Subgroups — C₂×C₄×#89137 #16812775

Order 3488.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#89137	C₂	1	2	yes	maximal
2	C₄×#89137	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×D₁₀₉	C₂²	1	1	yes	characteristic
5	C₂×#89137	C₄	1	8	yes	direct product factor
6	C₂×#89137	C₂²	1	4	yes	—
7	C₂×C₄×C₁₀₉	C₄	1	1	yes	characteristic, complemented
8	C₂×Dic₁₀₉	C₄	1	1	yes	characteristic, complemented
9	C₄×D₁₀₉	C₄	1	2	yes	complemented
10	C₄×D₁₀₉	C₂²	1	2	yes	—
11	C₂²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
12	C₂×D₁₀₉	C₂×C₄	1	1	yes	characteristic
13	C₂×D₁₀₉	C₂×C₄	1	4	yes	—
14	C₂×D₁₀₉	C₂³	1	1	yes	characteristic
15	#89137	C₂×C₄	1	8	yes	direct product factor
16	C₄×C₁₀₉	C₂×C₄	1	2	yes	complemented
17	Dic₁₀₉	C₂×C₄	1	2	yes	complemented
18	C₂×C₁₀₉	C₄²	1	2	yes	complemented
19	C₂×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
20	D₁₀₉	C₄²	1	2	yes	complemented
21	D₁₀₉	C₂²×C₄	1	2	yes	—
22	C₁₀₉	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₄²	—	109	1	no	maximal, Sylow
24	C₂²×C₄	—	109	2	no	—
25	C₂²×C₄	—	109	1	no	—
26	C₄²	—	109	4	no	—
27	C₂³	—	109	1	no	—
28	C₂×C₄	—	109	4	no	—
29	C₂×C₄	—	109	8	no	—
30	C₂×C₄	—	109	1	no	—
31	C₂×C₄	—	109	2	no	—
32	C₂×C₄	—	109	2	no	—
33	C₂×C₄	#89137	1	1	yes	characteristic, direct product factor
34	C₂²	—	109	4	no	—
35	C₂²	—	109	1	no	—
36	C₂²	—	109	1	no	—
37	C₂²	C₂×#89137	1	1	yes	characteristic
38	C₄	—	109	8	no	—
39	C₄	—	109	2	no	—
40	C₄	C₂×#89137	1	2	yes	direct product factor
41	C₂	—	109	2	no	—
42	C₂	—	109	2	no	—
43	C₂	C₄×#89137	1	2	yes	direct product factor
44	C₂	C₂²×#89137	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	#89137
commutator, hypocenter	C₁₀₉	C₂×C₄²
Frattini	C₂	C₂²×#89137
Fitting	C₂×C₄×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂×C₄
prime radical	C₂²×D₁₀₉	C₂²
cosocle	C₂×D₁₀₉	C₂³
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×#89137	C₂	direct (N × H)
5. C₂×#89137	C₄	direct (N × H)
7. C₂×C₄×C₁₀₉	C₄	semidirect
8. C₂×Dic₁₀₉	C₄	semidirect
9. C₄×D₁₀₉	C₄	semidirect
15. #89137	C₂×C₄	direct (N × H)
16. C₄×C₁₀₉	C₂×C₄	semidirect
17. Dic₁₀₉	C₂×C₄	semidirect
18. C₂×C₁₀₉	C₄²	semidirect
20. D₁₀₉	C₄²	semidirect
22. C₁₀₉	C₂×C₄²	semidirect
33. C₂×C₄	#89137	direct (N × H)
40. C₄	C₂×#89137	direct (N × H)
43. C₂	C₄×#89137	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#89137	2
C₄×#89137	2
C₂×C₄×D₁₀₉	2
C₂×C₄²	109

Subgroups — C2×C4×#89137 #16812775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#89137 #16812775