Subgroups — #26019923

Order 11392.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152003	C₂	1	2	yes	maximal, complemented
2	#19151978	C₂	1	1	yes	maximal, characteristic, complemented
3	#19151971	C₂	1	1	yes	maximal, characteristic
4	#19151945	C₂	1	2	yes	maximal
5	#322×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₃₅₆	—	2	2	no	—
7	C₂×#13083563	—	2	2	no	—
8	#15668012	C₂²	1	2	yes	—
9	#15668012	C₂²	1	1	yes	characteristic
10	#15668009	C₂²	1	1	yes	characteristic
11	#15667946	—	2	4	no	—
12	#15667934	—	2	4	no	—
13	C₄×C₈×C₈₉	C₂²	1	2	yes	—
14	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₇₈	—	2	1	no	—
16	C₂×Dic₁₇₈	—	2	2	no	—
17	C₂×D₃₅₆	—	2	1	no	—
18	C₂×D₃₅₆	—	2	2	no	—
19	Dic₃₅₆	—	4	4	no	—
20	#13083563	—	4	4	no	—
21	C₄⋊Dic₈₉	—	2	2	no	—
22	C₄⋊Dic₈₉	—	2	2	no	—
23	C₄⋊Dic₈₉	—	2	2	no	—
24	C₂×C₈×C₈₉	D₄	1	4	yes	—
25	C₂×C₈×C₈₉	D₄	1	2	yes	—
26	C₄²×C₈₉	C₂³	1	1	yes	characteristic
27	C₂²×D₈₉	—	4	1	no	—
28	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
30	C₂×Dic₈₉	—	4	2	no	—
31	C₂×Dic₈₉	—	4	1	no	—
32	D₃₅₆	—	4	2	no	—
33	D₃₅₆	—	4	4	no	—
34	Dic₁₇₈	—	4	2	no	—
35	Dic₁₇₈	—	4	4	no	—
36	C₈×C₈₉	—	2	4	no	—
37	C₈×C₈₉	D₈	1	4	yes	—
38	C₂²×C₈₉	#127	1	1	yes	characteristic
39	C₂×D₈₉	—	8	1	no	—
40	C₂×D₈₉	—	8	2	no	—
41	C₄×C₈₉	C₂×D₈	1	2	yes	—
42	C₄×C₈₉	#137	1	4	yes	—
43	Dic₈₉	—	8	1	no	—
44	Dic₈₉	—	8	2	no	—
45	C₂×C₈₉	#493	1	1	yes	characteristic
46	C₂×C₈₉	#497	1	2	yes	—
47	D₈₉	—	16	1	no	—
48	#1722	—	89	1	no	maximal, Sylow
49	C₈₉	#1722	1	1	yes	characteristic, complemented, Sylow
50	#500	—	89	2	no	—
51	#494	—	89	1	no	—
52	#492	—	89	1	no	—
53	#486	—	89	2	no	—
54	#322	D₈₉	1	1	yes	characteristic, complemented
55	C₂×Q₁₆	—	178	2	no	—
56	C₂×SD₁₆	—	178	2	no	—
57	C₄⋊Q₈	—	89	2	no	—
58	C₄⋊Q₈	—	89	1	no	—
59	#127	—	89	1	no	—
60	#107	—	178	4	no	—
61	#102	—	178	4	no	—
62	C₄×C₈	C₂×D₈₉	1	2	yes	—
63	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
64	C₂×Q₈	—	178	1	no	—
65	C₂×Q₈	—	178	2	no	—
66	C₂×D₄	—	178	2	no	—
67	C₂×D₄	—	178	1	no	—
68	Q₁₆	—	356	4	no	—
69	SD₁₆	—	356	4	no	—
70	C₂×C₈	D₃₅₆	1	4	yes	—
71	C₂×C₈	D₃₅₆	1	2	yes	—
72	C₄⋊C₄	—	178	2	no	—
73	C₄⋊C₄	—	178	2	no	—
74	C₄⋊C₄	—	178	2	no	—
75	C₄²	C₂²×D₈₉	1	1	yes	characteristic
76	C₂³	—	356	1	no	—
77	Q₈	—	356	2	no	—
78	Q₈	—	356	4	no	—
79	D₄	—	356	2	no	—
80	D₄	—	356	4	no	—
81	C₂×C₄	—	356	2	no	—
82	C₂×C₄	—	356	1	no	—
83	C₂×C₄	C₂×D₃₅₆	1	1	yes	characteristic
84	C₂×C₄	C₂×D₃₅₆	1	2	yes	—
85	C₈	—	2	4	no	—
86	C₈	D₇₁₂	1	4	yes	—
87	C₂²	—	712	1	no	—
88	C₂²	—	712	2	no	—
89	C₂²	#15668009	1	1	yes	characteristic
90	C₄	—	712	1	no	—
91	C₄	—	712	2	no	—
92	C₄	C₂×D₇₁₂	1	2	yes	—
93	C₄	#15668045	1	4	yes	—
94	C₂	—	1424	1	no	—
95	C₂	#19151975	1	1	yes	characteristic
96	C₂	#19151992	1	2	yes	—

	subgroup	G/H
center	C₂²	#15668009
commutator, cosocle	C₄²×C₈₉	C₂³
Frattini	C₄²	C₂²×D₈₉
Fitting	#322×C₈₉	C₂
socle	C₂²×C₈₉	#127
prime radical	#15668009	C₂²
hypercenter	#322	D₈₉
hypocenter	C₈₉	#1722
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
1. #19152003	C₂	semidirect
2. #19151978	C₂	semidirect
5. #322×C₈₉	C₂	semidirect
49. C₈₉	#1722	semidirect
54. #322	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152003	2
#19151978	2
#19151971	2
#19151945	2
#322×C₈₉	2
#1722	89