Subgroups — #16817791

Order 3712.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271214	C₂	1	3	yes	maximal
2	#14270885	C₂	1	3	yes	maximal, complemented
3	C₈²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₂₉	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₂₉	C₂²	1	3	yes	—
6	#11745168	C₄	1	6	yes	—
7	#11745162	C₄	1	6	yes	—
8	C₄×#6597	C₂²	1	3	yes	—
9	C₂×C₄×D₂₉	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₂₉	C₂×C₄	1	6	yes	—
11	C₄²×C₂₉	C₂³	1	1	yes	characteristic
12	C₄×Dic₂₉	C₂×C₄	1	3	yes	—
13	C₂×#6597	C₂×C₄	1	6	yes	—
14	C₂²×D₂₉	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₂₉	C₂²×C₄	1	3	yes	—
16	C₂×Dic₂₉	C₄²	1	3	yes	—
17	C₄×D₂₉	—	2	6	no	—
18	C₈×C₂₉	—	2	6	no	—
19	#6597	—	2	6	no	—
20	#1454	—	29	1	no	maximal, Sylow
21	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
22	C₂×D₂₉	—	2	3	no	—
23	C₄×C₂₉	#131	1	6	yes	—
24	Dic₂₉	—	2	3	no	—
25	#431	—	29	3	no	—
26	#322	—	29	3	no	—
27	C₈²	D₂₉	1	1	yes	characteristic, complemented
28	C₂×C₂₉	#405	1	3	yes	—
29	D₂₉	—	4	1	no	—
30	C₂×C₄²	—	29	1	no	—
31	C₄⋊C₈	—	29	6	no	—
32	C₂²⋊C₈	—	29	6	no	—
33	C₄×C₈	—	29	3	no	—
34	C₄×C₈	C₂×D₂₉	1	3	yes	—
35	C₂₉	#1454	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₄	—	29	3	no	—
37	C₂×C₈	—	29	6	no	—
38	C₂×C₈	C₄×D₂₉	1	6	yes	—
39	C₄²	—	29	3	no	—
40	C₄²	C₂²×D₂₉	1	1	yes	characteristic
41	C₂³	—	29	1	no	—
42	C₂×C₄	—	29	3	no	—
43	C₂×C₄	—	58	6	no	—
44	C₂×C₄	C₂×C₄×D₂₉	1	3	yes	—
45	C₈	—	2	6	no	—
46	C₈	—	58	6	no	—
47	C₂²	—	58	3	no	—
48	C₂²	C₄²×D₂₉	1	1	yes	characteristic
49	C₄	—	58	3	no	—
50	C₄	#11745263	1	6	yes	—
51	C₂	—	116	1	no	—
52	C₂	#14271117	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂×C₄²
Fitting	C₈²×C₂₉	C₂
prime radical	C₂²×D₂₉	C₄²
cosocle	C₄²×C₂₉	C₂³
hypercenter	C₈²	D₂₉
hypocenter	C₂₉	#1454
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #14270885	C₂	semidirect
3. C₈²×C₂₉	C₂	semidirect
27. C₈²	D₂₉	semidirect
35. C₂₉	#1454	semidirect

Maximal subgroups

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

subgroup	index
#14271214	2
#14270885	2
C₈²×C₂₉	2
#1454	29