Subgroups — #346×C₃₉₇ #38762000

Order 25408.

54 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	C₄	1	4	yes	complemented
7	C₂×C₄×C₃₉₇	C₈	1	2	yes	—
8	C₂×C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₃₉₇	C₈	1	2	yes	—
10	C₈×C₃₉₇	C₂×C₄	1	2	yes	—
11	C₂²×C₃₉₇	C₂×C₈	1	1	yes	characteristic
12	C₄×C₃₉₇	—	2	2	no	—
13	C₄×C₃₉₇	C₄²	1	1	yes	characteristic
14	C₄×C₃₉₇	C₂×C₈	1	1	yes	characteristic
15	C₂×C₃₉₇	C₄×C₈	1	1	yes	characteristic
16	C₂×C₃₉₇	M₃₂	1	2	yes	—
17	C₃₉₇	#346	1	1	yes	characteristic, direct product factor, Sylow
18	#346	C₃₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₁₆	C₂×C₃₉₇	1	2	yes	—
20	C₄×C₈	C₂×C₃₉₇	1	1	yes	characteristic
21	C₂×C₈	C₄×C₃₉₇	1	1	yes	characteristic
22	C₂×C₈	C₂²×C₃₉₇	1	1	yes	characteristic
23	C₄²	C₄×C₃₉₇	1	1	yes	characteristic
24	C₁₆	C₄×C₃₉₇	1	4	yes	complemented
25	C₂×C₄	C₈×C₃₉₇	1	2	yes	—
26	C₂×C₄	C₂×C₄×C₃₉₇	1	1	yes	characteristic
27	C₈	C₈×C₃₉₇	1	2	yes	—
28	C₈	C₂×C₄×C₃₉₇	1	2	yes	—
29	C₂²	C₂×C₈×C₃₉₇	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₄²×C₃₉₇	1	1	yes	characteristic
32	C₄	C₂×C₈×C₃₉₇	1	1	yes	characteristic
33	C₂	C₄×C₈×C₃₉₇	1	1	yes	characteristic
34	C₂	M₃₂×C₃₉₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₃₉₇	C₂²
commutator	C₂	C₄×C₈×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
6. C₁₆×C₃₉₇	C₄	semidirect
17. C₃₉₇	#346	direct (N × H)
18. #346	C₃₉₇	direct (N × H)
24. C₁₆	C₄×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
#346	397

Subgroups — #346×C397 #38762000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #346×C₃₉₇ #38762000