Finite Group Databasebeta

← #19146439

Subgroups — #19146439

Order 5504.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583545C211yesmaximal, characteristic, complemented
2#14583256C211yesmaximal, characteristic, complemented
3#14583234C211yesmaximal, characteristic, complemented
4#14583223C211yesmaximal, characteristic, complemented
5#14583196C211yesmaximal, characteristic, complemented
6#14583133C211yesmaximal, characteristic, complemented
7#14583126C211yesmaximal, characteristic, complemented
8#14583114C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic, complemented
10#14583032C211yesmaximal, characteristic, complemented
11C4×#10621882C211yesmaximal, characteristic, complemented
12D4×C43⋊C8C211yesmaximal, characteristic, complemented
13#14582893C211yesmaximal, characteristic, complemented
14C2×#13063245C211yesmaximal, characteristic, complemented
15C43×#553C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×#10621883C2211yescharacteristic, complemented
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C22×C43⋊C8C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic, complemented
23#13063313C2211yescharacteristic
24#13063310—21no—
25#13063304C2211yescharacteristic
26#13063299C2211yescharacteristic
27#13063298—21no—
28#13063293—21no—
29C4×D172C2211yescharacteristic
30C22⋊C4×D43—21no—
31#13063258C2211yescharacteristic, complemented
32#13063258C2211yescharacteristic, complemented
33#13063256C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35#13063248C2211yescharacteristic, complemented
36#13063248C2211yescharacteristic, complemented
37#13063248C2211yescharacteristic, complemented
38#13063246C2211yescharacteristic, complemented
39#13063245C2211yescharacteristic
40#13063245C2211yescharacteristic
41#13063245C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47C4×C43⋊C8C2211yescharacteristic, complemented
48#126×C43—21no—
49#125×C43C2211yescharacteristic, complemented
50#123×C43—21no—
51#121×C43—21no—
52#121×C43C2211yescharacteristic
53#121×C43C2211yescharacteristic, complemented
54C4×D4×C43—21no—
55C4×D4×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic, complemented
57#117×C43C2211yescharacteristic, complemented
58C2×C4⋊C4×C43C2211yescharacteristic
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43D411yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70#10621898—22no—
71#10621898—41no—
72C2×D172—21no—
73C2×D172—22no—
74C2×D172—41no—
75C2×D172C2311yescharacteristic
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×Dic86C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43D411yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43D411yescharacteristic
92C22⋊C4×C43D411yescharacteristic
93C42×C43—21no—
94C42×C43C2311yescharacteristic
95C22⋊Dic43—21no—
96#10621883—41no—
97#10621882—22no—
98#10621882—41no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103C4⋊Dic43C2311yescharacteristic
104Dic43⋊C4—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—
115C22×D43—21no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—81no—
119D4×C43—22no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—42no—
123D4×C43—81no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—81no—
132C2×C4×C43—81no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2411yescharacteristic
138C22⋊D43—42no—
139C22⋊D43—81no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142D172—21no—
143D172—21no—
144D172—21no—
145D172—42no—
146D172#4112yes—
147C4×D43—42no—
148C4×D43—81no—
149Dic86—21no—
150Dic86—21no—
151C43⋊C8—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43#13512yes—
164C22×C43C22×D411yescharacteristic
165C2×D43—22no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—84no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43C2×#4111yescharacteristic
180C4×C43H(5,𝔽2)11yescharacteristic
181Dic43—41no—
182Dic43—41no—
183#3297—431nomaximal, Sylow
184C2×C43—22no—
185C2×C43—41no—
186C2×C43—81no—
187C2×C43#54611yescharacteristic
188C2×C43C2×#13511yescharacteristic
189C2×C43#57611yescharacteristic
190D43—42no—
191D43—81no—
192#553D4311yescharacteristic, complemented
193#546—431no—
194#488—431no—
195#484—431no—
196#482—431no—
197#478—431no—
198#466—431no—
199#465—431no—
200#463—431no—
201#449—431no—
202#447—431no—
203C4×D8—431no—
204C8×D4—431no—
205#416—431no—
206C2×#102—431no—
207C43#329711yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C22×D4—431no—
210C2×SD16—431no—
211C2×D8—431no—
212C2×D8—431no—
213C22×C8—431no—
214C22×C8—431no—
215#126—21no—
216#125C2×D4311yescharacteristic, complemented
217#124—431no—
218#123—21no—
219#123—861no—
220C22⋊Q8—431no—
221#121—21no—
222#121—431no—
223#121—861no—
224#121C2×D4311yescharacteristic
225#121C2×D4311yescharacteristic, complemented
226#120—861no—
227C4×D4—21no—
228C4×D4—431no—
229C4×D4C2×D4311yescharacteristic
230C4×D4C2×D4311yescharacteristic, complemented
231#117C2×D4311yescharacteristic, complemented
232C2×C4⋊C4C2×D4311yescharacteristic
233C2×C22⋊C4—861no—
234#107—431no—
235#107—431no—
236#106—431no—
237C4⋊C8—431no—
238#103—431no—
239#103—431no—
240#103—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248C22⋊C8—431no—
249C22⋊C8—431no—
250C4×C8—431no—
251C24—861no—
252#41—862no—
253#41—1721no—
254C2×Q8—431no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—862no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—1721no—
264C2×D4C22⋊D4311yescharacteristic
265C2×D4C22×D4311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4C22×D4311yescharacteristic
271C22×C4C22×D4311yescharacteristic
272SD16—1721no—
273D8—862no—
274D8—1721no—
275C2×C8—431no—
276C2×C8—431no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8—1721no—
280C2×C8—1721no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—431no—
285C4⋊C4—861no—
286C4⋊C4C22⋊D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C4⋊C4C22×D4311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4C22⋊D4311yescharacteristic
300C22⋊C4C22⋊D4311yescharacteristic
301C42—21no—
302C42C22×D4311yescharacteristic
303C23—21no—
304C23—861no—
305C23—861no—
306C23—3441no—
307C23—1722no—
308C23—1722no—
309C23C2×C22⋊D4311yescharacteristic
310C23C2×C22⋊D4311yescharacteristic
311Q8—861no—
312Q8—861no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—432no—
319D4—861no—
320D4—861no—
321D4—861no—
322D4—3441no—
323D4—1722no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—3441no—
337C2×C4—1722no—
338C2×C4C2×C22⋊D4311yescharacteristic
339C2×C4C2×C22⋊D4311yescharacteristic
340C2×C4C2×C22⋊D4311yescharacteristic
341C2×C4C2×C22⋊D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—861no—
344C8—861no—
345C8—861no—
346C8—861no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—862no—
356C22—3444no—
357C22—1721no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22—1721no—
362C22#1306334512yes—
363C22C22×C22⋊D4311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—1721no—
372C4—1721no—
373C4#41×D4311yescharacteristic
374C4#1306337111yescharacteristic
375C2—22no—
376C2—41no—
377C2—81no—
378C2—3441no—
379C2—1722no—
380C2#1458353711yescharacteristic
381C2C2×#1306334511yescharacteristic
382C2#1458370211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#553C2
socleC22×C43C22×D4
hypercenter#553D43
hypocenterC43#3297
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. #14583545C2semidirect
2. #14583256C2semidirect
3. #14583234C2semidirect
4. #14583223C2semidirect
5. #14583196C2semidirect
6. #14583133C2semidirect
7. #14583126C2semidirect
8. #14583114C2semidirect
9. #14583042C2semidirect
10. #14583032C2semidirect
11. C4×#10621882C2semidirect
12. D4×C43⋊C8C2semidirect
13. #14582893C2semidirect
14. C2×#13063245C2semidirect
15. C43×#553C2semidirect
18. C2×#10621883C22semidirect
22. C22×C43⋊C8C22semidirect
31. #13063258C22semidirect
32. #13063258C22semidirect
33. #13063256C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. #13063248C22semidirect
36. #13063248C22semidirect
37. #13063248C22semidirect
38. #13063246C22semidirect
46. C22⋊(C43⋊C8)C22semidirect
47. C4×C43⋊C8C22semidirect
49. #125×C43C22semidirect
53. #121×C43C22semidirect
56. C4×D4×C43C22semidirect
57. #117×C43C22semidirect
192. #553D43semidirect
207. C43#3297semidirect
216. #125C2×D43semidirect
225. #121C2×D43semidirect
230. C4×D4C2×D43semidirect
231. #117C2×D43semidirect