Subgroups — #16819635

Order 3712.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270918	C₂	1	6	yes	maximal
2	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₂₉	C₄	1	3	yes	—
4	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
5	C₂×C₄²×C₂₉	C₂²	1	3	yes	—
6	C₂²×#6597	C₂²	1	4	yes	—
7	C₂²×C₄×C₂₉	C₂×C₄	1	3	yes	—
8	C₂²×C₄×C₂₉	C₂×C₄	1	3	yes	—
9	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
10	C₄²×C₂₉	—	2	6	no	—
11	C₄²×C₂₉	—	2	6	no	—
12	C₄²×C₂₉	C₈	1	4	yes	complemented
13	C₂×#6597	—	2	12	no	—
14	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₉	—	2	3	no	—
16	C₂×C₄×C₂₉	—	2	3	no	—
17	C₂×C₄×C₂₉	—	2	3	no	—
18	C₂×C₄×C₂₉	—	2	3	no	—
19	C₂×C₄×C₂₉	C₂×C₈	1	6	yes	—
20	C₂×C₄×C₂₉	M₁₆	1	6	yes	—
21	C₂×C₄×C₂₉	#41	1	6	yes	—
22	#6597	—	4	4	no	—
23	#1839	—	29	1	no	maximal, Sylow
24	C₂²×C₂₉	#117	1	3	yes	—
25	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
26	C₂²×C₂₉	C₂×M₁₆	1	3	yes	—
27	C₄×C₂₉	—	2	6	no	—
28	C₄×C₂₉	—	2	6	no	—
29	C₄×C₂₉	#126	1	4	yes	—
30	C₄³	D₂₉	1	1	yes	characteristic
31	#336	—	29	6	no	—
32	C₂×C₂₉	#383	1	1	yes	characteristic
33	C₂×C₂₉	#431	1	3	yes	—
34	C₂×C₂₉	#432	1	3	yes	—
35	C₂²×C₈	—	29	4	no	—
36	C₂×C₄²	Dic₂₉	1	3	yes	—
37	C₂×C₄²	Dic₂₉	1	1	yes	characteristic
38	C₂×C₄²	C₂×D₂₉	1	3	yes	—
39	C₂₉	#1839	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₄	C₂×Dic₂₉	1	3	yes	—
41	C₂²×C₄	C₂×Dic₂₉	1	3	yes	—
42	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
43	C₂×C₈	—	58	12	no	—
44	C₄²	—	2	6	no	—
45	C₄²	—	2	6	no	—
46	C₄²	#6597	1	4	yes	complemented
47	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
48	C₂×C₄	—	2	3	no	—
49	C₂×C₄	—	2	3	no	—
50	C₂×C₄	—	2	3	no	—
51	C₂×C₄	—	2	3	no	—
52	C₂×C₄	C₂×#6597	1	6	yes	—
53	C₂×C₄	#90777	1	6	yes	—
54	C₂×C₄	#90805	1	6	yes	—
55	C₈	—	116	4	no	—
56	C₂²	C₂²×#6597	1	1	yes	characteristic
57	C₂²	C₂×#90777	1	3	yes	—
58	C₂²	#11745288	1	3	yes	—
59	C₄	—	2	6	no	—
60	C₄	—	2	6	no	—
61	C₄	#11745238	1	4	yes	—
62	C₂	#14271031	1	1	yes	characteristic
63	C₂	#14271216	1	3	yes	—
64	C₂	#14271220	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₉
commutator	C₂²×C₂₉	C₂²×C₈
Fitting	C₄³×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₄³	D₂₉
hypocenter	C₂₉	#1839
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
12. C₄²×C₂₉	C₈	semidirect
39. C₂₉	#1839	semidirect
46. C₄²	#6597	semidirect

Maximal subgroups

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

subgroup	index
#14270918	2
C₄³×C₂₉	2
#1839	29