Subgroups — #36442331

Order 22784.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151317	C₂	1	1	yes	maximal, characteristic
2	#26018456	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1425	C₂	1	1	yes	maximal, characteristic
4	#19151428	—	2	1	no	—
5	#19151317	C₄	1	2	yes	—
6	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
7	#368×C₈₉	—	2	1	no	—
8	#15667948	—	4	1	no	—
9	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
10	#108×C₈₉	—	4	1	no	—
11	C₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₈₉	Q₈	1	1	yes	characteristic
13	#13083558	—	8	1	no	—
14	M₁₆×C₈₉	—	8	1	no	—
15	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
16	C₁₆×C₈₉	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₈₉	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
19	C₈×C₈₉	—	16	1	no	—
20	C₈×C₈₉	#107	1	1	yes	characteristic
21	C₈×C₈₉	Q₃₂	1	1	yes	characteristic
22	#10623494	—	16	1	no	—
23	C₂²×C₈₉	Q₆₄	1	1	yes	characteristic
24	C₄×C₈₉	#366	1	1	yes	characteristic
25	C₄×C₈₉	D₃₂	1	1	yes	characteristic
26	#7547	—	89	1	no	maximal, Sylow
27	C₂×C₈₉	—	2	1	no	—
28	C₂×C₈₉	#1423	1	1	yes	characteristic
29	C₂×C₆₄	—	89	1	no	—
30	#1425	—	89	1	no	—
31	#1425	D₈₉	1	1	yes	characteristic
32	C₈₉	#7547	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
34	#368	—	2	1	no	—
35	#368	—	178	1	no	—
36	C₆₄	—	89	2	no	—
37	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
38	#108	—	4	1	no	—
39	#108	—	356	1	no	—
40	C₃₂	Dic₁₇₈	1	1	yes	characteristic
41	C₃₂	C₄×D₈₉	1	1	yes	characteristic
42	M₁₆	—	8	1	no	—
43	M₁₆	—	712	1	no	—
44	C₂×C₈	#13083559	1	1	yes	characteristic
45	C₁₆	#13083553	1	1	yes	characteristic
46	C₁₆	#13083564	1	1	yes	characteristic
47	C₂×C₄	#15667953	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	1424	1	no	—
50	C₈	#15667945	1	1	yes	characteristic
51	C₈	#15667958	1	1	yes	characteristic
52	C₂²	#19151438	1	1	yes	characteristic
53	C₄	#19151423	1	1	yes	characteristic
54	C₄	#19151433	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#26018451	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19151433
commutator	C₃₂×C₈₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₈₉
Fitting	C₈₉×#1425	C₂
socle	C₂×C₈₉	#1423
prime radical	C₂²×C₈₉	Q₆₄
cosocle	C₂×C₃₂×C₈₉	C₂²
hypercenter	#1425	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 ◁ #1425

Complements

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

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

Maximal subgroups

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

subgroup	index
C₂×#19151317	2
#26018456	2
C₈₉×#1425	2
#7547	89