Subgroups — #14271541

Order 1856.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745306	C₂	1	2	yes	maximal
3	C₂×#90785	C₂	1	2	yes	maximal
4	C₂×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic
5	C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₂₉	C₂²	1	2	yes	—
7	C₂×Dic₅₈	C₂²	1	2	yes	—
8	Q₁₆×C₂₉	—	2	2	no	—
9	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	#90785	—	2	4	no	—
11	#90779	—	2	4	no	—
12	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₂×#6597	C₂²	1	1	yes	characteristic
14	Dic₁₁₆	—	2	2	no	—
15	Q₈×C₂₉	—	2	2	no	—
16	Q₈×C₂₉	—	2	2	no	—
17	C₂×C₄×C₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₉	—	2	2	no	—
20	C₂×Dic₂₉	D₄	1	2	yes	—
21	Dic₅₈	—	2	2	no	—
22	Dic₅₈	—	2	2	no	—
23	C₈×C₂₉	D₄	1	2	yes	—
24	#6597	D₄	1	2	yes	—
25	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
26	C₄×C₂₉	—	4	2	no	—
27	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
29	Dic₂₉	—	4	2	no	—
30	Dic₂₉	Q₁₆	1	4	yes	complemented
31	#494	—	29	1	no	maximal, Sylow
32	C₂×C₂₉	#127	1	1	yes	characteristic
33	C₂×C₂₉	C₂×Q₁₆	1	2	yes	—
34	C₂×Q₁₆	—	29	2	no	—
35	C₂×Q₁₆	—	29	1	no	—
36	C₂×Q₁₆	D₂₉	1	1	yes	characteristic
37	C₄⋊Q₈	—	29	2	no	—
38	C₄×C₈	—	29	1	no	—
39	C₂₉	#494	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	29	2	no	—
41	C₂×Q₈	C₂×D₂₉	1	2	yes	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	58	4	no	—
44	Q₁₆	—	58	2	no	—
45	C₂×C₈	—	29	1	no	—
46	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
47	C₄⋊C₄	—	58	4	no	—
48	C₄²	—	29	1	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	58	2	no	—
52	Q₈	—	58	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	29	2	no	—
55	C₂×C₄	—	58	2	no	—
56	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
57	C₈	—	29	2	no	—
58	C₈	C₂²⋊D₂₉	1	2	yes	—
59	C₂²	D₄×D₂₉	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	29	4	no	—
62	C₄	—	116	2	no	—
63	C₄	D₄×D₂₉	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
65	C₂	Q₁₆×D₂₉	1	2	yes	—
66	C₂	#11745302	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂×Q₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₄
hypercenter	C₂×Q₁₆	D₂₉
hypocenter	C₂₉	#494
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
30. Dic₂₉	Q₁₆	semidirect
39. C₂₉	#494	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₂₉	2
#11745306	2
C₂×#90785	2
C₂×Dic₁₁₆	2
C₈×Dic₂₉	2
#494	29