Subgroups — C₂²×#217 #5839

Order 192.

674 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₃	C₂	1	2	yes	maximal, complemented
3	C₂×#217	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₂²⋊C₄	—	3	1	no	maximal, Sylow
5	C₂⁴×C₃	—	2	8	no	—
6	C₂⁴×C₃	C₄	1	8	yes	complemented
7	C₂⁴×C₃	C₂²	1	6	yes	—
8	C₂⁴×C₃	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃	—	2	8	no	—
10	C₂²×Dic₃	C₂²	1	12	yes	complemented
11	#217	C₂²	1	16	yes	direct product factor
12	C₂⁵	D₃	1	1	yes	characteristic
13	C₂³×C₄	—	3	2	no	—
14	C₂×C₂²⋊C₄	—	3	12	no	—
15	C₂³×C₃	—	2	32	no	—
16	C₂³×C₃	—	2	24	no	—
17	C₂³×C₃	C₂×C₄	1	4	yes	—
18	C₂³×C₃	C₂×C₄	1	24	yes	complemented
19	C₂³×C₃	D₄	1	8	yes	—
20	C₂³×C₃	C₂³	1	4	yes	—
21	C₂³×C₃	C₂³	1	3	yes	—
22	C₂×Dic₃	—	2	24	no	—
23	C₂×Dic₃	C₂³	1	8	yes	complemented
24	C₂⁴	—	2	8	no	—
25	C₂⁴	Dic₃	1	8	yes	complemented
26	C₂⁴	C₂×D₃	1	6	yes	—
27	C₂⁴	C₂×D₃	1	1	yes	characteristic
28	C₂²×C₄	—	3	12	no	—
29	C₂²×C₄	—	6	8	no	—
30	C₂²⋊C₄	—	3	16	no	—
31	C₂²×C₃	—	2	48	no	—
32	C₂²×C₃	—	2	8	no	—
33	C₂²×C₃	C₂²⋊C₄	1	16	yes	complemented
34	C₂²×C₃	C₂²×C₄	1	6	yes	—
35	C₂²×C₃	C₂²×C₄	1	8	yes	complemented
36	C₂²×C₃	C₂×D₄	1	12	yes	—
37	C₂²×C₃	C₂⁴	1	1	yes	characteristic
38	Dic₃	—	2	8	no	—
39	C₂³	—	2	32	no	—
40	C₂³	—	2	24	no	—
41	C₂³	C₂×Dic₃	1	4	yes	—
42	C₂³	C₂×Dic₃	1	24	yes	complemented
43	C₂³	#67	1	8	yes	—
44	C₂³	C₂²×D₃	1	4	yes	—
45	C₂³	C₂²×D₃	1	3	yes	—
46	C₂×C₄	—	3	8	no	—
47	C₂×C₄	—	6	24	no	—
48	C₂×C₃	—	2	8	no	—
49	C₂×C₃	C₂×C₂²⋊C₄	1	12	yes	complemented
50	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
51	C₂×C₃	C₂²×D₄	1	2	yes	—
52	C₂²	—	2	48	no	—
53	C₂²	—	2	8	no	—
54	C₂²	#217	1	16	yes	direct product factor
55	C₂²	C₂²×Dic₃	1	6	yes	—
56	C₂²	C₂²×Dic₃	1	8	yes	complemented
57	C₂²	C₂×#67	1	12	yes	—
58	C₂²	C₂³×D₃	1	1	yes	characteristic
59	C₄	—	6	8	no	—
60	C₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	2	8	no	—
62	C₂	C₂×#217	1	12	yes	direct product factor
63	C₂	C₂³×Dic₃	1	1	yes	characteristic
64	C₂	C₂²×#67	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₃
commutator	C₂×C₃	C₂³×C₄
Frattini	C₂²	C₂³×D₃
Fitting, prime radical	C₂⁵×C₃	C₂
socle	C₂⁴×C₃	C₂²
cosocle	C₂²×C₃	C₂⁴
hypercenter	C₂⁵	D₃
hypocenter	C₃	C₂²×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
2. C₂³×Dic₃	C₂	semidirect
3. C₂×#217	C₂	direct (N × H)
6. C₂⁴×C₃	C₄	semidirect
10. C₂²×Dic₃	C₂²	semidirect
11. #217	C₂²	direct (N × H)
18. C₂³×C₃	C₂×C₄	semidirect
23. C₂×Dic₃	C₂³	semidirect
25. C₂⁴	Dic₃	semidirect
33. C₂²×C₃	C₂²⋊C₄	semidirect
35. C₂²×C₃	C₂²×C₄	semidirect
42. C₂³	C₂×Dic₃	semidirect
49. C₂×C₃	C₂×C₂²⋊C₄	semidirect
54. C₂²	#217	direct (N × H)
56. C₂²	C₂²×Dic₃	semidirect
60. C₃	C₂²×C₂²⋊C₄	semidirect
62. C₂	C₂×#217	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₃	2
C₂³×Dic₃	2
C₂×#217	2
C₂²×C₂²⋊C₄	3

Subgroups — C22×#217 #5839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#217 #5839