Subgroups — #16834552

Order 3712.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745212	C₂	1	2	yes	maximal
2	C₂×C₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#90796	—	2	2	no	—
4	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
5	#11745212	—	2	2	no	—
6	#11745212	C₄	1	4	yes	—
7	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic
8	C₂×#90768	C₄	1	1	yes	characteristic
9	C₁₆×D₂₉	—	2	2	no	—
10	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
11	C₂×#6599	—	4	2	no	—
12	#90796	—	2	4	no	—
13	#90796	—	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	#1381	—	29	1	no	maximal, Sylow
30	C₂²×C₂₉	#107	1	1	yes	characteristic
31	C₂×D₂₉	—	2	1	no	—
32	C₂×D₂₉	—	2	1	no	—
33	C₂×D₂₉	#103	1	2	yes	—
34	C₄×C₂₉	#95	1	1	yes	characteristic
35	C₄×C₂₉	#106	1	1	yes	characteristic
36	Dic₂₉	#102	1	2	yes	—
37	C₂²×C₁₆	—	29	1	no	—
38	C₂×#108	—	29	2	no	—
39	C₂×C₂₉	#340	1	1	yes	characteristic
40	C₂×C₂₉	#368	1	1	yes	characteristic
41	C₂×C₂₉	#368	1	1	yes	characteristic
42	D₂₉	—	2	2	no	—
43	C₂×M₁₆	—	58	2	no	—
44	C₂²×C₈	—	29	1	no	—
45	C₂×C₁₆	—	29	1	no	—
46	C₂×C₁₆	—	58	2	no	—
47	C₂×C₁₆	#1181	1	1	yes	characteristic
48	#108	—	29	4	no	—
49	#108	—	58	2	no	—
50	C₂₉	#1381	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₄	—	29	1	no	—
52	M₁₆	—	58	4	no	—
53	M₁₆	—	116	2	no	—
54	C₂×C₈	—	29	1	no	—
55	C₂×C₈	—	29	2	no	—
56	C₂×C₈	—	29	2	no	—
57	C₂×C₈	—	116	2	no	—
58	C₂×C₈	C₂×#1181	1	1	yes	characteristic
59	C₁₆	—	2	1	no	—
60	C₁₆	—	58	1	no	—
61	C₂³	—	29	1	no	—
62	C₂×C₄	—	29	1	no	—
63	C₂×C₄	—	29	2	no	—
64	C₂×C₄	—	29	2	no	—
65	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
66	C₈	—	29	2	no	—
67	C₈	—	116	4	no	—
68	C₈	C₄×#1181	1	1	yes	characteristic
69	C₈	C₂²⋊#1181	1	1	yes	characteristic
70	C₂²	—	29	2	no	—
71	C₂²	—	58	1	no	—
72	C₂²	—	58	1	no	—
73	C₂²	#11745210	1	1	yes	characteristic
74	C₄	—	29	2	no	—
75	C₄	#11745209	1	1	yes	characteristic
76	C₄	(C₂×#1181)⋊C₄	1	1	yes	characteristic
77	C₂	—	58	2	no	—
78	C₂	#14272037	1	1	yes	characteristic
79	C₂	#14272091	1	1	yes	characteristic
80	C₂	#14272092	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745210
commutator	C₈×C₂₉	C₄²
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂×C₁₆×C₂₉	C₄
socle	C₂²×C₂₉	#107
prime radical	C₂²×D₂₉	Q₁₆
cosocle	C₂×C₈×D₂₉	C₂²
hypercenter	C₂×C₁₆	#1181
hypocenter	C₂₉	#1381
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
50. C₂₉	#1381	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745212	2
C₂×C₁₆×D₂₉	2
#1381	29