Subgroups — C₂×C₁₁×C₁₆×C₆₇ #72200935

Order 23584.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₁₁×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₆×C₆₇	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₁₁×C₆₇	C₄	1	1	yes	characteristic
4	C₈×C₁₁×C₆₇	C₄	1	1	yes	characteristic
5	C₈×C₁₁×C₆₇	C₂²	1	1	yes	characteristic
6	C₂²×C₁₁×C₆₇	C₈	1	1	yes	characteristic
7	C₄×C₁₁×C₆₇	C₈	1	1	yes	characteristic
8	C₄×C₁₁×C₆₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₆₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₁×C₆₇	C₁₆	1	2	yes	direct product factor
11	C₂×C₁₁×C₆₇	C₂×C₈	1	1	yes	characteristic
12	C₂×C₈×C₆₇	C₂×C₁₁	1	1	yes	characteristic
13	C₁₆×C₆₇	C₂×C₁₁	1	2	yes	direct product factor
14	C₁₁×C₆₇	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₄×C₆₇	C₄×C₁₁	1	1	yes	characteristic
16	C₈×C₆₇	C₄×C₁₁	1	1	yes	characteristic
17	C₈×C₆₇	C₂²×C₁₁	1	1	yes	characteristic
18	C₂×C₁₁×C₁₆	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₆₇	C₈×C₁₁	1	1	yes	characteristic
20	C₄×C₆₇	C₈×C₁₁	1	1	yes	characteristic
21	C₄×C₆₇	C₂×C₄×C₁₁	1	1	yes	characteristic
22	C₂×C₈×C₁₁	C₂×C₆₇	1	1	yes	characteristic
23	C₁₁×C₁₆	C₂×C₆₇	1	2	yes	direct product factor
24	C₂×C₆₇	C₁₁×C₁₆	1	2	yes	direct product factor
25	C₂×C₆₇	C₂×C₈×C₁₁	1	1	yes	characteristic
26	C₂×C₄×C₁₁	C₄×C₆₇	1	1	yes	characteristic
27	C₈×C₁₁	C₄×C₆₇	1	1	yes	characteristic
28	C₈×C₁₁	C₂²×C₆₇	1	1	yes	characteristic
29	C₆₇	C₂×C₁₁×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²×C₁₁	C₈×C₆₇	1	1	yes	characteristic
31	C₄×C₁₁	C₈×C₆₇	1	1	yes	characteristic
32	C₄×C₁₁	C₂×C₄×C₆₇	1	1	yes	characteristic
33	C₂×C₁₆	C₁₁×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₁₁	C₁₆×C₆₇	1	2	yes	direct product factor
35	C₂×C₁₁	C₂×C₈×C₆₇	1	1	yes	characteristic
36	C₂×C₈	C₂×C₁₁×C₆₇	1	1	yes	characteristic
37	C₁₆	C₂×C₁₁×C₆₇	1	2	yes	direct product factor
38	C₁₁	C₂×C₁₆×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₄	C₄×C₁₁×C₆₇	1	1	yes	characteristic
40	C₈	C₄×C₁₁×C₆₇	1	1	yes	characteristic
41	C₈	C₂²×C₁₁×C₆₇	1	1	yes	characteristic
42	C₂²	C₈×C₁₁×C₆₇	1	1	yes	characteristic
43	C₄	C₈×C₁₁×C₆₇	1	1	yes	characteristic
44	C₄	C₂×C₄×C₁₁×C₆₇	1	1	yes	characteristic
45	C₂	C₁₁×C₁₆×C₆₇	1	2	yes	direct product factor
46	C₂	C₂×C₈×C₁₁×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₁₁×C₆₇
socle, prime radical	C₂²×C₁₁×C₆₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₆×C₆₇	C₂	direct (N × H)
9. C₂×C₁₆×C₆₇	C₁₁	direct (N × H)
10. C₂×C₁₁×C₆₇	C₁₆	direct (N × H)
13. C₁₆×C₆₇	C₂×C₁₁	direct (N × H)
14. C₁₁×C₆₇	C₂×C₁₆	direct (N × H)
18. C₂×C₁₁×C₁₆	C₆₇	direct (N × H)
23. C₁₁×C₁₆	C₂×C₆₇	direct (N × H)
24. C₂×C₆₇	C₁₁×C₁₆	direct (N × H)
29. C₆₇	C₂×C₁₁×C₁₆	direct (N × H)
33. C₂×C₁₆	C₁₁×C₆₇	direct (N × H)
34. C₂×C₁₁	C₁₆×C₆₇	direct (N × H)
37. C₁₆	C₂×C₁₁×C₆₇	direct (N × H)
38. C₁₁	C₂×C₁₆×C₆₇	direct (N × H)
45. C₂	C₁₁×C₁₆×C₆₇	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×C₈×C₁₁×C₆₇	2
C₁₁×C₁₆×C₆₇	2
C₂×C₁₆×C₆₇	11
C₂×C₁₁×C₁₆	67

Subgroups — C2×C11×C16×C67 #72200935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₁₆×C₆₇ #72200935