Subgroups — C₈×#13083549 #26018167

Order 11392.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13083549	C₂	1	2	yes	maximal
2	C₈²×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#13083549	C₄	1	4	yes	—
4	C₄×C₈×C₈₉	C₄	1	2	yes	—
5	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
6	#13083549	C₈	1	8	yes	direct product factor
7	C₂×C₈×C₈₉	C₈	1	4	yes	—
8	C₂×C₈×C₈₉	C₂×C₄	1	2	yes	—
9	C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₈₉	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₈₉	C₂×C₈	1	2	yes	—
12	C₈×C₈₉	C₁₆	1	8	yes	complemented
13	C₈×C₈₉	C₂×C₈	1	4	yes	—
14	C₂²×C₈₉	C₄×C₈	1	1	yes	characteristic
15	C₄×C₈₉	C₄×C₈	1	2	yes	—
16	C₄×C₈₉	C₂×C₁₆	1	4	yes	—
17	C₂×C₈₉	C₈²	1	1	yes	characteristic
18	C₂×C₈₉	C₄×C₁₆	1	2	yes	—
19	C₈×C₁₆	—	89	1	no	maximal, Sylow
20	C₈₉	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₁₆	—	89	2	no	—
22	C₈²	D₈₉	1	1	yes	characteristic
23	C₂×C₁₆	—	89	4	no	—
24	C₄×C₈	Dic₈₉	1	2	yes	—
25	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
26	C₂×C₈	#10623494	1	4	yes	—
27	C₂×C₈	C₄×D₈₉	1	2	yes	—
28	C₄²	C₂×Dic₈₉	1	1	yes	characteristic
29	C₁₆	—	89	8	no	—
30	C₂×C₄	C₄×Dic₈₉	1	1	yes	characteristic
31	C₂×C₄	C₂×#10623494	1	2	yes	—
32	C₈	#13083549	1	8	yes	direct product factor
33	C₈	C₈×D₈₉	1	4	yes	—
34	C₂²	C₄×#10623494	1	1	yes	characteristic
35	C₄	C₈×Dic₈₉	1	2	yes	—
36	C₄	C₂×#13083549	1	4	yes	—
37	C₂	C₈×#10623494	1	1	yes	characteristic
38	C₂	C₄×#13083549	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.