Subgroups — C₄×Dic₁₄₃₆ #37526539

Order 22976.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₃₆	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₇₁₈	C₂	1	2	yes	maximal
3	#26039949	C₂	1	1	yes	maximal, characteristic
4	#26039940	C₂	1	2	yes	maximal
5	C₄×C₈×C₃₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₁₈	C₂²	1	2	yes	—
7	Dic₁₄₃₆	C₄	1	4	yes	direct product factor
8	C₄⋊Dic₃₅₉	C₂²	1	2	yes	—
9	Dic₃₅₉⋊C₄	—	2	2	no	—
10	C₄×Dic₃₅₉	—	2	2	no	—
11	C₂×C₈×C₃₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₃₅₉	C₂²	1	1	yes	characteristic
13	C₄²×C₃₅₉	C₂²	1	1	yes	characteristic
14	Dic₇₁₈	—	2	2	no	—
15	Dic₇₁₈	C₂×C₄	1	4	yes	—
16	C₂×Dic₃₅₉	—	2	2	no	—
17	C₂×Dic₃₅₉	—	2	2	no	—
18	C₂×C₄×C₃₅₉	D₄	1	1	yes	characteristic
19	C₂×C₄×C₃₅₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₃₅₉	C₂³	1	1	yes	characteristic
21	C₈×C₃₅₉	—	2	1	no	—
22	C₈×C₃₅₉	C₂×C₄	1	2	yes	—
23	C₂²×C₃₅₉	C₂×D₄	1	1	yes	characteristic
24	C₄×C₃₅₉	—	2	1	no	—
25	C₄×C₃₅₉	Q₁₆	1	2	yes	complemented
26	C₄×C₃₅₉	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₃₅₉	#41	1	1	yes	characteristic
28	Dic₃₅₉	—	2	4	no	—
29	Dic₃₅₉	—	4	2	no	—
30	C₂×C₃₅₉	C₄×D₄	1	1	yes	characteristic
31	C₂×C₃₅₉	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₃₅₉	#135	1	1	yes	characteristic
33	C₃₅₉	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×Q₁₆	—	359	1	no	maximal, Sylow
35	C₂×Q₁₆	—	359	1	no	—
36	C₄×Q₈	—	359	2	no	—
37	#107	—	359	1	no	—
38	#103	—	359	2	no	—
39	C₄×C₈	D₃₅₉	1	1	yes	characteristic
40	C₂×Q₈	—	359	2	no	—
41	Q₁₆	—	359	4	no	—
42	C₂×C₈	C₂×D₃₅₉	1	1	yes	characteristic
43	C₂×C₈	C₂×D₃₅₉	1	1	yes	characteristic
44	C₄⋊C₄	—	359	2	no	—
45	C₄⋊C₄	—	718	2	no	—
46	C₄²	—	718	2	no	—
47	C₄²	C₂×D₃₅₉	1	1	yes	characteristic
48	Q₈	—	359	4	no	—
49	Q₈	—	718	2	no	—
50	C₂×C₄	—	718	2	no	—
51	C₂×C₄	—	718	2	no	—
52	C₂×C₄	D₁₄₃₆	1	1	yes	characteristic
53	C₂×C₄	D₁₄₃₆	1	1	yes	characteristic
54	C₂×C₄	C₂²×D₃₅₉	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	C₄×D₃₅₉	1	2	yes	—
57	C₂²	C₂×D₁₄₃₆	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	1436	2	no	—
60	C₄	—	718	4	no	—
61	C₄	Dic₁₄₃₆	1	2	yes	direct product factor
62	C₄	C₂×C₄×D₃₅₉	1	1	yes	characteristic
63	C₄	#19153341	1	1	yes	characteristic
64	C₂	C₄×D₁₄₃₆	1	1	yes	characteristic
65	C₂	C₂×Dic₁₄₃₆	1	1	yes	characteristic
66	C₂	#26040037	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₄₃₆
commutator	C₄×C₃₅₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₅₉
Fitting	C₄×C₈×C₃₅₉	C₂
socle, prime radical	C₂²×C₃₅₉	C₂×D₄
cosocle	C₂×C₄×C₃₅₉	C₂³
hypercenter	C₄×C₈	D₃₅₉
hypocenter	C₃₅₉	C₄×Q₁₆
LCS	G ▷ C₄×C₃₅₉ ▷ C₂×C₃₅₉ ▷ C₃₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
7. Dic₁₄₃₆	C₄	direct (N × H)
25. C₄×C₃₅₉	Q₁₆	semidirect
33. C₃₅₉	C₄×Q₁₆	semidirect
61. C₄	Dic₁₄₃₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₁₄₃₆	2
C₄×Dic₇₁₈	2
#26039949	2
#26039940	2
C₄×C₈×C₃₅₉	2
C₄×Q₁₆	359

Subgroups — C4×Dic1436 #37526539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₁₄₃₆ #37526539