Subgroups — D₃₉₇⋊M₁₆ #27163181

Order 12704.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263741	C₂	1	2	yes	maximal, complemented
2	#20263740	C₂	1	2	yes	maximal, complemented
3	D₃₉₇⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₃₉₇	C₂	1	1	yes	maximal, characteristic
5	#15691794	C₂²	1	4	yes	complemented
6	C₂²×D₃₉₇	C₄	1	1	yes	characteristic
7	C₂×Dic₃₉₇	C₂²	1	1	yes	characteristic
8	C₄×D₃₉₇	C₄	1	1	yes	characteristic
9	C₄×D₃₉₇	C₄	1	1	yes	characteristic
10	C₄×D₃₉₇	C₂²	1	1	yes	characteristic
11	C₄×D₃₉₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₃₉₇	C₄	1	1	yes	characteristic
13	C₂²×C₃₉₇	C₂×C₄	1	1	yes	characteristic
14	C₂×D₃₉₇	—	2	2	no	—
15	C₂×D₃₉₇	C₂×C₄	1	1	yes	characteristic
16	C₂×D₃₉₇	C₂×C₄	1	1	yes	characteristic
17	C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
18	C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
19	Dic₃₉₇	C₂×C₄	1	1	yes	characteristic
20	Dic₃₉₇	C₂³	1	1	yes	characteristic
21	C₂×C₃₉₇	—	2	1	no	—
22	C₂×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
23	D₃₉₇	—	2	1	no	—
24	D₃₉₇	M₁₆	1	2	yes	complemented
25	C₃₉₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	397	1	no	maximal, Sylow
27	C₂²×C₄	—	397	1	no	—
28	M₁₆	—	397	2	no	—
29	M₁₆	—	397	2	no	—
30	C₂×C₈	—	397	2	no	—
31	C₂³	—	397	1	no	—
32	C₂×C₄	—	397	1	no	—
33	C₂×C₄	—	397	1	no	—
34	C₂×C₄	—	397	1	no	—
35	C₂×C₄	—	397	1	no	—
36	C₂×C₄	—	397	1	no	—
37	C₂×C₄	#13097544	1	1	yes	characteristic
38	C₈	—	397	4	no	—
39	C₂²	—	794	2	no	—
40	C₂²	—	397	1	no	—
41	C₂²	—	397	1	no	—
42	C₂²	C₂×#13097544	1	1	yes	characteristic
43	C₄	—	397	1	no	—
44	C₄	—	397	1	no	—
45	C₄	C₂×#13097544	1	1	yes	characteristic
46	C₄	C₂×#13097544	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	794	1	no	—
49	C₂	—	397	2	no	—
50	C₂	C₂²×#13097544	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13097544
commutator, socle	C₂×C₃₉₇	C₂²×C₄
Frattini	C₂	C₂²×#13097544
Fitting	C₂×C₄×C₃₉₇	C₄
prime radical	C₂²×D₃₉₇	C₄
cosocle	Dic₃₉₇	C₂³
hypercenter	C₂×C₄	#13097544
hypocenter	C₃₉₇	C₂×M₁₆
LCS	G ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #20263741	C₂	semidirect
2. #20263740	C₂	semidirect
3. D₃₉₇⋊C₈	C₂	semidirect
5. #15691794	C₂²	semidirect
24. D₃₉₇	M₁₆	semidirect
25. C₃₉₇	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#20263741	2
#20263740	2
D₃₉₇⋊C₈	2
C₂×C₄×D₃₉₇	2
C₂×M₁₆	397

Subgroups — D397⋊M16 #27163181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₉₇⋊M₁₆ #27163181