Subgroups — C₂×Q₈⋊C₂₇ #88394

Order 432.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈⋊C₂₇	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₂₇	—	4	1	no	maximal
4	Q₈×C₉	—	3	1	no	—
5	Q₈×C₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₄×C₉	—	3	1	no	—
7	C₂×C₂₇	—	4	2	no	—
8	C₂×C₂₇	—	4	1	no	—
9	C₂×C₃×Q₈	C₉	1	1	yes	characteristic
10	C₂²×C₉	A₄	1	1	yes	characteristic
11	C₄×C₉	—	3	1	no	—
12	C₄×C₉	—	3	1	no	—
13	C₂₇	—	4	1	no	Sylow
14	C₃×Q₈	—	3	1	no	—
15	C₃×Q₈	C₂×C₉	1	1	yes	characteristic
16	C₂×C₃×C₄	—	3	1	no	—
17	C₂×C₉	SL(2,𝔽₃)	1	2	yes	—
18	C₂×C₉	C₂×A₄	1	1	yes	characteristic
19	C₂×Q₈	C₂₇	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₃	C₂²⋊C₉	1	1	yes	characteristic
21	C₃×C₄	—	3	1	no	—
22	C₃×C₄	—	3	1	no	—
23	C₉	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
24	Q₈	—	3	1	no	—
25	Q₈	C₂×C₂₇	1	1	yes	characteristic, complemented
26	C₂×C₄	—	3	1	no	—
27	C₂×C₃	Q₈⋊C₉	1	2	yes	—
28	C₂×C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic
29	C₂²	C₂²⋊C₂₇	1	1	yes	characteristic
30	C₄	—	3	1	no	—
31	C₄	—	3	1	no	—
32	C₃	C₂×Q₈⋊C₉	1	1	yes	characteristic
33	C₂	Q₈⋊C₂₇	1	2	yes	direct product factor
34	C₂	C₂×C₂²⋊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.