Finite Group Databasebeta

← #19145679

Subgroups — #19145679

Order 5504.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583512C211yesmaximal, characteristic, complemented
2#14583474C211yesmaximal, characteristic
3#14583293C211yesmaximal, characteristic, complemented
4#14583278C211yesmaximal, characteristic, complemented
5#14583256C211yesmaximal, characteristic, complemented
6#14583124C212yesmaximal, complemented
7#14583108C212yesmaximal, complemented
8#14583064C212yesmaximal
9#14583056C212yesmaximal, complemented
10#14582961C211yesmaximal, characteristic, complemented
11C43×#491C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic
13C2×Q8×D43C2211yescharacteristic
14C2×Dic172C2212yes—
15C2×#10621885C2212yes—
16C2×#10621885C2212yes—
17C2×#10621873C2212yes—
18#13063325C2211yescharacteristic
19#13063323C2211yescharacteristic
20#13063320—22no—
21#13063316—22no—
22#13063314C2211yescharacteristic
23#13063313C2211yescharacteristic
24#13063310—22no—
25#13063305C2212yes—
26#13063303—22no—
27#13063290C2212yes—
28#13063282C2211yescharacteristic
29Dic43⋊C8C2212yes—
30#13063248C2212yes—
31#13063245C2212yes—
32(C2×D43)⋊C8C2212yes—
33C4×C43⋊C8C2211yescharacteristic
34C4⋊Q8×C43C2211yescharacteristic
35#125×C43C2211yescharacteristic
36#103×C43C2212yes—
37#103×C43C2212yes—
38#97×C43C2211yescharacteristic
39C2×Q8×C43C2311yescharacteristic
40C2×Q8×C43C2311yescharacteristic
41#10621902—42no—
42Q8×D43—42no—
43C2×D172—21no—
44C2×D172C2311yescharacteristic
45C2×C4×D43—21no—
46C2×C4×D43—21no—
47C2×C4×D43C2311yescharacteristic
48C2×Dic86—21no—
49C2×Dic86C2311yescharacteristic
50C2×Dic86C2312yes—
51C2×C8×C43C2312yes—
52C4⋊C4×C43—22no—
53C4⋊C4×C43—22no—
54C4⋊C4×C43C2312yes—
55C42×C43C2311yescharacteristic
56#10621885—42no—
57#10621885—42no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4D412yes—
62C4⋊Dic43—22no—
63C4⋊Dic43—22no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—22no—
68C4×Dic43C2311yescharacteristic
69C2×C43⋊C8C2312yes—
70Dic172—42no—
71#10621873—42no—
72C22×D43—21no—
73C22×D43C2×D411yescharacteristic
74Q8×C43—22no—
75Q8×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43C2×D412yes—
80C2×C4×C43C2411yescharacteristic
81C2×Dic43—22no—
82C2×Dic43—21no—
83C2×Dic43C2×D412yes—
84C2×Dic43C2×D411yescharacteristic
85D172—22no—
86D172—42no—
87C4×D43—22no—
88C4×D43—42no—
89C4×D43—42no—
90Dic86—22no—
91Dic86—22no—
92Dic86—22no—
93Dic86—42no—
94C8×C43—22no—
95C43⋊C8—22no—
96C22×C43C22×D411yescharacteristic
97C2×D43—21no—
98C2×D43—22no—
99C2×D43—41no—
100C2×D43—42no—
101C4×C43—22no—
102C4×C43—41no—
103C4×C43—41no—
104C4×C43—42no—
105C4×C43H(5,𝔽2)12yes—
106Dic43—21no—
107Dic43—22no—
108Dic43—41no—
109Dic43—42no—
110#3223—431nomaximal, Sylow
111C2×C43#53511yescharacteristic
112C2×C43#57812yes—
113D43—41no—
114D43—81no—
115#541—431no—
116#536—431no—
117#497—431no—
118#494—431no—
119#491D4311yescharacteristic, complemented
120#488—431no—
121#464—432no—
122#462—432no—
123#452—432no—
124#451—432no—
125#433—431no—
126C43#322311yescharacteristic, complemented, Sylow
127C2×#41—431no—
128C22×Q8—431no—
129C2×Q16—432no—
130C2×Q16—432no—
131C2×Q16—432no—
132C2×SD16—432no—
133C4⋊Q8—431no—
134C4⋊Q8—431no—
135C4⋊Q8C2×D4311yescharacteristic
136#126—862no—
137#125—862no—
138#125C2×D4311yescharacteristic
139#124—431no—
140#124—431no—
141#123—862no—
142C22⋊Q8—432no—
143C22⋊Q8—862no—
144C4×Q8—432no—
145#117—431no—
146C4⋊C8—432no—
147#103—432no—
148#103C2×D4312yes—
149#103C2×D4312yes—
150#102—432no—
151C22⋊C8—432no—
152#97C2×D4311yescharacteristic
153C4×C8—431no—
154#41—1722no—
155C2×Q8—431no—
156C2×Q8—432no—
157C2×Q8—861no—
158C2×Q8—1722no—
159C2×Q8C22×D4311yescharacteristic
160C2×Q8C22×D4311yescharacteristic
161C2×D4—431no—
162C2×D4—861no—
163C22×C4—431no—
164C22×C4—861no—
165C22×C4—861no—
166Q16—1722no—
167Q16—1722no—
168Q16—1722no—
169SD16—1722no—
170C2×C8—432no—
171C2×C8C22×D4312yes—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—432no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4C22×D4312yes—
180C22⋊C4—432no—
181C22⋊C4—862no—
182C22⋊C4—862no—
183C22⋊C4—862no—
184C42—431no—
185C42—862no—
186C42C22×D4311yescharacteristic
187C23—431no—
188C23—861no—
189Q8—22no—
190Q8—22no—
191Q8—862no—
192Q8—862no—
193Q8—862no—
194Q8—1722no—
195D4—862no—
196D4—1722no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—432no—
201C2×C4—431no—
202C2×C4—862no—
203C2×C4—862no—
204C2×C4—861no—
205C2×C4—1722no—
206C2×C4—1722no—
207C2×C4D4×D4312yes—
208C2×C4C23×D4311yescharacteristic
209C8—22no—
210C8—862no—
211C22—862no—
212C22—861no—
213C22—1722no—
214C22—1721no—
215C22C2×D4×D4311yescharacteristic
216C4—22no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—862no—
221C4—861no—
222C4—1721no—
223C4—1722no—
224C4#1306337112yes—
225C2—3441no—
226C2—1721no—
227C2#1458346711yescharacteristic
228C2#1458371512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#491C2
socleC22×C43C22×D4
hypercenter#491D43
hypocenterC43#3223
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #14583512C2semidirect
3. #14583293C2semidirect
4. #14583278C2semidirect
5. #14583256C2semidirect
6. #14583124C2semidirect
7. #14583108C2semidirect
9. #14583056C2semidirect
10. #14582961C2semidirect
11. C43×#491C2semidirect
119. #491D43semidirect
126. C43#3223semidirect