Subgroups — Q₈×#66493 #14581384

Order 2624.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#66493	C₂	1	3	yes	maximal
2	C₄×#66493	C₂	1	3	yes	maximal
3	Q₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₄₁	C₄	1	1	yes	characteristic
5	C₂×#66493	C₂²	1	3	yes	—
6	C₂×#66493	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₄₁	C₄	1	3	yes	—
8	C₄×Dic₄₁	C₂²	1	3	yes	—
9	Q₈×C₄₁	C₈	1	4	yes	complemented
10	C₂×C₄×C₄₁	C₂×C₄	1	3	yes	—
11	C₂×Dic₄₁	C₂×C₄	1	3	yes	—
12	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
13	#66493	—	2	3	no	—
14	#66493	Q₈	1	2	yes	direct product factor
15	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₄₁	C₂×C₈	1	6	yes	—
17	Dic₄₁	—	2	3	no	—
18	Dic₄₁	C₂×Q₈	1	1	yes	characteristic
19	Dic₄₁	#41	1	1	yes	characteristic
20	C₂×C₄₁	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₄₁	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₄₁	#131	1	1	yes	characteristic
23	C₈×Q₈	—	41	1	no	maximal, Sylow
24	C₄₁	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
25	C₄×Q₈	—	41	1	no	—
26	C₄⋊C₈	—	41	3	no	—
27	C₄×C₈	—	41	3	no	—
28	C₂×Q₈	#4223	1	1	yes	characteristic
29	C₂×C₈	—	41	1	no	—
30	C₂×C₈	—	41	3	no	—
31	C₄⋊C₄	—	41	3	no	—
32	C₄²	—	41	3	no	—
33	Q₈	#66493	1	4	yes	direct product factor
34	C₂×C₄	—	41	1	no	—
35	C₂×C₄	—	41	3	no	—
36	C₂×C₄	C₂×#4223	1	3	yes	—
37	C₈	—	41	2	no	—
38	C₈	—	82	3	no	—
39	C₂²	C₂²×#4223	1	1	yes	characteristic
40	C₄	—	41	1	no	—
41	C₄	—	41	1	no	—
42	C₄	—	82	3	no	—
43	C₄	C₂×#66493	1	6	yes	—
44	C₂	Q₈×#4223	1	1	yes	characteristic
45	C₂	C₂²×#66493	1	1	yes	characteristic
46	C₂	#13050252	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.