Subgroups — #23765275

Order 10112.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₂₆₄	C₂	1	1	yes	maximal, characteristic
2	#19098645	C₂	1	2	yes	maximal, complemented
3	#19098363	C₂	1	2	yes	maximal, complemented
4	#19098338	C₂	1	1	yes	maximal, characteristic, complemented
5	#367×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₆₃₂	C₂²	1	2	yes	—
7	#14579123	—	2	2	no	—
8	D₁₂₆₄	C₄	1	4	yes	complemented
9	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
10	#14579081	—	2	2	no	—
11	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
13	#107×C₇₉	C₂²	1	2	yes	—
14	C₂×D₃₁₆	—	2	2	no	—
15	C₂×C₄×D₇₉	—	4	2	no	—
16	D₆₃₂	—	2	2	no	—
17	D₆₃₂	C₂×C₄	1	4	yes	complemented
18	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
19	(C₂×D₇₉)⋊C₄	—	4	2	no	—
20	C₄×Dic₇₉	D₄	1	1	yes	characteristic
21	C₇₉⋊C₁₆	—	2	1	no	—
22	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₇₉	—	2	2	no	—
24	C₁₆×C₇₉	C₂×C₄	1	2	yes	complemented
25	C₂²×D₇₉	—	4	2	no	—
26	C₂×C₄×C₇₉	—	4	2	no	—
27	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₇₉	D₈	1	2	yes	—
29	D₃₁₆	—	2	4	no	—
30	D₃₁₆	—	4	2	no	—
31	C₄×D₇₉	—	8	4	no	—
32	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₇₉	#41	1	1	yes	characteristic
34	C₇₉⋊C₈	—	2	1	no	—
35	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
36	C₂×D₇₉	—	4	4	no	—
37	C₂×D₇₉	—	8	2	no	—
38	C₂×D₇₉	—	8	2	no	—
39	C₄×C₇₉	—	8	2	no	—
40	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
41	C₄×C₇₉	#135	1	1	yes	characteristic
42	Dic₇₉	—	2	2	no	—
43	C₂×C₇₉	C₄×D₈	1	1	yes	characteristic
44	C₂×C₇₉	#509	1	2	yes	—
45	D₇₉	—	8	4	no	—
46	#2177	—	79	1	no	maximal, Sylow
47	C₇₉	#2177	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₁₆	—	79	1	no	—
49	C₄×D₈	—	79	2	no	—
50	#367	D₇₉	1	1	yes	characteristic, complemented
51	#357	—	79	2	no	—
52	#346	—	79	1	no	—
53	C₂×D₈	—	79	2	no	—
54	C₄×D₄	—	158	2	no	—
55	D₁₆	—	79	4	no	—
56	C₂×C₁₆	—	79	1	no	—
57	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
58	#107	C₂×D₇₉	1	2	yes	—
59	#102	—	158	2	no	—
60	C₄×C₈	—	79	1	no	—
61	C₂×D₄	—	158	2	no	—
62	C₂²×C₄	—	316	2	no	—
63	D₈	—	79	4	no	—
64	D₈	—	158	2	no	—
65	C₂×C₈	—	79	1	no	—
66	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
67	C₄⋊C₄	—	2	2	no	—
68	C₂²⋊C₄	—	316	2	no	—
69	C₄²	—	79	1	no	—
70	C₁₆	—	158	1	no	—
71	C₁₆	C₄×D₇₉	1	2	yes	complemented
72	C₂³	—	316	2	no	—
73	D₄	—	316	2	no	—
74	D₄	—	158	4	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	79	2	no	—
77	C₂×C₄	—	632	4	no	—
78	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
79	C₈	—	158	1	no	—
80	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
81	C₈	#11929625	1	1	yes	characteristic
82	C₂²	—	316	4	no	—
83	C₂²	—	632	2	no	—
84	C₂²	—	632	2	no	—
85	C₂²	D₈×D₇₉	1	1	yes	characteristic
86	C₄	—	8	2	no	—
87	C₄	—	158	2	no	—
88	C₄	#14579123	1	1	yes	characteristic
89	C₄	#14579184	1	1	yes	characteristic
90	C₂	—	632	4	no	—
91	C₂	#19098645	1	1	yes	characteristic
92	C₂	#19099000	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#367×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂×D₁₂₆₄	C₂
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	#367	D₇₉
hypocenter	C₇₉	#2177
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
2. #19098645	C₂	semidirect
3. #19098363	C₂	semidirect
4. #19098338	C₂	semidirect
5. #367×C₇₉	C₂	semidirect
8. D₁₂₆₄	C₄	semidirect
17. D₆₃₂	C₂×C₄	semidirect
24. C₁₆×C₇₉	C₂×C₄	semidirect
47. C₇₉	#2177	semidirect
50. #367	D₇₉	semidirect
71. C₁₆	C₄×D₇₉	semidirect