₄₃₃	—	4	1	no	—
23	C₄×C₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₄₃₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₄₃₃	#102	1	1	yes	characteristic
26	D₄₃₃	—	2	1	no	—
27	D₄₃₃	—	8	1	no	—
28	C₄₃₃	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	433	1	no	maximal, Sylow
30	#135	—	433	1	no	—
31	M₃₂	—	433	1	no	—
32	#106	—	433	1	no	—
33	#41	—	866	1	no	—
34	Q₁₆	#13181884	1	1	yes	characteristic, complemented
35	SD₁₆	—	866	1	no	—
36	D₈	—	433	1	no	—
37	C₂×C₈	—	433	1	no	—
38	C₄⋊C₄	—	866	1	no	—
39	C₁₆	—	866	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	866	1	no	—
42	D₄	—	1732	1	no	—
43	C₂×C₄	—	433	1	no	—
44	C₂×C₄	—	1732	1	no	—
45	C₂×C₄	—	1732	1	no	—
46	C₈	—	433	1	no	—
47	C₈	C₂×#13181884	1	1	yes	characteristic
48	C₂²	—	433	1	no	—
49	C₂²	—	1732	1	no	—
50	C₄	—	4	1	no	—
51	C₄	—	3464	1	no	—
52	C₄	—	433	1	no	—
53	C₄	C₂²⋊#13181884	1	1	yes	characteristic
54	C₂	—	866	1	no	—
55	C₂	—	3464	1	no	—
56	C₂	#28357282	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28357282
commutator	C₈×C₄₃₃	C₂×C₄
Frattini	C₈	C₂×#13181884
Fitting	Q₁₆×C₄₃₃	C₄
socle	C₂×C₄₃₃	#102
prime radical	#28357243	C₂
cosocle	C₈×D₄₃₃	C₂²
hypercenter	Q₁₆	#13181884
hypocenter	C₄₃₃	#360
LCS	G ▷ C₈×C₄₃₃ ▷ C₄×C₄₃₃ ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #28357295	C₂	semidirect
2. #28357288	C₂	semidirect
8. D₃₄₆₄	C₄	semidirect
10. Q₁₆×C₄₃₃	C₄	semidirect
28. C₄₃₃	#360	semidirect
34. Q₁₆	#13181884	semidirect

Maximal subgroups

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

subgroup	index
#28357295	2
#28357288	2
#28357243	2
#360	433