Subgroups — #34175006

Order 20224.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761464	C₂	1	1	yes	maximal, characteristic
2	#23761317	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1367	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₇₉⋊C₁₆)	—	2	1	no	—
5	C₄×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
7	C₄⋊C₁₆×C₇₉	—	2	1	no	—
8	C₈²×C₇₉	C₂²	1	1	yes	characteristic
9	C₂×C₇₉⋊C₁₆	—	2	1	no	—
10	C₂×C₇₉⋊C₁₆	—	4	1	no	—
11	C₂×C₇₉⋊C₁₆	C₈	1	1	yes	characteristic
12	C₂×C₇₉⋊C₁₆	C₈	1	1	yes	characteristic
13	C₂×C₁₆×C₇₉	—	4	1	no	—
14	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₇₉	Q₈	1	1	yes	characteristic
17	C₇₉⋊C₁₆	—	2	2	no	—
18	C₇₉⋊C₁₆	—	2	1	no	—
19	C₇₉⋊C₁₆	—	8	1	no	—
20	C₇₉⋊C₁₆	C₁₆	1	2	yes	complemented
21	C₂×C₈×C₇₉	—	2	1	no	—
22	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
23	C₂×C₈×C₇₉	M₁₆	1	1	yes	characteristic
24	C₂×C₈×C₇₉	SD₁₆	1	1	yes	characteristic
25	C₂×C₈×C₇₉	SD₁₆	1	1	yes	characteristic
26	C₄²×C₇₉	C₄⋊C₄	1	1	yes	characteristic
27	C₁₆×C₇₉	—	8	1	no	—
28	C₂×C₄×C₇₉	C₄⋊C₈	1	1	yes	characteristic
29	C₂×C₄×C₇₉	#106	1	1	yes	characteristic
30	C₂×C₄×C₇₉	#108	1	1	yes	characteristic
31	C₈×C₇₉	—	2	1	no	—
32	C₈×C₇₉	—	2	1	no	—
33	C₈×C₇₉	—	2	1	no	—
34	C₈×C₇₉	—	4	1	no	—
35	C₈×C₇₉	C₂×C₁₆	1	1	yes	characteristic
36	C₈×C₇₉	M₃₂	1	1	yes	characteristic
37	C₂²×C₇₉	#334	1	1	yes	characteristic
38	C₄×C₇₉	—	2	1	no	—
39	C₄×C₇₉	C₄⋊C₁₆	1	1	yes	characteristic
40	C₄×C₇₉	#364	1	1	yes	characteristic
41	C₄×C₇₉	#365	1	1	yes	characteristic
42	C₄×C₇₉	#365	1	1	yes	characteristic
43	#7099	—	79	1	no	maximal, Sylow
44	C₂×C₇₉	#1367	1	1	yes	characteristic
45	C₂×C₇₉	#1368	1	1	yes	characteristic
46	C₂×C₇₉	#1369	1	1	yes	characteristic
47	#1367	—	79	1	no	—
48	#1367	D₇₉	1	1	yes	characteristic
49	#1311	—	79	1	no	—
50	C₇₉	#7099	1	1	yes	characteristic, complemented, Sylow
51	C₄⋊C₁₆	—	2	1	no	—
52	C₄⋊C₁₆	—	158	1	no	—
53	C₄×C₁₆	—	79	1	no	—
54	C₄×C₁₆	—	79	1	no	—
55	C₈²	C₂×D₇₉	1	1	yes	characteristic
56	C₂×C₁₆	—	4	1	no	—
57	C₂×C₁₆	—	316	1	no	—
58	C₂×C₁₆	—	79	1	no	—
59	C₂×C₁₆	—	79	1	no	—
60	C₂×C₁₆	—	158	1	no	—
61	C₄×C₈	Dic₁₅₈	1	1	yes	characteristic
62	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
63	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
66	C₂×C₈	#11929607	1	1	yes	characteristic
67	C₂×C₈	#11929611	1	1	yes	characteristic
68	C₂×C₈	#11929612	1	1	yes	characteristic
69	C₄²	Dic₇₉⋊C₄	1	1	yes	characteristic
70	C₁₆	—	8	1	no	—
71	C₁₆	—	79	2	no	—
72	C₁₆	—	632	1	no	—
73	C₁₆	—	158	2	no	—
74	C₁₆	—	158	1	no	—
75	C₂×C₄	Dic₇₉⋊C₈	1	1	yes	characteristic
76	C₂×C₄	#14579092	1	1	yes	characteristic
77	C₂×C₄	#14579096	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	2	1	no	—
80	C₈	—	2	1	no	—
81	C₈	—	4	1	no	—
82	C₈	C₁₆×D₇₉	1	1	yes	characteristic
83	C₈	#14579100	1	1	yes	characteristic
84	C₂²	#19098313	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	Dic₇₉⋊C₁₆	1	1	yes	characteristic
87	C₄	#19098383	1	1	yes	characteristic
88	C₄	#19098385	1	1	yes	characteristic
89	C₄	#19098387	1	1	yes	characteristic
90	C₂	#23761463	1	1	yes	characteristic
91	C₂	#23761465	1	1	yes	characteristic
92	C₂	#23761467	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14579092
commutator	C₈×C₇₉	C₂×C₁₆
Frattini	C₈²	C₂×D₇₉
Fitting	C₇₉×#1367	C₂
socle, prime radical	C₂²×C₇₉	#334
cosocle	C₈²×C₇₉	C₂²
hypercenter	#1367	D₇₉
hypocenter	C₇₉	#7099
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1367

Complements

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

N	H ≅ G/N	type
20. C₇₉⋊C₁₆	C₁₆	semidirect
50. C₇₉	#7099	semidirect

Maximal subgroups

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

subgroup	index
#23761464	2
#23761317	2
C₇₉×#1367	2
#7099	79