Subgroups — #36442089

Order 22784.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26022534	C₂	1	1	yes	maximal, characteristic
2	#26018450	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1373	C₂	1	1	yes	maximal, characteristic
4	#19152003	—	2	1	no	—
5	#19151432	—	2	1	no	—
6	#19151426	—	2	1	no	—
7	#19151426	C₄	1	2	yes	—
8	#364×C₈₉	—	2	1	no	—
9	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	#15668012	—	4	1	no	—
11	#15667946	—	2	2	no	—
12	#15667946	—	4	1	no	—
13	#15667918	—	4	1	no	—
14	M₃₂×C₈₉	—	4	1	no	—
15	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
17	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
18	C₂×Dic₁₇₈	—	8	1	no	—
19	C₄⋊Dic₈₉	—	4	2	no	—
20	C₄⋊Dic₈₉	—	8	1	no	—
21	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
23	C₄²×C₈₉	SD₁₆	1	1	yes	characteristic
24	C₁₆×C₈₉	—	2	1	no	—
25	C₁₆×C₈₉	—	8	1	no	—
26	C₁₆×C₈₉	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₈₉	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₈₉	—	2	1	no	—
29	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
30	C₂×Dic₈₉	—	8	2	no	—
31	Dic₁₇₈	—	16	2	no	—
32	C₈×C₈₉	#101	1	1	yes	characteristic
33	C₈×C₈₉	#103	1	1	yes	characteristic
34	C₈×C₈₉	SD₃₂	1	1	yes	characteristic
35	C₈×C₈₉	Q₃₂	1	1	yes	characteristic
36	C₂²×C₈₉	#361	1	1	yes	characteristic
37	C₄×C₈₉	—	2	2	no	—
38	C₄×C₈₉	#332	1	1	yes	characteristic
39	C₄×C₈₉	#358	1	1	yes	characteristic
40	Dic₈₉	—	16	2	no	—
41	#7453	—	89	1	no	maximal, Sylow
42	C₂×C₈₉	—	2	1	no	—
43	C₂×C₈₉	#1365	1	1	yes	characteristic
44	#2254	—	89	1	no	—
45	#1422	—	89	1	no	—
46	#1373	D₈₉	1	1	yes	characteristic
47	C₈₉	#7453	1	1	yes	characteristic, complemented, Sylow
48	#500	—	178	1	no	—
49	M₆₄	—	178	1	no	—
50	#367	—	89	2	no	—
51	#367	—	178	1	no	—
52	#364	—	2	1	no	—
53	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
54	C₄⋊Q₈	—	356	1	no	—
55	M₃₂	—	4	1	no	—
56	C₂×C₁₆	C₄×D₈₉	1	1	yes	characteristic
57	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
58	#107	—	356	1	no	—
59	#107	—	178	2	no	—
60	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
61	C₃₂	—	356	1	no	—
62	C₂×Q₈	—	712	1	no	—
63	C₂×C₈	#13083551	1	1	yes	characteristic
64	C₂×C₈	#13083559	1	1	yes	characteristic
65	C₄⋊C₄	—	356	2	no	—
66	C₄⋊C₄	—	712	1	no	—
67	C₄²	#13083561	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	8	1	no	—
70	C₁₆	#13083563	1	1	yes	characteristic
71	C₁₆	Dic₃₅₆	1	1	yes	characteristic
72	Q₈	—	1424	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	712	2	no	—
75	C₂×C₄	#15667932	1	1	yes	characteristic
76	C₈	#15667930	1	1	yes	characteristic
77	C₈	#15667937	1	1	yes	characteristic
78	C₈	#15667956	1	1	yes	characteristic
79	C₈	#15667958	1	1	yes	characteristic
80	C₂²	#19151410	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	1424	2	no	—
83	C₄	#19151345	1	1	yes	characteristic
84	C₄	#19151401	1	1	yes	characteristic
85	C₂	—	2	1	no	—
86	C₂	#26018311	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26018311
commutator	C₂×C₁₆×C₈₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₈₉
Fitting	C₈₉×#1373	C₂
socle	C₂×C₈₉	#1365
prime radical	C₂²×C₈₉	#361
cosocle	C₄×C₁₆×C₈₉	C₂²
hypercenter	#1373	D₈₉
hypocenter	C₈₉	#7453
LCS	G ▷ C₂×C₁₆×C₈₉ ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

Complements

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

N	H ≅ G/N	type
47. C₈₉	#7453	semidirect

Maximal subgroups

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

subgroup	index
#26022534	2
#26018450	2
C₈₉×#1373	2
#7453	89