Subgroups — #14272078

Order 1856.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745281	C₂	1	1	yes	maximal, characteristic
2	#11745212	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#90809	—	2	1	no	—
5	#90796	—	2	1	no	—
6	Q₁₆×C₂₉	C₄	1	1	yes	characteristic
7	#90784	—	2	1	no	—
8	D₂₃₂	C₄	1	1	yes	characteristic
9	C₈×D₂₉	C₂²	1	1	yes	characteristic
10	#90770	—	2	1	no	—
11	Q₈×C₂₉	—	2	1	no	—
12	D₁₁₆	—	2	1	no	—
13	D₁₁₆	—	4	1	no	—
14	C₄×D₂₉	—	4	1	no	—
15	C₄×D₂₉	D₄	1	1	yes	characteristic
16	#6599	—	4	1	no	—
17	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
18	#6597	D₄	1	1	yes	characteristic
19	C₂×D₂₉	—	4	1	no	—
20	C₂×D₂₉	SD₁₆	1	1	yes	characteristic
21	C₄×C₂₉	—	4	1	no	—
22	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₂₉	D₈	1	1	yes	characteristic
24	#359	—	29	1	no	maximal, Sylow
25	C₂×C₂₉	#102	1	1	yes	characteristic
26	D₂₉	—	2	1	no	—
27	D₂₉	—	8	1	no	—
28	#135	—	29	1	no	—
29	C₂×C₁₆	—	29	1	no	—
30	#108	—	29	1	no	—
31	C₂₉	#359	1	1	yes	characteristic, complemented, Sylow
32	#41	—	58	1	no	—
33	Q₁₆	#1181	1	1	yes	characteristic
34	SD₁₆	—	58	1	no	—
35	D₈	—	29	1	no	—
36	M₁₆	—	58	1	no	—
37	C₂×C₈	—	29	1	no	—
38	C₁₆	—	58	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	58	1	no	—
41	D₄	—	116	1	no	—
42	C₂×C₄	—	29	1	no	—
43	C₂×C₄	—	116	1	no	—
44	C₈	—	29	1	no	—
45	C₈	—	116	1	no	—
46	C₈	C₂×#1181	1	1	yes	characteristic
47	C₂²	—	29	1	no	—
48	C₂²	—	116	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	29	1	no	—
51	C₄	C₂²⋊#1181	1	1	yes	characteristic
52	C₂	—	58	1	no	—
53	C₂	—	232	1	no	—
54	C₂	#11745223	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11745223
commutator	C₈×C₂₉	C₂×C₄
Frattini	C₈	C₂×#1181
Fitting	Q₁₆×C₂₉	C₄
socle	C₂×C₂₉	#102
prime radical	#11745281	C₂
cosocle	C₈×D₂₉	C₂²
hypercenter	Q₁₆	#1181
hypocenter	C₂₉	#359
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. #11745212	C₂	semidirect
3. D₂₉⋊C₁₆	C₂	semidirect
31. C₂₉	#359	semidirect

Maximal subgroups

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

subgroup	index
#11745281	2
#11745212	2
D₂₉⋊C₁₆	2
#359	29