Subgroups — #16817403

Order 3712.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271220	C₂	1	2	yes	maximal
2	C₂₉×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₂₉	C₄	1	2	yes	—
4	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
5	C₂₉×C₄⋊C₈	—	2	2	no	—
6	C₂²⋊#6597	C₄	1	4	yes	—
7	C₄⋊#6597	—	2	2	no	—
8	#11745151	—	2	2	no	—
9	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
11	M₁₆×C₂₉	—	4	2	no	—
12	C₂×C₈×C₂₉	—	2	2	no	—
13	C₄²×C₂₉	D₄	1	1	yes	characteristic
14	C₄²×C₂₉	D₄	1	2	yes	—
15	C₄²×C₂₉	Q₈	1	1	yes	characteristic
16	C₂×#6597	—	2	4	no	—
17	C₂³×C₂₉	C₄²	1	1	yes	characteristic
18	C₂×C₄×C₂₉	—	2	1	no	—
19	C₂×C₄×C₂₉	—	2	1	no	—
20	C₂×C₄×C₂₉	—	4	2	no	—
21	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
25	C₈×C₂₉	—	4	2	no	—
26	#6597	—	4	4	no	—
27	#1307	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	—	2	1	no	—
29	C₂²×C₂₉	—	2	2	no	—
30	C₂²×C₂₉	#95	1	1	yes	characteristic
31	C₄×C₂₉	—	2	1	no	—
32	C₄×C₂₉	—	2	2	no	—
33	C₄×C₂₉	—	2	2	no	—
34	C₄×C₂₉	#100	1	1	yes	characteristic
35	C₄×C₂₉	#101	1	1	yes	characteristic
36	#432	—	29	2	no	—
37	#423	D₂₉	1	1	yes	characteristic
38	C₂×C₂₉	—	4	1	no	—
39	C₂×C₂₉	#343	1	1	yes	characteristic
40	C₂×C₂₉	#344	1	2	yes	—
41	C₂×M₁₆	Dic₂₉	1	2	yes	—
42	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
43	C₄⋊C₈	—	2	2	no	—
44	C₄⋊C₈	—	58	2	no	—
45	C₂²⋊C₈	—	29	4	no	—
46	#97	—	58	2	no	—
47	C₂₉	#1307	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	C₄×D₂₉	1	2	yes	—
49	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
50	M₁₆	—	4	2	no	—
51	C₂×C₈	—	2	2	no	—
52	C₂×C₈	—	58	4	no	—
53	C₄²	Dic₅₈	1	1	yes	characteristic
54	C₄²	D₁₁₆	1	1	yes	characteristic
55	C₄²	C₂²⋊D₂₉	1	2	yes	—
56	C₂³	C₄×Dic₂₉	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	#90779	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
62	C₂×C₄	#90781	1	2	yes	—
63	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
64	C₈	—	4	2	no	—
65	C₈	—	116	4	no	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	2	no	—
68	C₂²	#11745179	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	2	2	no	—
71	C₄	—	2	2	no	—
72	C₄	#11745181	1	1	yes	characteristic
73	C₄	#11745184	1	1	yes	characteristic
74	C₂	—	4	1	no	—
75	C₂	#14270932	1	1	yes	characteristic
76	C₂	#14270935	1	2	yes	—

	subgroup	G/H
center	C₂²	#11745179
commutator, prime radical	C₂³×C₂₉	C₄²
Frattini	C₂×C₄²	C₂×D₂₉
Fitting	C₂₉×#423	C₂
socle	C₂²×C₂₉	#95
cosocle	C₂×C₄²×C₂₉	C₂²
hypercenter	#423	D₂₉
hypocenter	C₂₉	#1307
LCS	G ▷ C₂³×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
47. C₂₉	#1307	semidirect

Maximal subgroups

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

subgroup	index
#14271220	2
C₂₉×#423	2
#1307	29