Subgroups — C₃×#379 #5253

Order 192.

506 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₂²⋊C₄	C₂	1	6	yes	maximal, complemented
3	#379	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂⁴×C₃	—	2	12	no	—
5	C₂⁴×C₃	C₄	1	4	yes	complemented
6	C₂⁴×C₃	C₂²	1	3	yes	—
7	C₂²×C₃×C₄	C₂²	1	4	yes	complemented
8	C₃×C₂²⋊C₄	—	2	12	no	—
9	C₂⁵	C₂×C₃	1	1	yes	characteristic
10	C₂×C₂²⋊C₄	C₂×C₃	1	6	yes	complemented
11	C₂³×C₃	—	2	32	no	—
12	C₂³×C₃	—	2	24	no	—
13	C₂³×C₃	—	2	12	no	—
14	C₂³×C₃	C₂×C₄	1	6	yes	—
15	C₂³×C₃	D₄	1	12	yes	—
16	C₂³×C₃	C₂³	1	1	yes	characteristic
17	C₂×C₃×C₄	—	2	12	no	—
18	C₂⁴	—	2	12	no	—
19	C₂⁴	C₃×C₄	1	4	yes	complemented
20	C₂⁴	C₂²×C₃	1	3	yes	—
21	C₂²×C₄	C₂²×C₃	1	4	yes	complemented
22	C₂²⋊C₄	—	2	12	no	—
23	C₂²×C₃	—	2	32	no	—
24	C₂²×C₃	—	2	12	no	—
25	C₂²×C₃	—	2	24	no	—
26	C₂²×C₃	C₂²⋊C₄	1	12	yes	complemented
27	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₃	C₂×D₄	1	6	yes	—
29	C₃×C₄	—	4	4	no	—
30	C₂³	—	2	32	no	—
31	C₂³	—	2	24	no	—
32	C₂³	—	2	12	no	—
33	C₂³	C₂×C₃×C₄	1	6	yes	—
34	C₂³	C₃×D₄	1	12	yes	—
35	C₂³	C₂³×C₃	1	1	yes	characteristic
36	C₂×C₄	—	2	12	no	—
37	C₂×C₃	—	2	12	no	—
38	C₂×C₃	C₂×C₂²⋊C₄	1	3	yes	—
39	C₂×C₃	#120	1	4	yes	—
40	C₂²	—	2	32	no	—
41	C₂²	—	2	12	no	—
42	C₂²	—	2	24	no	—
43	C₂²	C₃×C₂²⋊C₄	1	12	yes	complemented
44	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
45	C₂²	C₂×C₃×D₄	1	6	yes	—
46	C₄	—	4	4	no	—
47	C₃	#379	1	1	yes	characteristic, direct product factor, Sylow
48	C₂	—	2	12	no	—
49	C₂	C₂×C₃×C₂²⋊C₄	1	3	yes	—
50	C₂	C₃×#120	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂³
commutator	C₂²	C₂²×C₃×C₄
Frattini, cosocle	C₂³	C₂³×C₃
prime radical	C₂⁵×C₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₂²⋊C₄	C₂	semidirect
3. #379	C₃	direct (N × H)
5. C₂⁴×C₃	C₄	semidirect
7. C₂²×C₃×C₄	C₂²	semidirect
10. C₂×C₂²⋊C₄	C₂×C₃	semidirect
19. C₂⁴	C₃×C₄	semidirect
21. C₂²×C₄	C₂²×C₃	semidirect
26. C₂²×C₃	C₂²⋊C₄	semidirect
43. C₂²	C₃×C₂²⋊C₄	semidirect
47. C₃	#379	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₃	2
C₂×C₃×C₂²⋊C₄	2
#379	3

Subgroups — C3×#379 #5253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#379 #5253