Subgroups — Q₈×#6597 #14271289

Order 1856.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#6597	C₂	1	3	yes	maximal
3	C₄×#6597	C₂	1	3	yes	maximal
4	C₂×Q₈×C₂₉	C₄	1	1	yes	characteristic
5	C₄⋊C₄×C₂₉	C₄	1	3	yes	—
6	C₄²×C₂₉	C₂²	1	3	yes	—
7	C₂×#6597	C₂²	1	3	yes	—
8	C₂×#6597	C₂²	1	1	yes	characteristic
9	Q₈×C₂₉	C₈	1	4	yes	complemented
10	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
11	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
12	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
13	#6597	—	2	3	no	—
14	#6597	Q₈	1	2	yes	direct product factor
15	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₂₉	—	2	3	no	—
17	C₄×C₂₉	C₂×C₈	1	6	yes	—
18	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₂₉	#41	1	1	yes	characteristic
20	C₈×Q₈	—	29	1	no	maximal, Sylow
21	C₂×C₂₉	C₄×Q₈	1	1	yes	characteristic
22	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
23	C₂×C₂₉	#131	1	1	yes	characteristic
24	C₄×Q₈	D₂₉	1	1	yes	characteristic
25	C₄⋊C₈	—	29	3	no	—
26	C₄×C₈	—	29	3	no	—
27	C₂₉	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₈	Dic₂₉	1	1	yes	characteristic
29	C₂×C₈	—	29	1	no	—
30	C₂×C₈	—	29	3	no	—
31	C₄⋊C₄	Dic₂₉	1	3	yes	—
32	C₄²	C₂×D₂₉	1	3	yes	—
33	Q₈	#6597	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₂₉	1	3	yes	—
35	C₂×C₄	C₂×Dic₂₉	1	3	yes	—
36	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
37	C₈	—	29	2	no	—
38	C₈	—	58	3	no	—
39	C₂²	C₂²×Dic₂₉	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×#6597	1	6	yes	—
42	C₄	Q₈×D₂₉	1	1	yes	characteristic
43	C₄	#90809	1	1	yes	characteristic
44	C₂	C₂²×#6597	1	1	yes	characteristic
45	C₂	Q₈×Dic₂₉	1	1	yes	characteristic
46	C₂	#11745310	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator	C₂×C₂₉	C₂²×C₈
Fitting	C₄×Q₈×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂²×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₄×Q₈	D₂₉
hypocenter	C₂₉	C₈×Q₈
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. Q₈×C₂₉	C₈	semidirect
14. #6597	Q₈	direct (N × H)
27. C₂₉	C₈×Q₈	semidirect
33. Q₈	#6597	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×Q₈×C₂₉	2
C₄⋊#6597	2
C₄×#6597	2
C₈×Q₈	29

Subgroups — Q8×#6597 #14271289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#6597 #14271289