Subgroups — #28357282

Order 13856.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20294105	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#13181884	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₄₃₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#13181884	—	2	1	no	—
5	#16812365	—	2	1	no	—
6	C₂²×D₄₃₃	—	2	1	no	—
7	D₁₇₃₂	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊D₄₃₃	—	2	1	no	—
9	C₄×D₄₃₃	C₂²	1	1	yes	characteristic
10	D₄×C₄₃₃	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₄₃₃	—	2	1	no	—
12	C₂×D₄₃₃	—	2	1	no	—
13	C₂×D₄₃₃	—	4	1	no	—
14	C₂×D₄₃₃	—	4	1	no	—
15	C₂×D₄₃₃	D₄	1	1	yes	characteristic
16	#13181884	—	4	1	no	—
17	C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
18	Dic₄₃₃	D₄	1	1	yes	characteristic
19	C₂×C₄₃₃	—	4	1	no	—
20	C₂×C₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
21	D₄₃₃	—	4	1	no	—
22	D₄₃₃	D₈	1	1	yes	characteristic
23	D₄₃₃	SD₁₆	1	1	yes	characteristic
24	C₄₃₃	#102	1	1	yes	characteristic, complemented, Sylow
25	#102	—	433	1	no	maximal, Sylow
26	C₂×D₄	—	433	1	no	—
27	C₂×C₈	—	433	1	no	—
28	C₄⋊C₄	—	433	1	no	—
29	C₂³	—	866	1	no	—
30	D₄	—	866	1	no	—
31	D₄	—	433	1	no	—
32	D₄	#13181884	1	1	yes	characteristic, complemented
33	C₂×C₄	—	866	1	no	—
34	C₂×C₄	—	433	1	no	—
35	C₈	—	866	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	866	1	no	—
38	C₂²	—	433	1	no	—
39	C₂²	—	1732	1	no	—
40	C₂²	—	1732	1	no	—
41	C₄	—	433	1	no	—
42	C₄	—	1732	1	no	—
43	C₄	C₂×#13181884	1	1	yes	characteristic
44	C₂	—	4	1	no	—
45	C₂	—	433	1	no	—
46	C₂	—	433	1	no	—
47	C₂	—	1732	1	no	—
48	C₂	C₂²⋊#13181884	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#13181884
commutator	C₄×C₄₃₃	C₂×C₄
Frattini	C₄	C₂×#13181884
Fitting	D₄×C₄₃₃	C₄
socle	C₂×C₄₃₃	C₂²⋊C₄
prime radical	D₄×D₄₃₃	C₂
cosocle	C₄×D₄₃₃	C₂²
hypercenter	D₄	#13181884
hypocenter	C₄₃₃	#102
LCS	G ▷ C₄×C₄₃₃ ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. #20294105	C₂	semidirect
2. C₄⋊#13181884	C₂	semidirect
7. D₁₇₃₂	C₄	semidirect
10. D₄×C₄₃₃	C₄	semidirect
24. C₄₃₃	#102	semidirect
32. D₄	#13181884	semidirect

Maximal subgroups

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

subgroup	index
#20294105	2
C₄⋊#13181884	2
D₄×D₄₃₃	2
#102	433