Subgroups — #26018235

Order 11392.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151728	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#13083549	C₂	1	1	yes	maximal, characteristic
3	#346×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₁₇₈	C₄	1	1	yes	characteristic
5	C₂×#13083549	—	2	1	no	—
6	C₄⋊#10623494	C₄	1	1	yes	characteristic
7	#15667941	—	2	1	no	—
8	#15667922	—	2	1	no	—
9	C₂×C₁₆×C₈₉	—	2	1	no	—
10	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₇₈	C₈	1	1	yes	characteristic
12	C₂×#10623494	—	2	1	no	—
13	C₄⋊Dic₈₉	C₈	1	1	yes	characteristic
14	#13083553	—	2	1	no	—
15	C₄×Dic₈₉	—	2	1	no	—
16	#13083549	—	4	1	no	—
17	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
19	C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₈₉	—	2	2	no	—
21	C₂×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₈₉	M₁₆	1	1	yes	characteristic
24	C₂×Dic₈₉	—	2	1	no	—
25	C₂×Dic₈₉	—	2	1	no	—
26	Dic₁₇₈	—	4	1	no	—
27	C₈×C₈₉	—	2	1	no	—
28	C₈×C₈₉	SD₁₆	1	1	yes	characteristic
29	C₈×C₈₉	Q₁₆	1	1	yes	characteristic
30	#10623494	—	4	1	no	—
31	C₂²×C₈₉	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₈₉	—	2	1	no	—
33	C₄×C₈₉	—	2	1	no	—
34	C₄×C₈₉	#103	1	1	yes	characteristic
35	C₄×C₈₉	#104	1	1	yes	characteristic
36	Dic₈₉	—	4	1	no	—
37	Dic₈₉	—	4	1	no	—
38	C₂×C₈₉	Q₈⋊C₈	1	1	yes	characteristic
39	C₂×C₈₉	#349	1	1	yes	characteristic
40	C₂×C₈₉	#350	1	1	yes	characteristic
41	#1338	—	89	1	no	maximal, Sylow
42	C₈₉	#1338	1	1	yes	characteristic, complemented, Sylow
43	#446	—	89	1	no	—
44	C₄⋊C₁₆	—	89	1	no	—
45	#346	D₈₉	1	1	yes	characteristic
46	C₄×Q₈	—	89	1	no	—
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	178	1	no	—
49	C₄⋊C₈	—	89	1	no	—
50	C₄⋊C₈	—	178	1	no	—
51	#97	—	178	1	no	—
52	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
53	C₂×Q₈	—	89	1	no	—
54	C₂×C₈	—	178	1	no	—
55	C₂×C₈	D₃₅₆	1	1	yes	characteristic
56	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
57	C₄⋊C₄	—	89	1	no	—
58	C₄⋊C₄	—	178	1	no	—
59	C₄²	—	178	1	no	—
60	C₄²	C₄×D₈₉	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₆	—	356	1	no	—
63	Q₈	—	356	1	no	—
64	C₂×C₄	—	178	1	no	—
65	C₂×C₄	—	178	1	no	—
66	C₂×C₄	#13083551	1	1	yes	characteristic
67	C₂×C₄	C₈×D₈₉	1	1	yes	characteristic
68	C₂×C₄	#13083557	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	356	1	no	—
71	C₈	#13083563	1	1	yes	characteristic
72	C₈	Dic₃₅₆	1	1	yes	characteristic
73	C₂²	#15667924	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	356	1	no	—
77	C₄	—	356	1	no	—
78	C₄	#15667937	1	1	yes	characteristic
79	C₄	#15667940	1	1	yes	characteristic
80	C₂	#19151330	1	1	yes	characteristic
81	C₂	#19151379	1	1	yes	characteristic
82	C₂	#19151383	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13083551
commutator	C₂×C₄×C₈₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₈₉
Fitting	#346×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	C₂²⋊C₈
cosocle	C₄×C₈×C₈₉	C₂²
hypercenter	#346	D₈₉
hypocenter	C₈₉	#1338
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
42. C₈₉	#1338	semidirect

Maximal subgroups

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

subgroup	index
#19151728	2
C₄⋊#13083549	2
#346×C₈₉	2
#1338	89