Subgroups — #22608099

Order 9344.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988966	C₂	1	1	yes	maximal, characteristic
2	#17988386	C₂	1	1	yes	maximal, characteristic
3	#356×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924018	—	2	1	no	—
5	C₂×#11924018	—	2	1	no	—
6	#14556591	C₄	1	1	yes	characteristic
7	#14556510	—	2	1	no	—
8	C₄×#10596831	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
10	#101×C₇₃	—	2	1	no	—
11	C₂×Dic₁₄₆	—	2	1	no	—
12	#11924018	—	4	2	no	—
13	#11924018	—	4	2	no	—
14	#11924012	—	4	1	no	—
15	C₂×#10596831	—	2	1	no	—
16	C₄⋊Dic₇₃	—	4	1	no	—
17	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
18	C₂×Q₈×C₇₃	D₄	1	1	yes	characteristic
19	M₁₆×C₇₃	—	4	1	no	—
20	C₄⋊C₄×C₇₃	—	4	1	no	—
21	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
22	Q₈×C₇₃	—	4	1	no	—
23	Q₈×C₇₃	—	4	1	no	—
24	C₂×C₄×C₇₃	—	2	1	no	—
25	C₂×C₄×C₇₃	—	2	1	no	—
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₇₃	—	4	1	no	—
29	Dic₁₄₆	—	4	1	no	—
30	Dic₁₄₆	—	4	1	no	—
31	C₈×C₇₃	—	8	1	no	—
32	#10596831	—	2	2	no	—
33	#10596831	—	8	1	no	—
34	C₂²×C₇₃	#99	1	1	yes	characteristic
35	C₄×C₇₃	—	2	2	no	—
36	C₄×C₇₃	—	2	1	no	—
37	C₄×C₇₃	—	4	1	no	—
38	C₄×C₇₃	—	4	1	no	—
39	Dic₇₃	—	8	1	no	—
40	C₂×C₇₃	—	2	1	no	—
41	C₂×C₇₃	#353	1	1	yes	characteristic
42	#1411	—	73	1	no	maximal, Sylow
43	C₇₃	#1411	1	1	yes	characteristic, complemented, Sylow
44	#494	—	73	1	no	—
45	#356	—	73	1	no	—
46	#356	D₇₃	1	1	yes	characteristic
47	C₂×Q₁₆	—	146	1	no	—
48	C₂×Q₁₆	—	146	1	no	—
49	C₄⋊Q₈	—	73	1	no	—
50	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
51	#101	—	2	1	no	—
52	#101	—	146	1	no	—
53	C₄×C₈	—	73	1	no	—
54	C₂×Q₈	—	146	1	no	—
55	C₂×Q₈	D₂₉₂	1	1	yes	characteristic
56	C₂×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
57	Q₁₆	—	292	2	no	—
58	Q₁₆	—	292	2	no	—
59	M₁₆	—	4	1	no	—
60	M₁₆	—	292	1	no	—
61	C₂×C₈	—	146	1	no	—
62	C₄⋊C₄	—	4	1	no	—
63	C₄⋊C₄	—	292	1	no	—
64	C₄²	C₄×D₇₃	1	1	yes	characteristic
65	Q₈	—	4	1	no	—
66	Q₈	—	4	1	no	—
67	Q₈	—	292	1	no	—
68	Q₈	—	292	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	292	1	no	—
73	C₂×C₄	#11924005	1	1	yes	characteristic
74	C₈	—	8	1	no	—
75	C₈	—	584	1	no	—
76	C₈	—	146	2	no	—
77	C₂²	#14556505	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	1	no	—
80	C₄	—	4	1	no	—
81	C₄	—	4	1	no	—
82	C₄	—	584	1	no	—
83	C₂	—	2	1	no	—
84	C₂	#17988379	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17988379
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₇₃
Fitting	#356×C₇₃	C₂
socle	C₂×C₇₃	#353
hypercenter	#356	D₇₃
hypocenter	C₇₃	#1411
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
43. C₇₃	#1411	semidirect