Subgroups — C₄×D₁₀₉⋊C₈ #20295982

Order 6976.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₀₉⋊C₈	C₂	1	2	yes	maximal
2	C₄×#11724786	C₂	1	4	yes	maximal, complemented
3	C₄²×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	D₁₀₉⋊C₈	C₄	1	8	yes	direct product factor
5	C₂×#11724786	C₂²	1	4	yes	—
6	C₂×C₄×D₁₀₉	C₄	1	2	yes	—
7	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
8	C₄×Dic₁₀₉	C₄	1	1	yes	characteristic
9	C₄×Dic₁₀₉	C₂²	1	2	yes	—
10	C₄²×C₁₀₉	C₄	1	1	yes	characteristic
11	C₂²×D₁₀₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
14	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
15	C₂×Dic₁₀₉	C₂³	1	1	yes	characteristic
16	C₄×D₁₀₉	C₈	1	8	yes	complemented
17	C₄×D₁₀₉	C₂×C₄	1	4	yes	—
18	#11724786	C₂×C₄	1	8	yes	complemented
19	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
20	C₂×D₁₀₉	C₄²	1	2	yes	—
21	C₂×D₁₀₉	C₂×C₈	1	4	yes	—
22	C₄×C₁₀₉	C₄²	1	2	yes	—
23	C₄×C₁₀₉	C₂×C₈	1	4	yes	complemented
24	Dic₁₀₉	C₂×C₈	1	4	yes	complemented
25	Dic₁₀₉	C₂²×C₄	1	2	yes	—
26	C₂×C₁₀₉	C₂×C₄²	1	1	yes	characteristic
27	C₂×C₁₀₉	C₂²×C₈	1	2	yes	—
28	D₁₀₉	C₄×C₈	1	4	yes	complemented
29	C₁₀₉	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₄×C₈	—	109	1	no	maximal, Sylow
31	C₂²×C₈	—	109	2	no	—
32	C₂×C₄²	—	109	1	no	—
33	C₄×C₈	—	109	4	no	—
34	C₂²×C₄	—	109	2	no	—
35	C₂²×C₄	—	109	1	no	—
36	C₂×C₈	—	109	4	no	—
37	C₂×C₈	—	109	8	no	—
38	C₄²	—	109	1	no	—
39	C₄²	—	109	2	no	—
40	C₄²	#89137	1	1	yes	characteristic
41	C₂³	—	109	1	no	—
42	C₂×C₄	—	109	1	no	—
43	C₂×C₄	—	109	2	no	—
44	C₂×C₄	—	109	4	no	—
45	C₂×C₄	—	109	8	no	—
46	C₂×C₄	C₂×#89137	1	1	yes	characteristic
47	C₂×C₄	C₂×#89137	1	2	yes	—
48	C₈	—	109	8	no	—
49	C₂²	—	109	2	no	—
50	C₂²	—	109	4	no	—
51	C₂²	C₂²×#89137	1	1	yes	characteristic
52	C₄	—	109	2	no	—
53	C₄	—	109	4	no	—
54	C₄	C₄×#89137	1	2	yes	—
55	C₄	D₁₀₉⋊C₈	1	4	yes	direct product factor
56	C₂	—	109	4	no	—
57	C₂	C₂×C₄×#89137	1	1	yes	characteristic
58	C₂	C₂×D₁₀₉⋊C₈	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄²	#89137
commutator, hypocenter	C₁₀₉	C₂×C₄×C₈
Frattini	C₂²	C₂²×#89137
Fitting	C₄²×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²×C₄
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄×#11724786	C₂	semidirect
4. D₁₀₉⋊C₈	C₄	direct (N × H)
16. C₄×D₁₀₉	C₈	semidirect
18. #11724786	C₂×C₄	semidirect
23. C₄×C₁₀₉	C₂×C₈	semidirect
24. Dic₁₀₉	C₂×C₈	semidirect
28. D₁₀₉	C₄×C₈	semidirect
29. C₁₀₉	C₂×C₄×C₈	semidirect
55. C₄	D₁₀₉⋊C₈	direct (N × H)

Subgroups — C4×D109⋊C8 #20295982

Conjugacy classes of subgroups

Complements

Subgroups — C₄×D₁₀₉⋊C₈ #20295982