Subgroups — #16817413

Order 3712.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270939	C₂	1	1	yes	maximal, characteristic
2	#14270939	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#322	C₂	1	1	yes	maximal, characteristic
4	C₄×C₈×C₂₉	C₄	1	2	yes	—
5	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×#90768	C₄	1	2	yes	—
7	C₂×#90768	C₄	1	2	yes	—
8	C₂×C₈×C₂₉	—	2	2	no	—
9	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
12	#90768	—	2	2	no	—
13	#90768	C₈	1	4	yes	complemented
14	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
16	C₈×C₂₉	—	4	2	no	—
17	C₈×C₂₉	C₂×C₈	1	2	yes	—
18	C₈×C₂₉	M₁₆	1	2	yes	—
19	#1313	—	29	1	no	maximal, Sylow
20	C₂²×C₂₉	#97	1	1	yes	characteristic
21	C₄×C₂₉	—	2	2	no	—
22	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
23	C₄×C₂₉	#97	1	1	yes	characteristic
24	#346	—	29	1	no	—
25	#346	—	29	1	no	—
26	#322	D₂₉	1	1	yes	characteristic
27	C₂×C₂₉	#322	1	1	yes	characteristic
28	C₂×C₂₉	#347	1	2	yes	—
29	C₂×C₁₆	—	29	2	no	—
30	C₂×C₁₆	—	29	2	no	—
31	C₄×C₈	Dic₂₉	1	2	yes	—
32	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
33	C₂₉	#1313	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₈	—	2	2	no	—
35	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
36	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
37	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
38	C₁₆	—	29	4	no	—
39	C₁₆	—	58	2	no	—
40	C₂×C₄	#90777	1	2	yes	—
41	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
42	C₈	—	4	2	no	—
43	C₈	C₈×D₂₉	1	2	yes	—
44	C₈	#90772	1	2	yes	—
45	C₂²	#11745151	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₈×Dic₂₉	1	1	yes	characteristic
48	C₄	#11745163	1	1	yes	characteristic
49	C₂	#14270885	1	1	yes	characteristic
50	C₂	#14270941	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₂₉
commutator	C₄×C₂₉	C₄×C₈
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#322	C₂
socle, prime radical	C₂²×C₂₉	#97
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#322	D₂₉
hypocenter	C₂₉	#1313
LCS	G ▷ C₄×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ #322

Complements

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

N	H ≅ G/N	type
13. #90768	C₈	semidirect
33. C₂₉	#1313	semidirect

Maximal subgroups

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

subgroup	index
#14270939	2
C₂₉×#322	2
#1313	29