Subgroups — #16835433

Order 3712.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745212	C₂	1	4	yes	maximal
2	#14272167	C₂	1	2	yes	maximal
3	C₄×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#90796	C₂²	1	4	yes	—
5	C₂×C₈×D₂₉	C₂²	1	2	yes	—
6	C₄²×D₂₉	C₂²	1	1	yes	characteristic
7	C₄⋊#6599	—	2	4	no	—
8	#11745212	—	2	8	no	—
9	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
10	C₈×Dic₂₉	C₄	1	2	yes	—
11	C₄×#6597	C₄	1	1	yes	characteristic
12	C₂×C₄×D₂₉	Q₈	1	2	yes	—
13	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
14	C₂×#6599	—	2	4	no	—
15	#90796	—	2	8	no	—
16	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
17	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₂₉	D₄	1	2	yes	—
20	C₂×#6597	C₂×C₄	1	2	yes	—
21	C₈×D₂₉	D₄	1	4	yes	—
22	C₈×D₂₉	Q₈	1	4	yes	—
23	C₂²×D₂₉	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
27	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
28	C₄×D₂₉	—	2	4	no	—
29	C₄×D₂₉	C₂×D₄	1	2	yes	—
30	C₄×D₂₉	C₂×Q₈	1	2	yes	—
31	#6599	—	4	4	no	—
32	C₈×C₂₉	C₄⋊C₄	1	4	yes	—
33	#6597	C₄⋊C₄	1	4	yes	—
34	#1848	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×D₂₉	—	2	2	no	—
37	C₂×D₂₉	C₄⋊Q₈	1	2	yes	—
38	C₄×C₂₉	#108	1	4	yes	complemented
39	C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
40	Dic₂₉	—	2	2	no	—
41	Dic₂₉	#127	1	1	yes	characteristic
42	Dic₂₉	C₄⋊Q₈	1	1	yes	characteristic
43	C₂×#108	—	29	4	no	—
44	#423	—	29	2	no	—
45	C₂×C₄×C₈	—	29	1	no	—
46	C₂×C₂₉	#384	1	1	yes	characteristic
47	C₂×C₂₉	C₂×#108	1	2	yes	—
48	D₂₉	—	2	2	no	—
49	C₂×M₁₆	—	29	4	no	—
50	C₂²×C₈	—	29	2	no	—
51	C₂×C₄²	—	29	1	no	—
52	#108	—	58	8	no	—
53	C₄⋊C₈	—	58	4	no	—
54	C₄×C₈	—	29	2	no	—
55	C₄×C₈	—	29	1	no	—
56	C₄×C₈	#1181	1	1	yes	characteristic
57	C₂₉	#1848	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	29	1	no	—
59	C₂²×C₄	—	29	2	no	—
60	M₁₆	—	58	8	no	—
61	C₂×C₈	—	29	2	no	—
62	C₂×C₈	—	29	4	no	—
63	C₂×C₈	—	29	4	no	—
64	C₂×C₈	—	58	4	no	—
65	C₂×C₈	C₂×#1181	1	2	yes	—
66	C₄²	—	29	2	no	—
67	C₄²	—	29	1	no	—
68	C₄²	C₂×#1181	1	1	yes	characteristic
69	C₂³	—	29	1	no	—
70	C₂×C₄	—	29	1	no	—
71	C₂×C₄	—	29	2	no	—
72	C₂×C₄	—	29	2	no	—
73	C₂×C₄	—	29	2	no	—
74	C₂×C₄	—	58	4	no	—
75	C₂×C₄	C₄⋊#1181	1	2	yes	—
76	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
77	C₈	—	29	4	no	—
78	C₈	—	116	4	no	—
79	C₈	C₄⋊#1181	1	4	yes	—
80	C₂²	—	29	2	no	—
81	C₂²	—	58	2	no	—
82	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
83	C₄	—	29	1	no	—
84	C₄	—	29	1	no	—
85	C₄	—	58	2	no	—
86	C₄	#11745212	1	4	yes	complemented
87	C₄	C₂×C₄⋊#1181	1	2	yes	—
88	C₂	—	58	2	no	—
89	C₂	#14272109	1	1	yes	characteristic
90	C₂	C₂×#11745212	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₄×C₈×C₂₉	C₄
socle	C₂²×C₂₉	C₂×C₄⋊C₄
prime radical	C₂²×D₂₉	C₂×Q₈
cosocle	C₂×C₄×D₂₉	C₂³
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	#1848
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
38. C₄×C₂₉	#108	semidirect
57. C₂₉	#1848	semidirect
86. C₄	#11745212	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
#14272167	2
C₄×C₈×D₂₉	2
#1848	29