Subgroups — #14271267

Order 1856.

108 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	C₂×#90785	C₂	1	1	yes	maximal, characteristic
3	#11745249	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#103	C₂	1	1	yes	maximal, characteristic
5	#11745164	C₂	1	1	yes	maximal, characteristic
6	#11745163	C₂	1	1	yes	maximal, characteristic
7	#11745156	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	#90785	C₄	1	4	yes	complemented
13	C₄⋊Dic₂₉	—	2	1	no	—
14	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
15	#90779	—	2	1	no	—
16	C₄×Dic₂₉	—	2	1	no	—
17	C₄×Dic₂₉	—	2	1	no	—
18	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
19	C₂×#6597	C₂²	1	1	yes	characteristic
20	Q₈×C₂₉	—	2	1	no	—
21	Q₈×C₂₉	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	—	2	1	no	—
24	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
25	C₂×Dic₂₉	—	2	1	no	—
26	C₂×Dic₂₉	—	2	1	no	—
27	C₂×Dic₂₉	D₄	1	1	yes	characteristic
28	C₂×Dic₂₉	D₄	1	1	yes	characteristic
29	Dic₅₈	—	2	1	no	—
30	Dic₅₈	C₂×C₄	1	2	yes	—
31	C₈×C₂₉	—	2	1	no	—
32	#6597	C₂×C₄	1	2	yes	—
33	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₂₉	—	2	2	no	—
35	C₄×C₂₉	—	4	1	no	—
36	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₂₉	#41	1	1	yes	characteristic
38	Dic₂₉	—	2	2	no	—
39	Dic₂₉	—	2	1	no	—
40	Dic₂₉	—	2	1	no	—
41	Dic₂₉	—	4	1	no	—
42	#441	—	29	1	no	maximal, Sylow
43	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
44	C₂×C₂₉	#137	1	1	yes	characteristic
45	C₂×C₂₉	#137	1	1	yes	characteristic
46	C₂×Q₁₆	—	29	1	no	—
47	C₄×Q₈	—	29	1	no	—
48	C₄×Q₈	—	29	1	no	—
49	#106	—	29	1	no	—
50	#103	—	29	1	no	—
51	#103	D₂₉	1	1	yes	characteristic
52	#97	—	29	1	no	—
53	C₂₉	#441	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	29	1	no	—
55	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic
56	Q₁₆	—	29	4	no	—
57	C₂×C₈	—	29	1	no	—
58	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
59	C₄⋊C₄	—	29	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	C₄²	—	58	1	no	—
65	C₄²	—	58	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	29	2	no	—
68	Q₈	—	58	1	no	—
69	Q₈	C₄×D₂₉	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	29	1	no	—
73	C₂×C₄	—	29	1	no	—
74	C₂×C₄	—	58	1	no	—
75	C₂×C₄	—	58	1	no	—
76	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	29	2	no	—
79	C₂²	D₄×D₂₉	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	4	1	no	—
82	C₄	—	58	1	no	—
83	C₄	—	58	2	no	—
84	C₄	—	58	1	no	—
85	C₄	—	116	1	no	—
86	C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
87	C₄	#90807	1	1	yes	characteristic
88	C₂	#11745243	1	1	yes	characteristic
89	C₂	#11745277	1	1	yes	characteristic
90	C₂	#11745280	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#103	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	#103	D₂₉
hypocenter	C₂₉	#441
LCS	G ▷ 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
12. #90785	C₄	semidirect
53. C₂₉	#441	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
C₂×#90785	2
#11745249	2
C₂₉×#103	2
#11745164	2
#11745163	2
#11745156	2
#441	29