Subgroups — C₁₆×#13097544 #38763406

Order 25408.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#13097544	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₃₉₇	C₂	1	1	yes	maximal, characteristic
4	D₃₉₇⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#13097544	C₄	1	1	yes	characteristic
6	#20263734	C₄	1	2	yes	complemented
7	C₈×D₃₉₇	C₂²	1	1	yes	characteristic
8	#20263706	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₃₉₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#13097544	C₈	1	2	yes	—
11	#15691794	C₈	1	2	yes	—
12	C₄×D₃₉₇	C₂×C₄	1	1	yes	characteristic
13	#15691787	C₂×C₄	1	1	yes	characteristic
14	C₈×C₃₉₇	C₂×C₄	1	1	yes	characteristic
15	C₂×D₃₉₇	C₂×C₈	1	1	yes	characteristic
16	#13097544	C₁₆	1	4	yes	direct product factor
17	C₄×C₃₉₇	C₄²	1	1	yes	characteristic
18	Dic₃₉₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₃₉₇	C₄×C₈	1	1	yes	characteristic
20	D₃₉₇	C₂×C₁₆	1	2	yes	—
21	C₃₉₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	397	1	no	maximal, Sylow
23	C₂×C₁₆	—	397	1	no	—
24	C₂×C₁₆	—	397	1	no	—
25	C₄×C₈	—	397	1	no	—
26	C₂×C₈	—	397	1	no	—
27	C₂×C₈	—	397	1	no	—
28	C₄²	—	397	1	no	—
29	C₁₆	—	397	2	no	—
30	C₁₆	—	397	1	no	—
31	C₁₆	#13097544	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	397	2	no	—
33	C₂×C₄	—	397	1	no	—
34	C₈	—	397	2	no	—
35	C₈	—	397	1	no	—
36	C₈	C₂×#13097544	1	1	yes	characteristic
37	C₂²	—	397	1	no	—
38	C₄	—	397	4	no	—
39	C₄	—	397	1	no	—
40	C₄	C₄×#13097544	1	1	yes	characteristic
41	C₂	—	397	2	no	—
42	C₂	C₈×#13097544	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#13097544
commutator, hypocenter	C₃₉₇	C₄×C₁₆
Frattini	C₈	C₂×#13097544
Fitting	C₁₆×C₃₉₇	C₄
socle	C₂×C₃₉₇	C₄×C₈
prime radical	C₂×D₃₉₇	C₂×C₈
cosocle	C₈×D₃₉₇	C₂²
LCS	G ▷ C₃₉₇
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
6. #20263734	C₄	semidirect
8. #20263706	C₄	semidirect
9. C₁₆×C₃₉₇	C₄	semidirect
16. #13097544	C₁₆	direct (N × H)
21. C₃₉₇	C₄×C₁₆	semidirect
31. C₁₆	#13097544	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃₉₇⋊C₁₆	2
C₈×#13097544	2
C₁₆×D₃₉₇	2
C₄×C₁₆	397

Subgroups — C16×#13097544 #38763406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×#13097544 #38763406