Subgroups — #11786138

Order 1152.

588 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#376	C₂	1	1	yes	maximal, characteristic
2	#10589390	C₂	1	6	yes	maximal
3	#69438	—	3	4	no	maximal
4	C₂×C₃²×C₄²	C₂²	1	3	yes	—
5	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	4	yes	—
6	C₃²×#95	C₄	1	4	yes	—
7	C₃×#376	D₃	1	4	yes	—
8	#4524	—	3	24	no	—
9	C₂²×C₃²×C₄	C₂×C₄	1	6	yes	—
10	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
11	C₃²×C₄²	—	2	6	no	—
12	C₂×C₃⋊(C₃⋊C₈)	—	2	12	no	—
13	#1840	—	9	1	no	Sylow
14	C₂×C₃×C₄²	C₂×D₃	1	12	yes	—
15	C₂²×C₃⋊C₈	—	3	16	no	—
16	C₃×#95	Dic₃	1	16	yes	—
17	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₃²×C₄	—	2	6	no	—
19	C₂×C₃²×C₄	—	2	12	no	—
20	C₂×C₃²×C₄	#41	1	6	yes	—
21	C₃⋊(C₃⋊C₈)	—	4	4	no	—
22	#376	C₃⋊D₃	1	1	yes	characteristic
23	#336	—	9	6	no	—
24	C₂²×C₃×C₄	C₂×Dic₃	1	24	yes	—
25	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
26	C₃×C₄²	—	2	24	no	—
27	C₂×C₃⋊C₈	—	6	48	no	—
28	C₂²×C₃²	#117	1	3	yes	—
29	C₂²×C₃²	#131	1	4	yes	—
30	C₃²×C₄	—	4	6	no	—
31	C₃²×C₄	#126	1	4	yes	—
32	C₂²×C₈	—	9	4	no	—
33	C₂×C₄²	C₂×C₃⋊D₃	1	3	yes	—
34	#95	C₃⋊Dic₃	1	4	yes	—
35	C₂³×C₃	C₂²×Dic₃	1	4	yes	—
36	C₂×C₃×C₄	—	2	24	no	—
37	C₂×C₃×C₄	—	2	48	no	—
38	C₂×C₃×C₄	#235	1	24	yes	—
39	C₃⋊C₈	—	12	16	no	—
40	C₂×C₃²	#383	1	1	yes	characteristic
41	C₂×C₃²	#433	1	6	yes	—
42	C₂²×C₄	C₂×C₃⋊Dic₃	1	6	yes	—
43	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
44	C₂×C₈	—	18	12	no	—
45	C₄²	—	2	6	no	—
46	C₂²×C₃	#926	1	12	yes	—
47	C₂²×C₃	#948	1	16	yes	—
48	C₃×C₄	—	4	24	no	—
49	C₃×C₄	#876	1	16	yes	—
50	C₃²	#1840	1	1	yes	characteristic, complemented, Sylow
51	C₂³	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
52	C₂×C₄	—	2	6	no	—
53	C₂×C₄	—	2	12	no	—
54	C₂×C₄	#3828	1	6	yes	—
55	C₈	—	36	4	no	—
56	C₂×C₃	#4937	1	4	yes	—
57	C₂×C₃	#5000	1	24	yes	—
58	C₂²	#64135	1	3	yes	—
59	C₂²	#64157	1	4	yes	—
60	C₄	—	4	6	no	—
61	C₄	#64085	1	4	yes	—
62	C₃	#69438	1	4	yes	complemented
63	C₂	#10592636	1	1	yes	characteristic
64	C₂	#10592699	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×C₃⋊D₃
commutator, socle, prime radical	C₂³×C₃²	C₂²×C₄
Fitting	C₃²×#376	C₂
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	#376	C₃⋊D₃
hypocenter	C₃²	#1840
LCS	G ▷ C₂³×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
50. C₃²	#1840	semidirect
62. C₃	#69438	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#376	2
#10589390	2
#69438	3