Subgroups — #11773065

Order 1152.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63540	C₂	1	1	yes	maximal, characteristic
2	#10589144	C₂	1	2	yes	maximal
3	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
4	C₃×#819	—	2	2	no	—
5	#63540	C₄	1	2	yes	—
6	#4493	—	6	2	no	—
7	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
8	C₃×#208	—	4	2	no	—
9	C₃⋊(C₃⋊C₁₆)	C₂×C₄	1	1	yes	characteristic
10	C₃⋊(C₃⋊C₁₆)	Q₈	1	1	yes	characteristic
11	#1425	—	9	1	no	maximal, Sylow
12	C₃×#108	—	6	2	no	—
13	#819	—	2	2	no	—
14	C₂×C₃⋊C₁₆	—	6	2	no	—
15	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
16	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
17	C₃²×C₈	Q₁₆	1	1	yes	characteristic
18	C₃×C₃⋊C₈	—	8	2	no	—
19	C₂×C₃₂	—	9	1	no	—
20	#368	—	9	2	no	—
21	C₃×M₁₆	—	12	2	no	—
22	C₂×C₃×C₈	—	2	2	no	—
23	#208	—	4	2	no	—
24	C₃⋊C₁₆	—	6	2	no	—
25	C₃⋊C₁₆	—	6	2	no	—
26	C₂²×C₃²	Q₃₂	1	1	yes	characteristic
27	C₃²×C₄	#107	1	1	yes	characteristic
28	C₃²×C₄	D₁₆	1	1	yes	characteristic
29	C₂×C₁₆	—	9	1	no	—
30	#108	—	6	2	no	—
31	C₃₂	—	9	2	no	—
32	C₂×C₃×C₄	—	2	2	no	—
33	C₃×C₈	—	2	2	no	—
34	C₃×C₈	—	2	2	no	—
35	C₃×C₈	—	24	2	no	—
36	C₃⋊C₈	—	8	2	no	—
37	C₂×C₃²	—	2	1	no	—
38	C₂×C₃²	#366	1	1	yes	characteristic
39	M₁₆	—	12	2	no	—
40	C₂×C₈	GO⁺(4,𝔽₂)	1	1	yes	characteristic
41	C₁₆	—	9	1	no	—
42	C₁₆	—	9	1	no	—
43	C₂²×C₃	—	2	2	no	—
44	C₃×C₄	—	2	2	no	—
45	C₃×C₄	—	2	2	no	—
46	C₃²	#1425	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄	#3774	1	1	yes	characteristic
48	C₈	—	24	2	no	—
49	C₈	#3773	1	1	yes	characteristic
50	C₈	#3776	1	1	yes	characteristic
51	C₂×C₃	—	2	2	no	—
52	C₂×C₃	—	4	2	no	—
53	C₂²	#63736	1	1	yes	characteristic
54	C₄	#63734	1	1	yes	characteristic
55	C₄	#63743	1	1	yes	characteristic
56	C₃	—	2	2	no	—
57	C₂	—	2	1	no	—
58	C₂	#10590068	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#63734
commutator	C₃⋊(C₃⋊C₁₆)	C₂×C₄
Frattini, hypercenter	C₂×C₈	GO⁺(4,𝔽₂)
Fitting	C₂×C₃²×C₈	D₄
socle	C₂×C₃²	#366
prime radical	C₂²×C₃²	Q₃₂
cosocle	C₂×C₃⋊(C₃⋊C₁₆)	C₂²
hypocenter	C₃²	#1425
LCS	G ▷ C₃⋊(C₃⋊C₁₆) ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
46. C₃²	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63540	2
#10589144	2
#1425	9