Subgroups — #49173940

Order 37504.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34037062	C₂	1	1	yes	maximal, characteristic, complemented
2	#34037058	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₂₉₃	C₂	1	1	yes	maximal, characteristic
4	#22627695	—	2	1	no	—
5	#22627674	—	2	1	no	—
6	D₈×D₂₉₃	—	2	1	no	—
7	D₄₆₈₈	C₄	1	1	yes	characteristic
8	#22627565	—	2	1	no	—
9	C₁₆×D₂₉₃	C₂²	1	1	yes	characteristic
10	D₁₆×C₂₉₃	C₄	1	1	yes	characteristic
11	#17989812	—	4	1	no	—
12	D₄×D₂₉₃	—	4	1	no	—
13	D₂₃₄₄	—	2	1	no	—
14	#17989787	—	4	1	no	—
15	C₈×D₂₉₃	D₄	1	1	yes	characteristic
16	#17989777	D₄	1	1	yes	characteristic
17	D₈×C₂₉₃	—	2	1	no	—
18	C₁₆×C₂₉₃	C₂×C₄	1	1	yes	characteristic
19	#14556880	—	8	1	no	—
20	C₂²×D₂₉₃	—	8	1	no	—
21	D₁₁₇₂	—	4	1	no	—
22	C₂²⋊D₂₉₃	—	8	1	no	—
23	C₄×D₂₉₃	D₈	1	1	yes	characteristic
24	#14556873	SD₁₆	1	1	yes	characteristic
25	D₄×C₂₉₃	—	4	1	no	—
26	C₈×C₂₉₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₉₃	—	8	1	no	—
28	C₂×D₂₉₃	—	8	1	no	—
29	C₂×D₂₉₃	—	16	2	no	—
30	C₂×D₂₉₃	SD₃₂	1	1	yes	characteristic
31	C₄×C₂₉₃	#102	1	1	yes	characteristic
32	Dic₂₉₃	D₁₆	1	1	yes	characteristic
33	C₂×C₂₉₃	—	16	1	no	—
34	C₂×C₂₉₃	#357	1	1	yes	characteristic
35	D₂₉₃	—	2	1	no	—
36	D₂₉₃	—	16	1	no	—
37	C₂₉₃	#1419	1	1	yes	characteristic, complemented, Sylow
38	#1419	—	293	1	no	maximal, Sylow
39	C₂×D₁₆	—	293	1	no	—
40	M₆₄	—	293	1	no	—
41	#368	—	293	1	no	—
42	C₂×D₈	—	586	1	no	—
43	D₁₆	—	293	1	no	—
44	D₁₆	—	586	1	no	—
45	D₁₆	#11924078	1	1	yes	characteristic
46	C₂×C₁₆	—	293	1	no	—
47	#108	—	586	1	no	—
48	C₃₂	—	586	1	no	—
49	C₂×D₄	—	1172	1	no	—
50	D₈	—	2	1	no	—
51	D₈	—	586	1	no	—
52	D₈	—	1172	1	no	—
53	M₁₆	—	1172	1	no	—
54	C₂×C₈	—	293	1	no	—
55	C₁₆	—	293	1	no	—
56	C₁₆	C₂×#11924078	1	1	yes	characteristic
57	C₂³	—	2344	1	no	—
58	D₄	—	4	1	no	—
59	D₄	—	2344	1	no	—
60	D₄	—	1172	1	no	—
61	C₂×C₄	—	293	1	no	—
62	C₈	—	293	1	no	—
63	C₈	—	2344	1	no	—
64	C₈	C₂²⋊#11924078	1	1	yes	characteristic
65	C₂²	—	8	1	no	—
66	C₂²	—	293	1	no	—
67	C₂²	—	2344	1	no	—
68	C₂²	—	4688	2	no	—
69	C₄	—	293	1	no	—
70	C₄	#22627686	1	1	yes	characteristic
71	C₂	—	16	1	no	—
72	C₂	—	586	1	no	—
73	C₂	—	4688	1	no	—
74	C₂	#34037041	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#34037041
commutator	C₁₆×C₂₉₃	C₂×C₄
Frattini	C₁₆	C₂×#11924078
Fitting	D₁₆×C₂₉₃	C₄
socle	C₂×C₂₉₃	#357
prime radical	D₁₆×D₂₉₃	C₂
cosocle	C₁₆×D₂₉₃	C₂²
hypercenter	D₁₆	#11924078
hypocenter	C₂₉₃	#1419
LCS	G ▷ C₁₆×C₂₉₃ ▷ C₈×C₂₉₃ ▷ C₄×C₂₉₃ ▷ C₂×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #34037062	C₂	semidirect
2. #34037058	C₂	semidirect
37. C₂₉₃	#1419	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
D₁₆×D₂₉₃	2
#1419	293