Subgroups — #17988948

Order 4672.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556590	C₂	1	1	yes	maximal, characteristic, complemented
2	#14556580	C₂	1	1	yes	maximal, characteristic
3	#14556515	C₂	1	1	yes	maximal, characteristic, complemented
4	#14556513	C₂	1	1	yes	maximal, characteristic
5	#14556511	C₂	1	1	yes	maximal, characteristic
6	#14556501	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₄₆	—	2	1	no	—
9	C₂×D₂₉₂	C₂²	1	1	yes	characteristic
10	C₂×#10596831	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
12	#11924007	—	2	1	no	—
13	#11924005	—	2	1	no	—
14	#11924005	—	2	1	no	—
15	C₄×Dic₇₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₇₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×D₇₃	—	2	1	no	—
20	Q₈×C₇₃	—	2	1	no	—
21	Q₈×C₇₃	—	2	1	no	—
22	C₂×C₄×C₇₃	—	2	1	no	—
23	C₂×C₄×C₇₃	—	2	1	no	—
24	C₂×C₄×C₇₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₇₃	—	2	1	no	—
26	C₂×Dic₇₃	D₄	1	1	yes	characteristic
27	C₂×Dic₇₃	D₄	1	1	yes	characteristic
28	D₂₉₂	—	2	1	no	—
29	D₂₉₂	—	2	1	no	—
30	Dic₁₄₆	—	4	2	no	—
31	C₈×C₇₃	—	2	1	no	—
32	#10596831	—	2	1	no	—
33	C₂²×C₇₃	C₂×D₄	1	1	yes	characteristic
34	C₂×D₇₃	—	4	1	no	—
35	C₂×D₇₃	—	4	1	no	—
36	C₂×D₇₃	—	4	1	no	—
37	C₄×C₇₃	—	4	1	no	—
38	C₄×C₇₃	—	4	1	no	—
39	C₄×C₇₃	#41	1	1	yes	characteristic
40	C₄×C₇₃	#41	1	1	yes	characteristic
41	Dic₇₃	—	2	1	no	—
42	Dic₇₃	—	2	1	no	—
43	Dic₇₃	—	4	1	no	—
44	C₂×C₇₃	#124	1	1	yes	characteristic
45	C₂×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
46	C₂×C₇₃	#137	1	1	yes	characteristic
47	D₇₃	—	8	1	no	—
48	C₇₃	#489	1	1	yes	characteristic, complemented, Sylow
49	#489	—	73	1	no	maximal, Sylow
50	C₄⋊Q₈	—	73	1	no	—
51	#124	—	73	1	no	—
52	#103	—	73	1	no	—
53	#103	D₇₃	1	1	yes	characteristic, complemented
54	#102	—	73	1	no	—
55	#102	—	73	1	no	—
56	#97	—	73	1	no	—
57	C₂×Q₈	—	146	1	no	—
58	C₂×Q₈	C₂×D₇₃	1	1	yes	characteristic
59	C₂×D₄	—	73	1	no	—
60	C₂×C₈	—	73	1	no	—
61	C₂×C₈	C₂×D₇₃	1	1	yes	characteristic
62	C₄⋊C₄	—	73	1	no	—
63	C₄⋊C₄	—	146	1	no	—
64	C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
65	C₂²⋊C₄	—	146	1	no	—
66	C₂²⋊C₄	—	146	1	no	—
67	C₄²	—	73	1	no	—
68	C₂³	—	146	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	292	2	no	—
72	D₄	—	146	1	no	—
73	D₄	—	146	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	73	1	no	—
77	C₂×C₄	—	73	1	no	—
78	C₂×C₄	—	146	1	no	—
79	C₂×C₄	C₂²×D₇₃	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	146	1	no	—
82	C₂²	—	292	1	no	—
83	C₂²	—	292	1	no	—
84	C₂²	—	292	1	no	—
85	C₂²	D₄×D₇₃	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	292	1	no	—
89	C₄	—	146	1	no	—
90	C₄	—	146	1	no	—
91	C₄	#11924027	1	1	yes	characteristic
92	C₄	#11924028	1	1	yes	characteristic
93	C₂	—	584	1	no	—
94	C₂	#14556577	1	1	yes	characteristic
95	C₂	#14556618	1	1	yes	characteristic
96	C₂	#14556623	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂³
Frattini	C₂×C₄	C₂²×D₇₃
Fitting	#103×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₄
prime radical	C₂×D₂₉₂	C₂²
hypercenter	#103	D₇₃
hypocenter	C₇₃	#489
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
1. #14556590	C₂	semidirect
3. #14556515	C₂	semidirect
6. #14556501	C₂	semidirect
7. #103×C₇₃	C₂	semidirect
48. C₇₃	#489	semidirect
53. #103	D₇₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14556590	2
#14556580	2
#14556515	2
#14556513	2
#14556511	2
#14556501	2
#103×C₇₃	2
#489	73