Subgroups — #34209324

Order 20224.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23765710	C₂	1	2	yes	maximal, complemented
2	#23761614	C₂	1	2	yes	maximal, complemented
3	D₅₀₅₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098996	—	2	2	no	—
7	#19098400	—	2	2	no	—
8	D₂₅₂₈	C₂²	1	2	yes	—
9	C₃₂×D₇₉	C₂²	1	1	yes	characteristic
10	C₇₉⋊C₆₄	C₂²	1	1	yes	characteristic
11	Q₆₄×C₇₉	C₂²	1	2	yes	—
12	C₆₄×C₇₉	C₂²	1	1	yes	characteristic
13	#14579184	—	4	2	no	—
14	#14579104	—	4	2	no	—
15	D₁₂₆₄	—	2	2	no	—
16	C₁₆×D₇₉	D₄	1	1	yes	characteristic
17	C₇₉⋊C₃₂	D₄	1	1	yes	characteristic
18	Q₃₂×C₇₉	—	2	2	no	—
19	C₃₂×C₇₉	C₂³	1	1	yes	characteristic
20	#11929625	—	8	2	no	—
21	#11929611	—	8	2	no	—
22	D₆₃₂	—	4	2	no	—
23	C₈×D₇₉	D₈	1	1	yes	characteristic
24	C₇₉⋊C₁₆	D₈	1	1	yes	characteristic
25	Q₁₆×C₇₉	—	4	2	no	—
26	C₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
27	Q₈×C₇₉	—	8	2	no	—
28	D₃₁₆	—	8	2	no	—
29	D₃₁₆	—	16	2	no	—
30	C₄×D₇₉	—	16	2	no	—
31	C₄×D₇₉	D₁₆	1	1	yes	characteristic
32	C₈×C₇₉	C₂×D₈	1	1	yes	characteristic
33	C₇₉⋊C₈	D₁₆	1	1	yes	characteristic
34	C₂×D₇₉	—	16	2	no	—
35	C₂×D₇₉	D₃₂	1	1	yes	characteristic
36	C₄×C₇₉	—	16	2	no	—
37	C₄×C₇₉	C₂×D₁₆	1	1	yes	characteristic
38	Dic₇₉	D₃₂	1	1	yes	characteristic
39	#13741	—	79	1	no	maximal, Sylow
40	C₂×C₇₉	C₂×D₃₂	1	1	yes	characteristic
41	D₇₉	—	2	1	no	—
42	D₇₉	—	32	2	no	—
43	#2262	—	79	2	no	—
44	Q₁₂₈	D₇₉	1	1	yes	characteristic, complemented
45	SD₁₂₈	—	79	2	no	—
46	D₆₄	—	79	1	no	—
47	C₂×C₆₄	—	79	1	no	—
48	C₇₉	#13741	1	1	yes	characteristic, complemented, Sylow
49	#508	—	158	2	no	—
50	Q₆₄	C₂×D₇₉	1	2	yes	—
51	SD₆₄	—	158	2	no	—
52	D₃₂	—	79	2	no	—
53	C₂×C₃₂	—	79	1	no	—
54	C₆₄	—	79	1	no	—
55	C₆₄	C₂×D₇₉	1	1	yes	characteristic
56	#135	—	316	2	no	—
57	Q₃₂	—	2	2	no	—
58	SD₃₂	—	316	2	no	—
59	D₁₆	—	158	2	no	—
60	C₂×C₁₆	—	79	1	no	—
61	C₃₂	—	79	1	no	—
62	C₃₂	C₂²×D₇₉	1	1	yes	characteristic
63	#41	—	632	2	no	—
64	Q₁₆	—	4	2	no	—
65	SD₁₆	—	632	2	no	—
66	D₈	—	316	2	no	—
67	C₂×C₈	—	79	1	no	—
68	C₁₆	—	79	1	no	—
69	C₁₆	D₄×D₇₉	1	1	yes	characteristic
70	Q₈	—	8	2	no	—
71	D₄	—	632	2	no	—
72	D₄	—	1264	2	no	—
73	C₂×C₄	—	79	1	no	—
74	C₂×C₄	—	1264	2	no	—
75	C₈	—	79	1	no	—
76	C₈	D₈×D₇₉	1	1	yes	characteristic
77	C₂²	—	79	1	no	—
78	C₂²	—	1264	2	no	—
79	C₄	—	16	2	no	—
80	C₄	—	79	1	no	—
81	C₄	D₁₆×D₇₉	1	1	yes	characteristic
82	C₂	—	158	1	no	—
83	C₂	—	2528	2	no	—
84	C₂	D₃₂×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₇₉
commutator, cosocle	C₃₂×C₇₉	C₂³
Frattini	C₃₂	C₂²×D₇₉
Fitting	C₇₉×Q₁₂₈	C₂
socle	C₂×C₇₉	C₂×D₃₂
hypercenter	Q₁₂₈	D₇₉
hypocenter	C₇₉	#13741
LCS	G ▷ C₃₂×C₇₉ ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ Q₁₂₈

Complements

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

N	H ≅ G/N	type
1. #23765710	C₂	semidirect
2. #23761614	C₂	semidirect
3. D₅₀₅₆	C₂	semidirect
4. C₆₄×D₇₉	C₂	semidirect
5. C₇₉×Q₁₂₈	C₂	semidirect
44. Q₁₂₈	D₇₉	semidirect
48. C₇₉	#13741	semidirect

Maximal subgroups

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

subgroup	index
#23765710	2
#23761614	2
D₅₀₅₆	2
C₆₄×D₇₉	2
C₇₉×Q₁₂₈	2
#13741	79