Subgroups — #16819179

Order 3712.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745151	C₂	1	3	yes	maximal
2	C₂×C₄×#6597	C₂	1	3	yes	maximal
3	C₂₉×#376	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₂₉	C₂²	1	3	yes	—
5	C₂²×#6597	C₂²	1	1	yes	characteristic
6	C₂²×#6597	C₂²	1	3	yes	—
7	C₂₉×#95	C₄	1	4	yes	—
8	#11745151	C₄	1	12	yes	complemented
9	C₄×#6597	C₄	1	12	yes	complemented
10	C₂²×C₄×C₂₉	C₂×C₄	1	6	yes	—
11	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
12	C₄²×C₂₉	C₂×C₄	1	6	yes	—
13	C₄²×C₂₉	C₂×C₄	1	6	yes	—
14	C₂×#6597	C₂×C₄	1	6	yes	—
15	C₂×#6597	C₂×C₄	1	6	yes	—
16	C₂×#6597	C₂×C₄	1	12	yes	—
17	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	—	2	12	no	—
19	C₂×C₄×C₂₉	C₄²	1	12	yes	—
20	C₂×C₄×C₂₉	C₂²×C₄	1	3	yes	—
21	C₂×C₄×C₂₉	C₂²×C₄	1	3	yes	—
22	#6597	C₄²	1	4	yes	—
23	#6597	C₄²	1	12	yes	—
24	#1726	—	29	1	no	maximal, Sylow
25	C₂²×C₂₉	C₂×C₄²	1	3	yes	—
26	C₂²×C₂₉	#131	1	4	yes	—
27	C₄×C₂₉	—	2	12	no	—
28	C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
29	C₄×C₂₉	C₂×C₄²	1	3	yes	—
30	C₂×#97	—	29	3	no	—
31	C₂×C₄×C₈	—	29	3	no	—
32	#376	D₂₉	1	1	yes	characteristic
33	C₂×C₂₉	C₄³	1	1	yes	characteristic
34	C₂×C₂₉	#405	1	6	yes	—
35	C₂²×C₈	—	29	1	no	—
36	C₂²×C₈	—	29	3	no	—
37	C₂×C₄²	C₂×D₂₉	1	3	yes	—
38	#97	—	29	12	no	—
39	C₄×C₈	—	29	12	no	—
40	#95	Dic₂₉	1	4	yes	—
41	C₂₉	#1726	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₄	C₂×Dic₂₉	1	6	yes	—
43	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
44	C₂×C₈	—	29	6	no	—
45	C₂×C₈	—	29	6	no	—
46	C₂×C₈	—	29	12	no	—
47	C₄²	C₄×D₂₉	1	6	yes	—
48	C₄²	C₄×D₂₉	1	6	yes	—
49	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
50	C₂×C₄	—	2	12	no	—
51	C₂×C₄	C₄×Dic₂₉	1	12	yes	—
52	C₂×C₄	C₂×C₄×D₂₉	1	3	yes	—
53	C₂×C₄	C₂×C₄×D₂₉	1	3	yes	—
54	C₈	—	29	4	no	—
55	C₈	—	29	12	no	—
56	C₂²	C₂×C₄×Dic₂₉	1	3	yes	—
57	C₂²	#11745310	1	4	yes	—
58	C₄	—	2	12	no	—
59	C₄	C₄²×D₂₉	1	1	yes	characteristic
60	C₄	C₄²×D₂₉	1	3	yes	—
61	C₂	C₄²×Dic₂₉	1	1	yes	characteristic
62	C₂	#14271119	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator	C₂×C₂₉	C₄³
Fitting	C₂₉×#376	C₂
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	#376	D₂₉
hypocenter	C₂₉	#1726
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
8. #11745151	C₄	semidirect
9. C₄×#6597	C₄	semidirect
41. C₂₉	#1726	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745151	2
C₂×C₄×#6597	2
C₂₉×#376	2
#1726	29