Finite Group Databasebeta

← #24992530

Subgroups — #24992530

Order 11008.

620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144059C211yesmaximal, characteristic
2#19137505C211yesmaximal, characteristic, complemented
3#19133156C211yesmaximal, characteristic, complemented
4#19133091C211yesmaximal, characteristic, complemented
5#19132497C211yesmaximal, characteristic, complemented
6#19132454C211yesmaximal, characteristic, complemented
7C43×#1478C211yesmaximal, characteristic, complemented
8C2×#13063351—21no—
9#14583449C2211yescharacteristic
10C2×D4×Dic43—21no—
11#14583114—22no—
12#14583104C412yescomplemented
13#14583094C412yescomplemented
14#14582923C2211yescharacteristic
15#14582898—21no—
16#14582798—21no—
17#14582774—22no—
18#14582765C2211yescharacteristic
19#14582759—21no—
20C4×C4⋊Dic43C2211yescharacteristic
21C2×C43⋊#95—21no—
22#14582634—21no—
23#14582634—21no—
24#14582634—22no—
25C2×C4×D4×C43C2211yescharacteristic
26C43×#431C2211yescharacteristic
27C43×#431C2211yescharacteristic
28C43×D4⋊C8—22no—
29C2×#10621898—21no—
30C23×Dic43—22no—
31#13063351—42no—
32#13063351—42no—
33C2×#10621883—22no—
34C2×#10621882—22no—
35C2×#10621877—21no—
36#13063325C2×C411yescharacteristic, complemented
37#13063322C2×C411yescharacteristic, complemented
38#13063313—21no—
39#13063299—21no—
40#13063299—21no—
41C4×D172—21no—
42C4×D172—21no—
43D4×Dic43—42no—
44D4×Dic43—42no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—22no—
48C2×C22⋊Dic43—22no—
49C2×C4×Dic43—21no—
50C4⋊(C43⋊C8)—21no—
51C4⋊(C43⋊C8)C2×C412yescomplemented
52#13063248—22no—
53#13063245—22no—
54C43⋊#95—22no—
55C43⋊#95—21no—
56C43⋊#95D411yescharacteristic
57C43⋊#95D411yescharacteristic
58C43⋊#95D412yes—
59C22×D4×C43D411yescharacteristic
60C23×C4×C43—21no—
61C4×D4×C43—21no—
62C4×D4×C43—21no—
63C4×D4×C43C2×C412yes—
64C4×D4×C43D412yes—
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C22⋊C4×C43—21no—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C22⋊C8×C43—21no—
71C22⋊C8×C43—21no—
72C4×C8×C43—21no—
73C4×C8×C43—21no—
74C24×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43C22⋊C412yes—
79C2×D4×C43D812yes—
80C2×D4×C43SD1612yes—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—21no—
84C22×C4×C43—82no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C2×C22⋊D43—41no—
89C22×Dic43—21no—
90C22×Dic43—22no—
91C22×Dic43—21no—
92C22×Dic43—44no—
93C22×Dic43—44no—
94C22×Dic43—82no—
95#10621898—41no—
96#10621898—41no—
97#10621898—41no—
98#10621898—41no—
99C2×D172—21no—
100C2×D172—21no—
101C2×D172—21no—
102C2×C4×D43—41no—
103C2×Dic86—21no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43C22⋊C412yes—
108C22⋊C4×C43—22no—
109C22⋊C4×C43—22no—
110C42×C43C22×C411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114C22⋊Dic43—44no—
115#10621883—44no—
116#10621882—44no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—41no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—42no—
122C4⋊Dic43—41no—
123C4⋊Dic43—41no—
124C4⋊Dic43—82no—
125C4×Dic43—41no—
126C4×Dic43—41no—
127#10621877—41no—
128#10621877—41no—
129C2×C43⋊C8—22no—
130C23×C43—22no—
131C23×C43—22no—
132C23×C43—22no—
133C23×C43—42no—
134C23×C43—42no—
135C23×C43#12011yescharacteristic
136C22×D43—41no—
137D4×C43—22no—
138D4×C43—22no—
139D4×C43—22no—
140D4×C43#10214yes—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—82no—
146C2×C4×C43—82no—
147C2×C4×C43C2×C22⋊C411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12311yescharacteristic
153C2×C4×C43C2×D811yescharacteristic
154C2×C4×C43C2×SD1611yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C43#13711yescharacteristic
157C22⋊D43—81no—
158C22⋊D43—81no—
159C2×Dic43—22no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—42no—
169C2×Dic43—88no—
170D172—41no—
171D172—41no—
172D172—81no—
173D172—81no—
174C4×D43—81no—
175C4×D43—81no—
176Dic86—41no—
177Dic86—41no—
178C8×C43—81no—
179C8×C43—81no—
180C43⋊C8—42no—
181#9179—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—24no—
185C22×C43—44no—
186C22×C43—44no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43#38611yescharacteristic
190C22×C43#44711yescharacteristic
191C22×C43#44811yescharacteristic
192C2×D43—81no—
193C2×D43—81no—
194C2×D43—81no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—42no—
200C4×C43C2×#10211yescharacteristic
201C4×C43#41711yescharacteristic
202C4×C43#48011yescharacteristic
203C4×C43#48111yescharacteristic
204Dic43—42no—
205Dic43—81no—
206Dic43—82no—
207Dic43—81no—
208#3036—431no—
209#2349—431no—
210#1517—431no—
211#1502—431no—
212#1478D4311yescharacteristic, complemented
213#1303—431no—
214#1286—431no—
215C2×C43—21no—
216C2×C43—21no—
217C2×C43—44no—
218C2×C43#187411yescharacteristic
219C2×C43#190411yescharacteristic
220C2×C43#190611yescharacteristic
221D43—161no—
222C2×AGL(1,ℤ/8)—861no—
223#532—431no—
224C2×C4×D4—861no—
225C2×C4×D4C2×D4311yescharacteristic
226#463—862no—
227#461—432no—
228#459—432no—
229#431C2×D4311yescharacteristic
230#431C2×D4311yescharacteristic
231#423—431no—
232#417—861no—
233#389—861no—
234#385—862no—
235#382—431no—
236#380—861no—
237C4×C4⋊C4—431no—
238C2×#95—861no—
239#327—861no—
240#327—861no—
241#327—862no—
242D4⋊C8—22no—
243C43#917911yescharacteristic, complemented, Sylow
244C2×#41—861no—
245C22×D4D17211yescharacteristic
246C23×C4—21no—
247C23×C4—862no—
248AGL(1,ℤ/8)—1722no—
249AGL(1,ℤ/8)—1722no—
250C2×SD16—862no—
251C2×D8—862no—
252C2×M16—861no—
253C4⋊Q8—431no—
254#127—431no—
255#124—861no—
256#121—861no—
257#121—861no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—861no—
261C4×D4—861no—
262C4×D4—1722no—
263C4×D4—1722no—
264C4×D4C4×D4312yes—
265C4×D4C22⋊D4312yes—
266C2×C4⋊C4—862no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4D17211yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—862no—
272C2×C42—861no—
273C2×C42C22×D4311yescharacteristic
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—432no—
277C4⋊C8—861no—
278#103—862no—
279#102—862no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C4×C8—21no—
283C4×C8—21no—
284#95—431no—
285#95—431no—
286#95—432no—
287#95—862no—
288#95—861no—
289C24—21no—
290#41—1721no—
291#41—1721no—
292#41—1721no—
293#41—1721no—
294C2×Q8—861no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—861no—
299C2×D4—861no—
300C2×D4—861no—
301C2×D4—1721no—
302C2×D4#1062187312yes—
303C2×D4D34412yes—
304C2×D4(C2×D43)⋊C412yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—82no—
309C22×C4—861no—
310C22×C4—862no—
311C22×C4—861no—
312C22×C4—3442no—
313C22×C4—1724no—
314C22×C4—1724no—
315C22×C4—1721no—
316C22×C4C2×D17211yescharacteristic
317C22×C4D4×D4311yescharacteristic
318C22×C4D4×D4311yescharacteristic
319SD16—1724no—
320D8—1724no—
321M16—1721no—
322M16—1721no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—862no—
326C4⋊C4—21no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—3442no—
330C4⋊C4—1722no—
331C4⋊C4—1721no—
332C4⋊C4—1721no—
333C4⋊C4(C2×D43)⋊C412yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—1724no—
337C22⋊C4—1721no—
338C22⋊C4—1721no—
339C42—1721no—
340C42—1721no—
341C42C2×C4×D4311yescharacteristic
342C42#1062190011yescharacteristic
343C42#1062190011yescharacteristic
344C42C2×C22⋊D4311yescharacteristic
345C23—22no—
346C23—22no—
347C23—22no—
348C23—42no—
349C23—42no—
350C23—1721no—
351C23#1306329511yescharacteristic
352Q8—1721no—
353Q8—1721no—
354D4—22no—
355D4—22no—
356D4—22no—
357D4—3441no—
358D4—3441no—
359D4—3441no—
360D4—3441no—
361D4—1721no—
362D4—1721no—
363D4#1306324714yes—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—862no—
371C2×C4—3448no—
372C2×C4—3441no—
373C2×C4—3441no—
374C2×C4—1721no—
375C2×C4—1722no—
376C2×C4—1721no—
377C2×C4—1722no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1722no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4C2×(C2×D43)⋊C411yescharacteristic
384C2×C4(C22⋊D43)⋊C411yescharacteristic
385C2×C4(C22⋊D43)⋊C411yescharacteristic
386C2×C4#1306329711yescharacteristic
387C2×C4#1306329711yescharacteristic
388C2×C4#1306330911yescharacteristic
389C2×C4C2×D34411yescharacteristic
390C2×C4C2×#1062187311yescharacteristic
391C2×C4#1306335311yescharacteristic
392C2×C4#1306335811yescharacteristic
393C8—81no—
394C8—81no—
395C8—1722no—
396C22—21no—
397C22—21no—
398C22—24no—
399C22—44no—
400C22—44no—
401C22—42no—
402C22—42no—
403C22—3441no—
404C22—3441no—
405C22—3441no—
406C22#1458277611yescharacteristic
407C22#1458303511yescharacteristic
408C22#1458304011yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—42no—
414C4—3442no—
415C4—3441no—
416C4—3441no—
417C4—1722no—
418C4C2×#1306324711yescharacteristic
419C4#1458290111yescharacteristic
420C4#1458321311yescharacteristic
421C4#1458321811yescharacteristic
422C2—21no—
423C2—21no—
424C2—44no—
425C2—6881no—
426C2#1913491011yescharacteristic
427C2#1913508011yescharacteristic
428C2#1913509411yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1478C2
socleC22×C43#386
prime radical#19144059C2
cosocleC2×C42×C43C23
hypercenter#1478D43
hypocenterC43#9179
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #19137505C2semidirect
3. #19133156C2semidirect
4. #19133091C2semidirect
5. #19132497C2semidirect
6. #19132454C2semidirect
7. C43×#1478C2semidirect
12. #14583104C4semidirect
13. #14583094C4semidirect
36. #13063325C2×C4semidirect
37. #13063322C2×C4semidirect
51. C4⋊(C43⋊C8)C2×C4semidirect
212. #1478D43semidirect
243. C43#9179semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191440592
#191375052
#191331562
#191330912
#191324972
#191324542
C43×#14782
#917943