Subgroups — #26022012

Order 11392.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13083549	C₂	1	1	yes	maximal, characteristic
2	#19151553	C₂	1	1	yes	maximal, characteristic
3	#19151416	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#13083558	C₄	1	1	yes	characteristic
6	#15667971	C₄	1	1	yes	characteristic
7	C₂×#13083549	—	2	2	no	—
8	C₂×#13083549	C₂²	1	2	yes	—
9	#15667922	C₄	1	2	yes	—
10	C₈×Dic₈₉	C₂²	1	2	yes	—
11	C₂²×C₈×C₈₉	C₂²	1	1	yes	characteristic
12	M₃₂×C₈₉	—	2	2	no	—
13	C₂×C₁₆×C₈₉	C₂²	1	2	yes	—
14	#13083558	—	2	2	no	—
15	C₂×#10623494	C₂×C₄	1	2	yes	—
16	C₄⋊Dic₈₉	C₈	1	2	yes	—
17	C₂²⋊Dic₈₉	C₈	1	2	yes	—
18	C₄×Dic₈₉	C₂×C₄	1	2	yes	—
19	#13083549	—	2	2	no	—
20	C₂²×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₈₉	D₄	1	2	yes	—
23	C₂×C₈×C₈₉	Q₈	1	2	yes	—
24	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
25	C₁₆×C₈₉	—	2	2	no	—
26	C₂³×C₈₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₈₉	M₁₆	1	2	yes	—
30	C₂×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₈₉	C₂×C₈	1	4	yes	—
32	C₈×C₈₉	C₄⋊C₄	1	2	yes	—
33	C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
34	C₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
35	#10623494	—	2	2	no	—
36	C₂²×C₈₉	—	2	2	no	—
37	C₂²×C₈₉	C₄⋊C₈	1	2	yes	—
38	C₂²×C₈₉	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₈₉	C₄⋊C₈	1	2	yes	—
40	C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
42	Dic₈₉	—	2	4	no	—
43	C₂×C₈₉	—	2	2	no	—
44	C₂×C₈₉	C₂×C₄⋊C₈	1	1	yes	characteristic
45	C₂×C₈₉	#504	1	2	yes	—
46	#2151	—	89	1	no	maximal, Sylow
47	C₈₉	#2151	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₃₂	D₈₉	1	1	yes	characteristic
49	C₂²×C₁₆	—	89	1	no	—
50	#405	—	89	1	no	—
51	C₄⋊C₁₆	—	89	4	no	—
52	C₂×M₁₆	—	89	1	no	—
53	C₂²×C₈	C₂×D₈₉	1	1	yes	characteristic
54	#117	—	89	1	no	—
55	M₃₂	—	2	2	no	—
56	C₂×C₁₆	—	89	2	no	—
57	C₂×C₁₆	—	178	2	no	—
58	C₂×C₁₆	C₂×D₈₉	1	2	yes	—
59	#97	—	89	2	no	—
60	C₄×C₈	—	89	2	no	—
61	C₂²×C₄	C₄×D₈₉	1	1	yes	characteristic
62	M₁₆	—	178	2	no	—
63	C₂×C₈	—	89	2	no	—
64	C₂×C₈	Dic₁₇₈	1	2	yes	—
65	C₂×C₈	C₄×D₈₉	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₈₉	1	2	yes	—
67	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
68	C₄⋊C₄	—	89	2	no	—
69	C₂²⋊C₄	—	89	2	no	—
70	C₄²	—	89	2	no	—
71	C₁₆	—	2	2	no	—
72	C₁₆	—	178	2	no	—
73	C₂³	C₈×D₈₉	1	1	yes	characteristic
74	C₂×C₄	—	89	4	no	—
75	C₂×C₄	#13083553	1	2	yes	—
76	C₂×C₄	C₈×D₈₉	1	1	yes	characteristic
77	C₂×C₄	#13083557	1	2	yes	—
78	C₂×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
79	C₈	—	178	2	no	—
80	C₈	#13083553	1	2	yes	—
81	C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
82	C₈	C₂×Dic₁₇₈	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	#15667941	1	2	yes	—
85	C₂²	C₂×C₈×D₈₉	1	1	yes	characteristic
86	C₄	—	178	4	no	—
87	C₄	#15667941	1	2	yes	—
88	C₄	C₂×#13083553	1	1	yes	characteristic
89	C₄	C₂×#13083557	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×#15667941	1	1	yes	characteristic
92	C₂	#19152016	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₈₉
commutator, socle	C₂²×C₈₉	C₂²×C₈
Fitting	C₂×M₃₂×C₈₉	C₂
prime radical	C₂³×C₈₉	C₂×C₈
cosocle	C₂×C₈×C₈₉	C₂³
hypercenter	C₂×M₃₂	D₈₉
hypocenter	C₈₉	#2151
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #19151416	C₂	semidirect
47. C₈₉	#2151	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13083549	2
#19151553	2
#19151416	2
C₂×M₃₂×C₈₉	2
#2151	89