Subgroups — #14272203

Order 1856.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#1181	C₂	1	2	yes	maximal
2	Q₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
3	#11745225	C₂	1	2	yes	maximal
4	#11745209	C₂	1	1	yes	maximal, characteristic
5	#11745208	C₂	1	1	yes	maximal, characteristic
6	Q₈×D₂₉	C₂²	1	2	yes	—
7	C₄⋊#1181	—	2	2	no	—
8	C₄⋊#1181	C₂²	1	2	yes	—
9	C₄×#1181	—	2	2	no	—
10	C₄×#1181	C₂²	1	1	yes	characteristic
11	D₂₉⋊C₈	C₂²	1	1	yes	characteristic
12	Q₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
13	#90785	C₄	1	2	yes	complemented
14	Dic₁₁₆	C₄	1	1	yes	characteristic, complemented
15	C₈×D₂₉	C₂²	1	1	yes	characteristic
16	C₂×#1181	—	2	2	no	—
17	C₂×#1181	D₄	1	2	yes	—
18	Q₈×C₂₉	C₂×C₄	1	2	yes	—
19	C₄×D₂₉	—	2	2	no	—
20	C₄×D₂₉	C₂³	1	1	yes	characteristic
21	Dic₅₈	—	2	2	no	—
22	Dic₅₈	C₂×C₄	1	2	yes	—
23	#6599	—	2	1	no	—
24	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
25	#6597	C₂×C₄	1	1	yes	characteristic
26	C₂×D₂₉	C₂×D₄	1	1	yes	characteristic
27	#1181	—	2	2	no	—
28	#1181	—	4	2	no	—
29	C₄×C₂₉	—	2	2	no	—
30	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	Dic₂₉	—	2	2	no	—
32	Dic₂₉	#41	1	1	yes	characteristic
33	#441	—	29	1	no	maximal, Sylow
34	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
35	D₂₉	#137	1	2	yes	—
36	C₂×Q₁₆	—	29	1	no	—
37	C₄×Q₈	—	29	2	no	—
38	#106	—	29	1	no	—
39	#103	—	29	2	no	—
40	#97	—	29	1	no	—
41	C₂₉	#441	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₈	—	29	2	no	—
43	Q₁₆	—	29	2	no	—
44	Q₁₆	—	29	1	no	—
45	Q₁₆	#1181	1	1	yes	characteristic, complemented
46	C₂×C₈	—	29	1	no	—
47	C₂×C₈	—	29	1	no	—
48	C₄⋊C₄	—	29	2	no	—
49	C₄⋊C₄	—	58	2	no	—
50	C₄²	—	29	1	no	—
51	C₄²	—	58	2	no	—
52	Q₈	—	29	2	no	—
53	Q₈	—	58	2	no	—
54	Q₈	C₂×#1181	1	2	yes	—
55	C₂×C₄	—	29	1	no	—
56	C₂×C₄	—	29	2	no	—
57	C₂×C₄	—	58	2	no	—
58	C₂×C₄	—	58	2	no	—
59	C₈	—	29	1	no	—
60	C₈	—	58	1	no	—
61	C₈	C₂×#1181	1	1	yes	characteristic
62	C₂²	—	29	1	no	—
63	C₄	—	2	2	no	—
64	C₄	—	29	1	no	—
65	C₄	—	58	2	no	—
66	C₄	—	58	2	no	—
67	C₄	—	116	2	no	—
68	C₄	C₂²×#1181	1	1	yes	characteristic
69	C₂	—	29	2	no	—
70	C₂	D₄×#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#1181
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₄	C₂²×#1181
Fitting	Q₁₆×C₂₉	C₄
socle	C₂×C₂₉	C₄×D₄
prime radical	C₂×D₂₉	C₂×D₄
cosocle	C₄×D₂₉	C₂³
hypercenter	Q₁₆	#1181
hypocenter	C₂₉	#441
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Q₁₆×C₂₉	C₄	semidirect
13. #90785	C₄	semidirect
14. Dic₁₁₆	C₄	semidirect
41. C₂₉	#441	semidirect
45. Q₁₆	#1181	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#1181	2
Q₁₆×D₂₉	2
#11745225	2
#11745209	2
#11745208	2
#441	29