Subgroups — #3416⋊C₃ #73281

Order 384.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#578⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#576⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#504⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#3416	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
5	2₋¹⁺⁴⋊C₃	—	2	1	no	—
6	#994	—	2	1	no	—
7	#131⋊C₃	C₂²	1	1	yes	characteristic
8	C₃×SD₃₂	—	4	1	no	maximal
9	#578	C₂×C₃	1	1	yes	characteristic
10	#576	C₂×C₃	1	1	yes	characteristic, complemented
11	#510	—	3	1	no	—
12	#509	—	3	1	no	—
13	#508	—	3	1	no	—
14	C₂×SD₃₂	—	3	1	no	—
15	#504	C₂×C₃	1	1	yes	characteristic, complemented
16	#41⋊C₃	—	4	1	no	—
17	#41⋊C₃	D₄	1	1	yes	characteristic
18	C₂×SL(2,𝔽₃)	—	4	1	no	—
19	C₃×Q₁₆	—	4	1	no	—
20	C₃×D₈	—	4	1	no	—
21	C₃×C₁₆	—	4	1	no	—
22	2₋¹⁺⁴	—	2	1	no	—
23	H(5,𝔽₂)	—	2	1	no	—
24	#137	—	6	1	no	—
25	AGL(1,ℤ/8)	—	6	1	no	—
26	#135	—	3	1	no	—
27	#135	—	3	1	no	—
28	C₂×Q₁₆	—	3	1	no	—
29	C₂×D₈	—	3	1	no	—
30	#131	C₂²×C₃	1	1	yes	characteristic
31	Q₃₂	—	3	1	no	—
32	SD₃₂	—	3	2	no	—
33	SD₃₂	—	3	1	no	—
34	SD₃₂	A₄	1	1	yes	characteristic
35	D₁₆	—	3	1	no	—
36	M₃₂	—	3	1	no	—
37	C₂×C₁₆	—	3	1	no	—
38	C₃×Q₈	—	8	1	no	—
39	C₃×D₄	—	8	1	no	—
40	SL(2,𝔽₃)	D₈	1	1	yes	characteristic
41	C₃×C₈	—	4	1	no	—
42	#41	—	4	1	no	—
43	#41	—	6	1	no	—
44	#41	—	6	1	no	—
45	#41	—	12	1	no	—
46	#41	C₃×D₄	1	1	yes	characteristic
47	C₂×Q₈	—	4	1	no	—
48	C₂×Q₈	—	6	1	no	—
49	C₂×D₄	—	6	1	no	—
50	C₂×D₄	—	12	1	no	—
51	Q₁₆	—	3	1	no	—
52	Q₁₆	—	6	1	no	—
53	Q₁₆	C₂×A₄	1	1	yes	characteristic
54	SD₁₆	—	6	1	no	—
55	SD₁₆	—	6	1	no	—
56	D₈	—	3	1	no	—
57	D₈	—	6	1	no	—
58	D₈	C₂×A₄	1	1	yes	characteristic
59	M₁₆	—	3	1	no	—
60	C₂×C₈	—	3	1	no	—
61	C₁₆	—	3	1	no	—
62	C₁₆	C₂×A₄	1	1	yes	characteristic
63	C₂²×C₃	—	16	1	no	—
64	C₃×C₄	—	4	1	no	—
65	C₃×C₄	—	16	1	no	—
66	C₂³	—	12	1	no	—
67	Q₈	—	2	1	no	—
68	Q₈	—	6	1	no	—
69	Q₈	—	12	1	no	—
70	Q₈	C₃×D₈	1	1	yes	characteristic
71	D₄	—	2	1	no	—
72	D₄	—	3	1	no	—
73	D₄	—	6	1	no	—
74	D₄	—	12	1	no	—
75	D₄	—	12	1	no	—
76	D₄	—	12	1	no	—
77	C₂×C₄	—	3	1	no	—
78	C₂×C₄	—	12	1	no	—
79	C₂×C₄	—	12	1	no	—
80	C₂×C₄	—	12	1	no	—
81	C₈	—	3	1	no	—
82	C₈	C₂²×A₄	1	1	yes	characteristic
83	C₂×C₃	—	4	1	no	—
84	C₂×C₃	—	32	1	no	—
85	C₂²	—	3	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	—	12	1	no	—
88	C₂²	—	48	1	no	—
89	C₄	—	3	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	12	1	no	—
92	C₄	D₄×A₄	1	1	yes	characteristic
93	C₃	—	4	1	no	Sylow
94	C₂	—	6	1	no	—
95	C₂	—	8	1	no	—
96	C₂	—	24	1	no	—
97	C₂	A₄×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	A₄×D₈
commutator, cosocle	#131	C₂²×C₃
Frattini	C₈	C₂²×A₄
Fitting	#3416	C₃
hypercenter	SD₃₂	A₄
hypocenter	Q₈	C₃×D₈
LCS	G ▷ #131 ▷ #41 ▷ Q₈
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. #578⋊C₃	C₂	semidirect
2. #576⋊C₃	C₂	semidirect
3. #504⋊C₃	C₂	semidirect
4. #3416	C₃	semidirect
10. #576	C₂×C₃	semidirect
15. #504	C₂×C₃	semidirect

Maximal subgroups

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

subgroup	index
#578⋊C₃	2
#576⋊C₃	2
#504⋊C₃	2
#3416	3
C₃×SD₃₂	4

Subgroups — #3416⋊C3 #73281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3416⋊C₃ #73281