Subgroups — #26018346

Order 11392.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15667948	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#13083558	—	2	2	no	—
4	#15667948	—	2	2	no	—
5	#15667948	C₄	1	4	yes	—
6	C₂²×C₈×C₈₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₈₉	—	2	2	no	—
8	C₂×C₁₆×C₈₉	C₄	1	2	yes	—
9	#13083558	—	2	4	no	—
10	#13083558	—	4	2	no	—
11	C₂×#10623494	—	4	2	no	—
12	C₂²×C₄×C₈₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₈₉	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₈₉	D₄	1	2	yes	—
16	C₂×C₈×C₈₉	Q₈	1	1	yes	characteristic
17	C₁₆×C₈₉	—	2	2	no	—
18	C₂³×C₈₉	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
22	C₂×C₄×C₈₉	SD₁₆	1	2	yes	—
23	C₈×C₈₉	C₄²	1	1	yes	characteristic
24	C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₈₉	C₄⋊C₄	1	2	yes	—
26	#10623494	—	4	4	no	—
27	C₂²×C₈₉	—	2	2	no	—
28	C₂²×C₈₉	#103	1	2	yes	—
29	C₂²×C₈₉	#107	1	1	yes	characteristic
30	C₄×C₈₉	#95	1	1	yes	characteristic
31	C₄×C₈₉	#102	1	2	yes	—
32	C₄×C₈₉	#106	1	1	yes	characteristic
33	C₂×C₈₉	—	2	2	no	—
34	C₂×C₈₉	#340	1	1	yes	characteristic
35	C₂×C₈₉	#368	1	2	yes	—
36	#1381	—	89	1	no	maximal, Sylow
37	C₈₉	#1381	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₁₆	D₈₉	1	1	yes	characteristic
39	C₂×#108	—	89	2	no	—
40	C₂×M₁₆	—	178	2	no	—
41	C₂²×C₈	C₂×D₈₉	1	1	yes	characteristic
42	C₂×C₁₆	—	2	2	no	—
43	C₂×C₁₆	Dic₈₉	1	2	yes	—
44	#108	—	89	4	no	—
45	#108	—	178	2	no	—
46	C₂²×C₄	D₃₅₆	1	1	yes	characteristic
47	M₁₆	—	356	2	no	—
48	M₁₆	—	178	4	no	—
49	C₂×C₈	—	356	2	no	—
50	C₂×C₈	Dic₁₇₈	1	1	yes	characteristic
51	C₂×C₈	C₄×D₈₉	1	2	yes	—
52	C₂×C₈	C₂×Dic₈₉	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₈₉	1	2	yes	—
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₃₅₆	1	1	yes	characteristic
56	C₂×C₄	#13083551	1	2	yes	—
57	C₂×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
58	C₂×C₄	D₇₁₂	1	1	yes	characteristic
59	C₂×C₄	#13083563	1	2	yes	—
60	C₈	—	356	4	no	—
61	C₈	C₄×Dic₈₉	1	1	yes	characteristic
62	C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
63	C₈	#13083553	1	2	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	#15667937	1	2	yes	—
66	C₂²	#15667946	1	1	yes	characteristic
67	C₄	#15667919	1	1	yes	characteristic
68	C₄	#15667934	1	2	yes	—
69	C₄	#15667944	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	#19151361	1	1	yes	characteristic
72	C₂	#19151428	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₇₁₂
commutator	C₈×C₈₉	C₄²
Frattini	C₂²×C₈	C₂×D₈₉
Fitting	C₂²×C₁₆×C₈₉	C₂
socle	C₂²×C₈₉	#107
prime radical	C₂³×C₈₉	Q₁₆
cosocle	C₂²×C₈×C₈₉	C₂²
hypercenter	C₂²×C₁₆	D₈₉
hypocenter	C₈₉	#1381
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
37. C₈₉	#1381	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15667948	2
C₂²×C₁₆×C₈₉	2
#1381	89