Subgroups — C₁₆×Dic₁₇₉ #26038212

Order 11456.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₇₉⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₁₇₉	C₄	1	1	yes	characteristic
6	C₁₇₉⋊C₁₆	C₄	1	2	yes	complemented
7	C₂×C₈×C₁₇₉	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₇₉	C₄	1	2	yes	complemented
9	C₂×Dic₁₇₉	C₈	1	2	yes	—
10	C₁₇₉⋊C₈	C₈	1	2	yes	—
11	C₂×C₄×C₁₇₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₇₉	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₇₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₁₇₉	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₇₉	C₄²	1	1	yes	characteristic
16	C₄×C₁₇₉	C₂×C₈	1	1	yes	characteristic
17	Dic₁₇₉	C₁₆	1	4	yes	direct product factor
18	C₂×C₁₇₉	C₄×C₈	1	1	yes	characteristic
19	C₂×C₁₇₉	C₂×C₁₆	1	2	yes	—
20	C₁₇₉	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₁₆	—	179	1	no	maximal, Sylow
22	C₂×C₁₆	—	179	1	no	—
23	C₂×C₁₆	D₁₇₉	1	1	yes	characteristic
24	C₄×C₈	—	179	1	no	—
25	C₂×C₈	—	179	1	no	—
26	C₂×C₈	C₂×D₁₇₉	1	1	yes	characteristic
27	C₄²	—	179	1	no	—
28	C₁₆	—	179	2	no	—
29	C₁₆	Dic₁₇₉	1	2	yes	direct product factor
30	C₂×C₄	—	179	2	no	—
31	C₂×C₄	C₄×D₁₇₉	1	1	yes	characteristic
32	C₈	—	179	2	no	—
33	C₈	C₄×D₁₇₉	1	1	yes	characteristic
34	C₈	C₂×Dic₁₇₉	1	1	yes	characteristic
35	C₂²	C₈×D₁₇₉	1	1	yes	characteristic
36	C₄	—	179	4	no	—
37	C₄	C₄×Dic₁₇₉	1	1	yes	characteristic
38	C₄	C₈×D₁₇₉	1	1	yes	characteristic
39	C₂	C₈×Dic₁₇₉	1	1	yes	characteristic
40	C₂	C₁₆×D₁₇₉	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₁₆	D₁₇₉
commutator, hypocenter	C₁₇₉	C₄×C₁₆
Frattini	C₂×C₈	C₂×D₁₇₉
Fitting	C₂×C₁₆×C₁₇₉	C₂
socle, prime radical	C₂²×C₁₇₉	C₂×C₈
cosocle	C₂×C₈×C₁₇₉	C₂²
LCS	G ▷ C₁₇₉
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. C₁₇₉⋊C₁₆	C₄	semidirect
8. C₁₆×C₁₇₉	C₄	semidirect
17. Dic₁₇₉	C₁₆	direct (N × H)
20. C₁₇₉	C₄×C₁₆	semidirect
29. C₁₆	Dic₁₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₇₉⋊C₁₆	2
C₈×Dic₁₇₉	2
C₂×C₁₆×C₁₇₉	2
C₄×C₁₆	179

Subgroups — C16×Dic179 #26038212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×Dic₁₇₉ #26038212