Subgroups — #366×C₃₀₇ #34087385

Order 19648.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₃₀₇	C₂	1	1	yes	maximal, characteristic
2	#107×C₃₀₇	C₂	1	2	yes	maximal
3	C₂×C₈×C₃₀₇	C₂²	1	1	yes	characteristic
4	C₄⋊C₄×C₃₀₇	—	2	2	no	—
5	C₁₆×C₃₀₇	C₄	1	2	yes	complemented
6	C₂×C₄×C₃₀₇	—	4	2	no	—
7	C₂×C₄×C₃₀₇	D₄	1	1	yes	characteristic
8	C₈×C₃₀₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₃₀₇	Q₈	1	1	yes	characteristic
10	C₂²×C₃₀₇	D₈	1	1	yes	characteristic
11	C₄×C₃₀₇	—	8	2	no	—
12	C₄×C₃₀₇	C₄⋊C₄	1	1	yes	characteristic
13	C₄×C₃₀₇	Q₁₆	1	1	yes	characteristic
14	C₂×C₃₀₇	#107	1	1	yes	characteristic
15	C₂×C₃₀₇	D₁₆	1	1	yes	characteristic
16	C₂×C₃₀₇	Q₃₂	1	1	yes	characteristic
17	C₃₀₇	#366	1	1	yes	characteristic, direct product factor, Sylow
18	#366	C₃₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₁₆	C₂×C₃₀₇	1	1	yes	characteristic
20	#107	C₂×C₃₀₇	1	2	yes	—
21	C₂×C₈	C₂²×C₃₀₇	1	1	yes	characteristic
22	C₄⋊C₄	—	2	2	no	—
23	C₁₆	C₄×C₃₀₇	1	2	yes	complemented
24	C₂×C₄	—	4	2	no	—
25	C₂×C₄	D₄×C₃₀₇	1	1	yes	characteristic
26	C₈	C₂×C₄×C₃₀₇	1	1	yes	characteristic
27	C₈	Q₈×C₃₀₇	1	1	yes	characteristic
28	C₂²	D₈×C₃₀₇	1	1	yes	characteristic
29	C₄	—	8	2	no	—
30	C₄	C₄⋊C₄×C₃₀₇	1	1	yes	characteristic
31	C₄	Q₁₆×C₃₀₇	1	1	yes	characteristic
32	C₂	#107×C₃₀₇	1	1	yes	characteristic
33	C₂	D₁₆×C₃₀₇	1	1	yes	characteristic
34	C₂	Q₃₂×C₃₀₇	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.