Subgroups — (C₂×#13097544)⋊C₄ #27163147

Order 12704.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13097544	C₂	1	2	yes	maximal
2	C₂×C₄×D₃₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#13097544	—	2	2	no	—
4	C₂×#13097544	—	2	2	no	—
5	C₂×#13097544	C₄	1	4	yes	complemented
6	C₂²×D₃₉₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₃₉₇	C₄	1	1	yes	characteristic, complemented
8	C₄×D₃₉₇	—	2	2	no	—
9	C₂×C₄×C₃₉₇	C₄	1	1	yes	characteristic, complemented
10	C₂²×C₃₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂×D₃₉₇	C₂×C₄	1	2	yes	—
12	C₂×D₃₉₇	D₄	1	1	yes	characteristic
13	C₂×D₃₉₇	D₄	1	2	yes	—
14	C₂×D₃₉₇	Q₈	1	1	yes	characteristic
15	#13097544	—	2	4	no	—
16	C₄×C₃₉₇	—	2	1	no	—
17	Dic₃₉₇	—	2	1	no	—
18	C₂×C₃₉₇	C₄²	1	1	yes	characteristic
19	C₂×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₃₉₇	C₄⋊C₄	1	1	yes	characteristic
21	D₃₉₇	C₂²⋊C₄	1	2	yes	—
22	D₃₉₇	C₄⋊C₄	1	2	yes	—
23	C₃₉₇	#95	1	1	yes	characteristic, complemented, Sylow
24	#95	—	397	1	no	maximal, Sylow
25	C₂²×C₄	—	397	2	no	—
26	C₂²×C₄	—	397	1	no	—
27	C₂³	—	397	1	no	—
28	C₂×C₄	—	794	2	no	—
29	C₂×C₄	—	794	2	no	—
30	C₂×C₄	—	794	2	no	—
31	C₂×C₄	—	397	4	no	—
32	C₂×C₄	—	397	1	no	—
33	C₂×C₄	#13097544	1	1	yes	characteristic, complemented
34	C₂²	—	397	2	no	—
35	C₂²	—	397	2	no	—
36	C₂²	—	397	1	no	—
37	C₂²	—	397	1	no	—
38	C₂²	C₂×#13097544	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	794	4	no	—
41	C₄	—	794	1	no	—
42	C₂	—	397	2	no	—
43	C₂	—	397	2	no	—
44	C₂	C₄×#13097544	1	1	yes	characteristic
45	C₂	C₂²⋊#13097544	1	1	yes	characteristic
46	C₂	C₄⋊#13097544	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#13097544
commutator	C₂×C₃₉₇	C₄²
Fitting	C₂×C₄×C₃₉₇	C₄
socle	C₂²×C₃₉₇	C₂×C₄
prime radical, cosocle	C₂²×D₃₉₇	C₂²
hypercenter	C₂×C₄	#13097544
hypocenter	C₃₉₇	#95
LCS	G ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
5. C₂×#13097544	C₄	semidirect
7. C₂×Dic₃₉₇	C₄	semidirect
9. C₂×C₄×C₃₉₇	C₄	semidirect
23. C₃₉₇	#95	semidirect
33. C₂×C₄	#13097544	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13097544	2
C₂×C₄×D₃₉₇	2
#95	397

Subgroups — (C2×#13097544)⋊C4 #27163147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#13097544)⋊C₄ #27163147