Subgroups — #16817691

Order 3712.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745142	C₂	1	1	yes	maximal, characteristic
2	#14270989	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#366	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
5	C₂₉×#107	—	2	1	no	—
6	#11745166	—	2	1	no	—
7	#11745142	C₄	1	2	yes	complemented
8	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
9	C₄⋊C₄×C₂₉	—	4	1	no	—
10	C₄⋊Dic₂₉	—	4	1	no	—
11	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₉	—	8	1	no	—
14	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
15	C₂×Dic₂₉	—	8	1	no	—
16	C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
18	#1423	—	29	1	no	maximal, Sylow
19	C₂²×C₂₉	D₁₆	1	1	yes	characteristic
20	C₄×C₂₉	—	16	1	no	—
21	C₄×C₂₉	#107	1	1	yes	characteristic
22	C₄×C₂₉	Q₃₂	1	1	yes	characteristic
23	Dic₂₉	—	16	1	no	—
24	C₂×C₃₂	—	29	1	no	—
25	#366	—	29	1	no	—
26	#366	D₂₉	1	1	yes	characteristic
27	C₂×C₂₉	#366	1	1	yes	characteristic
28	C₂×C₂₉	D₃₂	1	1	yes	characteristic
29	C₂×C₂₉	Q₆₄	1	1	yes	characteristic
30	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
31	#107	—	2	1	no	—
32	#107	—	58	1	no	—
33	C₃₂	—	29	2	no	—
34	C₂₉	#1423	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	116	1	no	—
38	C₁₆	Dic₅₈	1	1	yes	characteristic
39	C₁₆	C₄×D₂₉	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	232	1	no	—
42	C₂×C₄	#90782	1	1	yes	characteristic
43	C₈	#90779	1	1	yes	characteristic
44	C₈	#90785	1	1	yes	characteristic
45	C₂²	#11745174	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	464	1	no	—
48	C₄	#11745155	1	1	yes	characteristic
49	C₄	#11745177	1	1	yes	characteristic
50	C₂	#14270988	1	1	yes	characteristic
51	C₂	#14270998	1	1	yes	characteristic
52	C₂	#14271003	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745174
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂₉×#366	C₂
socle, prime radical	C₂²×C₂₉	D₁₆
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	#366	D₂₉
hypocenter	C₂₉	#1423
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
7. #11745142	C₄	semidirect
34. C₂₉	#1423	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745142	2
#14270989	2
C₂₉×#366	2
#1423	29