Subgroups — C₂²×#208 #5781

Order 192.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#208	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂²×M₁₆	—	3	1	no	maximal, Sylow
5	C₂⁴×C₃	C₄	1	1	yes	characteristic
6	C₂²×C₃×C₄	C₄	1	6	yes	—
7	C₂²×C₃×C₄	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄	C₂²	1	6	yes	—
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	#208	C₂²	1	16	yes	direct product factor
11	C₂×C₃⋊C₈	C₂²	1	12	yes	complemented
12	C₂³×C₄	D₃	1	1	yes	characteristic
13	C₂×M₁₆	—	3	12	no	—
14	C₂²×C₈	—	3	2	no	—
15	C₂³×C₃	—	2	4	no	—
16	C₂³×C₃	C₂×C₄	1	6	yes	—
17	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄	C₂×C₄	1	12	yes	—
19	C₂×C₃×C₄	C₂×C₄	1	6	yes	—
20	C₂×C₃×C₄	C₂×C₄	1	3	yes	—
21	C₂×C₃×C₄	C₂³	1	3	yes	—
22	C₂×C₃×C₄	C₂³	1	4	yes	—
23	C₃⋊C₈	C₂³	1	8	yes	complemented
24	C₂⁴	Dic₃	1	1	yes	characteristic
25	C₂²×C₄	Dic₃	1	1	yes	characteristic
26	C₂²×C₄	Dic₃	1	6	yes	—
27	C₂²×C₄	C₂×D₃	1	6	yes	—
28	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
29	M₁₆	—	3	16	no	—
30	C₂×C₈	—	3	12	no	—
31	C₂²×C₃	—	2	12	no	—
32	C₂²×C₃	M₁₆	1	4	yes	complemented
33	C₂²×C₃	C₂²×C₄	1	4	yes	—
34	C₂²×C₃	C₂²×C₄	1	3	yes	—
35	C₃×C₄	C₂²×C₄	1	3	yes	—
36	C₃×C₄	C₂²×C₄	1	4	yes	—
37	C₃×C₄	C₂⁴	1	1	yes	characteristic
38	C₂³	—	2	4	no	—
39	C₂³	C₂×Dic₃	1	6	yes	—
40	C₂³	C₂×Dic₃	1	1	yes	characteristic
41	C₂×C₄	C₂×Dic₃	1	12	yes	—
42	C₂×C₄	C₂×Dic₃	1	6	yes	—
43	C₂×C₄	C₂×Dic₃	1	3	yes	—
44	C₂×C₄	C₂²×D₃	1	3	yes	—
45	C₂×C₄	C₂²×D₃	1	4	yes	—
46	C₈	—	3	8	no	—
47	C₂×C₃	—	2	4	no	—
48	C₂×C₃	C₂×M₁₆	1	6	yes	complemented
49	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
50	C₂²	—	2	12	no	—
51	C₂²	#208	1	4	yes	direct product factor
52	C₂²	C₂²×Dic₃	1	4	yes	—
53	C₂²	C₂²×Dic₃	1	3	yes	—
54	C₄	C₂²×Dic₃	1	4	yes	—
55	C₄	C₂²×Dic₃	1	3	yes	—
56	C₄	C₂³×D₃	1	1	yes	characteristic
57	C₃	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
58	C₂	—	2	4	no	—
59	C₂	C₂×#208	1	6	yes	direct product factor
60	C₂	C₂³×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃
commutator	C₂×C₃	C₂³×C₄
Frattini	C₄	C₂³×D₃
Fitting	C₂³×C₃×C₄	C₂
socle	C₂³×C₃	C₂×C₄
prime radical	C₂⁴×C₃	C₄
cosocle	C₃×C₄	C₂⁴
hypercenter	C₂³×C₄	D₃
hypocenter	C₃	C₂²×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#208	C₂	direct (N × H)
3. C₂²×C₃⋊C₈	C₂	semidirect
10. #208	C₂²	direct (N × H)
11. C₂×C₃⋊C₈	C₂²	semidirect
23. C₃⋊C₈	C₂³	semidirect
32. C₂²×C₃	M₁₆	semidirect
48. C₂×C₃	C₂×M₁₆	semidirect
51. C₂²	#208	direct (N × H)
57. C₃	C₂²×M₁₆	semidirect
59. C₂	C₂×#208	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄	2
C₂×#208	2
C₂²×C₃⋊C₈	2
C₂²×M₁₆	3

Subgroups — C22×#208 #5781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#208 #5781