Subgroups — #34174992

Order 20224.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23761464	C₂	1	2	yes	maximal
2	C₇₉×#1710	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₇₉⋊C₁₆)	—	2	2	no	—
4	#500×C₇₉	C₄	1	2	yes	—
5	#487×C₇₉	—	2	2	no	—
6	C₈²×C₇₉	C₂²	1	1	yes	characteristic
7	C₂×C₇₉⋊C₁₆	—	4	2	no	—
8	C₄⋊Q₈×C₇₉	—	2	2	no	—
9	#107×C₇₉	—	4	2	no	—
10	#103×C₇₉	—	4	2	no	—
11	#103×C₇₉	—	4	2	no	—
12	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
13	C₄×C₈×C₇₉	D₄	1	2	yes	—
14	C₇₉⋊C₁₆	—	8	2	no	—
15	C₂×Q₈×C₇₉	—	4	2	no	—
16	C₂×C₈×C₇₉	—	2	1	no	—
17	C₂×C₈×C₇₉	D₈	1	2	yes	—
18	C₂×C₈×C₇₉	SD₁₆	1	2	yes	—
19	C₄⋊C₄×C₇₉	—	4	2	no	—
20	C₄⋊C₄×C₇₉	—	4	2	no	—
21	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
22	Q₈×C₇₉	—	8	2	no	—
23	Q₈×C₇₉	—	8	2	no	—
24	C₂×C₄×C₇₉	—	8	2	no	—
25	C₂×C₄×C₇₉	#100	1	1	yes	characteristic
26	C₂×C₄×C₇₉	#102	1	2	yes	—
27	C₈×C₇₉	—	2	2	no	—
28	C₈×C₇₉	—	2	2	no	—
29	C₈×C₇₉	—	2	2	no	—
30	C₂²×C₇₉	#331	1	1	yes	characteristic
31	C₄×C₇₉	—	2	1	no	—
32	C₄×C₇₉	—	16	2	no	—
33	C₄×C₇₉	#359	1	2	yes	—
34	C₄×C₇₉	#360	1	2	yes	—
35	#7093	—	79	1	no	maximal, Sylow
36	C₂×C₇₉	#1358	1	1	yes	characteristic
37	C₂×C₇₉	#1360	1	2	yes	—
38	#1710	D₇₉	1	1	yes	characteristic
39	#1367	—	79	2	no	—
40	C₇₉	#7093	1	1	yes	characteristic, complemented, Sylow
41	#500	Dic₇₉	1	2	yes	—
42	#487	—	2	2	no	—
43	C₄⋊C₁₆	—	158	2	no	—
44	C₈²	C₂×D₇₉	1	1	yes	characteristic
45	C₄⋊Q₈	—	2	2	no	—
46	C₂×C₁₆	—	316	2	no	—
47	#107	—	4	2	no	—
48	#103	—	4	2	no	—
49	#103	—	4	2	no	—
50	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
51	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
52	C₂×Q₈	—	4	2	no	—
53	C₂×C₈	—	2	1	no	—
54	C₂×C₈	#11929609	1	2	yes	—
55	C₂×C₈	#11929612	1	2	yes	—
56	C₄⋊C₄	—	4	2	no	—
57	C₄⋊C₄	—	4	2	no	—
58	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
59	C₁₆	—	632	2	no	—
60	Q₈	—	8	2	no	—
61	Q₈	—	8	2	no	—
62	C₂×C₄	—	8	2	no	—
63	C₂×C₄	#14579078	1	1	yes	characteristic
64	C₂×C₄	#14579082	1	2	yes	—
65	C₈	—	2	2	no	—
66	C₈	—	2	2	no	—
67	C₈	—	2	2	no	—
68	C₂²	#19098307	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	16	2	no	—
71	C₄	#19098370	1	2	yes	—
72	C₄	#19098373	1	2	yes	—
73	C₂	#23761439	1	1	yes	characteristic
74	C₂	#23761443	1	2	yes	—

	subgroup	G/H
center	C₂²	#19098307
commutator	C₄×C₈×C₇₉	C₂×C₄
Frattini	C₈²	C₂×D₇₉
Fitting	C₇₉×#1710	C₂
socle, prime radical	C₂²×C₇₉	#331
cosocle	C₈²×C₇₉	C₂²
hypercenter	#1710	D₇₉
hypocenter	C₇₉	#7093
LCS	G ▷ C₄×C₈×C₇₉ ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1710

Complements

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

N	H ≅ G/N	type
40. C₇₉	#7093	semidirect

Maximal subgroups

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

subgroup	index
#23761464	2
C₇₉×#1710	2
#7093	79