Subgroups — #347×C₁₃₁ #22552791

Order 8384.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₃₂×C₁₃₁	C₂	1	2	yes	maximal
2	#97×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₁₃₁	C₄	1	1	yes	characteristic
4	C₂×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
5	C₄²×C₁₃₁	C₄	1	1	yes	characteristic
6	C₁₆×C₁₃₁	C₄	1	4	yes	complemented
7	C₂×C₄×C₁₃₁	—	2	1	no	—
8	C₂×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₃₁	—	2	1	no	—
10	C₈×C₁₃₁	C₂×C₄	1	2	yes	—
11	C₂²×C₁₃₁	M₁₆	1	1	yes	characteristic
12	C₄×C₁₃₁	—	4	1	no	—
13	C₄×C₁₃₁	C₄²	1	1	yes	characteristic
14	C₄×C₁₃₁	M₁₆	1	1	yes	characteristic
15	C₂×C₁₃₁	—	2	1	no	—
16	C₂×C₁₃₁	#97	1	1	yes	characteristic
17	C₁₃₁	#347	1	1	yes	characteristic, direct product factor, Sylow
18	#347	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	M₃₂	C₂×C₁₃₁	1	2	yes	—
20	#97	C₂×C₁₃₁	1	1	yes	characteristic
21	C₂×C₈	C₄×C₁₃₁	1	1	yes	characteristic
22	C₂×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
23	C₄²	C₄×C₁₃₁	1	1	yes	characteristic
24	C₁₆	C₄×C₁₃₁	1	4	yes	complemented
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	C₂×C₄×C₁₃₁	1	2	yes	—
29	C₂²	M₁₆×C₁₃₁	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	C₄²×C₁₃₁	1	1	yes	characteristic
32	C₄	M₁₆×C₁₃₁	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#97×C₁₃₁	1	1	yes	characteristic

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

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