Subgroups — #22607909

Order 9344.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic
2	C₄×#11924003	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₁₄₆	C₄	1	1	yes	characteristic
5	C₂×#11924003	—	2	1	no	—
6	C₄⋊#10596831	C₄	1	1	yes	characteristic
7	#14556520	—	2	1	no	—
8	C₈×Dic₇₃	—	2	1	no	—
9	C₂×C₁₆×C₇₃	—	2	1	no	—
10	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₄₆	C₈	1	1	yes	characteristic
12	C₂×#10596831	—	2	1	no	—
13	C₄⋊Dic₇₃	C₈	1	1	yes	characteristic
14	#11924007	—	2	1	no	—
15	C₄×Dic₇₃	—	2	1	no	—
16	#11924003	—	2	2	no	—
17	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
19	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₇₃	—	4	1	no	—
21	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
24	C₂×Dic₇₃	—	2	1	no	—
25	C₂×Dic₇₃	—	2	1	no	—
26	Dic₁₄₆	—	2	1	no	—
27	Dic₁₄₆	C₁₆	1	2	yes	complemented
28	C₈×C₇₃	—	2	1	no	—
29	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₇₃	Q₁₆	1	1	yes	characteristic
31	#10596831	—	4	1	no	—
32	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₇₃	—	2	1	no	—
34	C₄×C₇₃	#103	1	1	yes	characteristic
35	C₄×C₇₃	#104	1	1	yes	characteristic
36	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₇₃	M₃₂	1	1	yes	characteristic
38	Dic₇₃	—	2	2	no	—
39	Dic₇₃	—	4	1	no	—
40	C₂×C₇₃	Q₈⋊C₈	1	1	yes	characteristic
41	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
42	C₂×C₇₃	#350	1	1	yes	characteristic
43	Q₈⋊C₁₆	—	73	1	no	maximal, Sylow
44	C₇₃	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
45	C₈×Q₈	—	73	1	no	—
46	C₄⋊C₁₆	D₇₃	1	1	yes	characteristic
47	C₄×C₁₆	—	73	1	no	—
48	C₄×Q₈	—	73	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	146	1	no	—
51	C₄⋊C₈	—	73	1	no	—
52	C₄⋊C₈	—	146	1	no	—
53	C₄×C₈	—	146	1	no	—
54	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
55	C₂×Q₈	—	73	1	no	—
56	C₂×C₈	—	146	1	no	—
57	C₂×C₈	D₂₉₂	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
59	C₄⋊C₄	—	73	1	no	—
60	C₄⋊C₄	—	146	1	no	—
61	C₄²	—	146	1	no	—
62	C₄²	C₄×D₇₃	1	1	yes	characteristic
63	C₁₆	—	4	1	no	—
64	C₁₆	—	146	2	no	—
65	Q₈	—	73	2	no	—
66	Q₈	—	146	1	no	—
67	C₂×C₄	—	146	1	no	—
68	C₂×C₄	—	146	1	no	—
69	C₂×C₄	#11924005	1	1	yes	characteristic
70	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
71	C₂×C₄	#11924011	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	292	1	no	—
74	C₈	#11924016	1	1	yes	characteristic
75	C₈	#11924018	1	1	yes	characteristic
76	C₂²	#14556503	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	292	1	no	—
79	C₄	—	146	2	no	—
80	C₄	#14556514	1	1	yes	characteristic
81	C₄	#14556517	1	1	yes	characteristic
82	C₄	C₁₆×D₇₃	1	1	yes	characteristic
83	C₄	#14556530	1	1	yes	characteristic
84	C₂	#17988317	1	1	yes	characteristic
85	C₂	#17988366	1	1	yes	characteristic
86	C₂	#17988372	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₇₃
commutator	C₄×C₇₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₇₃
Fitting	C₄⋊C₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	C₄⋊C₁₆	D₇₃
hypocenter	C₇₃	Q₈⋊C₁₆
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
27. Dic₁₄₆	C₁₆	semidirect
44. C₇₃	Q₈⋊C₁₆	semidirect