Subgroups — #49173941

Order 37504.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34037062	C₂	1	1	yes	maximal, characteristic
2	#34037058	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₂₉₃	C₂	1	1	yes	maximal, characteristic
4	#22627695	—	2	1	no	—
5	#22627674	—	2	1	no	—
6	Q₁₆×D₂₉₃	—	2	1	no	—
7	Dic₂₃₄₄	C₄	1	1	yes	characteristic
8	#22627570	—	2	1	no	—
9	C₁₆×D₂₉₃	C₂²	1	1	yes	characteristic
10	Q₃₂×C₂₉₃	C₄	1	1	yes	characteristic
11	#17989812	—	4	1	no	—
12	Q₈×D₂₉₃	—	4	1	no	—
13	Dic₁₁₇₂	—	2	1	no	—
14	#17989792	—	4	1	no	—
15	C₈×D₂₉₃	D₄	1	1	yes	characteristic
16	#17989777	D₄	1	1	yes	characteristic
17	Q₁₆×C₂₉₃	—	2	1	no	—
18	C₁₆×C₂₉₃	C₂×C₄	1	1	yes	characteristic
19	#14556880	—	8	1	no	—
20	Dic₅₈₆	—	4	1	no	—
21	Dic₅₈₆	—	8	1	no	—
22	C₄×D₂₉₃	—	8	1	no	—
23	C₄×D₂₉₃	D₈	1	1	yes	characteristic
24	#14556873	SD₁₆	1	1	yes	characteristic
25	Q₈×C₂₉₃	—	4	1	no	—
26	C₈×C₂₉₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×D₂₉₃	SD₃₂	1	1	yes	characteristic
28	C₄×C₂₉₃	—	8	1	no	—
29	C₄×C₂₉₃	#102	1	1	yes	characteristic
30	Dic₂₉₃	—	8	1	no	—
31	Dic₂₉₃	D₁₆	1	1	yes	characteristic
32	C₂×C₂₉₃	#357	1	1	yes	characteristic
33	D₂₉₃	—	2	1	no	—
34	C₂₉₃	#1420	1	1	yes	characteristic, complemented, Sylow
35	#1420	—	293	1	no	maximal, Sylow
36	C₂×Q₃₂	—	293	1	no	—
37	M₆₄	—	293	1	no	—
38	#368	—	293	1	no	—
39	C₂×Q₁₆	—	586	1	no	—
40	Q₃₂	—	293	1	no	—
41	Q₃₂	—	586	1	no	—
42	Q₃₂	#11924078	1	1	yes	characteristic
43	C₂×C₁₆	—	293	1	no	—
44	#108	—	586	1	no	—
45	C₃₂	—	586	1	no	—
46	C₂×Q₈	—	1172	1	no	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	586	1	no	—
49	Q₁₆	—	1172	1	no	—
50	M₁₆	—	1172	1	no	—
51	C₂×C₈	—	293	1	no	—
52	C₁₆	—	293	1	no	—
53	C₁₆	C₂×#11924078	1	1	yes	characteristic
54	Q₈	—	4	1	no	—
55	Q₈	—	2344	1	no	—
56	Q₈	—	1172	1	no	—
57	C₂×C₄	—	293	1	no	—
58	C₂×C₄	—	2344	1	no	—
59	C₈	—	293	1	no	—
60	C₈	—	2344	1	no	—
61	C₈	C₂²⋊#11924078	1	1	yes	characteristic
62	C₂²	—	293	1	no	—
63	C₄	—	8	1	no	—
64	C₄	—	293	1	no	—
65	C₄	—	2344	1	no	—
66	C₄	#22627686	1	1	yes	characteristic
67	C₂	—	586	1	no	—
68	C₂	#34037041	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#34037041
commutator	C₁₆×C₂₉₃	C₂×C₄
Frattini	C₁₆	C₂×#11924078
Fitting	Q₃₂×C₂₉₃	C₄
socle	C₂×C₂₉₃	#357
prime radical	C₂×D₂₉₃	SD₃₂
cosocle	C₁₆×D₂₉₃	C₂²
hypercenter	Q₃₂	#11924078
hypocenter	C₂₉₃	#1420
LCS	G ▷ C₁₆×C₂₉₃ ▷ C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
34. C₂₉₃	#1420	semidirect

Maximal subgroups

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

subgroup	index
#34037062	2
#34037058	2
Q₃₂×D₂₉₃	2
#1420	293