Subgroups — #16817367

Order 3712.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271187	C₂	1	2	yes	maximal
2	C₂×C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₉	C₄	1	2	yes	—
4	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×#90777	—	2	2	no	—
6	C₂₉×C₄⋊C₈	—	2	2	no	—
7	C₄⋊#6597	—	2	2	no	—
8	C₄⋊#6597	C₄	1	4	yes	—
9	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₂₉	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₂₉	—	2	2	no	—
13	C₂×C₈×C₂₉	—	4	2	no	—
14	C₄²×C₂₉	C₂×C₄	1	2	yes	—
15	C₄²×C₂₉	D₄	1	2	yes	—
16	#90777	—	4	2	no	—
17	#90777	—	4	2	no	—
18	C₂×#6597	—	2	4	no	—
19	C₂³×C₂₉	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	—	2	1	no	—
21	C₂×C₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	—	4	1	no	—
23	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
25	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
28	C₂×C₄×C₂₉	SD₁₆	1	2	yes	—
29	C₂×C₄×C₂₉	Q₁₆	1	1	yes	characteristic
30	C₈×C₂₉	—	4	2	no	—
31	#6597	—	4	4	no	—
32	#1292	—	29	1	no	maximal, Sylow
33	C₂²×C₂₉	—	2	1	no	—
34	C₂²×C₂₉	—	2	1	no	—
35	C₂²×C₂₉	#95	1	1	yes	characteristic
36	C₂²×C₂₉	#106	1	1	yes	characteristic
37	C₂²×C₂₉	#107	1	1	yes	characteristic
38	C₄×C₂₉	—	2	2	no	—
39	C₄×C₂₉	—	2	1	no	—
40	C₄×C₂₉	#100	1	1	yes	characteristic
41	C₄×C₂₉	#101	1	1	yes	characteristic
42	C₄×C₂₉	#102	1	2	yes	—
43	C₄×C₂₉	#103	1	2	yes	—
44	#423	—	29	2	no	—
45	C₂×C₄⋊C₈	D₂₉	1	1	yes	characteristic
46	C₂×C₂₉	—	2	1	no	—
47	C₂×C₂₉	—	2	1	no	—
48	C₂×C₂₉	#338	1	1	yes	characteristic
49	C₂×C₂₉	#340	1	1	yes	characteristic
50	C₂×C₂₉	#343	1	1	yes	characteristic
51	C₂×M₁₆	—	58	2	no	—
52	C₂²×C₈	Dic₂₉	1	2	yes	—
53	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
54	C₄⋊C₈	—	2	2	no	—
55	C₄⋊C₈	—	29	4	no	—
56	C₄⋊C₈	—	58	2	no	—
57	C₂₉	#1292	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	Dic₅₈	1	1	yes	characteristic
59	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
60	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
61	M₁₆	—	116	2	no	—
62	M₁₆	—	116	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	—	4	2	no	—
65	C₂×C₈	—	58	4	no	—
66	C₄²	C₄×D₂₉	1	2	yes	—
67	C₄²	C₂²⋊D₂₉	1	2	yes	—
68	C₂³	C₄⋊Dic₂₉	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	#90773	1	2	yes	—
73	C₂×C₄	D₂₃₂	1	1	yes	characteristic
74	C₂×C₄	Dic₁₁₆	1	1	yes	characteristic
75	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
76	C₂×C₄	#90779	1	2	yes	—
77	C₂×C₄	#90781	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
79	C₈	—	4	2	no	—
80	C₈	—	116	4	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	#11745165	1	1	yes	characteristic
84	C₂²	#11745166	1	1	yes	characteristic
85	C₂²	#11745179	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#11745164	1	2	yes	—
89	C₄	#11745169	1	2	yes	—
90	C₄	#11745181	1	1	yes	characteristic
91	C₄	#11745184	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	#14270921	1	1	yes	characteristic
95	C₂	#14270926	1	1	yes	characteristic
96	C₂	#14270932	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745179
commutator	C₂×C₄×C₂₉	C₄²
Frattini	C₂×C₄²	C₂×D₂₉
Fitting	C₂×C₂₉×C₄⋊C₈	C₂
socle	C₂²×C₂₉	#95
prime radical	C₂³×C₂₉	C₄⋊C₄
cosocle	C₂×C₄²×C₂₉	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₉
hypocenter	C₂₉	#1292
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
57. C₂₉	#1292	semidirect

Maximal subgroups

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

subgroup	index
#14271187	2
C₂×C₂₉×C₄⋊C₈	2
#1292	29