Subgroups — Q₁₂₈×D₇₉ #34209317

Order 20224.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₆₄×D₇₉	C₂	1	2	yes	maximal
2	Dic₂₅₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#23761617	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₇₉	C₂	1	1	yes	maximal, characteristic
5	C₇₉×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₃₂×D₇₉	—	2	2	no	—
7	Dic₁₂₆₄	C₂²	1	2	yes	—
8	#19098403	—	2	2	no	—
9	C₃₂×D₇₉	C₂²	1	1	yes	characteristic
10	C₇₉⋊C₆₄	C₂²	1	1	yes	characteristic
11	Q₆₄×C₇₉	C₂²	1	2	yes	—
12	C₆₄×C₇₉	C₂²	1	1	yes	characteristic
13	Q₁₆×D₇₉	—	4	2	no	—
14	Dic₆₃₂	—	2	2	no	—
15	#14579107	—	4	2	no	—
16	C₁₆×D₇₉	D₄	1	1	yes	characteristic
17	C₇₉⋊C₃₂	D₄	1	1	yes	characteristic
18	Q₃₂×C₇₉	—	2	2	no	—
19	C₃₂×C₇₉	C₂³	1	1	yes	characteristic
20	Q₈×D₇₉	—	8	2	no	—
21	Dic₃₁₆	—	4	2	no	—
22	#11929614	—	8	2	no	—
23	C₈×D₇₉	D₈	1	1	yes	characteristic
24	C₇₉⋊C₁₆	D₈	1	1	yes	characteristic
25	Q₁₆×C₇₉	—	4	2	no	—
26	C₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
27	Q₈×C₇₉	—	8	2	no	—
28	C₄×D₇₉	—	16	2	no	—
29	C₄×D₇₉	D₁₆	1	1	yes	characteristic
30	Dic₁₅₈	—	8	2	no	—
31	Dic₁₅₈	—	16	2	no	—
32	C₈×C₇₉	C₂×D₈	1	1	yes	characteristic
33	C₇₉⋊C₈	D₁₆	1	1	yes	characteristic
34	C₂×D₇₉	D₃₂	1	1	yes	characteristic
35	C₄×C₇₉	—	16	2	no	—
36	C₄×C₇₉	C₂×D₁₆	1	1	yes	characteristic
37	Dic₇₉	—	16	2	no	—
38	Dic₇₉	D₃₂	1	1	yes	characteristic
39	C₂×Q₁₂₈	—	79	1	no	maximal, Sylow
40	C₂×C₇₉	C₂×D₃₂	1	1	yes	characteristic
41	D₇₉	Q₁₂₈	1	2	yes	direct product factor
42	C₂×Q₆₄	—	79	2	no	—
43	Q₁₂₈	—	79	2	no	—
44	Q₁₂₈	—	79	1	no	—
45	Q₁₂₈	D₇₉	1	1	yes	characteristic, direct product factor
46	C₂×C₆₄	—	79	1	no	—
47	C₇₉	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₃₂	—	158	2	no	—
49	Q₆₄	—	79	2	no	—
50	Q₆₄	—	158	2	no	—
51	Q₆₄	C₂×D₇₉	1	2	yes	—
52	C₂×C₃₂	—	79	1	no	—
53	C₆₄	—	79	1	no	—
54	C₆₄	C₂×D₇₉	1	1	yes	characteristic
55	C₂×Q₁₆	—	316	2	no	—
56	Q₃₂	—	2	2	no	—
57	Q₃₂	—	316	2	no	—
58	Q₃₂	—	158	2	no	—
59	C₂×C₁₆	—	79	1	no	—
60	C₃₂	—	79	1	no	—
61	C₃₂	C₂²×D₇₉	1	1	yes	characteristic
62	C₂×Q₈	—	632	2	no	—
63	Q₁₆	—	4	2	no	—
64	Q₁₆	—	316	2	no	—
65	Q₁₆	—	632	2	no	—
66	C₂×C₈	—	79	1	no	—
67	C₁₆	—	79	1	no	—
68	C₁₆	D₄×D₇₉	1	1	yes	characteristic
69	Q₈	—	8	2	no	—
70	Q₈	—	632	2	no	—
71	Q₈	—	1264	2	no	—
72	C₂×C₄	—	79	1	no	—
73	C₂×C₄	—	1264	2	no	—
74	C₈	—	79	1	no	—
75	C₈	D₈×D₇₉	1	1	yes	characteristic
76	C₂²	—	79	1	no	—
77	C₄	—	16	2	no	—
78	C₄	—	79	1	no	—
79	C₄	—	1264	2	no	—
80	C₄	D₁₆×D₇₉	1	1	yes	characteristic
81	C₂	—	79	2	no	—
82	C₂	D₃₂×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₇₉
commutator, cosocle	C₃₂×C₇₉	C₂³
Frattini	C₃₂	C₂²×D₇₉
Fitting	C₇₉×Q₁₂₈	C₂
socle	C₂×C₇₉	C₂×D₃₂
prime radical	C₂×D₇₉	D₃₂
hypercenter	Q₁₂₈	D₇₉
hypocenter	C₇₉	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₇₉ ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ Q₁₂₈

Complements

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

N	H ≅ G/N	type
2. Dic₂₅₂₈	C₂	semidirect
3. #23761617	C₂	semidirect
5. C₇₉×Q₁₂₈	C₂	semidirect
41. D₇₉	Q₁₂₈	direct (N × H)
45. Q₁₂₈	D₇₉	direct (N × H)
47. C₇₉	C₂×Q₁₂₈	semidirect

Maximal subgroups

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

subgroup	index
Q₆₄×D₇₉	2
Dic₂₅₂₈	2
#23761617	2
C₆₄×D₇₉	2
C₇₉×Q₁₂₈	2
C₂×Q₁₂₈	79

Subgroups — Q128×D79 #34209317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₂₈×D₇₉ #34209317