Subgroups — #14271456

Order 1856.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745250	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#103	C₂	1	1	yes	maximal, characteristic
4	#11745183	C₂	1	1	yes	maximal, characteristic
5	#11745166	C₂	1	1	yes	maximal, characteristic
6	#11745162	C₂	1	1	yes	maximal, characteristic
7	#11745155	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₈	—	2	1	no	—
10	C₂×C₈×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	C₄×Dic₂₉	—	2	1	no	—
17	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
18	C₂×#6597	C₂²	1	1	yes	characteristic
19	Q₈×C₂₉	—	2	1	no	—
20	Q₈×C₂₉	Q₈	1	2	yes	complemented
21	C₂×C₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
24	C₂×Dic₂₉	—	2	1	no	—
25	C₂×Dic₂₉	—	2	1	no	—
26	C₂×Dic₂₉	D₄	1	1	yes	characteristic
27	C₂×Dic₂₉	D₄	1	1	yes	characteristic
28	Dic₅₈	—	4	2	no	—
29	C₈×C₂₉	—	2	1	no	—
30	#6597	—	2	1	no	—
31	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₄×C₂₉	—	2	2	no	—
33	C₄×C₂₉	—	4	1	no	—
34	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₂₉	#41	1	1	yes	characteristic
36	Dic₂₉	—	2	1	no	—
37	Dic₂₉	—	4	1	no	—
38	Dic₂₉	—	4	1	no	—
39	Dic₂₉	Q₁₆	1	2	yes	—
40	#477	—	29	1	no	maximal, Sylow
41	C₂×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
42	C₂×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
43	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
44	C₄⋊Q₈	—	29	1	no	—
45	C₄×Q₈	—	29	1	no	—
46	#107	—	29	1	no	—
47	#107	—	29	1	no	—
48	C₄⋊C₈	—	29	1	no	—
49	#103	—	29	1	no	—
50	#103	D₂₉	1	1	yes	characteristic
51	C₂₉	#477	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	58	1	no	—
53	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic
54	C₂×C₈	—	29	1	no	—
55	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
56	C₄⋊C₄	—	29	1	no	—
57	C₄⋊C₄	—	29	1	no	—
58	C₄⋊C₄	—	58	1	no	—
59	C₄⋊C₄	—	58	1	no	—
60	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
61	C₄²	—	29	1	no	—
62	C₄²	—	58	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	116	2	no	—
65	Q₈	Dic₅₈	1	2	yes	complemented
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	29	1	no	—
69	C₂×C₄	—	29	1	no	—
70	C₂×C₄	—	58	1	no	—
71	C₂×C₄	—	58	1	no	—
72	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	58	1	no	—
75	C₂²	D₄×D₂₉	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	29	2	no	—
79	C₄	—	58	1	no	—
80	C₄	—	116	1	no	—
81	C₄	—	116	1	no	—
82	C₄	C₂×Dic₅₈	1	1	yes	characteristic
83	C₄	#90807	1	1	yes	characteristic
84	C₂	#11745240	1	1	yes	characteristic
85	C₂	#11745276	1	1	yes	characteristic
86	C₂	Q₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#103	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
hypercenter	#103	D₂₉
hypocenter	C₂₉	#477
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
20. Q₈×C₂₉	Q₈	semidirect
51. C₂₉	#477	semidirect
65. Q₈	Dic₅₈	semidirect

Maximal subgroups

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

subgroup	index
Q₈×Dic₂₉	2
#11745250	2
C₂₉×#103	2
#11745183	2
#11745166	2
#11745162	2
#11745155	2
#477	29