Subgroups — C₈×#90768 #16817407

Order 3712.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#90768	C₂	1	2	yes	maximal
2	C₈²×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₂₉	C₄	1	2	yes	—
4	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×#90768	C₄	1	4	yes	—
6	C₂×C₈×C₂₉	C₈	1	4	yes	—
7	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
8	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
9	#90768	C₈	1	8	yes	direct product factor
10	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
12	C₈×C₂₉	C₁₆	1	8	yes	complemented
13	C₈×C₂₉	C₂×C₈	1	4	yes	—
14	C₈×C₁₆	—	29	1	no	maximal, Sylow
15	C₂²×C₂₉	C₄×C₈	1	1	yes	characteristic
16	C₄×C₂₉	C₄×C₈	1	2	yes	—
17	C₄×C₂₉	C₂×C₁₆	1	4	yes	—
18	C₄×C₁₆	—	29	2	no	—
19	C₈²	D₂₉	1	1	yes	characteristic
20	C₂×C₂₉	C₈²	1	1	yes	characteristic
21	C₂×C₂₉	C₄×C₁₆	1	2	yes	—
22	C₂×C₁₆	—	29	4	no	—
23	C₄×C₈	Dic₂₉	1	2	yes	—
24	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
25	C₂₉	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₈	#6597	1	4	yes	—
27	C₂×C₈	C₄×D₂₉	1	2	yes	—
28	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
29	C₁₆	—	29	8	no	—
30	C₂×C₄	C₂×#6597	1	2	yes	—
31	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
32	C₈	#90768	1	8	yes	direct product factor
33	C₈	C₈×D₂₉	1	4	yes	—
34	C₂²	C₄×#6597	1	1	yes	characteristic
35	C₄	C₂×#90768	1	4	yes	—
36	C₄	C₈×Dic₂₉	1	2	yes	—
37	C₂	C₈×#6597	1	1	yes	characteristic
38	C₂	C₄×#90768	1	2	yes	—

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.