Subgroups — C₂³×#11724784 #20295783

Order 6976.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11724784	C₂	1	14	yes	maximal, direct product factor
2	C₂³×C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11724784	C₂²	1	28	yes	direct product factor
4	C₂⁴×C₁₀₉	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₁₀₉	C₄	1	7	yes	—
6	C₂²×C₄×C₁₀₉	C₂²	1	7	yes	—
7	C₂³×C₁₀₉	C₈	1	8	yes	complemented
8	C₂³×C₁₀₉	C₂×C₄	1	7	yes	—
9	C₂×C₄×C₁₀₉	C₂×C₄	1	21	yes	—
10	C₂×C₄×C₁₀₉	C₂³	1	7	yes	—
11	#11724784	C₂³	1	8	yes	direct product factor
12	C₂²×C₁₀₉	C₂×C₈	1	28	yes	complemented
13	C₂²×C₁₀₉	C₂²×C₄	1	7	yes	—
14	C₄×C₁₀₉	C₂²×C₄	1	7	yes	—
15	C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
16	C₂×C₁₀₉	C₂²×C₈	1	14	yes	complemented
17	C₂×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
18	C₁₀₉	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₈	—	109	1	no	maximal, Sylow
20	C₂³×C₄	D₁₀₉	1	1	yes	characteristic
21	C₂²×C₈	—	109	14	no	—
22	C₂⁴	Dic₁₀₉	1	1	yes	characteristic
23	C₂²×C₄	Dic₁₀₉	1	7	yes	—
24	C₂²×C₄	C₂×D₁₀₉	1	7	yes	—
25	C₂×C₈	—	109	28	no	—
26	C₂³	#11724784	1	8	yes	direct product factor
27	C₂³	C₂×Dic₁₀₉	1	7	yes	—
28	C₂×C₄	C₂×Dic₁₀₉	1	21	yes	—
29	C₂×C₄	C₂²×D₁₀₉	1	7	yes	—
30	C₈	—	109	8	no	—
31	C₂²	C₂×#11724784	1	28	yes	direct product factor
32	C₂²	C₂²×Dic₁₀₉	1	7	yes	—
33	C₄	C₂²×Dic₁₀₉	1	7	yes	—
34	C₄	C₂³×D₁₀₉	1	1	yes	characteristic
35	C₂	C₂²×#11724784	1	14	yes	direct product factor
36	C₂	C₂³×Dic₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	D₁₀₉
commutator, hypocenter	C₁₀₉	C₂³×C₈
Frattini	C₄	C₂³×D₁₀₉
Fitting	C₂³×C₄×C₁₀₉	C₂
socle	C₂⁴×C₁₀₉	C₄
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#11724784	C₂	direct (N × H)
3. C₂×#11724784	C₂²	direct (N × H)
7. C₂³×C₁₀₉	C₈	semidirect
11. #11724784	C₂³	direct (N × H)
12. C₂²×C₁₀₉	C₂×C₈	semidirect
16. C₂×C₁₀₉	C₂²×C₈	semidirect
18. C₁₀₉	C₂³×C₈	semidirect
26. C₂³	#11724784	direct (N × H)
31. C₂²	C₂×#11724784	direct (N × H)
35. C₂	C₂²×#11724784	direct (N × H)

Subgroups — C23×#11724784 #20295783

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×#11724784 #20295783