Subgroups — #34175010

Order 20224.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761470	C₂	1	1	yes	maximal, characteristic
2	C₈×C₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#1370	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	D₈	1	1	yes	characteristic
25	C₂×C₈×C₇₉	Q₁₆	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	#107	1	1	yes	characteristic
30	C₂×C₄×C₇₉	#108	1	1	yes	characteristic
31	C₈×C₇₉	—	2	2	no	—
32	C₈×C₇₉	—	2	1	no	—
33	C₈×C₇₉	—	2	1	no	—
34	C₈×C₇₉	C₂×C₁₆	1	1	yes	characteristic
35	C₈×C₇₉	M₃₂	1	1	yes	characteristic
36	C₈×C₇₉	SD₃₂	1	1	yes	characteristic
37	C₈×C₇₉	SD₃₂	1	1	yes	characteristic
38	C₂²×C₇₉	#335	1	1	yes	characteristic
39	C₄×C₇₉	—	2	1	no	—
40	C₄×C₇₉	C₄⋊C₁₆	1	1	yes	characteristic
41	C₄×C₇₉	#364	1	1	yes	characteristic
42	C₄×C₇₉	#367	1	1	yes	characteristic
43	C₄×C₇₉	#368	1	1	yes	characteristic
44	#7101	—	79	1	no	maximal, Sylow
45	C₂×C₇₉	#1370	1	1	yes	characteristic
46	C₂×C₇₉	#1372	1	1	yes	characteristic
47	C₂×C₇₉	#1373	1	1	yes	characteristic
48	#1370	—	79	1	no	—
49	#1370	D₇₉	1	1	yes	characteristic
50	C₈×C₁₆	—	79	1	no	—
51	C₇₉	#7101	1	1	yes	characteristic, complemented, Sylow
52	C₄⋊C₁₆	—	2	1	no	—
53	C₄⋊C₁₆	—	158	1	no	—
54	C₄×C₁₆	—	79	1	no	—
55	C₄×C₁₆	—	79	1	no	—
56	C₈²	C₂×D₇₉	1	1	yes	characteristic
57	C₂×C₁₆	—	4	1	no	—
58	C₂×C₁₆	—	316	1	no	—
59	C₂×C₁₆	—	79	1	no	—
60	C₂×C₁₆	—	79	1	no	—
61	C₂×C₁₆	—	158	1	no	—
62	C₄×C₈	Dic₁₅₈	1	1	yes	characteristic
63	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
64	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
65	C₂×C₈	—	2	1	no	—
66	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
67	C₂×C₈	#11929607	1	1	yes	characteristic
68	C₂×C₈	#11929609	1	1	yes	characteristic
69	C₂×C₈	#11929614	1	1	yes	characteristic
70	C₄²	Dic₇₉⋊C₄	1	1	yes	characteristic
71	C₁₆	—	8	1	no	—
72	C₁₆	—	79	2	no	—
73	C₁₆	—	632	1	no	—
74	C₁₆	—	158	2	no	—
75	C₁₆	—	158	1	no	—
76	C₂×C₄	Dic₇₉⋊C₈	1	1	yes	characteristic
77	C₂×C₄	#14579094	1	1	yes	characteristic
78	C₂×C₄	#14579096	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	2	1	no	—
81	C₈	—	2	1	no	—
82	C₈	C₁₆×D₇₉	1	1	yes	characteristic
83	C₈	#14579100	1	1	yes	characteristic
84	C₈	#14579104	1	1	yes	characteristic
85	C₈	#14579105	1	1	yes	characteristic
86	C₂²	#19098315	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	Dic₇₉⋊C₁₆	1	1	yes	characteristic
89	C₄	#19098383	1	1	yes	characteristic
90	C₄	#19098390	1	1	yes	characteristic
91	C₄	#19098392	1	1	yes	characteristic
92	C₂	#23761469	1	1	yes	characteristic
93	C₂	#23761473	1	1	yes	characteristic
94	C₂	#23761475	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	#11929609
commutator	C₈×C₇₉	C₂×C₁₆
Frattini	C₈²	C₂×D₇₉
Fitting	C₇₉×#1370	C₂
socle, prime radical	C₂²×C₇₉	#335
cosocle	C₈²×C₇₉	C₂²
hypercenter	#1370	D₇₉
hypocenter	C₇₉	#7101
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈² ◁ #1370

Complements

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

N	H ≅ G/N	type
20. C₇₉⋊C₁₆	C₁₆	semidirect
51. C₇₉	#7101	semidirect

Maximal subgroups

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

subgroup	index
#23761470	2
C₈×C₇₉⋊C₁₆	2
C₇₉×#1370	2
#7101	79