Subgroups — Q₈×#3633 #11763924

Order 1088.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#595	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#3633	C₂	1	3	yes	maximal
3	C₄×#3633	C₂	1	3	yes	maximal
4	C₂×#3633	C₂²	1	3	yes	—
5	C₂×#3633	C₂²	1	1	yes	characteristic
6	Q₈×D₁₇	C₄	1	1	yes	characteristic
7	C₄⋊#595	C₄	1	3	yes	—
8	C₄×#595	C₂²	1	3	yes	—
9	C₂×#595	C₂×C₄	1	3	yes	—
10	C₂×#595	C₂³	1	1	yes	characteristic
11	#3633	—	2	3	no	—
12	#3633	Q₈	1	2	yes	direct product factor
13	Q₈×C₁₇	C₈	1	1	yes	characteristic, complemented
14	C₄×D₁₇	C₂×C₄	1	3	yes	—
15	Dic₃₄	C₈	1	3	yes	complemented
16	C₂×D₁₇	C₂²×C₄	1	1	yes	characteristic
17	#595	—	2	3	no	—
18	#595	C₂×Q₈	1	1	yes	characteristic
19	#595	#41	1	1	yes	characteristic
20	C₄×C₁₇	C₂×C₈	1	3	yes	—
21	Dic₁₇	C₂×C₈	1	3	yes	—
22	C₈×Q₈	—	17	1	no	maximal, Sylow
23	C₂×C₁₇	C₂²×C₈	1	1	yes	characteristic
24	D₁₇	C₄×Q₈	1	1	yes	characteristic
25	D₁₇	#131	1	1	yes	characteristic
26	C₄×Q₈	—	17	1	no	—
27	C₄⋊C₈	—	17	3	no	—
28	C₄×C₈	—	17	3	no	—
29	C₁₇	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₈	—	17	1	no	—
31	C₂×C₈	—	17	1	no	—
32	C₂×C₈	—	17	3	no	—
33	C₄⋊C₄	—	17	3	no	—
34	C₄²	—	17	3	no	—
35	Q₈	—	17	3	no	—
36	Q₈	#3633	1	1	yes	characteristic, direct product factor
37	C₂×C₄	—	17	1	no	—
38	C₂×C₄	—	17	3	no	—
39	C₂×C₄	—	17	3	no	—
40	C₈	—	17	2	no	—
41	C₈	—	34	3	no	—
42	C₂²	—	17	1	no	—
43	C₄	—	17	1	no	—
44	C₄	—	17	1	no	—
45	C₄	—	17	3	no	—
46	C₄	—	34	3	no	—
47	C₄	C₂×#3633	1	3	yes	—
48	C₂	—	17	1	no	—
49	C₂	—	17	1	no	—
50	C₂	C₂²×#3633	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.