Subgroups — #14271602

Order 1856.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745274	C₂	1	1	yes	maximal, characteristic
3	C₂₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745177	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745175	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₂₃₂	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745146	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×D₂₉	—	2	1	no	—
9	#90807	—	2	1	no	—
10	Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
11	D₈×C₂₉	C₂²	1	1	yes	characteristic
12	#90785	—	2	1	no	—
13	#90783	—	2	1	no	—
14	Dic₁₁₆	C₂²	1	1	yes	characteristic
15	Dic₁₁₆	C₂²	1	1	yes	characteristic
16	C₈×D₂₉	C₂²	1	1	yes	characteristic
17	C₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	#90768	C₂²	1	1	yes	characteristic
19	Q₈×C₂₉	—	2	1	no	—
20	D₄×C₂₉	—	2	1	no	—
21	C₂²⋊D₂₉	—	4	1	no	—
22	C₂×Dic₂₉	—	4	1	no	—
23	C₄×D₂₉	—	4	1	no	—
24	C₄×D₂₉	D₄	1	1	yes	characteristic
25	Dic₅₈	—	2	1	no	—
26	Dic₅₈	—	2	1	no	—
27	Dic₅₈	—	4	1	no	—
28	C₈×C₂₉	C₂³	1	1	yes	characteristic
29	#6597	D₄	1	1	yes	characteristic
30	C₂²×C₂₉	—	4	1	no	—
31	C₂×D₂₉	D₈	1	1	yes	characteristic
32	C₄×C₂₉	—	4	1	no	—
33	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	Dic₂₉	—	4	1	no	—
35	Dic₂₉	—	4	1	no	—
36	Dic₂₉	D₈	1	1	yes	characteristic
37	#510	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	—	8	1	no	—
39	C₂×C₂₉	C₂×D₈	1	1	yes	characteristic
40	D₂₉	—	2	1	no	—
41	#135	—	29	1	no	—
42	C₂×Q₁₆	—	29	1	no	—
43	Q₃₂	—	29	1	no	—
44	Q₃₂	—	29	1	no	—
45	SD₃₂	—	29	1	no	—
46	SD₃₂	D₂₉	1	1	yes	characteristic, complemented
47	M₃₂	—	29	1	no	—
48	C₂₉	#510	1	1	yes	characteristic, complemented, Sylow
49	#41	—	58	1	no	—
50	C₂×Q₈	—	58	1	no	—
51	Q₁₆	—	29	1	no	—
52	Q₁₆	—	29	1	no	—
53	Q₁₆	—	58	1	no	—
54	Q₁₆	C₂×D₂₉	1	1	yes	characteristic
55	SD₁₆	—	58	1	no	—
56	D₈	C₂×D₂₉	1	1	yes	characteristic
57	C₂×C₈	—	29	1	no	—
58	C₁₆	—	29	1	no	—
59	C₁₆	C₂×D₂₉	1	1	yes	characteristic
60	Q₈	—	2	1	no	—
61	Q₈	—	58	1	no	—
62	Q₈	—	58	1	no	—
63	Q₈	—	116	1	no	—
64	D₄	—	2	1	no	—
65	D₄	—	116	1	no	—
66	C₂×C₄	—	29	1	no	—
67	C₂×C₄	—	116	1	no	—
68	C₂×C₄	—	116	1	no	—
69	C₈	—	29	1	no	—
70	C₈	C₂²×D₂₉	1	1	yes	characteristic
71	C₂²	—	4	1	no	—
72	C₂²	—	29	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	29	1	no	—
75	C₄	—	116	1	no	—
76	C₄	—	116	1	no	—
77	C₄	D₄×D₂₉	1	1	yes	characteristic
78	C₂	—	8	1	no	—
79	C₂	—	58	1	no	—
80	C₂	D₈×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₂₉
commutator, cosocle	C₈×C₂₉	C₂³
Frattini	C₈	C₂²×D₂₉
Fitting	C₂₉×SD₃₂	C₂
socle	C₂×C₂₉	C₂×D₈
prime radical	#11745274	C₂
hypercenter	SD₃₂	D₂₉
hypocenter	C₂₉	#510
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. Q₁₆×D₂₉	C₂	semidirect
3. C₂₉×SD₃₂	C₂	semidirect
4. #11745177	C₂	semidirect
5. #11745175	C₂	semidirect
6. Dic₂₃₂	C₂	semidirect
7. #11745146	C₂	semidirect
46. SD₃₂	D₂₉	semidirect
48. C₂₉	#510	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×D₂₉	2
#11745274	2
C₂₉×SD₃₂	2
#11745177	2
#11745175	2
Dic₂₃₂	2
#11745146	2
#510	29