Subgroups — #11773073

Order 1152.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#368	C₂	1	1	yes	maximal, characteristic
2	#10588182	C₂	1	1	yes	maximal, characteristic
3	#10588176	C₂	1	1	yes	maximal, characteristic
4	#67582	—	3	1	no	maximal
5	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
6	C₉×#108	—	2	1	no	—
7	#63378	—	2	1	no	—
8	C₉⋊C₃₂	C₄	1	2	yes	complemented
9	C₃×#368	D₃	1	1	yes	characteristic
10	#4505	—	3	1	no	—
11	#4499	—	3	1	no	—
12	C₉×M₁₆	—	4	1	no	—
13	C₂×C₈×C₉	D₄	1	1	yes	characteristic
14	C₄⋊Dic₉	—	4	1	no	—
15	C₉×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₉×C₁₆	Q₈	1	1	yes	characteristic
17	#1426	—	9	1	no	Sylow
18	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic
19	C₃×#108	—	2	1	no	—
20	#818	—	6	1	no	—
21	C₃⋊C₃₂	—	3	2	no	—
22	C₂×C₄×C₉	D₈	1	1	yes	characteristic
23	C₂×Dic₉	—	8	1	no	—
24	C₈×C₉	—	8	1	no	—
25	C₈×C₉	C₄⋊C₄	1	1	yes	characteristic
26	C₈×C₉	Q₁₆	1	1	yes	characteristic
27	M₆₄	—	9	1	no	—
28	#368	D₉	1	1	yes	characteristic
29	#367	—	9	1	no	—
30	C₃×M₁₆	—	4	1	no	—
31	C₂×C₃×C₈	#67	1	1	yes	characteristic
32	C₄⋊Dic₃	—	12	1	no	—
33	C₃×C₁₆	Dic₆	1	1	yes	characteristic
34	C₃×C₁₆	C₄×D₃	1	1	yes	characteristic
35	C₂²×C₉	SD₃₂	1	1	yes	characteristic
36	C₄×C₉	#107	1	1	yes	characteristic
37	C₄×C₉	SD₃₂	1	1	yes	characteristic
38	Dic₉	—	16	1	no	—
39	C₂×C₁₆	C₂×D₉	1	1	yes	characteristic
40	#108	—	2	1	no	—
41	#107	—	18	1	no	—
42	C₃₂	—	9	2	no	—
43	C₂×C₃×C₄	#213	1	1	yes	characteristic
44	C₂×Dic₃	—	24	1	no	—
45	C₃×C₈	—	8	1	no	—
46	C₃×C₈	Dic₃⋊C₄	1	1	yes	characteristic
47	C₃×C₈	#216	1	1	yes	characteristic
48	C₂×C₉	—	2	1	no	—
49	C₂×C₉	#367	1	1	yes	characteristic
50	M₁₆	—	4	1	no	—
51	C₂×C₈	#611	1	1	yes	characteristic
52	C₄⋊C₄	—	36	1	no	—
53	C₁₆	Dic₁₈	1	1	yes	characteristic
54	C₁₆	C₄×D₉	1	1	yes	characteristic
55	C₂²×C₃	#828	1	1	yes	characteristic
56	C₃×C₄	#807	1	1	yes	characteristic
57	C₃×C₄	#827	1	1	yes	characteristic
58	Dic₃	—	48	1	no	—
59	C₉	#1426	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₄	—	72	1	no	—
61	C₂×C₄	#3673	1	1	yes	characteristic
62	C₈	—	8	1	no	—
63	C₈	Dic₉⋊C₄	1	1	yes	characteristic
64	C₈	#3674	1	1	yes	characteristic
65	C₂×C₃	—	2	1	no	—
66	C₂×C₃	#4490	1	1	yes	characteristic
67	C₂²	#63387	1	1	yes	characteristic
68	C₄	—	144	1	no	—
69	C₄	#63366	1	1	yes	characteristic
70	C₄	#63386	1	1	yes	characteristic
71	C₃	#67582	1	1	yes	characteristic
72	C₂	—	2	1	no	—
73	C₂	#10588167	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10588167
commutator	C₉×C₁₆	C₂×C₄
Frattini	C₂×C₃×C₁₆	C₂×D₃
Fitting	C₉×#368	C₂
socle	C₂×C₃	#4490
prime radical	C₂²×C₃	#828
cosocle	C₂×C₉×C₁₆	C₂²
hypercenter	#368	D₉
hypocenter	C₉	#1426
LCS	G ▷ C₉×C₁₆ ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
8. C₉⋊C₃₂	C₄	semidirect
59. C₉	#1426	semidirect

Maximal subgroups

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

subgroup	index
C₉×#368	2
#10588182	2
#10588176	2
#67582	3