Subgroups — #14271269

Order 1856.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic
2	#11745249	C₂	1	2	yes	maximal
3	C₂₉×#106	C₂	1	1	yes	maximal, characteristic
4	#11745163	C₂	1	1	yes	maximal, characteristic
5	#11745158	C₂	1	2	yes	maximal
6	C₂×Dic₅₈	C₂²	1	2	yes	—
7	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
9	#90779	—	2	2	no	—
10	C₄×Dic₂₉	—	2	2	no	—
11	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	C₂×#6597	C₂²	1	1	yes	characteristic
13	Dic₁₁₆	C₄	1	4	yes	complemented
14	C₂×C₄×C₂₉	—	2	2	no	—
15	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
16	C₂×Dic₂₉	—	2	2	no	—
17	C₂×Dic₂₉	D₄	1	2	yes	—
18	Dic₅₈	—	2	2	no	—
19	Dic₅₈	C₂×C₄	1	4	yes	—
20	C₈×C₂₉	C₂×C₄	1	2	yes	—
21	#6597	—	2	1	no	—
22	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
23	C₄×C₂₉	—	4	2	no	—
24	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₂₉	#41	1	1	yes	characteristic
26	Dic₂₉	—	2	4	no	—
27	Dic₂₉	—	2	2	no	—
28	#441	—	29	1	no	maximal, Sylow
29	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
30	C₂×C₂₉	#137	1	2	yes	—
31	C₂×Q₁₆	—	29	1	no	—
32	C₄×Q₈	—	29	2	no	—
33	#106	D₂₉	1	1	yes	characteristic
34	#103	—	29	2	no	—
35	#97	—	29	1	no	—
36	C₂₉	#441	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	29	2	no	—
38	Q₁₆	—	29	4	no	—
39	C₂×C₈	—	29	1	no	—
40	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
41	C₄⋊C₄	—	58	2	no	—
42	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
43	C₄²	—	29	1	no	—
44	C₄²	—	58	2	no	—
45	Q₈	—	29	4	no	—
46	Q₈	—	58	2	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	29	2	no	—
49	C₂×C₄	—	58	2	no	—
50	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
51	C₈	—	58	1	no	—
52	C₈	C₄×D₂₉	1	2	yes	—
53	C₂²	D₄×D₂₉	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	58	4	no	—
56	C₄	—	58	2	no	—
57	C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
58	C₄	#90809	1	1	yes	characteristic
59	C₂	#11745255	1	1	yes	characteristic
60	C₂	#11745277	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#106	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	#106	D₂₉
hypocenter	C₂₉	#441
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
13. Dic₁₁₆	C₄	semidirect
36. C₂₉	#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₆	2
#11745249	2
C₂₉×#106	2
#11745163	2
#11745158	2
#441	29