Subgroups — #26018302

Order 11392.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151978	C₂	1	1	yes	maximal, characteristic
2	#19151351	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₅₆	—	2	1	no	—
5	C₂×Dic₃₅₆	C₄	1	2	yes	—
6	#15668012	—	2	1	no	—
7	C₄⋊#10623494	—	2	1	no	—
8	C₂×C₁₆×C₈₉	—	2	1	no	—
9	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₇₈	—	2	2	no	—
11	Dic₃₅₆	—	4	2	no	—
12	Dic₃₅₆	—	4	1	no	—
13	Dic₃₅₆	—	4	1	no	—
14	C₂×#10623494	—	4	1	no	—
15	C₄⋊Dic₈₉	—	4	1	no	—
16	C₄⋊Dic₈₉	—	4	1	no	—
17	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
19	C₄²×C₈₉	D₄	1	1	yes	characteristic
20	C₁₆×C₈₉	—	4	1	no	—
21	C₂×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
23	C₂×C₄×C₈₉	SD₁₆	1	1	yes	characteristic
24	C₂×Dic₈₉	—	4	2	no	—
25	Dic₁₇₈	—	4	2	no	—
26	Dic₁₇₈	—	4	2	no	—
27	C₈×C₈₉	—	2	1	no	—
28	C₈×C₈₉	D₈	1	1	yes	characteristic
29	C₈×C₈₉	SD₁₆	1	1	yes	characteristic
30	#10623494	—	8	1	no	—
31	C₂²×C₈₉	#102	1	1	yes	characteristic
32	C₄×C₈₉	—	2	1	no	—
33	C₄×C₈₉	#100	1	1	yes	characteristic
34	C₄×C₈₉	#102	1	1	yes	characteristic
35	C₄×C₈₉	SD₃₂	1	1	yes	characteristic
36	C₄×C₈₉	Q₃₂	1	1	yes	characteristic
37	Dic₈₉	—	8	2	no	—
38	C₂×C₈₉	#331	1	1	yes	characteristic
39	C₂×C₈₉	#358	1	1	yes	characteristic
40	C₂×C₈₉	#362	1	1	yes	characteristic
41	#1362	—	89	1	no	maximal, Sylow
42	C₈₉	#1362	1	1	yes	characteristic, complemented, Sylow
43	#494	—	89	1	no	—
44	C₄⋊C₁₆	D₈₉	1	1	yes	characteristic
45	#335	—	89	1	no	—
46	C₂×Q₁₆	—	89	2	no	—
47	C₂×Q₁₆	—	178	1	no	—
48	C₄⋊Q₈	—	178	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₄⋊C₈	—	178	1	no	—
51	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
52	C₂×Q₈	—	178	2	no	—
53	Q₁₆	—	356	2	no	—
54	Q₁₆	—	356	1	no	—
55	Q₁₆	—	356	1	no	—
56	C₂×C₈	—	356	1	no	—
57	C₂×C₈	C₄×D₈₉	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
59	C₄⋊C₄	—	356	1	no	—
60	C₄⋊C₄	—	356	1	no	—
61	C₄²	D₃₅₆	1	1	yes	characteristic
62	C₁₆	—	4	1	no	—
63	Q₈	—	356	2	no	—
64	Q₈	—	356	2	no	—
65	C₂×C₄	—	356	2	no	—
66	C₂×C₄	#13083551	1	1	yes	characteristic
67	C₂×C₄	D₇₁₂	1	1	yes	characteristic
68	C₂×C₄	#13083563	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	712	1	no	—
71	C₈	#13083559	1	1	yes	characteristic
72	C₈	#13083561	1	1	yes	characteristic
73	C₂²	#15667934	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	712	2	no	—
76	C₄	#15667928	1	1	yes	characteristic
77	C₄	#15667932	1	1	yes	characteristic
78	C₄	#15667957	1	1	yes	characteristic
79	C₄	Dic₇₁₂	1	1	yes	characteristic
80	C₂	#19151341	1	1	yes	characteristic
81	C₂	#19151403	1	1	yes	characteristic
82	C₂	#19151415	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15667934
commutator	C₂×C₈×C₈₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₈₉
Fitting	C₄⋊C₁₆×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	#102
cosocle	C₄×C₈×C₈₉	C₂²
hypercenter	C₄⋊C₁₆	D₈₉
hypocenter	C₈₉	#1362
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
42. C₈₉	#1362	semidirect

Maximal subgroups

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

subgroup	index
#19151978	2
#19151351	2
C₄⋊C₁₆×C₈₉	2
#1362	89