Subgroups — #34032801

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	—	2	1	no	—
22	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₇₃	C₁₆	1	2	yes	complemented
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	D₁₆	1	1	yes	characteristic
30	#10596833	Q₃₂	1	1	yes	characteristic
31	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
32	C₈×C₇₃	M₃₂	1	1	yes	characteristic
33	#10596831	—	2	1	no	—
34	C₂²×C₇₃	#335	1	1	yes	characteristic
35	C₄×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
36	C₄×C₇₃	#364	1	1	yes	characteristic
37	Dic₇₃	—	2	1	no	—
38	Dic₇₃	#366	1	1	yes	characteristic
39	Dic₇₃	#368	1	1	yes	characteristic
40	#7100	—	73	1	no	maximal, Sylow
41	C₂×C₇₃	#1370	1	1	yes	characteristic
42	C₂×C₇₃	#1371	1	1	yes	characteristic
43	C₂×C₇₃	#1373	1	1	yes	characteristic
44	#1370	—	73	2	no	—
45	C₈×C₁₆	—	73	1	no	—
46	C₇₃	#7100	1	1	yes	characteristic, complemented, Sylow
47	C₄⋊C₁₆	—	146	2	no	—
48	C₄×C₁₆	—	73	1	no	—
49	C₄×C₁₆	—	73	1	no	—
50	C₈²	—	73	1	no	—
51	C₂×C₁₆	—	292	2	no	—
52	C₂×C₁₆	—	73	1	no	—
53	C₂×C₁₆	—	146	1	no	—
54	C₂×C₁₆	#10596842	1	1	yes	characteristic
55	C₄×C₈	—	73	1	no	—
56	C₄×C₈	—	73	1	no	—
57	C₄×C₈	—	73	1	no	—
58	C₂×C₈	—	73	1	no	—
59	C₂×C₈	—	73	1	no	—
60	C₂×C₈	—	73	1	no	—
61	C₂×C₈	—	146	1	no	—
62	C₂×C₈	C₂×#10596842	1	1	yes	characteristic
63	C₄²	—	73	1	no	—
64	C₁₆	—	584	2	no	—
65	C₁₆	—	146	2	no	—
66	C₁₆	—	146	1	no	—
67	C₁₆	#11924040	1	2	yes	complemented
68	C₂×C₄	—	73	1	no	—
69	C₂×C₄	—	73	1	no	—
70	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
71	C₈	—	73	1	no	—
72	C₈	—	73	1	no	—
73	C₈	—	146	1	no	—
74	C₈	—	146	2	no	—
75	C₈	—	146	1	no	—
76	C₈	C₂×#11924040	1	1	yes	characteristic
77	C₈	#14556688	1	1	yes	characteristic
78	C₂²	#17989677	1	1	yes	characteristic
79	C₄	—	73	1	no	—
80	C₄	—	73	1	no	—
81	C₄	—	146	1	no	—
82	C₄	C₄⋊#11924040	1	1	yes	characteristic
83	C₄	#17989692	1	1	yes	characteristic
84	C₂	#22626995	1	1	yes	characteristic
85	C₂	#22626997	1	1	yes	characteristic
86	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	#7100
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
23. C₁₆×C₇₃	C₁₆	semidirect
46. C₇₃	#7100	semidirect
67. C₁₆	#11924040	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
#7100	73