Subgroups — C₄×Q₈×C₃₃₇ #24924839

Order 10784.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₃₃₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×C₃₃₇	C₂	1	3	yes	maximal
3	C₄²×C₃₃₇	C₂	1	3	yes	maximal
4	Q₈×C₃₃₇	C₄	1	4	yes	direct product factor
5	C₂×C₄×C₃₃₇	C₂²	1	3	yes	—
6	C₂×C₄×C₃₃₇	C₂²	1	3	yes	—
7	C₂×C₄×C₃₃₇	C₂²	1	1	yes	characteristic
8	C₂²×C₃₃₇	C₂³	1	1	yes	characteristic
9	C₄×C₃₃₇	—	2	3	no	—
10	C₄×C₃₃₇	C₂×C₄	1	6	yes	—
11	C₄×C₃₃₇	Q₈	1	2	yes	direct product factor
12	C₂×C₃₃₇	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₃₃₇	C₂×Q₈	1	1	yes	characteristic
14	C₂×C₃₃₇	#41	1	1	yes	characteristic
15	C₃₃₇	C₄×Q₈	1	1	yes	characteristic, direct product factor, Sylow
16	C₄×Q₈	C₃₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×Q₈	C₂×C₃₃₇	1	1	yes	characteristic
18	C₄⋊C₄	C₂×C₃₃₇	1	3	yes	—
19	C₄²	C₂×C₃₃₇	1	3	yes	—
20	Q₈	C₄×C₃₃₇	1	4	yes	direct product factor
21	C₂×C₄	C₂²×C₃₃₇	1	3	yes	—
22	C₂×C₄	C₂²×C₃₃₇	1	3	yes	—
23	C₂×C₄	C₂²×C₃₃₇	1	1	yes	characteristic
24	C₂²	C₂³×C₃₃₇	1	1	yes	characteristic
25	C₄	—	2	3	no	—
26	C₄	C₂×C₄×C₃₃₇	1	6	yes	—
27	C₄	Q₈×C₃₃₇	1	2	yes	direct product factor
28	C₂	C₂²×C₄×C₃₃₇	1	1	yes	characteristic
29	C₂	C₂×Q₈×C₃₃₇	1	1	yes	characteristic
30	C₂	#41×C₃₃₇	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.