Subgroups — #11773045

Order 1152.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#366	C₂	1	1	yes	maximal, characteristic
2	#10589370	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊(C₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
4	#67576	—	3	4	no	maximal
5	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
6	C₃²×#107	—	2	1	no	—
7	#63645	—	2	1	no	—
8	C₃⋊(C₃⋊C₃₂)	C₄	1	2	yes	complemented
9	C₃×#366	D₃	1	4	yes	—
10	#4504	—	3	4	no	—
11	C₂×C₃⋊C₃₂	—	3	4	no	—
12	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
13	C₃²×C₄⋊C₄	—	4	1	no	—
14	C₄⋊(C₃⋊Dic₃)	—	4	1	no	—
15	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₃²×C₁₆	Q₈	1	1	yes	characteristic
17	#1424	—	9	1	no	Sylow
18	C₂×C₃×C₁₆	C₂×D₃	1	4	yes	—
19	C₃×#107	—	2	4	no	—
20	#818	—	6	4	no	—
21	C₃⋊C₃₂	—	3	8	no	—
22	C₂×C₃²×C₄	—	8	1	no	—
23	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
24	C₂×C₃⋊Dic₃	—	8	1	no	—
25	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
26	C₃²×C₈	Q₁₆	1	1	yes	characteristic
27	C₂×C₃₂	—	9	1	no	—
28	#366	—	9	1	no	—
29	#366	C₃⋊D₃	1	1	yes	characteristic
30	C₂×C₃×C₈	#67	1	4	yes	—
31	C₃×C₄⋊C₄	—	4	4	no	—
32	C₄⋊Dic₃	—	12	4	no	—
33	C₃×C₁₆	Dic₆	1	4	yes	—
34	C₃×C₁₆	C₄×D₃	1	4	yes	—
35	C₂²×C₃²	D₁₆	1	1	yes	characteristic
36	C₃²×C₄	—	16	1	no	—
37	C₃²×C₄	#107	1	1	yes	characteristic
38	C₃²×C₄	Q₃₂	1	1	yes	characteristic
39	C₃⋊Dic₃	—	16	1	no	—
40	C₂×C₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
41	#107	—	2	1	no	—
42	#107	—	18	1	no	—
43	C₃₂	—	9	2	no	—
44	C₂×C₃×C₄	—	8	4	no	—
45	C₂×C₃×C₄	#213	1	4	yes	—
46	C₂×Dic₃	—	24	4	no	—
47	C₃×C₈	Dic₃⋊C₄	1	4	yes	—
48	C₃×C₈	#216	1	4	yes	—
49	C₂×C₃²	#366	1	1	yes	characteristic
50	C₂×C₃²	SD₆₄	1	1	yes	characteristic
51	C₂×C₃²	SD₆₄	1	1	yes	characteristic
52	C₂×C₈	#638	1	1	yes	characteristic
53	C₄⋊C₄	—	4	1	no	—
54	C₄⋊C₄	—	36	1	no	—
55	C₁₆	#634	1	1	yes	characteristic
56	C₁₆	C₄×C₃⋊D₃	1	1	yes	characteristic
57	C₂²×C₃	#826	1	4	yes	—
58	C₃×C₄	—	16	4	no	—
59	C₃×C₄	#807	1	4	yes	—
60	C₃×C₄	#829	1	4	yes	—
61	Dic₃	—	48	4	no	—
62	C₃²	#1424	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₄	—	8	1	no	—
64	C₂×C₄	—	72	1	no	—
65	C₂×C₄	#3753	1	1	yes	characteristic
66	C₈	#3750	1	1	yes	characteristic
67	C₈	#3756	1	1	yes	characteristic
68	C₂×C₃	#4489	1	4	yes	—
69	C₂×C₃	#4520	1	4	yes	—
70	C₂×C₃	#4521	1	4	yes	—
71	C₂²	#63653	1	1	yes	characteristic
72	C₄	—	16	1	no	—
73	C₄	—	144	1	no	—
74	C₄	#63634	1	1	yes	characteristic
75	C₄	#63656	1	1	yes	characteristic
76	C₃	#67576	1	4	yes	complemented
77	C₂	#10589355	1	1	yes	characteristic
78	C₂	#10589386	1	1	yes	characteristic
79	C₂	#10589387	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63653
commutator	C₃²×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×C₃⋊D₃
Fitting	C₃²×#366	C₂
socle, prime radical	C₂²×C₃²	D₁₆
cosocle	C₂×C₃²×C₁₆	C₂²
hypercenter	#366	C₃⋊D₃
hypocenter	C₃²	#1424
LCS	G ▷ C₃²×C₁₆ ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
8. C₃⋊(C₃⋊C₃₂)	C₄	semidirect
62. C₃²	#1424	semidirect
76. C₃	#67576	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#366	2
#10589370	2
C₂×C₃⋊(C₃⋊C₃₂)	2
#67576	3