Subgroups — C₂²×#41⋊C₃ #5941

Order 192.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41⋊C₃	C₂	1	6	yes	maximal, direct product factor
2	C₂²×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#41	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
4	C₂²×C₃×C₄	—	4	1	no	maximal
5	#41⋊C₃	C₂²	1	4	yes	direct product factor
6	C₂×SL(2,𝔽₃)	C₂²	1	3	yes	complemented
7	C₂×#41	—	3	6	no	—
8	C₂×#41	C₂×C₃	1	6	yes	complemented
9	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic
10	C₂²×D₄	—	3	1	no	—
11	C₂³×C₄	—	3	1	no	—
12	C₂³×C₃	—	4	1	no	—
13	C₂×C₃×C₄	—	4	6	no	—
14	SL(2,𝔽₃)	C₂³	1	1	yes	characteristic, complemented
15	C₂⁴	—	3	1	no	—
16	#41	—	3	8	no	—
17	#41	—	3	12	no	—
18	#41	C₂²×C₃	1	4	yes	complemented
19	C₂×Q₈	—	3	3	no	—
20	C₂×Q₈	C₂²×C₃	1	3	yes	—
21	C₂×D₄	—	3	6	no	—
22	C₂×D₄	—	3	6	no	—
23	C₂²×C₄	—	3	1	no	—
24	C₂²×C₄	—	3	6	no	—
25	C₂²×C₄	—	3	6	no	—
26	C₂²×C₄	A₄	1	1	yes	characteristic
27	C₂²×C₃	—	4	4	no	—
28	C₂²×C₃	—	4	3	no	—
29	C₃×C₄	—	4	4	no	—
30	C₂³	—	3	6	no	—
31	C₂³	—	6	4	no	—
32	C₂³	C₂×A₄	1	1	yes	characteristic
33	Q₈	—	3	3	no	—
34	Q₈	—	3	2	no	—
35	Q₈	C₂³×C₃	1	1	yes	characteristic
36	D₄	—	3	4	no	—
37	D₄	—	3	12	no	—
38	C₂×C₄	—	3	3	no	—
39	C₂×C₄	—	3	3	no	—
40	C₂×C₄	—	3	12	no	—
41	C₂×C₄	—	3	4	no	—
42	C₂×C₄	C₂×A₄	1	6	yes	—
43	C₂×C₃	—	4	6	no	—
44	C₂×C₃	—	4	1	no	—
45	C₂²	—	3	4	no	—
46	C₂²	—	6	12	no	—
47	C₂²	#41⋊C₃	1	4	yes	direct product factor
48	C₂²	C₂²×A₄	1	3	yes	—
49	C₄	—	3	3	no	—
50	C₄	—	3	1	no	—
51	C₄	C₂²×A₄	1	4	yes	—
52	C₃	—	4	1	no	Sylow
53	C₂	—	6	4	no	—
54	C₂	C₂×#41⋊C₃	1	6	yes	direct product factor
55	C₂	C₂³×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	A₄
commutator, cosocle, hypocenter	Q₈	C₂³×C₃
Frattini	C₂	C₂³×A₄
Fitting	C₂²×#41	C₃
socle	C₂³	C₂×A₄
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#41⋊C₃	C₂	direct (N × H)
2. C₂²×SL(2,𝔽₃)	C₂	semidirect
3. C₂²×#41	C₃	semidirect
5. #41⋊C₃	C₂²	direct (N × H)
6. C₂×SL(2,𝔽₃)	C₂²	semidirect
8. C₂×#41	C₂×C₃	semidirect
14. SL(2,𝔽₃)	C₂³	semidirect
18. #41	C₂²×C₃	semidirect
47. C₂²	#41⋊C₃	direct (N × H)
54. C₂	C₂×#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
C₂²×SL(2,𝔽₃)	2
C₂²×#41	3
C₂²×C₃×C₄	4

Subgroups — C22×#41⋊C3 #5941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#41⋊C₃ #5941