Subgroups — #3391⋊C₃ #73270

Order 384.

125 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(#41⋊C₃)	C₂	1	2	yes	maximal, complemented
2	C₈×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	#3391	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂×#41⋊C₃	—	2	2	no	—
5	C₄×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₃×#107	—	4	1	no	maximal
7	#550	C₂×C₃	1	2	yes	—
8	#493	—	3	1	no	—
9	#459	—	3	2	no	—
10	C₈×Q₈	C₂×C₃	1	1	yes	characteristic
11	C₄×D₈	—	3	1	no	—
12	#41⋊C₃	—	4	2	no	—
13	C₂×SL(2,𝔽₃)	D₄	1	1	yes	characteristic
14	C₂×C₃×C₈	—	4	1	no	—
15	C₃×C₄⋊C₄	—	4	2	no	—
16	C₂×#41	—	2	2	no	—
17	C₂×D₈	—	3	2	no	—
18	C₂×D₈	—	3	1	no	—
19	#127	—	3	2	no	—
20	#121	—	6	2	no	—
21	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
22	C₄×D₄	—	3	2	no	—
23	#107	A₄	1	1	yes	characteristic
24	C₄⋊C₈	—	3	1	no	—
25	#102	—	3	2	no	—
26	C₄×C₈	—	3	1	no	—
27	C₂×C₃×C₄	—	4	1	no	—
28	C₂×C₃×C₄	—	8	2	no	—
29	SL(2,𝔽₃)	D₈	1	1	yes	characteristic, complemented
30	C₃×C₈	—	4	2	no	—
31	#41	—	4	2	no	—
32	#41	—	12	2	no	—
33	C₂×Q₈	C₃×D₄	1	1	yes	characteristic
34	C₂×D₄	—	3	2	no	—
35	C₂×D₄	—	6	2	no	—
36	C₂×D₄	—	6	2	no	—
37	C₂²×C₄	—	6	2	no	—
38	D₈	—	6	2	no	—
39	D₈	—	12	2	no	—
40	C₂×C₈	—	3	1	no	—
41	C₂×C₈	C₂×A₄	1	1	yes	characteristic
42	C₄⋊C₄	—	3	1	no	—
43	C₄⋊C₄	C₂×A₄	1	2	yes	—
44	C₂²⋊C₄	—	6	2	no	—
45	C₄²	—	3	1	no	—
46	C₂²×C₃	—	4	1	no	—
47	C₃×C₄	—	4	1	no	—
48	C₃×C₄	—	4	1	no	—
49	C₃×C₄	—	16	2	no	—
50	C₂³	—	6	2	no	—
51	Q₈	—	3	1	no	—
52	Q₈	C₃×D₈	1	1	yes	characteristic
53	D₄	—	6	2	no	—
54	D₄	—	6	2	no	—
55	D₄	—	12	2	no	—
56	D₄	—	12	2	no	—
57	D₄	—	24	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	3	1	no	—
60	C₂×C₄	—	3	1	no	—
61	C₂×C₄	—	12	2	no	—
62	C₂×C₄	—	12	2	no	—
63	C₂×C₄	C₂²×A₄	1	1	yes	characteristic
64	C₈	—	6	1	no	—
65	C₈	#41⋊C₃	1	2	yes	complemented
66	C₂×C₃	—	4	1	no	—
67	C₂×C₃	—	4	1	no	—
68	C₂×C₃	—	4	1	no	—
69	C₂²	—	12	2	no	—
70	C₂²	—	12	2	no	—
71	C₂²	—	12	2	no	—
72	C₂²	D₄×A₄	1	1	yes	characteristic
73	C₄	—	3	1	no	—
74	C₄	—	3	1	no	—
75	C₄	—	4	2	no	—
76	C₄	—	6	1	no	—
77	C₄	C₂×#41⋊C₃	1	1	yes	characteristic
78	C₄	#994	1	1	yes	characteristic
79	C₃	—	4	1	no	Sylow
80	C₂	—	24	2	no	—
81	C₂	C₄⋊(#41⋊C₃)	1	1	yes	characteristic
82	C₂	A₄×D₈	1	1	yes	characteristic
83	C₂	#576⋊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	#3391	C₃
hypercenter	#107	A₄
hypocenter	Q₈	C₃×D₈
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
1. C₄⋊(#41⋊C₃)	C₂	semidirect
2. C₈×SL(2,𝔽₃)	C₂	semidirect
3. #3391	C₃	semidirect
29. SL(2,𝔽₃)	D₈	semidirect
65. C₈	#41⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊(#41⋊C₃)	2
C₈×SL(2,𝔽₃)	2
#3391	3
C₃×#107	4

Subgroups — #3391⋊C3 #73270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3391⋊C₃ #73270