Subgroups — C₃×#563 #5893

Order 192.

196 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×#126	C₂	1	4	yes	maximal, complemented
3	C₃×#125	C₂	1	2	yes	maximal, complemented
4	C₃×#124	C₂	1	1	yes	maximal, characteristic
5	C₃×#123	C₂	1	2	yes	maximal
6	C₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
7	#563	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂×C₃×Q₈	C₂²	1	2	yes	—
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×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	4	yes	—
15	C₃×C₄⋊C₄	C₂²	1	4	yes	—
16	C₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₃×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₃×C₂²⋊C₄	C₂²	1	4	yes	—
19	C₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₃×C₄²	C₂²	1	1	yes	characteristic
21	C₃×C₄²	C₂²	1	2	yes	—
22	C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
23	#126	C₂×C₃	1	4	yes	complemented
24	#125	C₂×C₃	1	2	yes	complemented
25	#124	C₂×C₃	1	1	yes	characteristic
26	#123	C₂×C₃	1	2	yes	—
27	C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
28	C₂³×C₃	C₂³	1	2	yes	—
29	C₃×Q₈	—	4	2	no	—
30	C₃×Q₈	—	4	1	no	—
31	C₃×D₄	—	4	1	no	—
32	C₂×C₃×C₄	—	4	2	no	—
33	C₂×C₃×C₄	C₂³	1	2	yes	—
34	C₂×C₃×C₄	C₂³	1	4	yes	—
35	C₂×C₃×C₄	C₂³	1	2	yes	—
36	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₄	C₂³	1	4	yes	—
38	C₂×Q₈	C₂²×C₃	1	2	yes	—
39	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
40	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
41	C₂²×C₄	C₂²×C₃	1	2	yes	—
42	C₄⋊C₄	C₂²×C₃	1	2	yes	—
43	C₄⋊C₄	C₂²×C₃	1	4	yes	—
44	C₄⋊C₄	C₂²×C₃	1	4	yes	—
45	C₄⋊C₄	C₂²×C₃	1	4	yes	—
46	C₄⋊C₄	C₂²×C₃	1	2	yes	—
47	C₂²⋊C₄	C₂²×C₃	1	4	yes	—
48	C₂²⋊C₄	C₂²×C₃	1	4	yes	—
49	C₂²⋊C₄	C₂²×C₃	1	2	yes	—
50	C₄²	C₂²×C₃	1	1	yes	characteristic
51	C₄²	C₂²×C₃	1	2	yes	—
52	C₂²×C₃	—	2	2	no	—
53	C₂²×C₃	—	2	4	no	—
54	C₂²×C₃	C₂⁴	1	1	yes	characteristic
55	C₃×C₄	—	2	4	no	—
56	C₃×C₄	—	2	1	no	—
57	C₃×C₄	—	2	2	no	—
58	C₃×C₄	—	2	2	no	—
59	C₃×C₄	—	2	4	no	—
60	C₂³	C₂³×C₃	1	2	yes	—
61	Q₈	—	4	2	no	—
62	Q₈	—	4	1	no	—
63	D₄	—	4	1	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	C₂³×C₃	1	2	yes	—
66	C₂×C₄	C₂³×C₃	1	4	yes	—
67	C₂×C₄	C₂³×C₃	1	2	yes	—
68	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
69	C₂×C₄	C₂³×C₃	1	4	yes	—
70	C₂×C₃	—	4	2	no	—
71	C₂×C₃	H(5,𝔽₂)	1	1	yes	characteristic
72	C₂×C₃	2₋¹⁺⁴	1	2	yes	—
73	C₂²	—	2	2	no	—
74	C₂²	—	2	4	no	—
75	C₂²	C₂⁴×C₃	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	2	1	no	—
78	C₄	—	2	2	no	—
79	C₄	—	2	2	no	—
80	C₄	—	2	4	no	—
81	C₃	#563	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	—	4	2	no	—
83	C₂	C₃×H(5,𝔽₂)	1	1	yes	characteristic
84	C₂	C₃×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃
prime radical	C₂×C₃×D₄	C₂²
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×#126	C₂	semidirect
3. C₃×#125	C₂	semidirect
6. C₃×C₂²⋊Q₈	C₂	semidirect
7. #563	C₃	direct (N × H)
22. C₄⋊Q₈	C₂×C₃	semidirect
23. #126	C₂×C₃	semidirect
24. #125	C₂×C₃	semidirect
27. C₂²⋊Q₈	C₂×C₃	semidirect
81. C₃	#563	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×#126	2
C₃×#125	2
C₃×#124	2
C₃×#123	2
C₃×C₂²⋊Q₈	2
#563	3

Subgroups — C3×#563 #5893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#563 #5893