Subgroups — #22624887

Order 9344.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989473	C₂	1	1	yes	maximal, characteristic
2	#17989450	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	—	2	1	no	—
5	C₄⋊#10596833	—	2	1	no	—
6	Q₈×Dic₇₃	—	2	1	no	—
7	#14556525	C₄	1	1	yes	characteristic
8	#14556515	—	2	1	no	—
9	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596833	—	4	1	no	—
12	#11924031	—	2	2	no	—
13	C₂×#10596831	D₄	1	1	yes	characteristic
14	C₄⋊Dic₇₃	—	2	1	no	—
15	C₄⋊Dic₇₃	—	4	1	no	—
16	C₄×Dic₇₃	—	4	1	no	—
17	C₄×Dic₇₃	D₄	1	1	yes	characteristic
18	C₂×Q₈×C₇₃	—	2	1	no	—
19	Q₁₆×C₇₃	—	2	1	no	—
20	Q₁₆×C₇₃	C₈	1	2	yes	complemented
21	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
22	Q₈×C₇₃	—	2	2	no	—
23	Q₈×C₇₃	—	4	1	no	—
24	C₂×C₄×C₇₃	—	4	1	no	—
25	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₇₃	—	4	1	no	—
27	C₂×Dic₇₃	D₈	1	1	yes	characteristic
28	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
29	#10596833	—	8	1	no	—
30	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₇₃	M₁₆	1	1	yes	characteristic
32	#10596831	—	2	1	no	—
33	C₂²×C₇₃	#102	1	1	yes	characteristic
34	C₄×C₇₃	—	4	2	no	—
35	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₇₃	#104	1	1	yes	characteristic
37	Dic₇₃	—	2	1	no	—
38	Dic₇₃	—	8	1	no	—
39	Dic₇₃	SD₃₂	1	1	yes	characteristic
40	Dic₇₃	Q₃₂	1	1	yes	characteristic
41	C₂×C₇₃	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₇₃	#358	1	1	yes	characteristic
43	C₂×C₇₃	#359	1	1	yes	characteristic
44	#1332	—	73	1	no	maximal, Sylow
45	C₇₃	#1332	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₁₆	—	73	1	no	—
47	C₄×C₁₆	—	73	1	no	—
48	#335	—	73	1	no	—
49	C₂×Q₁₆	#64408	1	1	yes	characteristic
50	C₄×Q₈	—	146	1	no	—
51	C₂×C₁₆	—	146	1	no	—
52	#107	—	73	1	no	—
53	C₄⋊C₈	—	146	1	no	—
54	#103	—	146	1	no	—
55	C₄×C₈	—	73	1	no	—
56	C₂×Q₈	—	2	1	no	—
57	Q₁₆	—	2	1	no	—
58	Q₁₆	#10596833	1	2	yes	complemented
59	C₂×C₈	—	292	1	no	—
60	C₂×C₈	—	73	1	no	—
61	C₂×C₈	C₂×#64408	1	1	yes	characteristic
62	C₄⋊C₄	—	292	1	no	—
63	C₄⋊C₄	—	146	1	no	—
64	C₄²	—	292	1	no	—
65	C₄²	—	73	1	no	—
66	C₁₆	—	146	2	no	—
67	Q₈	—	2	2	no	—
68	Q₈	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	292	1	no	—
71	C₂×C₄	—	73	1	no	—
72	C₂×C₄	—	73	1	no	—
73	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
74	C₈	—	584	1	no	—
75	C₈	—	146	1	no	—
76	C₈	C₂×#10596833	1	1	yes	characteristic
77	C₈	#11924037	1	1	yes	characteristic
78	C₂²	#14556653	1	1	yes	characteristic
79	C₄	—	4	2	no	—
80	C₄	—	584	1	no	—
81	C₄	—	73	1	no	—
82	C₄	—	73	1	no	—
83	C₄	—	146	1	no	—
84	C₄	C₂²⋊#10596833	1	1	yes	characteristic
85	C₄	#14556655	1	1	yes	characteristic
86	C₂	D₄⋊#10596833	1	1	yes	characteristic
87	C₂	#17989500	1	1	yes	characteristic
88	C₂	#17989502	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556653
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×Q₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#102
hypercenter	C₂×Q₁₆	#64408
hypocenter	C₇₃	#1332
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
20. Q₁₆×C₇₃	C₈	semidirect
45. C₇₃	#1332	semidirect
58. Q₁₆	#10596833	semidirect