Subgroups — C₄⋊(#41⋊C₃) #5446

Order 192.

87 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41⋊C₃	C₂	1	2	yes	maximal, complemented
2	C₄×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	#550	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	#41⋊C₃	—	2	2	no	—
5	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₃×C₄⋊C₄	—	4	1	no	maximal
7	C₂×#41	C₂×C₃	1	2	yes	—
8	#127	—	3	1	no	—
9	#121	—	3	2	no	—
10	C₄×Q₈	C₂×C₃	1	1	yes	characteristic
11	C₄×D₄	—	3	1	no	—
12	C₂×C₃×C₄	—	4	1	no	—
13	C₂×C₃×C₄	—	4	2	no	—
14	SL(2,𝔽₃)	D₄	1	1	yes	characteristic, complemented
15	#41	—	2	2	no	—
16	#41	—	6	2	no	—
17	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
18	C₂×D₄	—	3	2	no	—
19	C₂×D₄	—	3	2	no	—
20	C₂×D₄	—	3	1	no	—
21	C₂²×C₄	—	3	2	no	—
22	C₄⋊C₄	—	3	1	no	—
23	C₄⋊C₄	A₄	1	1	yes	characteristic
24	C₂²⋊C₄	—	3	2	no	—
25	C₄²	—	3	1	no	—
26	C₂²×C₃	—	4	1	no	—
27	C₃×C₄	—	4	2	no	—
28	C₃×C₄	—	8	2	no	—
29	C₂³	—	3	2	no	—
30	Q₈	—	3	1	no	—
31	Q₈	C₃×D₄	1	1	yes	characteristic
32	D₄	—	6	2	no	—
33	D₄	—	6	2	no	—
34	D₄	—	6	2	no	—
35	D₄	—	12	2	no	—
36	C₂×C₄	—	3	1	no	—
37	C₂×C₄	—	3	1	no	—
38	C₂×C₄	—	6	2	no	—
39	C₂×C₄	—	6	2	no	—
40	C₂×C₄	C₂×A₄	1	2	yes	—
41	C₂×C₄	C₂×A₄	1	1	yes	characteristic
42	C₂×C₃	—	4	1	no	—
43	C₂×C₃	—	4	1	no	—
44	C₂×C₃	—	4	1	no	—
45	C₂²	—	6	2	no	—
46	C₂²	—	6	2	no	—
47	C₂²	—	6	2	no	—
48	C₂²	C₂²×A₄	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	3	1	no	—
51	C₄	—	3	1	no	—
52	C₄	—	6	1	no	—
53	C₄	#41⋊C₃	1	2	yes	complemented
54	C₃	—	4	1	no	Sylow
55	C₂	—	12	2	no	—
56	C₂	D₄×A₄	1	1	yes	characteristic
57	C₂	C₂×#41⋊C₃	1	1	yes	characteristic
58	C₂	#994	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle	C₂²	C₂²×A₄
commutator, cosocle	C₂×Q₈	C₂²×C₃
Fitting	#550	C₃
hypercenter	C₄⋊C₄	A₄
hypocenter	Q₈	C₃×D₄
LCS	G ▷ C₂×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#41⋊C₃	C₂	semidirect
2. C₄×SL(2,𝔽₃)	C₂	semidirect
3. #550	C₃	semidirect
14. SL(2,𝔽₃)	D₄	semidirect
53. C₄	#41⋊C₃	semidirect

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
#550	3
C₃×C₄⋊C₄	4

Subgroups — C4⋊(#41⋊C3) #5446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(#41⋊C₃) #5446