Subgroups — C₂×C₇×C₈×C₁₄₉ #72194673

Order 16688.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₇×C₈×C₁₄₉	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₇×C₁₄₉	C₄	1	1	yes	characteristic
4	C₄×C₇×C₁₄₉	C₄	1	1	yes	characteristic
5	C₄×C₇×C₁₄₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₄₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇×C₁₄₉	C₈	1	2	yes	direct product factor
8	C₂×C₇×C₁₄₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₄₉	C₂×C₇	1	1	yes	characteristic
10	C₈×C₁₄₉	C₂×C₇	1	2	yes	direct product factor
11	C₇×C₁₄₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₁₄₉	C₄×C₇	1	1	yes	characteristic
13	C₄×C₁₄₉	C₄×C₇	1	1	yes	characteristic
14	C₄×C₁₄₉	C₂²×C₇	1	1	yes	characteristic
15	C₂×C₁₄₉	C₇×C₈	1	2	yes	direct product factor
16	C₂×C₁₄₉	C₂×C₄×C₇	1	1	yes	characteristic
17	C₁₄₉	C₂×C₇×C₈	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₇×C₈	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₄×C₇	C₂×C₁₄₉	1	1	yes	characteristic
20	C₇×C₈	C₂×C₁₄₉	1	2	yes	direct product factor
21	C₂²×C₇	C₄×C₁₄₉	1	1	yes	characteristic
22	C₄×C₇	C₄×C₁₄₉	1	1	yes	characteristic
23	C₄×C₇	C₂²×C₁₄₉	1	1	yes	characteristic
24	C₂×C₈	C₇×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₇	C₈×C₁₄₉	1	2	yes	direct product factor
26	C₂×C₇	C₂×C₄×C₁₄₉	1	1	yes	characteristic
27	C₂×C₄	C₂×C₇×C₁₄₉	1	1	yes	characteristic
28	C₈	C₂×C₇×C₁₄₉	1	2	yes	direct product factor
29	C₇	C₂×C₈×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	C₄×C₇×C₁₄₉	1	1	yes	characteristic
31	C₄	C₄×C₇×C₁₄₉	1	1	yes	characteristic
32	C₄	C₂²×C₇×C₁₄₉	1	1	yes	characteristic
33	C₂	C₇×C₈×C₁₄₉	1	2	yes	direct product factor
34	C₂	C₂×C₄×C₇×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₇×C₁₄₉
socle, prime radical	C₂²×C₇×C₁₄₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×C₈×C₁₄₉	C₂	direct (N × H)
6. C₂×C₈×C₁₄₉	C₇	direct (N × H)
7. C₂×C₇×C₁₄₉	C₈	direct (N × H)
10. C₈×C₁₄₉	C₂×C₇	direct (N × H)
11. C₇×C₁₄₉	C₂×C₈	direct (N × H)
15. C₂×C₁₄₉	C₇×C₈	direct (N × H)
17. C₁₄₉	C₂×C₇×C₈	direct (N × H)
18. C₂×C₇×C₈	C₁₄₉	direct (N × H)
20. C₇×C₈	C₂×C₁₄₉	direct (N × H)
24. C₂×C₈	C₇×C₁₄₉	direct (N × H)
25. C₂×C₇	C₈×C₁₄₉	direct (N × H)
28. C₈	C₂×C₇×C₁₄₉	direct (N × H)
29. C₇	C₂×C₈×C₁₄₉	direct (N × H)
33. C₂	C₇×C₈×C₁₄₉	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×C₄×C₇×C₁₄₉	2
C₇×C₈×C₁₄₉	2
C₂×C₈×C₁₄₉	7
C₂×C₇×C₈	149

Subgroups — C2×C7×C8×C149 #72194673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₈×C₁₄₉ #72194673