Subgroups — C₄×#41⋊C₃ #5438

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×SL(2,𝔽₃)	C₂	1	2	yes	maximal, complemented
3	C₄×#41	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	#41⋊C₃	C₄	1	2	yes	direct product factor
5	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₃×C₄²	—	4	1	no	maximal
7	C₂×#41	C₂×C₃	1	1	yes	characteristic
8	C₄×Q₈	C₂×C₃	1	2	yes	—
9	C₄×D₄	—	3	2	no	—
10	#117	—	3	1	no	—
11	C₂×C₄²	—	3	1	no	—
12	C₂×C₃×C₄	—	4	2	no	—
13	C₂×C₃×C₄	—	4	1	no	—
14	SL(2,𝔽₃)	C₂×C₄	1	1	yes	characteristic, complemented
15	#41	—	3	2	no	—
16	#41	C₃×C₄	1	2	yes	complemented
17	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
18	C₂×D₄	—	3	1	no	—
19	C₂²×C₄	—	3	1	no	—
20	C₂²×C₄	—	3	2	no	—
21	C₄⋊C₄	—	3	2	no	—
22	C₂²⋊C₄	—	3	2	no	—
23	C₄²	—	3	1	no	—
24	C₄²	—	3	2	no	—
25	C₄²	A₄	1	1	yes	characteristic
26	C₂²×C₃	—	4	1	no	—
27	C₃×C₄	—	4	2	no	—
28	C₃×C₄	—	4	4	no	—
29	C₂³	—	3	1	no	—
30	Q₈	—	3	1	no	—
31	Q₈	C₂×C₃×C₄	1	1	yes	characteristic
32	D₄	—	3	2	no	—
33	D₄	—	3	2	no	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₄	—	3	2	no	—
36	C₂×C₄	—	3	2	no	—
37	C₂×C₄	—	3	2	no	—
38	C₂×C₄	—	6	4	no	—
39	C₂×C₄	C₂×A₄	1	1	yes	characteristic
40	C₂×C₄	C₂×A₄	1	2	yes	—
41	C₂×C₃	—	4	1	no	—
42	C₂×C₃	—	4	2	no	—
43	C₂²	—	3	2	no	—
44	C₂²	—	6	2	no	—
45	C₂²	C₂²×A₄	1	1	yes	characteristic
46	C₄	—	3	1	no	—
47	C₄	—	3	1	no	—
48	C₄	—	6	2	no	—
49	C₄	C₄×A₄	1	2	yes	—
50	C₄	#41⋊C₃	1	4	yes	direct product factor
51	C₃	—	4	1	no	Sylow
52	C₂	—	6	2	no	—
53	C₂	C₂×C₄×A₄	1	1	yes	characteristic
54	C₂	C₂×#41⋊C₃	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄²	A₄
commutator, hypocenter	Q₈	C₂×C₃×C₄
Frattini, socle	C₂²	C₂²×A₄
Fitting	C₄×#41	C₃
prime radical	C₂×#41⋊C₃	C₂
cosocle	C₂×Q₈	C₂²×C₃
LCS	G ▷ Q₈
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄×SL(2,𝔽₃)	C₂	semidirect
3. C₄×#41	C₃	semidirect
4. #41⋊C₃	C₄	direct (N × H)
14. SL(2,𝔽₃)	C₂×C₄	semidirect
16. #41	C₃×C₄	semidirect
50. C₄	#41⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#41⋊C₃	2
C₄×SL(2,𝔽₃)	2
C₄×#41	3
C₃×C₄²	4

Subgroups — C4×#41⋊C3 #5438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#41⋊C₃ #5438