Subgroups — #16834550

Order 3712.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745210	C₂	1	2	yes	maximal
2	C₂×C₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊#1181	—	2	2	no	—
4	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
5	#11745210	—	2	2	no	—
6	#11745210	C₄	1	4	yes	complemented
7	C₂×C₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
8	C₂×#90768	C₄	1	1	yes	characteristic, complemented
9	C₁₆×D₂₉	—	2	2	no	—
10	C₂²×#1181	—	4	2	no	—
11	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
12	C₄⋊#1181	—	2	4	no	—
13	C₄⋊#1181	—	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	D₈	1	1	yes	characteristic
21	C₂×#1181	—	4	4	no	—
22	C₂×#1181	—	8	2	no	—
23	C₂×#1181	—	8	2	no	—
24	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×Dic₂₉	Q₁₆	1	1	yes	characteristic
26	C₄×D₂₉	C₂²⋊C₄	1	2	yes	—
27	C₄×D₂₉	SD₁₆	1	2	yes	—
28	C₈×C₂₉	C₄²	1	1	yes	characteristic
29	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	#6597	C₄⋊C₄	1	2	yes	—
31	#1380	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	#107	1	1	yes	characteristic
33	C₂×D₂₉	#102	1	2	yes	—
34	C₂×D₂₉	D₁₆	1	1	yes	characteristic
35	C₂×D₂₉	SD₃₂	1	2	yes	—
36	C₂×D₂₉	Q₃₂	1	1	yes	characteristic
37	#1181	—	8	4	no	—
38	C₄×C₂₉	#95	1	1	yes	characteristic
39	C₄×C₂₉	#106	1	1	yes	characteristic
40	Dic₂₉	#103	1	2	yes	—
41	C₂²×C₁₆	—	29	1	no	—
42	C₂×#107	—	29	2	no	—
43	C₂×C₂₉	#340	1	1	yes	characteristic
44	C₂×C₂₉	#366	1	1	yes	characteristic
45	C₂×C₂₉	#367	1	1	yes	characteristic
46	D₂₉	#357	1	2	yes	—
47	D₂₉	#358	1	2	yes	—
48	C₂²×C₈	—	29	1	no	—
49	C₂×C₄⋊C₄	—	58	2	no	—
50	C₂×C₁₆	—	29	1	no	—
51	C₂×C₁₆	—	58	2	no	—
52	C₂×C₁₆	#1181	1	1	yes	characteristic, complemented
53	#107	—	29	4	no	—
54	#107	—	58	2	no	—
55	C₂₉	#1380	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	—	29	1	no	—
57	C₂²×C₄	—	116	2	no	—
58	C₂×C₈	—	29	1	no	—
59	C₂×C₈	—	29	2	no	—
60	C₂×C₈	—	29	2	no	—
61	C₂×C₈	C₂×#1181	1	1	yes	characteristic
62	C₄⋊C₄	—	58	4	no	—
63	C₄⋊C₄	—	116	2	no	—
64	C₁₆	—	2	1	no	—
65	C₁₆	—	58	1	no	—
66	C₂³	—	29	1	no	—
67	C₂×C₄	—	29	1	no	—
68	C₂×C₄	—	29	2	no	—
69	C₂×C₄	—	29	2	no	—
70	C₂×C₄	—	116	4	no	—
71	C₂×C₄	—	232	2	no	—
72	C₂×C₄	—	232	2	no	—
73	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
74	C₈	—	29	2	no	—
75	C₈	C₄×#1181	1	1	yes	characteristic
76	C₈	C₂²⋊#1181	1	1	yes	characteristic
77	C₂²	—	29	2	no	—
78	C₂²	—	29	1	no	—
79	C₂²	—	29	1	no	—
80	C₂²	—	29	2	no	—
81	C₂²	#11745210	1	1	yes	characteristic
82	C₄	—	29	2	no	—
83	C₄	—	232	4	no	—
84	C₄	#11745209	1	1	yes	characteristic
85	C₄	(C₂×#1181)⋊C₄	1	1	yes	characteristic
86	C₂	—	29	2	no	—
87	C₂	—	29	2	no	—
88	C₂	#14272037	1	1	yes	characteristic
89	C₂	#14272089	1	1	yes	characteristic
90	C₂	#14272090	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	D₈
cosocle	C₂×C₈×D₂₉	C₂²
hypercenter	C₂×C₁₆	#1181
hypocenter	C₂₉	#1380
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
6. #11745210	C₄	semidirect
7. C₂×C₁₆×C₂₉	C₄	semidirect
8. C₂×#90768	C₄	semidirect
52. C₂×C₁₆	#1181	semidirect
55. C₂₉	#1380	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745210	2
C₂×C₁₆×D₂₉	2
#1380	29