Subgroups — #23763018

Order 10112.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098968	C₂	1	4	yes	maximal
2	#19098943	C₂	1	2	yes	maximal
3	C₈²×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₁₆	—	2	4	no	—
5	#14579161	C₂²	1	4	yes	—
6	#14579095	—	2	8	no	—
7	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₇₉	C₂²	1	2	yes	—
9	C₂×Dic₁₅₈	—	2	4	no	—
10	Dic₃₁₆	—	4	8	no	—
11	C₄⋊Dic₇₉	—	2	8	no	—
12	C₂×C₈×C₇₉	D₄	1	2	yes	—
13	C₂×C₈×C₇₉	D₄	1	4	yes	—
14	C₄²×C₇₉	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
17	C₂×Dic₇₉	—	4	4	no	—
18	Dic₁₅₈	—	4	8	no	—
19	C₈×C₇₉	D₈	1	4	yes	—
20	C₈×C₇₉	Q₁₆	1	8	yes	complemented
21	C₂²×C₇₉	#127	1	1	yes	characteristic
22	C₄×C₇₉	C₂×D₈	1	2	yes	—
23	C₄×C₇₉	C₂×Q₁₆	1	4	yes	—
24	Dic₇₉	—	8	4	no	—
25	C₂×C₇₉	#493	1	1	yes	characteristic
26	C₂×C₇₉	#494	1	2	yes	—
27	#1713	—	79	1	no	maximal, Sylow
28	C₇₉	#1713	1	1	yes	characteristic, complemented, Sylow
29	#500	—	79	4	no	—
30	#494	—	79	2	no	—
31	C₈²	D₇₉	1	1	yes	characteristic
32	C₂×Q₁₆	—	158	4	no	—
33	C₄⋊Q₈	—	79	4	no	—
34	#107	—	158	8	no	—
35	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
36	C₄×C₈	C₂×D₇₉	1	2	yes	—
37	C₂×Q₈	—	158	4	no	—
38	Q₁₆	—	316	8	no	—
39	C₂×C₈	D₃₁₆	1	2	yes	—
40	C₂×C₈	D₃₁₆	1	4	yes	—
41	C₄⋊C₄	—	158	8	no	—
42	C₄²	C₂²×D₇₉	1	1	yes	characteristic
43	Q₈	—	316	8	no	—
44	C₂×C₄	—	316	4	no	—
45	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
46	C₂×C₄	C₂×D₃₁₆	1	2	yes	—
47	C₈	D₆₃₂	1	4	yes	—
48	C₈	Dic₃₁₆	1	8	yes	complemented
49	C₂²	#14579158	1	1	yes	characteristic
50	C₄	—	632	4	no	—
51	C₄	C₂×D₆₃₂	1	2	yes	—
52	C₄	C₂×Dic₃₁₆	1	4	yes	—
53	C₂	#19098940	1	1	yes	characteristic
54	C₂	#19098943	1	2	yes	—

	subgroup	G/H
center	C₂²	#14579158
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	C₈²×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#127
hypercenter	C₈²	D₇₉
hypocenter	C₇₉	#1713
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₇₉	Q₁₆	semidirect
28. C₇₉	#1713	semidirect
48. C₈	Dic₃₁₆	semidirect