Subgroups — #16837776

Order 3776.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745671	C₂	1	4	yes	maximal, complemented
2	#14273724	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₅₉	C₂²	1	2	yes	—
6	C₂×D₂₃₆	—	2	2	no	—
7	C₂×D₂₃₆	C₂²	1	2	yes	—
8	C₄⋊C₄×C₅₉	—	2	2	no	—
9	C₄²×C₅₉	C₂²	1	1	yes	characteristic
10	#11745671	—	2	8	no	—
11	C₂×C₅₉⋊C₈	C₂²	1	2	yes	—
12	C₂²×D₅₉	—	2	2	no	—
13	Q₈×C₅₉	—	2	4	no	—
14	C₂×C₄×C₅₉	—	2	2	no	—
15	C₂×C₄×C₅₉	D₄	1	2	yes	—
16	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
17	D₂₃₆	—	2	4	no	—
18	D₂₃₆	—	4	4	no	—
19	C₅₉⋊C₈	D₄	1	4	yes	complemented
20	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
21	C₂×D₅₉	—	4	2	no	—
22	C₂×D₅₉	—	4	4	no	—
23	C₄×C₅₉	—	4	2	no	—
24	C₄×C₅₉	SD₁₆	1	4	yes	complemented
25	C₄×C₅₉	C₂×D₄	1	2	yes	—
26	C₂×C₅₉	#127	1	1	yes	characteristic
27	C₂×C₅₉	C₂×SD₁₆	1	2	yes	—
28	D₅₉	—	8	2	no	—
29	#492	—	59	1	no	maximal, Sylow
30	C₅₉	#492	1	1	yes	characteristic, complemented, Sylow
31	C₂×SD₁₆	—	59	4	no	—
32	C₄⋊Q₈	D₅₉	1	1	yes	characteristic, complemented
33	#127	—	59	1	no	—
34	C₄×C₈	—	59	1	no	—
35	C₂×Q₈	C₂×D₅₉	1	2	yes	—
36	C₂×D₄	—	59	2	no	—
37	C₂×D₄	—	118	2	no	—
38	SD₁₆	—	118	8	no	—
39	C₂×C₈	—	59	2	no	—
40	C₄⋊C₄	—	2	2	no	—
41	C₄²	C₂×D₅₉	1	1	yes	characteristic
42	C₂³	—	118	2	no	—
43	Q₈	—	2	4	no	—
44	D₄	—	118	4	no	—
45	D₄	—	236	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	C₂²⋊D₅₉	1	2	yes	—
48	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
49	C₈	—	59	4	no	—
50	C₂²	—	236	2	no	—
51	C₂²	—	236	4	no	—
52	C₂²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	#11745671	1	4	yes	complemented
55	C₄	D₄×D₅₉	1	2	yes	—
56	C₂	—	472	2	no	—
57	C₂	#14273723	1	1	yes	characteristic
58	C₂	C₂×#11745671	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₅₉
commutator, cosocle	C₂×C₄×C₅₉	C₂³
Frattini	C₂×C₄	C₂²×D₅₉
Fitting	C₄⋊Q₈×C₅₉	C₂
socle	C₂²×C₅₉	C₂×D₄
prime radical	#14273724	C₂
hypercenter	C₄⋊Q₈	D₅₉
hypocenter	C₅₉	#492
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#11745671	C₂	semidirect
3. C₄×C₅₉⋊C₈	C₂	semidirect
4. C₄⋊Q₈×C₅₉	C₂	semidirect
19. C₅₉⋊C₈	D₄	semidirect
24. C₄×C₅₉	SD₁₆	semidirect
30. C₅₉	#492	semidirect
32. C₄⋊Q₈	D₅₉	semidirect
54. C₄	#11745671	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745671	2
#14273724	2
C₄×C₅₉⋊C₈	2
C₄⋊Q₈×C₅₉	2
#492	59