Subgroups — C₂×#16812787 #20296103

Order 6976.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812787	C₂	1	8	yes	maximal, direct product factor
2	C₂×#13182039	C₂	1	3	yes	maximal, complemented
3	C₂×D₁₀₉⋊C₈	C₂	1	3	yes	maximal, complemented
4	C₂×#13182030	C₂	1	1	yes	maximal, characteristic
5	#13182039	C₂²	1	12	yes	complemented
6	D₁₀₉⋊C₈	C₂²	1	12	yes	complemented
7	C₂×#11724786	C₂²	1	1	yes	characteristic
8	C₂×#11724786	C₂²	1	3	yes	—
9	#13182030	C₄	1	4	yes	—
10	#13182030	C₂²	1	4	yes	—
11	C₂×D₄₃₆	C₄	1	3	yes	—
12	C₂×C₄×D₁₀₉	C₂²	1	3	yes	—
13	C₂×Q₈×C₁₀₉	C₄	1	1	yes	characteristic
14	C₂²×D₁₀₉	C₂×C₄	1	3	yes	—
15	Q₈×C₁₀₉	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
17	C₂×Dic₁₀₉	C₂³	1	1	yes	characteristic
18	D₄₃₆	C₂×C₄	1	12	yes	—
19	C₄×D₁₀₉	C₂×C₄	1	6	yes	—
20	C₄×D₁₀₉	C₂³	1	6	yes	—
21	#11724786	C₂³	1	2	yes	—
22	#11724786	C₂³	1	6	yes	—
23	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₁₀₉	—	2	6	no	—
25	C₂×D₁₀₉	C₂²×C₄	1	6	yes	—
26	C₄×C₁₀₉	C₂²×C₄	1	6	yes	—
27	Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
28	Dic₁₀₉	C₂⁴	1	1	yes	characteristic
29	C₂×C₁₀₉	#131	1	2	yes	complemented
30	C₂×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
31	D₁₀₉	—	2	6	no	—
32	C₁₀₉	C₂×#131	1	1	yes	characteristic, complemented, Sylow
33	C₂×#131	—	109	1	no	maximal, Sylow
34	C₂×#41	—	109	1	no	—
35	#131	—	109	8	no	—
36	C₂×M₁₆	—	109	3	no	—
37	C₂²×C₈	—	109	3	no	—
38	#41	—	109	4	no	—
39	#41	—	109	4	no	—
40	C₂×Q₈	#89137	1	1	yes	characteristic
41	C₂×D₄	—	109	3	no	—
42	C₂²×C₄	—	109	3	no	—
43	M₁₆	—	109	12	no	—
44	C₂×C₈	—	109	1	no	—
45	C₂×C₈	—	109	3	no	—
46	C₂×C₈	—	109	12	no	—
47	C₂³	—	109	3	no	—
48	Q₈	C₂×#89137	1	4	yes	—
49	D₄	—	109	12	no	—
50	C₂×C₄	—	109	1	no	—
51	C₂×C₄	—	109	6	no	—
52	C₂×C₄	—	109	6	no	—
53	C₂×C₄	C₂×#89137	1	3	yes	—
54	C₈	—	109	2	no	—
55	C₈	—	109	6	no	—
56	C₂²	—	109	6	no	—
57	C₂²	—	218	6	no	—
58	C₂²	C₂²×#89137	1	1	yes	characteristic
59	C₄	—	109	1	no	—
60	C₄	—	109	1	no	—
61	C₄	C₂²×#89137	1	6	yes	—
62	C₂	—	218	6	no	—
63	C₂	#16812787	1	2	yes	direct product factor
64	C₂	C₂³×#89137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#89137
commutator	C₂×C₁₀₉	C₂³×C₄
Frattini	C₂	C₂³×#89137
Fitting	C₂×Q₈×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²×C₄
hypercenter	C₂×Q₈	#89137
hypocenter	C₁₀₉	C₂×#131
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #16812787	C₂	direct (N × H)
2. C₂×#13182039	C₂	semidirect
3. C₂×D₁₀₉⋊C₈	C₂	semidirect
5. #13182039	C₂²	semidirect
6. D₁₀₉⋊C₈	C₂²	semidirect
29. C₂×C₁₀₉	#131	semidirect
32. C₁₀₉	C₂×#131	semidirect
63. C₂	#16812787	direct (N × H)

Subgroups — C2×#16812787 #20296103

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16812787 #20296103