Subgroups — #34032804

Order 18688.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626995	C₂	1	2	yes	maximal
2	C₁₆×#10596833	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11924040	—	2	2	no	—
4	#17989473	C₄	1	1	yes	characteristic
5	C₈×#10596833	C₂²	1	1	yes	characteristic
6	C₁₆×Dic₇₃	C₄	1	1	yes	characteristic
7	C₂×#11924040	—	4	2	no	—
8	C₂×#11924031	—	2	1	no	—
9	C₄×#10596833	D₄	1	1	yes	characteristic
10	C₄×#10596833	Q₈	1	1	yes	characteristic
11	C₂×#11924003	C₈	1	1	yes	characteristic
12	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₇₃	C₈	1	1	yes	characteristic
14	#11924040	—	8	2	no	—
15	C₂×#10596833	—	2	1	no	—
16	C₂×#10596833	D₈	1	1	yes	characteristic
17	C₂×#10596833	Q₁₆	1	1	yes	characteristic
18	#11924031	—	2	2	no	—
19	C₂×#10596831	M₁₆	1	1	yes	characteristic
20	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
21	#11924003	C₁₆	1	2	yes	complemented
22	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₇₃	—	2	1	no	—
24	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
25	C₂×Dic₇₃	#107	1	1	yes	characteristic
26	C₂×Dic₇₃	#108	1	1	yes	characteristic
27	#10596833	—	2	2	no	—
28	#10596833	—	2	1	no	—
29	#10596833	SD₃₂	1	2	yes	—
30	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₇₃	M₃₂	1	1	yes	characteristic
32	#10596831	—	2	1	no	—
33	C₂²×C₇₃	#335	1	1	yes	characteristic
34	C₄×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
35	C₄×C₇₃	#364	1	1	yes	characteristic
36	Dic₇₃	—	2	1	no	—
37	Dic₇₃	#367	1	1	yes	characteristic
38	Dic₇₃	#368	1	1	yes	characteristic
39	#7101	—	73	1	no	maximal, Sylow
40	C₂×C₇₃	#1370	1	1	yes	characteristic
41	C₂×C₇₃	#1372	1	1	yes	characteristic
42	C₂×C₇₃	#1373	1	1	yes	characteristic
43	#1370	—	73	2	no	—
44	C₈×C₁₆	—	73	1	no	—
45	C₇₃	#7101	1	1	yes	characteristic, complemented, Sylow
46	C₄⋊C₁₆	—	146	2	no	—
47	C₄×C₁₆	—	73	1	no	—
48	C₄×C₁₆	—	73	1	no	—
49	C₈²	—	73	1	no	—
50	C₂×C₁₆	—	292	2	no	—
51	C₂×C₁₆	—	73	1	no	—
52	C₂×C₁₆	—	146	1	no	—
53	C₂×C₁₆	#10596842	1	1	yes	characteristic
54	C₄×C₈	—	73	1	no	—
55	C₄×C₈	—	73	1	no	—
56	C₄×C₈	—	73	1	no	—
57	C₂×C₈	—	73	1	no	—
58	C₂×C₈	—	73	1	no	—
59	C₂×C₈	—	73	1	no	—
60	C₂×C₈	—	146	1	no	—
61	C₂×C₈	C₂×#10596842	1	1	yes	characteristic
62	C₄²	—	73	1	no	—
63	C₁₆	—	2	1	no	—
64	C₁₆	—	584	2	no	—
65	C₁₆	—	73	2	no	—
66	C₁₆	—	146	2	no	—
67	C₂×C₄	—	73	1	no	—
68	C₂×C₄	—	73	1	no	—
69	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
70	C₈	—	73	2	no	—
71	C₈	—	146	1	no	—
72	C₈	—	146	2	no	—
73	C₈	—	146	1	no	—
74	C₈	#14556686	1	1	yes	characteristic
75	C₈	#14556687	1	1	yes	characteristic
76	C₂²	#17989677	1	1	yes	characteristic
77	C₄	—	73	1	no	—
78	C₄	—	73	1	no	—
79	C₄	—	146	1	no	—
80	C₄	#17989690	1	1	yes	characteristic
81	C₄	#17989691	1	1	yes	characteristic
82	C₂	#22626996	1	1	yes	characteristic
83	C₂	#22626998	1	1	yes	characteristic
84	C₂	#22626999	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17989677
commutator	C₈×C₇₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#10596842
Fitting	C₂×C₁₆×C₇₃	C₈
socle, prime radical	C₂²×C₇₃	#335
cosocle	C₈×#10596833	C₂²
hypercenter	C₂×C₁₆	#10596842
hypocenter	C₇₃	#7101
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
21. #11924003	C₁₆	semidirect
45. C₇₃	#7101	semidirect

Maximal subgroups

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

subgroup	index
#22626995	2
C₁₆×#10596833	2
#7101	73