Subgroups — C₂×Q₈×C₂₇ #88408

Order 432.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₂₇	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₄×C₂₇	C₂	1	3	yes	maximal
3	C₂×Q₈×C₉	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₂₇	C₂²	1	1	yes	characteristic
5	C₄×C₂₇	C₂²	1	6	yes	—
6	Q₈×C₉	C₂×C₃	1	4	yes	—
7	C₂×C₄×C₉	C₂×C₃	1	3	yes	—
8	C₂×C₂₇	Q₈	1	2	yes	direct product factor
9	C₂×C₂₇	C₂³	1	1	yes	characteristic
10	C₂×C₃×Q₈	C₉	1	1	yes	characteristic
11	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
12	C₄×C₉	C₂²×C₃	1	6	yes	—
13	C₂₇	C₂×Q₈	1	1	yes	characteristic, direct product factor, Sylow
14	C₃×Q₈	C₂×C₉	1	4	yes	—
15	C₂×C₃×C₄	C₂×C₉	1	3	yes	—
16	C₂×C₉	C₃×Q₈	1	2	yes	—
17	C₂×C₉	C₂³×C₃	1	1	yes	characteristic
18	C₂×Q₈	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²×C₃	C₂²×C₉	1	1	yes	characteristic
20	C₃×C₄	C₂²×C₉	1	6	yes	—
21	C₉	C₂×C₃×Q₈	1	1	yes	characteristic
22	Q₈	C₂×C₂₇	1	4	yes	direct product factor
23	C₂×C₄	C₂×C₂₇	1	3	yes	—
24	C₂×C₃	Q₈×C₉	1	2	yes	—
25	C₂×C₃	C₂³×C₉	1	1	yes	characteristic
26	C₂²	C₂²×C₂₇	1	1	yes	characteristic
27	C₄	C₂²×C₂₇	1	6	yes	—
28	C₃	C₂×Q₈×C₉	1	1	yes	characteristic
29	C₂	Q₈×C₂₇	1	2	yes	direct product factor
30	C₂	C₂³×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.