Subgroups — #22611818

Order 9344.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989019	C₂	1	1	yes	maximal, characteristic
2	#17988705	C₂	1	2	yes	maximal, complemented
3	#17988417	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988395	C₂	1	2	yes	maximal, complemented
5	#346×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556613	C₂²	1	2	yes	—
7	#14556597	—	2	2	no	—
8	Dic₅₈₄	C₄	1	1	yes	characteristic, complemented
9	#14556536	C₄	1	2	yes	complemented
10	D₁₁₆₈	C₄	1	1	yes	characteristic, complemented
11	#14556527	C₂²	1	2	yes	—
12	#14556519	—	2	2	no	—
13	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	#11924028	—	2	2	no	—
17	Dic₂₉₂	C₂×C₄	1	2	yes	—
18	#11924017	—	2	2	no	—
19	D₅₈₄	C₂×C₄	1	2	yes	—
20	#11924012	—	2	2	no	—
21	#11924011	—	4	2	no	—
22	C₈×D₇₃	—	4	2	no	—
23	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
25	C₄²×C₇₃	D₄	1	1	yes	characteristic
26	C₁₆×C₇₃	—	2	1	no	—
27	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₃	—	2	1	no	—
30	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₇₃	—	4	2	no	—
32	D₂₉₂	—	2	2	no	—
33	C₄×D₇₃	—	4	2	no	—
34	Dic₁₄₆	—	2	2	no	—
35	C₈×C₇₃	D₈	1	2	yes	—
36	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₇₃	#41	1	1	yes	characteristic
38	#10596831	—	4	2	no	—
39	C₂²×C₇₃	#135	1	1	yes	characteristic
40	C₂×D₇₃	—	4	2	no	—
41	C₄×C₇₃	—	4	1	no	—
42	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
43	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
44	Dic₇₃	—	4	2	no	—
45	C₂×C₇₃	—	2	1	no	—
46	C₂×C₇₃	C₄×D₈	1	1	yes	characteristic
47	D₇₃	—	8	2	no	—
48	#2179	—	73	1	no	maximal, Sylow
49	C₇₃	#2179	1	1	yes	characteristic, complemented, Sylow
50	#508	—	73	1	no	—
51	#443	—	73	2	no	—
52	#368	—	73	1	no	—
53	#359	—	73	2	no	—
54	#346	D₇₃	1	1	yes	characteristic, complemented
55	#135	—	73	2	no	—
56	#131	—	146	2	no	—
57	Q₃₂	—	73	1	no	—
58	SD₃₂	—	73	2	no	—
59	D₁₆	—	73	1	no	—
60	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
61	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
62	#108	—	73	2	no	—
63	#104	—	146	2	no	—
64	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
65	#41	—	146	2	no	—
66	Q₁₆	—	73	2	no	—
67	SD₁₆	—	146	2	no	—
68	D₈	—	73	2	no	—
69	M₁₆	—	292	2	no	—
70	M₁₆	—	146	2	no	—
71	C₂×C₈	—	292	2	no	—
72	C₂×C₈	D₂₉₂	1	1	yes	characteristic
73	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
74	C₄²	D₂₉₂	1	1	yes	characteristic
75	C₁₆	—	2	1	no	—
76	C₁₆	C₄×D₇₃	1	1	yes	characteristic
77	C₁₆	C₄×D₇₃	1	1	yes	characteristic
78	Q₈	—	146	2	no	—
79	D₄	—	292	2	no	—
80	D₄	—	146	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	292	2	no	—
83	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
84	C₈	—	292	2	no	—
85	C₈	D₅₈₄	1	2	yes	—
86	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
87	C₈	#11924028	1	1	yes	characteristic
88	C₂²	—	292	2	no	—
89	C₂²	#14556613	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	292	2	no	—
92	C₄	C₄×D₂₉₂	1	1	yes	characteristic
93	C₄	C₂×D₅₈₄	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	584	2	no	—
96	C₂	C₄×D₅₈₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₅₈₄
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#346×C₇₃	C₂
socle	C₂×C₇₃	C₄×D₈
hypercenter	#346	D₇₃
hypocenter	C₇₃	#2179
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #17988705	C₂	semidirect
3. #17988417	C₂	semidirect
4. #17988395	C₂	semidirect
5. #346×C₇₃	C₂	semidirect
8. Dic₅₈₄	C₄	semidirect
9. #14556536	C₄	semidirect
10. D₁₁₆₈	C₄	semidirect
49. C₇₃	#2179	semidirect
54. #346	D₇₃	semidirect