Subgroups — #16821765

Order 3712.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271568	C₂	1	1	yes	maximal, characteristic
2	#14270988	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	#11745231	—	2	1	no	—
7	C₂₉×#107	—	2	1	no	—
8	C₂₉×#107	C₂²	1	2	yes	—
9	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	#11745166	—	2	1	no	—
11	#11745166	C₂²	1	2	yes	—
12	C₂×#90768	C₂²	1	2	yes	—
13	C₂×Q₈×C₂₉	—	4	1	no	—
14	C₂×Dic₅₈	—	4	1	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	—	2	2	no	—
21	C₄⋊Dic₂₉	—	4	1	no	—
22	#90768	Q₈	1	4	yes	complemented
23	Q₈×C₂₉	—	8	2	no	—
24	C₂×C₄×C₂₉	—	4	2	no	—
25	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
26	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₂₉	—	4	2	no	—
29	Dic₅₈	—	8	2	no	—
30	C₈×C₂₉	Q₁₆	1	2	yes	—
31	C₈×C₂₉	C₂×Q₈	1	2	yes	—
32	#2252	—	29	1	no	maximal, Sylow
33	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
34	C₄×C₂₉	—	8	2	no	—
35	C₄×C₂₉	D₁₆	1	2	yes	—
36	C₄×C₂₉	Q₃₂	1	2	yes	—
37	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
38	C₄×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
39	Dic₂₉	—	8	2	no	—
40	#500	—	29	1	no	—
41	#500	D₂₉	1	1	yes	characteristic
42	#366	—	29	4	no	—
43	C₄×C₁₆	—	29	1	no	—
44	C₂×C₂₉	#500	1	1	yes	characteristic
45	C₂×C₂₉	C₂×D₁₆	1	1	yes	characteristic
46	C₂×C₂₉	C₂×Q₃₂	1	1	yes	characteristic
47	C₄⋊Q₈	—	2	1	no	—
48	C₄⋊Q₈	—	58	1	no	—
49	C₂×C₁₆	—	29	2	no	—
50	#107	—	2	1	no	—
51	#107	—	29	2	no	—
52	#107	—	58	1	no	—
53	#107	C₂×D₂₉	1	2	yes	—
54	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
55	C₂₉	#2252	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	4	1	no	—
57	C₂×Q₈	—	116	1	no	—
58	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
59	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
60	C₄⋊C₄	—	2	2	no	—
61	C₄⋊C₄	—	4	1	no	—
62	C₄⋊C₄	—	58	2	no	—
63	C₄⋊C₄	—	116	1	no	—
64	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
65	C₁₆	—	29	4	no	—
66	Q₈	—	8	2	no	—
67	Q₈	—	232	2	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	—	116	2	no	—
70	C₂×C₄	#90782	1	1	yes	characteristic
71	C₂×C₄	#90782	1	1	yes	characteristic
72	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
73	C₈	#90785	1	2	yes	—
74	C₈	Q₈×D₂₉	1	2	yes	—
75	C₂²	C₂×#90782	1	1	yes	characteristic
76	C₄	—	8	2	no	—
77	C₄	—	232	2	no	—
78	C₄	#11745174	1	2	yes	—
79	C₄	#11745177	1	2	yes	—
80	C₄	C₂×#90785	1	1	yes	characteristic
81	C₄	#11745306	1	1	yes	characteristic
82	C₂	#14271566	1	1	yes	characteristic
83	C₂	C₂×#11745174	1	1	yes	characteristic
84	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	#2252
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
22. #90768	Q₈	semidirect
55. C₂₉	#2252	semidirect

Maximal subgroups

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

subgroup	index
#14271568	2
#14270988	2
C₄×#90768	2
C₂₉×#500	2
#2252	29