Finite Group Databasebeta

← #19146491

Subgroups — #19146491

Order 5504.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583558C211yesmaximal, characteristic, complemented
2#14583256C211yesmaximal, characteristic, complemented
3#14583240C211yesmaximal, characteristic, complemented
4#14583217C211yesmaximal, characteristic, complemented
5#14583203C211yesmaximal, characteristic, complemented
6#14583133C211yesmaximal, characteristic, complemented
7#14583126C211yesmaximal, characteristic, complemented
8#14583114C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic, complemented
10#14583037C211yesmaximal, characteristic, complemented
11C4×#10621883C211yesmaximal, characteristic, complemented
12D4×C43⋊C8C211yesmaximal, characteristic, complemented
13#14582893C211yesmaximal, characteristic, complemented
14C2×#13063248C211yesmaximal, characteristic, complemented
15C43×#553C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C22×C43⋊C8C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic
23#13063313C2211yescharacteristic
24#13063311—21no—
25#13063304C2211yescharacteristic
26#13063303—21no—
27#13063299C2211yescharacteristic
28#13063297—21no—
29C4×Dic86C2211yescharacteristic
30(C22⋊D43)⋊C4—21no—
31#13063258C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063248C2211yescharacteristic
36#13063248C2211yescharacteristic
37#13063248C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48#126×C43—21no—
49#125×C43C2211yescharacteristic
50#123×C43—21no—
51#121×C43—21no—
52#121×C43C2211yescharacteristic
53#121×C43C2211yescharacteristic
54C4×D4×C43—21no—
55C4×D4×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic
57#117×C43C2211yescharacteristic
58C2×C4⋊C4×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43D411yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C22×Dic43—21no—
70#10621898—22no—
71#10621898—41no—
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×Dic86—22no—
75C2×Dic86—21no—
76C2×Dic86—41no—
77C2×Dic86C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43D411yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C22⋊C4×C43D411yescharacteristic
91C22⋊C4×C43D411yescharacteristic
92C42×C43—21no—
93C42×C43C2311yescharacteristic
94C22⋊Dic43—21no—
95#10621883—22no—
96#10621883—41no—
97#10621882—41no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115D4×C43—22no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—42no—
119D4×C43—81no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—42no—
135C22⋊D43—42no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—42no—
140D172—21no—
141D172—21no—
142C4×D43—42no—
143Dic86—21no—
144Dic86—21no—
145Dic86—21no—
146Dic86—42no—
147Dic86#4112yes—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43#13512yes—
161C22×C43C22×D411yescharacteristic
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43C2×#4111yescharacteristic
173C4×C43H(5,𝔽2)11yescharacteristic
174Dic43—22no—
175Dic43—41no—
176Dic43—41no—
177#3301—431nomaximal, Sylow
178C2×C43—22no—
179C2×C43—41no—
180C2×C43—81no—
181C2×C43#54611yescharacteristic
182C2×C43C2×#13511yescharacteristic
183C2×C43#57711yescharacteristic
184D43—81no—
185#553D4311yescharacteristic, complemented
186#548—431no—
187#488—431no—
188#485—431no—
189#481—431no—
190#479—431no—
191#466—431no—
192#465—431no—
193#463—431no—
194#449—431no—
195#448—431no—
196C4×SD16—431no—
197C8×D4—431no—
198#416—431no—
199C2×#103—431no—
200C43#330111yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C22×Q8—431no—
203C2×SD16—431no—
204C2×SD16—431no—
205C2×D8—431no—
206C22×C8—431no—
207C22×C8—431no—
208#126—21no—
209#125C2×D4311yescharacteristic
210#124—431no—
211#124—861no—
212#123—21no—
213C22⋊Q8—431no—
214C22⋊Q8—861no—
215#121—21no—
216#121—431no—
217#121—861no—
218#121C2×D4311yescharacteristic
219#121C2×D4311yescharacteristic
220C4×Q8—431no—
221C4×D4—21no—
222C4×D4—861no—
223C4×D4C2×D4311yescharacteristic
224C4×D4C2×D4311yescharacteristic
225#117C2×D4311yescharacteristic
226C2×C4⋊C4C2×D4311yescharacteristic
227#107—431no—
228#106—431no—
229#106—431no—
230C4⋊C8—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241C22⋊C8—431no—
242C22⋊C8—431no—
243C4×C8—431no—
244#41—862no—
245#41—1721no—
246C2×Q8—431no—
247C2×Q8—431no—
248C2×Q8—862no—
249C2×Q8—861no—
250C2×Q8—1721no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—431no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4C22⋊D4311yescharacteristic
257C2×D4C22×D4311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263C22×C4C22×D4311yescharacteristic
264SD16—862no—
265SD16—1721no—
266D8—1721no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—431no—
271C2×C8—1721no—
272C2×C8—1721no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—431no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4C22⋊D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C4⋊C4C22×D4311yescharacteristic
282C4⋊C4C22×D4311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4C22⋊D4311yescharacteristic
292C22⋊C4C22⋊D4311yescharacteristic
293C42—21no—
294C42—861no—
295C42C22×D4311yescharacteristic
296C23—21no—
297C23—861no—
298C23C2×C22⋊D4311yescharacteristic
299C23C2×C22⋊D4311yescharacteristic
300Q8—432no—
301Q8—861no—
302Q8—861no—
303Q8—861no—
304Q8—1722no—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—861no—
311D4—861no—
312D4—1722no—
313D4—1722no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—1722no—
327C2×C4—1722no—
328C2×C4C2×C22⋊D4311yescharacteristic
329C2×C4C2×C22⋊D4311yescharacteristic
330C2×C4C2×C22⋊D4311yescharacteristic
331C2×C4C2×C22⋊D4311yescharacteristic
332C2×C4C23×D4311yescharacteristic
333C8—861no—
334C8—861no—
335C8—861no—
336C8—861no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22#1306334512yes—
349C22C22×C22⋊D4311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—862no—
358C4—1721no—
359C4—1721no—
360C4#41×D4311yescharacteristic
361C4#1306337111yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—3441no—
366C2#1458353711yescharacteristic
367C2C2×#1306334511yescharacteristic
368C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#553C2
socleC22×C43C22×D4
hypercenter#553D43
hypocenterC43#3301
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #14583558C2semidirect
2. #14583256C2semidirect
3. #14583240C2semidirect
4. #14583217C2semidirect
5. #14583203C2semidirect
6. #14583133C2semidirect
7. #14583126C2semidirect
8. #14583114C2semidirect
9. #14583042C2semidirect
10. #14583037C2semidirect
11. C4×#10621883C2semidirect
12. D4×C43⋊C8C2semidirect
13. #14582893C2semidirect
14. C2×#13063248C2semidirect
15. C43×#553C2semidirect
185. #553D43semidirect
200. C43#3301semidirect