Subgroups — #16817411

Order 3712.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#90768	C₂	1	1	yes	maximal, characteristic
2	C₈×#6597	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₉	C₄	1	2	yes	—
5	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×#90768	C₄	1	2	yes	—
7	C₄×#6597	C₄	1	1	yes	characteristic
8	C₄×#6597	C₄	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂×#6597	C₈	1	2	yes	—
13	C₂×#6597	C₈	1	2	yes	—
14	C₁₆×C₂₉	—	2	2	no	—
15	#90768	—	2	2	no	—
16	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
19	C₈×C₂₉	M₁₆	1	2	yes	—
20	C₈×C₂₉	M₁₆	1	2	yes	—
21	#6597	—	2	2	no	—
22	#6597	C₁₆	1	4	yes	complemented
23	#1312	—	29	1	no	maximal, Sylow
24	C₂²×C₂₉	C₄×C₈	1	1	yes	characteristic
25	C₄×C₂₉	#97	1	1	yes	characteristic
26	C₄×C₂₉	#97	1	1	yes	characteristic
27	C₄×C₂₉	C₂×C₁₆	1	2	yes	—
28	C₄×C₂₉	M₃₂	1	2	yes	—
29	C₄×C₁₆	—	29	1	no	—
30	C₄×C₁₆	D₂₉	1	1	yes	characteristic
31	C₈²	—	29	1	no	—
32	C₂×C₂₉	#322	1	1	yes	characteristic
33	C₂×C₂₉	C₄×C₁₆	1	1	yes	characteristic
34	C₂×C₂₉	#346	1	1	yes	characteristic
35	C₂×C₁₆	—	29	2	no	—
36	C₂×C₁₆	Dic₂₉	1	2	yes	—
37	C₄×C₈	—	29	1	no	—
38	C₄×C₈	—	29	1	no	—
39	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
40	C₂₉	#1312	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₈	—	29	2	no	—
42	C₂×C₈	—	29	2	no	—
43	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
44	C₂×C₈	C₂×Dic₂₉	1	1	yes	characteristic
45	C₄²	C₄×D₂₉	1	1	yes	characteristic
46	C₁₆	—	2	2	no	—
47	C₁₆	—	58	2	no	—
48	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
49	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
50	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
51	C₈	—	29	4	no	—
52	C₈	—	58	2	no	—
53	C₈	#90772	1	2	yes	—
54	C₈	#90777	1	2	yes	—
55	C₂²	C₈×Dic₂₉	1	1	yes	characteristic
56	C₄	C₁₆×D₂₉	1	2	yes	—
57	C₄	#11745146	1	2	yes	—
58	C₄	#11745151	1	1	yes	characteristic
59	C₄	#11745163	1	1	yes	characteristic
60	C₂	#14270885	1	1	yes	characteristic
61	C₂	C₁₆×Dic₂₉	1	1	yes	characteristic
62	C₂	#14270938	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₂₉
commutator	C₂×C₂₉	C₄×C₁₆
Fitting	C₄×C₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₄×C₈
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	#1312
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. #6597	C₁₆	semidirect
40. C₂₉	#1312	semidirect

Maximal subgroups

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

subgroup	index
C₄×#90768	2
C₈×#6597	2
C₄×C₁₆×C₂₉	2
#1312	29