Subgroups — #49161068

Order 37504.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34036531	C₂	1	1	yes	maximal, characteristic
2	#34035956	C₂	1	2	yes	maximal
3	#34035954	C₂	1	2	yes	maximal
4	#34035905	C₂	1	1	yes	maximal, characteristic
5	#500×C₂₉₃	C₂	1	1	yes	maximal, characteristic
6	#22627616	—	2	1	no	—
7	C₂×#17989777	C₂²	1	2	yes	—
8	#22627558	C₂²	1	1	yes	characteristic
9	#22627558	C₂²	1	1	yes	characteristic
10	#22627556	—	2	1	no	—
11	C₄⋊Q₈×C₂₉₃	—	2	1	no	—
12	#107×C₂₉₃	—	2	1	no	—
13	#107×C₂₉₃	C₂²	1	2	yes	—
14	C₄×C₈×C₂₉₃	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₂₉₃	—	2	1	no	—
16	C₄⋊Dic₂₉₃	—	2	1	no	—
17	#17989781	—	4	1	no	—
18	#17989781	—	4	1	no	—
19	#17989777	Q₈	1	4	yes	complemented
20	C₂×Q₈×C₂₉₃	—	4	1	no	—
21	C₂×C₈×C₂₉₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₂₉₃	—	2	2	no	—
24	C₄⋊C₄×C₂₉₃	—	4	1	no	—
25	C₄²×C₂₉₃	D₄	1	1	yes	characteristic
26	C₂×Dic₂₉₃	—	4	1	no	—
27	C₂×Dic₂₉₃	—	4	1	no	—
28	Q₈×C₂₉₃	—	8	2	no	—
29	C₂×C₄×C₂₉₃	—	4	2	no	—
30	C₂×C₄×C₂₉₃	D₈	1	1	yes	characteristic
31	C₂×C₄×C₂₉₃	D₈	1	1	yes	characteristic
32	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
33	C₈×C₂₉₃	Q₁₆	1	2	yes	—
34	C₈×C₂₉₃	C₂×Q₈	1	2	yes	—
35	C₂²×C₂₉₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₂₉₃	—	2	1	no	—
37	C₄×C₂₉₃	—	2	1	no	—
38	C₄×C₂₉₃	—	8	2	no	—
39	C₄×C₂₉₃	C₄⋊Q₈	1	1	yes	characteristic
40	C₄×C₂₉₃	C₂×Q₁₆	1	1	yes	characteristic
41	Dic₂₉₃	—	8	1	no	—
42	Dic₂₉₃	—	8	1	no	—
43	C₂×C₂₉₃	#500	1	1	yes	characteristic
44	C₂×C₂₉₃	#509	1	1	yes	characteristic
45	C₂×C₂₉₃	#510	1	1	yes	characteristic
46	C₂₉₃	#2255	1	1	yes	characteristic, complemented, Sylow
47	#2255	—	293	1	no	maximal, Sylow
48	#500	D₂₉₃	1	1	yes	characteristic
49	#499	—	293	1	no	—
50	#367	—	293	2	no	—
51	#366	—	293	2	no	—
52	#346	—	293	1	no	—
53	C₄⋊Q₈	—	2	1	no	—
54	#125	—	586	1	no	—
55	C₂×C₁₆	—	293	2	no	—
56	#107	—	2	1	no	—
57	#107	—	293	1	no	—
58	#107	—	293	1	no	—
59	#107	C₂×D₂₉₃	1	2	yes	—
60	#106	—	586	1	no	—
61	C₄×C₈	C₂×D₂₉₃	1	1	yes	characteristic
62	C₂×Q₈	—	4	1	no	—
63	C₂×C₈	C₂²⋊D₂₉₃	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	586	1	no	—
68	C₄⋊C₄	—	586	1	no	—
69	C₄⋊C₄	—	1172	1	no	—
70	C₄⋊C₄	—	1172	1	no	—
71	C₄²	C₂²⋊D₂₉₃	1	1	yes	characteristic
72	C₁₆	—	293	4	no	—
73	Q₈	—	8	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	1172	1	no	—
76	C₂×C₄	—	1172	1	no	—
77	C₂×C₄	#17989787	1	1	yes	characteristic
78	C₂×C₄	#17989787	1	1	yes	characteristic
79	C₂×C₄	C₂×C₂²⋊D₂₉₃	1	1	yes	characteristic
80	C₈	#17989792	1	2	yes	—
81	C₈	Q₈×D₂₉₃	1	2	yes	—
82	C₂²	C₂×#17989787	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	2	no	—
86	C₄	—	2344	1	no	—
87	C₄	—	2344	1	no	—
88	C₄	#22627622	1	1	yes	characteristic
89	C₄	C₂×#17989792	1	1	yes	characteristic
90	C₂	#34036532	1	1	yes	characteristic
91	C₂	#34036565	1	1	yes	characteristic
92	C₂	#34036570	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#17989787
commutator, cosocle	C₂×C₈×C₂₉₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₉₃
Fitting	#500×C₂₉₃	C₂
socle, prime radical	C₂²×C₂₉₃	C₂×D₈
hypercenter	#500	D₂₉₃
hypocenter	C₂₉₃	#2255
LCS	G ▷ C₂×C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
19. #17989777	Q₈	semidirect
46. C₂₉₃	#2255	semidirect

Maximal subgroups

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

subgroup	index
#34036531	2
#34035956	2
#34035954	2
#34035905	2
#500×C₂₉₃	2
#2255	293