Subgroups — C₂×#16812645 #20295453

Order 6976.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₃₆	C₂	1	1	yes	maximal, characteristic
2	#16812645	C₂	1	4	yes	maximal, direct product factor
3	C₂×#13182004	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₁₈	—	2	1	no	—
6	Dic₄₃₆	—	2	1	no	—
7	Dic₄₃₆	C₂²	1	2	yes	—
8	#13182004	C₂²	1	2	yes	—
9	C₂×Q₈×C₁₀₉	—	2	1	no	—
10	Q₁₆×C₁₀₉	—	2	1	no	—
11	Q₁₆×C₁₀₉	C₂²	1	2	yes	—
12	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
13	Q₈×C₁₀₉	—	2	2	no	—
14	Q₈×C₁₀₉	—	4	1	no	—
15	C₂×C₄×C₁₀₉	—	4	1	no	—
16	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
17	C₂×Dic₁₀₉	—	4	1	no	—
18	Dic₂₁₈	—	2	2	no	—
19	Dic₂₁₈	—	4	1	no	—
20	C₈×C₁₀₉	D₄	1	1	yes	characteristic
21	C₈×C₁₀₉	C₂³	1	1	yes	characteristic
22	C₂²×C₁₀₉	D₈	1	1	yes	characteristic
23	C₄×C₁₀₉	—	4	2	no	—
24	C₄×C₁₀₉	D₈	1	1	yes	characteristic
25	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
26	Dic₁₀₉	—	4	2	no	—
27	C₂×C₁₀₉	Q₃₂	1	2	yes	complemented
28	C₂×C₁₀₉	C₂×D₈	1	1	yes	characteristic
29	C₁₀₉	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₃₂	—	109	1	no	maximal, Sylow
31	C₂×Q₁₆	—	109	1	no	—
32	C₂×Q₁₆	D₁₀₉	1	1	yes	characteristic
33	Q₃₂	—	109	4	no	—
34	C₂×C₁₆	—	109	1	no	—
35	C₂×Q₈	—	2	1	no	—
36	C₂×Q₈	—	218	1	no	—
37	Q₁₆	—	2	1	no	—
38	Q₁₆	—	109	2	no	—
39	Q₁₆	—	218	1	no	—
40	Q₁₆	C₂×D₁₀₉	1	2	yes	—
41	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
42	C₁₆	—	109	2	no	—
43	Q₈	—	2	2	no	—
44	Q₈	—	4	1	no	—
45	Q₈	—	436	1	no	—
46	Q₈	—	218	2	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	436	1	no	—
49	C₂×C₄	C₂²⋊D₁₀₉	1	1	yes	characteristic
50	C₈	C₂²⋊D₁₀₉	1	1	yes	characteristic
51	C₈	C₂²×D₁₀₉	1	1	yes	characteristic
52	C₂²	#13182014	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	436	2	no	—
55	C₄	#13182014	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₁₀₉	1	1	yes	characteristic
57	C₂	#16812645	1	2	yes	direct product factor
58	C₂	C₂×#13182014	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13182014
commutator	C₈×C₁₀₉	C₂³
Frattini	C₈	C₂²×D₁₀₉
Fitting	C₂×Q₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	D₈
hypercenter	C₂×Q₁₆	D₁₀₉
hypocenter	C₁₀₉	C₂×Q₃₂
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #16812645	C₂	direct (N × H)
27. C₂×C₁₀₉	Q₃₂	semidirect
29. C₁₀₉	C₂×Q₃₂	semidirect
57. C₂	#16812645	direct (N × H)

Subgroups — C2×#16812645 #20295453

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16812645 #20295453