Subgroups — #36442334

Order 22784.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26018456	C₂	1	1	yes	maximal, characteristic
2	#26018454	C₂	1	1	yes	maximal, characteristic
3	C₈₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	#19151428	—	2	1	no	—
5	#19151424	—	2	1	no	—
6	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
7	C₆₄×C₈₉	C₄	1	2	yes	complemented
8	#15667948	—	4	1	no	—
9	#15667946	—	4	1	no	—
10	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
11	C₃₂×C₈₉	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₈₉	Q₈	1	1	yes	characteristic
13	#13083558	—	8	1	no	—
14	C₄⋊Dic₈₉	—	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	C₂×Dic₈₉	—	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	SD₆₄	1	1	yes	characteristic
24	C₄×C₈₉	#366	1	1	yes	characteristic
25	C₄×C₈₉	SD₆₄	1	1	yes	characteristic
26	Dic₈₉	—	32	1	no	—
27	#7548	—	89	1	no	maximal, Sylow
28	C₂×C₈₉	—	2	1	no	—
29	C₂×C₈₉	#1424	1	1	yes	characteristic
30	M₁₂₈	D₈₉	1	1	yes	characteristic
31	#1425	—	89	1	no	—
32	#1424	—	89	1	no	—
33	C₈₉	#7548	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
35	#368	—	178	1	no	—
36	#366	—	178	1	no	—
37	C₆₄	Dic₈₉	1	2	yes	complemented
38	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
39	#108	—	356	1	no	—
40	#107	—	356	1	no	—
41	C₃₂	Dic₁₇₈	1	1	yes	characteristic
42	C₃₂	C₂×Dic₈₉	1	1	yes	characteristic
43	M₁₆	—	712	1	no	—
44	C₂×C₈	D₇₁₂	1	1	yes	characteristic
45	C₄⋊C₄	—	712	1	no	—
46	C₁₆	C₄⋊Dic₈₉	1	1	yes	characteristic
47	C₁₆	Dic₃₅₆	1	1	yes	characteristic
48	C₂×C₄	—	1424	1	no	—
49	C₂×C₄	D₁₄₂₄	1	1	yes	characteristic
50	C₈	—	1424	1	no	—
51	C₈	#15667946	1	1	yes	characteristic
52	C₈	Dic₇₁₂	1	1	yes	characteristic
53	C₂²	#19151437	1	1	yes	characteristic
54	C₄	—	2848	1	no	—
55	C₄	#19151424	1	1	yes	characteristic
56	C₄	#19151437	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#26018454	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26018454
commutator	C₃₂×C₈₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₈₉
Fitting	C₈₉×M₁₂₈	C₂
socle	C₂×C₈₉	#1424
prime radical	C₂²×C₈₉	SD₆₄
cosocle	C₂×C₃₂×C₈₉	C₂²
hypercenter	M₁₂₈	D₈₉
hypocenter	C₈₉	#7548
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
7. C₆₄×C₈₉	C₄	semidirect
33. C₈₉	#7548	semidirect
37. C₆₄	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26018456	2
#26018454	2
C₈₉×M₁₂₈	2
#7548	89