Subgroups — C₇×Q₈×C₂₇ #13094144

Order 1512.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₂₇	C₂	1	3	yes	maximal
2	C₇×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₂₇	C₂²	1	1	yes	characteristic
4	C₄×C₇×C₉	C₂×C₃	1	3	yes	—
5	Q₈×C₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₂₇	Q₈	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×Q₈	C₉	1	1	yes	characteristic
8	C₂×C₇×C₉	C₂²×C₃	1	1	yes	characteristic
9	C₄×C₂₇	C₂×C₇	1	3	yes	—
10	C₃×C₄×C₇	C₂×C₉	1	3	yes	—
11	Q₈×C₉	C₃×C₇	1	1	yes	characteristic
12	C₇×C₉	C₃×Q₈	1	1	yes	characteristic
13	C₇×Q₈	C₂₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₂₇	C₂²×C₇	1	1	yes	characteristic
15	C₂×C₃×C₇	C₂²×C₉	1	1	yes	characteristic
16	C₄×C₉	C₂×C₃×C₇	1	3	yes	—
17	C₄×C₇	C₂×C₂₇	1	3	yes	—
18	C₂₇	C₇×Q₈	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×Q₈	C₇×C₉	1	1	yes	characteristic
20	C₃×C₇	Q₈×C₉	1	1	yes	characteristic
21	C₂×C₉	C₂²×C₃×C₇	1	1	yes	characteristic
22	C₂×C₇	C₂²×C₂₇	1	1	yes	characteristic
23	C₃×C₄	C₂×C₇×C₉	1	3	yes	—
24	C₉	C₃×C₇×Q₈	1	1	yes	characteristic
25	Q₈	C₇×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₇	Q₈×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₂²×C₇×C₉	1	1	yes	characteristic
28	C₄	C₂×C₇×C₂₇	1	3	yes	—
29	C₃	C₇×Q₈×C₉	1	1	yes	characteristic
30	C₂	C₂²×C₇×C₂₇	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.