Subgroups — C₂×C₂²⋊C₈₁ #10619523

Order 648.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊C₈₁	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₂×C₈₁	—	4	1	no	maximal
4	C₂²×C₂₇	—	3	1	no	—
5	C₂²×C₂₇	—	3	1	no	—
6	C₂²×C₂₇	C₂×C₃	1	1	yes	characteristic
7	C₈₁	—	4	1	no	Sylow
8	C₂³×C₉	C₉	1	1	yes	characteristic
9	C₂×C₂₇	—	3	1	no	—
10	C₂×C₂₇	—	3	1	no	—
11	C₂×C₂₇	A₄	1	1	yes	characteristic
12	C₂²×C₉	—	3	1	no	—
13	C₂²×C₉	—	3	1	no	—
14	C₂²×C₉	C₂×C₉	1	1	yes	characteristic
15	C₂₇	C₂×A₄	1	1	yes	characteristic
16	C₂³×C₃	C₂₇	1	1	yes	characteristic
17	C₂×C₉	—	3	1	no	—
18	C₂×C₉	—	3	1	no	—
19	C₂×C₉	C₂²⋊C₉	1	1	yes	characteristic
20	C₂²×C₃	—	3	1	no	—
21	C₂²×C₃	—	3	1	no	—
22	C₂²×C₃	C₂×C₂₇	1	1	yes	characteristic
23	C₉	C₂×C₂²⋊C₉	1	1	yes	characteristic
24	C₂³	C₈₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	3	1	no	—
26	C₂×C₃	—	3	1	no	—
27	C₂×C₃	C₂²⋊C₂₇	1	1	yes	characteristic
28	C₂²	—	3	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	C₂×C₈₁	1	1	yes	characteristic, complemented
31	C₃	C₂×C₂²⋊C₂₇	1	1	yes	characteristic
32	C₂	—	3	1	no	—
33	C₂	—	3	1	no	—
34	C₂	C₂²⋊C₈₁	1	1	yes	characteristic, direct product factor

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.