Subgroups — C₂²×Dic₁₇₁₈ #42117880

Order 27488.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₁₈	C₂	1	12	yes	maximal, direct product factor
2	C₂²×Dic₈₅₉	C₂	1	2	yes	maximal
3	C₂²×C₄×C₈₅₉	C₂	1	1	yes	maximal, characteristic
4	Dic₁₇₁₈	C₂²	1	16	yes	direct product factor
5	C₂×Dic₈₅₉	C₂²	1	12	yes	—
6	C₂³×C₈₅₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈₅₉	C₂²	1	6	yes	—
8	C₂²×C₈₅₉	Q₈	1	4	yes	complemented
9	C₂²×C₈₅₉	C₂³	1	3	yes	—
10	C₄×C₈₅₉	C₂³	1	4	yes	—
11	Dic₈₅₉	C₂³	1	8	yes	—
12	C₂×C₈₅₉	C₂×Q₈	1	6	yes	complemented
13	C₂×C₈₅₉	C₂⁴	1	1	yes	characteristic
14	C₈₅₉	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₂²×Q₈	—	859	1	no	maximal, Sylow
16	C₂×Q₈	—	859	12	no	—
17	C₂²×C₄	—	859	2	no	—
18	C₂²×C₄	D₈₅₉	1	1	yes	characteristic
19	C₂³	C₂×D₈₅₉	1	1	yes	characteristic
20	Q₈	—	859	16	no	—
21	C₂×C₄	—	859	12	no	—
22	C₂×C₄	C₂×D₈₅₉	1	6	yes	—
23	C₂²	Dic₁₇₁₈	1	4	yes	direct product factor
24	C₂²	C₂²×D₈₅₉	1	3	yes	—
25	C₄	—	859	8	no	—
26	C₄	C₂²×D₈₅₉	1	4	yes	—
27	C₂	C₂×Dic₁₇₁₈	1	6	yes	direct product factor
28	C₂	C₂³×D₈₅₉	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.