Subgroups — Q₈×#157 #64290

Order 288.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#157	C₂	1	3	yes	maximal
3	C₄×#157	C₂	1	3	yes	maximal
4	C₂×#157	C₂²	1	3	yes	—
5	C₂×#157	C₂²	1	1	yes	characteristic
6	C₃²×Q₈	C₄	1	1	yes	characteristic, complemented
7	C₄×C₃⋊D₃	C₂²	1	3	yes	—
8	#634	C₄	1	3	yes	complemented
9	D₃×Q₈	—	6	2	no	—
10	C₂×C₃⋊D₃	C₂³	1	1	yes	characteristic
11	#157	—	2	3	no	—
12	#157	Q₈	1	2	yes	direct product factor
13	C₃²×C₄	C₂×C₄	1	3	yes	—
14	C₃⋊Dic₃	C₂×C₄	1	3	yes	—
15	C₄×Q₈	—	9	1	no	maximal, Sylow
16	C₃×Q₈	—	2	2	no	—
17	C₄×D₃	—	6	6	no	—
18	Dic₆	—	6	6	no	—
19	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
20	C₃⋊D₃	C₂×Q₈	1	1	yes	characteristic
21	C₃⋊D₃	#41	1	1	yes	characteristic
22	C₂×Q₈	—	9	1	no	—
23	C₄⋊C₄	—	9	3	no	—
24	C₄²	—	9	3	no	—
25	C₂×D₃	—	6	2	no	—
26	C₃×C₄	—	2	6	no	—
27	Dic₃	—	6	6	no	—
28	C₃²	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
29	Q₈	—	9	3	no	—
30	Q₈	#157	1	1	yes	characteristic, direct product factor
31	C₂×C₄	—	9	1	no	—
32	C₂×C₄	—	9	3	no	—
33	C₂×C₄	—	9	3	no	—
34	C₂×C₃	—	2	2	no	—
35	D₃	—	6	2	no	—
36	D₃	—	6	2	no	—
37	C₂²	—	9	1	no	—
38	C₄	—	9	2	no	—
39	C₄	—	9	3	no	—
40	C₄	—	18	3	no	—
41	C₄	C₂×#157	1	3	yes	—
42	C₃	—	2	2	no	—
43	C₂	—	9	1	no	—
44	C₂	—	9	1	no	—
45	C₂	C₂²×#157	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.