Subgroups — #41×C₃⋊D₃ #64365

Order 288.

492 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#3832	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#3830	C₂	1	3	yes	maximal, complemented
5	D₄×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
6	#3828	C₂	1	3	yes	maximal, complemented
7	C₂×C₄×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
8	D₃×#41	—	3	4	no	maximal
9	C₂²×C₃⋊D₃	C₂²	1	3	yes	—
10	C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₃²×D₄	C₂²	1	3	yes	complemented
12	C₂×C₃²×C₄	C₂²	1	3	yes	complemented
13	#638	C₂²	1	6	yes	complemented
14	C₂×C₃⋊Dic₃	C₂²	1	3	yes	complemented
15	C₄⋊(C₃⋊D₃)	C₂²	1	3	yes	complemented
16	C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
17	C₄×C₃⋊D₃	C₂²	1	3	yes	—
18	C₄×C₃⋊D₃	C₂²	1	3	yes	complemented
19	C₄×C₃⋊D₃	C₂²	1	3	yes	complemented
20	#634	C₂²	1	3	yes	complemented
21	C₃×#41	D₃	1	4	yes	complemented
22	#239	—	3	4	no	—
23	D₃×Q₈	—	3	4	no	—
24	#237	—	3	12	no	—
25	D₃×D₄	—	3	12	no	—
26	#235	—	3	12	no	—
27	C₂×C₄×D₃	—	3	12	no	—
28	C₂²×C₃²	C₂³	1	3	yes	—
29	C₂×C₃⋊D₃	—	2	6	no	—
30	C₂×C₃⋊D₃	C₂³	1	3	yes	—
31	C₂×C₃⋊D₃	C₂³	1	1	yes	characteristic
32	C₃²×C₄	C₂³	1	3	yes	—
33	C₃²×C₄	C₂³	1	1	yes	characteristic
34	C₃⋊Dic₃	C₂³	1	3	yes	—
35	C₃⋊Dic₃	C₂³	1	1	yes	characteristic
36	C₂×#41	—	9	1	no	Sylow
37	C₂²×D₃	—	3	12	no	—
38	C₃×Q₈	C₂×D₃	1	4	yes	complemented
39	C₃×D₄	C₂×D₃	1	12	yes	complemented
40	C₂×C₃×C₄	C₂×D₃	1	12	yes	complemented
41	#67	—	3	24	no	—
42	C₂×Dic₃	—	3	12	no	—
43	D₁₂	—	3	12	no	—
44	C₄×D₃	—	3	4	no	—
45	C₄×D₃	—	3	12	no	—
46	C₄×D₃	—	3	12	no	—
47	C₄×D₃	—	3	12	no	—
48	Dic₆	—	3	12	no	—
49	C₂×C₃²	—	2	3	no	—
50	C₂×C₃²	C₂⁴	1	1	yes	characteristic
51	C₃⋊D₃	—	2	3	no	—
52	C₃⋊D₃	#41	1	2	yes	direct product factor
53	#41	—	9	1	no	—
54	#41	—	9	3	no	—
55	#41	—	9	3	no	—
56	#41	C₃⋊D₃	1	1	yes	characteristic, direct product factor
57	C₂×Q₈	—	9	1	no	—
58	C₂×D₄	—	9	3	no	—
59	C₂²×C₄	—	9	3	no	—
60	C₂²×C₃	C₂²×D₃	1	12	yes	—
61	C₂×D₃	—	3	4	no	—
62	C₂×D₃	—	3	12	no	—
63	C₂×D₃	—	6	24	no	—
64	C₃×C₄	C₂²×D₃	1	12	yes	—
65	C₃×C₄	C₂²×D₃	1	4	yes	—
66	Dic₃	—	3	12	no	—
67	Dic₃	—	3	4	no	—
68	C₃²	C₂×#41	1	1	yes	characteristic, complemented, Sylow
69	C₂³	—	9	3	no	—
70	Q₈	—	9	3	no	—
71	Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
72	D₄	—	9	6	no	—
73	D₄	—	9	3	no	—
74	D₄	C₂×C₃⋊D₃	1	3	yes	complemented
75	C₂×C₄	—	9	3	no	—
76	C₂×C₄	—	9	3	no	—
77	C₂×C₄	—	9	3	no	—
78	C₂×C₄	—	9	1	no	—
79	C₂×C₄	—	9	3	no	—
80	C₂×C₄	C₂×C₃⋊D₃	1	3	yes	complemented
81	C₂×C₃	—	2	12	no	—
82	C₂×C₃	C₂³×D₃	1	4	yes	—
83	D₃	—	3	8	no	—
84	D₃	—	6	12	no	—
85	C₂²	—	9	1	no	—
86	C₂²	—	9	3	no	—
87	C₂²	—	18	6	no	—
88	C₂²	C₂²×C₃⋊D₃	1	3	yes	—
89	C₄	—	9	1	no	—
90	C₄	—	9	3	no	—
91	C₄	C₂²×C₃⋊D₃	1	3	yes	—
92	C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
93	C₃	D₃×#41	1	4	yes	complemented
94	C₂	—	2	3	no	—
95	C₂	—	9	2	no	—
96	C₂	—	18	3	no	—
97	C₂	C₂³×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×C₃⋊D₃
commutator, socle, cosocle	C₂×C₃²	C₂⁴
Frattini	C₂	C₂³×C₃⋊D₃
Fitting	C₃²×#41	C₂
hypercenter	#41	C₃⋊D₃
hypocenter	C₃²	C₂×#41
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₃²×#41	C₂	semidirect
2. #3832	C₂	semidirect
3. Q₈×C₃⋊D₃	C₂	semidirect
4. #3830	C₂	semidirect
5. D₄×C₃⋊D₃	C₂	semidirect
6. #3828	C₂	semidirect
7. C₂×C₄×C₃⋊D₃	C₂	semidirect
10. C₃²×Q₈	C₂²	semidirect
11. C₃²×D₄	C₂²	semidirect
12. C₂×C₃²×C₄	C₂²	semidirect
13. #638	C₂²	semidirect
14. C₂×C₃⋊Dic₃	C₂²	semidirect
15. C₄⋊(C₃⋊D₃)	C₂²	semidirect
18. C₄×C₃⋊D₃	C₂²	semidirect
19. C₄×C₃⋊D₃	C₂²	semidirect
20. #634	C₂²	semidirect
21. C₃×#41	D₃	semidirect
38. C₃×Q₈	C₂×D₃	semidirect
39. C₃×D₄	C₂×D₃	semidirect
40. C₂×C₃×C₄	C₂×D₃	semidirect
52. C₃⋊D₃	#41	direct (N × H)
56. #41	C₃⋊D₃	direct (N × H)
68. C₃²	C₂×#41	semidirect
71. Q₈	C₂×C₃⋊D₃	semidirect
74. D₄	C₂×C₃⋊D₃	semidirect
80. C₂×C₄	C₂×C₃⋊D₃	semidirect
93. C₃	D₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#41	2
#3832	2
Q₈×C₃⋊D₃	2
#3830	2
D₄×C₃⋊D₃	2
#3828	2
C₂×C₄×C₃⋊D₃	2
D₃×#41	3

Subgroups — #41×C3⋊D3 #64365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×C₃⋊D₃ #64365