Finite Group Databasebeta

← #19135040

Subgroups — #19135040

Order 5504.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#14583406C211yesmaximal, characteristic
2C2×#13063282C211yesmaximal, characteristic, complemented
3C2×#13063252C211yesmaximal, characteristic, complemented
4#14582862C211yesmaximal, characteristic, complemented
5#14582660C211yesmaximal, characteristic, complemented
6#14582659C211yesmaximal, characteristic, complemented
7C2×#104×C43C211yesmaximal, characteristic, complemented
8C22×C4×D43C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10#13063306—21no—
11#13063301C412yescomplemented
12#13063296C412yescomplemented
13#13063293—21no—
14C4×C22⋊D43—22no—
15#13063284C2211yescharacteristic
16#13063282—22no—
17#13063282—22no—
18C2×Dic43⋊C4—21no—
19C2×(C2×D43)⋊C4—21no—
20C2×C4×Dic43C2211yescharacteristic
21#13063252—22no—
22(C2×D43)⋊C8—22no—
23C2×#41×C43C2211yescharacteristic
24C2×M16×C43C2211yescharacteristic
25C2×C42×C43C2211yescharacteristic
26#104×C43—22no—
27C23×D43D411yescharacteristic
28#41×C43—21no—
29#41×C43—21no—
30#41×C43—21no—
31#41×C43—21no—
32C2×Q8×C43C2×C411yescharacteristic
33C2×D4×C43—21no—
34C2×D4×C43C2×C411yescharacteristic
35C22×C4×C43—21no—
36C22×C4×C43—21no—
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—22no—
39C22×Dic43—21no—
40C22×Dic43D411yescharacteristic
41C2×C4×D43—21no—
42C2×C4×D43—21no—
43C2×C4×D43—21no—
44C2×C4×D43—21no—
45C2×C4×D43C2×C412yes—
46C2×C4×D43D412yes—
47M16×C43—21no—
48M16×C43—21no—
49C2×C8×C43—21no—
50C42×C43—21no—
51C42×C43D412yescomplemented
52C22⋊Dic43—22no—
53C22⋊Dic43—21no—
54(C2×D43)⋊C4—24no—
55(C2×D43)⋊C4—22no—
56C4⋊Dic43C2×C412yes—
57Dic43⋊C4—24no—
58Dic43⋊C4—22no—
59C4×Dic43—21no—
60C4×Dic43—21no—
61C4×Dic43D412yescomplemented
62#10621877—21no—
63#10621877—21no—
64C2×C43⋊C8—21no—
65C23×C43—21no—
66C23×C43C2×D411yescharacteristic
67C22×D43—21no—
68C22×D43—21no—
69C22×D43—42no—
70C22×D43C22⋊C412yes—
71Q8×C43—21no—
72Q8×C43—21no—
73D4×C43—21no—
74D4×C43—21no—
75D4×C43—41no—
76D4×C43—41no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—42no—
80C2×C4×C43—41no—
81C2×C4×C43—41no—
82C2×C4×C43C22×C411yescharacteristic
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2×D411yescharacteristic
85C2×C4×C43C2×D411yescharacteristic
86C2×C4×C43#4111yescharacteristic
87C2×C4×C43#4111yescharacteristic
88C22⋊D43—44no—
89C2×Dic43—21no—
90C2×Dic43—21no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—42no—
94C2×Dic43C22⋊C412yes—
95C4×D43—22no—
96C4×D43—22no—
97C4×D43—22no—
98C4×D43—22no—
99C8×C43—41no—
100C43⋊C8—41no—
101C22×C43—22no—
102C22×C43—41no—
103C22×C43—42no—
104C22×C43C2×C22⋊C411yescharacteristic
105C22×C43#12011yescharacteristic
106C22×C43#12311yescharacteristic
107C2×D43—22no—
108C2×D43—22no—
109C2×D43—22no—
110C2×D43—42no—
111C2×D43—42no—
112C4×C43—42no—
113C4×C43—41no—
114C4×C43C4×D411yescharacteristic
115C4×C43C4×D411yescharacteristic
116C4×C43#12111yescharacteristic
117C4×C43#12111yescharacteristic
118Dic43—22no—
119Dic43—42no—
120Dic43—42no—
121#1897—431nomaximal, Sylow
122C2×C43—21no—
123C2×C43—21no—
124C2×C43—81no—
125C2×C43#38611yescharacteristic
126C2×C43#42112yes—
127D43—42no—
128#525—431no—
129C2×#117—431no—
130C2×#104—431no—
131C2×#104D4311yescharacteristic, complemented
132#407—431no—
133#339—431no—
134#339—431no—
135C43#189711yescharacteristic, complemented, Sylow
136C2×#41C2×D4311yescharacteristic
137C23×C4—431no—
138C2×M16—431no—
139C2×M16C2×D4311yescharacteristic
140#123—861no—
141C22⋊Q8—432no—
142#121—432no—
143#120—861no—
144C4×D4—862no—
145#117—431no—
146#117—862no—
147#117—862no—
148C2×C4⋊C4—861no—
149C2×C22⋊C4—861no—
150C2×C42—431no—
151C2×C42C2×D4311yescharacteristic
152#104—22no—
153#104—862no—
154C22⋊C8—862no—
155C24—431no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160C2×Q8C4×D4311yescharacteristic
161C2×D4—21no—
162C2×D4—862no—
163C2×D4C4×D4311yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—431no—
167C22×C4—432no—
168C22×C4—432no—
169C22×C4—861no—
170C22×C4—861no—
171C22×C4—861no—
172C22×C4—861no—
173C22×C4—861no—
174C22×C4C22×D4311yescharacteristic
175M16—21no—
176M16—21no—
177M16—861no—
178M16—861no—
179C2×C8—21no—
180C2×C8—861no—
181C4⋊C4—432no—
182C4⋊C4—862no—
183C4⋊C4—864no—
184C22⋊C4—862no—
185C22⋊C4—864no—
186C22⋊C4—862no—
187C22⋊C4—861no—
188C42—21no—
189C42—432no—
190C42—861no—
191C42—861no—
192C42C22⋊D4312yescomplemented
193C23—21no—
194C23—432no—
195C23—861no—
196C23—861no—
197C23—1722no—
198C23D4×D4311yescharacteristic
199Q8—21no—
200Q8—21no—
201D4—21no—
202D4—21no—
203D4—41no—
204D4—41no—
205D4—1724no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—432no—
212C2×C4—861no—
213C2×C4—861no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4—862no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—1722no—
221C2×C4C2×C4×D4311yescharacteristic
222C2×C4#1062189811yescharacteristic
223C2×C4D4×D4311yescharacteristic
224C2×C4D4×D4311yescharacteristic
225C2×C4#1062190011yescharacteristic
226C2×C4C2×C22⋊D4311yescharacteristic
227C8—41no—
228C8—1721no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—862no—
233C22—862no—
234C22—862no—
235C22—1722no—
236C22—1722no—
237C22C22⋊C4×D4311yescharacteristic
238C22#1306329311yescharacteristic
239C22#1306330711yescharacteristic
240C4—42no—
241C4—41no—
242C4—862no—
243C4—1722no—
244C4—1722no—
245C4(C22⋊D43)⋊C411yescharacteristic
246C4C4×C22⋊D4311yescharacteristic
247C4#1306329611yescharacteristic
248C4#1306329811yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—1722no—
253C2#1458277511yescharacteristic
254C2#1458291412yes—
subgroupG/H
centerC2×C4D4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC2×#104×C43C2
socleC22×C43C2×C22⋊C4
hypercenterC2×#104D43
hypocenterC43#1897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#13063282C2semidirect
3. C2×#13063252C2semidirect
4. #14582862C2semidirect
5. #14582660C2semidirect
6. #14582659C2semidirect
7. C2×#104×C43C2semidirect
11. #13063301C4semidirect
12. #13063296C4semidirect
51. C42×C43D4semidirect
61. C4×Dic43D4semidirect
131. C2×#104D43semidirect
135. C43#1897semidirect
192. C42C22⋊D43semidirect