Subgroups — #14271571

Order 1856.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745252	C₂	1	1	yes	maximal, characteristic
2	#11745250	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#107	C₂	1	1	yes	maximal, characteristic
4	#11745165	C₂	1	1	yes	maximal, characteristic
5	#11745163	C₂	1	1	yes	maximal, characteristic
6	#11745156	C₂	1	1	yes	maximal, characteristic
7	#11745155	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₅₈	—	2	1	no	—
9	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₂₉	—	2	1	no	—
13	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
15	#90779	—	2	1	no	—
16	#90779	—	2	1	no	—
17	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
18	C₂×#6597	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₂₉	—	2	1	no	—
20	C₂×C₄×C₂₉	—	2	1	no	—
21	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₂₉	—	2	1	no	—
23	C₂×Dic₂₉	—	2	1	no	—
24	C₂×Dic₂₉	D₄	1	1	yes	characteristic
25	C₂×Dic₂₉	D₄	1	1	yes	characteristic
26	Dic₅₈	—	4	2	no	—
27	C₈×C₂₉	Q₈	1	2	yes	complemented
28	#6597	Q₈	1	2	yes	complemented
29	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₂₉	—	4	1	no	—
31	C₄×C₂₉	—	4	1	no	—
32	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
34	Dic₂₉	—	2	1	no	—
35	Dic₂₉	—	2	1	no	—
36	Dic₂₉	—	4	1	no	—
37	Dic₂₉	—	4	1	no	—
38	#501	—	29	1	no	maximal, Sylow
39	C₂×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
40	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
41	C₂×C₂₉	#137	1	1	yes	characteristic
42	C₄⋊Q₈	—	29	1	no	—
43	#125	—	29	1	no	—
44	#107	—	29	1	no	—
45	#107	D₂₉	1	1	yes	characteristic
46	#106	—	29	1	no	—
47	#106	—	29	1	no	—
48	#97	—	29	1	no	—
49	C₂₉	#501	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	58	1	no	—
51	C₂×C₈	—	29	1	no	—
52	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
53	C₄⋊C₄	—	29	1	no	—
54	C₄⋊C₄	—	29	1	no	—
55	C₄⋊C₄	—	58	1	no	—
56	C₄⋊C₄	—	58	1	no	—
57	C₄⋊C₄	—	58	1	no	—
58	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
60	C₄²	—	29	1	no	—
61	Q₈	—	116	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	29	1	no	—
65	C₂×C₄	—	29	1	no	—
66	C₂×C₄	—	58	1	no	—
67	C₂×C₄	—	58	1	no	—
68	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
69	C₈	—	29	2	no	—
70	C₈	Dic₅₈	1	2	yes	complemented
71	C₂²	D₄×D₂₉	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	58	1	no	—
75	C₄	—	58	1	no	—
76	C₄	—	116	1	no	—
77	C₄	—	116	1	no	—
78	C₄	C₂×Dic₅₈	1	1	yes	characteristic
79	C₄	Q₈×D₂₉	1	1	yes	characteristic
80	C₂	#11745250	1	1	yes	characteristic
81	C₂	#11745273	1	1	yes	characteristic
82	C₂	#11745280	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#107	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
hypercenter	#107	D₂₉
hypocenter	C₂₉	#501
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
27. C₈×C₂₉	Q₈	semidirect
28. #6597	Q₈	semidirect
49. C₂₉	#501	semidirect
70. C₈	Dic₅₈	semidirect

Maximal subgroups

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

subgroup	index
#11745252	2
#11745250	2
C₂₉×#107	2
#11745165	2
#11745163	2
#11745156	2
#11745155	2
#501	29