Subgroups — #11773058

Order 1152.

75 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₃₂	C₂	1	1	yes	maximal, characteristic
2	#10588183	C₂	1	2	yes	maximal
3	#67593	—	3	1	no	maximal
4	C₂×C₉×C₁₆	C₂²	1	1	yes	characteristic
5	#63372	—	2	2	no	—
6	C₉×C₃₂	C₄	1	2	yes	—
7	C₂×C₃×C₃₂	D₃	1	1	yes	characteristic
8	#4506	—	3	2	no	—
9	C₂×C₈×C₉	D₄	1	1	yes	characteristic
10	#3667	—	4	2	no	—
11	C₉×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₉×C₁₆	Q₈	1	1	yes	characteristic
13	#1425	—	9	1	no	Sylow
14	C₂×C₃×C₁₆	C₂×D₃	1	1	yes	characteristic
15	#819	—	6	2	no	—
16	C₃×C₃₂	Dic₃	1	2	yes	—
17	C₂×C₄×C₉	D₈	1	1	yes	characteristic
18	C₈×C₉	C₄⋊C₄	1	1	yes	characteristic
19	C₈×C₉	Q₁₆	1	1	yes	characteristic
20	C₉⋊C₈	—	8	2	no	—
21	C₂×C₃₂	D₉	1	1	yes	characteristic
22	#368	—	9	2	no	—
23	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
24	#208	—	12	2	no	—
25	C₃×C₁₆	Dic₆	1	1	yes	characteristic
26	C₃×C₁₆	C₂×Dic₃	1	1	yes	characteristic
27	C₂²×C₉	Q₃₂	1	1	yes	characteristic
28	C₄×C₉	#107	1	1	yes	characteristic
29	C₄×C₉	D₁₆	1	1	yes	characteristic
30	C₂×C₁₆	C₂×D₉	1	1	yes	characteristic
31	#108	—	18	2	no	—
32	C₃₂	Dic₉	1	2	yes	—
33	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
34	C₃×C₈	Dic₁₂	1	1	yes	characteristic
35	C₃×C₈	C₄⋊Dic₃	1	1	yes	characteristic
36	C₃⋊C₈	—	24	2	no	—
37	C₂×C₉	—	2	1	no	—
38	C₂×C₉	#366	1	1	yes	characteristic
39	M₁₆	—	36	2	no	—
40	C₂×C₈	D₃₆	1	1	yes	characteristic
41	C₁₆	Dic₁₈	1	1	yes	characteristic
42	C₁₆	C₂×Dic₉	1	1	yes	characteristic
43	C₂²×C₃	Dic₂₄	1	1	yes	characteristic
44	C₃×C₄	D₄₈	1	1	yes	characteristic
45	C₃×C₄	#818	1	1	yes	characteristic
46	C₉	#1425	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄	D₇₂	1	1	yes	characteristic
48	C₈	—	72	2	no	—
49	C₈	Dic₃₆	1	1	yes	characteristic
50	C₈	C₄⋊Dic₉	1	1	yes	characteristic
51	C₂×C₃	—	2	1	no	—
52	C₂×C₃	#4504	1	1	yes	characteristic
53	C₂²	Dic₇₂	1	1	yes	characteristic
54	C₄	D₁₄₄	1	1	yes	characteristic
55	C₄	#63378	1	1	yes	characteristic
56	C₃	#67593	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#10588181	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₄₄
commutator	C₉×C₁₆	C₂×C₄
Frattini	C₂×C₃×C₁₆	C₂×D₃
Fitting	C₂×C₉×C₃₂	C₂
socle	C₂×C₃	#4504
prime radical	C₂²×C₃	Dic₂₄
cosocle	C₂×C₉×C₁₆	C₂²
hypercenter	C₂×C₃₂	D₉
hypocenter	C₉	#1425
LCS	G ▷ C₉×C₁₆ ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
46. C₉	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₃₂	2
#10588183	2
#67593	3