Subgroups — Q₈×C₃⋊#261 #11929189

Order 1248.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊#261)	C₂	1	3	yes	maximal
3	C₄×C₃⋊#261	C₂	1	3	yes	maximal
4	Q₈×#261	—	3	1	no	maximal, Hall
5	C₂×C₃⋊#261	C₂²	1	3	yes	—
6	C₂×C₃⋊#261	C₂²	1	1	yes	characteristic
7	C₃×Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
8	C₃×C₄×D₁₃	C₂²	1	3	yes	—
9	C₃×Dic₂₆	C₄	1	3	yes	complemented
10	Q₈×D₁₃	D₃	1	1	yes	characteristic
11	C₄⋊#261	—	3	3	no	—
12	C₄×#261	—	3	3	no	—
13	C₂×C₃×D₁₃	C₂³	1	1	yes	characteristic
14	C₃⋊#261	—	2	3	no	—
15	C₃⋊#261	Q₈	1	2	yes	direct product factor
16	C₃×C₄×C₁₃	C₂×C₄	1	3	yes	—
17	C₃×Dic₁₃	C₂×C₄	1	3	yes	—
18	C₂×#261	—	3	1	no	—
19	C₂×#261	—	3	3	no	—
20	Q₈×C₁₃	Dic₃	1	1	yes	characteristic, complemented
21	C₄×D₁₃	C₂×D₃	1	3	yes	—
22	Dic₂₆	Dic₃	1	3	yes	complemented
23	Q₈×Dic₃	—	13	1	no	maximal, Hall
24	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
25	C₃×D₁₃	C₂×Q₈	1	1	yes	characteristic
26	C₃×D₁₃	#41	1	1	yes	characteristic
27	C₂×D₁₃	C₂²×D₃	1	1	yes	characteristic
28	#261	—	3	2	no	—
29	#261	—	6	3	no	—
30	C₄×C₁₃	C₂×Dic₃	1	3	yes	—
31	Dic₁₃	C₂×Dic₃	1	3	yes	—
32	C₂×C₃×Q₈	—	13	1	no	—
33	C₄⋊Dic₃	—	13	3	no	—
34	C₄×Dic₃	—	13	3	no	—
35	C₃×C₁₃	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
36	C₄×Q₈	—	39	1	no	Sylow
37	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
38	D₁₃	D₃×Q₈	1	1	yes	characteristic
39	D₁₃	#239	1	1	yes	characteristic
40	C₃×Q₈	—	13	3	no	—
41	C₃×Q₈	#261	1	1	yes	characteristic, complemented
42	C₂×C₃×C₄	—	13	3	no	—
43	C₂×Dic₃	—	13	1	no	—
44	C₂×Dic₃	—	13	3	no	—
45	C₂×Q₈	—	13	1	no	—
46	C₄⋊C₄	—	39	3	no	—
47	C₄²	—	39	3	no	—
48	C₁₃	Q₈×Dic₃	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	13	1	no	—
50	C₃×C₄	—	13	3	no	—
51	C₃×C₄	C₂×#261	1	3	yes	—
52	Dic₃	—	13	2	no	—
53	Dic₃	—	26	3	no	—
54	Q₈	—	13	3	no	—
55	Q₈	C₃⋊#261	1	1	yes	characteristic, direct product factor
56	C₂×C₄	—	13	3	no	—
57	C₂×C₄	—	39	1	no	—
58	C₂×C₄	—	39	3	no	—
59	C₂×C₃	—	13	1	no	—
60	C₂×C₃	—	13	1	no	—
61	C₂×C₃	C₂²×#261	1	1	yes	characteristic
62	C₂²	—	13	1	no	—
63	C₄	—	13	3	no	—
64	C₄	—	39	2	no	—
65	C₄	—	78	3	no	—
66	C₄	C₂×C₃⋊#261	1	3	yes	—
67	C₃	Q₈×#261	1	1	yes	characteristic, complemented, Sylow
68	C₂	—	13	1	no	—
69	C₂	—	13	1	no	—
70	C₂	C₂²×C₃⋊#261	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×C₃⋊#261
commutator, socle	C₂×C₃×C₁₃	C₂²×C₄
Fitting	C₃×Q₈×C₁₃	C₄
prime radical, cosocle	C₂×C₃×D₁₃	C₂³
hypercenter	Q₈	C₃⋊#261
hypocenter	C₃×C₁₃	C₄×Q₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ Q₈

Complements

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

N	H ≅ G/N	type
7. C₃×Q₈×C₁₃	C₄	semidirect
9. C₃×Dic₂₆	C₄	semidirect
15. C₃⋊#261	Q₈	direct (N × H)
20. Q₈×C₁₃	Dic₃	semidirect
22. Dic₂₆	Dic₃	semidirect
35. C₃×C₁₃	C₄×Q₈	semidirect
41. C₃×Q₈	#261	semidirect
48. C₁₃	Q₈×Dic₃	semidirect
55. Q₈	C₃⋊#261	direct (N × H)
67. C₃	Q₈×#261	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×Q₈×D₁₃	2
C₄⋊(C₃⋊#261)	2
C₄×C₃⋊#261	2
Q₈×#261	3
Q₈×Dic₃	13

Subgroups — Q8×C3⋊#261 #11929189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₃⋊#261 #11929189