Subgroups — Q₁₆×Dic₁₉₃ #27135354

Order 12352.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₁₉₃	C₂	1	2	yes	maximal
2	#20259833	C₂	1	1	yes	maximal, characteristic
3	#20259823	C₂	1	2	yes	maximal
4	C₈×Dic₁₉₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₁₉₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#13095393	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₁₉₃	—	2	2	no	—
8	C₄⋊Dic₁₉₃	C₂²	1	2	yes	—
9	C₄×Dic₁₉₃	—	2	2	no	—
10	C₄×Dic₁₉₃	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₁₉₃	C₂²	1	2	yes	—
12	Q₁₆×C₁₉₃	C₄	1	4	yes	complemented
13	C₂×C₈×C₁₉₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₉₃	—	2	2	no	—
15	C₂×Dic₁₉₃	D₄	1	1	yes	characteristic
16	C₂×Dic₁₉₃	D₄	1	1	yes	characteristic
17	#13095393	—	2	1	no	—
18	Q₈×C₁₉₃	—	2	2	no	—
19	Q₈×C₁₉₃	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₁₉₃	—	2	2	no	—
21	C₂×C₄×C₁₉₃	C₂³	1	1	yes	characteristic
22	C₈×C₁₉₃	C₂×C₄	1	2	yes	—
23	C₂²×C₁₉₃	C₂×D₄	1	1	yes	characteristic
24	C₄×C₁₉₃	—	2	4	no	—
25	C₄×C₁₉₃	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₁₉₃	#41	1	1	yes	characteristic
27	Dic₁₉₃	—	2	1	no	—
28	Dic₁₉₃	—	4	2	no	—
29	Dic₁₉₃	Q₁₆	1	2	yes	direct product factor
30	C₂×C₁₉₃	C₄×D₄	1	1	yes	characteristic
31	C₂×C₁₉₃	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₁₉₃	#135	1	1	yes	characteristic
33	C₁₉₃	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×Q₁₆	—	193	1	no	maximal, Sylow
35	C₂×Q₁₆	D₁₉₃	1	1	yes	characteristic
36	C₄×Q₈	—	193	2	no	—
37	#107	—	193	1	no	—
38	#103	—	193	2	no	—
39	C₄×C₈	—	193	1	no	—
40	C₂×Q₈	C₂×D₁₉₃	1	2	yes	—
41	Q₁₆	Dic₁₉₃	1	4	yes	direct product factor
42	C₂×C₈	—	193	1	no	—
43	C₂×C₈	C₂×D₁₉₃	1	1	yes	characteristic
44	C₄⋊C₄	—	386	2	no	—
45	C₄⋊C₄	—	193	2	no	—
46	C₄²	—	386	2	no	—
47	C₄²	—	193	1	no	—
48	Q₈	—	2	2	no	—
49	Q₈	C₂×Dic₁₉₃	1	4	yes	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	386	2	no	—
52	C₂×C₄	—	193	1	no	—
53	C₂×C₄	—	193	1	no	—
54	C₂×C₄	C₂²×D₁₉₃	1	1	yes	characteristic
55	C₈	—	386	1	no	—
56	C₈	C₂×Dic₁₉₃	1	2	yes	—
57	C₂²	D₄×D₁₉₃	1	1	yes	characteristic
58	C₄	—	2	4	no	—
59	C₄	—	772	2	no	—
60	C₄	—	386	1	no	—
61	C₄	—	193	2	no	—
62	C₄	C₂²×Dic₁₉₃	1	1	yes	characteristic
63	C₄	#15690554	1	1	yes	characteristic
64	C₂	D₄×Dic₁₉₃	1	1	yes	characteristic
65	C₂	Q₁₆×D₁₉₃	1	1	yes	characteristic
66	C₂	#20259922	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₉₃
commutator	C₄×C₁₉₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₉₃
Fitting	C₂×Q₁₆×C₁₉₃	C₂
socle, prime radical	C₂²×C₁₉₃	C₂×D₄
cosocle	C₂×C₄×C₁₉₃	C₂³
hypercenter	C₂×Q₁₆	D₁₉₃
hypocenter	C₁₉₃	C₄×Q₁₆
LCS	G ▷ C₄×C₁₉₃ ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
12. Q₁₆×C₁₉₃	C₄	semidirect
29. Dic₁₉₃	Q₁₆	direct (N × H)
33. C₁₉₃	C₄×Q₁₆	semidirect
41. Q₁₆	Dic₁₉₃	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×Dic₁₉₃	2
#20259833	2
#20259823	2
C₈×Dic₁₉₃	2
C₂×Q₁₆×C₁₉₃	2
C₄×Q₁₆	193

Subgroups — Q16×Dic193 #27135354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×Dic₁₉₃ #27135354