Subgroups — #22611333

Order 9344.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988635	C₂	1	3	yes	maximal
2	C₂×#14556509	C₂	1	3	yes	maximal
3	#338×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₄₆	C₂²	1	1	yes	characteristic
5	C₂×#11924012	C₂²	1	3	yes	—
6	#14556526	—	2	6	no	—
7	#14556509	—	2	6	no	—
8	C₂×M₁₆×C₇₃	C₂²	1	3	yes	—
9	C₂×Dic₁₄₆	—	2	3	no	—
10	C₂×Dic₁₄₆	—	2	3	no	—
11	C₂²×Dic₇₃	Q₈	1	2	yes	—
12	#11924012	—	2	3	no	—
13	#11924012	D₄	1	6	yes	—
14	C₂×#10596831	—	2	3	no	—
15	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
16	M₁₆×C₇₃	—	2	3	no	—
17	M₁₆×C₇₃	—	2	3	no	—
18	C₂×C₈×C₇₃	—	2	3	no	—
19	C₂³×C₇₃	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₇₃	C₂×D₄	1	3	yes	—
21	C₂×C₄×C₇₃	#41	1	3	yes	—
22	C₂×Dic₇₃	—	2	6	no	—
23	Dic₁₄₆	—	4	3	no	—
24	Dic₁₄₆	—	4	1	no	—
25	C₈×C₇₃	—	4	3	no	—
26	#10596831	—	2	6	no	—
27	C₂²×C₇₃	—	4	1	no	—
28	C₂²×C₇₃	C₂²⋊Q₈	1	3	yes	—
29	C₄×C₇₃	#121	1	3	yes	—
30	C₄×C₇₃	#126	1	1	yes	characteristic
31	Dic₇₃	—	4	2	no	—
32	C₂×C₇₃	—	2	3	no	—
33	C₂×C₇₃	#396	1	1	yes	characteristic
34	#2070	—	73	1	no	maximal, Sylow
35	C₇₃	#2070	1	1	yes	characteristic, complemented, Sylow
36	#430	—	73	3	no	—
37	C₂×#101	—	73	3	no	—
38	#338	D₇₃	1	1	yes	characteristic
39	C₂²×Q₈	—	73	1	no	—
40	C₂×M₁₆	—	73	3	no	—
41	C₂×M₁₆	C₂×D₇₃	1	3	yes	—
42	#108	—	146	6	no	—
43	#101	—	146	6	no	—
44	C₂×Q₈	—	146	3	no	—
45	C₂×Q₈	—	146	3	no	—
46	C₂²×C₄	—	73	2	no	—
47	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
48	M₁₆	—	2	3	no	—
49	M₁₆	—	2	3	no	—
50	M₁₆	—	73	6	no	—
51	M₁₆	—	146	3	no	—
52	C₂×C₈	—	2	3	no	—
53	C₂×C₈	—	146	3	no	—
54	C₂³	Q₈×D₇₃	1	1	yes	characteristic
55	Q₈	—	292	3	no	—
56	Q₈	—	292	1	no	—
57	C₂×C₄	—	146	6	no	—
58	C₂×C₄	D₄×D₇₃	1	3	yes	—
59	C₂×C₄	#11924028	1	3	yes	—
60	C₈	—	4	3	no	—
61	C₈	—	146	6	no	—
62	C₂²	—	4	1	no	—
63	C₂²	#14556569	1	3	yes	—
64	C₄	—	292	2	no	—
65	C₄	#14556564	1	3	yes	—
66	C₄	#14556585	1	1	yes	characteristic
67	C₂	—	2	3	no	—
68	C₂	#17988511	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17988511
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#338×C₇₃	C₂
socle	C₂×C₇₃	#396
hypercenter	#338	D₇₃
hypocenter	C₇₃	#2070
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
35. C₇₃	#2070	semidirect