Subgroups — Q₈×#64438 #14558581

Order 2368.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#64438	C₂	1	3	yes	maximal
2	C₄×#64438	C₂	1	3	yes	maximal
3	Q₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₃₇	C₄	1	1	yes	characteristic
5	C₂×#64438	C₂²	1	3	yes	—
6	C₂×#64438	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₃₇	C₄	1	3	yes	—
8	C₄×Dic₃₇	C₂²	1	3	yes	—
9	Q₈×C₃₇	C₈	1	4	yes	complemented
10	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
11	C₂×Dic₃₇	C₂×C₄	1	3	yes	—
12	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
13	#64438	—	2	3	no	—
14	#64438	Q₈	1	2	yes	direct product factor
15	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₃₇	C₂×C₈	1	6	yes	—
17	Dic₃₇	—	2	3	no	—
18	Dic₃₇	C₂×Q₈	1	1	yes	characteristic
19	Dic₃₇	#41	1	1	yes	characteristic
20	C₂×C₃₇	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₃₇	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₃₇	#131	1	1	yes	characteristic
23	C₈×Q₈	—	37	1	no	maximal, Sylow
24	C₃₇	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
25	C₄×Q₈	—	37	1	no	—
26	C₄⋊C₈	—	37	3	no	—
27	C₄×C₈	—	37	3	no	—
28	C₂×Q₈	#3866	1	1	yes	characteristic
29	C₂×C₈	—	37	1	no	—
30	C₂×C₈	—	37	3	no	—
31	C₄⋊C₄	—	37	3	no	—
32	C₄²	—	37	3	no	—
33	Q₈	#64438	1	4	yes	direct product factor
34	C₂×C₄	—	37	1	no	—
35	C₂×C₄	—	37	3	no	—
36	C₂×C₄	C₂×#3866	1	3	yes	—
37	C₈	—	37	2	no	—
38	C₈	—	74	3	no	—
39	C₂²	C₂²×#3866	1	1	yes	characteristic
40	C₄	—	37	1	no	—
41	C₄	—	37	1	no	—
42	C₄	—	74	3	no	—
43	C₄	C₂×#64438	1	6	yes	—
44	C₂	Q₈×#3866	1	1	yes	characteristic
45	C₂	C₂²×#64438	1	1	yes	characteristic
46	C₂	#11924624	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.