Subgroups — C₃×#354 #4601

Order 192.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#124	C₂	1	1	yes	maximal, characteristic
2	C₃×#99	C₂	1	2	yes	maximal
3	#354	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×Q₈	C₄	1	1	yes	characteristic, complemented
5	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
6	C₃×C₂²⋊C₄	—	2	2	no	—
7	C₃×C₂²⋊C₄	—	2	2	no	—
8	C₃×C₄²	C₄	1	1	yes	characteristic, complemented
9	#124	C₂×C₃	1	1	yes	characteristic
10	#99	C₂×C₃	1	2	yes	—
11	C₂³×C₃	D₄	1	2	yes	—
12	C₃×Q₈	—	4	1	no	—
13	C₃×D₄	—	4	1	no	—
14	C₂×C₃×C₄	—	2	1	no	—
15	C₂×C₃×C₄	—	2	1	no	—
16	C₂×C₃×C₄	—	4	2	no	—
17	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×Q₈	C₃×C₄	1	1	yes	characteristic, complemented
19	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
20	C₂²⋊C₄	—	2	2	no	—
21	C₂²⋊C₄	—	2	2	no	—
22	C₄²	C₃×C₄	1	1	yes	characteristic, complemented
23	C₂²×C₃	—	2	2	no	—
24	C₂²×C₃	—	4	2	no	—
25	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₃×C₄	—	2	1	no	—
27	C₃×C₄	—	4	1	no	—
28	C₃×C₄	—	4	1	no	—
29	C₃×C₄	—	8	2	no	—
30	C₂³	C₃×D₄	1	2	yes	—
31	Q₈	—	4	1	no	—
32	D₄	—	4	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	4	2	no	—
36	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
37	C₂×C₃	—	2	1	no	—
38	C₂×C₃	—	4	2	no	—
39	C₂×C₃	#99	1	1	yes	characteristic
40	C₂²	—	2	2	no	—
41	C₂²	—	4	2	no	—
42	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	4	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	8	2	no	—
47	C₃	#354	1	1	yes	characteristic, direct product factor, Sylow
48	C₂	—	2	1	no	—
49	C₂	—	4	2	no	—
50	C₂	C₃×#99	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#99
commutator	C₂×C₄	C₂×C₃×C₄
Frattini, cosocle	C₂×D₄	C₂²×C₃
prime radical	C₂×C₃×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃ ◁ C₂×C₃×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. #354	C₃	direct (N × H)
4. C₂×C₃×Q₈	C₄	semidirect
8. C₃×C₄²	C₄	semidirect
18. C₂×Q₈	C₃×C₄	semidirect
22. C₄²	C₃×C₄	semidirect
47. C₃	#354	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#124	2
C₃×#99	2
#354	3

Subgroups — C3×#354 #4601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#354 #4601