Finite Group Databasebeta

← #19133122

Subgroups — #19133122

Order 5504.

326 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 63 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#121×D43C211yesmaximal, characteristic
2#14582861C211yesmaximal, characteristic, complemented
3#14582761C211yesmaximal, characteristic, complemented
4#14582634C211yesmaximal, characteristic, complemented
5#14582633C211yesmaximal, characteristic, complemented
6#14582632C211yesmaximal, characteristic, complemented
7C43×#327C211yesmaximal, characteristic, complemented
8C2×D4×D43—21no—
9C2×D4×D43C411yescharacteristic, complemented
10C22×C4×D43C2211yescharacteristic
11C2×#10621872—21no—
12#13063300C411yescharacteristic, complemented
13#13063299C2211yescharacteristic
14#13063298—21no—
15#13063297—21no—
16#13063296C411yescharacteristic, complemented
17C4⋊C4×D43C411yescharacteristic, complemented
18C2×(C2×D43)⋊C4—21no—
19C22⋊C4×D43—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic, complemented
21(C2×D43)⋊C8—21no—
22C43⋊#95—21no—
23C43⋊#95C2211yescharacteristic, complemented
24#121×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic, complemented
26#95×C43C2211yescharacteristic, complemented
27C23×D43—21no—
28C23×D43D411yescharacteristic
29C2×D4×C43—21no—
30C2×D4×C43C2×C411yescharacteristic
31C22×C4×C43—21no—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C22×Dic43—21no—
37C22×Dic43D411yescharacteristic
38D4×D43—42no—
39D4×D43—42no—
40D4×D43—42no—
41C2×D172—21no—
42C2×D172C2×C411yescharacteristic
43C2×C4×D43—21no—
44C2×C4×D43—42no—
45C2×C4×D43C2×C411yescharacteristic
46C2×C4×D43C2×C411yescharacteristic
47C2×C4×D43D411yescharacteristic
48C2×C4×D43D411yescharacteristic
49C2×C8×C43—21no—
50C4⋊C4×C43C2×C411yescharacteristic
51C22⋊C4×C43—21no—
52C22⋊Dic43—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—42no—
56C4⋊Dic43C2×C411yescharacteristic
57Dic43⋊C4—21no—
58C2×C43⋊C8—21no—
59#10621872—42no—
60C23×C43—21no—
61C23×C43C2×D411yescharacteristic
62C22×D43—21no—
63C22×D43—21no—
64C22×D43—22no—
65C22×D43—21no—
66C22×D43—41no—
67C22×D43—42no—
68C22×D43—42no—
69C22×D43—42no—
70C22×D43C22⋊C411yescharacteristic
71C22×D43C22⋊C411yescharacteristic
72D4×C43—41no—
73D4×C43—41no—
74D4×C43—41no—
75C2×C4×C43—21no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43C22×C411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C22⋊D43—42no—
83C22⋊D43—42no—
84C22⋊D43—41no—
85C22⋊D43—41no—
86C2×Dic43—21no—
87C2×Dic43—41no—
88C2×Dic43—41no—
89C2×Dic43—41no—
90C2×Dic43—41no—
91C2×Dic43C22⋊C411yescharacteristic
92C2×Dic43C22⋊C411yescharacteristic
93D172—41no—
94D172—42no—
95C4×D43—22no—
96C4×D43—22no—
97C4×D43—41no—
98C4×D43—41no—
99C4×D43—42no—
100C8×C43—41no—
101C43⋊C8—41no—
102C22×C43—21no—
103C22×C43—21no—
104C22×C43—41no—
105C22×C43—41no—
106C22×C43—41no—
107C22×C43C2×C22⋊C411yescharacteristic
108C22×C43AGL(1,ℤ/8)11yescharacteristic
109C22×C43AGL(1,ℤ/8)11yescharacteristic
110C2×D43—21no—
111C2×D43—21no—
112C2×D43—21no—
113C2×D43—21no—
114C2×D43—21no—
115C2×D43—42no—
116C2×D43—42no—
117C2×D43—41no—
118C2×D43—41no—
119C2×D43—41no—
120C2×D43—84no—
121C2×D43#9912yes—
122C4×C43—21no—
123C4×C43—21no—
124C4×C43—41no—
125C4×C43—81no—
126Dic43—21no—
127Dic43—21no—
128Dic43—41no—
129Dic43—81no—
130#1510—431nomaximal, Sylow
131C2×C43—21no—
132C2×C43—21no—
133C2×C43—81no—
134C2×C43C2×#9911yescharacteristic
135C2×C43#41811yescharacteristic
136C2×C43#42111yescharacteristic
137D43—22no—
138D43—41no—
139D43—81no—
140C2×#121—431no—
141#407—431no—
142#381—431no—
143#327—431no—
144#327—431no—
145#327—431no—
146#327D4311yescharacteristic, complemented
147C43#151011yescharacteristic, complemented, Sylow
148C22×D4—431no—
149C22×D4—861no—
150C23×C4—431no—
151C2×M16—861no—
152#121—431no—
153#121—431no—
154#121—431no—
155#121—861no—
156#121—861no—
157#121C2×D4311yescharacteristic
158C2×C4⋊C4—431no—
159C2×C22⋊C4—861no—
160C2×C22⋊C4—861no—
161C22⋊C8—431no—
162C22⋊C8—861no—
163C22⋊C8C2×D4311yescharacteristic, complemented
164#95—431no—
165#95—861no—
166#95C2×D4311yescharacteristic, complemented
167C24—431no—
168C24—861no—
169C2×D4—21no—
170C2×D4—431no—
171C2×D4—861no—
172C2×D4—861no—
173C2×D4—861no—
174C2×D4—861no—
175C2×D4—1722no—
176C2×D4—1722no—
177C2×D4—1722no—
178C2×D4C4×D4311yescharacteristic
179C22×C4—21no—
180C22×C4—431no—
181C22×C4—431no—
182C22×C4—431no—
183C22×C4—431no—
184C22×C4—431no—
185C22×C4—861no—
186C22×C4—861no—
187C22×C4—1722no—
188C22×C4C22×D4311yescharacteristic
189M16—1722no—
190C2×C8—21no—
191C2×C8—861no—
192C4⋊C4—431no—
193C4⋊C4—861no—
194C4⋊C4C4×D4311yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—861no—
197C22⋊C4—861no—
198C22⋊C4—861no—
199C22⋊C4—1722no—
200C23—21no—
201C23—431no—
202C23—431no—
203C23—862no—
204C23—861no—
205C23—861no—
206C23—861no—
207C23—1721no—
208C23—1722no—
209C23—1722no—
210C23—1722no—
211C23D4×D4311yescharacteristic
212D4—41no—
213D4—41no—
214D4—41no—
215D4—1721no—
216D4—1722no—
217D4—1722no—
218D4—1722no—
219D4—1721no—
220D4—1721no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—431no—
227C2×C4—431no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—861no—
231C2×C4—1721no—
232C2×C4—1721no—
233C2×C4—1722no—
234C2×C4—1721no—
235C2×C4—1721no—
236C2×C4—1721no—
237C2×C4—1721no—
238C2×C4C2×C4×D4311yescharacteristic
239C2×C4D4×D4311yescharacteristic
240C8—41no—
241C8—1721no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—432no—
248C22—861no—
249C22—861no—
250C22—861no—
251C22—861no—
252C22—861no—
253C22—3444no—
254C22—1722no—
255C22—1722no—
256C22—1721no—
257C22—1721no—
258C22—1721no—
259C22C22⋊C4×D4311yescharacteristic
260C22#1306334911yescharacteristic
261C22#1306335211yescharacteristic
262C4—21no—
263C4—21no—
264C4—41no—
265C4—81no—
266C4—861no—
267C4—861no—
268C4—3441no—
269C4—1721no—
270C2—21no—
271C2—21no—
272C2—81no—
273C2—862no—
274C2—3441no—
275C2—1721no—
276C2#99×D4311yescharacteristic
277C2#1458290211yescharacteristic
278C2#1458291411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#327C2
socleC22×C43C2×C22⋊C4
hypercenter#327D43
hypocenterC43#1510
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14582861C2semidirect
3. #14582761C2semidirect
4. #14582634C2semidirect
5. #14582633C2semidirect
6. #14582632C2semidirect
7. C43×#327C2semidirect
9. C2×D4×D43C4semidirect
12. #13063300C4semidirect
16. #13063296C4semidirect
17. C4⋊C4×D43C4semidirect
20. C22⋊(C43⋊C8)C22semidirect
23. C43⋊#95C22semidirect
25. C22⋊C8×C43C22semidirect
26. #95×C43C22semidirect
146. #327D43semidirect
147. C43#1510semidirect
163. C22⋊C8C2×D43semidirect
166. #95C2×D43semidirect