Subgroups — #49161062

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	#34035956	C₂	1	2	yes	maximal
3	#34035955	C₂	1	1	yes	maximal, characteristic
4	C₁₆×Dic₂₉₃	C₂	1	1	yes	maximal, characteristic
5	#366×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	1	yes	characteristic
24	C₂×Dic₂₉₃	D₈	1	1	yes	characteristic
25	#14556873	Q₁₆	1	2	yes	—
26	C₂×C₄×C₂₉₃	—	4	2	no	—
27	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
28	C₈×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
29	C₈×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
30	C₂²×C₂₉₃	C₂×D₈	1	1	yes	characteristic
31	C₄×C₂₉₃	—	8	2	no	—
32	C₄×C₂₉₃	C₄⋊Q₈	1	1	yes	characteristic
33	C₄×C₂₉₃	C₂×Q₁₆	1	1	yes	characteristic
34	Dic₂₉₃	—	2	1	no	—
35	Dic₂₉₃	—	2	1	no	—
36	Dic₂₉₃	—	8	2	no	—
37	C₂×C₂₉₃	#500	1	1	yes	characteristic
38	C₂×C₂₉₃	#508	1	1	yes	characteristic
39	C₂×C₂₉₃	#508	1	1	yes	characteristic
40	C₂₉₃	#2253	1	1	yes	characteristic, complemented, Sylow
41	#2253	—	293	1	no	maximal, Sylow
42	#499	—	293	2	no	—
43	#367	—	293	2	no	—
44	#366	—	293	1	no	—
45	#366	D₂₉₃	1	1	yes	characteristic
46	C₄×C₁₆	—	293	1	no	—
47	#125	—	586	2	no	—
48	C₂×C₁₆	—	293	1	no	—
49	C₂×C₁₆	C₂×D₂₉₃	1	1	yes	characteristic
50	#107	—	293	2	no	—
51	#107	C₂×D₂₉₃	1	2	yes	—
52	#106	—	586	2	no	—
53	C₄×C₈	—	293	1	no	—
54	C₂×C₈	—	293	1	no	—
55	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
56	C₄⋊C₄	—	2	2	no	—
57	C₄⋊C₄	—	586	2	no	—
58	C₄⋊C₄	—	1172	2	no	—
59	C₄⋊C₄	—	1172	2	no	—
60	C₄²	—	293	1	no	—
61	C₁₆	—	293	2	no	—
62	C₁₆	Dic₅₈₆	1	2	yes	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	—	293	1	no	—
65	C₂×C₄	—	293	1	no	—
66	C₂×C₄	—	1172	2	no	—
67	C₂×C₄	D₄×D₂₉₃	1	1	yes	characteristic
68	C₈	—	293	2	no	—
69	C₈	Q₈×D₂₉₃	1	1	yes	characteristic
70	C₈	C₂×Dic₅₈₆	1	1	yes	characteristic
71	C₂²	D₈×D₂₉₃	1	1	yes	characteristic
72	C₄	—	8	2	no	—
73	C₄	—	2344	2	no	—
74	C₄	—	586	1	no	—
75	C₄	—	586	1	no	—
76	C₄	#22627623	1	1	yes	characteristic
77	C₄	Q₁₆×D₂₉₃	1	1	yes	characteristic
78	C₂	#34036533	1	1	yes	characteristic
79	C₂	#34036558	1	1	yes	characteristic
80	C₂	#34036562	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₂₉₃
commutator, cosocle	C₂×C₈×C₂₉₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₉₃
Fitting	#366×C₂₉₃	C₂
socle, prime radical	C₂²×C₂₉₃	C₂×D₈
hypercenter	#366	D₂₉₃
hypocenter	C₂₉₃	#2253
LCS	G ▷ C₂×C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
40. 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
#34035956	2
#34035955	2
C₁₆×Dic₂₉₃	2
#366×C₂₉₃	2
#2253	293