Subgroups — #1425×C₁₃₇ #31776436

Order 17536.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#368×C₁₃₇	C₂	1	2	yes	maximal
3	C₂×C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
4	#108×C₁₃₇	—	2	2	no	—
5	C₃₂×C₁₃₇	C₄	1	2	yes	—
6	M₁₆×C₁₃₇	—	4	2	no	—
7	C₂×C₈×C₁₃₇	D₄	1	1	yes	characteristic
8	C₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₃₇	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₃₇	D₈	1	1	yes	characteristic
11	C₈×C₁₃₇	—	8	2	no	—
12	C₈×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₁₃₇	Q₁₆	1	1	yes	characteristic
14	C₂²×C₁₃₇	Q₃₂	1	1	yes	characteristic
15	C₄×C₁₃₇	#107	1	1	yes	characteristic
16	C₄×C₁₃₇	D₁₆	1	1	yes	characteristic
17	C₂×C₁₃₇	—	2	1	no	—
18	C₂×C₁₃₇	#366	1	1	yes	characteristic
19	C₁₃₇	#1425	1	1	yes	characteristic, direct product factor, Sylow
20	#1425	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃₂	C₂×C₁₃₇	1	1	yes	characteristic
22	#368	C₂×C₁₃₇	1	2	yes	—
23	C₂×C₁₆	C₂²×C₁₃₇	1	1	yes	characteristic
24	#108	—	2	2	no	—
25	C₃₂	C₄×C₁₃₇	1	2	yes	—
26	M₁₆	—	4	2	no	—
27	C₂×C₈	D₄×C₁₃₇	1	1	yes	characteristic
28	C₁₆	C₂×C₄×C₁₃₇	1	1	yes	characteristic
29	C₁₆	Q₈×C₁₃₇	1	1	yes	characteristic
30	C₂×C₄	D₈×C₁₃₇	1	1	yes	characteristic
31	C₈	—	8	2	no	—
32	C₈	C₄⋊C₄×C₁₃₇	1	1	yes	characteristic
33	C₈	Q₁₆×C₁₃₇	1	1	yes	characteristic
34	C₂²	Q₃₂×C₁₃₇	1	1	yes	characteristic
35	C₄	#107×C₁₃₇	1	1	yes	characteristic
36	C₄	D₁₆×C₁₃₇	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#366×C₁₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃₇	D₁₆
commutator	C₁₆	C₂×C₄×C₁₃₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₃₇
socle	C₂×C₁₃₇	#366
prime radical	C₂²×C₁₃₇	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₇ ◁ C₂×C₄×C₁₃₇ ◁ C₂×C₈×C₁₃₇ ◁ C₂×C₁₆×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
19. C₁₃₇	#1425	direct (N × H)
20. #1425	C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₂×C₁₃₇	2
#368×C₁₃₇	2
#1425	137

Subgroups — #1425×C137 #31776436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1425×C₁₃₇ #31776436