Subgroups — C₃×#533 #5863

Order 192.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
2	C₃×#125	C₂	1	2	yes	maximal, complemented
3	C₃×C₂²⋊Q₈	C₂	1	4	yes	maximal
4	C₃×C₄×Q₈	C₂	1	4	yes	maximal, complemented
5	C₃×#117	C₂	1	2	yes	maximal
6	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
7	#533	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂×C₃×Q₈	C₂²	1	4	yes	—
9	C₂²×C₃×C₄	C₂²	1	2	yes	—
10	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₃×C₄⋊C₄	C₂²	1	4	yes	—
12	C₃×C₄⋊C₄	C₂²	1	8	yes	—
13	C₃×C₄⋊C₄	C₂²	1	4	yes	—
14	C₃×C₂²⋊C₄	C₂²	1	4	yes	—
15	C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₃×C₄²	C₂²	1	1	yes	characteristic
17	C₃×C₄²	C₂²	1	2	yes	—
18	C₃×C₄²	C₂²	1	4	yes	—
19	C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
20	#125	C₂×C₃	1	2	yes	complemented
21	C₂²⋊Q₈	C₂×C₃	1	4	yes	—
22	C₄×Q₈	C₂×C₃	1	4	yes	complemented
23	#117	C₂×C₃	1	2	yes	—
24	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
25	C₂³×C₃	C₂³	1	1	yes	characteristic
26	C₃×Q₈	—	2	8	no	—
27	C₂×C₃×C₄	—	2	4	no	—
28	C₂×C₃×C₄	Q₈	1	4	yes	complemented
29	C₂×C₃×C₄	C₂³	1	2	yes	—
30	C₂×C₃×C₄	C₂³	1	8	yes	—
31	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
32	C₂×C₃×C₄	C₂³	1	2	yes	—
33	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
34	C₂×Q₈	C₂²×C₃	1	4	yes	—
35	C₂²×C₄	C₂²×C₃	1	2	yes	—
36	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
37	C₄⋊C₄	C₂²×C₃	1	4	yes	—
38	C₄⋊C₄	C₂²×C₃	1	8	yes	—
39	C₄⋊C₄	C₂²×C₃	1	4	yes	—
40	C₂²⋊C₄	C₂²×C₃	1	4	yes	—
41	C₄²	C₂²×C₃	1	2	yes	—
42	C₄²	C₂²×C₃	1	1	yes	characteristic
43	C₄²	C₂²×C₃	1	1	yes	characteristic
44	C₄²	C₂²×C₃	1	4	yes	—
45	C₂²×C₃	—	2	2	no	—
46	C₂²×C₃	C₂×Q₈	1	2	yes	—
47	C₂²×C₃	C₂⁴	1	1	yes	characteristic
48	C₃×C₄	—	2	2	no	—
49	C₃×C₄	—	2	8	no	—
50	C₃×C₄	C₂×Q₈	1	2	yes	—
51	C₃×C₄	C₂×Q₈	1	2	yes	—
52	C₃×C₄	#41	1	4	yes	—
53	C₂³	C₂³×C₃	1	1	yes	characteristic
54	Q₈	—	2	8	no	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	C₃×Q₈	1	4	yes	complemented
57	C₂×C₄	C₂³×C₃	1	2	yes	—
58	C₂×C₄	C₂³×C₃	1	8	yes	—
59	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
60	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
61	C₂×C₄	C₂³×C₃	1	2	yes	—
62	C₂×C₃	—	2	2	no	—
63	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
64	C₂×C₃	C₂×#41	1	2	yes	—
65	C₂²	—	2	2	no	—
66	C₂²	C₂×C₃×Q₈	1	2	yes	—
67	C₂²	C₂⁴×C₃	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	—	2	8	no	—
70	C₄	C₂×C₃×Q₈	1	2	yes	—
71	C₄	C₂×C₃×Q₈	1	2	yes	—
72	C₄	C₃×#41	1	4	yes	—
73	C₃	#533	1	1	yes	characteristic, direct product factor, Sylow
74	C₂	—	2	2	no	—
75	C₂	C₂²×C₃×Q₈	1	1	yes	characteristic
76	C₂	C₂×C₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃
socle	C₂²×C₃	C₂⁴
prime radical	C₂³×C₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ 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
4. C₃×C₄×Q₈	C₂	semidirect
7. #533	C₃	direct (N × H)
19. C₄⋊Q₈	C₂×C₃	semidirect
20. #125	C₂×C₃	semidirect
22. C₄×Q₈	C₂×C₃	semidirect
28. C₂×C₃×C₄	Q₈	semidirect
56. C₂×C₄	C₃×Q₈	semidirect
73. C₃	#533	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×C₄×Q₈	2
C₃×#117	2
C₂×C₃×C₄²	2
#533	3

Subgroups — C3×#533 #5863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#533 #5863