Subgroups — #14271530

Order 1856.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745306	C₂	1	1	yes	maximal, characteristic
2	#11745252	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#103	C₂	1	1	yes	maximal, characteristic
4	#11745183	C₂	1	1	yes	maximal, characteristic
5	#11745164	C₂	1	1	yes	maximal, characteristic
6	#11745163	C₂	1	1	yes	maximal, characteristic
7	#11745158	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
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	#90779	—	2	1	no	—
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	Q₈×C₂₉	—	2	1	no	—
20	Q₈×C₂₉	—	2	1	no	—
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	—	2	1	no	—
29	Dic₅₈	—	2	1	no	—
30	C₈×C₂₉	—	2	1	no	—
31	#6597	—	2	1	no	—
32	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₉	—	4	1	no	—
34	C₄×C₂₉	—	4	1	no	—
35	C₄×C₂₉	#41	1	1	yes	characteristic
36	C₄×C₂₉	#41	1	1	yes	characteristic
37	Dic₂₉	—	2	1	no	—
38	Dic₂₉	—	2	1	no	—
39	Dic₂₉	—	4	1	no	—
40	Dic₂₉	—	4	1	no	—
41	#491	—	29	1	no	maximal, Sylow
42	C₂×C₂₉	#124	1	1	yes	characteristic
43	C₂×C₂₉	#137	1	1	yes	characteristic
44	C₂×C₂₉	#137	1	1	yes	characteristic
45	C₄⋊Q₈	—	29	1	no	—
46	#125	—	29	1	no	—
47	#103	—	29	1	no	—
48	#103	—	29	1	no	—
49	#103	—	29	1	no	—
50	#103	D₂₉	1	1	yes	characteristic
51	#97	—	29	1	no	—
52	C₂₉	#491	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₈	—	29	1	no	—
54	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic
55	C₂×C₈	—	29	1	no	—
56	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
57	C₄⋊C₄	—	29	1	no	—
58	C₄⋊C₄	—	58	1	no	—
59	C₄⋊C₄	—	58	1	no	—
60	C₄⋊C₄	—	58	1	no	—
61	C₄⋊C₄	—	58	1	no	—
62	C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
63	C₄²	—	29	1	no	—
64	Q₈	—	2	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	58	1	no	—
67	Q₈	—	58	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	29	1	no	—
71	C₂×C₄	—	29	1	no	—
72	C₂×C₄	—	58	1	no	—
73	C₂×C₄	—	58	1	no	—
74	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	58	1	no	—
77	C₂²	D₄×D₂₉	1	1	yes	characteristic
78	C₄	—	4	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	58	1	no	—
81	C₄	—	58	1	no	—
82	C₄	—	116	1	no	—
83	C₄	—	116	1	no	—
84	C₄	#90805	1	1	yes	characteristic
85	C₄	#90807	1	1	yes	characteristic
86	C₂	#11745247	1	1	yes	characteristic
87	C₂	#11745277	1	1	yes	characteristic
88	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×#103	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
hypercenter	#103	D₂₉
hypocenter	C₂₉	#491
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
52. C₂₉	#491	semidirect

Maximal subgroups

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

subgroup	index
#11745306	2
#11745252	2
C₂₉×#103	2
#11745183	2
#11745164	2
#11745163	2
#11745158	2
#491	29