Subgroups — #26021357

Order 11392.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152398	C₂	1	3	yes	maximal, complemented
2	#19151566	C₂	1	3	yes	maximal, complemented
3	#338×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13083574	C₂²	1	3	yes	—
5	#15668045	—	2	6	no	—
6	#15668040	—	2	6	no	—
7	#15668034	—	2	6	no	—
8	C₂²×#10623494	C₂²	1	1	yes	characteristic
9	#15667924	—	2	6	no	—
10	C₂×M₁₆×C₈₉	C₂²	1	3	yes	—
11	#13083574	—	2	6	no	—
12	#13083574	—	2	6	no	—
13	C₂×Dic₁₇₈	D₄	1	3	yes	—
14	C₂×D₃₅₆	D₄	1	3	yes	—
15	C₂×C₂²⋊D₈₉	—	2	3	no	—
16	C₂×C₄×D₈₉	—	2	3	no	—
17	Dic₃₅₆	—	2	6	no	—
18	#13083563	—	2	12	no	—
19	D₇₁₂	—	2	6	no	—
20	C₂×#10623494	—	2	3	no	—
21	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₈₉	—	2	6	no	—
23	C₂×C₈×C₈₉	D₄	1	6	yes	—
24	C₂³×C₈₉	#41	1	1	yes	characteristic
25	C₂²×D₈₉	—	2	3	no	—
26	C₂×C₄×C₈₉	C₂×D₄	1	3	yes	—
27	C₂×C₄×C₈₉	C₂×D₄	1	3	yes	—
28	C₂²⋊D₈₉	—	4	6	no	—
29	C₂×Dic₈₉	—	2	3	no	—
30	D₃₅₆	—	2	6	no	—
31	C₄×D₈₉	—	4	3	no	—
32	C₄×D₈₉	—	4	3	no	—
33	Dic₁₇₈	—	2	6	no	—
34	C₈×C₈₉	—	2	6	no	—
35	#10623494	—	4	1	no	—
36	C₂²×C₈₉	—	4	1	no	—
37	C₂²×C₈₉	#121	1	3	yes	—
38	C₂×D₈₉	—	4	6	no	—
39	C₂×D₈₉	—	4	3	no	—
40	C₄×C₈₉	#120	1	3	yes	—
41	C₄×C₈₉	#127	1	1	yes	characteristic
42	Dic₈₉	—	4	3	no	—
43	C₂×C₈₉	—	2	3	no	—
44	C₂×C₈₉	#392	1	1	yes	characteristic
45	D₈₉	—	8	3	no	—
46	#2017	—	89	1	no	maximal, Sylow
47	C₈₉	#2017	1	1	yes	characteristic, complemented, Sylow
48	#575	—	89	3	no	—
49	#408	—	89	3	no	—
50	#338	D₈₉	1	1	yes	characteristic, complemented
51	C₂×#41	—	89	3	no	—
52	#137	—	178	6	no	—
53	AGL(1,ℤ/8)	—	178	6	no	—
54	#135	—	178	6	no	—
55	C₂×M₁₆	C₂×D₈₉	1	3	yes	—
56	C₂²×C₈	—	89	1	no	—
57	C₂²⋊C₈	—	178	6	no	—
58	#41	—	178	6	no	—
59	#41	—	178	6	no	—
60	C₂×Q₈	—	89	3	no	—
61	C₂×D₄	—	89	3	no	—
62	C₂×D₄	—	178	3	no	—
63	C₂²×C₄	—	178	3	no	—
64	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
65	Q₁₆	—	178	6	no	—
66	SD₁₆	—	178	12	no	—
67	D₈	—	178	6	no	—
68	M₁₆	—	2	6	no	—
69	C₂×C₈	—	178	3	no	—
70	C₂×C₈	D₃₅₆	1	6	yes	—
71	C₂³	—	178	3	no	—
72	C₂³	#13083575	1	1	yes	characteristic
73	Q₈	—	178	6	no	—
74	D₄	—	356	6	no	—
75	D₄	—	178	6	no	—
76	C₂×C₄	—	356	3	no	—
77	C₂×C₄	—	356	3	no	—
78	C₂×C₄	—	178	3	no	—
79	C₂×C₄	D₄×D₈₉	1	3	yes	—
80	C₂×C₄	C₂×D₃₅₆	1	3	yes	—
81	C₈	—	2	6	no	—
82	C₈	—	356	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	356	6	no	—
85	C₂²	—	356	3	no	—
86	C₂²	#15667987	1	3	yes	—
87	C₄	—	356	3	no	—
88	C₄	#15667982	1	3	yes	—
89	C₄	#15668009	1	1	yes	characteristic
90	C₂	—	2	3	no	—
91	C₂	—	712	3	no	—
92	C₂	#19151508	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15668009
commutator, cosocle	C₂²×C₄×C₈₉	C₂³
Frattini	C₂²×C₄	C₂²×D₈₉
Fitting	#338×C₈₉	C₂
socle	C₂×C₈₉	#392
hypercenter	#338	D₈₉
hypocenter	C₈₉	#2017
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #19152398	C₂	semidirect
2. #19151566	C₂	semidirect
3. #338×C₈₉	C₂	semidirect
47. C₈₉	#2017	semidirect
50. #338	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152398	2
#19151566	2
#338×C₈₉	2
#2017	89