Subgroups — #26019864

Order 11392.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151949	C₂	1	3	yes	maximal, complemented
2	#19151945	C₂	1	3	yes	maximal
3	C₈²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#15668012	C₂²	1	3	yes	—
5	#15668009	C₂²	1	1	yes	characteristic
6	#15667937	—	2	6	no	—
7	#15667934	—	2	6	no	—
8	C₄×C₈×C₈₉	C₂²	1	3	yes	—
9	C₂×Dic₁₇₈	—	2	3	no	—
10	C₂×D₃₅₆	—	2	3	no	—
11	C₄⋊Dic₈₉	—	2	3	no	—
12	C₄⋊Dic₈₉	—	2	3	no	—
13	C₂×C₈×C₈₉	D₄	1	6	yes	—
14	C₄²×C₈₉	C₂³	1	1	yes	characteristic
15	C₂²×D₈₉	—	4	1	no	—
16	C₂×C₄×C₈₉	C₂×D₄	1	3	yes	—
17	C₂×Dic₈₉	—	4	3	no	—
18	D₃₅₆	—	4	6	no	—
19	Dic₁₇₈	—	4	6	no	—
20	C₈×C₈₉	—	2	6	no	—
21	C₂²×C₈₉	#127	1	1	yes	characteristic
22	C₂×D₈₉	—	8	3	no	—
23	C₄×C₈₉	#135	1	6	yes	—
24	Dic₈₉	—	8	3	no	—
25	C₂×C₈₉	#495	1	3	yes	—
26	D₈₉	—	16	1	no	—
27	#1711	—	89	1	no	maximal, Sylow
28	C₈₉	#1711	1	1	yes	characteristic, complemented, Sylow
29	#487	—	89	3	no	—
30	#486	—	89	3	no	—
31	C₈²	D₈₉	1	1	yes	characteristic, complemented
32	C₄⋊Q₈	—	89	3	no	—
33	#127	—	89	1	no	—
34	#103	—	178	6	no	—
35	#102	—	178	6	no	—
36	C₄×C₈	C₂×D₈₉	1	3	yes	—
37	C₂×Q₈	—	178	3	no	—
38	C₂×D₄	—	178	3	no	—
39	C₂×C₈	D₃₅₆	1	6	yes	—
40	C₄⋊C₄	—	178	3	no	—
41	C₄⋊C₄	—	178	3	no	—
42	C₄²	C₂²×D₈₉	1	1	yes	characteristic
43	C₂³	—	356	1	no	—
44	Q₈	—	356	6	no	—
45	D₄	—	356	6	no	—
46	C₂×C₄	—	356	3	no	—
47	C₂×C₄	C₂×D₃₅₆	1	3	yes	—
48	C₈	—	2	6	no	—
49	C₂²	—	712	3	no	—
50	C₂²	#15668009	1	1	yes	characteristic
51	C₄	—	712	3	no	—
52	C₄	#15668034	1	6	yes	—
53	C₂	—	1424	1	no	—
54	C₂	#19151982	1	3	yes	—

	subgroup	G/H
center	C₂²	#15668009
commutator, cosocle	C₄²×C₈₉	C₂³
Frattini	C₄²	C₂²×D₈₉
Fitting	C₈²×C₈₉	C₂
socle	C₂²×C₈₉	#127
prime radical	#15668009	C₂²
hypercenter	C₈²	D₈₉
hypocenter	C₈₉	#1711
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #19151949	C₂	semidirect
3. C₈²×C₈₉	C₂	semidirect
28. C₈₉	#1711	semidirect
31. C₈²	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151949	2
#19151945	2
C₈²×C₈₉	2
#1711	89