Subgroups — #22624949

Order 9344.

86 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	#17988991	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	—	2	1	no	—
5	C₄⋊#10596833	—	2	1	no	—
6	#14556590	—	2	1	no	—
7	#14556525	C₄	1	1	yes	characteristic
8	#14556524	—	2	1	no	—
9	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
10	#107×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#10596833	—	4	1	no	—
12	#11924031	—	4	1	no	—
13	C₂×Dic₁₄₆	—	4	1	no	—
14	C₂×#10596831	D₄	1	1	yes	characteristic
15	C₄⋊Dic₇₃	—	2	1	no	—
16	#11924007	—	4	1	no	—
17	C₄×Dic₇₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄⋊C₄×C₇₃	—	2	1	no	—
20	C₂×C₄×C₇₃	—	4	1	no	—
21	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×Dic₇₃	—	4	1	no	—
23	C₂×Dic₇₃	D₈	1	1	yes	characteristic
24	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
25	Dic₁₄₆	—	8	1	no	—
26	Dic₁₄₆	—	8	1	no	—
27	#10596833	—	8	1	no	—
28	C₈×C₇₃	—	2	1	no	—
29	#10596831	SD₁₆	1	1	yes	characteristic
30	#10596831	Q₁₆	1	1	yes	characteristic
31	C₂²×C₇₃	#102	1	1	yes	characteristic
32	C₄×C₇₃	—	8	1	no	—
33	C₄×C₇₃	#101	1	1	yes	characteristic
34	C₄×C₇₃	#103	1	1	yes	characteristic
35	Dic₇₃	—	2	1	no	—
36	Dic₇₃	—	8	1	no	—
37	Dic₇₃	D₁₆	1	1	yes	characteristic
38	Dic₇₃	SD₃₂	1	1	yes	characteristic
39	C₂×C₇₃	#332	1	1	yes	characteristic
40	C₂×C₇₃	#357	1	1	yes	characteristic
41	C₂×C₇₃	#362	1	1	yes	characteristic
42	#1364	—	73	1	no	maximal, Sylow
43	C₇₃	#1364	1	1	yes	characteristic, complemented, Sylow
44	#500	—	73	1	no	—
45	C₄⋊C₁₆	—	73	1	no	—
46	#335	—	73	1	no	—
47	C₄⋊Q₈	—	146	1	no	—
48	C₂×C₁₆	—	146	1	no	—
49	#107	—	73	1	no	—
50	#107	—	146	1	no	—
51	#107	#64408	1	1	yes	characteristic
52	C₄⋊C₈	—	146	1	no	—
53	C₄×C₈	—	73	1	no	—
54	C₂×Q₈	—	292	1	no	—
55	C₂×C₈	—	292	1	no	—
56	C₂×C₈	—	73	1	no	—
57	C₂×C₈	C₂×#64408	1	1	yes	characteristic
58	C₄⋊C₄	—	2	1	no	—
59	C₄⋊C₄	—	292	1	no	—
60	C₄⋊C₄	—	146	1	no	—
61	C₄²	—	73	1	no	—
62	C₁₆	—	292	1	no	—
63	Q₈	—	584	1	no	—
64	Q₈	—	584	1	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	292	1	no	—
67	C₂×C₄	—	73	1	no	—
68	C₂×C₄	—	73	1	no	—
69	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	584	1	no	—
72	C₈	—	73	1	no	—
73	C₈	—	73	1	no	—
74	C₂²	#14556653	1	1	yes	characteristic
75	C₄	—	8	1	no	—
76	C₄	—	584	1	no	—
77	C₄	—	73	1	no	—
78	C₄	—	73	1	no	—
79	C₄	—	146	1	no	—
80	C₄	#14556652	1	1	yes	characteristic
81	C₄	#14556654	1	1	yes	characteristic
82	C₂	#17989446	1	1	yes	characteristic
83	C₂	#17989499	1	1	yes	characteristic
84	C₂	#17989506	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556653
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₂×C₈	C₂×#64408
Fitting	#107×C₇₃	C₄
socle	C₂²×C₇₃	#102
hypercenter	#107	#64408
hypocenter	C₇₃	#1364
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
43. C₇₃	#1364	semidirect