Subgroups — #11773053

Order 1152.

102 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	#10589140	C₂	1	2	yes	maximal
3	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic
4	C₃×#818	—	2	2	no	—
5	#63540	C₄	1	2	yes	complemented
6	#4489	—	6	2	no	—
7	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
8	C₃×C₄⋊Dic₃	—	4	2	no	—
9	C₃⋊(C₃⋊C₁₆)	C₂×C₄	1	1	yes	characteristic
10	C₃⋊(C₃⋊C₁₆)	Q₈	1	1	yes	characteristic
11	#1424	—	9	1	no	maximal, Sylow
12	C₃×#107	—	6	2	no	—
13	#818	—	2	2	no	—
14	C₂×C₃⋊C₁₆	—	6	2	no	—
15	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
16	C₂×C₃×Dic₃	—	8	2	no	—
17	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
18	C₃²×C₈	Q₁₆	1	1	yes	characteristic
19	C₂×C₃₂	—	9	1	no	—
20	#366	—	9	2	no	—
21	C₂×C₃×C₈	—	2	2	no	—
22	C₃×C₄⋊C₄	—	12	2	no	—
23	C₄⋊Dic₃	—	4	2	no	—
24	C₃⋊C₁₆	—	6	2	no	—
25	C₃⋊C₁₆	—	6	2	no	—
26	C₂²×C₃²	D₁₆	1	1	yes	characteristic
27	C₃²×C₄	#107	1	1	yes	characteristic
28	C₃²×C₄	Q₃₂	1	1	yes	characteristic
29	C₃×Dic₃	—	16	2	no	—
30	C₂×C₁₆	—	9	1	no	—
31	#107	—	6	2	no	—
32	C₃₂	—	9	2	no	—
33	C₂×C₃×C₄	—	2	2	no	—
34	C₂×C₃×C₄	—	24	2	no	—
35	C₂×Dic₃	—	8	2	no	—
36	C₃×C₈	—	2	2	no	—
37	C₃×C₈	—	2	2	no	—
38	C₂×C₃²	#366	1	1	yes	characteristic
39	C₂×C₃²	SD₆₄	1	2	yes	—
40	C₂×C₈	GO⁺(4,𝔽₂)	1	1	yes	characteristic
41	C₄⋊C₄	—	12	2	no	—
42	C₁₆	—	9	1	no	—
43	C₁₆	—	9	1	no	—
44	C₂²×C₃	—	2	2	no	—
45	C₃×C₄	—	2	2	no	—
46	C₃×C₄	—	2	2	no	—
47	C₃×C₄	—	48	2	no	—
48	Dic₃	—	16	2	no	—
49	C₃²	#1424	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₄	—	24	2	no	—
51	C₂×C₄	#3774	1	1	yes	characteristic
52	C₈	#3773	1	1	yes	characteristic
53	C₈	#3776	1	1	yes	characteristic
54	C₂×C₃	—	2	2	no	—
55	C₂×C₃	—	2	2	no	—
56	C₂×C₃	—	2	2	no	—
57	C₂²	#63734	1	1	yes	characteristic
58	C₄	—	48	2	no	—
59	C₄	#63736	1	1	yes	characteristic
60	C₄	#63743	1	1	yes	characteristic
61	C₃	—	2	2	no	—
62	C₂	#10590025	1	2	yes	—
63	C₂	#10590068	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63734
commutator	C₃⋊(C₃⋊C₁₆)	C₂×C₄
Frattini, hypercenter	C₂×C₈	GO⁺(4,𝔽₂)
Fitting	C₂×C₃²×C₈	D₄
socle, prime radical	C₂²×C₃²	D₁₆
cosocle	C₂×C₃⋊(C₃⋊C₁₆)	C₂²
hypocenter	C₃²	#1424
LCS	G ▷ C₃⋊(C₃⋊C₁₆) ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
5. #63540	C₄	semidirect
49. C₃²	#1424	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
#10589140	2
#1424	9