Subgroups — #16821734

Order 3712.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271565	C₂	1	1	yes	maximal, characteristic, complemented
2	#14271540	C₂	1	1	yes	maximal, characteristic
3	#14270965	C₂	1	4	yes	maximal, complemented
4	C₂₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₂₃₂	—	2	1	no	—
6	C₂×D₂₃₂	C₂²	1	2	yes	—
7	#11745236	—	2	1	no	—
8	#11745232	—	2	1	no	—
9	C₂×C₁₆×C₂₉	C₂²	1	2	yes	—
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#11745166	C₂²	1	2	yes	—
12	#11745165	—	2	1	no	—
13	C₂×D₁₁₆	—	2	2	no	—
14	C₂×D₁₁₆	—	4	2	no	—
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
17	C₄²×C₂₉	D₄	1	1	yes	characteristic
18	C₄⋊Dic₂₉	—	2	2	no	—
19	#90779	—	4	2	no	—
20	D₂₃₂	—	2	4	no	—
21	D₂₃₂	—	4	2	no	—
22	C₁₆×C₂₉	—	2	2	no	—
23	C₂²×D₂₉	—	4	2	no	—
24	C₂×C₄×C₂₉	D₈	1	2	yes	—
25	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₂₉	—	4	2	no	—
27	D₁₁₆	—	4	2	no	—
28	D₁₁₆	—	4	2	no	—
29	D₁₁₆	—	8	4	no	—
30	C₈×C₂₉	SD₁₆	1	2	yes	—
31	C₈×C₂₉	#41	1	2	yes	—
32	#2244	—	29	1	no	maximal, Sylow
33	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
34	C₂×D₂₉	—	8	2	no	—
35	C₂×D₂₉	—	8	4	no	—
36	C₄×C₂₉	—	2	2	no	—
37	C₄×C₂₉	#124	1	1	yes	characteristic
38	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
39	Dic₂₉	—	8	2	no	—
40	#499	—	29	1	no	—
41	#493	—	29	1	no	—
42	#357	—	29	4	no	—
43	#346	D₂₉	1	1	yes	characteristic, complemented
44	C₂×C₂₉	#486	1	1	yes	characteristic
45	C₂×C₂₉	#509	1	2	yes	—
46	D₂₉	—	16	2	no	—
47	C₂×D₈	—	29	2	no	—
48	C₂×D₈	—	58	1	no	—
49	#127	—	58	1	no	—
50	#125	—	58	1	no	—
51	C₂×C₁₆	C₂×D₂₉	1	2	yes	—
52	#107	—	29	2	no	—
53	#106	—	58	1	no	—
54	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
55	C₂₉	#2244	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₄	—	58	2	no	—
57	C₂×D₄	—	116	2	no	—
58	D₈	—	58	4	no	—
59	D₈	—	116	2	no	—
60	C₂×C₈	D₁₁₆	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
62	C₄⋊C₄	—	58	2	no	—
63	C₄⋊C₄	—	116	2	no	—
64	C₄²	D₁₁₆	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	C₂³	—	116	2	no	—
67	D₄	—	116	2	no	—
68	D₄	—	116	2	no	—
69	D₄	—	232	4	no	—
70	C₂×C₄	—	116	2	no	—
71	C₂×C₄	D₂₃₂	1	2	yes	—
72	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
73	C₈	#90773	1	2	yes	—
74	C₈	#90805	1	2	yes	—
75	C₂²	—	232	2	no	—
76	C₂²	—	232	4	no	—
77	C₂²	C₂×D₂₃₂	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	232	2	no	—
80	C₄	#11745237	1	1	yes	characteristic
81	C₄	C₂×#90773	1	1	yes	characteristic
82	C₂	—	464	2	no	—
83	C₂	#14271510	1	1	yes	characteristic
84	C₂	#14271601	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₃₂
commutator, cosocle	C₂×C₈×C₂₉	C₂³
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂₉×#346	C₂
socle	C₂²×C₂₉	C₂×D₈
prime radical	#14271540	C₂
hypercenter	#346	D₂₉
hypocenter	C₂₉	#2244
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
1. #14271565	C₂	semidirect
3. #14270965	C₂	semidirect
4. C₂₉×#346	C₂	semidirect
43. #346	D₂₉	semidirect
55. C₂₉	#2244	semidirect

Maximal subgroups

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

subgroup	index
#14271565	2
#14271540	2
#14270965	2
C₂₉×#346	2
#2244	29