Subgroups — #11786140

Order 1152.

374 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592347	C₂	1	1	yes	maximal, characteristic
2	#10590207	C₂	1	6	yes	maximal
3	C₂²×#622	C₂²	1	4	yes	—
4	C₂×C₄×C₃⋊Dic₃	C₂²	1	3	yes	—
5	C₃²×#95	C₄	1	1	yes	characteristic
6	#63658	C₄	1	3	yes	—
7	#4648	—	6	2	no	—
8	C₂²×C₃²×C₄	C₂×C₄	1	3	yes	—
9	C₂²×C₃⋊Dic₃	C₂×C₄	1	3	yes	—
10	C₂²×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
11	C₂×#622	—	2	12	no	—
12	C₄×C₃⋊Dic₃	—	2	6	no	—
13	#1840	—	9	1	no	maximal, Sylow
14	C₂×C₄×Dic₃	—	6	6	no	—
15	C₃×#95	—	2	2	no	—
16	C₃⋊#95	—	6	6	no	—
17	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₃²×C₄	—	2	3	no	—
19	C₂×C₃²×C₄	—	2	6	no	—
20	C₂×C₃⋊Dic₃	—	2	3	no	—
21	C₂×C₃⋊Dic₃	—	2	3	no	—
22	C₂×C₃⋊Dic₃	—	2	3	no	—
23	C₂×C₃⋊Dic₃	#41	1	6	yes	—
24	#622	—	4	4	no	—
25	#376	—	9	1	no	—
26	#336	—	9	6	no	—
27	C₂²×C₃×C₄	—	2	6	no	—
28	C₂²×Dic₃	—	6	2	no	—
29	C₂²×Dic₃	—	6	6	no	—
30	C₄×Dic₃	—	6	24	no	—
31	C₂²×C₃²	#117	1	3	yes	—
32	C₂²×C₃²	#131	1	1	yes	characteristic
33	C₂²×C₃²	#131	1	3	yes	—
34	C₃²×C₄	—	4	3	no	—
35	C₃⋊Dic₃	—	4	3	no	—
36	C₃⋊Dic₃	#126	1	4	yes	—
37	C₂²×C₈	—	9	4	no	—
38	C₂×C₄²	—	9	3	no	—
39	#95	—	9	3	no	—
40	#95	#157	1	1	yes	characteristic
41	C₂³×C₃	—	2	2	no	—
42	C₂×C₃×C₄	—	2	12	no	—
43	C₂×C₃×C₄	—	4	12	no	—
44	C₂×Dic₃	—	6	12	no	—
45	C₂×Dic₃	—	6	12	no	—
46	C₂×Dic₃	—	12	6	no	—
47	C₂×Dic₃	—	12	6	no	—
48	C₂×C₃²	#383	1	1	yes	characteristic
49	C₂×C₃²	#433	1	3	yes	—
50	C₂×C₃²	#433	1	3	yes	—
51	C₂²×C₄	—	9	1	no	—
52	C₂²×C₄	—	9	3	no	—
53	C₂²×C₄	C₂×#157	1	3	yes	—
54	C₂×C₈	—	18	12	no	—
55	C₄²	—	18	6	no	—
56	C₂²×C₃	—	2	6	no	—
57	C₂²×C₃	—	2	6	no	—
58	C₂²×C₃	—	2	2	no	—
59	C₃×C₄	—	4	12	no	—
60	Dic₃	—	6	8	no	—
61	Dic₃	—	12	12	no	—
62	C₃²	#1840	1	1	yes	characteristic, complemented, Sylow
63	C₂³	C₂²×#157	1	1	yes	characteristic
64	C₂×C₄	—	2	3	no	—
65	C₂×C₄	—	2	6	no	—
66	C₂×C₄	—	9	6	no	—
67	C₂×C₄	—	18	3	no	—
68	C₂×C₄	—	18	3	no	—
69	C₂×C₄	—	18	3	no	—
70	C₈	—	36	4	no	—
71	C₂×C₃	—	2	2	no	—
72	C₂×C₃	—	2	6	no	—
73	C₂×C₃	—	2	6	no	—
74	C₂²	#64286	1	3	yes	—
75	C₂²	#64287	1	3	yes	—
76	C₂²	#64289	1	1	yes	characteristic
77	C₄	—	4	3	no	—
78	C₄	—	9	4	no	—
79	C₄	—	36	3	no	—
80	C₃	—	2	2	no	—
81	C₂	#10593737	1	1	yes	characteristic
82	C₂	#10593744	1	3	yes	—
83	C₂	#10593753	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#157
commutator, socle, prime radical	C₂³×C₃²	C₂²×C₄
Fitting	C₃²×#95	C₄
cosocle	C₂²×C₃⋊Dic₃	C₂³
hypercenter	#95	#157
hypocenter	C₃²	#1840
LCS	G ▷ C₂³×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

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

Maximal subgroups

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

subgroup	index
#10592347	2
#10590207	2
#1840	9