Subgroups — #34001023

Order 18688.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625091	C₂	1	1	yes	maximal, characteristic
2	#22624967	C₂	1	1	yes	maximal, characteristic
3	#22612212	C₂	1	1	yes	maximal, characteristic
4	#17989519	—	2	1	no	—
5	#17989509	—	2	1	no	—
6	#17988991	—	2	1	no	—
7	#17988415	C₄	1	1	yes	characteristic
8	#17988414	—	2	1	no	—
9	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
10	#367×C₇₃	C₄	1	1	yes	characteristic
11	#14556665	—	4	1	no	—
12	#14556641	—	4	1	no	—
13	#14556590	—	4	1	no	—
14	C₂×#11924003	D₄	1	1	yes	characteristic
15	#14556525	—	2	1	no	—
16	#14556524	—	4	1	no	—
17	C₈×Dic₇₃	D₄	1	1	yes	characteristic
18	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
19	#107×C₇₃	—	2	1	no	—
20	#11924031	—	8	1	no	—
21	C₂×Dic₁₄₆	—	8	1	no	—
22	C₂×#10596831	D₈	1	1	yes	characteristic
23	C₄⋊Dic₇₃	—	4	1	no	—
24	#11924007	—	8	1	no	—
25	C₄×Dic₇₃	SD₁₆	1	1	yes	characteristic
26	#11924003	SD₁₆	1	1	yes	characteristic
27	#11924003	Q₁₆	1	1	yes	characteristic
28	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₄⋊C₄×C₇₃	—	4	1	no	—
30	C₁₆×C₇₃	—	2	1	no	—
31	C₂×C₄×C₇₃	—	8	1	no	—
32	C₂×C₄×C₇₃	#102	1	1	yes	characteristic
33	C₂×Dic₇₃	—	2	1	no	—
34	C₂×Dic₇₃	—	8	1	no	—
35	Dic₁₄₆	—	16	2	no	—
36	C₈×C₇₃	#101	1	1	yes	characteristic
37	C₈×C₇₃	#103	1	1	yes	characteristic
38	#10596831	SD₃₂	1	1	yes	characteristic
39	#10596831	Q₃₂	1	1	yes	characteristic
40	C₂²×C₇₃	#361	1	1	yes	characteristic
41	C₄×C₇₃	—	16	1	no	—
42	C₄×C₇₃	#332	1	1	yes	characteristic
43	C₄×C₇₃	#358	1	1	yes	characteristic
44	Dic₇₃	—	2	2	no	—
45	Dic₇₃	—	16	1	no	—
46	#7453	—	73	1	no	maximal, Sylow
47	C₂×C₇₃	—	2	1	no	—
48	C₂×C₇₃	#1365	1	1	yes	characteristic
49	#2254	—	73	1	no	—
50	#1422	—	73	1	no	—
51	#1373	—	73	1	no	—
52	C₇₃	#7453	1	1	yes	characteristic, complemented, Sylow
53	#500	—	146	1	no	—
54	M₆₄	—	146	1	no	—
55	#367	—	73	1	no	—
56	#367	—	146	1	no	—
57	#367	#64408	1	1	yes	characteristic
58	#364	—	146	1	no	—
59	C₄×C₁₆	—	73	1	no	—
60	C₄⋊Q₈	—	292	1	no	—
61	M₃₂	—	292	1	no	—
62	C₂×C₁₆	—	73	1	no	—
63	C₂×C₁₆	C₂×#64408	1	1	yes	characteristic
64	#107	—	2	1	no	—
65	#107	—	292	1	no	—
66	#107	—	146	1	no	—
67	C₄×C₈	—	73	1	no	—
68	C₃₂	—	292	1	no	—
69	C₂×Q₈	—	584	1	no	—
70	C₂×C₈	—	73	1	no	—
71	C₂×C₈	C₂²⋊#64408	1	1	yes	characteristic
72	C₄⋊C₄	—	4	1	no	—
73	C₄⋊C₄	—	292	1	no	—
74	C₄⋊C₄	—	584	1	no	—
75	C₄²	—	73	1	no	—
76	C₁₆	—	2	1	no	—
77	C₁₆	—	584	1	no	—
78	C₁₆	—	73	1	no	—
79	C₁₆	—	73	1	no	—
80	Q₈	—	1168	2	no	—
81	C₂×C₄	—	8	1	no	—
82	C₂×C₄	—	584	1	no	—
83	C₂×C₄	—	146	1	no	—
84	C₂×C₄	#14556653	1	1	yes	characteristic
85	C₈	—	73	1	no	—
86	C₈	—	73	1	no	—
87	C₈	#14556652	1	1	yes	characteristic
88	C₈	#14556654	1	1	yes	characteristic
89	C₂²	#17989505	1	1	yes	characteristic
90	C₄	—	16	1	no	—
91	C₄	—	1168	1	no	—
92	C₄	—	146	2	no	—
93	C₄	#17989446	1	1	yes	characteristic
94	C₄	#17989500	1	1	yes	characteristic
95	C₂	—	2	1	no	—
96	C₂	#22624950	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22624950
commutator	C₂×C₁₆×C₇₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×#64408
Fitting	#367×C₇₃	C₄
socle	C₂×C₇₃	#1365
prime radical	C₂²×C₇₃	#361
cosocle	C₁₆×Dic₇₃	C₂²
hypercenter	#367	#64408
hypocenter	C₇₃	#7453
LCS	G ▷ C₂×C₁₆×C₇₃ ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #367

Complements

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

N	H ≅ G/N	type
52. C₇₃	#7453	semidirect

Maximal subgroups

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

subgroup	index
#22625091	2
#22624967	2
#22612212	2
#7453	73