Subgroups — #22612159

Order 9344.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988992	C₂	1	1	yes	maximal, characteristic
2	#17988967	C₂	1	1	yes	maximal, characteristic
3	#17988392	C₂	1	4	yes	maximal
4	C₄×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₉₂	—	2	1	no	—
6	C₂×Dic₂₉₂	C₂²	1	2	yes	—
7	#14556591	—	2	1	no	—
8	#14556591	—	2	1	no	—
9	#14556525	—	2	1	no	—
10	#14556525	C₂²	1	2	yes	—
11	C₂×C₁₆×C₇₃	C₂²	1	2	yes	—
12	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₄₆	—	2	2	no	—
14	C₂×Dic₁₄₆	—	4	1	no	—
15	Dic₂₉₂	—	2	4	no	—
16	Dic₂₉₂	—	4	2	no	—
17	C₄⋊Dic₇₃	—	2	2	no	—
18	C₄⋊Dic₇₃	—	4	1	no	—
19	C₄⋊Dic₇₃	—	4	1	no	—
20	C₄⋊Dic₇₃	—	4	1	no	—
21	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
22	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
23	C₄²×C₇₃	D₄	1	1	yes	characteristic
24	C₁₆×C₇₃	—	2	2	no	—
25	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
26	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₇₃	—	4	2	no	—
29	C₂×Dic₇₃	—	4	2	no	—
30	Dic₁₄₆	—	4	2	no	—
31	Dic₁₄₆	—	4	2	no	—
32	Dic₁₄₆	—	8	2	no	—
33	C₈×C₇₃	SD₁₆	1	2	yes	—
34	C₈×C₇₃	#41	1	2	yes	—
35	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₇₃	SD₃₂	1	2	yes	—
37	C₄×C₇₃	Q₃₂	1	2	yes	—
38	C₄×C₇₃	#124	1	1	yes	characteristic
39	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
40	Dic₇₃	—	8	2	no	—
41	Dic₇₃	—	8	2	no	—
42	C₂×C₇₃	#486	1	1	yes	characteristic
43	C₂×C₇₃	C₂×SD₃₂	1	1	yes	characteristic
44	C₂×C₇₃	C₂×Q₃₂	1	1	yes	characteristic
45	#2241	—	73	1	no	maximal, Sylow
46	C₇₃	#2241	1	1	yes	characteristic, complemented, Sylow
47	#500	—	73	1	no	—
48	#494	—	73	1	no	—
49	#358	—	73	4	no	—
50	C₄×C₁₆	D₇₃	1	1	yes	characteristic
51	C₂×Q₁₆	—	73	2	no	—
52	C₂×Q₁₆	—	146	1	no	—
53	C₄⋊Q₈	—	146	1	no	—
54	C₄⋊Q₈	—	146	1	no	—
55	C₂×C₁₆	C₂×D₇₃	1	2	yes	—
56	#107	—	73	2	no	—
57	#107	—	146	1	no	—
58	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
59	C₂×Q₈	—	292	1	no	—
60	C₂×Q₈	—	146	2	no	—
61	Q₁₆	—	292	2	no	—
62	Q₁₆	—	146	4	no	—
63	C₂×C₈	D₂₉₂	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
65	C₄⋊C₄	—	292	1	no	—
66	C₄⋊C₄	—	292	1	no	—
67	C₄⋊C₄	—	292	1	no	—
68	C₄⋊C₄	—	146	2	no	—
69	C₄²	D₂₉₂	1	1	yes	characteristic
70	C₁₆	—	2	2	no	—
71	Q₈	—	292	2	no	—
72	Q₈	—	292	2	no	—
73	Q₈	—	584	2	no	—
74	C₂×C₄	—	292	2	no	—
75	C₂×C₄	—	292	2	no	—
76	C₂×C₄	D₅₈₄	1	1	yes	characteristic
77	C₂×C₄	D₅₈₄	1	1	yes	characteristic
78	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
79	C₈	#11924017	1	2	yes	—
80	C₈	#11924028	1	2	yes	—
81	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
82	C₄	—	584	2	no	—
83	C₄	—	584	2	no	—
84	C₄	#14556536	1	2	yes	—
85	C₄	Dic₅₈₄	1	2	yes	—
86	C₄	#14556579	1	1	yes	characteristic
87	C₄	C₂×#11924017	1	1	yes	characteristic
88	C₂	#17988934	1	1	yes	characteristic
89	C₂	C₂×#14556536	1	1	yes	characteristic
90	C₂	C₂×Dic₅₈₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₅₈₄
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₄×C₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	C₄×C₁₆	D₇₃
hypocenter	C₇₃	#2241
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
46. C₇₃	#2241	semidirect