Subgroups — #16821721

Order 3712.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271543	C₂	1	1	yes	maximal, characteristic
2	#14270966	C₂	1	4	yes	maximal
3	C₄×#90768	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#500	C₂	1	1	yes	maximal, characteristic
5	C₂₉×C₄⋊Q₈	—	2	1	no	—
6	C₂×Dic₁₁₆	—	2	1	no	—
7	C₂×Dic₁₁₆	C₂²	1	2	yes	—
8	#11745231	—	2	1	no	—
9	C₂₉×#107	—	2	1	no	—
10	C₂₉×#107	C₂²	1	2	yes	—
11	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×#90768	C₂²	1	2	yes	—
13	C₂×Q₈×C₂₉	—	4	1	no	—
14	C₂×Dic₅₈	—	2	2	no	—
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₂₉	—	2	2	no	—
18	C₄⋊C₄×C₂₉	—	4	1	no	—
19	C₄²×C₂₉	D₄	1	1	yes	characteristic
20	C₄⋊Dic₂₉	—	4	1	no	—
21	C₄⋊Dic₂₉	—	4	1	no	—
22	Dic₁₁₆	—	2	4	no	—
23	Dic₁₁₆	—	4	2	no	—
24	#90768	—	2	2	no	—
25	Q₈×C₂₉	—	8	2	no	—
26	C₂×C₄×C₂₉	—	4	2	no	—
27	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
28	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₂₉	—	4	2	no	—
31	Dic₅₈	—	4	2	no	—
32	Dic₅₈	—	4	2	no	—
33	C₈×C₂₉	SD₁₆	1	2	yes	—
34	C₈×C₂₉	#41	1	2	yes	—
35	#2241	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
37	C₄×C₂₉	—	8	2	no	—
38	C₄×C₂₉	SD₃₂	1	2	yes	—
39	C₄×C₂₉	Q₃₂	1	2	yes	—
40	C₄×C₂₉	#124	1	1	yes	characteristic
41	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
42	Dic₂₉	—	8	2	no	—
43	#500	D₂₉	1	1	yes	characteristic
44	#494	—	29	1	no	—
45	#358	—	29	4	no	—
46	C₄×C₁₆	—	29	1	no	—
47	C₂×C₂₉	#486	1	1	yes	characteristic
48	C₂×C₂₉	C₂×SD₃₂	1	1	yes	characteristic
49	C₂×C₂₉	C₂×Q₃₂	1	1	yes	characteristic
50	C₂×Q₁₆	—	29	2	no	—
51	C₂×Q₁₆	—	58	1	no	—
52	C₄⋊Q₈	—	2	1	no	—
53	C₄⋊Q₈	—	58	1	no	—
54	C₂×C₁₆	—	29	2	no	—
55	#107	—	2	1	no	—
56	#107	C₂×D₂₉	1	2	yes	—
57	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
58	C₂₉	#2241	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	4	1	no	—
60	C₂×Q₈	—	58	2	no	—
61	Q₁₆	—	58	4	no	—
62	Q₁₆	—	116	2	no	—
63	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	116	1	no	—
68	C₄⋊C₄	—	116	1	no	—
69	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
70	C₁₆	—	58	2	no	—
71	Q₈	—	8	2	no	—
72	Q₈	—	116	2	no	—
73	Q₈	—	116	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	116	2	no	—
76	C₂×C₄	#90782	1	1	yes	characteristic
77	C₂×C₄	#90782	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
79	C₈	#90784	1	2	yes	—
80	C₈	#90809	1	2	yes	—
81	C₂²	C₂×#90782	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	232	2	no	—
84	C₄	#11745175	1	2	yes	—
85	C₄	#11745177	1	2	yes	—
86	C₄	C₂×#90784	1	1	yes	characteristic
87	C₄	#11745309	1	1	yes	characteristic
88	C₂	#14271511	1	1	yes	characteristic
89	C₂	C₂×#11745175	1	1	yes	characteristic
90	C₂	C₂×#11745177	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#90782
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂₉×#500	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
hypercenter	#500	D₂₉
hypocenter	C₂₉	#2241
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
58. C₂₉	#2241	semidirect

Maximal subgroups

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

subgroup	index
#14271543	2
#14270966	2
C₄×#90768	2
C₂₉×#500	2
#2241	29