Subgroups — C₈×#13108049 #27169047

Order 12928.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13108049	C₂	1	2	yes	maximal
2	C₈²×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#13108049	C₄	1	4	yes	—
4	C₄×C₈×C₁₀₁	C₄	1	2	yes	—
5	C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
6	#13108049	C₈	1	8	yes	direct product factor
7	C₂×C₈×C₁₀₁	C₈	1	4	yes	—
8	C₂×C₈×C₁₀₁	C₂×C₄	1	2	yes	—
9	C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₁₀₁	C₂×C₈	1	2	yes	—
12	C₈×C₁₀₁	C₁₆	1	8	yes	complemented
13	C₈×C₁₀₁	C₂×C₈	1	4	yes	—
14	C₂²×C₁₀₁	C₄×C₈	1	1	yes	characteristic
15	C₄×C₁₀₁	C₄×C₈	1	2	yes	—
16	C₄×C₁₀₁	C₂×C₁₆	1	4	yes	—
17	C₂×C₁₀₁	C₈²	1	1	yes	characteristic
18	C₂×C₁₀₁	C₄×C₁₆	1	2	yes	—
19	C₈×C₁₆	—	101	1	no	maximal, Sylow
20	C₁₀₁	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₁₆	—	101	2	no	—
22	C₈²	D₁₀₁	1	1	yes	characteristic
23	C₂×C₁₆	—	101	4	no	—
24	C₄×C₈	Dic₁₀₁	1	2	yes	—
25	C₄×C₈	C₂×D₁₀₁	1	1	yes	characteristic
26	C₂×C₈	#11717579	1	4	yes	—
27	C₂×C₈	C₄×D₁₀₁	1	2	yes	—
28	C₄²	C₂×Dic₁₀₁	1	1	yes	characteristic
29	C₁₆	—	101	8	no	—
30	C₂×C₄	C₄×Dic₁₀₁	1	1	yes	characteristic
31	C₂×C₄	C₂×#11717579	1	2	yes	—
32	C₈	#13108049	1	8	yes	direct product factor
33	C₈	C₈×D₁₀₁	1	4	yes	—
34	C₂²	C₄×#11717579	1	1	yes	characteristic
35	C₄	C₈×Dic₁₀₁	1	2	yes	—
36	C₄	C₂×#13108049	1	4	yes	—
37	C₂	C₈×#11717579	1	1	yes	characteristic
38	C₂	C₄×#13108049	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₁₀₁
commutator, hypocenter	C₁₀₁	C₈×C₁₆
Frattini	C₄×C₈	C₂×D₁₀₁
Fitting	C₈²×C₁₀₁	C₂
socle, prime radical	C₂²×C₁₀₁	C₄×C₈
cosocle	C₄×C₈×C₁₀₁	C₂²
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
6. #13108049	C₈	direct (N × H)
12. C₈×C₁₀₁	C₁₆	semidirect
20. C₁₀₁	C₈×C₁₆	semidirect
32. C₈	#13108049	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#13108049	2
C₈²×C₁₀₁	2
C₈×C₁₆	101

Subgroups — C8×#13108049 #27169047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13108049 #27169047