Subgroups — C₄⋊#13182004 #20294845

Order 6976.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182004	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#13182004	—	2	2	no	—
4	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
6	C₄²×C₁₀₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₉	C₈	1	1	yes	characteristic
8	C₂×C₄×C₁₀₉	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
10	C₈×C₁₀₉	—	2	1	no	—
11	C₈×C₁₀₉	D₄	1	1	yes	characteristic
12	C₈×C₁₀₉	Q₈	1	1	yes	characteristic
13	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₀₉	—	2	1	no	—
15	C₄×C₁₀₉	C₁₆	1	2	yes	complemented
16	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
18	C₂×C₁₀₉	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₀₉	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₁₀₉	M₃₂	1	1	yes	characteristic
21	C₁₀₉	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	109	1	no	maximal, Sylow
23	C₂×C₁₆	—	109	2	no	—
24	C₄×C₈	D₁₀₉	1	1	yes	characteristic
25	C₂×C₈	Dic₁₀₉	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
27	C₄²	Dic₁₀₉	1	1	yes	characteristic
28	C₁₆	—	218	2	no	—
29	C₂×C₄	#11724784	1	1	yes	characteristic
30	C₂×C₄	#11724784	1	1	yes	characteristic
31	C₂×C₄	C₂×Dic₁₀₉	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	Dic₂₁₈	1	1	yes	characteristic
34	C₈	D₄₃₆	1	1	yes	characteristic
35	C₂²	C₂×#11724784	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	#13182004	1	2	yes	complemented
38	C₄	C₄⋊Dic₁₀₉	1	1	yes	characteristic
39	C₄	#13182013	1	1	yes	characteristic
40	C₂	C₄⋊#11724784	1	1	yes	characteristic
41	C₂	C₂×#13182004	1	1	yes	characteristic
42	C₂	#16812639	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₀₉
commutator	C₂×C₁₀₉	C₂×C₁₆
Fitting	C₄×C₈×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×C₈
hypercenter	C₄×C₈	D₁₀₉
hypocenter	C₁₀₉	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
15. C₄×C₁₀₉	C₁₆	semidirect
21. C₁₀₉	C₄⋊C₁₆	semidirect
37. C₄	#13182004	semidirect

Subgroups — C4⋊#13182004 #20294845

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊#13182004 #20294845