Subgroups — C₂³×C₈×C₃₆₇ #37553883

Order 23488.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₃₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₃₆₇	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₃₆₇	C₄	1	1	yes	characteristic
4	C₂²×C₄×C₃₆₇	C₄	1	7	yes	—
5	C₂²×C₄×C₃₆₇	C₂²	1	7	yes	—
6	C₂×C₈×C₃₆₇	C₂²	1	28	yes	direct product factor
7	C₂³×C₃₆₇	C₈	1	8	yes	direct product factor
8	C₂³×C₃₆₇	C₂×C₄	1	7	yes	—
9	C₂×C₄×C₃₆₇	C₂×C₄	1	21	yes	—
10	C₂×C₄×C₃₆₇	C₂³	1	7	yes	—
11	C₈×C₃₆₇	C₂³	1	8	yes	direct product factor
12	C₂²×C₃₆₇	C₂×C₈	1	28	yes	direct product factor
13	C₂²×C₃₆₇	C₂²×C₄	1	7	yes	—
14	C₄×C₃₆₇	C₂²×C₄	1	7	yes	—
15	C₄×C₃₆₇	C₂⁴	1	1	yes	characteristic
16	C₂×C₃₆₇	C₂²×C₈	1	14	yes	direct product factor
17	C₂×C₃₆₇	C₂³×C₄	1	1	yes	characteristic
18	C₃₆₇	C₂³×C₈	1	1	yes	characteristic, direct product factor, Sylow
19	C₂³×C₈	C₃₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂³×C₄	C₂×C₃₆₇	1	1	yes	characteristic
21	C₂²×C₈	C₂×C₃₆₇	1	14	yes	direct product factor
22	C₂⁴	C₄×C₃₆₇	1	1	yes	characteristic
23	C₂²×C₄	C₄×C₃₆₇	1	7	yes	—
24	C₂²×C₄	C₂²×C₃₆₇	1	7	yes	—
25	C₂×C₈	C₂²×C₃₆₇	1	28	yes	direct product factor
26	C₂³	C₈×C₃₆₇	1	8	yes	direct product factor
27	C₂³	C₂×C₄×C₃₆₇	1	7	yes	—
28	C₂×C₄	C₂×C₄×C₃₆₇	1	21	yes	—
29	C₂×C₄	C₂³×C₃₆₇	1	7	yes	—
30	C₈	C₂³×C₃₆₇	1	8	yes	direct product factor
31	C₂²	C₂×C₈×C₃₆₇	1	28	yes	direct product factor
32	C₂²	C₂²×C₄×C₃₆₇	1	7	yes	—
33	C₄	C₂²×C₄×C₃₆₇	1	7	yes	—
34	C₄	C₂⁴×C₃₆₇	1	1	yes	characteristic
35	C₂	C₂²×C₈×C₃₆₇	1	14	yes	direct product factor
36	C₂	C₂³×C₄×C₃₆₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁴×C₃₆₇
socle, prime radical	C₂⁴×C₃₆₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₈×C₃₆₇	C₂	direct (N × H)
6. C₂×C₈×C₃₆₇	C₂²	direct (N × H)
7. C₂³×C₃₆₇	C₈	direct (N × H)
11. C₈×C₃₆₇	C₂³	direct (N × H)
12. C₂²×C₃₆₇	C₂×C₈	direct (N × H)
16. C₂×C₃₆₇	C₂²×C₈	direct (N × H)
18. C₃₆₇	C₂³×C₈	direct (N × H)
19. C₂³×C₈	C₃₆₇	direct (N × H)
21. C₂²×C₈	C₂×C₃₆₇	direct (N × H)
25. C₂×C₈	C₂²×C₃₆₇	direct (N × H)
26. C₂³	C₈×C₃₆₇	direct (N × H)
30. C₈	C₂³×C₃₆₇	direct (N × H)
31. C₂²	C₂×C₈×C₃₆₇	direct (N × H)
35. C₂	C₂²×C₈×C₃₆₇	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×C₄×C₃₆₇	2
C₂²×C₈×C₃₆₇	2
C₂³×C₈	367

Subgroups — C23×C8×C367 #37553883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₈×C₃₆₇ #37553883