Subgroups — #28357132

Order 13856.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄₃₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#16812358	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₄₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄₃₃	C₄	1	1	yes	characteristic
5	C₂×Dic₄₃₃	C₄	1	1	yes	characteristic
6	C₄×D₄₃₃	—	2	1	no	—
7	C₄×D₄₃₃	—	2	1	no	—
8	#16812358	—	2	1	no	—
9	C₂×C₄×C₄₃₃	C₂²	1	1	yes	characteristic
10	C₈×C₄₃₃	—	2	1	no	—
11	C₂²×C₄₃₃	C₂×C₄	1	1	yes	characteristic
12	C₂×D₄₃₃	—	2	1	no	—
13	C₂×D₄₃₃	—	2	1	no	—
14	C₂×D₄₃₃	C₈	1	2	yes	complemented
15	C₄×C₄₃₃	D₄	1	1	yes	characteristic
16	C₄×C₄₃₃	D₄	1	1	yes	characteristic
17	Dic₄₃₃	—	2	1	no	—
18	C₂×C₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄₃₃	C₂×C₈	1	1	yes	characteristic
20	C₂×C₄₃₃	M₁₆	1	1	yes	characteristic
21	D₄₃₃	—	2	2	no	—
22	C₄₃₃	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
23	C₂²⋊C₈	—	433	1	no	maximal, Sylow
24	C₂²×C₄	—	433	1	no	—
25	C₂×C₈	—	433	1	no	—
26	C₂×C₈	D₄₃₃	1	1	yes	characteristic, complemented
27	C₂³	—	433	1	no	—
28	C₂×C₄	—	866	1	no	—
29	C₂×C₄	—	866	1	no	—
30	C₂×C₄	—	433	1	no	—
31	C₂×C₄	C₂×D₄₃₃	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	866	1	no	—
34	C₂²	—	866	1	no	—
35	C₂²	—	866	1	no	—
36	C₂²	—	433	2	no	—
37	C₂²	C₄×D₄₃₃	1	1	yes	characteristic
38	C₄	—	866	1	no	—
39	C₄	C₂²⋊D₄₃₃	1	1	yes	characteristic
40	C₄	D₁₇₃₂	1	1	yes	characteristic
41	C₂	—	866	2	no	—
42	C₂	#20294074	1	1	yes	characteristic
43	C₂	C₈×D₄₃₃	1	1	yes	characteristic
44	C₂	#20294080	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₄₃₃
commutator	C₂×C₄₃₃	C₂×C₈
Fitting	C₂×C₈×C₄₃₃	C₂
socle	C₂²×C₄₃₃	C₂×C₄
prime radical	C₂²×D₄₃₃	C₄
cosocle	C₂×C₄×C₄₃₃	C₂²
hypercenter	C₂×C₈	D₄₃₃
hypocenter	C₄₃₃	C₂²⋊C₈
LCS	G ▷ C₂×C₄₃₃ ▷ C₄₃₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#16812358	C₂	semidirect
3. C₂×C₈×C₄₃₃	C₂	semidirect
14. C₂×D₄₃₃	C₈	semidirect
22. C₄₃₃	C₂²⋊C₈	semidirect
26. C₂×C₈	D₄₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₄₃₃	2
C₂×#16812358	2
C₂×C₈×C₄₃₃	2
C₂²⋊C₈	433