Subgroups — #16819164

Order 3712.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271566	C₂	1	2	yes	maximal, complemented
2	#14271536	C₂	1	1	yes	maximal, characteristic
3	#14271511	C₂	1	2	yes	maximal
4	#14270884	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₁₆×C₂₉	—	2	2	no	—
7	C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×#90773	—	2	2	no	—
9	#11745236	C₂²	1	1	yes	characteristic
10	#11745231	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#11745157	—	2	4	no	—
13	#11745155	—	2	4	no	—
14	C₄×#6597	C₂²	1	2	yes	—
15	C₂×Q₈×C₂₉	—	2	2	no	—
16	C₂×D₁₁₆	—	2	2	no	—
17	C₂×D₁₁₆	—	2	1	no	—
18	C₂×Dic₅₈	—	2	1	no	—
19	Q₁₆×C₂₉	—	4	4	no	—
20	C₂×C₈×C₂₉	D₄	1	2	yes	—
21	C₄⋊C₄×C₂₉	—	2	2	no	—
22	C₄⋊C₄×C₂₉	—	2	2	no	—
23	C₄²×C₂₉	C₂³	1	1	yes	characteristic
24	C₄⋊Dic₂₉	—	2	2	no	—
25	C₂×#6597	D₄	1	4	yes	—
26	#90773	—	4	4	no	—
27	C₂²×D₂₉	—	4	1	no	—
28	Q₈×C₂₉	—	4	4	no	—
29	C₂×C₄×C₂₉	—	4	2	no	—
30	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
31	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₂₉	—	4	1	no	—
33	D₁₁₆	—	4	2	no	—
34	D₁₁₆	—	4	4	no	—
35	Dic₅₈	—	4	2	no	—
36	C₈×C₂₉	D₈	1	4	yes	—
37	#6597	—	2	4	no	—
38	#1722	—	29	1	no	maximal, Sylow
39	C₂²×C₂₉	#127	1	1	yes	characteristic
40	C₂×D₂₉	—	8	1	no	—
41	C₂×D₂₉	—	8	2	no	—
42	C₄×C₂₉	—	8	2	no	—
43	C₄×C₂₉	C₂×D₈	1	2	yes	—
44	C₄×C₂₉	#137	1	4	yes	—
45	Dic₂₉	—	8	1	no	—
46	#500	—	29	2	no	—
47	#494	D₂₉	1	1	yes	characteristic, complemented
48	#492	—	29	1	no	—
49	#486	—	29	2	no	—
50	#322	—	29	1	no	—
51	C₂×C₂₉	#493	1	1	yes	characteristic
52	C₂×C₂₉	#497	1	2	yes	—
53	D₂₉	—	16	1	no	—
54	C₂×Q₁₆	—	2	2	no	—
55	C₂×SD₁₆	—	58	2	no	—
56	C₄⋊Q₈	—	29	1	no	—
57	C₄⋊Q₈	C₂×D₂₉	1	2	yes	—
58	#127	—	29	1	no	—
59	#107	—	58	4	no	—
60	#102	—	58	4	no	—
61	C₄×C₈	—	29	2	no	—
62	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
63	C₂₉	#1722	1	1	yes	characteristic, complemented, Sylow
64	C₂×Q₈	—	2	2	no	—
65	C₂×Q₈	—	58	1	no	—
66	C₂×D₄	—	58	2	no	—
67	C₂×D₄	—	58	1	no	—
68	Q₁₆	—	4	4	no	—
69	SD₁₆	—	116	4	no	—
70	C₂×C₈	—	29	4	no	—
71	C₂×C₈	C₂²⋊D₂₉	1	2	yes	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	—	58	2	no	—
75	C₄²	C₂²×D₂₉	1	1	yes	characteristic
76	C₂³	—	116	1	no	—
77	Q₈	—	4	4	no	—
78	Q₈	—	116	2	no	—
79	D₄	—	116	4	no	—
80	D₄	—	116	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	116	1	no	—
83	C₂×C₄	D₄×D₂₉	1	2	yes	—
84	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
85	C₈	—	58	4	no	—
86	C₈	#90782	1	4	yes	—
87	C₂²	—	232	1	no	—
88	C₂²	—	232	2	no	—
89	C₂²	#11745302	1	1	yes	characteristic
90	C₄	—	8	2	no	—
91	C₄	—	232	1	no	—
92	C₄	#11745280	1	4	yes	—
93	C₄	C₂×#90782	1	2	yes	—
94	C₂	—	464	1	no	—
95	C₂	#14271539	1	1	yes	characteristic
96	C₂	#14271556	1	2	yes	—

	subgroup	G/H
center	C₂²	#11745302
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂₉×#494	C₂
socle	C₂²×C₂₉	#127
prime radical	#11745236	C₂²
hypercenter	#494	D₂₉
hypocenter	C₂₉	#1722
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
1. #14271566	C₂	semidirect
4. #14270884	C₂	semidirect
5. C₂₉×#494	C₂	semidirect
47. #494	D₂₉	semidirect
63. C₂₉	#1722	semidirect

Maximal subgroups

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

subgroup	index
#14271566	2
#14271536	2
#14271511	2
#14270884	2
C₂₉×#494	2
#1722	29