Subgroups — #26018431

Order 11392.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₄₂₄	C₂	1	1	yes	maximal, characteristic
2	#19151424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₇₁₂	—	2	1	no	—
5	D₁₄₂₄	—	2	1	no	—
6	D₁₄₂₄	C₄	1	2	yes	complemented
7	#15667946	—	2	1	no	—
8	C₂×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
9	C₃₂×C₈₉	—	2	1	no	—
10	C₂×D₃₅₆	—	4	1	no	—
11	D₇₁₂	—	2	2	no	—
12	D₇₁₂	—	4	1	no	—
13	C₄⋊Dic₈₉	—	4	1	no	—
14	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
15	C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₈₉	D₄	1	1	yes	characteristic
17	C₂²×D₈₉	—	8	1	no	—
18	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
19	C₂×Dic₈₉	—	8	1	no	—
20	D₃₅₆	—	4	2	no	—
21	D₃₅₆	—	8	1	no	—
22	C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₈₉	SD₁₆	1	1	yes	characteristic
24	C₂²×C₈₉	D₁₆	1	1	yes	characteristic
25	C₂×D₈₉	—	8	2	no	—
26	C₂×D₈₉	—	16	1	no	—
27	C₂×D₈₉	—	16	1	no	—
28	C₄×C₈₉	#102	1	1	yes	characteristic
29	C₄×C₈₉	SD₃₂	1	1	yes	characteristic
30	Dic₈₉	—	16	1	no	—
31	C₂×C₈₉	#357	1	1	yes	characteristic
32	C₂×C₈₉	D₃₂	1	1	yes	characteristic
33	C₂×C₈₉	SD₆₄	1	1	yes	characteristic
34	D₈₉	—	16	2	no	—
35	#1415	—	89	1	no	maximal, Sylow
36	C₈₉	#1415	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₁₆	—	89	1	no	—
38	C₂×C₃₂	D₈₉	1	1	yes	characteristic, complemented
39	#366	—	89	1	no	—
40	C₂×D₈	—	178	1	no	—
41	D₁₆	—	89	2	no	—
42	D₁₆	—	178	1	no	—
43	C₂×C₁₆	C₂×D₈₉	1	1	yes	characteristic
44	#107	—	178	1	no	—
45	C₃₂	—	2	1	no	—
46	C₂×D₄	—	356	1	no	—
47	D₈	—	356	1	no	—
48	D₈	—	178	2	no	—
49	C₂×C₈	D₃₅₆	1	1	yes	characteristic
50	C₄⋊C₄	—	356	1	no	—
51	C₁₆	C₄×D₈₉	1	1	yes	characteristic
52	C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
53	C₂³	—	712	1	no	—
54	D₄	—	356	2	no	—
55	D₄	—	712	1	no	—
56	C₂×C₄	—	712	1	no	—
57	C₂×C₄	D₇₁₂	1	1	yes	characteristic
58	C₈	#13083551	1	1	yes	characteristic
59	C₈	#13083563	1	1	yes	characteristic
60	C₂²	—	1424	1	no	—
61	C₂²	—	1424	1	no	—
62	C₂²	—	712	2	no	—
63	C₂²	D₁₄₂₄	1	1	yes	characteristic
64	C₄	—	1424	1	no	—
65	C₄	#15667934	1	1	yes	characteristic
66	C₄	#15667957	1	1	yes	characteristic
67	C₂	—	1424	2	no	—
68	C₂	#19151400	1	1	yes	characteristic
69	C₂	D₂₈₄₈	1	1	yes	characteristic
70	C₂	#19151437	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₄₂₄
commutator	C₁₆×C₈₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₉
Fitting	C₂×C₃₂×C₈₉	C₂
socle	C₂²×C₈₉	D₁₆
prime radical	C₂×D₁₄₂₄	C₂
cosocle	C₂×C₁₆×C₈₉	C₂²
hypercenter	C₂×C₃₂	D₈₉
hypocenter	C₈₉	#1415
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #19151424	C₂	semidirect
3. C₂×C₃₂×C₈₉	C₂	semidirect
6. D₁₄₂₄	C₄	semidirect
36. C₈₉	#1415	semidirect
38. C₂×C₃₂	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₄₂₄	2
#19151424	2
C₂×C₃₂×C₈₉	2
#1415	89