Subgroups — C₈×Q₈×C₂₂₉ #28411058

Order 14656.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₂₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×C₂₂₉	C₂	1	3	yes	maximal
3	C₄×C₈×C₂₂₉	C₂	1	3	yes	maximal
4	C₂×Q₈×C₂₂₉	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₂₉	C₂²	1	3	yes	—
6	C₂×C₈×C₂₂₉	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₂₂₉	C₄	1	3	yes	—
8	C₄²×C₂₂₉	C₂²	1	3	yes	—
9	Q₈×C₂₂₉	C₈	1	4	yes	direct product factor
10	C₂×C₄×C₂₂₉	C₂×C₄	1	3	yes	—
11	C₂×C₄×C₂₂₉	C₂×C₄	1	3	yes	—
12	C₂×C₄×C₂₂₉	C₂³	1	1	yes	characteristic
13	C₈×C₂₂₉	—	2	3	no	—
14	C₈×C₂₂₉	Q₈	1	2	yes	direct product factor
15	C₂²×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₂₂₉	—	2	3	no	—
17	C₄×C₂₂₉	C₂×C₈	1	6	yes	—
18	C₄×C₂₂₉	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₂₂₉	#41	1	1	yes	characteristic
20	C₂×C₂₂₉	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₂₂₉	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₂₂₉	#131	1	1	yes	characteristic
23	C₂₂₉	C₈×Q₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₈×Q₈	C₂₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₄×Q₈	C₂×C₂₂₉	1	1	yes	characteristic
26	C₄⋊C₈	C₂×C₂₂₉	1	3	yes	—
27	C₄×C₈	C₂×C₂₂₉	1	3	yes	—
28	C₂×Q₈	C₄×C₂₂₉	1	1	yes	characteristic
29	C₂×C₈	C₂²×C₂₂₉	1	3	yes	—
30	C₂×C₈	C₂²×C₂₂₉	1	1	yes	characteristic
31	C₄⋊C₄	C₄×C₂₂₉	1	3	yes	—
32	C₄²	C₂²×C₂₂₉	1	3	yes	—
33	Q₈	C₈×C₂₂₉	1	4	yes	direct product factor
34	C₂×C₄	C₂×C₄×C₂₂₉	1	3	yes	—
35	C₂×C₄	C₂×C₄×C₂₂₉	1	3	yes	—
36	C₂×C₄	C₂³×C₂₂₉	1	1	yes	characteristic
37	C₈	—	2	3	no	—
38	C₈	Q₈×C₂₂₉	1	2	yes	direct product factor
39	C₂²	C₂²×C₄×C₂₂₉	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×C₈×C₂₂₉	1	6	yes	—
42	C₄	C₂×Q₈×C₂₂₉	1	1	yes	characteristic
43	C₄	#41×C₂₂₉	1	1	yes	characteristic
44	C₂	C₄×Q₈×C₂₂₉	1	1	yes	characteristic
45	C₂	C₂²×C₈×C₂₂₉	1	1	yes	characteristic
46	C₂	#131×C₂₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₂₂₉	C₂²
commutator	C₂	C₂²×C₈×C₂₂₉
Frattini, cosocle	C₂×C₄	C₂³×C₂₂₉
socle, prime radical	C₂²×C₂₂₉	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
9. Q₈×C₂₂₉	C₈	direct (N × H)
14. C₈×C₂₂₉	Q₈	direct (N × H)
23. C₂₂₉	C₈×Q₈	direct (N × H)
24. C₈×Q₈	C₂₂₉	direct (N × H)
33. Q₈	C₈×C₂₂₉	direct (N × H)
38. C₈	Q₈×C₂₂₉	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×C₂₂₉	2
C₄⋊C₈×C₂₂₉	2
C₄×C₈×C₂₂₉	2
C₈×Q₈	229

Subgroups — C8×Q8×C229 #28411058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×Q₈×C₂₂₉ #28411058