Subgroups — C₂²×C₄×C₇×C₁₉₃ #72199136

Order 21616.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇×C₁₉₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×C₁₉₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₇×C₁₉₃	C₄	1	4	yes	direct product factor
4	C₂²×C₇×C₁₉₃	C₂²	1	3	yes	—
5	C₄×C₇×C₁₉₃	C₂²	1	4	yes	direct product factor
6	C₂²×C₄×C₁₉₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇×C₁₉₃	C₂×C₄	1	6	yes	direct product factor
8	C₂×C₇×C₁₉₃	C₂³	1	1	yes	characteristic
9	C₂³×C₁₉₃	C₂×C₇	1	1	yes	characteristic
10	C₂×C₄×C₁₉₃	C₂×C₇	1	6	yes	direct product factor
11	C₇×C₁₉₃	C₂²×C₄	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₁₉₃	C₄×C₇	1	4	yes	direct product factor
13	C₂²×C₁₉₃	C₂²×C₇	1	3	yes	—
14	C₄×C₁₉₃	C₂²×C₇	1	4	yes	direct product factor
15	C₂×C₁₉₃	C₂×C₄×C₇	1	6	yes	direct product factor
16	C₂×C₁₉₃	C₂³×C₇	1	1	yes	characteristic
17	C₁₉₃	C₂²×C₄×C₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²×C₄×C₇	C₁₉₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂³×C₇	C₂×C₁₉₃	1	1	yes	characteristic
20	C₂×C₄×C₇	C₂×C₁₉₃	1	6	yes	direct product factor
21	C₂²×C₇	C₄×C₁₉₃	1	4	yes	direct product factor
22	C₂²×C₇	C₂²×C₁₉₃	1	3	yes	—
23	C₄×C₇	C₂²×C₁₉₃	1	4	yes	direct product factor
24	C₂²×C₄	C₇×C₁₉₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₇	C₂×C₄×C₁₉₃	1	6	yes	direct product factor
26	C₂×C₇	C₂³×C₁₉₃	1	1	yes	characteristic
27	C₂³	C₂×C₇×C₁₉₃	1	1	yes	characteristic
28	C₂×C₄	C₂×C₇×C₁₉₃	1	6	yes	direct product factor
29	C₇	C₂²×C₄×C₁₉₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	C₄×C₇×C₁₉₃	1	4	yes	direct product factor
31	C₂²	C₂²×C₇×C₁₉₃	1	3	yes	—
32	C₄	C₂²×C₇×C₁₉₃	1	4	yes	direct product factor
33	C₂	C₂×C₄×C₇×C₁₉₃	1	6	yes	direct product factor
34	C₂	C₂³×C₇×C₁₉₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₇×C₁₉₃
socle, prime radical	C₂³×C₇×C₁₉₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇×C₁₉₃	C₂	direct (N × H)
3. C₂²×C₇×C₁₉₃	C₄	direct (N × H)
5. C₄×C₇×C₁₉₃	C₂²	direct (N × H)
6. C₂²×C₄×C₁₉₃	C₇	direct (N × H)
7. C₂×C₇×C₁₉₃	C₂×C₄	direct (N × H)
10. C₂×C₄×C₁₉₃	C₂×C₇	direct (N × H)
11. C₇×C₁₉₃	C₂²×C₄	direct (N × H)
12. C₂²×C₁₉₃	C₄×C₇	direct (N × H)
14. C₄×C₁₉₃	C₂²×C₇	direct (N × H)
15. C₂×C₁₉₃	C₂×C₄×C₇	direct (N × H)
17. C₁₉₃	C₂²×C₄×C₇	direct (N × H)
18. C₂²×C₄×C₇	C₁₉₃	direct (N × H)
20. C₂×C₄×C₇	C₂×C₁₉₃	direct (N × H)
21. C₂²×C₇	C₄×C₁₉₃	direct (N × H)
23. C₄×C₇	C₂²×C₁₉₃	direct (N × H)
24. C₂²×C₄	C₇×C₁₉₃	direct (N × H)
25. C₂×C₇	C₂×C₄×C₁₉₃	direct (N × H)
28. C₂×C₄	C₂×C₇×C₁₉₃	direct (N × H)
29. C₇	C₂²×C₄×C₁₉₃	direct (N × H)
30. C₂²	C₄×C₇×C₁₉₃	direct (N × H)
32. C₄	C₂²×C₇×C₁₉₃	direct (N × H)
33. C₂	C₂×C₄×C₇×C₁₉₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₇×C₁₉₃	2
C₂×C₄×C₇×C₁₉₃	2
C₂²×C₄×C₁₉₃	7
C₂²×C₄×C₇	193

Subgroups — C22×C4×C7×C193 #72199136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₇×C₁₉₃ #72199136