Subgroups — Q₆₄×D₇₉ #23765703

Order 10112.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₇₉	C₂	1	2	yes	maximal
2	Dic₁₂₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098403	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₇₉	C₂	1	1	yes	maximal, characteristic
5	Q₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₇₉	—	2	2	no	—
7	Dic₆₃₂	C₂²	1	2	yes	—
8	#14579107	—	2	2	no	—
9	C₁₆×D₇₉	C₂²	1	1	yes	characteristic
10	C₇₉⋊C₃₂	C₂²	1	1	yes	characteristic
11	Q₃₂×C₇₉	C₂²	1	2	yes	—
12	C₃₂×C₇₉	C₂²	1	1	yes	characteristic
13	Q₈×D₇₉	—	4	2	no	—
14	Dic₃₁₆	—	2	2	no	—
15	#11929614	—	4	2	no	—
16	C₈×D₇₉	D₄	1	1	yes	characteristic
17	C₇₉⋊C₁₆	D₄	1	1	yes	characteristic
18	Q₁₆×C₇₉	—	2	2	no	—
19	C₁₆×C₇₉	C₂³	1	1	yes	characteristic
20	Q₈×C₇₉	—	4	2	no	—
21	C₄×D₇₉	—	8	2	no	—
22	C₄×D₇₉	D₈	1	1	yes	characteristic
23	Dic₁₅₈	—	4	2	no	—
24	Dic₁₅₈	—	8	2	no	—
25	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
26	C₇₉⋊C₈	D₈	1	1	yes	characteristic
27	C₂×D₇₉	D₁₆	1	1	yes	characteristic
28	C₄×C₇₉	—	8	2	no	—
29	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
30	Dic₇₉	—	8	2	no	—
31	Dic₇₉	D₁₆	1	1	yes	characteristic
32	C₂×C₇₉	C₂×D₁₆	1	1	yes	characteristic
33	D₇₉	Q₆₄	1	2	yes	direct product factor
34	C₂×Q₆₄	—	79	1	no	maximal, Sylow
35	C₇₉	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₃₂	—	79	2	no	—
37	Q₆₄	—	79	2	no	—
38	Q₆₄	—	79	1	no	—
39	Q₆₄	D₇₉	1	1	yes	characteristic, direct product factor
40	C₂×C₃₂	—	79	1	no	—
41	C₂×Q₁₆	—	158	2	no	—
42	Q₃₂	—	79	2	no	—
43	Q₃₂	—	158	2	no	—
44	Q₃₂	C₂×D₇₉	1	2	yes	—
45	C₂×C₁₆	—	79	1	no	—
46	C₃₂	—	79	1	no	—
47	C₃₂	C₂×D₇₉	1	1	yes	characteristic
48	C₂×Q₈	—	316	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	316	2	no	—
51	Q₁₆	—	158	2	no	—
52	C₂×C₈	—	79	1	no	—
53	C₁₆	—	79	1	no	—
54	C₁₆	C₂²×D₇₉	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	316	2	no	—
57	Q₈	—	632	2	no	—
58	C₂×C₄	—	79	1	no	—
59	C₂×C₄	—	632	2	no	—
60	C₈	—	79	1	no	—
61	C₈	D₄×D₇₉	1	1	yes	characteristic
62	C₂²	—	79	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	79	1	no	—
65	C₄	—	632	2	no	—
66	C₄	D₈×D₇₉	1	1	yes	characteristic
67	C₂	—	79	2	no	—
68	C₂	D₁₆×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₇₉
commutator, cosocle	C₁₆×C₇₉	C₂³
Frattini	C₁₆	C₂²×D₇₉
Fitting	Q₆₄×C₇₉	C₂
socle	C₂×C₇₉	C₂×D₁₆
prime radical	C₂×D₇₉	D₁₆
hypercenter	Q₆₄	D₇₉
hypocenter	C₇₉	C₂×Q₆₄
LCS	G ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₁₂₆₄	C₂	semidirect
3. #19098403	C₂	semidirect
5. Q₆₄×C₇₉	C₂	semidirect
33. D₇₉	Q₆₄	direct (N × H)
35. C₇₉	C₂×Q₆₄	semidirect
39. Q₆₄	D₇₉	direct (N × H)

Subgroups — Q64×D79 #23765703

Conjugacy classes of subgroups

Complements

Subgroups — Q₆₄×D₇₉ #23765703