Finite Group Databasebeta

← #25072671

Subgroups — #25072671

Order 11008.

1048 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145052C211yesmaximal, characteristic, complemented
2#19144717C211yesmaximal, characteristic, complemented
3#19144686C211yesmaximal, characteristic
4#19133729C214yesmaximal, complemented
5#19133667C214yesmaximal, complemented
6#19133321C211yesmaximal, characteristic, complemented
7#19133042C211yesmaximal, characteristic, complemented
8#19133038C211yesmaximal, characteristic, complemented
9C2×C43×#554C211yesmaximal, characteristic, complemented
10C2×#13063356—22no—
11#14583449C2211yescharacteristic
12#14583291—22no—
13#14583278C2212yescomplemented
14#14583273C2212yescomplemented
15#14583217—21no—
16#14583212—21no—
17#14583194C2212yescomplemented
18#14583189C2212yes—
19#14583099C2212yescomplemented
20#14583094C2212yes—
21#14583038—21no—
22#14583033—21no—
23#14583009—22no—
24#14582997—22no—
25#14582956C2211yescharacteristic
26#14582956C2211yescharacteristic
27C4×#10621877C2211yescharacteristic
28#14582648C2214yescomplemented
29Q8⋊(C43⋊C8)C2214yescomplemented
30D4⋊(C43⋊C8)C2214yes—
31C43×#554—22no—
32C43×#554—22no—
33C43×#554—22no—
34C43×#554C2214yes—
35C2×C4⋊Q8×C43C2211yescharacteristic
36C2×#125×C43—21no—
37C2×C22⋊Q8×C43—21no—
38C2×C22⋊Q8×C43—22no—
39C2×C4×Q8×C43C2211yescharacteristic
40C2×C4×D4×C43—21no—
41C2×C4×D4×C43C2211yescharacteristic
42C22×C4⋊C4×C43—21no—
43C2×#10621898—21no—
44#13063356—48no—
45C2×#10621885—24no—
46C2×#10621884—22no—
47C2×#10621884—24no—
48C2×#10621882—22no—
49C2×#10621877—21no—
50#13063325C2311yescharacteristic
51#13063322C2311yescharacteristic
52#13063313—21no—
53#13063299—21no—
54#13063299—21no—
55C4×D172—21no—
56C4×D172—21no—
57#13063258—22no—
58#13063256—22no—
59C4⋊(C43⋊C8)C2312yes—
60C4⋊(C43⋊C8)C2312yes—
61#13063249—22no—
62#13063246—22no—
63#13063245—22no—
64#13063245—22no—
65C22⋊(C43⋊C8)—21no—
66C22⋊(C43⋊C8)—21no—
67#13063236—21no—
68#13063236—21no—
69#13063236—21no—
70C4×C43⋊C8C2312yes—
71C22×Q8×C43D411yescharacteristic
72C22×Q8×C43D412yes—
73C22×D4×C43D411yescharacteristic
74C23×C4×C43—22no—
75C23×C4×C43—21no—
76C4⋊Q8×C43—21no—
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43D412yes—
79C4⋊Q8×C43C2312yes—
80#125×C43—24no—
81#125×C43—24no—
82C22⋊Q8×C43—24no—
83C22⋊Q8×C43—28no—
84C22⋊Q8×C43—24no—
85C22⋊Q8×C43—28no—
86C4×Q8×C43—21no—
87C4×Q8×C43—21no—
88C4×Q8×C43D412yes—
89C4×Q8×C43C2312yes—
90C4×D4×C43—24no—
91C4×D4×C43—24no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43D412yes—
95C4×D4×C43C2312yes—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—24no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—24no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43C2311yescharacteristic
109C24×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—42no—
113C2×Q8×C43—44no—
114C2×Q8×C43C2×D412yes—
115C2×Q8×C43C2×D414yes—
116C2×D4×C43—24no—
117C2×D4×C43—21no—
118C2×D4×C43C2×D412yes—
119C22×C4×C43—28no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—44no—
127C22×C4×C43—84no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C2×C22⋊D43—41no—
132#10621898—44no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×C4×D43—41no—
137C2×Dic86—21no—
138C4⋊C4×C43—28no—
139C4⋊C4×C43—28no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43C2×D412yes—
149C4⋊C4×C43C2×D412yes—
150C22⋊C4×C43—28no—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—22no—
153C42×C43—22no—
154C42×C43—22no—
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C42×C43C2411yescharacteristic
159#10621885—48no—
160#10621884—48no—
161#10621884—44no—
162#10621882—44no—
163(C2×D43)⋊C4—41no—
164(C2×D43)⋊C4—41no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167#10621877—24no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C23×C43—24no—
172C23×C43—22no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43#12011yescharacteristic
176C22×D43—41no—
177Q8×C43—22no—
178Q8×C43—22no—
179Q8×C43—44no—
180Q8×C43—42no—
181Q8×C43—82no—
182D4×C43—24no—
183D4×C43—22no—
184D4×C43#13714yescomplemented
185C2×C4×C43—22no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—24no—
192C2×C4×C43—44no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—44no—
197C2×C4×C43—44no—
198C2×C4×C43—88no—
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#12011yescharacteristic
201C2×C4×C43#12011yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C22⋊D43—82no—
206C2×Dic43—41no—
207D172—42no—
208D172—42no—
209D172—42no—
210C4×D43—82no—
211Dic86—42no—
212C43⋊C8—24no—
213C43⋊C8—42no—
214C43⋊C8—42no—
215#18525—431nomaximal, Sylow
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—24no—
219C22×C43—48no—
220C22×C43—42no—
221C22×C43—42no—
222C22×C43#45312yes—
223C22×C43C2×#12011yescharacteristic
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—42no—
232C4×C43—42no—
233C4×C43—42no—
234C4×C43—44no—
235C4×C43C2×#13712yes—
236C4×C43#57512yes—
237Dic43—81no—
238C2×#554D4311yescharacteristic, complemented
239#3152—431no—
240#3112—431no—
241#3109—431no—
242#1632—434no—
243#1622—434no—
244#1558—431no—
245#1491—431no—
246#1490—431no—
247C2×C43—22no—
248C2×C43—44no—
249C2×C43#300411yescharacteristic
250C2×C43#300511yescharacteristic
251C2×C43C2×#45311yescharacteristic
252D43—161no—
253C2×#137—862no—
254#554—22no—
255#554—22no—
256#554—22no—
257#554C2×D4314yes—
258#532—431no—
259C2×C4⋊Q8C2×D4311yescharacteristic
260C2×#125—21no—
261C2×C22⋊Q8—21no—
262C2×C22⋊Q8—22no—
263C2×C4×Q8C2×D4311yescharacteristic
264C2×C4×D4—21no—
265C2×C4×D4C2×D4311yescharacteristic
266C22×C4⋊C4—21no—
267#497—862no—
268#494—432no—
269#492—432no—
270#481—861no—
271#480—861no—
272#477—432no—
273#476—432no—
274#460—432no—
275#459—432no—
276#448—861no—
277#447—861no—
278#442—862no—
279#440—862no—
280#432—431no—
281#432—431no—
282C4×M16—431no—
283#333—434no—
284Q8⋊C8—434no—
285D4⋊C8—434no—
286C43#1852511yescharacteristic, complemented, Sylow
287C2×#41—861no—
288C22×Q8C22⋊D4311yescharacteristic
289C22×Q8C22⋊D4312yes—
290C22×D4C22⋊D4311yescharacteristic
291C23×C4—22no—
292C23×C4—21no—
293#137—1728no—
294C2×Q16—864no—
295C2×SD16—864no—
296C2×SD16—862no—
297C2×D8—862no—
298C2×M16—861no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—431no—
302C4⋊Q8C22⋊D4312yes—
303C4⋊Q8C22×D4312yes—
304#127—431no—
305#125—24no—
306#125—24no—
307#124—861no—
308C22⋊Q8—24no—
309C22⋊Q8—28no—
310C22⋊Q8—24no—
311C22⋊Q8—28no—
312#121—861no—
313#121—861no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8C22⋊D4312yes—
317C4×Q8C22×D4312yes—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—861no—
323C4×D4—861no—
324C4×D4C22⋊D4312yes—
325C4×D4C22×D4312yes—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4C22⋊D4311yescharacteristic
334C2×C4⋊C4C22⋊D4311yescharacteristic
335C2×C22⋊C4—22no—
336C2×C22⋊C4—21no—
337C2×C42—21no—
338C2×C42C22×D4311yescharacteristic
339#107—862no—
340#106—862no—
341C4⋊C8—432no—
342C4⋊C8—432no—
343#103—862no—
344#102—862no—
345#102—862no—
346#102—862no—
347C22⋊C8—861no—
348C22⋊C8—861no—
349#97—861no—
350#97—861no—
351#97—861no—
352C4×C8—432no—
353C24—21no—
354#41—1724no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—42no—
358C2×Q8—44no—
359C2×Q8—861no—
360C2×Q8C2×C22⋊D4312yes—
361C2×Q8C2×C22⋊D4314yes—
362C2×D4—24no—
363C2×D4—21no—
364C2×D4—861no—
365C2×D4—861no—
366C2×D4—861no—
367C2×D4—1721no—
368C2×D4C2×C22⋊D4312yes—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—28no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—44no—
377C22×C4—84no—
378C22×C4—1721no—
379C22×C4C2×C22⋊D4311yescharacteristic
380C22×C4C2×C22⋊D4311yescharacteristic
381C22×C4C2×C22⋊D4311yescharacteristic
382Q16—1728no—
383SD16—1728no—
384SD16—1724no—
385D8—1724no—
386M16—864no—
387C2×C8—862no—
388C2×C8—862no—
389C2×C8—862no—
390C4⋊C4—28no—
391C4⋊C4—28no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—861no—
401C4⋊C4—861no—
402C4⋊C4C2×C22⋊D4312yes—
403C4⋊C4C2×C22⋊D4312yes—
404C22⋊C4—28no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—1721no—
408C22⋊C4—1721no—
409C42—22no—
410C42—22no—
411C42C2×C22⋊D4311yescharacteristic
412C42C2×C22⋊D4311yescharacteristic
413C42C2×C22⋊D4311yescharacteristic
414C42C23×D4311yescharacteristic
415C23—24no—
416C23—22no—
417C23—42no—
418C23—42no—
419C23—1721no—
420C23#1306329411yescharacteristic
421Q8—22no—
422Q8—22no—
423Q8—44no—
424Q8—42no—
425Q8—82no—
426Q8—1722no—
427D4—24no—
428D4—22no—
429D4—3442no—
430D4—1722no—
431D4—1722no—
432D4—1722no—
433D4#1306335614yescomplemented
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—88no—
448C2×C4—3442no—
449C2×C4—1721no—
450C2×C4#1306329411yescharacteristic
451C2×C4#1306329411yescharacteristic
452C2×C4#1306329411yescharacteristic
453C2×C4C22×C22⋊D4311yescharacteristic
454C2×C4C22×C22⋊D4311yescharacteristic
455C2×C4C22×C22⋊D4311yescharacteristic
456C8—864no—
457C8—1722no—
458C8—1722no—
459C22—21no—
460C22—21no—
461C22—24no—
462C22—48no—
463C22—42no—
464C22—42no—
465C22—3441no—
466C22—3441no—
467C22—3441no—
468C22#1458306712yes—
469C22C2×#1306329411yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—44no—
478C4—3441no—
479C4C2×#1306335612yes—
480C4#1458369712yes—
481C2—22no—
482C2—44no—
483C2—6881no—
484C2#1914382911yescharacteristic
485C2#1914383711yescharacteristic
486C2C2×#1458306711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#554C2
socleC22×C43C2×#120
prime radical#19144686C2
hypercenterC2×#554D43
hypocenterC43#18525
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #19145052C2semidirect
2. #19144717C2semidirect
4. #19133729C2semidirect
5. #19133667C2semidirect
6. #19133321C2semidirect
7. #19133042C2semidirect
8. #19133038C2semidirect
9. C2×C43×#554C2semidirect
13. #14583278C22semidirect
14. #14583273C22semidirect
17. #14583194C22semidirect
19. #14583099C22semidirect
28. #14582648C22semidirect
29. Q8⋊(C43⋊C8)C22semidirect
184. D4×C43#137semidirect
238. C2×#554D43semidirect
286. C43#18525semidirect
433. D4#13063356semidirect

Maximal subgroups

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

subgroupindex
#191450522
#191447172
#191446862
#191337292
#191336672
#191333212
#191330422
#191330382
C2×C43×#5542
#1852543