Subgroups — #37526248

Order 22976.

58 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	#26039949	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₃₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₁₈	—	2	1	no	—
5	Dic₁₄₃₆	—	2	1	no	—
6	Dic₁₄₃₆	C₄	1	2	yes	complemented
7	C₄⋊Dic₃₅₉	—	2	1	no	—
8	C₂×C₈×C₃₅₉	C₂²	1	1	yes	characteristic
9	C₁₆×C₃₅₉	—	2	1	no	—
10	Dic₇₁₈	—	2	2	no	—
11	Dic₇₁₈	—	4	1	no	—
12	C₂×Dic₃₅₉	—	4	1	no	—
13	C₂×Dic₃₅₉	—	4	1	no	—
14	C₂×C₄×C₃₅₉	D₄	1	1	yes	characteristic
15	C₈×C₃₅₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₃₅₉	D₄	1	1	yes	characteristic
17	C₂²×C₃₅₉	D₈	1	1	yes	characteristic
18	C₄×C₃₅₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₃₅₉	SD₁₆	1	1	yes	characteristic
20	Dic₃₅₉	—	4	2	no	—
21	Dic₃₅₉	—	8	1	no	—
22	C₂×C₃₅₉	#102	1	1	yes	characteristic
23	C₂×C₃₅₉	SD₃₂	1	1	yes	characteristic
24	C₂×C₃₅₉	Q₃₂	1	1	yes	characteristic
25	C₃₅₉	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	359	1	no	maximal, Sylow
27	C₂×Q₁₆	—	359	1	no	—
28	C₂×C₁₆	D₃₅₉	1	1	yes	characteristic
29	#107	—	359	1	no	—
30	C₂×Q₈	—	718	1	no	—
31	Q₁₆	—	359	2	no	—
32	Q₁₆	—	718	1	no	—
33	C₂×C₈	C₂×D₃₅₉	1	1	yes	characteristic
34	C₄⋊C₄	—	718	1	no	—
35	C₁₆	—	2	1	no	—
36	Q₈	—	1436	1	no	—
37	Q₈	—	718	2	no	—
38	C₂×C₄	—	1436	1	no	—
39	C₂×C₄	—	1436	1	no	—
40	C₂×C₄	D₁₄₃₆	1	1	yes	characteristic
41	C₈	C₄×D₃₅₉	1	1	yes	characteristic
42	C₈	C₂²⋊D₃₅₉	1	1	yes	characteristic
43	C₂²	D₂₈₇₂	1	1	yes	characteristic
44	C₄	—	2872	1	no	—
45	C₄	—	1436	2	no	—
46	C₄	(C₂×D₃₅₉)⋊C₄	1	1	yes	characteristic
47	C₄	#19153330	1	1	yes	characteristic
48	C₂	#26039937	1	1	yes	characteristic
49	C₂	#26039960	1	1	yes	characteristic
50	C₂	Dic₂₈₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₈₇₂
commutator	C₈×C₃₅₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₃₅₉
Fitting	C₂×C₁₆×C₃₅₉	C₂
socle, prime radical	C₂²×C₃₅₉	D₈
cosocle	C₂×C₈×C₃₅₉	C₂²
hypercenter	C₂×C₁₆	D₃₅₉
hypocenter	C₃₅₉	#358
LCS	G ▷ C₈×C₃₅₉ ▷ C₄×C₃₅₉ ▷ C₂×C₃₅₉ ▷ C₃₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. Dic₁₄₃₆	C₄	semidirect
25. C₃₅₉	#358	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₄₃₆	2
#26039949	2
C₂×C₁₆×C₃₅₉	2
#358	359