Subgroups — #22625860

Order 9344.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989453	C₂	1	6	yes	maximal
2	#17988432	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10596833	C₂²	1	4	yes	—
4	C₂×C₄×Dic₇₃	C₂²	1	3	yes	—
5	#14556498	C₄	1	3	yes	—
6	#95×C₇₃	C₄	1	1	yes	characteristic
7	C₂×#10596833	—	2	12	no	—
8	C₂²×Dic₇₃	C₂×C₄	1	3	yes	—
9	C₂²×Dic₇₃	C₂³	1	1	yes	characteristic
10	C₄×Dic₇₃	—	2	6	no	—
11	C₂²×C₄×C₇₃	C₂×C₄	1	3	yes	—
12	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₇₃	—	2	3	no	—
14	C₂×C₄×C₇₃	—	2	6	no	—
15	C₂×Dic₇₃	—	2	3	no	—
16	C₂×Dic₇₃	—	2	3	no	—
17	C₂×Dic₇₃	—	2	3	no	—
18	C₂×Dic₇₃	#41	1	6	yes	—
19	#10596833	—	4	4	no	—
20	C₂²×C₇₃	#117	1	3	yes	—
21	C₂²×C₇₃	#131	1	3	yes	—
22	C₂²×C₇₃	#131	1	1	yes	characteristic
23	C₄×C₇₃	—	4	3	no	—
24	Dic₇₃	—	4	3	no	—
25	Dic₇₃	#126	1	4	yes	—
26	C₂×C₇₃	#383	1	1	yes	characteristic
27	C₂×C₇₃	#433	1	3	yes	—
28	C₂×C₇₃	#433	1	3	yes	—
29	#1840	—	73	1	no	maximal, Sylow
30	C₇₃	#1840	1	1	yes	characteristic, complemented, Sylow
31	#376	—	73	1	no	—
32	#336	—	73	6	no	—
33	C₂²×C₈	—	73	4	no	—
34	C₂×C₄²	—	73	3	no	—
35	#95	—	73	3	no	—
36	#95	#64408	1	1	yes	characteristic
37	C₂²×C₄	—	73	1	no	—
38	C₂²×C₄	—	73	3	no	—
39	C₂²×C₄	C₂×#64408	1	3	yes	—
40	C₂×C₈	—	146	12	no	—
41	C₄²	—	146	6	no	—
42	C₂³	C₂²×#64408	1	1	yes	characteristic
43	C₂×C₄	—	2	6	no	—
44	C₂×C₄	—	2	3	no	—
45	C₂×C₄	—	73	6	no	—
46	C₂×C₄	—	146	3	no	—
47	C₂×C₄	—	146	3	no	—
48	C₂×C₄	—	146	3	no	—
49	C₈	—	292	4	no	—
50	C₂²	#14556670	1	3	yes	—
51	C₂²	#14556678	1	3	yes	—
52	C₂²	#14556679	1	1	yes	characteristic
53	C₄	—	4	3	no	—
54	C₄	—	292	3	no	—
55	C₄	—	73	4	no	—
56	C₂	#17989532	1	1	yes	characteristic
57	C₂	#17989611	1	3	yes	—
58	C₂	#17989612	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#64408
commutator, socle	C₂³×C₇₃	C₂²×C₄
Fitting	#95×C₇₃	C₄
hypercenter	#95	#64408
hypocenter	C₇₃	#1840
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
30. C₇₃	#1840	semidirect