Subgroups — #26018435

Order 11392.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152030	C₂	1	1	yes	maximal, characteristic
2	C₂×#15667918	C₂	1	1	yes	maximal, characteristic, complemented
3	#368×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#15668034	—	2	1	no	—
5	Dic₇₁₂	C₄	1	1	yes	characteristic
6	#15667957	—	2	1	no	—
7	D₁₄₂₄	C₄	1	1	yes	characteristic
8	#15667918	—	2	1	no	—
9	C₂×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	#108×C₈₉	—	2	1	no	—
11	#13083574	—	4	1	no	—
12	Dic₃₅₆	—	2	1	no	—
13	#13083563	—	4	1	no	—
14	D₇₁₂	—	2	1	no	—
15	M₁₆×C₈₉	—	4	1	no	—
16	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
17	C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₈₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
20	C₂²⋊D₈₉	—	8	1	no	—
21	D₃₅₆	—	4	1	no	—
22	C₄×D₈₉	—	8	1	no	—
23	Dic₁₇₈	—	4	1	no	—
24	C₈×C₈₉	—	8	1	no	—
25	C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₈₉	SD₁₆	1	1	yes	characteristic
27	C₂²×C₈₉	SD₃₂	1	1	yes	characteristic
28	C₂×D₈₉	—	8	1	no	—
29	C₄×C₈₉	#102	1	1	yes	characteristic
30	C₄×C₈₉	D₁₆	1	1	yes	characteristic
31	Dic₈₉	—	8	1	no	—
32	C₂×C₈₉	—	2	1	no	—
33	C₂×C₈₉	#357	1	1	yes	characteristic
34	D₈₉	—	16	1	no	—
35	#1417	—	89	1	no	maximal, Sylow
36	C₈₉	#1417	1	1	yes	characteristic, complemented, Sylow
37	#508	—	89	1	no	—
38	C₂×C₃₂	—	89	1	no	—
39	#368	D₈₉	1	1	yes	characteristic, complemented
40	#135	—	178	1	no	—
41	Q₃₂	—	89	1	no	—
42	SD₃₂	—	178	1	no	—
43	D₁₆	—	89	1	no	—
44	C₂×C₁₆	C₂×D₈₉	1	1	yes	characteristic
45	#108	—	2	1	no	—
46	C₃₂	—	178	1	no	—
47	#41	—	356	1	no	—
48	Q₁₆	—	178	1	no	—
49	SD₁₆	—	356	1	no	—
50	D₈	—	178	1	no	—
51	M₁₆	—	4	1	no	—
52	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
53	C₁₆	C₄×D₈₉	1	1	yes	characteristic
54	C₁₆	D₃₅₆	1	1	yes	characteristic
55	Q₈	—	356	1	no	—
56	D₄	—	356	1	no	—
57	D₄	—	712	1	no	—
58	C₂×C₄	—	712	1	no	—
59	C₂×C₄	#13083559	1	1	yes	characteristic
60	C₈	—	8	1	no	—
61	C₈	#13083551	1	1	yes	characteristic
62	C₈	#13083561	1	1	yes	characteristic
63	C₂²	—	712	1	no	—
64	C₂²	#15667955	1	1	yes	characteristic
65	C₄	—	712	1	no	—
66	C₄	#15667932	1	1	yes	characteristic
67	C₄	#15667953	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	1424	1	no	—
70	C₂	#19151398	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15667953
commutator	C₁₆×C₈₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₉
Fitting	#368×C₈₉	C₂
socle	C₂×C₈₉	#357
prime radical	#19152030	C₂
cosocle	C₂×C₁₆×C₈₉	C₂²
hypercenter	#368	D₈₉
hypocenter	C₈₉	#1417
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
2. C₂×#15667918	C₂	semidirect
3. #368×C₈₉	C₂	semidirect
36. C₈₉	#1417	semidirect
39. #368	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152030	2
C₂×#15667918	2
#368×C₈₉	2
#1417	89