Subgroups — D₈×Dic₃₅₉ #37526526

Order 22976.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₃₅₉	C₂	1	2	yes	maximal, complemented
2	#26039949	C₂	1	1	yes	maximal, characteristic, complemented
3	#26039936	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₃₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₃₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₅₉	—	2	2	no	—
7	C₂×C₃₅₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₃₅₉	C₂²	1	2	yes	—
9	C₂²⋊Dic₃₅₉	—	2	2	no	—
10	C₄×Dic₃₅₉	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₃₅₉	C₂²	1	2	yes	—
12	D₈×C₃₅₉	C₄	1	4	yes	complemented
13	C₂×C₈×C₃₅₉	C₂²	1	1	yes	characteristic
14	C₂×Dic₃₅₉	—	2	2	no	—
15	C₂×Dic₃₅₉	—	4	4	no	—
16	C₂×Dic₃₅₉	D₄	1	1	yes	characteristic
17	C₂×Dic₃₅₉	D₄	1	1	yes	characteristic
18	C₃₅₉⋊C₈	—	2	1	no	—
19	C₂³×C₃₅₉	—	2	2	no	—
20	D₄×C₃₅₉	—	2	2	no	—
21	D₄×C₃₅₉	C₂×C₄	1	4	yes	complemented
22	C₂×C₄×C₃₅₉	C₂³	1	1	yes	characteristic
23	C₈×C₃₅₉	C₂×C₄	1	2	yes	complemented
24	C₂²×C₃₅₉	—	2	4	no	—
25	C₂²×C₃₅₉	—	4	2	no	—
26	C₂²×C₃₅₉	—	4	2	no	—
27	C₂²×C₃₅₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₃₅₉	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₃₅₉	#41	1	1	yes	characteristic
30	Dic₃₅₉	—	2	1	no	—
31	Dic₃₅₉	—	4	2	no	—
32	Dic₃₅₉	D₈	1	2	yes	direct product factor
33	C₂×C₃₅₉	—	4	4	no	—
34	C₂×C₃₅₉	C₄×D₄	1	1	yes	characteristic
35	C₂×C₃₅₉	C₂×D₈	1	1	yes	characteristic
36	C₂×C₃₅₉	#135	1	1	yes	characteristic
37	C₃₅₉	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
38	C₄×D₈	—	359	1	no	maximal, Sylow
39	C₂×D₈	D₃₅₉	1	1	yes	characteristic
40	C₄×D₄	—	359	2	no	—
41	#107	—	359	1	no	—
42	#102	—	359	2	no	—
43	C₄×C₈	—	359	1	no	—
44	C₂×D₄	C₂×D₃₅₉	1	2	yes	—
45	C₂²×C₄	—	718	2	no	—
46	D₈	Dic₃₅₉	1	4	yes	direct product factor
47	C₂×C₈	—	359	1	no	—
48	C₂×C₈	C₂×D₃₅₉	1	1	yes	characteristic
49	C₄⋊C₄	—	359	2	no	—
50	C₂²⋊C₄	—	718	2	no	—
51	C₄²	—	359	1	no	—
52	C₂³	—	2	2	no	—
53	D₄	—	2	2	no	—
54	D₄	C₂×Dic₃₅₉	1	4	yes	complemented
55	C₂×C₄	—	359	1	no	—
56	C₂×C₄	—	359	1	no	—
57	C₂×C₄	—	1436	4	no	—
58	C₂×C₄	—	718	2	no	—
59	C₂×C₄	C₂²×D₃₅₉	1	1	yes	characteristic
60	C₈	—	718	1	no	—
61	C₈	C₂×Dic₃₅₉	1	2	yes	complemented
62	C₂²	—	2	4	no	—
63	C₂²	—	4	2	no	—
64	C₂²	—	4	2	no	—
65	C₂²	D₄×D₃₅₉	1	1	yes	characteristic
66	C₄	—	359	2	no	—
67	C₄	—	1436	2	no	—
68	C₄	—	718	1	no	—
69	C₄	C₂²×Dic₃₅₉	1	1	yes	characteristic
70	C₄	#19153340	1	1	yes	characteristic
71	C₂	—	4	4	no	—
72	C₂	D₄×Dic₃₅₉	1	1	yes	characteristic
73	C₂	D₈×D₃₅₉	1	1	yes	characteristic
74	C₂	#26040034	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₅₉
commutator	C₄×C₃₅₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₅₉
Fitting, prime radical	C₂×D₈×C₃₅₉	C₂
socle	C₂²×C₃₅₉	C₂×D₄
cosocle	C₂×C₄×C₃₅₉	C₂³
hypercenter	C₂×D₈	D₃₅₉
hypocenter	C₃₅₉	C₄×D₈
LCS	G ▷ C₄×C₃₅₉ ▷ C₂×C₃₅₉ ▷ C₃₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×Dic₃₅₉	C₂	semidirect
2. #26039949	C₂	semidirect
3. #26039936	C₂	semidirect
4. C₈×Dic₃₅₉	C₂	semidirect
12. D₈×C₃₅₉	C₄	semidirect
21. D₄×C₃₅₉	C₂×C₄	semidirect
23. C₈×C₃₅₉	C₂×C₄	semidirect
32. Dic₃₅₉	D₈	direct (N × H)
37. C₃₅₉	C₄×D₈	semidirect
46. D₈	Dic₃₅₉	direct (N × H)
54. D₄	C₂×Dic₃₅₉	semidirect
61. C₈	C₂×Dic₃₅₉	semidirect

Maximal subgroups

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

subgroup	index
D₄×Dic₃₅₉	2
#26039949	2
#26039936	2
C₈×Dic₃₅₉	2
C₂×D₈×C₃₅₉	2
C₄×D₈	359

Subgroups — D8×Dic359 #37526526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×Dic₃₅₉ #37526526