Subgroups — #33999981

Order 18688.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624844	C₂	1	2	yes	maximal
2	#22607847	C₂	1	1	yes	maximal, characteristic
3	C₄×#11924031	C₄	1	4	yes	—
4	C₄×#11924003	C₄	1	1	yes	characteristic
5	C₈×#10596831	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₇₃	C₄	1	1	yes	characteristic
7	C₂×#11924031	—	2	4	no	—
8	C₂×#11924003	C₈	1	2	yes	—
9	C₄×#10596831	C₂×C₄	1	2	yes	—
10	C₂×C₁₆×C₇₃	C₈	1	2	yes	—
11	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
12	#11924031	—	4	4	no	—
13	C₂×#10596831	M₁₆	1	4	yes	—
14	#11924003	—	2	2	no	—
15	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
16	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₇₃	C₄²	1	1	yes	characteristic
18	C₁₆×C₇₃	C₁₆	1	4	yes	complemented
19	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
20	C₂×C₄×C₇₃	#97	1	2	yes	—
21	C₈×C₇₃	C₂×C₁₆	1	2	yes	—
22	C₈×C₇₃	M₃₂	1	2	yes	—
23	#10596831	—	2	4	no	—
24	C₂²×C₇₃	#322	1	1	yes	characteristic
25	C₄×C₇₃	C₄×C₁₆	1	1	yes	characteristic
26	C₄×C₇₃	#346	1	1	yes	characteristic
27	C₄×C₇₃	#347	1	4	yes	—
28	#7053	—	73	1	no	maximal, Sylow
29	C₂×C₇₃	#1312	1	1	yes	characteristic
30	C₂×C₇₃	#1313	1	2	yes	—
31	#1312	—	73	2	no	—
32	#1311	—	73	1	no	—
33	C₇₃	#7053	1	1	yes	characteristic, complemented, Sylow
34	C₄×C₁₆	—	73	4	no	—
35	C₄×C₁₆	—	73	1	no	—
36	C₄×C₁₆	#64408	1	1	yes	characteristic
37	C₈²	—	73	1	no	—
38	C₂×C₁₆	—	73	2	no	—
39	C₂×C₁₆	—	146	4	no	—
40	C₂×C₁₆	#10596833	1	2	yes	—
41	C₄×C₈	—	73	2	no	—
42	C₄×C₈	C₂×#64408	1	1	yes	characteristic
43	C₂×C₈	—	73	4	no	—
44	C₂×C₈	C₂×#10596833	1	1	yes	characteristic
45	C₂×C₈	#11924036	1	1	yes	characteristic
46	C₄²	C₄×#64408	1	1	yes	characteristic
47	C₁₆	—	292	4	no	—
48	C₁₆	—	146	2	no	—
49	C₁₆	#11924031	1	4	yes	complemented
50	C₂×C₄	C₄×#10596833	1	1	yes	characteristic
51	C₂×C₄	#14556645	1	2	yes	—
52	C₈	—	146	4	no	—
53	C₈	C₂×#11924031	1	2	yes	—
54	C₈	#14556666	1	2	yes	—
55	C₂²	#17989428	1	1	yes	characteristic
56	C₄	C₄×#11924031	1	1	yes	characteristic
57	C₄	#17989476	1	1	yes	characteristic
58	C₄	#17989478	1	4	yes	—
59	C₂	#22624844	1	1	yes	characteristic
60	C₂	#22624848	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×#64408
commutator	C₄×C₇₃	C₄×C₁₆
Frattini	C₄×C₈	C₂×#64408
Fitting	C₄×C₁₆×C₇₃	C₄
socle, prime radical	C₂²×C₇₃	#322
cosocle	C₈×#10596831	C₂²
hypercenter	C₄×C₁₆	#64408
hypocenter	C₇₃	#7053
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
18. C₁₆×C₇₃	C₁₆	semidirect
33. C₇₃	#7053	semidirect
49. C₁₆	#11924031	semidirect

Maximal subgroups

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

subgroup	index
#22624844	2
#22607847	2
#7053	73