Subgroups — Q₈×#3624 #11763857

Order 1088.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#3624	C₂	1	3	yes	maximal
3	C₄×#3624	C₂	1	3	yes	maximal
4	C₂×Q₈×C₁₇	C₄	1	1	yes	characteristic
5	C₂×#3624	C₂²	1	3	yes	—
6	C₂×#3624	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₁₇	C₄	1	3	yes	—
8	C₄×Dic₁₇	C₂²	1	3	yes	—
9	Q₈×C₁₇	C₈	1	4	yes	complemented
10	C₂×C₄×C₁₇	C₂×C₄	1	3	yes	—
11	C₂×Dic₁₇	C₂×C₄	1	3	yes	—
12	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
13	#3624	—	2	3	no	—
14	#3624	Q₈	1	2	yes	direct product factor
15	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₁₇	C₂×C₈	1	6	yes	—
17	Dic₁₇	—	2	3	no	—
18	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
19	Dic₁₇	#41	1	1	yes	characteristic
20	C₈×Q₈	—	17	1	no	maximal, Sylow
21	C₂×C₁₇	C₄×Q₈	1	1	yes	characteristic
22	C₂×C₁₇	C₂²×C₈	1	1	yes	characteristic
23	C₂×C₁₇	#131	1	1	yes	characteristic
24	C₄×Q₈	—	17	1	no	—
25	C₄⋊C₈	—	17	3	no	—
26	C₄×C₈	—	17	3	no	—
27	C₁₇	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₈	#595	1	1	yes	characteristic
29	C₂×C₈	—	17	1	no	—
30	C₂×C₈	—	17	3	no	—
31	C₄⋊C₄	—	17	3	no	—
32	C₄²	—	17	3	no	—
33	Q₈	#3624	1	4	yes	direct product factor
34	C₂×C₄	—	17	1	no	—
35	C₂×C₄	—	17	3	no	—
36	C₂×C₄	C₂×#595	1	3	yes	—
37	C₈	—	17	2	no	—
38	C₈	—	34	3	no	—
39	C₂²	C₂²×#595	1	1	yes	characteristic
40	C₄	—	17	1	no	—
41	C₄	—	17	1	no	—
42	C₄	—	34	3	no	—
43	C₄	C₂×#3624	1	6	yes	—
44	C₂	#10587680	1	1	yes	characteristic
45	C₂	Q₈×#595	1	1	yes	characteristic
46	C₂	C₂²×#3624	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.