Subgroups — #26018537

Order 11392.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151649	C₂	1	2	yes	maximal
2	C₄×C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#19151319	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#10623494	C₂	1	2	yes	maximal, complemented
5	#322×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₈₉	C₄	1	2	yes	—
7	C₄²×D₈₉	C₂²	1	1	yes	characteristic
8	#15667941	C₄	1	4	yes	—
9	#15667924	C₄	1	4	yes	—
10	C₄×#10623494	C₂²	1	2	yes	—
11	C₄×#10623494	C₂²	1	1	yes	characteristic
12	C₈×Dic₈₉	C₄	1	2	yes	—
13	C₄×C₈×C₈₉	C₂²	1	2	yes	—
14	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₈₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
17	C₂×#10623494	C₂×C₄	1	4	yes	—
18	C₂×#10623494	C₂×C₄	1	2	yes	—
19	C₈×D₈₉	C₈	1	8	yes	complemented
20	C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₈₉	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₈₉	C₂×C₄	1	4	yes	—
23	C₂×C₈×C₈₉	C₂×C₄	1	2	yes	—
24	C₄²×C₈₉	C₂³	1	1	yes	characteristic
25	C₂²×D₈₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₈₉	C₂²×C₄	1	2	yes	—
28	C₂×Dic₈₉	C₄²	1	2	yes	—
29	C₂×Dic₈₉	C₄²	1	1	yes	characteristic
30	C₄×D₈₉	—	2	4	no	—
31	C₄×D₈₉	C₂×C₈	1	4	yes	—
32	C₈×C₈₉	—	2	4	no	—
33	C₈×C₈₉	C₂×C₈	1	4	yes	—
34	#10623494	—	2	4	no	—
35	#10623494	C₂×C₈	1	4	yes	—
36	C₂²×C₈₉	C₂×C₄²	1	1	yes	characteristic
37	C₂×D₈₉	—	2	2	no	—
38	C₂×D₈₉	C₄×C₈	1	2	yes	—
39	C₄×C₈₉	C₂²×C₈	1	2	yes	—
40	C₄×C₈₉	#131	1	4	yes	—
41	Dic₈₉	—	2	2	no	—
42	Dic₈₉	C₄×C₈	1	2	yes	—
43	C₂×C₈₉	C₂×C₄×C₈	1	1	yes	characteristic
44	C₂×C₈₉	#405	1	2	yes	—
45	D₈₉	—	2	2	no	—
46	#1450	—	89	1	no	maximal, Sylow
47	C₈₉	#1450	1	1	yes	characteristic, complemented, Sylow
48	#431	—	89	2	no	—
49	C₂×C₄×C₈	—	89	1	no	—
50	#322	—	89	1	no	—
51	#322	D₈₉	1	1	yes	characteristic, complemented
52	C₈²	—	89	2	no	—
53	C₂²×C₈	—	89	2	no	—
54	C₂×C₄²	—	89	1	no	—
55	C₄⋊C₈	—	89	4	no	—
56	C₂²⋊C₈	—	89	4	no	—
57	C₄×C₈	—	89	2	no	—
58	C₄×C₈	—	89	1	no	—
59	C₄×C₈	—	89	2	no	—
60	C₄×C₈	C₂×D₈₉	1	2	yes	—
61	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
62	C₂²×C₄	—	89	1	no	—
63	C₂²×C₄	—	89	2	no	—
64	C₂×C₈	—	89	2	no	—
65	C₂×C₈	—	89	8	no	—
66	C₂×C₈	—	89	4	no	—
67	C₂×C₈	C₄×D₈₉	1	4	yes	—
68	C₂×C₈	C₄×D₈₉	1	2	yes	—
69	C₄²	—	89	1	no	—
70	C₄²	—	89	2	no	—
71	C₄²	C₂²×D₈₉	1	1	yes	characteristic
72	C₂³	—	89	1	no	—
73	C₂×C₄	—	89	1	no	—
74	C₂×C₄	—	89	4	no	—
75	C₂×C₄	—	89	2	no	—
76	C₂×C₄	—	178	4	no	—
77	C₂×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
78	C₂×C₄	C₂×C₄×D₈₉	1	2	yes	—
79	C₈	—	2	4	no	—
80	C₈	—	89	4	no	—
81	C₈	—	178	4	no	—
82	C₈	C₈×D₈₉	1	4	yes	—
83	C₂²	—	89	2	no	—
84	C₂²	—	178	2	no	—
85	C₂²	C₄²×D₈₉	1	1	yes	characteristic
86	C₄	—	89	2	no	—
87	C₄	—	178	2	no	—
88	C₄	C₂×C₈×D₈₉	1	2	yes	—
89	C₄	#15668020	1	4	yes	—
90	C₂	—	178	2	no	—
91	C₂	C₄×C₈×D₈₉	1	1	yes	characteristic
92	C₂	#19151555	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₈₉
commutator	C₂×C₈₉	C₂×C₄×C₈
Fitting	#322×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄²
prime radical	C₂²×D₈₉	C₄²
cosocle	C₄²×C₈₉	C₂³
hypercenter	#322	D₈₉
hypocenter	C₈₉	#1450
LCS	G ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
3. #19151319	C₂	semidirect
4. C₈×#10623494	C₂	semidirect
5. #322×C₈₉	C₂	semidirect
19. C₈×D₈₉	C₈	semidirect
47. C₈₉	#1450	semidirect
51. #322	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151649	2
C₄×C₈×D₈₉	2
#19151319	2
C₈×#10623494	2
#322×C₈₉	2
#1450	89