Subgroups — #16817449

Order 3712.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271242	C₂	1	1	yes	maximal, characteristic
2	#14270939	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90772	—	2	1	no	—
5	C₄×D₁₁₆	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₂₉	—	2	1	no	—
7	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	#11745168	—	2	1	no	—
9	C₂×#90768	—	2	1	no	—
10	C₄⋊#6597	C₄	1	1	yes	characteristic
11	C₂×D₁₁₆	C₈	1	1	yes	characteristic
12	C₂×C₄×D₂₉	—	2	1	no	—
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
15	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
16	#90781	—	2	1	no	—
17	C₄⋊Dic₂₉	C₈	1	1	yes	characteristic
18	C₂×#6597	—	2	1	no	—
19	#90772	—	4	1	no	—
20	#90772	—	4	1	no	—
21	C₁₆×C₂₉	—	4	1	no	—
22	#90768	—	2	2	no	—
23	C₂²×D₂₉	—	2	1	no	—
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
27	C₂×Dic₂₉	—	2	1	no	—
28	D₁₁₆	—	4	1	no	—
29	C₄×D₂₉	—	4	1	no	—
30	C₄×D₂₉	—	4	1	no	—
31	C₈×C₂₉	—	2	1	no	—
32	C₈×C₂₉	D₈	1	1	yes	characteristic
33	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
34	#6597	—	4	1	no	—
35	#1330	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₂₉	—	4	1	no	—
38	C₂×D₂₉	—	4	1	no	—
39	C₂×D₂₉	—	4	1	no	—
40	C₄×C₂₉	—	2	1	no	—
41	C₄×C₂₉	—	2	1	no	—
42	C₄×C₂₉	#102	1	1	yes	characteristic
43	C₄×C₂₉	#104	1	1	yes	characteristic
44	Dic₂₉	—	4	1	no	—
45	#436	—	29	1	no	—
46	C₄⋊C₁₆	D₂₉	1	1	yes	characteristic, complemented
47	#346	—	29	1	no	—
48	C₂×C₂₉	D₄⋊C₈	1	1	yes	characteristic
49	C₂×C₂₉	#349	1	1	yes	characteristic
50	C₂×C₂₉	#350	1	1	yes	characteristic
51	D₂₉	—	8	1	no	—
52	C₂×M₁₆	—	58	1	no	—
53	C₄×D₄	—	29	1	no	—
54	C₂×C₁₆	—	2	1	no	—
55	C₂×C₁₆	—	58	1	no	—
56	C₄⋊C₈	—	29	1	no	—
57	C₂²⋊C₈	—	58	1	no	—
58	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
59	C₂₉	#1330	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₄	—	29	1	no	—
61	C₂²×C₄	—	58	1	no	—
62	M₁₆	—	116	1	no	—
63	M₁₆	—	116	1	no	—
64	C₂×C₈	—	58	1	no	—
65	C₂×C₈	D₁₁₆	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
67	C₄⋊C₄	—	29	1	no	—
68	C₂²⋊C₄	—	58	1	no	—
69	C₄²	C₄×D₂₉	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	58	2	no	—
72	C₂³	—	58	1	no	—
73	D₄	—	116	1	no	—
74	C₂×C₄	—	58	1	no	—
75	C₂×C₄	—	116	1	no	—
76	C₂×C₄	—	116	1	no	—
77	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
78	C₂×C₄	#90772	1	1	yes	characteristic
79	C₂×C₄	#90781	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	116	1	no	—
82	C₈	#90782	1	1	yes	characteristic
83	C₈	#90784	1	1	yes	characteristic
84	C₂²	—	116	1	no	—
85	C₂²	—	116	1	no	—
86	C₂²	—	116	1	no	—
87	C₂²	#11745168	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	116	1	no	—
91	C₄	#11745157	1	1	yes	characteristic
92	C₄	#11745173	1	1	yes	characteristic
93	C₂	—	232	1	no	—
94	C₂	#14270890	1	1	yes	characteristic
95	C₂	#14270944	1	1	yes	characteristic
96	C₂	#14270946	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#90781
commutator	C₂×C₄×C₂₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×C₄⋊C₁₆	C₂
socle	C₂²×C₂₉	C₂²⋊C₈
prime radical	C₂×D₁₁₆	C₈
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	C₄⋊C₁₆	D₂₉
hypocenter	C₂₉	#1330
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #14270939	C₂	semidirect
3. C₂₉×C₄⋊C₁₆	C₂	semidirect
46. C₄⋊C₁₆	D₂₉	semidirect
59. C₂₉	#1330	semidirect

Maximal subgroups

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

subgroup	index
#14271242	2
#14270939	2
C₂₉×C₄⋊C₁₆	2
#1330	29