Subgroups — Q₈×#11924040 #22627154

Order 9344.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924040	C₂	1	3	yes	maximal
2	C₄×#11924040	C₂	1	3	yes	maximal
3	Q₈×#10596833	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924040	C₂²	1	3	yes	—
5	C₂×#11924040	C₂²	1	1	yes	characteristic
6	C₄⋊#10596833	C₄	1	3	yes	—
7	C₄×#10596833	C₂²	1	3	yes	—
8	Q₈×Dic₇₃	C₄	1	1	yes	characteristic
9	#11924040	—	2	3	no	—
10	#11924040	Q₈	1	2	yes	direct product factor
11	C₂×#10596833	C₂×C₄	1	3	yes	—
12	C₂×#10596833	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₇₃	C₈	1	3	yes	—
14	C₄×Dic₇₃	C₂×C₄	1	3	yes	—
15	C₂×Q₈×C₇₃	C₈	1	1	yes	characteristic
16	Q₈×C₇₃	C₁₆	1	4	yes	complemented
17	C₂×C₄×C₇₃	C₂×C₈	1	3	yes	—
18	C₂×Dic₇₃	C₂×C₈	1	3	yes	—
19	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
20	#10596833	—	2	3	no	—
21	#10596833	C₂×Q₈	1	1	yes	characteristic
22	#10596833	#41	1	1	yes	characteristic
23	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
24	C₄×C₇₃	C₂×C₁₆	1	6	yes	—
25	Dic₇₃	—	2	3	no	—
26	Dic₇₃	C₄×Q₈	1	1	yes	characteristic
27	Dic₇₃	#131	1	1	yes	characteristic
28	C₂×C₇₃	C₈×Q₈	1	1	yes	characteristic
29	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
30	C₂×C₇₃	#504	1	1	yes	characteristic
31	Q₈×C₁₆	—	73	1	no	maximal, Sylow
32	C₇₃	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₈×Q₈	—	73	1	no	—
34	C₄⋊C₁₆	—	73	3	no	—
35	C₄×C₁₆	—	73	3	no	—
36	C₄×Q₈	—	73	1	no	—
37	C₂×C₁₆	—	73	1	no	—
38	C₂×C₁₆	—	73	3	no	—
39	C₄⋊C₈	—	73	3	no	—
40	C₄×C₈	—	73	3	no	—
41	C₂×Q₈	#10596842	1	1	yes	characteristic
42	C₂×C₈	—	73	1	no	—
43	C₂×C₈	—	73	3	no	—
44	C₄⋊C₄	—	73	3	no	—
45	C₄²	—	73	3	no	—
46	C₁₆	—	73	2	no	—
47	C₁₆	—	146	3	no	—
48	Q₈	#11924040	1	4	yes	direct product factor
49	C₂×C₄	—	73	1	no	—
50	C₂×C₄	—	73	3	no	—
51	C₂×C₄	C₂×#10596842	1	3	yes	—
52	C₈	—	73	1	no	—
53	C₈	—	73	1	no	—
54	C₈	—	146	3	no	—
55	C₂²	C₂²×#10596842	1	1	yes	characteristic
56	C₄	—	73	1	no	—
57	C₄	—	73	1	no	—
58	C₄	—	146	3	no	—
59	C₄	C₂×#11924040	1	6	yes	—
60	C₂	Q₈×#10596842	1	1	yes	characteristic
61	C₂	C₂²×#11924040	1	1	yes	characteristic
62	C₂	#17989709	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10596842
commutator	C₂×C₇₃	C₂²×C₁₆
Fitting	C₂×Q₈×C₇₃	C₈
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	C₂×Q₈	#10596842
hypocenter	C₇₃	Q₈×C₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
10. #11924040	Q₈	direct (N × H)
16. Q₈×C₇₃	C₁₆	semidirect
32. C₇₃	Q₈×C₁₆	semidirect
48. Q₈	#11924040	direct (N × H)

Subgroups — Q8×#11924040 #22627154

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×#11924040 #22627154