Finite Group Databasebeta

← #25251258

Subgroups — #25251258

Order 11008.

534 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145108C211yesmaximal, characteristic
2C4×Q16×D43C211yesmaximal, characteristic
3#19136760C211yesmaximal, characteristic, complemented
4#19136759C211yesmaximal, characteristic, complemented
5#19136756C211yesmaximal, characteristic, complemented
6#19136746C211yesmaximal, characteristic, complemented
7#19136745C211yesmaximal, characteristic, complemented
8#19136736C211yesmaximal, characteristic, complemented
9#19136735C211yesmaximal, characteristic, complemented
10#19136382C211yesmaximal, characteristic
11#19136380C211yesmaximal, characteristic
12#19136349C211yesmaximal, characteristic
13#19136313C211yesmaximal, characteristic
14#19136313C211yesmaximal, characteristic
15C43×#2229C211yesmaximal, characteristic, complemented
16C2×Q16×D43C2211yescharacteristic
17#14583455—21no—
18C4×Q8×D43—21no—
19C2×#13063264C2211yescharacteristic
20C2×#13063264C2211yescharacteristic
21#14583303C2211yescharacteristic
22#14583303C2211yescharacteristic
23#14583301C2211yescharacteristic
24#14583298—21no—
25#14583296—21no—
26C4×Dic172C2211yescharacteristic
27Q16×Dic43C2211yescharacteristic
28#14582993C2211yescharacteristic
29C4×#10621885—21no—
30#14582991—21no—
31#14582936C2211yescharacteristic
32#14582936C2211yescharacteristic
33#14582934—21no—
34#107×D43C2211yescharacteristic
35#103×D43—21no—
36C4×C8×D43C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582725C2211yescharacteristic
41#14582724C2211yescharacteristic
42#14582724C2211yescharacteristic
43C4⋊(C43⋊C16)C2211yescharacteristic
44Dic43⋊C16C2211yescharacteristic
45Dic43⋊C16C2211yescharacteristic
46#14582704C2211yescharacteristic
47#14582704C2211yescharacteristic
48#14582703C2211yescharacteristic
49#14582703C2211yescharacteristic
50#14582702C2211yescharacteristic
51#14582702C2211yescharacteristic
52C43×#499C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic
55C43×#366C2211yescharacteristic
56C43×C4⋊C16C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#358C2211yescharacteristic
59C2×Q8×D43—21no—
60C2×Dic172C2311yescharacteristic
61C2×#10621885—21no—
62Q16×D43—22no—
63Q16×D43Q814yescomplemented
64C2×C8×D43D411yescharacteristic
65C2×C8×D43C2311yescharacteristic
66#13063324—21no—
67#13063324—21no—
68#13063317—21no—
69#13063303—41no—
70#13063303—41no—
71Q8×Dic43—21no—
72C4×Dic86—21no—
73C4×Dic86—41no—
74#13063290—21no—
75#13063290—41no—
76#13063290—41no—
77#13063290—41no—
78#13063283—21no—
79#13063283—21no—
80C4⋊C4×D43—21no—
81C4⋊C4×D43—41no—
82C42×D43—41no—
83C42×D43D411yescharacteristic
84#13063264—22no—
85#13063264—22no—
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063259C2311yescharacteristic
90#13063259C2311yescharacteristic
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063257—21no—
95#13063256—21no—
96#13063256—21no—
97#13063250—21no—
98#13063249—21no—
99#13063248—21no—
100C4×C43⋊C8D411yescharacteristic
101C8×Dic43D411yescharacteristic
102C8×Dic43C2311yescharacteristic
103C2×Q16×C43C2311yescharacteristic
104#125×C43—21no—
105C4×Q8×C43—21no—
106C2×C16×C43C2311yescharacteristic
107C2×C16×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#106×C43—21no—
112#103×C43—21no—
113C4×C8×C43C2311yescharacteristic
114C2×Q8×C43—21no—
115Q8×D43—24no—
116Q8×D43—42no—
117C2×C4×D43—41no—
118C2×C4×D43—41no—
119C2×C4×D43D811yescharacteristic
120C2×C4×D43D811yescharacteristic
121C2×C4×D43C2×D411yescharacteristic
122C2×Dic86—21no—
123C2×Dic86—41no—
124C2×Dic86—41no—
125C2×Dic86—41no—
126Q16×C43—21no—
127Q16×C43C2×Q812yes—
128C2×C8×C43C2×D411yescharacteristic
129C2×C8×C43C2411yescharacteristic
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C42×C43—41no—
137C42×C43C2×D411yescharacteristic
138#10621885—24no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4—41no—
141C4⋊Dic43—21no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43—41no—
145Dic43⋊C4—41no—
146Dic43⋊C4—41no—
147Dic43⋊C4—41no—
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152C4×Dic43—41no—
153C4×Dic43—41no—
154C4×Dic43—41no—
155C4×Dic43—41no—
156C4×Dic43—41no—
157C4×Dic43D811yescharacteristic
158C4×Dic43D811yescharacteristic
159C4×Dic43C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162Dic172—21no—
163Dic172C2×Q812yes—
164C8×D43—22no—
165C8×D43C2×Q812yes—
166C8×D43#4112yes—
167C16×C43—21no—
168C16×C43—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C22×D43C2×D811yescharacteristic
172Q8×C43—22no—
173Q8×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43C2×D811yescharacteristic
179C2×C4×C43C2×D811yescharacteristic
180C2×C4×C43C22×D411yescharacteristic
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43C2×D811yescharacteristic
186C2×Dic43C2×D811yescharacteristic
187C2×Dic43C2×D811yescharacteristic
188C4×D43—22no—
189C4×D43—41no—
190C4×D43—44no—
191C4×D43—82no—
192C4×D43C22⋊Q812yes—
193C4×D43#13712yes—
194Dic86—22no—
195Dic86—41no—
196Dic86—44no—
197Dic86—82no—
198Dic86—82no—
199C8×C43—21no—
200C8×C43C22×Q811yescharacteristic
201C8×C43C2×#4111yescharacteristic
202C43⋊C8—21no—
203C43⋊C8C22⋊Q812yes—
204#33628—431nomaximal, Sylow
205C22×C43C22×D811yescharacteristic
206C2×D43—21no—
207C2×D43—21no—
208C2×D43#47412yes—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—42no—
212C4×C43—81no—
213C4×C43—81no—
214C4×C43—81no—
215C4×C43C2×C22⋊Q811yescharacteristic
216C4×C43C2×#13711yescharacteristic
217Dic43—21no—
218Dic43—42no—
219Dic43—81no—
220Dic43—81no—
221Dic43—81no—
222Dic43#47412yes—
223Dic43#51012yes—
224#3160—431no—
225C2×C4×Q16—431no—
226#2229—431no—
227#2229—431no—
228#2229—431no—
229#2229D4311yescharacteristic, complemented
230#2227—431no—
231#2227—431no—
232#2225—431no—
233#2225—431no—
234#2159—431no—
235#2159—431no—
236#2150—431no—
237#2141—431no—
238#2141—431no—
239C2×C43C2×#47411yescharacteristic
240C2×C43C2×#51011yescharacteristic
241C2×C43#341411yescharacteristic
242D43—22no—
243C22×Q16—431no—
244#533—861no—
245C2×C4×Q8—861no—
246C2×M32—431no—
247C2×M32—431no—
248#500—431no—
249#500—431no—
250#499—431no—
251#499—861no—
252#499C2×D4311yescharacteristic
253#498—861no—
254C4×Q16—431no—
255C4×Q16—431no—
256C4×Q16—431no—
257C4×Q16—861no—
258C4×Q16—861no—
259C4×Q16C2×D4311yescharacteristic
260#427—431no—
261#427—431no—
262#427—861no—
263C2×#107—431no—
264C2×#103—861no—
265C2×C4×C8—431no—
266#367—431no—
267#367—431no—
268#367—431no—
269#367C2×D4311yescharacteristic
270#366—431no—
271#366—431no—
272#366—431no—
273#366C2×D4311yescharacteristic
274C4⋊C16—431no—
275C4⋊C16—431no—
276C4⋊C16—431no—
277C4⋊C16C2×D4311yescharacteristic
278#358—431no—
279#358—431no—
280#358—431no—
281#358—431no—
282#358—431no—
283#358—431no—
284#358C2×D4311yescharacteristic
285#358C2×D4311yescharacteristic
286C43#3362811yescharacteristic, complemented, Sylow
287C22×Q8—861no—
288C2×Q16—434no—
289C2×Q16—431no—
290C2×Q16—862no—
291C2×Q16—861no—
292C2×Q16C22×D4311yescharacteristic
293C22×C8—431no—
294C22×C8—431no—
295C4⋊Q8—861no—
296C4⋊Q8—861no—
297#125—21no—
298#125—861no—
299C22⋊Q8—1721no—
300C22⋊Q8—1721no—
301C4×Q8—21no—
302C4×Q8—861no—
303C4×Q8—861no—
304C4×Q8—861no—
305C4×Q8—1721no—
306C4×Q8—1721no—
307C4×Q8—1721no—
308C4×Q8—1721no—
309#117—861no—
310#117—861no—
311C2×C4⋊C4—861no—
312C2×C4⋊C4—1721no—
313C2×C42—431no—
314C2×C42—1721no—
315M32—862no—
316M32—862no—
317C2×C16—431no—
318C2×C16—431no—
319C2×C16C22×D4311yescharacteristic
320C2×C16C22×D4311yescharacteristic
321#107—431no—
322#107—431no—
323#107—431no—
324#107—861no—
325#107—861no—
326#107—861no—
327#107C22×D4311yescharacteristic
328#107C22×D4311yescharacteristic
329#107C22×D4311yescharacteristic
330#106—21no—
331#106—861no—
332#106—861no—
333#106—861no—
334#103—21no—
335#103—861no—
336#103—861no—
337#103—861no—
338C4×C8—431no—
339C4×C8—431no—
340C4×C8—431no—
341C4×C8C22×D4311yescharacteristic
342C2×Q8—21no—
343C2×Q8—864no—
344C2×Q8—861no—
345C2×Q8—1721no—
346C2×Q8—1721no—
347C2×Q8—1721no—
348C2×Q8—1722no—
349C22×C4—431no—
350C22×C4—431no—
351C22×C4—431no—
352C22×C4—1721no—
353C22×C4—1721no—
354Q16—21no—
355Q16—432no—
356Q16—864no—
357Q16—861no—
358Q16Q8×D4312yes—
359C2×C8—431no—
360C2×C8—432no—
361C2×C8—432no—
362C2×C8—431no—
363C2×C8—862no—
364C2×C8D4×D4311yescharacteristic
365C2×C8C23×D4311yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—861no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—1721no—
376C4⋊C4—1721no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C22⋊C4—1721no—
384C22⋊C4—1721no—
385C42—41no—
386C42—431no—
387C42—431no—
388C42—431no—
389C42—1721no—
390C42—1721no—
391C42—1721no—
392C42—1721no—
393C42—1721no—
394C42D4×D4311yescharacteristic
395C16—21no—
396C16—21no—
397C16—861no—
398C16—861no—
399C23—431no—
400Q8—22no—
401Q8—41no—
402Q8—862no—
403Q8—3442no—
404Q8—3442no—
405Q8—1724no—
406Q8—1721no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—431no—
412C2×C4—431no—
413C2×C4—432no—
414C2×C4—432no—
415C2×C4—431no—
416C2×C4—862no—
417C2×C4—3442no—
418C2×C4—1721no—
419C2×C4—1724no—
420C2×C4—1721no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4D8×D4311yescharacteristic
425C2×C4D8×D4311yescharacteristic
426C2×C4C2×D4×D4311yescharacteristic
427C8—21no—
428C8—432no—
429C8—861no—
430C8C2×Q8×D4311yescharacteristic
431C8#41×D4311yescharacteristic
432C22—432no—
433C22—861no—
434C22—861no—
435C22C2×D8×D4311yescharacteristic
436C4—21no—
437C4—21no—
438C4—42no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—432no—
443C4—432no—
444C4—861no—
445C4—3441no—
446C4—3441no—
447C4—3441no—
448C4—1722no—
449C4C22⋊Q8×D4311yescharacteristic
450C4#137×D4311yescharacteristic
451C2—862no—
452C2#474×D4311yescharacteristic
453C2#510×D4311yescharacteristic
454C2#1914772811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2229C2
socleC22×C43C22×D8
prime radicalC22×D43C2×D8
hypercenter#2229D43
hypocenterC43#33628
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
3. #19136760C2semidirect
4. #19136759C2semidirect
5. #19136756C2semidirect
6. #19136746C2semidirect
7. #19136745C2semidirect
8. #19136736C2semidirect
9. #19136735C2semidirect
15. C43×#2229C2semidirect
63. Q16×D43Q8semidirect
229. #2229D43semidirect
286. C43#33628semidirect

Maximal subgroups

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

subgroupindex
#191451082
C4×Q16×D432
#191367602
#191367592
#191367562
#191367462
#191367452
#191367362
#191367352
#191363822
#191363802
#191363492
#191363132
C43×#22292
#3362843