Subgroups — #16819646

Order 3712.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#6597	C₂	1	6	yes	maximal
2	C₂₉×#376	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₂₉	C₂²	1	3	yes	—
4	C₂²×#6597	C₂²	1	4	yes	—
5	C₂₉×#95	C₄	1	4	yes	—
6	C₄⋊#6597	—	2	12	no	—
7	C₂²×C₄×C₂₉	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
9	C₄²×C₂₉	D₄	1	6	yes	—
10	C₄²×C₂₉	Q₈	1	6	yes	—
11	C₂×#6597	—	2	12	no	—
12	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₉	—	2	12	no	—
14	C₂×C₄×C₂₉	C₄⋊C₄	1	12	yes	—
15	C₂×C₄×C₂₉	C₂×D₄	1	3	yes	—
16	C₂×C₄×C₂₉	C₂×Q₈	1	3	yes	—
17	#6597	—	4	4	no	—
18	#1843	—	29	1	no	maximal, Sylow
19	C₂²×C₂₉	C₂×C₄⋊C₄	1	3	yes	—
20	C₂²×C₂₉	#131	1	4	yes	—
21	C₄×C₂₉	—	2	12	no	—
22	C₄×C₂₉	#127	1	1	yes	characteristic
23	C₄×C₂₉	C₄⋊Q₈	1	3	yes	—
24	C₂×C₄⋊C₈	—	29	6	no	—
25	#376	D₂₉	1	1	yes	characteristic
26	C₂×C₂₉	#384	1	1	yes	characteristic
27	C₂×C₂₉	#424	1	6	yes	—
28	C₂²×C₈	—	29	4	no	—
29	C₂×C₄²	C₂×D₂₉	1	3	yes	—
30	C₄⋊C₈	—	58	12	no	—
31	#95	Dic₂₉	1	4	yes	—
32	C₂₉	#1843	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₄	C₂×Dic₂₉	1	6	yes	—
34	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
35	C₂×C₈	—	58	12	no	—
36	C₄²	Dic₅₈	1	6	yes	—
37	C₄²	D₁₁₆	1	6	yes	—
38	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₂₉	1	12	yes	—
41	C₂×C₄	C₂×Dic₅₈	1	3	yes	—
42	C₂×C₄	C₂×D₁₁₆	1	3	yes	—
43	C₈	—	116	4	no	—
44	C₂²	C₂×C₄⋊Dic₂₉	1	3	yes	—
45	C₂²	#11745310	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#11745231	1	3	yes	—
48	C₄	#11745236	1	1	yes	characteristic
49	C₂	#14271033	1	1	yes	characteristic
50	C₂	#14271190	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator, socle, prime radical	C₂³×C₂₉	C₂²×C₄
Fitting	C₂₉×#376	C₂
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#376	D₂₉
hypocenter	C₂₉	#1843
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
32. C₂₉	#1843	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#6597	2
C₂₉×#376	2
#1843	29