Subgroups — C₃×C₈×C₇⋊C₈ #13051113

Order 1344.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₇⋊C₈	C₂	1	2	yes	maximal
3	C₈×C₇⋊C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₇×C₈	C₄	1	2	yes	—
5	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₇⋊C₈	C₄	1	4	yes	—
7	C₄×C₇×C₈	C₂×C₃	1	1	yes	characteristic
8	C₄×C₇⋊C₈	C₂×C₃	1	2	yes	—
9	C₃×C₈²	—	7	1	no	maximal, Hall
10	C₂×C₃×C₄×C₇	C₂×C₄	1	2	yes	—
11	C₂×C₃×C₄×C₇	C₂×C₄	1	1	yes	characteristic
12	C₃×C₇×C₈	C₈	1	4	yes	complemented
13	C₃×C₇⋊C₈	C₈	1	8	yes	direct product factor
14	C₂×C₇×C₈	C₃×C₄	1	2	yes	—
15	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₇⋊C₈	C₃×C₄	1	4	yes	—
17	C₃×C₄×C₈	—	7	2	no	—
18	C₃×C₄×C₈	D₇	1	1	yes	characteristic
19	C₂²×C₃×C₇	C₄²	1	1	yes	characteristic
20	C₃×C₄×C₇	C₂×C₈	1	4	yes	—
21	C₃×C₄×C₇	C₂×C₈	1	2	yes	—
22	C₈²	—	7	1	no	Sylow
23	C₂×C₄×C₇	C₂×C₃×C₄	1	2	yes	—
24	C₂×C₄×C₇	C₂×C₃×C₄	1	1	yes	characteristic
25	C₇×C₈	C₃×C₈	1	4	yes	complemented
26	C₇⋊C₈	C₃×C₈	1	8	yes	direct product factor
27	C₂×C₃×C₈	—	7	4	no	—
28	C₂×C₃×C₈	Dic₇	1	2	yes	—
29	C₃×C₄²	C₂×D₇	1	1	yes	characteristic
30	C₂×C₃×C₇	C₄×C₈	1	1	yes	characteristic
31	C₂×C₃×C₇	C₄×C₈	1	2	yes	—
32	C₄×C₈	—	7	2	no	—
33	C₄×C₈	C₃×D₇	1	1	yes	characteristic
34	C₂²×C₇	C₃×C₄²	1	1	yes	characteristic
35	C₄×C₇	C₂×C₃×C₈	1	4	yes	—
36	C₄×C₇	C₂×C₃×C₈	1	2	yes	—
37	C₂×C₃×C₄	C₄×D₇	1	2	yes	—
38	C₂×C₃×C₄	C₂×Dic₇	1	1	yes	characteristic
39	C₃×C₈	—	7	8	no	—
40	C₃×C₈	C₇⋊C₈	1	4	yes	direct product factor
41	C₃×C₇	C₈²	1	1	yes	characteristic, complemented, Hall
42	C₂×C₈	—	7	4	no	—
43	C₂×C₈	C₃×Dic₇	1	2	yes	—
44	C₄²	C₂×C₃×D₇	1	1	yes	characteristic
45	C₂×C₇	C₃×C₄×C₈	1	1	yes	characteristic
46	C₂×C₇	C₃×C₄×C₈	1	2	yes	—
47	C₂²×C₃	C₄×Dic₇	1	1	yes	characteristic
48	C₃×C₄	C₈×D₇	1	4	yes	—
49	C₃×C₄	C₂×C₇⋊C₈	1	2	yes	—
50	C₂×C₄	C₃×C₄×D₇	1	2	yes	—
51	C₂×C₄	C₂×C₃×Dic₇	1	1	yes	characteristic
52	C₈	—	7	8	no	—
53	C₈	C₃×C₇⋊C₈	1	4	yes	direct product factor
54	C₇	C₃×C₈²	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃	C₄×C₇⋊C₈	1	1	yes	characteristic
56	C₂×C₃	C₈×Dic₇	1	2	yes	—
57	C₂²	C₃×C₄×Dic₇	1	1	yes	characteristic
58	C₄	C₃×C₈×D₇	1	4	yes	—
59	C₄	C₂×C₃×C₇⋊C₈	1	2	yes	—
60	C₃	C₈×C₇⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	C₃×C₄×C₇⋊C₈	1	1	yes	characteristic
62	C₂	C₃×C₈×Dic₇	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₃×C₄×C₈	D₇
commutator, hypocenter	C₇	C₃×C₈²
Frattini	C₄²	C₂×C₃×D₇
Fitting	C₃×C₄×C₇×C₈	C₂
socle, prime radical	C₂²×C₃×C₇	C₄²
cosocle	C₄²×C₇	C₂²×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₈×C₇⋊C₈	C₃	direct (N × H)
12. C₃×C₇×C₈	C₈	semidirect
13. C₃×C₇⋊C₈	C₈	direct (N × H)
25. C₇×C₈	C₃×C₈	semidirect
26. C₇⋊C₈	C₃×C₈	direct (N × H)
40. C₃×C₈	C₇⋊C₈	direct (N × H)
41. C₃×C₇	C₈²	semidirect
53. C₈	C₃×C₇⋊C₈	direct (N × H)
54. C₇	C₃×C₈²	semidirect
60. C₃	C₈×C₇⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₇×C₈	2
C₃×C₄×C₇⋊C₈	2
C₈×C₇⋊C₈	3
C₃×C₈²	7

Subgroups — C3×C8×C7⋊C8 #13051113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×C₇⋊C₈ #13051113