Subgroups — #34087608

Order 19648.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₀₇⋊C₈	C₂	1	2	yes	maximal
2	C₄×C₈×C₃₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₀₇⋊C₈	C₄	1	4	yes	—
4	C₂×C₈×C₃₀₇	C₄	1	2	yes	—
5	C₄²×C₃₀₇	C₂²	1	1	yes	characteristic
6	C₃₀₇⋊C₈	—	2	4	no	—
7	C₂×C₄×C₃₀₇	C₂×C₄	1	2	yes	—
8	C₂×C₄×C₃₀₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₃₀₇	C₈	1	4	yes	complemented
10	C₂²×C₃₀₇	C₄²	1	1	yes	characteristic
11	C₄×C₃₀₇	C₂×C₈	1	2	yes	—
12	C₄×C₃₀₇	M₁₆	1	4	yes	—
13	C₂×C₃₀₇	C₄×C₈	1	1	yes	characteristic
14	C₂×C₃₀₇	#97	1	2	yes	—
15	C₃₀₇	#322	1	1	yes	characteristic, complemented, Sylow
16	#322	—	307	1	no	maximal, Sylow
17	C₄×C₈	—	307	2	no	—
18	C₄×C₈	D₃₀₇	1	1	yes	characteristic
19	C₂×C₈	—	307	4	no	—
20	C₂×C₈	Dic₃₀₇	1	2	yes	—
21	C₄²	C₂×D₃₀₇	1	1	yes	characteristic
22	C₂×C₄	C₄×D₃₀₇	1	2	yes	—
23	C₂×C₄	C₂×Dic₃₀₇	1	1	yes	characteristic
24	C₈	—	614	4	no	—
25	C₈	C₃₀₇⋊C₈	1	4	yes	complemented
26	C₂²	C₄×Dic₃₀₇	1	1	yes	characteristic
27	C₄	C₂×C₃₀₇⋊C₈	1	2	yes	—
28	C₄	#19096809	1	4	yes	—
29	C₂	C₄×C₃₀₇⋊C₈	1	1	yes	characteristic
30	C₂	#23754170	1	2	yes	—

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.