Subgroups — #16834562

Order 3712.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉⋊#108	C₂	1	2	yes	maximal
2	C₂×#11745146	C₂	1	1	yes	maximal, characteristic
3	D₂₉⋊M₁₆	—	2	2	no	—
4	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
5	#11745212	—	2	2	no	—
6	#11745211	C₄	1	4	yes	—
7	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
8	C₂×#90768	C₄	1	1	yes	characteristic
9	#11745146	—	2	2	no	—
10	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
11	#90800	—	4	2	no	—
12	#90796	—	2	4	no	—
13	D₂₉⋊C₈	—	4	2	no	—
14	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×#6597	Q₈	1	1	yes	characteristic
16	C₈×D₂₉	C₂×C₄	1	2	yes	—
17	C₈×D₂₉	D₄	1	2	yes	—
18	C₁₆×C₂₉	—	2	1	no	—
19	#90768	—	2	1	no	—
20	C₂²×D₂₉	Q₁₆	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂×Dic₂₉	D₈	1	1	yes	characteristic
23	C₄×D₂₉	C₂²⋊C₄	1	2	yes	—
24	C₄×D₂₉	SD₁₆	1	2	yes	—
25	#6599	—	4	4	no	—
26	C₈×C₂₉	C₄²	1	1	yes	characteristic
27	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	#6597	C₄⋊C₄	1	2	yes	—
29	#1385	—	29	1	no	maximal, Sylow
30	C₂²×C₂₉	#107	1	1	yes	characteristic
31	C₂×D₂₉	—	4	1	no	—
32	C₂×D₂₉	#103	1	2	yes	—
33	C₄×C₂₉	#95	1	1	yes	characteristic
34	C₄×C₂₉	#106	1	1	yes	characteristic
35	Dic₂₉	#102	1	2	yes	—
36	C₂×M₃₂	—	29	1	no	—
37	C₂×#108	—	29	2	no	—
38	C₂×C₂₉	—	2	1	no	—
39	C₂×C₂₉	#340	1	1	yes	characteristic
40	D₂₉	—	2	2	no	—
41	C₂×M₁₆	—	58	2	no	—
42	C₂²×C₈	—	29	1	no	—
43	M₃₂	—	58	2	no	—
44	C₂×C₁₆	—	29	1	no	—
45	C₂×C₁₆	#1181	1	1	yes	characteristic
46	#108	—	29	4	no	—
47	#108	—	58	2	no	—
48	C₂₉	#1385	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₄	—	29	1	no	—
50	M₁₆	—	58	4	no	—
51	M₁₆	—	116	2	no	—
52	C₂×C₈	—	29	1	no	—
53	C₂×C₈	—	29	2	no	—
54	C₂×C₈	—	29	2	no	—
55	C₂×C₈	—	116	2	no	—
56	C₂×C₈	C₂×#1181	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	58	1	no	—
59	C₂³	—	29	1	no	—
60	C₂×C₄	—	29	1	no	—
61	C₂×C₄	—	29	2	no	—
62	C₂×C₄	—	29	2	no	—
63	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
64	C₈	—	29	2	no	—
65	C₈	—	116	4	no	—
66	C₈	C₄×#1181	1	1	yes	characteristic
67	C₈	C₂²⋊#1181	1	1	yes	characteristic
68	C₂²	—	29	2	no	—
69	C₂²	—	116	1	no	—
70	C₂²	#11745210	1	1	yes	characteristic
71	C₄	—	29	2	no	—
72	C₄	#11745209	1	1	yes	characteristic
73	C₄	(C₂×#1181)⋊C₄	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	58	2	no	—
76	C₂	#14272037	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745209
commutator	C₈×C₂₉	C₄²
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂×C₁₆×C₂₉	C₄
socle	C₂×C₂₉	#340
prime radical	C₂²×D₂₉	Q₁₆
cosocle	C₂×C₈×D₂₉	C₂²
hypercenter	C₂×C₁₆	#1181
hypocenter	C₂₉	#1385
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
48. C₂₉	#1385	semidirect

Maximal subgroups

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

subgroup	index
D₂₉⋊#108	2
C₂×#11745146	2
#1385	29