Subgroups — #49161064

Order 37504.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34036531	C₂	1	2	yes	maximal
2	#34035957	C₂	1	2	yes	maximal
3	#34035955	C₂	1	2	yes	maximal
4	C₄×C₁₆×C₂₉₃	C₂	1	1	yes	maximal, characteristic
5	#22627616	—	2	2	no	—
6	#22627558	C₂²	1	4	yes	—
7	#22627556	—	2	2	no	—
8	C₂×C₁₆×C₂₉₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₂₉₃	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₉₃	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₂₉₃	—	2	4	no	—
12	#17989781	—	4	4	no	—
13	C₂×C₈×C₂₉₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
15	C₄²×C₂₉₃	D₄	1	1	yes	characteristic
16	C₁₆×C₂₉₃	Q₈	1	2	yes	—
17	C₁₆×C₂₉₃	Q₈	1	2	yes	—
18	C₂×Dic₂₉₃	—	4	4	no	—
19	C₂×C₄×C₂₉₃	D₈	1	2	yes	—
20	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
21	C₈×C₂₉₃	Q₁₆	1	2	yes	—
22	C₈×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
23	C₈×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
24	C₂²×C₂₉₃	C₂×D₈	1	1	yes	characteristic
25	C₄×C₂₉₃	—	2	2	no	—
26	C₄×C₂₉₃	C₄⋊Q₈	1	1	yes	characteristic
27	C₄×C₂₉₃	C₂×Q₁₆	1	1	yes	characteristic
28	Dic₂₉₃	—	8	4	no	—
29	C₂×C₂₉₃	#500	1	1	yes	characteristic
30	C₂×C₂₉₃	#508	1	2	yes	—
31	C₂₉₃	#2253	1	1	yes	characteristic, complemented, Sylow
32	#2253	—	293	1	no	maximal, Sylow
33	#499	—	293	2	no	—
34	#367	—	293	2	no	—
35	#366	—	293	2	no	—
36	C₄×C₁₆	D₂₉₃	1	1	yes	characteristic
37	#125	—	586	2	no	—
38	C₂×C₁₆	C₂×D₂₉₃	1	1	yes	characteristic
39	C₂×C₁₆	C₂×D₂₉₃	1	1	yes	characteristic
40	#107	—	293	4	no	—
41	#106	—	586	2	no	—
42	C₄×C₈	C₂×D₂₉₃	1	1	yes	characteristic
43	C₂×C₈	D₁₁₇₂	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
45	C₄⋊C₄	—	586	4	no	—
46	C₄⋊C₄	—	1172	4	no	—
47	C₄²	D₁₁₇₂	1	1	yes	characteristic
48	C₁₆	Dic₅₈₆	1	2	yes	—
49	C₁₆	Dic₅₈₆	1	2	yes	—
50	C₂×C₄	—	1172	4	no	—
51	C₂×C₄	D₂₃₄₄	1	2	yes	—
52	C₂×C₄	C₂×D₁₁₇₂	1	1	yes	characteristic
53	C₈	Dic₁₁₇₂	1	2	yes	—
54	C₈	C₂×Dic₅₈₆	1	1	yes	characteristic
55	C₈	C₂×Dic₅₈₆	1	1	yes	characteristic
56	C₂²	C₂×D₂₃₄₄	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	2344	4	no	—
59	C₄	#22627624	1	1	yes	characteristic
60	C₄	C₂×Dic₁₁₇₂	1	1	yes	characteristic
61	C₂	#34036534	1	1	yes	characteristic
62	C₂	#34036561	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₃₄₄
commutator, cosocle	C₂×C₈×C₂₉₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₉₃
Fitting	C₄×C₁₆×C₂₉₃	C₂
socle, prime radical	C₂²×C₂₉₃	C₂×D₈
hypercenter	C₄×C₁₆	D₂₉₃
hypocenter	C₂₉₃	#2253
LCS	G ▷ C₂×C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
31. C₂₉₃	#2253	semidirect

Maximal subgroups

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

subgroup	index
#34036531	2
#34035957	2
#34035955	2
C₄×C₁₆×C₂₉₃	2
#2253	293