Subgroups — Dic₁₅₁₃₆ #72292608

Order 60544.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₇₅₆₈	C₂	1	2	yes	maximal
2	Dic₃₇₈₄	—	2	2	no	—
3	Dic₁₈₉₂	—	4	2	no	—
4	Dic₉₄₆	—	8	2	no	—
5	C₁₁×C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic
6	C₁₁×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
7	C₁₁×C₁₆×C₄₃	D₄	1	1	yes	characteristic
8	C₈×C₁₁×C₄₃	D₈	1	1	yes	characteristic
9	Dic₁₃₇₆	—	11	1	no	maximal, Hall
10	Dic₆₈₈	—	11	2	no	—
11	C₄₃×C₆₄	D₁₁	1	1	yes	characteristic
12	C₄×C₁₁×C₄₃	D₁₆	1	1	yes	characteristic
13	Dic₄₇₃	—	16	2	no	—
14	Dic₃₅₂	—	43	1	no	maximal, Hall
15	Dic₃₄₄	—	22	2	no	—
16	C₃₂×C₄₃	C₂×D₁₁	1	1	yes	characteristic
17	C₂×C₁₁×C₄₃	D₃₂	1	1	yes	characteristic
18	Dic₁₇₆	—	43	2	no	—
19	C₁₁×C₆₄	D₄₃	1	1	yes	characteristic
20	Dic₁₇₂	—	44	2	no	—
21	C₁₆×C₄₃	D₄₄	1	1	yes	characteristic
22	C₁₁×C₄₃	Q₁₂₈	1	1	yes	characteristic, complemented, Hall
23	Dic₈₈	—	86	2	no	—
24	C₁₁×C₃₂	C₂×D₄₃	1	1	yes	characteristic
25	Dic₈₆	—	88	2	no	—
26	C₈×C₄₃	D₈₈	1	1	yes	characteristic
27	Dic₄₄	—	172	2	no	—
28	C₁₁×C₁₆	D₁₇₂	1	1	yes	characteristic
29	C₄×C₄₃	D₁₇₆	1	1	yes	characteristic
30	Dic₄₃	—	176	2	no	—
31	Q₁₂₈	—	473	1	no	Sylow
32	Dic₂₂	—	344	2	no	—
33	C₈×C₁₁	D₃₄₄	1	1	yes	characteristic
34	C₂×C₄₃	D₃₅₂	1	1	yes	characteristic
35	Q₆₄	—	473	2	no	—
36	C₆₄	D₄₇₃	1	1	yes	characteristic
37	C₄×C₁₁	D₆₈₈	1	1	yes	characteristic
38	Dic₁₁	—	688	2	no	—
39	C₄₃	Dic₃₅₂	1	1	yes	characteristic, complemented, Sylow
40	Q₃₂	—	946	2	no	—
41	C₃₂	C₂×D₄₇₃	1	1	yes	characteristic
42	C₂×C₁₁	D₁₃₇₆	1	1	yes	characteristic
43	Q₁₆	—	1892	2	no	—
44	C₁₆	D₁₈₉₂	1	1	yes	characteristic
45	C₁₁	Dic₁₃₇₆	1	1	yes	characteristic, complemented, Sylow
46	Q₈	—	3784	2	no	—
47	C₈	D₃₇₈₄	1	1	yes	characteristic
48	C₄	—	7568	2	no	—
49	C₄	D₇₅₆₈	1	1	yes	characteristic
50	C₂	D₁₅₁₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₅₁₃₆
commutator, cosocle	C₁₁×C₃₂×C₄₃	C₂²
Frattini	C₃₂	C₂×D₄₇₃
Fitting	C₁₁×C₄₃×C₆₄	C₂
socle, prime radical	C₂×C₁₁×C₄₃	D₃₂
hypercenter	C₆₄	D₄₇₃
hypocenter	C₁₁×C₄₃	Q₁₂₈
LCS	G ▷ C₁₁×C₃₂×C₄₃ ▷ C₁₁×C₁₆×C₄₃ ▷ C₈×C₁₁×C₄₃ ▷ C₄×C₁₁×C₄₃ ▷ C₂×C₁₁×C₄₃ ▷ C₁₁×C₄₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ C₆₄

Complements

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

N	H ≅ G/N	type
22. C₁₁×C₄₃	Q₁₂₈	semidirect
39. C₄₃	Dic₃₅₂	semidirect
45. C₁₁	Dic₁₃₇₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Dic₇₅₆₈	2
C₁₁×C₄₃×C₆₄	2
Dic₁₃₇₆	11
Dic₃₅₂	43

Subgroups — Dic15136 #72292608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₅₁₃₆ #72292608