Subgroups — #11773670

Order 1152.

534 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592384	C₂	1	3	yes	maximal
2	C₃²×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	#10589320	C₂	1	3	yes	maximal, complemented
4	#68049	—	3	4	no	maximal
5	C₄²×C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₃²×C₄×C₈	C₂²	1	3	yes	—
7	#63647	C₄	1	6	yes	—
8	#63641	C₄	1	6	yes	—
9	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	3	yes	—
10	#4685	—	3	12	no	—
11	C₃×C₈²	D₃	1	4	yes	complemented
12	#4454	—	3	12	no	—
13	C₂×C₄×C₃⋊D₃	C₂×C₄	1	3	yes	—
14	C₂×C₃²×C₈	C₂×C₄	1	6	yes	—
15	C₃²×C₄²	C₂³	1	1	yes	characteristic
16	C₄×C₃⋊Dic₃	C₂×C₄	1	3	yes	—
17	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	6	yes	—
18	#1454	—	9	1	no	Sylow
19	C₄²×D₃	—	3	4	no	—
20	C₃×C₄×C₈	C₂×D₃	1	12	yes	—
21	(C₂×D₃)⋊C₈	—	3	24	no	—
22	Dic₃⋊C₈	—	3	24	no	—
23	C₄×C₃⋊C₈	—	3	12	no	—
24	C₂²×C₃⋊D₃	C₄²	1	1	yes	characteristic
25	C₂×C₃²×C₄	C₂²×C₄	1	3	yes	—
26	C₂×C₃⋊Dic₃	C₄²	1	3	yes	—
27	C₄×C₃⋊D₃	—	2	6	no	—
28	C₃²×C₈	—	2	6	no	—
29	C₃⋊(C₃⋊C₈)	—	2	6	no	—
30	#431	—	9	3	no	—
31	#322	—	9	3	no	—
32	C₈²	C₃⋊D₃	1	1	yes	characteristic, complemented
33	C₂×C₄×D₃	—	3	12	no	—
34	C₂×C₃×C₈	C₄×D₃	1	24	yes	—
35	C₃×C₄²	C₂²×D₃	1	4	yes	—
36	C₄×Dic₃	—	3	12	no	—
37	C₂×C₃⋊C₈	—	3	24	no	—
38	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₃⋊D₃	—	2	3	no	—
40	C₃²×C₄	#131	1	6	yes	—
41	C₃⋊Dic₃	—	2	3	no	—
42	C₂×C₄²	—	9	1	no	—
43	C₄⋊C₈	—	9	6	no	—
44	C₂²⋊C₈	—	9	6	no	—
45	C₄×C₈	—	9	3	no	—
46	C₄×C₈	C₂×C₃⋊D₃	1	3	yes	—
47	C₂²×D₃	—	3	4	no	—
48	C₂×C₃×C₄	C₂×C₄×D₃	1	12	yes	—
49	C₂×Dic₃	—	3	12	no	—
50	C₄×D₃	—	6	24	no	—
51	C₃×C₈	—	2	24	no	—
52	C₃⋊C₈	—	6	24	no	—
53	C₂×C₃²	#405	1	3	yes	—
54	C₃⋊D₃	—	4	1	no	—
55	C₂²×C₄	—	9	3	no	—
56	C₂×C₈	—	9	6	no	—
57	C₂×C₈	C₄×C₃⋊D₃	1	6	yes	—
58	C₄²	—	9	3	no	—
59	C₄²	C₂²×C₃⋊D₃	1	1	yes	characteristic
60	C₂²×C₃	C₄²×D₃	1	4	yes	—
61	C₂×D₃	—	6	12	no	—
62	C₃×C₄	#901	1	24	yes	—
63	Dic₃	—	6	12	no	—
64	C₃²	#1454	1	1	yes	characteristic, complemented, Sylow
65	C₂³	—	9	1	no	—
66	C₂×C₄	—	9	3	no	—
67	C₂×C₄	—	18	6	no	—
68	C₂×C₄	C₂×C₄×C₃⋊D₃	1	3	yes	—
69	C₈	—	2	6	no	—
70	C₈	—	18	6	no	—
71	C₂×C₃	#4689	1	12	yes	—
72	D₃	—	12	4	no	—
73	C₂²	—	18	3	no	—
74	C₂²	C₄²×C₃⋊D₃	1	1	yes	characteristic
75	C₄	—	18	3	no	—
76	C₄	#64110	1	6	yes	—
77	C₃	#68049	1	4	yes	complemented
78	C₂	—	36	1	no	—
79	C₂	#10592388	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×C₃⋊D₃
commutator, socle	C₂²×C₃²	C₂×C₄²
Fitting	C₃²×C₈²	C₂
prime radical	C₂²×C₃⋊D₃	C₄²
cosocle	C₃²×C₄²	C₂³
hypercenter	C₈²	C₃⋊D₃
hypocenter	C₃²	#1454
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. C₃²×C₈²	C₂	semidirect
3. #10589320	C₂	semidirect
11. C₃×C₈²	D₃	semidirect
32. C₈²	C₃⋊D₃	semidirect
64. C₃²	#1454	semidirect
77. C₃	#68049	semidirect

Maximal subgroups

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

subgroup	index
#10592384	2
C₃²×C₈²	2
#10589320	2
#68049	3