Subgroups — #16817481

Order 3712.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271421	C₂	1	1	yes	maximal, characteristic
2	#14270920	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#349	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
5	#11745288	—	2	1	no	—
6	#11745286	—	2	1	no	—
7	C₂×Dic₁₁₆	C₄	1	1	yes	characteristic, complemented
8	C₂₉×M₃₂	—	2	1	no	—
9	#11745165	C₄	1	1	yes	characteristic, complemented
10	#11745164	—	2	1	no	—
11	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
12	C₂×Dic₅₈	—	2	1	no	—
13	M₁₆×C₂₉	—	4	1	no	—
14	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₂²⋊Dic₂₉	—	4	1	no	—
17	C₂²⋊Dic₂₉	—	4	1	no	—
18	C₄⋊Dic₂₉	—	2	1	no	—
19	C₄⋊Dic₂₉	—	4	1	no	—
20	#90779	—	4	1	no	—
21	C₄×Dic₂₉	—	2	2	no	—
22	Dic₁₁₆	—	4	1	no	—
23	C₁₆×C₂₉	—	4	1	no	—
24	C₂³×C₂₉	D₈	1	1	yes	characteristic
25	C₂×C₄×C₂₉	—	2	1	no	—
26	C₂×C₄×C₂₉	—	2	1	no	—
27	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
29	C₂×Dic₂₉	—	4	2	no	—
30	C₂×Dic₂₉	—	4	1	no	—
31	C₂×Dic₂₉	—	4	1	no	—
32	Dic₅₈	—	4	1	no	—
33	Dic₅₈	—	4	1	no	—
34	C₈×C₂₉	—	2	1	no	—
35	C₈×C₂₉	—	2	1	no	—
36	#1340	—	29	1	no	maximal, Sylow
37	C₂²×C₂₉	—	2	1	no	—
38	C₂²×C₂₉	—	4	1	no	—
39	C₂²×C₂₉	#102	1	1	yes	characteristic
40	C₄×C₂₉	—	2	1	no	—
41	C₄×C₂₉	#99	1	1	yes	characteristic
42	C₄×C₂₉	#104	1	1	yes	characteristic
43	Dic₂₉	—	8	1	no	—
44	Dic₂₉	—	8	2	no	—
45	Dic₂₉	—	8	1	no	—
46	#470	—	29	1	no	—
47	#349	D₂₉	1	1	yes	characteristic
48	H(3,ℤ/4)	—	29	1	no	—
49	C₂×C₂₉	—	2	1	no	—
50	C₂×C₂₉	—	4	1	no	—
51	C₂×C₂₉	#327	1	1	yes	characteristic
52	C₂×Q₁₆	—	29	1	no	—
53	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
54	C₂²⋊Q₈	—	58	1	no	—
55	#117	—	58	1	no	—
56	M₃₂	—	2	1	no	—
57	#106	—	29	1	no	—
58	#103	—	58	1	no	—
59	C₂₉	#1340	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	58	1	no	—
61	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
62	Q₁₆	—	116	1	no	—
63	M₁₆	—	4	1	no	—
64	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
66	C₄⋊C₄	—	58	1	no	—
67	C₄⋊C₄	—	116	1	no	—
68	C₄⋊C₄	—	116	1	no	—
69	C₂²⋊C₄	—	116	1	no	—
70	C₂²⋊C₄	—	116	1	no	—
71	C₄²	—	58	2	no	—
72	C₁₆	—	4	1	no	—
73	C₂³	D₂₃₂	1	1	yes	characteristic
74	Q₈	—	116	1	no	—
75	Q₈	—	116	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	116	2	no	—
79	C₂×C₄	—	116	1	no	—
80	C₂×C₄	—	116	1	no	—
81	C₂×C₄	#90773	1	1	yes	characteristic
82	C₂×C₄	#90781	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#11745169	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	232	1	no	—
90	C₄	—	232	2	no	—
91	C₄	—	232	1	no	—
92	C₄	#11745154	1	1	yes	characteristic
93	C₄	#11745173	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#14270898	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270898
commutator	C₂×C₈×C₂₉	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₂₉
Fitting	C₂₉×#349	C₂
socle	C₂×C₂₉	#327
prime radical	C₂³×C₂₉	D₈
cosocle	C₂×M₁₆×C₂₉	C₂²
hypercenter	#349	D₂₉
hypocenter	C₂₉	#1340
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
7. C₂×Dic₁₁₆	C₄	semidirect
9. #11745165	C₄	semidirect
59. C₂₉	#1340	semidirect

Maximal subgroups

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

subgroup	index
#14271421	2
#14270920	2
C₂₉×#349	2
#1340	29