Subgroups — C₄×C₇₁⋊C₆₄ #31885255

Order 18176.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇₁⋊C₆₄	C₂	1	2	yes	maximal
2	C₄×C₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₇₁⋊C₆₄	C₄	1	4	yes	direct product factor
4	C₂×C₃₂×C₇₁	C₄	1	1	yes	characteristic
5	C₂×C₃₂×C₇₁	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₇₁	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₇₁	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₇₁	C₈	1	1	yes	characteristic
10	C₃₂×C₇₁	C₈	1	2	yes	—
11	C₃₂×C₇₁	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₇₁	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₇₁	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₇₁	C₁₆	1	1	yes	characteristic
15	C₁₆×C₇₁	C₁₆	1	2	yes	—
16	C₁₆×C₇₁	C₄²	1	1	yes	characteristic
17	C₁₆×C₇₁	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₇₁	C₃₂	1	2	yes	—
19	C₂×C₄×C₇₁	C₂×C₁₆	1	1	yes	characteristic
20	C₈×C₇₁	C₃₂	1	2	yes	—
21	C₈×C₇₁	C₄×C₈	1	1	yes	characteristic
22	C₈×C₇₁	C₂×C₁₆	1	1	yes	characteristic
23	C₂²×C₇₁	C₂×C₃₂	1	1	yes	characteristic
24	C₄×C₇₁	C₆₄	1	4	yes	complemented
25	C₄×C₇₁	C₄×C₁₆	1	1	yes	characteristic
26	C₄×C₇₁	C₂×C₃₂	1	1	yes	characteristic
27	C₄×C₆₄	—	71	1	no	maximal, Sylow
28	C₂×C₇₁	C₄×C₃₂	1	1	yes	characteristic
29	C₂×C₇₁	C₂×C₆₄	1	2	yes	—
30	C₂×C₆₄	—	71	2	no	—
31	C₄×C₃₂	D₇₁	1	1	yes	characteristic
32	C₇₁	C₄×C₆₄	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃₂	Dic₇₁	1	1	yes	characteristic
34	C₂×C₃₂	C₂×D₇₁	1	1	yes	characteristic
35	C₄×C₁₆	Dic₇₁	1	1	yes	characteristic
36	C₆₄	—	71	4	no	—
37	C₂×C₁₆	C₇₁⋊C₈	1	1	yes	characteristic
38	C₂×C₁₆	C₂×Dic₇₁	1	1	yes	characteristic
39	C₄×C₈	C₇₁⋊C₈	1	1	yes	characteristic
40	C₃₂	C₇₁⋊C₈	1	2	yes	—
41	C₃₂	C₄×D₇₁	1	2	yes	—
42	C₂×C₈	C₇₁⋊C₁₆	1	1	yes	characteristic
43	C₂×C₈	C₂×C₇₁⋊C₈	1	1	yes	characteristic
44	C₄²	C₇₁⋊C₁₆	1	1	yes	characteristic
45	C₁₆	C₇₁⋊C₁₆	1	2	yes	—
46	C₁₆	C₄×Dic₇₁	1	1	yes	characteristic
47	C₁₆	C₂×C₇₁⋊C₈	1	1	yes	characteristic
48	C₂×C₄	C₇₁⋊C₃₂	1	2	yes	—
49	C₂×C₄	C₂×C₇₁⋊C₁₆	1	1	yes	characteristic
50	C₈	C₇₁⋊C₃₂	1	2	yes	—
51	C₈	C₄×C₇₁⋊C₈	1	1	yes	characteristic
52	C₈	C₂×C₇₁⋊C₁₆	1	1	yes	characteristic
53	C₂²	C₂×C₇₁⋊C₃₂	1	1	yes	characteristic
54	C₄	C₇₁⋊C₆₄	1	4	yes	direct product factor
55	C₄	C₄×C₇₁⋊C₁₆	1	1	yes	characteristic
56	C₄	C₂×C₇₁⋊C₃₂	1	1	yes	characteristic
57	C₂	C₄×C₇₁⋊C₃₂	1	1	yes	characteristic
58	C₂	C₂×C₇₁⋊C₆₄	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₃₂	D₇₁
commutator, hypocenter	C₇₁	C₄×C₆₄
Frattini	C₂×C₃₂	C₂×D₇₁
Fitting	C₄×C₃₂×C₇₁	C₂
socle, prime radical	C₂²×C₇₁	C₂×C₃₂
cosocle	C₂×C₃₂×C₇₁	C₂²
LCS	G ▷ C₇₁
UCS	C₁ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
3. C₇₁⋊C₆₄	C₄	direct (N × H)
24. C₄×C₇₁	C₆₄	semidirect
32. C₇₁	C₄×C₆₄	semidirect
54. C₄	C₇₁⋊C₆₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇₁⋊C₆₄	2
C₄×C₃₂×C₇₁	2
C₄×C₆₄	71

Subgroups — C4×C71⋊C64 #31885255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇₁⋊C₆₄ #31885255