Subgroups — #3395⋊C₃ #73272

Order 384.

103 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#557⋊C₃	C₂	1	2	yes	maximal
2	C₈×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
3	#3395	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₄×SL(2,𝔽₃)	—	2	2	no	—
5	C₄×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₃×#107	—	4	1	no	maximal
7	#557	C₂×C₃	1	2	yes	—
8	#494	—	3	1	no	—
9	#462	—	3	2	no	—
10	C₈×Q₈	C₂×C₃	1	1	yes	characteristic
11	C₄×Q₁₆	—	3	1	no	—
12	C₂×SL(2,𝔽₃)	D₄	1	1	yes	characteristic
13	C₂×C₃×C₈	—	4	1	no	—
14	C₃×C₄⋊C₄	—	4	2	no	—
15	C₂×Q₁₆	—	3	2	no	—
16	C₂×Q₁₆	—	3	1	no	—
17	C₄⋊Q₈	—	3	2	no	—
18	#125	—	6	2	no	—
19	C₄×Q₈	—	2	2	no	—
20	C₄×Q₈	—	3	2	no	—
21	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
22	#107	A₄	1	1	yes	characteristic
23	C₄⋊C₈	—	3	1	no	—
24	#103	—	3	2	no	—
25	C₄×C₈	—	3	1	no	—
26	C₂×C₃×C₄	—	4	1	no	—
27	C₂×C₃×C₄	—	8	2	no	—
28	SL(2,𝔽₃)	Q₁₆	1	1	yes	characteristic, complemented
29	C₃×C₈	—	4	2	no	—
30	C₂×Q₈	—	3	2	no	—
31	C₂×Q₈	C₃×D₄	1	1	yes	characteristic
32	Q₁₆	—	6	2	no	—
33	Q₁₆	—	12	2	no	—
34	C₂×C₈	—	3	1	no	—
35	C₂×C₈	C₂×A₄	1	1	yes	characteristic
36	C₄⋊C₄	—	3	1	no	—
37	C₄⋊C₄	—	6	2	no	—
38	C₄⋊C₄	—	6	2	no	—
39	C₄⋊C₄	—	6	2	no	—
40	C₄⋊C₄	C₂×A₄	1	2	yes	—
41	C₄²	—	3	1	no	—
42	C₄²	—	6	2	no	—
43	C₂²×C₃	—	4	1	no	—
44	C₃×C₄	—	4	1	no	—
45	C₃×C₄	—	4	1	no	—
46	C₃×C₄	—	16	2	no	—
47	Q₈	—	3	1	no	—
48	Q₈	—	6	2	no	—
49	Q₈	—	6	2	no	—
50	Q₈	C₃×Q₁₆	1	1	yes	characteristic
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	3	1	no	—
53	C₂×C₄	—	3	1	no	—
54	C₂×C₄	—	6	2	no	—
55	C₂×C₄	C₂²×A₄	1	1	yes	characteristic
56	C₈	—	6	1	no	—
57	C₈	#41⋊C₃	1	2	yes	—
58	C₂×C₃	—	4	1	no	—
59	C₂×C₃	—	4	1	no	—
60	C₂×C₃	—	4	1	no	—
61	C₂²	D₄×A₄	1	1	yes	characteristic
62	C₄	—	3	1	no	—
63	C₄	—	3	1	no	—
64	C₄	—	4	2	no	—
65	C₄	—	6	1	no	—
66	C₄	—	12	2	no	—
67	C₄	C₂×#41⋊C₃	1	1	yes	characteristic
68	C₄	#994	1	1	yes	characteristic
69	C₃	—	4	1	no	Sylow
70	C₂	C₄⋊(#41⋊C₃)	1	1	yes	characteristic
71	C₂	A₄×Q₁₆	1	1	yes	characteristic
72	C₂	#578⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₄×A₄
commutator, cosocle	C₄×Q₈	C₂²×C₃
Frattini	C₂×C₄	C₂²×A₄
Fitting	#3395	C₃
prime radical	C₂×SL(2,𝔽₃)	D₄
hypercenter	#107	A₄
hypocenter	Q₈	C₃×Q₁₆
LCS	G ▷ C₄×Q₈ ▷ C₂×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. #3395	C₃	semidirect
28. SL(2,𝔽₃)	Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
#557⋊C₃	2
C₈×SL(2,𝔽₃)	2
#3395	3
C₃×#107	4

Subgroups — #3395⋊C3 #73272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3395⋊C₃ #73272