Subgroups — #548⋊C₃ #5444

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	#548	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
5	#41⋊C₃	—	2	1	no	—
6	C₂×SL(2,𝔽₃)	—	2	1	no	—
7	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
8	C₃×C₂²⋊C₄	—	4	1	no	maximal
9	C₂×#41	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic
11	#124	—	3	1	no	—
12	C₂²⋊Q₈	—	3	1	no	—
13	#121	—	3	1	no	—
14	C₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
15	C₄×D₄	—	3	1	no	—
16	C₂³×C₃	—	4	1	no	—
17	C₂×C₃×C₄	—	4	1	no	—
18	C₂×C₃×C₄	—	4	1	no	—
19	SL(2,𝔽₃)	D₄	1	1	yes	characteristic, complemented
20	#41	—	2	1	no	—
21	#41	—	6	1	no	—
22	C₂×Q₈	—	2	1	no	—
23	C₂×Q₈	—	3	1	no	—
24	C₂×Q₈	—	6	1	no	—
25	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
26	C₂×D₄	—	3	1	no	—
27	C₂×D₄	—	3	1	no	—
28	C₂²×C₄	—	3	1	no	—
29	C₂²×C₄	—	3	1	no	—
30	C₄⋊C₄	—	3	1	no	—
31	C₄⋊C₄	—	3	1	no	—
32	C₂²⋊C₄	—	3	2	no	—
33	C₂²⋊C₄	—	3	1	no	—
34	C₂²⋊C₄	A₄	1	1	yes	characteristic
35	C₄²	—	3	1	no	—
36	C₂²×C₃	—	4	2	no	—
37	C₂²×C₃	—	4	1	no	—
38	C₂²×C₃	—	8	1	no	—
39	C₂²×C₃	—	8	1	no	—
40	C₃×C₄	—	8	1	no	—
41	C₃×C₄	—	8	1	no	—
42	C₂³	—	3	1	no	—
43	C₂³	C₂×A₄	1	1	yes	characteristic
44	Q₈	—	3	1	no	—
45	Q₈	—	6	1	no	—
46	Q₈	—	6	1	no	—
47	Q₈	C₃×D₄	1	1	yes	characteristic
48	D₄	—	6	1	no	—
49	D₄	—	6	1	no	—
50	D₄	—	6	2	no	—
51	C₂×C₄	—	3	1	no	—
52	C₂×C₄	—	3	1	no	—
53	C₂×C₄	—	3	1	no	—
54	C₂×C₄	—	6	1	no	—
55	C₂×C₄	—	6	1	no	—
56	C₂×C₄	—	6	1	no	—
57	C₂×C₄	—	6	1	no	—
58	C₂×C₄	C₂×A₄	1	1	yes	characteristic
59	C₂×C₄	C₂×A₄	1	1	yes	characteristic
60	C₂×C₃	—	4	1	no	—
61	C₂×C₃	—	4	1	no	—
62	C₂×C₃	—	4	1	no	—
63	C₂×C₃	—	8	2	no	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	—	6	1	no	—
67	C₂²	—	6	1	no	—
68	C₂²	—	6	1	no	—
69	C₂²	#41⋊C₃	1	2	yes	complemented
70	C₂²	C₂²×A₄	1	1	yes	characteristic
71	C₄	—	2	1	no	—
72	C₄	—	2	1	no	—
73	C₄	—	3	1	no	—
74	C₄	—	3	1	no	—
75	C₄	—	6	1	no	—
76	C₄	—	6	1	no	—
77	C₃	—	4	1	no	Sylow
78	C₂	—	2	2	no	—
79	C₂	—	12	1	no	—
80	C₂	D₄×A₄	1	1	yes	characteristic
81	C₂	C₂×#41⋊C₃	1	1	yes	characteristic
82	C₂	2₋¹⁺⁴⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle	C₂²	C₂²×A₄
commutator, cosocle	C₂×Q₈	C₂²×C₃
Fitting	#548	C₃
hypercenter	C₂²⋊C₄	A₄
hypocenter	Q₈	C₃×D₄
LCS	G ▷ C₂×Q₈ ▷ Q₈
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#41⋊C₃	C₂	semidirect
2. C₂²×SL(2,𝔽₃)	C₂	semidirect
3. C₄×SL(2,𝔽₃)	C₂	semidirect
4. #548	C₃	semidirect
9. C₂×#41	C₂×C₃	semidirect
14. C₄×Q₈	C₂×C₃	semidirect
19. SL(2,𝔽₃)	D₄	semidirect
69. C₂²	#41⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41⋊C₃	2
C₂²×SL(2,𝔽₃)	2
C₄×SL(2,𝔽₃)	2
#548	3
C₃×C₂²⋊C₄	4

Subgroups — #548⋊C3 #5444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #548⋊C₃ #5444