Subgroups — C₃×#544 #5874

Order 192.

206 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	4	yes	maximal, complemented
2	C₃×#125	C₂	1	4	yes	maximal, complemented
3	C₃×C₂²⋊Q₈	C₂	1	4	yes	maximal
4	C₃×#117	C₂	1	2	yes	maximal
5	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
6	#544	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	4	yes	—
8	C₂²×C₃×C₄	C₂²	1	2	yes	—
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₃×C₄⋊C₄	C₂²	1	4	yes	—
11	C₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₄⋊C₄	C₂²	1	4	yes	—
14	C₃×C₄⋊C₄	C₂²	1	8	yes	—
15	C₃×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₃×C₄²	C₂²	1	4	yes	—
17	C₄⋊Q₈	C₂×C₃	1	4	yes	complemented
18	#125	C₂×C₃	1	4	yes	complemented
19	C₂²⋊Q₈	C₂×C₃	1	4	yes	—
20	#117	C₂×C₃	1	2	yes	—
21	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
22	C₂³×C₃	C₂³	1	1	yes	characteristic
23	C₃×Q₈	—	4	4	no	—
24	C₂×C₃×C₄	—	4	2	no	—
25	C₂×C₃×C₄	Q₈	1	4	yes	complemented
26	C₂×C₃×C₄	C₂³	1	4	yes	—
27	C₂×C₃×C₄	C₂³	1	4	yes	—
28	C₂×C₃×C₄	C₂³	1	4	yes	—
29	C₂×C₃×C₄	C₂³	1	2	yes	—
30	C₂×Q₈	C₂²×C₃	1	4	yes	—
31	C₂²×C₄	C₂²×C₃	1	2	yes	—
32	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
33	C₄⋊C₄	C₂²×C₃	1	4	yes	—
34	C₄⋊C₄	C₂²×C₃	1	2	yes	—
35	C₄⋊C₄	C₂²×C₃	1	2	yes	—
36	C₄⋊C₄	C₂²×C₃	1	4	yes	—
37	C₄⋊C₄	C₂²×C₃	1	8	yes	—
38	C₂²⋊C₄	C₂²×C₃	1	4	yes	—
39	C₄²	C₂²×C₃	1	4	yes	—
40	C₂²×C₃	—	2	1	no	—
41	C₂²×C₃	—	2	1	no	—
42	C₂²×C₃	C₂×Q₈	1	2	yes	—
43	C₂²×C₃	C₂⁴	1	1	yes	characteristic
44	C₃×C₄	—	2	4	no	—
45	C₃×C₄	—	2	4	no	—
46	C₃×C₄	—	2	4	no	—
47	C₃×C₄	C₂×Q₈	1	4	yes	—
48	C₂³	C₂³×C₃	1	1	yes	characteristic
49	Q₈	—	4	4	no	—
50	C₂×C₄	—	4	2	no	—
51	C₂×C₄	C₃×Q₈	1	4	yes	complemented
52	C₂×C₄	C₂³×C₃	1	4	yes	—
53	C₂×C₄	C₂³×C₃	1	4	yes	—
54	C₂×C₄	C₂³×C₃	1	4	yes	—
55	C₂×C₄	C₂³×C₃	1	2	yes	—
56	C₂×C₃	—	2	2	no	—
57	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
58	C₂×C₃	H(5,𝔽₂)	1	1	yes	characteristic
59	C₂×C₃	2₋¹⁺⁴	1	1	yes	characteristic
60	C₂²	—	2	1	no	—
61	C₂²	—	2	1	no	—
62	C₂²	C₂×C₃×Q₈	1	2	yes	—
63	C₂²	C₂⁴×C₃	1	1	yes	characteristic
64	C₄	—	2	4	no	—
65	C₄	—	2	4	no	—
66	C₄	—	2	4	no	—
67	C₄	C₂×C₃×Q₈	1	4	yes	—
68	C₃	#544	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	—	2	2	no	—
70	C₂	C₂²×C₃×Q₈	1	1	yes	characteristic
71	C₂	C₃×H(5,𝔽₂)	1	1	yes	characteristic
72	C₂	C₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃
prime radical	C₂³×C₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₄⋊Q₈	C₂	semidirect
2. C₃×#125	C₂	semidirect
6. #544	C₃	direct (N × H)
17. C₄⋊Q₈	C₂×C₃	semidirect
18. #125	C₂×C₃	semidirect
25. C₂×C₃×C₄	Q₈	semidirect
51. C₂×C₄	C₃×Q₈	semidirect
68. C₃	#544	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×C₄⋊Q₈	2
C₃×#125	2
C₃×C₂²⋊Q₈	2
C₃×#117	2
C₂×C₃×C₄⋊C₄	2
#544	3

Subgroups — C3×#544 #5874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#544 #5874