Subgroups — #22626982

Order 9344.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989692	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×#10596842	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989631	C₂	1	1	yes	maximal, characteristic
4	#14556688	—	2	1	no	—
5	C₄×#10596842	—	2	1	no	—
6	#14556679	—	2	1	no	—
7	#14556662	C₄	1	1	yes	characteristic
8	#14556656	—	2	1	no	—
9	C₈×#64408	C₂²	1	1	yes	characteristic
10	#14556614	C₄	1	1	yes	characteristic
11	C₂×#10596842	—	2	2	no	—
12	#11924040	—	4	1	no	—
13	#11924038	—	2	1	no	—
14	#11924038	—	4	1	no	—
15	#11924036	—	4	1	no	—
16	#11924036	D₄	1	1	yes	characteristic
17	C₄×#64408	D₄	1	1	yes	characteristic
18	#11924029	—	2	1	no	—
19	#11924015	—	2	1	no	—
20	D₅₈₄	C₈	1	1	yes	characteristic, complemented
21	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
22	Q₁₆×C₇₃	C₈	1	1	yes	characteristic, complemented
23	C₂×#64408	—	2	1	no	—
24	#10596842	—	2	4	no	—
25	Q₈×C₇₃	—	2	1	no	—
26	D₂₉₂	—	2	1	no	—
27	D₂₉₂	—	4	1	no	—
28	C₄×D₇₃	—	4	1	no	—
29	C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	#10596833	—	4	1	no	—
31	#10596833	D₈	1	1	yes	characteristic
32	#10596833	SD₁₆	1	1	yes	characteristic
33	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
34	#10596831	M₁₆	1	1	yes	characteristic
35	C₂×D₇₃	—	4	1	no	—
36	C₂×D₇₃	#104	1	1	yes	characteristic
37	#64408	—	2	2	no	—
38	C₄×C₇₃	—	4	1	no	—
39	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
40	Dic₇₃	#102	1	1	yes	characteristic
41	C₂×C₇₃	D₄⋊C₈	1	1	yes	characteristic
42	D₇₃	—	2	1	no	—
43	D₇₃	—	8	1	no	—
44	#1335	—	73	1	no	maximal, Sylow
45	C₇₃	#1335	1	1	yes	characteristic, complemented, Sylow
46	#443	—	73	1	no	—
47	#364	—	73	1	no	—
48	C₈²	—	73	1	no	—
49	#135	—	73	1	no	—
50	#131	—	146	1	no	—
51	M₃₂	—	146	1	no	—
52	#108	—	73	1	no	—
53	#104	—	146	1	no	—
54	C₄×C₈	—	73	1	no	—
55	C₄×C₈	—	146	1	no	—
56	#41	—	146	1	no	—
57	Q₁₆	#10596842	1	1	yes	characteristic, complemented
58	SD₁₆	—	146	1	no	—
59	D₈	—	73	1	no	—
60	M₁₆	—	292	1	no	—
61	M₁₆	—	146	1	no	—
62	C₂×C₈	—	292	1	no	—
63	C₂×C₈	—	73	1	no	—
64	C₂×C₈	—	73	1	no	—
65	C₂×C₈	—	146	2	no	—
66	C₄²	—	73	1	no	—
67	C₁₆	—	292	1	no	—
68	Q₈	—	2	1	no	—
69	D₄	—	292	1	no	—
70	D₄	—	146	1	no	—
71	C₂×C₄	—	292	1	no	—
72	C₂×C₄	—	73	1	no	—
73	C₂×C₄	—	146	1	no	—
74	C₈	—	292	1	no	—
75	C₈	—	73	1	no	—
76	C₈	—	73	1	no	—
77	C₈	—	73	1	no	—
78	C₈	—	146	4	no	—
79	C₈	C₂×#10596842	1	1	yes	characteristic
80	C₂²	—	292	1	no	—
81	C₂²	—	73	1	no	—
82	C₄	—	4	1	no	—
83	C₄	—	73	1	no	—
84	C₄	—	146	2	no	—
85	C₄	C₂²⋊#10596842	1	1	yes	characteristic
86	C₂	—	584	1	no	—
87	C₂	—	146	1	no	—
88	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	#1335
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
1. #17989692	C₂	semidirect
2. C₈×#10596842	C₂	semidirect
20. D₅₈₄	C₈	semidirect
22. Q₁₆×C₇₃	C₈	semidirect
45. C₇₃	#1335	semidirect
57. Q₁₆	#10596842	semidirect