Subgroups — #14272209

Order 1856.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745348	C₂	1	2	yes	maximal, complemented
2	#11745281	C₂	1	1	yes	maximal, characteristic
3	#11745226	C₂	1	2	yes	maximal, complemented
4	#11745211	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745208	C₂	1	1	yes	maximal, characteristic, complemented
6	#90809	C₂²	1	2	yes	—
7	C₄×#1181	C₂²	1	1	yes	characteristic
8	#90796	—	2	2	no	—
9	#90796	C₂²	1	2	yes	—
10	D₂₉⋊C₈	—	2	2	no	—
11	D₂₉⋊C₈	C₂²	1	1	yes	characteristic
12	Q₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
13	#90784	C₄	1	2	yes	complemented
14	D₂₃₂	C₄	1	1	yes	characteristic, complemented
15	C₈×D₂₉	C₂²	1	1	yes	characteristic
16	C₂×#1181	—	2	1	no	—
17	Q₈×C₂₉	C₂×C₄	1	2	yes	—
18	D₁₁₆	—	2	2	no	—
19	D₁₁₆	C₂×C₄	1	2	yes	—
20	C₄×D₂₉	—	2	2	no	—
21	C₄×D₂₉	C₂³	1	1	yes	characteristic
22	#6599	—	2	2	no	—
23	#6599	D₄	1	2	yes	—
24	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
25	#6597	C₂×C₄	1	1	yes	characteristic
26	C₂×D₂₉	—	2	2	no	—
27	C₂×D₂₉	#41	1	1	yes	characteristic
28	#1181	—	4	1	no	—
29	C₄×C₂₉	—	2	2	no	—
30	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	Dic₂₉	C₂×D₄	1	1	yes	characteristic
32	#444	—	29	1	no	maximal, Sylow
33	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
34	D₂₉	—	2	1	no	—
35	D₂₉	—	4	2	no	—
36	#135	—	29	1	no	—
37	#131	—	29	2	no	—
38	#108	—	29	1	no	—
39	#104	—	29	2	no	—
40	#97	—	29	1	no	—
41	C₂₉	#444	1	1	yes	characteristic, complemented, Sylow
42	#41	—	29	2	no	—
43	Q₁₆	#1181	1	1	yes	characteristic, complemented
44	SD₁₆	—	29	2	no	—
45	D₈	—	29	1	no	—
46	M₁₆	—	29	2	no	—
47	M₁₆	—	58	2	no	—
48	C₂×C₈	—	29	1	no	—
49	C₂×C₈	—	29	1	no	—
50	C₂×C₈	—	58	2	no	—
51	C₄²	—	29	1	no	—
52	Q₈	C₂×#1181	1	2	yes	—
53	D₄	—	29	2	no	—
54	D₄	—	58	2	no	—
55	C₂×C₄	—	29	1	no	—
56	C₂×C₄	—	58	2	no	—
57	C₂×C₄	—	58	1	no	—
58	C₈	—	29	2	no	—
59	C₈	—	29	1	no	—
60	C₈	—	58	2	no	—
61	C₈	C₂×#1181	1	1	yes	characteristic
62	C₂²	—	29	1	no	—
63	C₂²	—	58	2	no	—
64	C₄	—	2	2	no	—
65	C₄	—	29	1	no	—
66	C₄	—	116	1	no	—
67	C₄	C₂²×#1181	1	1	yes	characteristic
68	C₂	—	58	1	no	—
69	C₂	—	116	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	#11745281	C₂
cosocle	C₄×D₂₉	C₂³
hypercenter	Q₁₆	#1181
hypocenter	C₂₉	#444
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
1. #11745348	C₂	semidirect
3. #11745226	C₂	semidirect
4. #11745211	C₂	semidirect
5. #11745208	C₂	semidirect
12. Q₁₆×C₂₉	C₄	semidirect
13. #90784	C₄	semidirect
14. D₂₃₂	C₄	semidirect
41. C₂₉	#444	semidirect
43. Q₁₆	#1181	semidirect

Maximal subgroups

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

subgroup	index
#11745348	2
#11745281	2
#11745226	2
#11745211	2
#11745208	2
#444	29