Subgroups — #16819652

Order 3712.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745166	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	#11745166	—	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	D₈	1	4	yes	—
23	C₂×C₄×C₂₉	Q₁₆	1	4	yes	—
24	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
26	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
27	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
28	C₂×Dic₂₉	—	4	4	no	—
29	C₂×Dic₂₉	—	4	8	no	—
30	C₈×C₂₉	C₄⋊C₄	1	8	yes	complemented
31	#1845	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂²×C₂₉	#127	1	1	yes	characteristic
34	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
35	C₂²×C₂₉	C₂×D₈	1	2	yes	—
36	C₂²×C₂₉	C₂×Q₁₆	1	2	yes	—
37	C₄×C₂₉	#107	1	8	yes	complemented
38	C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
39	C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
40	Dic₂₉	—	8	4	no	—
41	C₂×#107	—	29	4	no	—
42	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
43	#384	—	29	2	no	—
44	C₂×C₂₉	#384	1	1	yes	characteristic
45	C₂×C₂₉	C₂×#107	1	2	yes	—
46	C₂×C₂₉	#493	1	1	yes	characteristic
47	C₂×C₂₉	#494	1	1	yes	characteristic
48	C₂×C₂₉	#500	1	2	yes	—
49	C₂²×C₈	C₂×D₂₉	1	2	yes	—
50	C₂×C₄⋊C₄	—	29	4	no	—
51	C₂×C₄⋊C₄	—	58	4	no	—
52	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
53	#107	—	58	8	no	—
54	C₄×C₈	Dic₂₉	1	4	yes	complemented
55	C₂₉	#1845	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	—	58	4	no	—
57	C₂²×C₄	D₁₁₆	1	2	yes	—
58	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
59	C₂×C₈	Dic₅₈	1	4	yes	—
60	C₂×C₈	D₁₁₆	1	4	yes	—
61	C₂×C₈	C₂×Dic₂₉	1	4	yes	—
62	C₄⋊C₄	—	58	8	no	—
63	C₄⋊C₄	—	116	8	no	—
64	C₄²	Dic₅₈	1	2	yes	—
65	C₄²	C₂×Dic₂₉	1	2	yes	—
66	C₂³	C₂×D₁₁₆	1	1	yes	characteristic
67	C₂×C₄	—	116	4	no	—
68	C₂×C₄	—	116	8	no	—
69	C₂×C₄	D₂₃₂	1	4	yes	—
70	C₂×C₄	Dic₁₁₆	1	4	yes	—
71	C₂×C₄	C₄⋊Dic₂₉	1	4	yes	—
72	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
73	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
74	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
75	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
76	C₈	C₄⋊Dic₂₉	1	8	yes	complemented
77	C₂²	#11745231	1	1	yes	characteristic
78	C₂²	#11745236	1	1	yes	characteristic
79	C₂²	C₂×D₂₃₂	1	2	yes	—
80	C₂²	C₂×Dic₁₁₆	1	2	yes	—
81	C₂²	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
82	C₄	—	232	4	no	—
83	C₄	#11745166	1	8	yes	complemented
84	C₄	#11745231	1	2	yes	—
85	C₄	C₂×C₄⋊Dic₂₉	1	2	yes	—
86	C₂	#14271033	1	1	yes	characteristic
87	C₂	C₂×#11745166	1	2	yes	—
88	C₂	#14271540	1	1	yes	characteristic
89	C₂	#14271543	1	1	yes	characteristic
90	C₂	#14271568	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	#1845
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
30. C₈×C₂₉	C₄⋊C₄	semidirect
37. C₄×C₂₉	#107	semidirect
54. C₄×C₈	Dic₂₉	semidirect
55. C₂₉	#1845	semidirect
76. C₈	C₄⋊Dic₂₉	semidirect
83. C₄	#11745166	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745166	2
#14271033	2
C₂×C₄×C₈×C₂₉	2
#1845	29