Subgroups — #16821779

Order 3712.

120 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	#14270990	C₂	1	2	yes	maximal
3	#14270988	C₂	1	2	yes	maximal
4	#14270939	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#499	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#125	—	2	1	no	—
7	#11745231	—	2	1	no	—
8	C₂₉×#107	C₂²	1	1	yes	characteristic
9	C₂₉×#107	C₂²	1	1	yes	characteristic
10	C₂₉×#106	—	2	1	no	—
11	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#11745166	—	2	1	no	—
13	#11745166	C₂²	1	2	yes	—
14	C₂×#90768	C₂²	1	2	yes	—
15	C₂×Dic₅₈	—	4	1	no	—
16	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₂₉	—	2	1	no	—
19	C₄⋊C₄×C₂₉	—	2	1	no	—
20	C₄⋊C₄×C₂₉	—	4	1	no	—
21	C₄⋊C₄×C₂₉	—	4	1	no	—
22	C₄²×C₂₉	D₄	1	1	yes	characteristic
23	C₄⋊Dic₂₉	—	2	2	no	—
24	C₄⋊Dic₂₉	—	4	1	no	—
25	#90768	Q₈	1	4	yes	complemented
26	C₂×C₄×C₂₉	—	4	1	no	—
27	C₂×C₄×C₂₉	—	4	1	no	—
28	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₂₉	—	4	2	no	—
32	Dic₅₈	—	8	2	no	—
33	C₈×C₂₉	Q₁₆	1	2	yes	—
34	C₈×C₂₉	C₂×Q₈	1	2	yes	—
35	#2255	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
37	C₄×C₂₉	—	2	1	no	—
38	C₄×C₂₉	—	2	1	no	—
39	C₄×C₂₉	—	8	1	no	—
40	C₄×C₂₉	—	8	1	no	—
41	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
42	C₄×C₂₉	C₂×Q₁₆	1	1	yes	characteristic
43	Dic₂₉	—	8	2	no	—
44	#500	—	29	1	no	—
45	#499	D₂₉	1	1	yes	characteristic
46	#367	—	29	2	no	—
47	#366	—	29	2	no	—
48	#346	—	29	1	no	—
49	C₂×C₂₉	#500	1	1	yes	characteristic
50	C₂×C₂₉	#509	1	1	yes	characteristic
51	C₂×C₂₉	#510	1	1	yes	characteristic
52	C₄⋊Q₈	—	58	1	no	—
53	#125	—	2	1	no	—
54	C₂×C₁₆	—	29	2	no	—
55	#107	—	29	2	no	—
56	#107	—	58	1	no	—
57	#107	C₂×D₂₉	1	1	yes	characteristic
58	#107	C₂×D₂₉	1	1	yes	characteristic
59	#106	—	2	1	no	—
60	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
61	C₂₉	#2255	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	116	1	no	—
63	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
65	C₄⋊C₄	—	2	1	no	—
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	4	1	no	—
68	C₄⋊C₄	—	4	1	no	—
69	C₄⋊C₄	—	58	2	no	—
70	C₄⋊C₄	—	116	1	no	—
71	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
72	C₁₆	—	29	4	no	—
73	Q₈	—	232	2	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	116	2	no	—
77	C₂×C₄	#90782	1	1	yes	characteristic
78	C₂×C₄	#90782	1	1	yes	characteristic
79	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
80	C₈	#90785	1	2	yes	—
81	C₈	Q₈×D₂₉	1	2	yes	—
82	C₂²	C₂×#90782	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	8	1	no	—
87	C₄	—	232	2	no	—
88	C₄	C₂×#90785	1	1	yes	characteristic
89	C₄	#11745306	1	1	yes	characteristic
90	C₂	#14271566	1	1	yes	characteristic
91	C₂	#14271598	1	1	yes	characteristic
92	C₂	#14271603	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#90782
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂₉×#499	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
hypercenter	#499	D₂₉
hypocenter	C₂₉	#2255
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
25. #90768	Q₈	semidirect
61. C₂₉	#2255	semidirect

Maximal subgroups

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

subgroup	index
#14271568	2
#14270990	2
#14270988	2
#14270939	2
C₂₉×#499	2
#2255	29