Subgroups — #34176175

Order 20224.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761604	C₂	1	1	yes	maximal, characteristic
2	#23761602	C₂	1	1	yes	maximal, characteristic
3	C₇₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	#19098393	—	2	1	no	—
5	#19098389	—	2	1	no	—
6	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
7	C₆₄×C₇₉	C₄	1	2	yes	complemented
8	#14579097	—	4	1	no	—
9	#14579095	—	4	1	no	—
10	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
11	C₃₂×C₇₉	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₇₉	Q₈	1	1	yes	characteristic
13	#11929608	—	8	1	no	—
14	C₄⋊Dic₇₉	—	8	1	no	—
15	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
16	C₁₆×C₇₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₇₉	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₇₉	D₁₆	1	1	yes	characteristic
19	C₂×Dic₇₉	—	16	1	no	—
20	C₈×C₇₉	#107	1	1	yes	characteristic
21	C₈×C₇₉	Q₃₂	1	1	yes	characteristic
22	C₇₉⋊C₈	—	16	1	no	—
23	C₂²×C₇₉	SD₆₄	1	1	yes	characteristic
24	C₄×C₇₉	#366	1	1	yes	characteristic
25	C₄×C₇₉	SD₆₄	1	1	yes	characteristic
26	Dic₇₉	—	32	1	no	—
27	#7548	—	79	1	no	maximal, Sylow
28	C₂×C₇₉	—	2	1	no	—
29	C₂×C₇₉	#1424	1	1	yes	characteristic
30	M₁₂₈	D₇₉	1	1	yes	characteristic
31	#1425	—	79	1	no	—
32	#1424	—	79	1	no	—
33	C₇₉	#7548	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
35	#368	—	158	1	no	—
36	#366	—	158	1	no	—
37	C₆₄	Dic₇₉	1	2	yes	complemented
38	C₂×C₁₆	D₃₁₆	1	1	yes	characteristic
39	#108	—	316	1	no	—
40	#107	—	316	1	no	—
41	C₃₂	Dic₁₅₈	1	1	yes	characteristic
42	C₃₂	C₂×Dic₇₉	1	1	yes	characteristic
43	M₁₆	—	632	1	no	—
44	C₂×C₈	D₆₃₂	1	1	yes	characteristic
45	C₄⋊C₄	—	632	1	no	—
46	C₁₆	C₄⋊Dic₇₉	1	1	yes	characteristic
47	C₁₆	Dic₃₁₆	1	1	yes	characteristic
48	C₂×C₄	—	1264	1	no	—
49	C₂×C₄	D₁₂₆₄	1	1	yes	characteristic
50	C₈	—	1264	1	no	—
51	C₈	#14579095	1	1	yes	characteristic
52	C₈	Dic₆₃₂	1	1	yes	characteristic
53	C₂²	#19098402	1	1	yes	characteristic
54	C₄	—	2528	1	no	—
55	C₄	#19098389	1	1	yes	characteristic
56	C₄	#19098402	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#23761602	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23761602
commutator	C₃₂×C₇₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₉
Fitting	C₇₉×M₁₂₈	C₂
socle	C₂×C₇₉	#1424
prime radical	C₂²×C₇₉	SD₆₄
cosocle	C₂×C₃₂×C₇₉	C₂²
hypercenter	M₁₂₈	D₇₉
hypocenter	C₇₉	#7548
LCS	G ▷ C₃₂×C₇₉ ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
7. C₆₄×C₇₉	C₄	semidirect
33. C₇₉	#7548	semidirect
37. C₆₄	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23761604	2
#23761602	2
C₇₉×M₁₂₈	2
#7548	79