Subgroups — #16817464

Order 3712.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271281	C₂	1	1	yes	maximal, characteristic
2	C₈×#6597	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745266	C₄	1	1	yes	characteristic
5	#11745263	—	2	1	no	—
6	C₂₉×M₃₂	—	2	1	no	—
7	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	#11745167	C₄	1	1	yes	characteristic
9	#11745153	—	2	1	no	—
10	C₄×#6597	—	2	1	no	—
11	#90805	—	2	1	no	—
12	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₄²×C₂₉	D₄	1	1	yes	characteristic
15	#90777	—	2	1	no	—
16	C₂×#6597	—	2	2	no	—
17	Dic₁₁₆	C₈	1	1	yes	characteristic, complemented
18	D₂₃₂	C₈	1	1	yes	characteristic, complemented
19	#90773	—	2	1	no	—
20	#90772	—	4	1	no	—
21	C₈×D₂₉	—	4	1	no	—
22	C₁₆×C₂₉	—	4	1	no	—
23	C₂×C₄×C₂₉	—	2	1	no	—
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₂₉	—	4	1	no	—
26	D₁₁₆	—	2	1	no	—
27	C₄×D₂₉	—	4	1	no	—
28	Dic₅₈	—	2	1	no	—
29	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
30	C₈×C₂₉	M₁₆	1	1	yes	characteristic
31	C₈×C₂₉	D₈	1	1	yes	characteristic
32	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
33	#6597	—	2	4	no	—
34	#6597	—	4	1	no	—
35	#1335	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	#104	1	1	yes	characteristic
37	C₂×D₂₉	—	4	1	no	—
38	C₄×C₂₉	—	2	2	no	—
39	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₂₉	#102	1	1	yes	characteristic
41	Dic₂₉	—	4	1	no	—
42	#443	—	29	1	no	—
43	#364	D₂₉	1	1	yes	characteristic, complemented
44	C₈²	—	29	1	no	—
45	C₂×C₂₉	—	2	1	no	—
46	C₂×C₂₉	D₄⋊C₈	1	1	yes	characteristic
47	D₂₉	—	8	1	no	—
48	#135	—	29	1	no	—
49	#131	—	58	1	no	—
50	M₃₂	—	2	1	no	—
51	#108	—	29	1	no	—
52	#104	—	58	1	no	—
53	C₄×C₈	—	58	1	no	—
54	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
55	C₂₉	#1335	1	1	yes	characteristic, complemented, Sylow
56	#41	—	58	1	no	—
57	Q₁₆	—	29	1	no	—
58	SD₁₆	—	58	1	no	—
59	D₈	—	29	1	no	—
60	M₁₆	—	58	1	no	—
61	M₁₆	—	116	1	no	—
62	C₂×C₈	—	58	2	no	—
63	C₂×C₈	—	116	1	no	—
64	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
66	C₄²	D₁₁₆	1	1	yes	characteristic
67	C₁₆	—	4	1	no	—
68	Q₈	—	58	1	no	—
69	D₄	—	58	1	no	—
70	D₄	—	116	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	116	1	no	—
73	C₂×C₄	#90781	1	1	yes	characteristic
74	C₈	—	58	4	no	—
75	C₈	—	116	1	no	—
76	C₈	C₈×D₂₉	1	1	yes	characteristic
77	C₈	#90772	1	1	yes	characteristic
78	C₈	#90782	1	1	yes	characteristic
79	C₈	#90784	1	1	yes	characteristic
80	C₂²	—	116	1	no	—
81	C₂²	#11745173	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	116	1	no	—
84	C₄	#11745157	1	1	yes	characteristic
85	C₄	#11745168	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	232	1	no	—
88	C₂	#14270890	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#90782
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#364	C₂
socle	C₂×C₂₉	D₄⋊C₈
prime radical	#11745266	C₄
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#364	D₂₉
hypocenter	C₂₉	#1335
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. C₈×#6597	C₂	semidirect
3. C₂₉×#364	C₂	semidirect
17. Dic₁₁₆	C₈	semidirect
18. D₂₃₂	C₈	semidirect
43. #364	D₂₉	semidirect
55. C₂₉	#1335	semidirect

Maximal subgroups

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

subgroup	index
#14271281	2
C₈×#6597	2
C₂₉×#364	2
#1335	29