Subgroups — C₂×#16812610 #20294975

Order 6976.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11724784	C₂	1	2	yes	maximal
2	#16812610	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄²×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11724784	C₄	1	8	yes	complemented
5	C₂×#11724784	C₂²	1	4	yes	—
6	C₂²×C₄×C₁₀₉	C₄	1	2	yes	—
7	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
8	C₄²×C₁₀₉	C₄	1	2	yes	—
9	C₄²×C₁₀₉	C₂²	1	2	yes	—
10	C₂³×C₁₀₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₀₉	—	2	4	no	—
12	C₂×C₄×C₁₀₉	C₂×C₄	1	4	yes	—
13	C₂×C₄×C₁₀₉	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
16	#11724784	C₂×C₄	1	8	yes	complemented
17	C₂²×C₁₀₉	C₄²	1	2	yes	—
18	C₂²×C₁₀₉	M₁₆	1	4	yes	—
19	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₁₀₉	—	2	4	no	—
21	C₄×C₁₀₉	C₄²	1	2	yes	—
22	C₄×C₁₀₉	C₂²×C₄	1	2	yes	—
23	C₂×C₁₀₉	#97	1	4	yes	complemented
24	C₂×C₁₀₉	C₂×C₄²	1	1	yes	characteristic
25	C₂×C₁₀₉	C₂×M₁₆	1	2	yes	—
26	C₁₀₉	C₂×#97	1	1	yes	characteristic, complemented, Sylow
27	C₂×#97	—	109	1	no	maximal, Sylow
28	C₂²×C₈	—	109	2	no	—
29	C₂×C₄²	D₁₀₉	1	1	yes	characteristic
30	#97	—	109	4	no	—
31	C₂²×C₄	Dic₁₀₉	1	2	yes	—
32	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
33	C₂×C₈	—	109	8	no	—
34	C₂×C₈	—	109	4	no	—
35	C₄²	Dic₁₀₉	1	2	yes	—
36	C₄²	C₂×D₁₀₉	1	2	yes	—
37	C₂³	C₂×Dic₁₀₉	1	1	yes	characteristic
38	C₂×C₄	—	2	4	no	—
39	C₂×C₄	C₄×D₁₀₉	1	4	yes	—
40	C₂×C₄	C₂×Dic₁₀₉	1	4	yes	—
41	C₂×C₄	C₂×Dic₁₀₉	1	1	yes	characteristic
42	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
43	C₈	—	109	8	no	—
44	C₂²	C₄×Dic₁₀₉	1	2	yes	—
45	C₂²	#13182013	1	4	yes	—
46	C₂²	C₂²×Dic₁₀₉	1	1	yes	characteristic
47	C₄	—	2	4	no	—
48	C₄	C₄×Dic₁₀₉	1	2	yes	—
49	C₄	C₂×C₄×D₁₀₉	1	2	yes	—
50	C₂	#16812610	1	4	yes	direct product factor
51	C₂	C₂×C₄×Dic₁₀₉	1	1	yes	characteristic
52	C₂	C₂×#13182013	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₀₉
commutator	C₂×C₁₀₉	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	C₂×C₄²×C₁₀₉	C₂
socle	C₂³×C₁₀₉	C₂×C₄
hypercenter	C₂×C₄²	D₁₀₉
hypocenter	C₁₀₉	C₂×#97
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #16812610	C₂	direct (N × H)
4. C₂×#11724784	C₄	semidirect
16. #11724784	C₂×C₄	semidirect
23. C₂×C₁₀₉	#97	semidirect
26. C₁₀₉	C₂×#97	semidirect
50. C₂	#16812610	direct (N × H)

Subgroups — C2×#16812610 #20294975

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16812610 #20294975