Subgroups — #11772199

Order 1152.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10593256	C₂	1	2	yes	maximal
2	#10590135	C₂	1	1	yes	maximal, characteristic
3	#64214	—	2	2	no	—
4	C₈×#157	C₂²	1	1	yes	characteristic
5	#63764	C₄	1	1	yes	characteristic
6	C₁₆×C₃⋊D₃	C₄	1	1	yes	characteristic
7	C₄×#157	Q₈	1	1	yes	characteristic
8	#3787	D₄	1	1	yes	characteristic
9	#3771	—	4	2	no	—
10	C₈×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
11	#3708	—	2	1	no	—
12	C₃²×C₁₆	C₈	1	1	yes	characteristic
13	C₃⋊(C₃⋊C₁₆)	C₈	1	1	yes	characteristic
14	#1369	—	9	1	no	maximal, Sylow
15	D₃×C₁₆	—	12	1	no	—
16	C₂×#157	—	2	1	no	—
17	C₄×C₃⋊D₃	C₄⋊C₄	1	1	yes	characteristic
18	#622	SD₁₆	1	2	yes	—
19	C₃²×C₈	C₂×C₈	1	1	yes	characteristic
20	C₃⋊(C₃⋊C₈)	M₁₆	1	1	yes	characteristic
21	#364	—	9	2	no	—
22	#346	—	9	1	no	—
23	D₃×C₈	—	12	1	no	—
24	C₃×C₁₆	—	4	1	no	—
25	C₃⋊C₁₆	—	12	1	no	—
26	C₂×C₃⋊D₃	#108	1	1	yes	characteristic
27	#157	—	4	1	no	—
28	C₃²×C₄	C₄⋊C₈	1	1	yes	characteristic
29	C₃⋊Dic₃	#106	1	1	yes	characteristic
30	M₃₂	—	18	2	no	—
31	C₂×C₁₆	—	9	1	no	—
32	C₂×C₁₆	—	9	1	no	—
33	C₄×C₈	—	9	1	no	—
34	C₄×D₃	—	12	1	no	—
35	C₃×C₈	—	4	1	no	—
36	C₃⋊C₈	—	12	1	no	—
37	C₂×C₃²	#334	1	1	yes	characteristic
38	C₃⋊D₃	—	2	1	no	—
39	C₂×C₈	—	9	1	no	—
40	C₂×C₈	—	9	1	no	—
41	C₄²	—	9	1	no	—
42	C₁₆	—	9	1	no	—
43	C₁₆	—	18	1	no	—
44	C₁₆	—	36	2	no	—
45	C₁₆	AGL(1,𝔽₉)	1	1	yes	characteristic
46	C₂×D₃	—	12	1	no	—
47	C₃×C₄	—	4	1	no	—
48	Dic₃	—	12	1	no	—
49	C₃²	#1369	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₄	—	9	1	no	—
51	C₂×C₄	—	18	1	no	—
52	C₈	—	9	2	no	—
53	C₈	—	9	1	no	—
54	C₈	C₂×AGL(1,𝔽₉)	1	1	yes	characteristic
55	C₂×C₃	—	4	1	no	—
56	D₃	—	12	2	no	—
57	C₂²	—	9	1	no	—
58	C₄	—	9	1	no	—
59	C₄	—	36	1	no	—
60	C₄	C₄⋊AGL(1,𝔽₉)	1	1	yes	characteristic
61	C₃	—	4	1	no	—
62	C₂	—	18	1	no	—
63	C₂	#10593252	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10593252
commutator	C₃²×C₈	C₂×C₈
Frattini	C₈	C₂×AGL(1,𝔽₉)
Fitting	C₃²×C₁₆	C₈
socle	C₂×C₃²	#334
prime radical	C₂×C₃⋊D₃	#108
cosocle	C₈×#157	C₂²
hypercenter	C₁₆	AGL(1,𝔽₉)
hypocenter	C₃²	#1369
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
49. C₃²	#1369	semidirect

Maximal subgroups

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

subgroup	index
#10593256	2
#10590135	2
#1369	9