Subgroups — #2916⋊C₃ #73248

Order 384.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#568⋊C₃	C₂	1	2	yes	maximal
2	C₂×#131⋊C₃	C₂	1	1	yes	maximal, characteristic
3	#2916	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂×#41⋊C₃	C₂²	1	1	yes	characteristic
5	#131⋊C₃	—	2	2	no	—
6	#131⋊C₃	C₄	1	2	yes	—
7	C₃×#108	—	4	1	no	maximal
8	#568	C₂×C₃	1	2	yes	—
9	C₂×#131	C₂×C₃	1	1	yes	characteristic
10	#430	—	3	2	no	—
11	C₂×#108	—	3	1	no	—
12	C₂×#108	—	3	1	no	—
13	#41⋊C₃	C₂×C₄	1	1	yes	characteristic
14	#41⋊C₃	D₄	1	1	yes	characteristic
15	C₂×SL(2,𝔽₃)	Q₈	1	1	yes	characteristic
16	C₃×M₁₆	—	4	2	no	—
17	C₂×C₃×C₈	—	4	1	no	—
18	C₂×#41	C₂²×C₃	1	1	yes	characteristic
19	#131	—	2	2	no	—
20	#131	—	3	2	no	—
21	#131	—	6	2	no	—
22	#131	C₃×C₄	1	2	yes	—
23	C₂×M₁₆	—	3	1	no	—
24	C₂×M₁₆	—	3	2	no	—
25	C₂×M₁₆	—	3	2	no	—
26	C₂²×C₈	—	3	1	no	—
27	#108	—	3	2	no	—
28	#108	—	3	2	no	—
29	#108	—	3	1	no	—
30	#108	A₄	1	1	yes	characteristic
31	C₂×C₃×C₄	—	4	1	no	—
32	SL(2,𝔽₃)	C₄⋊C₄	1	1	yes	characteristic
33	C₃×C₈	—	4	2	no	—
34	C₃×C₈	—	8	2	no	—
35	#41	—	3	1	no	—
36	#41	—	3	1	no	—
37	#41	C₂×C₃×C₄	1	1	yes	characteristic
38	#41	C₃×D₄	1	1	yes	characteristic
39	C₂×Q₈	C₃×Q₈	1	1	yes	characteristic
40	C₂×D₄	—	3	1	no	—
41	C₂²×C₄	—	3	1	no	—
42	M₁₆	—	3	2	no	—
43	M₁₆	—	3	2	no	—
44	M₁₆	—	3	2	no	—
45	M₁₆	—	6	2	no	—
46	M₁₆	—	6	2	no	—
47	M₁₆	C₂×A₄	1	2	yes	—
48	C₂×C₈	—	3	1	no	—
49	C₂×C₈	—	3	2	no	—
50	C₂×C₈	—	3	2	no	—
51	C₂×C₈	—	6	2	no	—
52	C₂×C₈	—	6	2	no	—
53	C₂×C₈	C₂×A₄	1	1	yes	characteristic
54	C₂²×C₃	—	4	1	no	—
55	C₃×C₄	—	4	1	no	—
56	C₃×C₄	—	4	1	no	—
57	C₂³	—	3	1	no	—
58	Q₈	—	3	1	no	—
59	Q₈	C₃×C₄⋊C₄	1	1	yes	characteristic
60	D₄	—	3	1	no	—
61	D₄	—	3	1	no	—
62	D₄	—	3	2	no	—
63	C₂×C₄	—	3	1	no	—
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	3	1	no	—
66	C₂×C₄	—	3	1	no	—
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	C₂²×A₄	1	1	yes	characteristic
69	C₈	—	2	2	no	—
70	C₈	—	3	2	no	—
71	C₈	—	6	2	no	—
72	C₈	C₄×A₄	1	2	yes	—
73	C₂×C₃	—	4	1	no	—
74	C₂×C₃	—	8	1	no	—
75	C₂²	—	3	1	no	—
76	C₂²	—	3	1	no	—
77	C₂²	—	12	1	no	—
78	C₂²	Q₈×A₄	1	1	yes	characteristic
79	C₄	—	3	1	no	—
80	C₄	—	3	1	no	—
81	C₄	C₂×C₄×A₄	1	1	yes	characteristic
82	C₄	D₄×A₄	1	1	yes	characteristic
83	C₃	—	4	1	no	Sylow
84	C₂	—	2	1	no	—
85	C₂	—	6	1	no	—
86	C₂	—	6	1	no	—
87	C₂	A₄×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×A₄
commutator	#41	C₂×C₃×C₄
Frattini	C₂×C₄	C₂²×A₄
Fitting	#2916	C₃
socle	C₂	A₄×C₄⋊C₄
prime radical	C₂×#41⋊C₃	C₂²
cosocle	C₂×#41	C₂²×C₃
hypercenter	#108	A₄
hypocenter	Q₈	C₃×C₄⋊C₄
LCS	G ▷ #41 ▷ Q₈
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. #2916	C₃	semidirect

Maximal subgroups

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

subgroup	index
#568⋊C₃	2
C₂×#131⋊C₃	2
#2916	3
C₃×#108	4

Subgroups — #2916⋊C3 #73248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2916⋊C₃ #73248