Subgroups — #14272173

Order 1856.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745345	C₂	1	2	yes	maximal
2	C₂×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
3	#11745210	C₂	1	2	yes	maximal, complemented
4	#11745209	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
6	C₂²⋊#1181	—	2	2	no	—
7	C₄⋊#1181	C₂²	1	4	yes	—
8	C₄×#1181	—	2	2	no	—
9	C₂×C₈×C₂₉	C₄	1	1	yes	characteristic, complemented
10	C₂×#6597	C₄	1	1	yes	characteristic, complemented
11	C₈×D₂₉	C₄	1	1	yes	characteristic, complemented
12	C₈×D₂₉	C₄	1	1	yes	characteristic, complemented
13	C₈×D₂₉	C₂²	1	1	yes	characteristic
14	C₈×D₂₉	C₂²	1	1	yes	characteristic
15	C₂²×D₂₉	D₄	1	1	yes	characteristic
16	C₂×#1181	—	2	4	no	—
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₂₉	Q₈	1	1	yes	characteristic
19	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
20	C₄×D₂₉	D₄	1	1	yes	characteristic
21	C₄×D₂₉	Q₈	1	1	yes	characteristic
22	C₄×D₂₉	C₂³	1	1	yes	characteristic
23	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
25	#6597	C₂×C₄	1	1	yes	characteristic
26	#6597	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₂₉	—	2	2	no	—
29	C₂×D₂₉	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₂₉	C₂×D₄	1	1	yes	characteristic
31	#1181	—	4	4	no	—
32	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
35	Dic₂₉	C₂×Q₈	1	1	yes	characteristic
36	#427	—	29	1	no	maximal, Sylow
37	C₂×C₂₉	—	2	1	no	—
38	C₂×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
39	D₂₉	—	2	1	no	—
40	D₂₉	#135	1	2	yes	—
41	C₂²×C₈	—	29	1	no	—
42	#117	—	29	2	no	—
43	#107	—	29	2	no	—
44	#106	—	29	2	no	—
45	C₂₉	#427	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	—	29	1	no	—
47	C₂×C₈	—	29	1	no	—
48	C₂×C₈	—	29	1	no	—
49	C₂×C₈	—	29	1	no	—
50	C₂×C₈	—	29	1	no	—
51	C₂×C₈	—	29	1	no	—
52	C₂×C₈	#1181	1	1	yes	characteristic, complemented
53	C₄⋊C₄	—	29	4	no	—
54	C₂²⋊C₄	—	58	2	no	—
55	C₄²	—	58	2	no	—
56	C₂³	—	29	1	no	—
57	C₂×C₄	—	29	1	no	—
58	C₂×C₄	—	29	1	no	—
59	C₂×C₄	—	29	1	no	—
60	C₂×C₄	—	29	1	no	—
61	C₂×C₄	—	29	1	no	—
62	C₂×C₄	—	58	4	no	—
63	C₂×C₄	C₂×#1181	1	1	yes	characteristic
64	C₈	—	29	1	no	—
65	C₈	—	29	1	no	—
66	C₈	C₂×#1181	1	1	yes	characteristic
67	C₈	C₂×#1181	1	1	yes	characteristic
68	C₂²	—	29	1	no	—
69	C₂²	—	29	1	no	—
70	C₂²	—	58	2	no	—
71	C₂²	C₄⋊#1181	1	1	yes	characteristic
72	C₄	—	29	1	no	—
73	C₄	—	29	1	no	—
74	C₄	—	116	4	no	—
75	C₄	C₄⋊#1181	1	1	yes	characteristic
76	C₄	C₂²×#1181	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	29	2	no	—
79	C₂	—	58	1	no	—
80	C₂	C₂×C₄⋊#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#1181
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₄	C₂²×#1181
Fitting	C₂×C₈×C₂₉	C₄
socle	C₂×C₂₉	C₂×C₄⋊C₄
prime radical	C₂²×D₂₉	D₄
cosocle	C₄×D₂₉	C₂³
hypercenter	C₂×C₈	#1181
hypocenter	C₂₉	#427
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #11745210	C₂	semidirect
4. #11745209	C₂	semidirect
9. C₂×C₈×C₂₉	C₄	semidirect
10. C₂×#6597	C₄	semidirect
11. C₈×D₂₉	C₄	semidirect
12. C₈×D₂₉	C₄	semidirect
45. C₂₉	#427	semidirect
52. C₂×C₈	#1181	semidirect

Maximal subgroups

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

subgroup	index
#11745345	2
C₂×C₈×D₂₉	2
#11745210	2
#11745209	2
#427	29