Subgroups — #36469136

Order 22784.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26022480	C₂	1	4	yes	maximal
2	#26019870	C₂	1	1	yes	maximal, characteristic
3	#26019862	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1311	C₂	1	1	yes	maximal, characteristic
5	#19152003	—	2	2	no	—
6	#19152003	C₂²	1	2	yes	—
7	#19151978	C₂²	1	2	yes	—
8	#19151949	—	2	2	no	—
9	#19151403	—	2	8	no	—
10	C₄×C₁₆×C₈₉	C₂²	1	2	yes	—
11	C₈²×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₃₅₆	—	2	4	no	—
13	#15668012	—	2	2	no	—
14	#15668012	—	2	2	no	—
15	#15667946	—	2	4	no	—
16	#15667946	—	4	4	no	—
17	#15667937	—	4	4	no	—
18	C₂×C₁₆×C₈₉	D₄	1	4	yes	—
19	C₄×C₈×C₈₉	D₄	1	2	yes	—
20	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₇₈	—	4	2	no	—
22	C₂×Dic₁₇₈	—	4	2	no	—
23	Dic₃₅₆	—	4	8	no	—
24	C₄⋊Dic₈₉	—	4	2	no	—
25	C₄⋊Dic₈₉	—	4	2	no	—
26	C₄⋊Dic₈₉	—	4	4	no	—
27	C₂×C₈×C₈₉	D₈	1	4	yes	—
28	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
29	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
30	C₁₆×C₈₉	—	2	4	no	—
31	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
32	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
33	C₂×Dic₈₉	—	8	2	no	—
34	C₂×Dic₈₉	—	8	2	no	—
35	Dic₁₇₈	—	8	4	no	—
36	Dic₁₇₈	—	8	4	no	—
37	C₈×C₈₉	—	2	4	no	—
38	C₈×C₈₉	#135	1	4	yes	—
39	C₂²×C₈₉	#493	1	1	yes	characteristic
40	C₄×C₈₉	#495	1	2	yes	—
41	C₄×C₈₉	#510	1	4	yes	—
42	Dic₈₉	—	16	2	no	—
43	Dic₈₉	—	16	2	no	—
44	#12514	—	89	1	no	maximal, Sylow
45	C₂×C₈₉	#1709	1	1	yes	characteristic
46	C₂×C₈₉	#2251	1	2	yes	—
47	#2241	—	89	4	no	—
48	#1713	—	89	1	no	—
49	#1710	—	89	1	no	—
50	#1311	D₈₉	1	1	yes	characteristic
51	C₈₉	#12514	1	1	yes	characteristic, complemented, Sylow
52	#500	—	89	2	no	—
53	#500	—	178	2	no	—
54	#494	—	89	2	no	—
55	#487	—	178	2	no	—
56	#358	—	178	8	no	—
57	C₄×C₁₆	C₂×D₈₉	1	2	yes	—
58	C₈²	C₂×D₈₉	1	1	yes	characteristic
59	C₂×Q₁₆	—	178	4	no	—
60	C₄⋊Q₈	—	178	2	no	—
61	C₄⋊Q₈	—	178	2	no	—
62	C₂×C₁₆	D₃₅₆	1	4	yes	—
63	#107	—	356	4	no	—
64	#107	—	178	4	no	—
65	#103	—	356	4	no	—
66	C₄×C₈	D₃₅₆	1	2	yes	—
67	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
68	C₂×Q₈	—	356	2	no	—
69	C₂×Q₈	—	356	2	no	—
70	Q₁₆	—	356	8	no	—
71	C₂×C₈	D₇₁₂	1	4	yes	—
72	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
73	C₄⋊C₄	—	356	2	no	—
74	C₄⋊C₄	—	356	2	no	—
75	C₄⋊C₄	—	356	4	no	—
76	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
77	C₁₆	—	2	4	no	—
78	Q₈	—	712	4	no	—
79	Q₈	—	712	4	no	—
80	C₂×C₄	—	712	2	no	—
81	C₂×C₄	—	712	2	no	—
82	C₂×C₄	#15668009	1	1	yes	characteristic
83	C₂×C₄	C₂×D₇₁₂	1	2	yes	—
84	C₈	—	2	4	no	—
85	C₈	#15668034	1	4	yes	—
86	C₂²	#19151975	1	1	yes	characteristic
87	C₄	—	1424	2	no	—
88	C₄	—	1424	2	no	—
89	C₄	#19151982	1	2	yes	—
90	C₄	#19152041	1	4	yes	—
91	C₂	#26019858	1	1	yes	characteristic
92	C₂	#26022523	1	2	yes	—

	subgroup	G/H
center	C₂²	#19151975
commutator, cosocle	C₄×C₈×C₈₉	C₂³
Frattini	C₄×C₈	C₂²×D₈₉
Fitting	C₈₉×#1311	C₂
socle, prime radical	C₂²×C₈₉	#493
hypercenter	#1311	D₈₉
hypocenter	C₈₉	#12514
LCS	G ▷ C₄×C₈×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1311

Complements

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

N	H ≅ G/N	type
51. C₈₉	#12514	semidirect

Maximal subgroups

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

subgroup	index
#26022480	2
#26019870	2
#26019862	2
C₈₉×#1311	2
#12514	89