Subgroups — #16821379

Order 3712.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271595	C₂	1	1	yes	maximal, characteristic
2	#14271281	C₂	1	2	yes	maximal, complemented
3	#14270993	C₂	1	1	yes	maximal, characteristic, complemented
4	#14270971	C₂	1	2	yes	maximal, complemented
5	C₂₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745266	C₂²	1	2	yes	—
7	#11745263	—	2	2	no	—
8	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#11745167	C₂²	1	2	yes	—
12	#11745153	—	2	2	no	—
13	Dic₂₃₂	C₄	1	1	yes	characteristic, complemented
14	#11745148	C₄	1	2	yes	complemented
15	D₄₆₄	C₄	1	1	yes	characteristic, complemented
16	#90805	—	2	2	no	—
17	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
19	C₄²×C₂₉	D₄	1	1	yes	characteristic
20	#90777	—	2	2	no	—
21	Dic₁₁₆	C₂×C₄	1	2	yes	—
22	D₂₃₂	C₂×C₄	1	2	yes	—
23	#90773	—	2	2	no	—
24	#90772	—	4	2	no	—
25	C₈×D₂₉	—	4	2	no	—
26	C₁₆×C₂₉	—	2	1	no	—
27	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	—	2	1	no	—
30	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₂₉	—	4	2	no	—
32	D₁₁₆	—	2	2	no	—
33	C₄×D₂₉	—	4	2	no	—
34	Dic₅₈	—	2	2	no	—
35	C₈×C₂₉	D₈	1	2	yes	—
36	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₂₉	#41	1	1	yes	characteristic
38	#6597	—	4	2	no	—
39	#2179	—	29	1	no	maximal, Sylow
40	C₂²×C₂₉	#135	1	1	yes	characteristic
41	C₂×D₂₉	—	4	2	no	—
42	C₄×C₂₉	—	4	1	no	—
43	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
44	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
45	Dic₂₉	—	4	2	no	—
46	#508	—	29	1	no	—
47	#443	—	29	2	no	—
48	#368	—	29	1	no	—
49	#359	—	29	2	no	—
50	#346	D₂₉	1	1	yes	characteristic, complemented
51	C₂×C₂₉	—	2	1	no	—
52	C₂×C₂₉	C₄×D₈	1	1	yes	characteristic
53	D₂₉	—	8	2	no	—
54	#135	—	29	2	no	—
55	#131	—	58	2	no	—
56	Q₃₂	—	29	1	no	—
57	SD₃₂	—	29	2	no	—
58	D₁₆	—	29	1	no	—
59	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
60	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
61	#108	—	29	2	no	—
62	#104	—	58	2	no	—
63	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
64	C₂₉	#2179	1	1	yes	characteristic, complemented, Sylow
65	#41	—	58	2	no	—
66	Q₁₆	—	29	2	no	—
67	SD₁₆	—	58	2	no	—
68	D₈	—	29	2	no	—
69	M₁₆	—	58	2	no	—
70	M₁₆	—	116	2	no	—
71	C₂×C₈	—	116	2	no	—
72	C₂×C₈	D₁₁₆	1	1	yes	characteristic
73	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
74	C₄²	D₁₁₆	1	1	yes	characteristic
75	C₁₆	—	2	1	no	—
76	C₁₆	C₄×D₂₉	1	1	yes	characteristic
77	C₁₆	C₄×D₂₉	1	1	yes	characteristic
78	Q₈	—	58	2	no	—
79	D₄	—	58	2	no	—
80	D₄	—	116	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	116	2	no	—
83	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
84	C₈	—	116	2	no	—
85	C₈	D₂₃₂	1	2	yes	—
86	C₈	C₂×C₄×D₂₉	1	1	yes	characteristic
87	C₈	#90805	1	1	yes	characteristic
88	C₂²	—	116	2	no	—
89	C₂²	#11745266	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	116	2	no	—
92	C₄	C₄×D₁₁₆	1	1	yes	characteristic
93	C₄	C₂×D₂₃₂	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	232	2	no	—
96	C₂	C₄×D₂₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₂₃₂
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₂₉×#346	C₂
socle	C₂×C₂₉	C₄×D₈
prime radical	#14271595	C₂
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	#346	D₂₉
hypocenter	C₂₉	#2179
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #14271281	C₂	semidirect
3. #14270993	C₂	semidirect
4. #14270971	C₂	semidirect
5. C₂₉×#346	C₂	semidirect
13. Dic₂₃₂	C₄	semidirect
14. #11745148	C₄	semidirect
15. D₄₆₄	C₄	semidirect
50. #346	D₂₉	semidirect
64. C₂₉	#2179	semidirect

Maximal subgroups

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

subgroup	index
#14271595	2
#14271281	2
#14270993	2
#14270971	2
C₂₉×#346	2
#2179	29