Subgroups — C₄⋊C₁₆×C₃₉₇ #38762017

Order 25408.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₃₉₇	C₂	1	2	yes	maximal
2	C₄×C₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₃₉₇	C₄	1	1	yes	characteristic
4	C₂×C₈×C₃₉₇	C₂²	1	1	yes	characteristic
5	C₄²×C₃₉₇	C₄	1	1	yes	characteristic
6	C₁₆×C₃₉₇	—	2	2	no	—
7	C₂×C₄×C₃₉₇	C₈	1	1	yes	characteristic
8	C₂×C₄×C₃₉₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
10	C₈×C₃₉₇	—	2	1	no	—
11	C₈×C₃₉₇	D₄	1	1	yes	characteristic
12	C₈×C₃₉₇	Q₈	1	1	yes	characteristic
13	C₂²×C₃₉₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₃₉₇	—	2	1	no	—
15	C₄×C₃₉₇	C₁₆	1	2	yes	complemented
16	C₄×C₃₉₇	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₃₉₇	M₁₆	1	1	yes	characteristic
18	C₂×C₃₉₇	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₃₉₇	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₃₉₇	M₃₂	1	1	yes	characteristic
21	C₃₉₇	C₄⋊C₁₆	1	1	yes	characteristic, direct product factor, Sylow
22	C₄⋊C₁₆	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×C₁₆	C₂×C₃₉₇	1	2	yes	—
24	C₄×C₈	C₂×C₃₉₇	1	1	yes	characteristic
25	C₂×C₈	C₄×C₃₉₇	1	1	yes	characteristic
26	C₂×C₈	C₂²×C₃₉₇	1	1	yes	characteristic
27	C₄²	C₄×C₃₉₇	1	1	yes	characteristic
28	C₁₆	—	2	2	no	—
29	C₂×C₄	C₈×C₃₉₇	1	1	yes	characteristic
30	C₂×C₄	C₈×C₃₉₇	1	1	yes	characteristic
31	C₂×C₄	C₂×C₄×C₃₉₇	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	D₄×C₃₉₇	1	1	yes	characteristic
34	C₈	Q₈×C₃₉₇	1	1	yes	characteristic
35	C₂²	C₂×C₈×C₃₉₇	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	C₁₆×C₃₉₇	1	2	yes	complemented
38	C₄	C₄⋊C₄×C₃₉₇	1	1	yes	characteristic
39	C₄	M₁₆×C₃₉₇	1	1	yes	characteristic
40	C₂	C₄⋊C₈×C₃₉₇	1	1	yes	characteristic
41	C₂	C₂×C₁₆×C₃₉₇	1	1	yes	characteristic
42	C₂	M₃₂×C₃₉₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₃₉₇	C₂²
commutator	C₂	C₂×C₁₆×C₃₉₇
Frattini, cosocle	C₂×C₈	C₂²×C₃₉₇
socle, prime radical	C₂²×C₃₉₇	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₉₇ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₄×C₃₉₇	C₁₆	semidirect
21. C₃₉₇	C₄⋊C₁₆	direct (N × H)
22. C₄⋊C₁₆	C₃₉₇	direct (N × H)
37. C₄	C₁₆×C₃₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×C₃₉₇	2
C₄×C₈×C₃₉₇	2
C₄⋊C₁₆	397

Subgroups — C4⋊C16×C397 #38762017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₁₆×C₃₉₇ #38762017