Subgroups — #36442332

Order 22784.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26018456	C₂	1	2	yes	maximal
2	C₂×C₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic
3	#19151428	—	2	2	no	—
4	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
5	C₆₄×C₈₉	C₄	1	2	yes	—
6	#15667948	—	4	2	no	—
7	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
8	C₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic
9	C₃₂×C₈₉	Q₈	1	1	yes	characteristic
10	#13083558	—	8	2	no	—
11	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
12	C₁₆×C₈₉	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₈₉	Q₁₆	1	1	yes	characteristic
14	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
15	C₈×C₈₉	#107	1	1	yes	characteristic
16	C₈×C₈₉	Q₃₂	1	1	yes	characteristic
17	#10623494	—	16	2	no	—
18	C₂²×C₈₉	Q₆₄	1	1	yes	characteristic
19	C₄×C₈₉	#366	1	1	yes	characteristic
20	C₄×C₈₉	D₃₂	1	1	yes	characteristic
21	#7547	—	89	1	no	maximal, Sylow
22	C₂×C₈₉	—	2	1	no	—
23	C₂×C₈₉	#1423	1	1	yes	characteristic
24	C₂×C₆₄	D₈₉	1	1	yes	characteristic
25	#1425	—	89	2	no	—
26	C₈₉	#7547	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
28	#368	—	178	2	no	—
29	C₆₄	Dic₈₉	1	2	yes	—
30	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
31	#108	—	356	2	no	—
32	C₃₂	Dic₁₇₈	1	1	yes	characteristic
33	C₃₂	C₂×Dic₈₉	1	1	yes	characteristic
34	M₁₆	—	712	2	no	—
35	C₂×C₈	D₇₁₂	1	1	yes	characteristic
36	C₁₆	C₄⋊Dic₈₉	1	1	yes	characteristic
37	C₁₆	Dic₃₅₆	1	1	yes	characteristic
38	C₂×C₄	D₁₄₂₄	1	1	yes	characteristic
39	C₈	—	1424	2	no	—
40	C₈	#15667946	1	1	yes	characteristic
41	C₈	Dic₇₁₂	1	1	yes	characteristic
42	C₂²	Dic₁₄₂₄	1	1	yes	characteristic
43	C₄	#19151424	1	1	yes	characteristic
44	C₄	D₂₈₄₈	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#26018452	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₂₈₄₈
commutator	C₃₂×C₈₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₈₉
Fitting	C₂×C₆₄×C₈₉	C₂
socle	C₂×C₈₉	#1423
prime radical	C₂²×C₈₉	Q₆₄
cosocle	C₂×C₃₂×C₈₉	C₂²
hypercenter	C₂×C₆₄	D₈₉
hypocenter	C₈₉	#7547
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
26. C₈₉	#7547	semidirect

Maximal subgroups

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

subgroup	index
#26018456	2
C₂×C₆₄×C₈₉	2
#7547	89