Subgroups — #11783532

Order 1152.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592821	C₂	1	3	yes	maximal
2	C₃²×#338	C₂	1	1	yes	maximal, characteristic
3	#10589423	C₂	1	3	yes	maximal
4	#68717	—	3	4	no	maximal
5	C₂×C₃²×M₁₆	C₂²	1	3	yes	—
6	#64135	C₂²	1	3	yes	—
7	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
8	#63642	C₄	1	6	yes	complemented
9	C₈×C₃⋊Dic₃	C₄	1	6	yes	complemented
10	#5122	—	3	12	no	—
11	C₃×#338	D₃	1	4	yes	—
12	#4557	—	3	12	no	—
13	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
14	C₃²×M₁₆	—	2	6	no	—
15	C₂×C₃²×C₈	C₂×C₄	1	6	yes	—
16	#3757	—	2	3	no	—
17	C₄⋊(C₃⋊Dic₃)	—	2	3	no	—
18	C₄×C₃⋊Dic₃	C₂×C₄	1	6	yes	—
19	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	3	yes	—
20	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	3	yes	—
21	#1747	—	9	1	no	Sylow
22	C₂×C₃×M₁₆	C₂×D₃	1	12	yes	—
23	#926	—	3	12	no	—
24	C₂²×C₃⋊C₈	—	3	4	no	—
25	#815	—	3	24	no	—
26	C₈×Dic₃	—	3	24	no	—
27	C₂³×C₃²	#41	1	1	yes	characteristic
28	C₂×C₃²×C₄	C₂²×C₄	1	3	yes	—
29	C₂×C₃²×C₄	#41	1	3	yes	—
30	C₂×C₃⋊Dic₃	—	2	6	no	—
31	C₃²×C₈	—	2	6	no	—
32	C₃⋊(C₃⋊C₈)	C₄²	1	1	yes	characteristic
33	C₃⋊(C₃⋊C₈)	C₄²	1	3	yes	—
34	#405	—	9	3	no	—
35	#338	C₃⋊D₃	1	1	yes	characteristic
36	H(3,ℤ/4)	—	9	3	no	—
37	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
38	C₃×M₁₆	—	2	24	no	—
39	C₂×C₃×C₈	C₄×D₃	1	24	yes	—
40	#217	—	6	12	no	—
41	C₄⋊Dic₃	—	6	12	no	—
42	C₄×Dic₃	—	3	24	no	—
43	C₂×C₃⋊C₈	—	3	12	no	—
44	C₂×C₃⋊C₈	—	3	12	no	—
45	C₂²×C₃²	—	4	1	no	—
46	C₂²×C₃²	#117	1	3	yes	—
47	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
48	C₃²×C₄	#117	1	3	yes	—
49	C₃⋊Dic₃	—	4	6	no	—
50	C₂×M₁₆	C₂×C₃⋊D₃	1	3	yes	—
51	C₂²×C₈	—	9	1	no	—
52	#117	—	9	3	no	—
53	#97	—	9	6	no	—
54	C₄×C₈	—	9	6	no	—
55	C₂³×C₃	#239	1	4	yes	—
56	C₂×C₃×C₄	C₂×C₄×D₃	1	12	yes	—
57	C₂×C₃×C₄	#237	1	12	yes	—
58	C₂×Dic₃	—	6	24	no	—
59	C₃×C₈	—	2	24	no	—
60	C₃⋊C₈	—	3	4	no	—
61	C₃⋊C₈	—	3	12	no	—
62	C₂×C₃²	—	2	3	no	—
63	C₂×C₃²	#376	1	1	yes	characteristic
64	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
65	M₁₆	—	2	6	no	—
66	C₂×C₈	—	9	3	no	—
67	C₂×C₈	—	9	3	no	—
68	C₂×C₈	C₄×C₃⋊D₃	1	6	yes	—
69	C₄⋊C₄	—	18	3	no	—
70	C₂²⋊C₄	—	18	3	no	—
71	C₄²	—	9	6	no	—
72	C₂²×C₃	—	4	4	no	—
73	C₂²×C₃	#892	1	12	yes	—
74	C₃×C₄	C₄²×D₃	1	4	yes	—
75	C₃×C₄	#877	1	12	yes	—
76	Dic₃	—	12	24	no	—
77	C₃²	#1747	1	1	yes	characteristic, complemented, Sylow
78	C₂³	#3832	1	1	yes	characteristic
79	C₂×C₄	—	18	6	no	—
80	C₂×C₄	C₂×C₄×C₃⋊D₃	1	3	yes	—
81	C₂×C₄	#3830	1	3	yes	—
82	C₈	—	2	6	no	—
83	C₈	—	9	1	no	—
84	C₈	—	9	3	no	—
85	C₂×C₃	—	2	12	no	—
86	C₂×C₃	#4648	1	4	yes	—
87	C₂²	—	4	1	no	—
88	C₂²	#64101	1	3	yes	—
89	C₄	—	36	6	no	—
90	C₄	C₄²×C₃⋊D₃	1	1	yes	characteristic
91	C₄	#64086	1	3	yes	—
92	C₃	#68717	1	4	yes	complemented
93	C₂	—	2	3	no	—
94	C₂	#10592347	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×C₃⋊D₃
commutator	C₃²×C₄	C₂×C₄²
Frattini	C₂²×C₄	C₂²×C₃⋊D₃
Fitting	C₃²×#338	C₂
socle	C₂×C₃²	#376
prime radical	C₂³×C₃²	#41
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	#338	C₃⋊D₃
hypocenter	C₃²	#1747
LCS	G ▷ C₃²×C₄ ▷ C₃²
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
8. #63642	C₄	semidirect
9. C₈×C₃⋊Dic₃	C₄	semidirect
77. C₃²	#1747	semidirect
92. C₃	#68717	semidirect

Maximal subgroups

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

subgroup	index
#10592821	2
C₃²×#338	2
#10589423	2
#68717	3