Subgroups — #22624946

Order 9344.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989508	C₂	1	1	yes	maximal, characteristic
2	#17989451	C₂	1	1	yes	maximal, characteristic
3	#17988965	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	—	2	1	no	—
5	C₄⋊#10596833	—	2	1	no	—
6	C₂×Dic₂₉₂	C₄	1	1	yes	characteristic
7	C₂×#11924018	—	2	1	no	—
8	#14556589	—	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	—	4	1	no	—
13	C₂×Dic₁₄₆	—	2	1	no	—
14	Dic₂₉₂	—	4	1	no	—
15	#11924018	—	4	1	no	—
16	#11924018	—	4	1	no	—
17	C₂×#10596831	D₄	1	1	yes	characteristic
18	#11924007	—	4	1	no	—
19	#11924007	—	4	1	no	—
20	C₄×Dic₇₃	D₄	1	1	yes	characteristic
21	C₂×Q₈×C₇₃	—	2	1	no	—
22	Q₁₆×C₇₃	—	4	1	no	—
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	Q₈×C₇₃	—	4	1	no	—
25	Q₈×C₇₃	—	4	1	no	—
26	C₂×C₄×C₇₃	—	4	1	no	—
27	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₇₃	—	4	1	no	—
29	C₂×Dic₇₃	D₈	1	1	yes	characteristic
30	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
31	Dic₁₄₆	—	4	1	no	—
32	Dic₁₄₆	—	4	1	no	—
33	#10596833	—	8	1	no	—
34	C₈×C₇₃	—	2	1	no	—
35	#10596831	D₈	1	1	yes	characteristic
36	#10596831	SD₁₆	1	1	yes	characteristic
37	C₂²×C₇₃	#102	1	1	yes	characteristic
38	C₄×C₇₃	—	8	1	no	—
39	C₄×C₇₃	#100	1	1	yes	characteristic
40	C₄×C₇₃	#102	1	1	yes	characteristic
41	Dic₇₃	—	2	1	no	—
42	Dic₇₃	—	8	1	no	—
43	Dic₇₃	SD₃₂	1	1	yes	characteristic
44	Dic₇₃	Q₃₂	1	1	yes	characteristic
45	C₂×C₇₃	#331	1	1	yes	characteristic
46	C₂×C₇₃	#358	1	1	yes	characteristic
47	C₂×C₇₃	#362	1	1	yes	characteristic
48	#1362	—	73	1	no	maximal, Sylow
49	C₇₃	#1362	1	1	yes	characteristic, complemented, Sylow
50	#494	—	73	1	no	—
51	C₄⋊C₁₆	—	73	1	no	—
52	#335	—	73	1	no	—
53	C₂×Q₁₆	—	73	1	no	—
54	C₂×Q₁₆	—	146	1	no	—
55	C₂×Q₁₆	#64408	1	1	yes	characteristic
56	C₄⋊Q₈	—	146	1	no	—
57	C₂×C₁₆	—	146	1	no	—
58	C₄⋊C₈	—	146	1	no	—
59	C₄×C₈	—	73	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	146	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	292	1	no	—
64	Q₁₆	—	292	1	no	—
65	Q₁₆	—	292	1	no	—
66	C₂×C₈	—	292	1	no	—
67	C₂×C₈	—	73	1	no	—
68	C₂×C₈	C₂×#64408	1	1	yes	characteristic
69	C₄⋊C₄	—	292	1	no	—
70	C₄⋊C₄	—	292	1	no	—
71	C₄²	—	73	1	no	—
72	C₁₆	—	292	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	292	1	no	—
76	Q₈	—	292	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	292	1	no	—
79	C₂×C₄	—	73	1	no	—
80	C₂×C₄	—	73	1	no	—
81	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	584	1	no	—
84	C₈	—	73	1	no	—
85	C₈	—	73	1	no	—
86	C₂²	#14556653	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	584	1	no	—
89	C₄	—	73	1	no	—
90	C₄	—	73	1	no	—
91	C₄	—	146	1	no	—
92	C₄	#14556651	1	1	yes	characteristic
93	C₄	#14556653	1	1	yes	characteristic
94	C₂	#17989445	1	1	yes	characteristic
95	C₂	#17989500	1	1	yes	characteristic
96	C₂	#17989506	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556653
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×Q₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#102
hypercenter	C₂×Q₁₆	#64408
hypocenter	C₇₃	#1362
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×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
49. C₇₃	#1362	semidirect