Subgroups — #22611330

Order 9344.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988635	C₂	1	3	yes	maximal, complemented
2	C₂×#14556507	C₂	1	3	yes	maximal
3	#338×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₂₉₂	C₂²	1	1	yes	characteristic
5	C₂×#11924012	C₂²	1	3	yes	—
6	#14556526	—	2	6	no	—
7	#14556507	—	2	6	no	—
8	C₂×M₁₆×C₇₃	C₂²	1	3	yes	—
9	C₂³×D₇₃	Q₈	1	2	yes	—
10	C₂×D₂₉₂	—	2	3	no	—
11	C₂×D₂₉₂	—	2	3	no	—
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	C₂²×D₇₃	—	2	6	no	—
21	C₂²×D₇₃	—	8	2	no	—
22	C₂×C₄×C₇₃	C₂×D₄	1	3	yes	—
23	C₂×C₄×C₇₃	#41	1	3	yes	—
24	D₂₉₂	—	4	3	no	—
25	D₂₉₂	—	4	1	no	—
26	C₈×C₇₃	—	4	3	no	—
27	#10596831	—	2	6	no	—
28	C₂²×C₇₃	—	4	1	no	—
29	C₂²×C₇₃	C₂²⋊Q₈	1	3	yes	—
30	C₂×D₇₃	—	4	2	no	—
31	C₂×D₇₃	—	8	6	no	—
32	C₄×C₇₃	#121	1	3	yes	—
33	C₄×C₇₃	#126	1	1	yes	characteristic
34	C₂×C₇₃	—	2	3	no	—
35	C₂×C₇₃	#396	1	1	yes	characteristic
36	D₇₃	—	8	2	no	—
37	#2069	—	73	1	no	maximal, Sylow
38	C₇₃	#2069	1	1	yes	characteristic, complemented, Sylow
39	#430	—	73	3	no	—
40	C₂×#100	—	73	3	no	—
41	#338	D₇₃	1	1	yes	characteristic, complemented
42	C₂²×D₄	—	73	1	no	—
43	C₂×M₁₆	—	73	3	no	—
44	C₂×M₁₆	C₂×D₇₃	1	3	yes	—
45	#108	—	146	6	no	—
46	#100	—	146	6	no	—
47	C₂⁴	—	73	2	no	—
48	C₂×D₄	—	146	3	no	—
49	C₂×D₄	—	146	3	no	—
50	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
51	M₁₆	—	2	3	no	—
52	M₁₆	—	2	3	no	—
53	M₁₆	—	73	6	no	—
54	M₁₆	—	146	3	no	—
55	C₂×C₈	—	2	3	no	—
56	C₂×C₈	—	146	3	no	—
57	C₂³	—	584	2	no	—
58	C₂³	—	146	6	no	—
59	C₂³	Q₈×D₇₃	1	1	yes	characteristic
60	D₄	—	292	3	no	—
61	D₄	—	292	1	no	—
62	C₂×C₄	D₄×D₇₃	1	3	yes	—
63	C₂×C₄	#11924028	1	3	yes	—
64	C₈	—	4	3	no	—
65	C₈	—	146	6	no	—
66	C₂²	—	4	1	no	—
67	C₂²	—	292	2	no	—
68	C₂²	—	584	6	no	—
69	C₂²	#14556569	1	3	yes	—
70	C₄	#14556564	1	3	yes	—
71	C₄	#14556585	1	1	yes	characteristic
72	C₂	—	2	3	no	—
73	C₂	—	584	2	no	—
74	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	#2069
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
1. #17988635	C₂	semidirect
3. #338×C₇₃	C₂	semidirect
38. C₇₃	#2069	semidirect
41. #338	D₇₃	semidirect