Subgroups — #11773052

Order 1152.

129 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
2	C₃×#4504	C₂	1	2	yes	maximal
3	#67576	—	3	2	no	maximal
4	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
5	C₃×#818	—	2	2	no	—
6	C₃⋊(C₃⋊C₃₂)	C₄	1	2	yes	complemented
7	C₃×#366	—	3	2	no	—
8	#4504	D₃	1	2	yes	—
9	C₂×C₃⋊C₃₂	—	3	2	no	—
10	C₂×C₃⋊C₃₂	—	6	1	no	—
11	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
12	C₃×C₄⋊Dic₃	—	4	2	no	—
13	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
14	C₃²×C₁₆	Q₈	1	1	yes	characteristic
15	#1424	—	9	1	no	Sylow
16	C₂×C₃×C₁₆	—	2	1	no	—
17	C₂×C₃×C₁₆	C₂×D₃	1	2	yes	—
18	C₃×#107	—	6	2	no	—
19	#818	—	2	2	no	—
20	C₃⋊C₃₂	—	3	4	no	—
21	C₃⋊C₃₂	—	6	2	no	—
22	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
23	C₂×C₃×Dic₃	—	8	2	no	—
24	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
25	C₃²×C₈	Q₁₆	1	1	yes	characteristic
26	C₂×C₃₂	—	9	1	no	—
27	#366	—	3	2	no	—
28	C₂×C₃×C₈	—	2	1	no	—
29	C₂×C₃×C₈	#67	1	2	yes	—
30	C₃×C₄⋊C₄	—	12	2	no	—
31	C₄⋊Dic₃	—	4	2	no	—
32	C₃×C₁₆	—	2	1	no	—
33	C₃×C₁₆	—	2	1	no	—
34	C₃×C₁₆	Dic₆	1	2	yes	—
35	C₃×C₁₆	C₄×D₃	1	2	yes	—
36	C₂²×C₃²	D₁₆	1	1	yes	characteristic
37	C₃²×C₄	#107	1	1	yes	characteristic
38	C₃²×C₄	Q₃₂	1	1	yes	characteristic
39	C₃×Dic₃	—	16	2	no	—
40	C₂×C₁₆	D₃²	1	1	yes	characteristic
41	#107	—	6	2	no	—
42	C₃₂	—	9	2	no	—
43	C₂×C₃×C₄	—	2	1	no	—
44	C₂×C₃×C₄	—	24	2	no	—
45	C₂×C₃×C₄	#213	1	2	yes	—
46	C₂×Dic₃	—	8	2	no	—
47	C₃×C₈	—	2	1	no	—
48	C₃×C₈	—	2	1	no	—
49	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
50	C₃×C₈	#216	1	2	yes	—
51	C₂×C₃²	#366	1	1	yes	characteristic
52	C₂×C₃²	SD₆₄	1	2	yes	—
53	C₂×C₈	#625	1	1	yes	characteristic
54	C₄⋊C₄	—	12	2	no	—
55	C₁₆	#624	1	1	yes	characteristic
56	C₁₆	#627	1	1	yes	characteristic
57	C₂²×C₃	—	2	1	no	—
58	C₂²×C₃	#826	1	2	yes	—
59	C₃×C₄	—	2	1	no	—
60	C₃×C₄	—	2	1	no	—
61	C₃×C₄	—	48	2	no	—
62	C₃×C₄	#807	1	2	yes	—
63	C₃×C₄	#829	1	2	yes	—
64	Dic₃	—	16	2	no	—
65	C₃²	#1424	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₄	—	24	2	no	—
67	C₂×C₄	#3713	1	1	yes	characteristic
68	C₈	#3718	1	1	yes	characteristic
69	C₈	#3724	1	1	yes	characteristic
70	C₂×C₃	—	2	2	no	—
71	C₂×C₃	—	2	1	no	—
72	C₂×C₃	#4489	1	2	yes	—
73	C₂×C₃	#4520	1	2	yes	—
74	C₂×C₃	#4521	1	2	yes	—
75	C₂²	#63545	1	1	yes	characteristic
76	C₄	—	48	2	no	—
77	C₄	#63550	1	1	yes	characteristic
78	C₄	#63576	1	1	yes	characteristic
79	C₃	—	2	1	no	—
80	C₃	#67576	1	2	yes	complemented
81	C₂	#10589072	1	2	yes	—
82	C₂	#10589140	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63545
commutator	C₃²×C₁₆	C₂×C₄
Frattini, hypercenter	C₂×C₁₆	D₃²
Fitting, cosocle	C₂×C₃²×C₁₆	C₂²
socle, prime radical	C₂²×C₃²	D₁₆
hypocenter	C₃²	#1424
LCS	G ▷ C₃²×C₁₆ ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. C₃⋊(C₃⋊C₃₂)	C₄	semidirect
65. C₃²	#1424	semidirect
80. C₃	#67576	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊(C₃⋊C₃₂)	2
C₃×#4504	2
#67576	3