Subgroups — C₄×#208 #4922

Order 192.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×#208	C₂	1	2	yes	maximal
3	#803	C₂	1	2	yes	maximal, complemented
4	C₄×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄×M₁₆	—	3	1	no	maximal, Sylow
6	C₂²×C₃×C₄	C₄	1	2	yes	—
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₃×C₄²	C₄	1	2	yes	—
9	C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₃×C₄²	C₂²	1	1	yes	characteristic
11	#208	C₄	1	8	yes	direct product factor
12	C₂×C₃⋊C₈	C₂²	1	4	yes	—
13	C₂×M₁₆	—	3	2	no	—
14	C₂×C₄²	D₃	1	1	yes	characteristic
15	#97	—	3	2	no	—
16	C₄×C₈	—	3	2	no	—
17	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄	—	2	4	no	—
19	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
20	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
21	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
24	C₃⋊C₈	C₂×C₄	1	8	yes	complemented
25	C₂²×C₄	Dic₃	1	2	yes	—
26	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
27	M₁₆	—	3	8	no	—
28	C₂×C₈	—	3	4	no	—
29	C₄²	Dic₃	1	2	yes	—
30	C₄²	C₂×D₃	1	1	yes	characteristic
31	C₄²	C₂×D₃	1	1	yes	characteristic
32	C₂²×C₃	—	2	2	no	—
33	C₂²×C₃	C₄²	1	2	yes	—
34	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
35	C₃×C₄	—	2	2	no	—
36	C₃×C₄	C₄²	1	2	yes	—
37	C₃×C₄	M₁₆	1	4	yes	complemented
38	C₃×C₄	C₂²×C₄	1	2	yes	—
39	C₂³	C₂×Dic₃	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	C₄×D₃	1	4	yes	—
42	C₂×C₄	C₂×Dic₃	1	2	yes	—
43	C₂×C₄	C₂×Dic₃	1	2	yes	—
44	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
45	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
46	C₈	—	3	8	no	—
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
49	C₂×C₃	C₂×M₁₆	1	2	yes	—
50	C₂²	—	2	2	no	—
51	C₂²	C₄×Dic₃	1	2	yes	—
52	C₂²	C₂²×Dic₃	1	1	yes	characteristic
53	C₄	—	2	2	no	—
54	C₄	#208	1	4	yes	direct product factor
55	C₄	C₄×Dic₃	1	2	yes	—
56	C₄	C₂×C₄×D₃	1	2	yes	—
57	C₃	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
58	C₂	—	2	2	no	—
59	C₂	C₂×#208	1	2	yes	—
60	C₂	C₂×C₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₃
commutator	C₂×C₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₂×C₃×C₄²	C₂
socle	C₂²×C₃	C₂²×C₄
prime radical	C₂³×C₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂³
hypercenter	C₂×C₄²	D₃
hypocenter	C₃	C₄×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. #803	C₂	semidirect
4. C₄×C₃⋊C₈	C₂	semidirect
11. #208	C₄	direct (N × H)
24. C₃⋊C₈	C₂×C₄	semidirect
37. C₃×C₄	M₁₆	semidirect
54. C₄	#208	direct (N × H)
57. C₃	C₄×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²	2
C₂×#208	2
#803	2
C₄×C₃⋊C₈	2
C₄×M₁₆	3

Subgroups — C4×#208 #4922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#208 #4922