Subgroups — #14271257

Order 1856.

110 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×#107	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₂₉	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	1	yes	characteristic
18	C₂×Dic₂₉	D₄	1	1	yes	characteristic
19	Dic₅₈	—	2	2	no	—
20	Dic₅₈	C₂×C₄	1	4	yes	—
21	C₈×C₂₉	C₂×C₄	1	2	yes	—
22	#6597	—	2	1	no	—
23	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
24	C₄×C₂₉	—	4	2	no	—
25	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₂₉	#41	1	1	yes	characteristic
27	Dic₂₉	—	2	4	no	—
28	Dic₂₉	—	2	1	no	—
29	Dic₂₉	Q₁₆	1	2	yes	complemented
30	C₄×Q₁₆	—	29	1	no	maximal, Sylow
31	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
32	C₂×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
33	C₂×C₂₉	#135	1	1	yes	characteristic
34	C₂×Q₁₆	—	29	1	no	—
35	C₄×Q₈	—	29	2	no	—
36	#107	D₂₉	1	1	yes	characteristic
37	#103	—	29	2	no	—
38	C₄×C₈	—	29	1	no	—
39	C₂₉	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	29	2	no	—
41	Q₁₆	—	29	4	no	—
42	C₂×C₈	—	29	1	no	—
43	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
44	C₄⋊C₄	—	58	2	no	—
45	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
46	C₄²	—	29	1	no	—
47	C₄²	—	58	2	no	—
48	Q₈	—	29	4	no	—
49	Q₈	—	58	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	29	1	no	—
52	C₂×C₄	—	29	1	no	—
53	C₂×C₄	—	58	2	no	—
54	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
55	C₈	—	58	1	no	—
56	C₈	C₄×D₂₉	1	2	yes	—
57	C₂²	D₄×D₂₉	1	1	yes	characteristic
58	C₄	—	4	2	no	—
59	C₄	—	29	2	no	—
60	C₄	—	58	4	no	—
61	C₄	—	58	1	no	—
62	C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
63	C₄	#90809	1	1	yes	characteristic
64	C₂	#11745255	1	1	yes	characteristic
65	C₂	#11745274	1	1	yes	characteristic
66	C₂	Q₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#107	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	#107	D₂₉
hypocenter	C₂₉	C₄×Q₁₆
LCS	G ▷ 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
13. Dic₁₁₆	C₄	semidirect
29. Dic₂₉	Q₁₆	semidirect
39. C₂₉	C₄×Q₁₆	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×#107	2
C₈×Dic₂₉	2
#11745158	2
C₄×Q₁₆	29