Subgroups — #14272204

Order 1856.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#1181	C₂	1	2	yes	maximal, complemented
2	D₈×D₂₉	C₂	1	1	yes	maximal, characteristic
3	#11745223	C₂	1	2	yes	maximal, complemented
4	#11745209	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745208	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#1181	—	2	2	no	—
7	D₄×D₂₉	C₂²	1	2	yes	—
8	C₂²⋊#1181	—	2	2	no	—
9	C₄⋊#1181	C₂²	1	2	yes	—
10	C₄×#1181	C₂²	1	1	yes	characteristic
11	D₂₉⋊C₈	C₂²	1	1	yes	characteristic
12	D₈×C₂₉	C₄	1	1	yes	characteristic, complemented
13	#90782	C₄	1	2	yes	complemented
14	D₂₃₂	C₄	1	1	yes	characteristic, complemented
15	C₈×D₂₉	C₂²	1	1	yes	characteristic
16	C₂²×D₂₉	—	2	2	no	—
17	C₂×#1181	—	2	2	no	—
18	C₂×#1181	—	4	4	no	—
19	C₂×#1181	D₄	1	2	yes	—
20	D₄×C₂₉	C₂×C₄	1	2	yes	complemented
21	C₂²⋊D₂₉	—	2	2	no	—
22	D₁₁₆	C₂×C₄	1	2	yes	complemented
23	C₄×D₂₉	C₂³	1	1	yes	characteristic
24	#6599	—	2	1	no	—
25	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic, complemented
26	#6597	C₂×C₄	1	1	yes	characteristic, complemented
27	C₂²×C₂₉	—	2	2	no	—
28	C₂×D₂₉	—	2	2	no	—
29	C₂×D₂₉	—	4	2	no	—
30	C₂×D₂₉	—	4	2	no	—
31	C₂×D₂₉	C₂×D₄	1	1	yes	characteristic
32	#1181	—	2	2	no	—
33	#1181	—	4	2	no	—
34	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
35	Dic₂₉	#41	1	1	yes	characteristic
36	#442	—	29	1	no	maximal, Sylow
37	C₂×C₂₉	—	4	2	no	—
38	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
39	D₂₉	—	4	2	no	—
40	D₂₉	AGL(1,ℤ/8)	1	2	yes	—
41	C₂×D₈	—	29	1	no	—
42	C₄×D₄	—	29	2	no	—
43	#106	—	29	1	no	—
44	#102	—	29	2	no	—
45	#97	—	29	1	no	—
46	C₂₉	#442	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₄	—	29	2	no	—
48	C₂²×C₄	—	58	2	no	—
49	D₈	—	29	2	no	—
50	D₈	—	29	1	no	—
51	D₈	#1181	1	1	yes	characteristic, complemented
52	C₂×C₈	—	29	1	no	—
53	C₂×C₈	—	29	1	no	—
54	C₄⋊C₄	—	29	2	no	—
55	C₂²⋊C₄	—	58	2	no	—
56	C₄²	—	29	1	no	—
57	C₂³	—	58	2	no	—
58	D₄	—	29	2	no	—
59	D₄	—	58	2	no	—
60	D₄	C₂×#1181	1	2	yes	complemented
61	C₂×C₄	—	29	1	no	—
62	C₂×C₄	—	29	2	no	—
63	C₂×C₄	—	58	2	no	—
64	C₂×C₄	—	116	4	no	—
65	C₈	—	29	1	no	—
66	C₈	—	58	1	no	—
67	C₈	C₂×#1181	1	1	yes	characteristic, complemented
68	C₂²	—	2	2	no	—
69	C₂²	—	29	1	no	—
70	C₂²	—	58	2	no	—
71	C₂²	—	116	2	no	—
72	C₂²	—	116	2	no	—
73	C₄	—	29	1	no	—
74	C₄	—	58	2	no	—
75	C₄	—	116	2	no	—
76	C₄	C₂²×#1181	1	1	yes	characteristic
77	C₂	—	4	2	no	—
78	C₂	—	29	2	no	—
79	C₂	—	116	2	no	—
80	C₂	D₄×#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#1181
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₄	C₂²×#1181
Fitting	D₈×C₂₉	C₄
socle	C₂×C₂₉	C₄×D₄
prime radical	D₈×D₂₉	C₂
cosocle	C₄×D₂₉	C₂³
hypercenter	D₈	#1181
hypocenter	C₂₉	#442
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#1181	C₂	semidirect
3. #11745223	C₂	semidirect
4. #11745209	C₂	semidirect
5. #11745208	C₂	semidirect
12. D₈×C₂₉	C₄	semidirect
13. #90782	C₄	semidirect
14. D₂₃₂	C₄	semidirect
20. D₄×C₂₉	C₂×C₄	semidirect
22. D₁₁₆	C₂×C₄	semidirect
25. C₈×C₂₉	C₂×C₄	semidirect
26. #6597	C₂×C₄	semidirect
46. C₂₉	#442	semidirect
51. D₈	#1181	semidirect
60. D₄	C₂×#1181	semidirect
67. C₈	C₂×#1181	semidirect

Maximal subgroups

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

subgroup	index
D₄×#1181	2
D₈×D₂₉	2
#11745223	2
#11745209	2
#11745208	2
#442	29