Subgroups — #22626328

Order 9344.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×#64408	C₂	1	2	yes	maximal
2	#17989514	C₂	1	1	yes	maximal, characteristic
3	#17989500	C₂	1	2	yes	maximal
4	#17989474	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
6	Q₈×#64408	—	2	2	no	—
7	#14556664	C₂²	1	1	yes	characteristic
8	#14556660	C₂²	1	2	yes	—
9	#14556654	—	2	2	no	—
10	C₈×#64408	C₂²	1	1	yes	characteristic
11	Q₁₆×D₇₃	C₂²	1	2	yes	—
12	Dic₅₈₄	C₄	1	1	yes	characteristic, complemented
13	#14556537	C₄	1	2	yes	complemented
14	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
15	Q₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
16	#11924036	D₄	1	1	yes	characteristic
17	C₄⋊#64408	—	2	2	no	—
18	C₄⋊#64408	—	4	2	no	—
19	C₄×#64408	—	4	2	no	—
20	C₄×#64408	D₄	1	1	yes	characteristic
21	#11924031	—	2	1	no	—
22	Q₈×D₇₃	—	2	2	no	—
23	Dic₂₉₂	C₂×C₄	1	2	yes	—
24	#11924018	—	2	2	no	—
25	C₈×D₇₃	C₂³	1	1	yes	characteristic
26	#11924003	C₂×C₄	1	1	yes	characteristic
27	Q₁₆×C₇₃	C₂×C₄	1	2	yes	—
28	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×#64408	—	4	2	no	—
30	C₂×#64408	D₈	1	2	yes	—
31	Q₈×C₇₃	—	2	2	no	—
32	C₄×D₇₃	—	4	2	no	—
33	C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
34	Dic₁₄₆	—	2	2	no	—
35	Dic₁₄₆	—	4	2	no	—
36	#10596833	—	2	1	no	—
37	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	#10596831	#41	1	1	yes	characteristic
39	C₂×D₇₃	C₂×D₈	1	1	yes	characteristic
40	#64408	—	2	2	no	—
41	#64408	—	8	2	no	—
42	C₄×C₇₃	—	4	2	no	—
43	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
44	Dic₇₃	—	4	2	no	—
45	Dic₇₃	#135	1	1	yes	characteristic
46	C₂×C₇₃	C₄×D₈	1	1	yes	characteristic
47	D₇₃	#510	1	2	yes	—
48	#2176	—	73	1	no	maximal, Sylow
49	C₇₃	#2176	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₃₂	—	73	1	no	—
51	C₄×Q₁₆	—	73	2	no	—
52	#367	—	73	1	no	—
53	#358	—	73	2	no	—
54	#346	—	73	1	no	—
55	C₂×Q₁₆	—	73	2	no	—
56	C₄×Q₈	—	146	2	no	—
57	Q₃₂	—	73	2	no	—
58	Q₃₂	—	73	1	no	—
59	Q₃₂	#64408	1	1	yes	characteristic, complemented
60	C₂×C₁₆	—	73	1	no	—
61	C₂×C₁₆	—	73	1	no	—
62	#107	—	73	2	no	—
63	#103	—	146	2	no	—
64	C₄×C₈	—	73	1	no	—
65	C₂×Q₈	—	146	2	no	—
66	Q₁₆	—	73	2	no	—
67	Q₁₆	—	146	2	no	—
68	Q₁₆	C₂×#64408	1	2	yes	—
69	C₂×C₈	—	73	1	no	—
70	C₂×C₈	—	73	1	no	—
71	C₄⋊C₄	—	292	2	no	—
72	C₄⋊C₄	—	146	2	no	—
73	C₄²	—	292	2	no	—
74	C₄²	—	73	1	no	—
75	C₁₆	—	73	1	no	—
76	C₁₆	—	146	1	no	—
77	C₁₆	C₂×#64408	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	Q₈	—	292	2	no	—
80	Q₈	—	146	2	no	—
81	C₂×C₄	—	292	2	no	—
82	C₂×C₄	—	292	2	no	—
83	C₂×C₄	—	73	1	no	—
84	C₂×C₄	—	73	2	no	—
85	C₈	—	73	1	no	—
86	C₈	—	146	1	no	—
87	C₈	C₂²×#64408	1	1	yes	characteristic
88	C₂²	—	73	1	no	—
89	C₄	—	4	2	no	—
90	C₄	—	292	2	no	—
91	C₄	—	584	2	no	—
92	C₄	—	73	1	no	—
93	C₄	—	146	2	no	—
94	C₄	D₄×#64408	1	1	yes	characteristic
95	C₂	—	73	2	no	—
96	C₂	D₈×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#64408
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₈	C₂²×#64408
Fitting	Q₃₂×C₇₃	C₄
socle	C₂×C₇₃	C₄×D₈
hypercenter	Q₃₂	#64408
hypocenter	C₇₃	#2176
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
12. Dic₅₈₄	C₄	semidirect
13. #14556537	C₄	semidirect
15. Q₃₂×C₇₃	C₄	semidirect
49. C₇₃	#2176	semidirect
59. Q₃₂	#64408	semidirect