Subgroups — #16819649

Order 3712.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745165	C₂	1	4	yes	maximal
2	#14271033	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
5	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊Dic₂₉	—	2	4	no	—
7	C₂×C₄⋊Dic₂₉	C₂²	1	4	yes	—
8	C₄×C₈×C₂₉	C₄	1	4	yes	complemented
9	#11745165	—	2	8	no	—
10	C₂²×C₄×C₂₉	D₄	1	2	yes	—
11	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
12	C₂²×Dic₂₉	—	2	4	no	—
13	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₂₉	D₄	1	4	yes	—
15	C₂×C₈×C₂₉	Q₈	1	4	yes	—
16	C₄²×C₂₉	C₂×C₄	1	2	yes	—
17	C₄²×C₂₉	Q₈	1	2	yes	—
18	C₄⋊Dic₂₉	—	2	8	no	—
19	C₄⋊Dic₂₉	—	4	8	no	—
20	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₂₉	SD₁₆	1	8	yes	—
23	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
26	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
27	C₂×Dic₂₉	—	4	4	no	—
28	C₂×Dic₂₉	—	4	8	no	—
29	C₈×C₂₉	C₄⋊C₄	1	8	yes	complemented
30	#1844	—	29	1	no	maximal, Sylow
31	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂²×C₂₉	#127	1	1	yes	characteristic
33	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
34	C₂²×C₂₉	C₂×SD₁₆	1	4	yes	—
35	C₄×C₂₉	#106	1	8	yes	complemented
36	C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
37	C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
38	Dic₂₉	—	8	4	no	—
39	C₂×#106	—	29	4	no	—
40	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
41	#384	—	29	2	no	—
42	C₂×C₂₉	#384	1	1	yes	characteristic
43	C₂×C₂₉	C₂×#106	1	2	yes	—
44	C₂×C₂₉	#492	1	2	yes	—
45	C₂×C₂₉	#498	1	2	yes	—
46	C₂²×C₈	C₂×D₂₉	1	2	yes	—
47	C₂×C₄⋊C₄	—	29	4	no	—
48	C₂×C₄⋊C₄	—	58	4	no	—
49	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
50	#106	—	58	8	no	—
51	C₄×C₈	Dic₂₉	1	4	yes	complemented
52	C₂₉	#1844	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₄	—	58	4	no	—
54	C₂²×C₄	D₁₁₆	1	2	yes	—
55	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
56	C₂×C₈	Dic₅₈	1	4	yes	—
57	C₂×C₈	D₁₁₆	1	4	yes	—
58	C₂×C₈	C₂×Dic₂₉	1	4	yes	—
59	C₄⋊C₄	—	58	8	no	—
60	C₄⋊C₄	—	116	8	no	—
61	C₄²	Dic₅₈	1	2	yes	—
62	C₄²	C₂×Dic₂₉	1	2	yes	—
63	C₂³	C₂×D₁₁₆	1	1	yes	characteristic
64	C₂×C₄	—	116	4	no	—
65	C₂×C₄	—	116	8	no	—
66	C₂×C₄	#90773	1	8	yes	—
67	C₂×C₄	C₄⋊Dic₂₉	1	4	yes	—
68	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
69	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
70	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
71	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
72	C₈	C₄⋊Dic₂₉	1	8	yes	complemented
73	C₂²	#11745231	1	1	yes	characteristic
74	C₂²	#11745236	1	1	yes	characteristic
75	C₂²	C₂×#90773	1	4	yes	—
76	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
77	C₄	—	232	4	no	—
78	C₄	#11745165	1	8	yes	complemented
79	C₄	#11745231	1	2	yes	—
80	C₄	C₂×C₄⋊Dic₂₉	1	2	yes	—
81	C₂	#14271033	1	1	yes	characteristic
82	C₂	C₂×#11745165	1	2	yes	—
83	C₂	#14271536	1	2	yes	—
84	C₂	#14271561	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₁₆
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₄×C₈×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×C₄×C₈	D₂₉
hypocenter	C₂₉	#1844
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₄×C₈×C₂₉	C₄	semidirect
29. C₈×C₂₉	C₄⋊C₄	semidirect
35. C₄×C₂₉	#106	semidirect
51. C₄×C₈	Dic₂₉	semidirect
52. C₂₉	#1844	semidirect
72. C₈	C₄⋊Dic₂₉	semidirect
78. C₄	#11745165	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745165	2
#14271033	2
C₂×C₄×C₈×C₂₉	2
#1844	29