Subgroups — #34032754

Order 18688.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626948	C₂	1	1	yes	maximal, characteristic
2	#22626948	C₂	1	1	yes	maximal, characteristic
3	#22624842	C₂	1	1	yes	maximal, characteristic
4	C₄×#11924040	C₄	1	2	yes	—
5	C₄×#11924040	C₄	1	2	yes	—
6	#17989473	C₄	1	1	yes	characteristic
7	C₈×#10596833	C₂²	1	1	yes	characteristic
8	C₁₆×Dic₇₃	C₄	1	1	yes	characteristic
9	C₂×#11924040	—	2	2	no	—
10	C₂×#11924040	—	2	2	no	—
11	C₂×#11924031	C₈	1	2	yes	—
12	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
13	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
14	C₂×#11924003	C₈	1	1	yes	characteristic
15	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆×C₇₃	C₈	1	1	yes	characteristic
17	#11924040	—	4	2	no	—
18	#11924040	—	4	2	no	—
19	C₂×#10596833	M₁₆	1	2	yes	—
20	C₂×#10596833	M₁₆	1	2	yes	—
21	#11924031	C₁₆	1	4	yes	complemented
22	C₂×#10596831	C₂×C₈	1	1	yes	characteristic
23	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
24	#11924003	—	2	1	no	—
25	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
26	C₁₆×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
28	C₂×Dic₇₃	#97	1	1	yes	characteristic
29	C₂×Dic₇₃	#97	1	1	yes	characteristic
30	#10596833	—	2	2	no	—
31	#10596833	—	2	2	no	—
32	C₈×C₇₃	M₃₂	1	1	yes	characteristic
33	C₈×C₇₃	M₃₂	1	1	yes	characteristic
34	#10596831	C₂×C₁₆	1	2	yes	—
35	C₂²×C₇₃	#322	1	1	yes	characteristic
36	C₄×C₇₃	C₄×C₁₆	1	1	yes	characteristic
37	C₄×C₇₃	#346	1	1	yes	characteristic
38	Dic₇₃	#347	1	2	yes	—
39	Dic₇₃	#347	1	2	yes	—
40	#7053	—	73	1	no	maximal, Sylow
41	C₂×C₇₃	#1312	1	1	yes	characteristic
42	C₂×C₇₃	#1313	1	1	yes	characteristic
43	C₂×C₇₃	#1313	1	1	yes	characteristic
44	#1312	—	73	1	no	—
45	#1312	—	73	1	no	—
46	#1311	—	73	1	no	—
47	C₇₃	#7053	1	1	yes	characteristic, complemented, Sylow
48	C₄×C₁₆	—	73	1	no	—
49	C₄×C₁₆	—	73	1	no	—
50	C₄×C₁₆	—	73	2	no	—
51	C₄×C₁₆	—	73	2	no	—
52	C₈²	—	73	1	no	—
53	C₂×C₁₆	—	73	2	no	—
54	C₂×C₁₆	—	73	1	no	—
55	C₂×C₁₆	—	146	2	no	—
56	C₂×C₁₆	—	146	2	no	—
57	C₂×C₁₆	#10596842	1	1	yes	characteristic
58	C₄×C₈	—	73	1	no	—
59	C₄×C₈	—	73	1	no	—
60	C₄×C₈	—	73	1	no	—
61	C₂×C₈	—	73	1	no	—
62	C₂×C₈	—	73	2	no	—
63	C₂×C₈	—	73	2	no	—
64	C₂×C₈	C₂×#10596842	1	1	yes	characteristic
65	C₄²	—	73	1	no	—
66	C₁₆	—	2	1	no	—
67	C₁₆	—	292	2	no	—
68	C₁₆	—	292	2	no	—
69	C₁₆	—	73	4	no	—
70	C₁₆	—	146	1	no	—
71	C₂×C₄	—	73	1	no	—
72	C₂×C₄	—	73	1	no	—
73	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
74	C₈	—	73	2	no	—
75	C₈	—	146	2	no	—
76	C₈	—	146	2	no	—
77	C₈	#14556687	1	1	yes	characteristic
78	C₈	#14556688	1	1	yes	characteristic
79	C₂²	#17989671	1	1	yes	characteristic
80	C₄	—	73	2	no	—
81	C₄	—	73	2	no	—
82	C₄	#64408⋊C₁₆	1	1	yes	characteristic
83	C₄	#17989681	1	1	yes	characteristic
84	C₂	#22626949	1	1	yes	characteristic
85	C₂	#22626950	1	1	yes	characteristic
86	C₂	#22626951	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#10596842
commutator	C₄×C₇₃	C₄×C₁₆
Frattini	C₂×C₈	C₂×#10596842
Fitting	C₂×C₁₆×C₇₃	C₈
socle, prime radical	C₂²×C₇₃	#322
cosocle	C₈×#10596833	C₂²
hypercenter	C₂×C₁₆	#10596842
hypocenter	C₇₃	#7053
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
21. #11924031	C₁₆	semidirect
47. C₇₃	#7053	semidirect

Maximal subgroups

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

subgroup	index
#22626948	2
#22624842	2
#7053	73