Subgroups — #23761364

Order 10112.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#19098316	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₉⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
6	C₂×Q₁₆×C₇₉	C₄	1	1	yes	characteristic
7	C₄×Q₈×C₇₉	—	2	1	no	—
8	#107×C₇₉	C₄	1	1	yes	characteristic
9	#103×C₇₉	—	2	1	no	—
10	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₇₉⋊C₈	—	4	1	no	—
12	C₇₉⋊C₁₆	—	2	2	no	—
13	C₂×Q₈×C₇₉	—	2	1	no	—
14	Q₁₆×C₇₉	—	2	1	no	—
15	Q₁₆×C₇₉	C₈	1	2	yes	complemented
16	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
18	C₄⋊C₄×C₇₉	—	2	1	no	—
19	C₄⋊C₄×C₇₉	—	4	1	no	—
20	C₄²×C₇₉	—	4	1	no	—
21	C₄²×C₇₉	D₄	1	1	yes	characteristic
22	Q₈×C₇₉	—	2	2	no	—
23	Q₈×C₇₉	—	4	1	no	—
24	C₂×C₄×C₇₉	—	4	1	no	—
25	C₂×C₄×C₇₉	—	4	1	no	—
26	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
28	C₂×C₄×C₇₉	SD₁₆	1	1	yes	characteristic
29	C₈×C₇₉	—	2	1	no	—
30	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
31	C₈×C₇₉	M₁₆	1	1	yes	characteristic
32	C₇₉⋊C₈	—	8	1	no	—
33	C₂²×C₇₉	#102	1	1	yes	characteristic
34	C₄×C₇₉	—	2	1	no	—
35	C₄×C₇₉	—	4	2	no	—
36	C₄×C₇₉	—	8	1	no	—
37	C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₄×C₇₉	#104	1	1	yes	characteristic
39	C₄×C₇₉	SD₃₂	1	1	yes	characteristic
40	C₄×C₇₉	Q₃₂	1	1	yes	characteristic
41	C₂×C₇₉	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₇₉	#358	1	1	yes	characteristic
43	C₂×C₇₉	#359	1	1	yes	characteristic
44	#1332	—	79	1	no	maximal, Sylow
45	C₇₉	#1332	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₁₆	D₇₉	1	1	yes	characteristic
47	C₄×C₁₆	—	79	1	no	—
48	#335	—	79	1	no	—
49	C₂×Q₁₆	Dic₇₉	1	1	yes	characteristic
50	C₄×Q₈	—	2	1	no	—
51	C₂×C₁₆	—	158	1	no	—
52	#107	Dic₇₉	1	1	yes	characteristic
53	C₄⋊C₈	—	158	1	no	—
54	#103	—	2	1	no	—
55	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
56	C₂×Q₈	—	2	1	no	—
57	Q₁₆	—	2	1	no	—
58	Q₁₆	C₇₉⋊C₈	1	2	yes	complemented
59	C₂×C₈	—	316	1	no	—
60	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
61	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
62	C₄⋊C₄	—	2	1	no	—
63	C₄⋊C₄	—	4	1	no	—
64	C₄²	—	4	1	no	—
65	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
66	C₁₆	—	158	2	no	—
67	Q₈	—	2	2	no	—
68	Q₈	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	4	1	no	—
71	C₂×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
72	C₂×C₄	#11929609	1	1	yes	characteristic
73	C₂×C₄	#11929612	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	632	1	no	—
76	C₈	C₂×C₇₉⋊C₈	1	1	yes	characteristic
77	C₈	#11929608	1	1	yes	characteristic
78	C₂²	#14579082	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	4	2	no	—
81	C₄	—	8	1	no	—
82	C₄	C₂²⋊(C₇₉⋊C₈)	1	1	yes	characteristic
83	C₄	#14579088	1	1	yes	characteristic
84	C₄	#14579104	1	1	yes	characteristic
85	C₄	#14579107	1	1	yes	characteristic
86	C₂	D₄⋊(C₇₉⋊C₈)	1	1	yes	characteristic
87	C₂	#19098367	1	1	yes	characteristic
88	C₂	#19098370	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#11929609
commutator	C₈×C₇₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₉
Fitting	C₄×Q₁₆×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#102
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	C₄×Q₁₆	D₇₉
hypocenter	C₇₉	#1332
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
15. Q₁₆×C₇₉	C₈	semidirect
45. C₇₉	#1332	semidirect
58. Q₁₆	C₇₉⋊C₈	semidirect