Subgroups — C₂²×C₁₆×C₃₆₇ #37553820

Order 23488.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₃₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×C₃₆₇	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₃₆₇	C₄	1	1	yes	characteristic
4	C₂×C₈×C₃₆₇	C₄	1	3	yes	—
5	C₂×C₈×C₃₆₇	C₂²	1	3	yes	—
6	C₁₆×C₃₆₇	C₂²	1	4	yes	direct product factor
7	C₂³×C₃₆₇	C₈	1	1	yes	characteristic
8	C₂×C₄×C₃₆₇	C₈	1	3	yes	—
9	C₂×C₄×C₃₆₇	C₂×C₄	1	3	yes	—
10	C₈×C₃₆₇	C₂×C₄	1	3	yes	—
11	C₈×C₃₆₇	C₂³	1	1	yes	characteristic
12	C₂²×C₃₆₇	C₁₆	1	4	yes	direct product factor
13	C₂²×C₃₆₇	C₂×C₈	1	3	yes	—
14	C₄×C₃₆₇	C₂×C₈	1	3	yes	—
15	C₄×C₃₆₇	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₃₆₇	C₂×C₁₆	1	6	yes	direct product factor
17	C₂×C₃₆₇	C₂²×C₈	1	1	yes	characteristic
18	C₃₆₇	C₂²×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²×C₁₆	C₃₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂²×C₈	C₂×C₃₆₇	1	1	yes	characteristic
21	C₂×C₁₆	C₂×C₃₆₇	1	6	yes	direct product factor
22	C₂²×C₄	C₄×C₃₆₇	1	1	yes	characteristic
23	C₂×C₈	C₄×C₃₆₇	1	3	yes	—
24	C₂×C₈	C₂²×C₃₆₇	1	3	yes	—
25	C₁₆	C₂²×C₃₆₇	1	4	yes	direct product factor
26	C₂³	C₈×C₃₆₇	1	1	yes	characteristic
27	C₂×C₄	C₈×C₃₆₇	1	3	yes	—
28	C₂×C₄	C₂×C₄×C₃₆₇	1	3	yes	—
29	C₈	C₂×C₄×C₃₆₇	1	3	yes	—
30	C₈	C₂³×C₃₆₇	1	1	yes	characteristic
31	C₂²	C₁₆×C₃₆₇	1	4	yes	direct product factor
32	C₂²	C₂×C₈×C₃₆₇	1	3	yes	—
33	C₄	C₂×C₈×C₃₆₇	1	3	yes	—
34	C₄	C₂²×C₄×C₃₆₇	1	1	yes	characteristic
35	C₂	C₂×C₁₆×C₃₆₇	1	6	yes	direct product factor
36	C₂	C₂²×C₈×C₃₆₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂³×C₃₆₇
socle, prime radical	C₂³×C₃₆₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₆×C₃₆₇	C₂	direct (N × H)
6. C₁₆×C₃₆₇	C₂²	direct (N × H)
12. C₂²×C₃₆₇	C₁₆	direct (N × H)
16. C₂×C₃₆₇	C₂×C₁₆	direct (N × H)
18. C₃₆₇	C₂²×C₁₆	direct (N × H)
19. C₂²×C₁₆	C₃₆₇	direct (N × H)
21. C₂×C₁₆	C₂×C₃₆₇	direct (N × H)
25. C₁₆	C₂²×C₃₆₇	direct (N × H)
31. C₂²	C₁₆×C₃₆₇	direct (N × H)
35. C₂	C₂×C₁₆×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
C₂²×C₈×C₃₆₇	2
C₂×C₁₆×C₃₆₇	2
C₂²×C₁₆	367

Subgroups — C22×C16×C367 #37553820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₆×C₃₆₇ #37553820