Subgroups — #23761372

Order 10112.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19098681	C₂	1	1	yes	maximal, characteristic
2	C₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#364×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#14579183	C₄	1	1	yes	characteristic
5	#14579167	—	2	1	no	—
6	#14579097	C₄	1	1	yes	characteristic
7	#14579089	—	2	1	no	—
8	C₄×C₇₉⋊C₈	—	2	1	no	—
9	M₃₂×C₇₉	—	2	1	no	—
10	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
11	#11929624	—	2	1	no	—
12	Dic₃₁₆	C₈	1	1	yes	characteristic, complemented
13	#11929613	—	2	1	no	—
14	D₆₃₂	C₈	1	1	yes	characteristic, complemented
15	#11929608	—	2	1	no	—
16	#11929607	—	4	1	no	—
17	C₂×C₇₉⋊C₈	—	2	2	no	—
18	C₈×D₇₉	—	4	1	no	—
19	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
21	C₄²×C₇₉	D₄	1	1	yes	characteristic
22	C₁₆×C₇₉	—	4	1	no	—
23	C₂×C₄×C₇₉	—	2	1	no	—
24	C₂×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₇₉	—	4	1	no	—
26	D₃₁₆	—	2	1	no	—
27	C₄×D₇₉	—	4	1	no	—
28	Dic₁₅₈	—	2	1	no	—
29	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
30	C₈×C₇₉	M₁₆	1	1	yes	characteristic
31	C₈×C₇₉	D₈	1	1	yes	characteristic
32	C₈×C₇₉	SD₁₆	1	1	yes	characteristic
33	C₇₉⋊C₈	—	2	4	no	—
34	C₇₉⋊C₈	—	4	1	no	—
35	C₂²×C₇₉	#104	1	1	yes	characteristic
36	C₂×D₇₉	—	4	1	no	—
37	C₄×C₇₉	—	2	2	no	—
38	C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₇₉	#102	1	1	yes	characteristic
40	Dic₇₉	—	4	1	no	—
41	C₂×C₇₉	—	2	1	no	—
42	C₂×C₇₉	D₄⋊C₈	1	1	yes	characteristic
43	D₇₉	—	8	1	no	—
44	#1335	—	79	1	no	maximal, Sylow
45	C₇₉	#1335	1	1	yes	characteristic, complemented, Sylow
46	#443	—	79	1	no	—
47	#364	D₇₉	1	1	yes	characteristic, complemented
48	C₈²	—	79	1	no	—
49	#135	—	79	1	no	—
50	#131	—	158	1	no	—
51	M₃₂	—	2	1	no	—
52	#108	—	79	1	no	—
53	#104	—	158	1	no	—
54	C₄×C₈	—	158	1	no	—
55	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
56	#41	—	158	1	no	—
57	Q₁₆	—	79	1	no	—
58	SD₁₆	—	158	1	no	—
59	D₈	—	79	1	no	—
60	M₁₆	—	316	1	no	—
61	M₁₆	—	158	1	no	—
62	C₂×C₈	—	316	1	no	—
63	C₂×C₈	—	158	2	no	—
64	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
66	C₄²	D₃₁₆	1	1	yes	characteristic
67	C₁₆	—	4	1	no	—
68	Q₈	—	158	1	no	—
69	D₄	—	316	1	no	—
70	D₄	—	158	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	316	1	no	—
73	C₂×C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
74	C₈	—	316	1	no	—
75	C₈	—	158	4	no	—
76	C₈	C₈×D₇₉	1	1	yes	characteristic
77	C₈	#11929607	1	1	yes	characteristic
78	C₈	#11929609	1	1	yes	characteristic
79	C₈	#11929611	1	1	yes	characteristic
80	C₂²	—	316	1	no	—
81	C₂²	#14579087	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	316	1	no	—
84	C₄	(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
85	C₄	#14579081	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	632	1	no	—
88	C₂	#19098290	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#11929609
commutator	C₈×C₇₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₉
Fitting	#364×C₇₉	C₂
socle	C₂×C₇₉	D₄⋊C₈
prime radical	#14579183	C₄
cosocle	C₄×C₈×C₇₉	C₂²
hypercenter	#364	D₇₉
hypocenter	C₇₉	#1335
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. C₈×C₇₉⋊C₈	C₂	semidirect
3. #364×C₇₉	C₂	semidirect
12. Dic₃₁₆	C₈	semidirect
14. D₆₃₂	C₈	semidirect
45. C₇₉	#1335	semidirect
47. #364	D₇₉	semidirect