Subgroups — #22609528

Order 9344.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988992	C₂	1	1	yes	maximal, characteristic
2	#17988985	C₂	1	2	yes	maximal
3	#17988967	C₂	1	1	yes	maximal, characteristic
4	#17988938	C₂	1	2	yes	maximal
5	C₈²×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₉₂	—	2	2	no	—
7	#14556591	C₂²	1	2	yes	—
8	#14556591	C₂²	1	2	yes	—
9	#14556525	—	2	2	no	—
10	#14556523	—	2	4	no	—
11	#14556516	—	2	4	no	—
12	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₄₆	—	2	2	no	—
16	C₂×Dic₁₄₆	—	2	2	no	—
17	Dic₂₉₂	—	4	4	no	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	—	2	2	no	—
20	C₄⋊Dic₇₃	—	2	2	no	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	C₂×C₈×C₇₃	D₄	1	2	yes	—
23	C₂×C₈×C₇₃	D₄	1	2	yes	—
24	C₂×C₈×C₇₃	D₄	1	2	yes	—
25	C₄²×C₇₃	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₇₃	—	4	2	no	—
30	C₂×Dic₇₃	—	4	2	no	—
31	Dic₁₄₆	—	4	4	no	—
32	Dic₁₄₆	—	4	4	no	—
33	C₈×C₇₃	—	2	2	no	—
34	C₈×C₇₃	SD₁₆	1	4	yes	—
35	C₈×C₇₃	Q₁₆	1	4	yes	complemented
36	C₂²×C₇₃	#127	1	1	yes	characteristic
37	C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
38	C₄×C₇₃	C₂×Q₁₆	1	2	yes	—
39	C₄×C₇₃	#135	1	2	yes	—
40	Dic₇₃	—	8	2	no	—
41	Dic₇₃	—	8	2	no	—
42	C₂×C₇₃	#492	1	1	yes	characteristic
43	C₂×C₇₃	#494	1	1	yes	characteristic
44	C₂×C₇₃	#495	1	1	yes	characteristic
45	#1707	—	73	1	no	maximal, Sylow
46	C₇₃	#1707	1	1	yes	characteristic, complemented, Sylow
47	#500	—	73	1	no	—
48	#498	—	73	2	no	—
49	#494	—	73	1	no	—
50	#487	—	73	2	no	—
51	C₈²	D₇₃	1	1	yes	characteristic
52	C₂×Q₁₆	—	146	2	no	—
53	C₄⋊Q₈	—	73	2	no	—
54	C₄⋊Q₈	—	73	2	no	—
55	#107	—	146	2	no	—
56	#106	—	146	4	no	—
57	#103	—	146	4	no	—
58	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
59	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
60	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
61	C₂×Q₈	—	146	2	no	—
62	C₂×Q₈	—	146	2	no	—
63	Q₁₆	—	292	4	no	—
64	C₂×C₈	D₂₉₂	1	2	yes	—
65	C₂×C₈	D₂₉₂	1	2	yes	—
66	C₂×C₈	D₂₉₂	1	2	yes	—
67	C₄⋊C₄	—	146	2	no	—
68	C₄⋊C₄	—	146	2	no	—
69	C₄⋊C₄	—	146	2	no	—
70	C₄⋊C₄	—	146	2	no	—
71	C₄²	C₂²×D₇₃	1	1	yes	characteristic
72	Q₈	—	292	4	no	—
73	Q₈	—	292	4	no	—
74	C₂×C₄	—	292	2	no	—
75	C₂×C₄	—	292	2	no	—
76	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
77	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
78	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	#11924017	1	4	yes	—
81	C₈	Dic₂₉₂	1	4	yes	complemented
82	C₂²	#14556588	1	1	yes	characteristic
83	C₄	—	584	2	no	—
84	C₄	—	584	2	no	—
85	C₄	C₂×#11924017	1	2	yes	—
86	C₄	C₂×Dic₂₉₂	1	2	yes	—
87	C₄	#14556613	1	2	yes	—
88	C₂	#17988960	1	1	yes	characteristic
89	C₂	#17988967	1	1	yes	characteristic
90	C₂	#17988971	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556588
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	C₈²×C₇₃	C₂
socle	C₂²×C₇₃	#127
hypercenter	C₈²	D₇₃
hypocenter	C₇₃	#1707
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
35. C₈×C₇₃	Q₁₆	semidirect
46. C₇₃	#1707	semidirect
81. C₈	Dic₂₉₂	semidirect