Subgroups — Q₈×C₂²⋊(C₁₃⋊C₃) #11929261

Order 1248.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊(C₁₃⋊C₃)	C₂	1	3	yes	maximal
2	C₂²×Q₈×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₂²⋊(C₁₃⋊C₃)	C₂²	1	1	yes	characteristic
4	Q₈×C₁₃⋊C₃	—	4	1	no	maximal
5	C₂×Q₈×C₁₃	—	3	3	no	—
6	C₂×Q₈×C₁₃	—	3	1	no	—
7	C₂²×C₄×C₁₃	C₂×C₃	1	3	yes	—
8	C₂²⋊(C₁₃⋊C₃)	Q₈	1	1	yes	characteristic, direct product factor
9	C₄×C₁₃⋊C₃	—	4	3	no	—
10	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
11	Q₈×C₁₃	—	3	2	no	—
12	Q₈×C₁₃	—	3	3	no	—
13	Q₈×C₁₃	A₄	1	1	yes	characteristic, complemented
14	C₂×C₄×C₁₃	—	3	3	no	—
15	C₂×C₄×C₁₃	—	3	3	no	—
16	Q₈×A₄	—	13	1	no	maximal, Hall
17	C₂×C₁₃⋊C₃	—	4	1	no	—
18	C₂²×C₁₃	—	3	1	no	—
19	C₂²×C₁₃	—	3	1	no	—
20	C₂²×C₁₃	C₃×Q₈	1	1	yes	characteristic, complemented
21	C₄×C₁₃	—	3	3	no	—
22	C₄×C₁₃	C₂×A₄	1	3	yes	—
23	C₄×A₄	—	13	3	no	—
24	C₁₃⋊C₃	—	4	1	no	Hall
25	C₂²×Q₈	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₃	—	3	1	no	—
27	C₂×C₁₃	—	3	1	no	—
28	C₂×C₁₃	C₂²×A₄	1	1	yes	characteristic
29	C₂×A₄	—	13	1	no	—
30	C₃×Q₈	—	52	1	no	—
31	C₂×Q₈	—	3	3	no	—
32	C₂×Q₈	—	3	1	no	—
33	C₂²×C₄	C₂×C₁₃⋊C₃	1	3	yes	—
34	C₁₃	Q₈×A₄	1	1	yes	characteristic, complemented, Sylow
35	A₄	—	13	1	no	—
36	C₃×C₄	—	52	3	no	—
37	C₂³	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
38	Q₈	—	3	2	no	—
39	Q₈	—	3	3	no	—
40	Q₈	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
41	C₂×C₄	—	3	3	no	—
42	C₂×C₄	—	3	3	no	—
43	C₂×C₃	—	52	1	no	—
44	C₂²	—	3	1	no	—
45	C₂²	—	3	1	no	—
46	C₂²	Q₈×C₁₃⋊C₃	1	1	yes	characteristic, complemented
47	C₄	—	3	3	no	—
48	C₄	C₂×C₂²⋊(C₁₃⋊C₃)	1	3	yes	—
49	C₃	—	52	1	no	Sylow
50	C₂	—	3	1	no	—
51	C₂	—	3	1	no	—
52	C₂	C₂²×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×Q₈×C₁₃	C₃	semidirect
8. C₂²⋊(C₁₃⋊C₃)	Q₈	direct (N × H)
13. Q₈×C₁₃	A₄	semidirect
20. C₂²×C₁₃	C₃×Q₈	semidirect
25. C₂²×Q₈	C₁₃⋊C₃	semidirect
34. C₁₃	Q₈×A₄	semidirect
40. Q₈	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
46. C₂²	Q₈×C₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊(C₁₃⋊C₃)	2
C₂²×Q₈×C₁₃	3
Q₈×C₁₃⋊C₃	4
Q₈×A₄	13

Subgroups — Q8×C22⋊(C13⋊C3) #11929261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₂²⋊(C₁₃⋊C₃) #11929261