Subgroups — #22610085

Order 9344.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#10596831	C₂	1	6	yes	maximal
2	#376×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10596831	C₂²	1	4	yes	—
4	C₄⋊#10596831	—	2	12	no	—
5	C₂×C₄²×C₇₃	C₂²	1	3	yes	—
6	#95×C₇₃	C₄	1	4	yes	—
7	C₂×#10596831	—	2	12	no	—
8	C₂²×C₄×C₇₃	C₂×C₄	1	6	yes	—
9	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
10	C₄²×C₇₃	D₄	1	6	yes	—
11	C₄²×C₇₃	Q₈	1	6	yes	—
12	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₇₃	—	2	12	no	—
14	C₂×C₄×C₇₃	C₄⋊C₄	1	12	yes	—
15	C₂×C₄×C₇₃	C₂×D₄	1	3	yes	—
16	C₂×C₄×C₇₃	C₂×Q₈	1	3	yes	—
17	#10596831	—	4	4	no	—
18	C₂²×C₇₃	C₂×C₄⋊C₄	1	3	yes	—
19	C₂²×C₇₃	#131	1	4	yes	—
20	C₄×C₇₃	—	2	12	no	—
21	C₄×C₇₃	#127	1	1	yes	characteristic
22	C₄×C₇₃	C₄⋊Q₈	1	3	yes	—
23	C₂×C₇₃	#384	1	1	yes	characteristic
24	C₂×C₇₃	#424	1	6	yes	—
25	#1843	—	73	1	no	maximal, Sylow
26	C₇₃	#1843	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₄⋊C₈	—	73	6	no	—
28	#376	D₇₃	1	1	yes	characteristic
29	C₂²×C₈	—	73	4	no	—
30	C₂×C₄²	C₂×D₇₃	1	3	yes	—
31	C₄⋊C₈	—	146	12	no	—
32	#95	Dic₇₃	1	4	yes	—
33	C₂²×C₄	C₂×Dic₇₃	1	6	yes	—
34	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
35	C₂×C₈	—	146	12	no	—
36	C₄²	Dic₁₄₆	1	6	yes	—
37	C₄²	D₂₉₂	1	6	yes	—
38	C₂³	C₂²×Dic₇₃	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₇₃	1	12	yes	—
41	C₂×C₄	C₂×D₂₉₂	1	3	yes	—
42	C₂×C₄	C₂×Dic₁₄₆	1	3	yes	—
43	C₈	—	292	4	no	—
44	C₂²	C₂×C₄⋊Dic₇₃	1	3	yes	—
45	C₂²	#14556598	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#14556588	1	1	yes	characteristic
48	C₄	#14556591	1	3	yes	—
49	C₂	#17988457	1	1	yes	characteristic
50	C₂	#17988614	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₇₃
commutator, socle	C₂³×C₇₃	C₂²×C₄
Fitting	#376×C₇₃	C₂
hypercenter	#376	D₇₃
hypocenter	C₇₃	#1843
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
26. C₇₃	#1843	semidirect