Subgroups — C₇×C₁₃²×C₁₆ #72196653

Order 18928.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₈×C₁₃²	C₂	1	1	yes	maximal, characteristic
2	C₁₃²×C₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄×C₇×C₁₃²	C₄	1	1	yes	characteristic
4	C₂×C₇×C₁₃²	C₈	1	1	yes	characteristic
5	C₇×C₁₃×C₁₆	C₁₃	1	14	yes	maximal, direct product factor
6	C₈×C₁₃²	C₂×C₇	1	1	yes	characteristic
7	C₇×C₁₃²	C₁₆	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₈×C₁₃	C₂×C₁₃	1	14	yes	—
9	C₄×C₁₃²	C₄×C₇	1	1	yes	characteristic
10	C₄×C₇×C₁₃	C₄×C₁₃	1	14	yes	—
11	C₂×C₁₃²	C₇×C₈	1	1	yes	characteristic
12	C₁₃×C₁₆	C₇×C₁₃	1	14	yes	direct product factor
13	C₂×C₇×C₁₃	C₈×C₁₃	1	14	yes	—
14	C₁₃²	C₇×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
15	C₇×C₁₆	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
16	C₈×C₁₃	C₂×C₇×C₁₃	1	14	yes	—
17	C₇×C₁₃	C₁₃×C₁₆	1	14	yes	direct product factor
18	C₇×C₈	C₂×C₁₃²	1	1	yes	characteristic
19	C₄×C₁₃	C₄×C₇×C₁₃	1	14	yes	—
20	C₄×C₇	C₄×C₁₃²	1	1	yes	characteristic
21	C₂×C₁₃	C₇×C₈×C₁₃	1	14	yes	—
22	C₁₆	C₇×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₇	C₈×C₁₃²	1	1	yes	characteristic
24	C₁₃	C₇×C₁₃×C₁₆	1	14	yes	direct product factor
25	C₈	C₂×C₇×C₁₃²	1	1	yes	characteristic
26	C₇	C₁₃²×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
27	C₄	C₄×C₇×C₁₃²	1	1	yes	characteristic
28	C₂	C₇×C₈×C₁₃²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₇×C₁₃²
socle, prime radical	C₂×C₇×C₁₃²	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃²×C₁₆	C₇	direct (N × H)
5. C₇×C₁₃×C₁₆	C₁₃	direct (N × H)
7. C₇×C₁₃²	C₁₆	direct (N × H)
12. C₁₃×C₁₆	C₇×C₁₃	direct (N × H)
14. C₁₃²	C₇×C₁₆	direct (N × H)
15. C₇×C₁₆	C₁₃²	direct (N × H)
17. C₇×C₁₃	C₁₃×C₁₆	direct (N × H)
22. C₁₆	C₇×C₁₃²	direct (N × H)
24. C₁₃	C₇×C₁₃×C₁₆	direct (N × H)
26. C₇	C₁₃²×C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₈×C₁₃²	2
C₁₃²×C₁₆	7
C₇×C₁₃×C₁₆	13

Subgroups — C7×C132×C16 #72196653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₃²×C₁₆ #72196653