Subgroups — #22626978

Order 9344.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64408⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#17989677	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×#64408	C₂	1	1	yes	maximal, characteristic
4	#14556686	—	2	1	no	—
5	C₄⋊#10596842	—	2	1	no	—
6	Q₈×#64408	—	2	1	no	—
7	#14556660	C₄	1	1	yes	characteristic
8	#14556654	—	2	1	no	—
9	C₈×#64408	C₂²	1	1	yes	characteristic
10	Q₁₆×D₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596842	—	4	1	no	—
12	#11924040	—	2	2	no	—
13	#11924036	D₄	1	1	yes	characteristic
14	C₄⋊#64408	—	2	1	no	—
15	C₄⋊#64408	—	4	1	no	—
16	C₄×#64408	—	4	1	no	—
17	C₄×#64408	D₄	1	1	yes	characteristic
18	Q₈×D₇₃	—	2	1	no	—
19	Dic₂₉₂	C₈	1	1	yes	characteristic, complemented
20	#11924018	—	2	1	no	—
21	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
22	Q₁₆×C₇₃	C₈	1	1	yes	characteristic, complemented
23	C₂×#64408	—	4	1	no	—
24	C₂×#64408	D₈	1	1	yes	characteristic
25	C₂×#64408	SD₁₆	1	1	yes	characteristic
26	#10596842	—	8	1	no	—
27	Q₈×C₇₃	—	2	1	no	—
28	C₄×D₇₃	—	4	1	no	—
29	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	Dic₁₄₆	—	2	1	no	—
31	Dic₁₄₆	—	4	1	no	—
32	#10596833	—	2	1	no	—
33	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
34	#10596831	M₁₆	1	1	yes	characteristic
35	C₂×D₇₃	#102	1	1	yes	characteristic
36	#64408	—	2	1	no	—
37	#64408	—	8	1	no	—
38	#64408	SD₃₂	1	1	yes	characteristic
39	#64408	Q₃₂	1	1	yes	characteristic
40	C₄×C₇₃	—	4	1	no	—
41	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
42	Dic₇₃	—	4	1	no	—
43	Dic₇₃	#104	1	1	yes	characteristic
44	C₂×C₇₃	D₄⋊C₈	1	1	yes	characteristic
45	D₇₃	#358	1	1	yes	characteristic
46	D₇₃	#359	1	1	yes	characteristic
47	#1332	—	73	1	no	maximal, Sylow
48	C₇₃	#1332	1	1	yes	characteristic, complemented, Sylow
49	C₄×Q₁₆	—	73	1	no	—
50	C₄×C₁₆	—	73	1	no	—
51	#335	—	73	1	no	—
52	C₂×Q₁₆	—	73	1	no	—
53	C₄×Q₈	—	146	1	no	—
54	C₂×C₁₆	—	146	1	no	—
55	#107	—	73	1	no	—
56	C₄⋊C₈	—	146	1	no	—
57	#103	—	146	1	no	—
58	C₄×C₈	—	73	1	no	—
59	C₂×Q₈	—	146	1	no	—
60	Q₁₆	—	73	1	no	—
61	Q₁₆	—	146	1	no	—
62	Q₁₆	#10596842	1	1	yes	characteristic, complemented
63	C₂×C₈	—	292	1	no	—
64	C₂×C₈	—	73	1	no	—
65	C₂×C₈	—	73	1	no	—
66	C₄⋊C₄	—	292	1	no	—
67	C₄⋊C₄	—	146	1	no	—
68	C₄²	—	292	1	no	—
69	C₄²	—	73	1	no	—
70	C₁₆	—	146	2	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	292	1	no	—
73	Q₈	—	146	1	no	—
74	C₂×C₄	—	292	1	no	—
75	C₂×C₄	—	292	1	no	—
76	C₂×C₄	—	73	1	no	—
77	C₂×C₄	—	73	1	no	—
78	C₂×C₄	—	73	1	no	—
79	C₈	—	584	1	no	—
80	C₈	—	73	1	no	—
81	C₈	—	146	1	no	—
82	C₈	C₂×#10596842	1	1	yes	characteristic
83	C₂²	—	73	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	292	1	no	—
86	C₄	—	584	1	no	—
87	C₄	—	73	1	no	—
88	C₄	—	73	1	no	—
89	C₄	—	73	1	no	—
90	C₄	—	146	1	no	—
91	C₄	C₂²⋊#10596842	1	1	yes	characteristic
92	C₂	—	73	1	no	—
93	C₂	—	73	1	no	—
94	C₂	D₄⋊#10596842	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄⋊#10596842
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₈	C₂×#10596842
Fitting	Q₁₆×C₇₃	C₈
socle	C₂×C₇₃	D₄⋊C₈
hypercenter	Q₁₆	#10596842
hypocenter	C₇₃	#1332
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₂₉₂	C₈	semidirect
22. Q₁₆×C₇₃	C₈	semidirect
48. C₇₃	#1332	semidirect
62. Q₁₆	#10596842	semidirect