Subgroups — #2971⋊C₃ #73252

Order 384.

117 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₈×SL(2,𝔽₃)	C₂	1	2	yes	maximal, complemented
3	#2971	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂×#41⋊C₃	C₄	1	1	yes	characteristic
5	C₄×SL(2,𝔽₃)	C₄	1	1	yes	characteristic
6	C₄×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
7	C₃×#97	—	4	1	no	maximal
8	C₄×#41	C₂×C₃	1	1	yes	characteristic
9	C₈×Q₈	C₂×C₃	1	2	yes	—
10	#436	—	3	2	no	—
11	#432	—	3	1	no	—
12	C₄×M₁₆	—	3	1	no	—
13	#41⋊C₃	—	2	1	no	—
14	C₂×SL(2,𝔽₃)	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×C₈	—	4	2	no	—
16	C₃×C₄²	—	4	1	no	—
17	C₂×#41	C₃×C₄	1	1	yes	characteristic
18	C₂×M₁₆	—	3	2	no	—
19	C₄×Q₈	C₃×C₄	1	1	yes	characteristic
20	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
21	C₄×D₄	—	3	1	no	—
22	C₄×D₄	—	3	1	no	—
23	#117	—	3	1	no	—
24	C₂×C₄²	—	3	1	no	—
25	C₄⋊C₈	—	3	2	no	—
26	C₂²⋊C₈	—	3	2	no	—
27	#97	—	3	1	no	—
28	#97	A₄	1	1	yes	characteristic
29	C₄×C₈	—	3	2	no	—
30	C₂×C₃×C₄	—	4	1	no	—
31	C₂×C₃×C₄	—	4	1	no	—
32	C₂×C₃×C₄	—	4	1	no	—
33	SL(2,𝔽₃)	M₁₆	1	1	yes	characteristic, complemented
34	C₃×C₈	—	4	4	no	—
35	#41	—	2	1	no	—
36	#41	—	6	1	no	—
37	C₂×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
38	C₂×D₄	—	3	1	no	—
39	C₂²×C₄	—	3	1	no	—
40	C₂²×C₄	—	3	1	no	—
41	C₂²×C₄	—	3	1	no	—
42	M₁₆	—	6	4	no	—
43	C₂×C₈	—	3	2	no	—
44	C₂×C₈	C₂×A₄	1	2	yes	—
45	C₄⋊C₄	—	3	1	no	—
46	C₄⋊C₄	—	3	1	no	—
47	C₂²⋊C₄	—	3	2	no	—
48	C₄²	—	3	1	no	—
49	C₄²	—	3	1	no	—
50	C₄²	—	3	1	no	—
51	C₄²	C₂×A₄	1	1	yes	characteristic
52	C₂²×C₃	—	4	1	no	—
53	C₃×C₄	—	4	2	no	—
54	C₃×C₄	—	8	1	no	—
55	C₃×C₄	—	8	1	no	—
56	C₂³	—	3	1	no	—
57	Q₈	—	3	1	no	—
58	Q₈	C₃×M₁₆	1	1	yes	characteristic
59	D₄	—	6	1	no	—
60	D₄	—	6	1	no	—
61	C₂×C₄	—	3	1	no	—
62	C₂×C₄	—	3	1	no	—
63	C₂×C₄	—	3	1	no	—
64	C₂×C₄	—	6	1	no	—
65	C₂×C₄	—	6	1	no	—
66	C₂×C₄	—	6	2	no	—
67	C₂×C₄	—	12	1	no	—
68	C₂×C₄	C₄×A₄	1	1	yes	characteristic
69	C₂×C₄	C₄×A₄	1	1	yes	characteristic
70	C₂×C₄	C₂²×A₄	1	1	yes	characteristic
71	C₈	—	6	2	no	—
72	C₈	#41⋊C₃	1	4	yes	complemented
73	C₂×C₃	—	4	1	no	—
74	C₂×C₃	—	4	1	no	—
75	C₂×C₃	—	4	1	no	—
76	C₂²	—	6	1	no	—
77	C₂²	—	6	1	no	—
78	C₂²	—	6	1	no	—
79	C₂²	C₂×C₄×A₄	1	1	yes	characteristic
80	C₄	—	2	1	no	—
81	C₄	—	2	1	no	—
82	C₄	—	3	1	no	—
83	C₄	—	3	1	no	—
84	C₄	—	6	1	no	—
85	C₄	—	6	1	no	—
86	C₄	C₂×#41⋊C₃	1	2	yes	—
87	C₃	—	4	1	no	Sylow
88	C₂	—	12	1	no	—
89	C₂	C₄×#41⋊C₃	1	1	yes	characteristic
90	C₂	A₄×M₁₆	1	1	yes	characteristic
91	C₂	#568⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×A₄
commutator	C₂×Q₈	C₂×C₃×C₄
Fitting	#2971	C₃
socle	C₂²	C₂×C₄×A₄
prime radical	C₂×#41⋊C₃	C₄
cosocle	C₄×Q₈	C₂²×C₃
hypercenter	#97	A₄
hypocenter	Q₈	C₃×M₁₆
LCS	G ▷ C₂×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
2. C₈×SL(2,𝔽₃)	C₂	semidirect
3. #2971	C₃	semidirect
33. SL(2,𝔽₃)	M₁₆	semidirect
72. 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
#2971	3
C₃×#97	4

Subgroups — #2971⋊C3 #73252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2971⋊C₃ #73252