Subgroups — #49161032

Order 37504.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34036509	C₂	1	1	yes	maximal, characteristic
2	#34035932	C₂	1	4	yes	maximal
3	#34035905	C₂	1	1	yes	maximal, characteristic
4	#499×C₂₉₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₁₇₂	—	2	1	no	—
6	C₂×Dic₁₁₇₂	C₂²	1	2	yes	—
7	#22627624	—	2	1	no	—
8	C₂×#17989777	C₂²	1	2	yes	—
9	#125×C₂₉₃	—	2	1	no	—
10	#107×C₂₉₃	C₂²	1	2	yes	—
11	#106×C₂₉₃	—	2	1	no	—
12	C₄×C₈×C₂₉₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₅₈₆	—	2	2	no	—
14	Dic₁₁₇₂	—	2	4	no	—
15	Dic₁₁₇₂	—	4	2	no	—
16	C₄⋊Dic₂₉₃	—	4	2	no	—
17	#17989777	—	2	2	no	—
18	C₂×C₈×C₂₉₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₂₉₃	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₂₉₃	—	2	2	no	—
21	C₄⋊C₄×C₂₉₃	—	4	2	no	—
22	C₄²×C₂₉₃	D₄	1	1	yes	characteristic
23	Dic₅₈₆	—	4	2	no	—
24	Dic₅₈₆	—	4	2	no	—
25	C₂×Dic₂₉₃	—	4	2	no	—
26	C₂×C₄×C₂₉₃	—	4	2	no	—
27	C₂×C₄×C₂₉₃	D₈	1	2	yes	—
28	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
29	C₈×C₂₉₃	SD₁₆	1	2	yes	—
30	C₈×C₂₉₃	#41	1	2	yes	—
31	C₂²×C₂₉₃	C₂×D₈	1	1	yes	characteristic
32	C₄×C₂₉₃	—	2	2	no	—
33	C₄×C₂₉₃	—	8	2	no	—
34	C₄×C₂₉₃	#124	1	1	yes	characteristic
35	C₄×C₂₉₃	C₂×SD₁₆	1	1	yes	characteristic
36	Dic₂₉₃	—	8	2	no	—
37	C₂×C₂₉₃	#486	1	1	yes	characteristic
38	C₂×C₂₉₃	#510	1	2	yes	—
39	C₂₉₃	#2245	1	1	yes	characteristic, complemented, Sylow
40	#2245	—	293	1	no	maximal, Sylow
41	#499	D₂₉₃	1	1	yes	characteristic
42	#494	—	293	1	no	—
43	#358	—	293	4	no	—
44	#346	—	293	1	no	—
45	C₂×Q₁₆	—	293	2	no	—
46	C₂×Q₁₆	—	586	1	no	—
47	C₄⋊Q₈	—	586	1	no	—
48	#125	—	2	1	no	—
49	C₂×C₁₆	—	293	2	no	—
50	#107	C₂×D₂₉₃	1	2	yes	—
51	#106	—	2	1	no	—
52	C₄×C₈	C₂×D₂₉₃	1	1	yes	characteristic
53	C₂×Q₈	—	586	2	no	—
54	Q₁₆	—	586	4	no	—
55	Q₁₆	—	1172	2	no	—
56	C₂×C₈	C₂²⋊D₂₉₃	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₂₉₃	1	1	yes	characteristic
58	C₄⋊C₄	—	2	2	no	—
59	C₄⋊C₄	—	4	2	no	—
60	C₄⋊C₄	—	1172	2	no	—
61	C₄²	C₂²⋊D₂₉₃	1	1	yes	characteristic
62	C₁₆	—	586	2	no	—
63	Q₈	—	1172	2	no	—
64	Q₈	—	1172	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	1172	2	no	—
67	C₂×C₄	#17989787	1	2	yes	—
68	C₂×C₄	C₂×C₂²⋊D₂₉₃	1	1	yes	characteristic
69	C₈	#17989789	1	2	yes	—
70	C₈	#17989803	1	2	yes	—
71	C₂²	C₂×#17989787	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	2344	2	no	—
75	C₄	#22627613	1	1	yes	characteristic
76	C₄	C₂×#17989789	1	1	yes	characteristic
77	C₂	#34036477	1	1	yes	characteristic
78	C₂	#34036569	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#17989787
commutator, cosocle	C₂×C₈×C₂₉₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₉₃
Fitting	#499×C₂₉₃	C₂
socle, prime radical	C₂²×C₂₉₃	C₂×D₈
hypercenter	#499	D₂₉₃
hypocenter	C₂₉₃	#2245
LCS	G ▷ C₂×C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
39. C₂₉₃	#2245	semidirect

Maximal subgroups

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

subgroup	index
#34036509	2
#34035932	2
#34035905	2
#499×C₂₉₃	2
#2245	293