Subgroups — #34091523

Order 19904.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#23755644	C₂	1	1	yes	maximal, characteristic
3	#108×C₃₁₁	C₂	1	1	yes	maximal, characteristic
4	#19097299	—	2	1	no	—
5	C₃₁₁⋊C₁₆	C₄	1	2	yes	—
6	M₁₆×C₃₁₁	—	2	1	no	—
7	C₂×C₈×C₃₁₁	C₂²	1	1	yes	characteristic
8	C₃₁₁⋊C₈	—	4	1	no	—
9	C₂×C₄×C₃₁₁	D₄	1	1	yes	characteristic
10	C₈×C₃₁₁	—	4	1	no	—
11	C₈×C₃₁₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₁₁	Q₈	1	1	yes	characteristic
13	C₂²×C₃₁₁	Q₁₆	1	1	yes	characteristic
14	C₄×C₃₁₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₃₁₁	D₈	1	1	yes	characteristic
16	C₂×C₃₁₁	—	2	1	no	—
17	C₂×C₃₁₁	#107	1	1	yes	characteristic
18	C₃₁₁	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	311	1	no	maximal, Sylow
20	C₂×C₁₆	—	311	1	no	—
21	#108	—	311	1	no	—
22	#108	D₃₁₁	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	622	1	no	—
25	C₂×C₈	C₂×D₃₁₁	1	1	yes	characteristic
26	C₁₆	—	311	2	no	—
27	C₂×C₄	C₂²⋊D₃₁₁	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	1244	1	no	—
30	C₈	C₄×D₃₁₁	1	1	yes	characteristic
31	C₈	Dic₆₂₂	1	1	yes	characteristic
32	C₂²	#19097305	1	1	yes	characteristic
33	C₄	Dic₃₁₁⋊C₄	1	1	yes	characteristic
34	C₄	#19097300	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#23755641	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₃₁₁	#368	semidirect

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