Subgroups — #22611839

Order 9344.

126 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	#17988405	C₂	1	2	yes	maximal
4	#17988362	C₂	1	2	yes	maximal
5	C₄×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₄×Dic₁₄₆	C₄	1	1	yes	characteristic
7	C₂×#11924003	C₂²	1	2	yes	—
8	C₄⋊#10596831	C₄	1	1	yes	characteristic
9	#14556520	C₄	1	2	yes	—
10	C₈×Dic₇₃	C₂²	1	2	yes	—
11	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₄₆	C₈	1	1	yes	characteristic
15	C₂×#10596831	C₂×C₄	1	2	yes	—
16	C₄⋊Dic₇₃	C₈	1	1	yes	characteristic
17	#11924007	C₈	1	2	yes	—
18	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
19	#11924003	—	2	2	no	—
20	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
22	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₇₃	—	2	1	no	—
24	C₁₆×C₇₃	Q₈	1	2	yes	complemented
25	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
29	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
30	Dic₁₄₆	—	2	2	no	—
31	C₈×C₇₃	—	2	1	no	—
32	C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
33	C₈×C₇₃	#41	1	1	yes	characteristic
34	#10596831	—	2	2	no	—
35	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
36	C₄×C₇₃	—	2	1	no	—
37	C₄×C₇₃	M₃₂	1	2	yes	—
38	C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
39	C₄×C₇₃	#131	1	1	yes	characteristic
40	Dic₇₃	—	2	2	no	—
41	Dic₇₃	—	2	2	no	—
42	C₂×C₇₃	C₈×Q₈	1	1	yes	characteristic
43	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
44	C₂×C₇₃	#504	1	1	yes	characteristic
45	#2183	—	73	1	no	maximal, Sylow
46	C₇₃	#2183	1	1	yes	characteristic, complemented, Sylow
47	C₈×Q₈	—	73	1	no	—
48	C₄⋊C₁₆	—	73	2	no	—
49	C₄⋊C₁₆	—	73	1	no	—
50	#346	—	73	2	no	—
51	C₄×C₁₆	D₇₃	1	1	yes	characteristic
52	C₄×Q₈	—	73	1	no	—
53	C₂×C₁₆	—	73	2	no	—
54	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
55	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
56	C₄⋊C₈	—	73	2	no	—
57	C₄⋊C₈	—	73	1	no	—
58	C₄×C₈	—	73	2	no	—
59	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
60	C₂×Q₈	—	73	1	no	—
61	C₂×C₈	—	73	2	no	—
62	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
63	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
64	C₄⋊C₄	—	73	2	no	—
65	C₄⋊C₄	—	73	1	no	—
66	C₄²	—	73	2	no	—
67	C₄²	C₄×D₇₃	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	146	2	no	—
70	C₁₆	Dic₁₄₆	1	2	yes	complemented
71	Q₈	—	146	2	no	—
72	C₂×C₄	—	73	2	no	—
73	C₂×C₄	—	73	2	no	—
74	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
75	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
76	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	146	2	no	—
79	C₈	C₂×Dic₁₄₆	1	1	yes	characteristic
80	C₈	#11924028	1	1	yes	characteristic
81	C₂²	C₂×C₈×D₇₃	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	146	2	no	—
84	C₄	—	146	2	no	—
85	C₄	#14556530	1	2	yes	—
86	C₄	C₄×Dic₁₄₆	1	1	yes	characteristic
87	C₄	#14556597	1	1	yes	characteristic
88	C₂	C₈×Dic₁₄₆	1	1	yes	characteristic
89	C₂	C₂×#14556530	1	1	yes	characteristic
90	C₂	#17989003	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₃
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	C₄×C₁₆×C₇₃	C₂
hypercenter	C₄×C₁₆	D₇₃
hypocenter	C₇₃	#2183
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
24. C₁₆×C₇₃	Q₈	semidirect
46. C₇₃	#2183	semidirect
70. C₁₆	Dic₁₄₆	semidirect