Subgroups — C₈²×C₁₁×C₂₃ #72194151

Order 16192.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₁₁×C₂₃	C₂	1	3	yes	maximal
2	C₂×C₈×C₁₁×C₂₃	C₄	1	6	yes	—
3	C₄²×C₁₁×C₂₃	C₂²	1	1	yes	characteristic
4	C₂×C₄×C₁₁×C₂₃	C₂×C₄	1	3	yes	—
5	C₈×C₁₁×C₂₃	C₈	1	12	yes	direct product factor
6	C₈²×C₂₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₁₁×C₂₃	C₄²	1	1	yes	characteristic
8	C₄×C₁₁×C₂₃	C₂×C₈	1	6	yes	—
9	C₄×C₈×C₂₃	C₂×C₁₁	1	3	yes	—
10	C₈²×C₁₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₁×C₂₃	C₄×C₈	1	3	yes	—
12	C₂×C₈×C₂₃	C₄×C₁₁	1	6	yes	—
13	C₄²×C₂₃	C₂²×C₁₁	1	1	yes	characteristic
14	C₄×C₈×C₁₁	C₂×C₂₃	1	3	yes	—
15	C₁₁×C₂₃	C₈²	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₄×C₂₃	C₂×C₄×C₁₁	1	3	yes	—
17	C₈×C₂₃	C₈×C₁₁	1	12	yes	direct product factor
18	C₂×C₈×C₁₁	C₄×C₂₃	1	6	yes	—
19	C₄²×C₁₁	C₂²×C₂₃	1	1	yes	characteristic
20	C₂²×C₂₃	C₄²×C₁₁	1	1	yes	characteristic
21	C₄×C₂₃	C₂×C₈×C₁₁	1	6	yes	—
22	C₂×C₄×C₁₁	C₂×C₄×C₂₃	1	3	yes	—
23	C₈×C₁₁	C₈×C₂₃	1	12	yes	direct product factor
24	C₈²	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₂₃	C₄×C₈×C₁₁	1	3	yes	—
26	C₂²×C₁₁	C₄²×C₂₃	1	1	yes	characteristic
27	C₄×C₁₁	C₂×C₈×C₂₃	1	6	yes	—
28	C₄×C₈	C₂×C₁₁×C₂₃	1	3	yes	—
29	C₂₃	C₈²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₁₁	C₄×C₈×C₂₃	1	3	yes	—
31	C₂×C₈	C₄×C₁₁×C₂₃	1	6	yes	—
32	C₄²	C₂²×C₁₁×C₂₃	1	1	yes	characteristic
33	C₁₁	C₈²×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₄	C₂×C₄×C₁₁×C₂₃	1	3	yes	—
35	C₈	C₈×C₁₁×C₂₃	1	12	yes	direct product factor
36	C₂²	C₄²×C₁₁×C₂₃	1	1	yes	characteristic
37	C₄	C₂×C₈×C₁₁×C₂₃	1	6	yes	—
38	C₂	C₄×C₈×C₁₁×C₂₃	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄²	C₂²×C₁₁×C₂₃
socle, prime radical	C₂²×C₁₁×C₂₃	C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₈×C₁₁×C₂₃	C₈	direct (N × H)
6. C₈²×C₂₃	C₁₁	direct (N × H)
10. C₈²×C₁₁	C₂₃	direct (N × H)
15. C₁₁×C₂₃	C₈²	direct (N × H)
17. C₈×C₂₃	C₈×C₁₁	direct (N × H)
23. C₈×C₁₁	C₈×C₂₃	direct (N × H)
24. C₈²	C₁₁×C₂₃	direct (N × H)
29. C₂₃	C₈²×C₁₁	direct (N × H)
33. C₁₁	C₈²×C₂₃	direct (N × H)
35. C₈	C₈×C₁₁×C₂₃	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×C₈×C₁₁×C₂₃	2
C₈²×C₂₃	11
C₈²×C₁₁	23

Subgroups — C82×C11×C23 #72194151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈²×C₁₁×C₂₃ #72194151