Subgroups — #26018549

Order 11392.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151651	C₂	1	2	yes	maximal
2	#19151320	C₂	1	2	yes	maximal, complemented
3	#19151319	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₄⋊#10623494	C₄	1	4	yes	—
7	C₂²⋊#10623494	C₄	1	4	yes	—
8	C₄×#10623494	C₂²	1	2	yes	—
9	C₄×#10623494	C₂²	1	2	yes	—
10	C₂×M₁₆×C₈₉	C₄	1	2	yes	—
11	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
12	#97×C₈₉	C₄	1	2	yes	—
13	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#10623494	C₂×C₄	1	4	yes	—
16	C₂×#10623494	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₈₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
19	M₁₆×C₈₉	—	2	4	no	—
20	C₂×C₈×C₈₉	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₈₉	C₂×C₄	1	2	yes	—
22	C₄²×C₈₉	C₂×C₄	1	2	yes	—
23	C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₈₉	C₂³	1	1	yes	characteristic
25	C₂³×C₈₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₈₉	—	2	2	no	—
27	C₂×C₄×C₈₉	—	2	4	no	—
28	C₂×C₄×C₈₉	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₈₉	C₄²	1	2	yes	—
30	C₂×C₄×C₈₉	C₂²×C₄	1	2	yes	—
31	C₂×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₈₉	—	2	2	no	—
33	C₈×C₈₉	M₁₆	1	4	yes	—
34	#10623494	—	2	4	no	—
35	#10623494	—	2	4	no	—
36	C₂²×C₈₉	—	2	1	no	—
37	C₂²×C₈₉	—	2	2	no	—
38	C₂²×C₈₉	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₈₉	—	2	1	no	—
40	C₄×C₈₉	—	2	2	no	—
41	C₄×C₈₉	C₂×M₁₆	1	2	yes	—
42	C₄×C₈₉	#131	1	4	yes	—
43	C₂×C₈₉	—	4	1	no	—
44	C₂×C₈₉	C₄×M₁₆	1	1	yes	characteristic
45	C₂×C₈₉	#405	1	2	yes	—
46	#1453	—	89	1	no	maximal, Sylow
47	C₈₉	#1453	1	1	yes	characteristic, complemented, Sylow
48	#431	—	89	2	no	—
49	C₄×M₁₆	D₈₉	1	1	yes	characteristic
50	#322	—	89	1	no	—
51	#322	—	89	2	no	—
52	C₈²	—	89	1	no	—
53	C₂×M₁₆	Dic₈₉	1	2	yes	—
54	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
55	C₄⋊C₈	—	89	4	no	—
56	C₂²⋊C₈	—	89	4	no	—
57	#97	Dic₈₉	1	2	yes	—
58	C₄×C₈	—	89	2	no	—
59	C₄×C₈	—	89	2	no	—
60	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
61	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
62	C₂²×C₄	C₄×D₈₉	1	2	yes	—
63	C₂²×C₄	C₂×Dic₈₉	1	1	yes	characteristic
64	M₁₆	—	2	4	no	—
65	C₂×C₈	—	89	4	no	—
66	C₂×C₈	—	89	4	no	—
67	C₂×C₈	C₂×Dic₈₉	1	2	yes	—
68	C₂×C₈	C₂×Dic₈₉	1	2	yes	—
69	C₄²	C₄×D₈₉	1	2	yes	—
70	C₄²	C₂×Dic₈₉	1	1	yes	characteristic
71	C₄²	C₂²×D₈₉	1	1	yes	characteristic
72	C₂³	C₄×Dic₈₉	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄×Dic₈₉	1	1	yes	characteristic
76	C₂×C₄	C₄×Dic₈₉	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₈₉	1	2	yes	—
78	C₂×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	178	4	no	—
81	C₈	—	178	4	no	—
82	C₈	#13083558	1	4	yes	—
83	C₂²	—	2	1	no	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄×Dic₈₉	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	C₂×#13083558	1	2	yes	—
89	C₄	#15668020	1	4	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₄×#13083558	1	1	yes	characteristic
92	C₂	#19151556	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₈₉
commutator, socle	C₂²×C₈₉	C₂×C₄²
Fitting	C₄×M₁₆×C₈₉	C₂
prime radical	C₂³×C₈₉	C₄²
cosocle	C₄²×C₈₉	C₂³
hypercenter	C₄×M₁₆	D₈₉
hypocenter	C₈₉	#1453
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #19151320	C₂	semidirect
3. #19151319	C₂	semidirect
4. C₈×#10623494	C₂	semidirect
47. C₈₉	#1453	semidirect

Maximal subgroups

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

subgroup	index
#19151651	2
#19151320	2
#19151319	2
C₈×#10623494	2
C₄×M₁₆×C₈₉	2
#1453	89