Subgroups — #49161063

Order 37504.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34036530	C₂	1	2	yes	maximal
2	#34035957	C₂	1	1	yes	maximal, characteristic
3	#34035954	C₂	1	2	yes	maximal
4	C₁₆×Dic₂₉₃	C₂	1	1	yes	maximal, characteristic
5	#367×C₂₉₃	C₂	1	1	yes	maximal, characteristic
6	#22627615	—	2	2	no	—
7	C₂×#17989777	C₂²	1	1	yes	characteristic
8	#22627558	C₂²	1	2	yes	—
9	#22627555	—	2	2	no	—
10	C₈×Dic₂₉₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₂₉₃	C₂²	1	1	yes	characteristic
12	#107×C₂₉₃	C₂²	1	2	yes	—
13	C₂×#14556873	D₄	1	1	yes	characteristic
14	C₄⋊Dic₂₉₃	—	2	2	no	—
15	C₄⋊Dic₂₉₃	—	4	2	no	—
16	#17989781	—	4	2	no	—
17	C₄×Dic₂₉₃	D₄	1	1	yes	characteristic
18	#17989777	Q₈	1	2	yes	—
19	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₂₉₃	—	2	2	no	—
21	C₁₆×C₂₉₃	Q₈	1	2	yes	—
22	C₂×Dic₂₉₃	—	4	2	no	—
23	C₂×Dic₂₉₃	D₈	1	2	yes	—
24	#14556873	Q₁₆	1	2	yes	—
25	C₂×C₄×C₂₉₃	—	4	2	no	—
26	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
27	C₈×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
28	C₈×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₂₉₃	C₂×D₈	1	1	yes	characteristic
30	C₄×C₂₉₃	—	8	2	no	—
31	C₄×C₂₉₃	C₄⋊Q₈	1	1	yes	characteristic
32	C₄×C₂₉₃	C₂×Q₁₆	1	1	yes	characteristic
33	Dic₂₉₃	—	2	2	no	—
34	Dic₂₉₃	—	8	2	no	—
35	C₂×C₂₉₃	#500	1	1	yes	characteristic
36	C₂×C₂₉₃	#508	1	2	yes	—
37	C₂₉₃	#2253	1	1	yes	characteristic, complemented, Sylow
38	#2253	—	293	1	no	maximal, Sylow
39	#499	—	293	2	no	—
40	#367	—	293	1	no	—
41	#367	D₂₉₃	1	1	yes	characteristic
42	#366	—	293	2	no	—
43	C₄×C₁₆	—	293	1	no	—
44	#125	—	586	2	no	—
45	C₂×C₁₆	—	293	1	no	—
46	C₂×C₁₆	C₂×D₂₉₃	1	1	yes	characteristic
47	#107	—	293	2	no	—
48	#107	C₂×D₂₉₃	1	2	yes	—
49	#106	—	586	2	no	—
50	C₄×C₈	—	293	1	no	—
51	C₂×C₈	—	293	1	no	—
52	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
53	C₄⋊C₄	—	2	2	no	—
54	C₄⋊C₄	—	586	2	no	—
55	C₄⋊C₄	—	1172	2	no	—
56	C₄⋊C₄	—	1172	2	no	—
57	C₄²	—	293	1	no	—
58	C₁₆	—	293	2	no	—
59	C₁₆	Dic₅₈₆	1	2	yes	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	293	2	no	—
62	C₂×C₄	—	1172	2	no	—
63	C₂×C₄	D₄×D₂₉₃	1	1	yes	characteristic
64	C₈	—	293	2	no	—
65	C₈	Q₈×D₂₉₃	1	1	yes	characteristic
66	C₈	C₂×Dic₅₈₆	1	1	yes	characteristic
67	C₂²	D₈×D₂₉₃	1	1	yes	characteristic
68	C₄	—	8	2	no	—
69	C₄	—	2344	2	no	—
70	C₄	—	586	2	no	—
71	C₄	#22627623	1	1	yes	characteristic
72	C₄	Q₁₆×D₂₉₃	1	1	yes	characteristic
73	C₂	#34036533	1	1	yes	characteristic
74	C₂	#34036560	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₂₉₃
commutator, cosocle	C₂×C₈×C₂₉₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₉₃
Fitting	#367×C₂₉₃	C₂
socle, prime radical	C₂²×C₂₉₃	C₂×D₈
hypercenter	#367	D₂₉₃
hypocenter	C₂₉₃	#2253
LCS	G ▷ C₂×C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

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

Maximal subgroups

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

subgroup	index
#34036530	2
#34035957	2
#34035954	2
C₁₆×Dic₂₉₃	2
#367×C₂₉₃	2
#2253	293