Subgroups — C₂×Dic₁₁₆₈ #22612236

Order 9344.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₈₄	C₂	1	2	yes	maximal
2	Dic₁₁₆₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₉₂	—	2	2	no	—
5	Dic₅₈₄	—	2	2	no	—
6	Dic₅₈₄	C₂²	1	4	yes	—
7	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₇₃	C₂²	1	2	yes	—
9	C₂×Dic₁₄₆	—	4	2	no	—
10	Dic₂₉₂	—	2	4	no	—
11	Dic₂₉₂	—	4	2	no	—
12	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
13	C₁₆×C₇₃	D₄	1	1	yes	characteristic
14	C₁₆×C₇₃	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
16	C₂×Dic₇₃	—	8	2	no	—
17	Dic₁₄₆	—	4	4	no	—
18	Dic₁₄₆	—	8	2	no	—
19	C₈×C₇₃	D₈	1	1	yes	characteristic
20	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₇₃	D₁₆	1	1	yes	characteristic
22	C₄×C₇₃	D₁₆	1	1	yes	characteristic
23	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
24	Dic₇₃	—	8	4	no	—
25	C₂×C₇₃	Q₆₄	1	2	yes	complemented
26	C₂×C₇₃	C₂×D₁₆	1	1	yes	characteristic
27	C₂×Q₆₄	—	73	1	no	maximal, Sylow
28	C₇₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
29	C₂×Q₃₂	—	73	2	no	—
30	Q₆₄	—	73	4	no	—
31	C₂×C₃₂	D₇₃	1	1	yes	characteristic
32	C₂×Q₁₆	—	146	2	no	—
33	Q₃₂	—	73	4	no	—
34	Q₃₂	—	146	2	no	—
35	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
36	C₃₂	C₂×D₇₃	1	2	yes	—
37	C₂×Q₈	—	292	2	no	—
38	Q₁₆	—	292	2	no	—
39	Q₁₆	—	146	4	no	—
40	C₂×C₈	D₂₉₂	1	1	yes	characteristic
41	C₁₆	D₂₉₂	1	1	yes	characteristic
42	C₁₆	C₂²×D₇₃	1	1	yes	characteristic
43	Q₈	—	292	4	no	—
44	Q₈	—	584	2	no	—
45	C₂×C₄	—	584	2	no	—
46	C₂×C₄	D₅₈₄	1	1	yes	characteristic
47	C₈	D₅₈₄	1	1	yes	characteristic
48	C₈	C₂×D₂₉₂	1	1	yes	characteristic
49	C₂²	D₁₁₆₈	1	1	yes	characteristic
50	C₄	—	584	4	no	—
51	C₄	D₁₁₆₈	1	1	yes	characteristic
52	C₄	C₂×D₅₈₄	1	1	yes	characteristic
53	C₂	Dic₁₁₆₈	1	2	yes	direct product factor
54	C₂	C₂×D₁₁₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₁₆₈
commutator	C₁₆×C₇₃	C₂³
Frattini	C₁₆	C₂²×D₇₃
Fitting	C₂×C₃₂×C₇₃	C₂
socle	C₂²×C₇₃	D₁₆
hypercenter	C₂×C₃₂	D₇₃
hypocenter	C₇₃	C₂×Q₆₄
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₁₁₆₈	C₂	direct (N × H)
25. C₂×C₇₃	Q₆₄	semidirect
28. C₇₃	C₂×Q₆₄	semidirect
53. C₂	Dic₁₁₆₈	direct (N × H)

Subgroups — C2×Dic1168 #22612236

Conjugacy classes of subgroups

Complements

Subgroups — C₂×Dic₁₁₆₈ #22612236