Subgroups — #11773669

Order 1152.

267 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10588367	C₂	1	3	yes	maximal
2	C₈²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#10588131	C₂	1	3	yes	maximal, complemented
4	#68049	—	3	1	no	maximal
5	C₄²×D₉	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₉	C₂²	1	3	yes	—
7	(C₂×D₉)⋊C₈	C₄	1	6	yes	—
8	Dic₉⋊C₈	C₄	1	6	yes	—
9	C₄×C₉⋊C₈	C₂²	1	3	yes	—
10	#4685	—	3	3	no	—
11	C₃×C₈²	D₃	1	1	yes	characteristic
12	#4454	—	3	3	no	—
13	C₂×C₄×D₉	C₂×C₄	1	3	yes	—
14	C₂×C₈×C₉	C₂×C₄	1	6	yes	—
15	C₄²×C₉	C₂³	1	1	yes	characteristic
16	C₄×Dic₉	C₂×C₄	1	3	yes	—
17	C₂×C₉⋊C₈	C₂×C₄	1	6	yes	—
18	#1454	—	9	1	no	Sylow
19	C₄²×D₃	—	3	1	no	—
20	C₃×C₄×C₈	C₂×D₃	1	3	yes	—
21	(C₂×D₃)⋊C₈	—	3	6	no	—
22	Dic₃⋊C₈	—	3	6	no	—
23	C₄×C₃⋊C₈	—	3	3	no	—
24	C₂²×D₉	C₄²	1	1	yes	characteristic
25	C₂×C₄×C₉	C₂²×C₄	1	3	yes	—
26	C₂×Dic₉	C₄²	1	3	yes	—
27	C₄×D₉	—	2	6	no	—
28	C₈×C₉	—	2	6	no	—
29	C₉⋊C₈	—	2	6	no	—
30	#431	—	9	3	no	—
31	#322	—	9	3	no	—
32	C₈²	D₉	1	1	yes	characteristic, complemented
33	C₂×C₄×D₃	—	3	3	no	—
34	C₂×C₃×C₈	C₄×D₃	1	6	yes	—
35	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
36	C₄×Dic₃	—	3	3	no	—
37	C₂×C₃⋊C₈	—	3	6	no	—
38	C₂²×C₉	C₂×C₄²	1	1	yes	characteristic
39	C₂×D₉	—	2	3	no	—
40	C₄×C₉	#131	1	6	yes	—
41	Dic₉	—	2	3	no	—
42	C₂×C₄²	—	9	1	no	—
43	C₄⋊C₈	—	9	6	no	—
44	C₂²⋊C₈	—	9	6	no	—
45	C₄×C₈	—	9	3	no	—
46	C₄×C₈	C₂×D₉	1	3	yes	—
47	C₂²×D₃	—	3	1	no	—
48	C₂×C₃×C₄	C₂×C₄×D₃	1	3	yes	—
49	C₂×Dic₃	—	3	3	no	—
50	C₄×D₃	—	6	6	no	—
51	C₃×C₈	—	2	6	no	—
52	C₃⋊C₈	—	6	6	no	—
53	C₂×C₉	#405	1	3	yes	—
54	D₉	—	4	1	no	—
55	C₂²×C₄	—	9	3	no	—
56	C₂×C₈	—	9	6	no	—
57	C₂×C₈	C₄×D₉	1	6	yes	—
58	C₄²	—	9	3	no	—
59	C₄²	C₂²×D₉	1	1	yes	characteristic
60	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
61	C₂×D₃	—	6	3	no	—
62	C₃×C₄	#901	1	6	yes	—
63	Dic₃	—	6	3	no	—
64	C₉	#1454	1	1	yes	characteristic, complemented, Sylow
65	C₂³	—	9	1	no	—
66	C₂×C₄	—	9	3	no	—
67	C₂×C₄	—	18	6	no	—
68	C₂×C₄	C₂×C₄×D₉	1	3	yes	—
69	C₈	—	2	6	no	—
70	C₈	—	18	6	no	—
71	C₂×C₃	#4689	1	3	yes	—
72	D₃	—	12	1	no	—
73	C₂²	—	18	3	no	—
74	C₂²	C₄²×D₉	1	1	yes	characteristic
75	C₄	—	18	3	no	—
76	C₄	#63464	1	6	yes	—
77	C₃	#68049	1	1	yes	characteristic
78	C₂	—	36	1	no	—
79	C₂	#10588371	1	3	yes	—

	subgroup	G/H
center	C₄²	C₂²×D₉
commutator	C₂²×C₉	C₂×C₄²
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₈²×C₉	C₂
socle	C₂²×C₃	C₄²×D₃
prime radical	C₂²×D₉	C₄²
cosocle	C₄²×C₉	C₂³
hypercenter	C₈²	D₉
hypocenter	C₉	#1454
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. C₈²×C₉	C₂	semidirect
3. #10588131	C₂	semidirect
32. C₈²	D₉	semidirect
64. C₉	#1454	semidirect

Maximal subgroups

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

subgroup	index
#10588367	2
C₈²×C₉	2
#10588131	2
#68049	3