Finite Group Databasebeta

← #25082081

Subgroups — #25082081

Order 11008.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144078C211yesmaximal, characteristic, complemented
2#19144044C211yesmaximal, characteristic
3#19143703C211yesmaximal, characteristic, complemented
4#19134036C212yesmaximal, complemented
5#19134029C212yesmaximal, complemented
6#19133986C212yesmaximal, complemented
7#19133981C212yesmaximal, complemented
8#19133370C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10C2×#14582645C211yesmaximal, characteristic, complemented
11C43×#3226C211yesmaximal, characteristic, complemented
12C2×#13063356—21no—
13C2×#13063345—21no—
14C4×#10621898C2211yescharacteristic
15#14583118—21no—
16#14583111—21no—
17#14583106—21no—
18#14583106C2211yescharacteristic
19#14583106C2212yes—
20#14583101—21no—
21#14583101C2211yescharacteristic
22#14583101C2212yes—
23#14583096C2211yescharacteristic
24#14583091C2211yescharacteristic
25C8×Dic86C2212yes—
26C8×D172C2212yes—
27(C22⋊D43)⋊C8—22no—
28#14582951—21no—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C4⋊C8×D43—21no—
33#14582908—21no—
34#14582895—21no—
35#14582652C2212yes—
36#14582652C2212yes—
37#14582645C2212yes—
38#14582645C2212yes—
39#14582645C2212yes—
40#14582643C2212yes—
41C43×#532C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#500C2212yes—
44C43×#486C2212yes—
45C43×#480—22no—
46C43×#474—21no—
47C43×#474—21no—
48C43×#431C2211yescharacteristic
49C2×#10621898D411yescharacteristic
50#13063356—44no—
51#13063345—44no—
52C2×#10621885—22no—
53C2×#10621885—21no—
54C2×#10621883—21no—
55C2×#10621884—22no—
56C2×#10621884—21no—
57C2×#10621882—21no—
58C2×#10621877—21no—
59C22×C43⋊C8—21no—
60C22×C43⋊C8—21no—
61C2×C8×D43—22no—
62C4×Dic86D411yescharacteristic
63C4×Dic86C2311yescharacteristic
64C4×D172D411yescharacteristic
65C4×D172C2311yescharacteristic
66C4×C22⋊D43—21no—
67C4×C22⋊D43—21no—
68#13063284D411yescharacteristic
69#13063282—21no—
70C42×D43—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)—21no—
74C4⋊(C43⋊C8)C2311yescharacteristic
75C4⋊(C43⋊C8)C2311yescharacteristic
76C4⋊(C43⋊C8)C2312yes—
77C4⋊(C43⋊C8)C2312yes—
78Dic43⋊C8—22no—
79#13063249—22no—
80#13063249—22no—
81#13063249—21no—
82#13063249—21no—
83#13063246—21no—
84#13063246—21no—
85(C2×D43)⋊C8—22no—
86C8×Dic43—22no—
87C2×#41×C43—21no—
88C22×Q8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43C2311yescharacteristic
93C4⋊Q8×C43C2312yes—
94#127×C43C2311yescharacteristic
95#124×C43—21no—
96#121×C43—21no—
97#121×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C42×C43C2311yescharacteristic
103#107×C43—22no—
104#107×C43—22no—
105C4⋊C8×C43D411yescharacteristic
106C4⋊C8×C43D411yescharacteristic
107#102×C43—22no—
108#102×C43—22no—
109C22⋊C8×C43D412yes—
110C4×C8×C43C2312yes—
111#41×C43—42no—
112#41×C43—42no—
113C2×Q8×C43—21no—
114C2×Q8×C43—22no—
115C2×Q8×C43—41no—
116C2×Q8×C43—42no—
117C2×Q8×C43—42no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C2×C22⋊D43—21no—
128#10621898—22no—
129#10621898D814yes—
130C2×D172C2×D411yescharacteristic
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×Dic86C2×D411yescharacteristic
135C2×C8×C43C2×D412yes—
136C2×C8×C43C2×D412yes—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—41no—
142C4⋊C4×C43—41no—
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C42×C43C2×D411yescharacteristic
146C42×C43C2×D411yescharacteristic
147C42×C43#4111yescharacteristic
148C42×C43C2411yescharacteristic
149C22⋊Dic43—21no—
150#10621885—42no—
151#10621885—44no—
152#10621884—42no—
153#10621884—44no—
154#10621883—42no—
155#10621882—42no—
156(C2×D43)⋊C4—21no—
157(C2×D43)⋊C4—21no—
158C4⋊Dic43C2×D411yescharacteristic
159C4⋊Dic43C2×D411yescharacteristic
160Dic43⋊C4—21no—
161Dic43⋊C4—21no—
162C4×Dic43—21no—
163C4×Dic43—21no—
164C4×Dic43—21no—
165#10621877—42no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8—21no—
168C2×C43⋊C8—21no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—42no—
171C2×C43⋊C8—81no—
172C8×D43—82no—
173C23×C43—41no—
174C23×C43#12111yescharacteristic
175C22×D43—21no—
176Q8×C43—42no—
177Q8×C43—41no—
178Q8×C43—42no—
179Q8×C43—41no—
180Q8×C43—82no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—81no—
186D4×C43—82no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—42no—
192C2×C4×C43—82no—
193C2×C4×C43—82no—
194C2×C4×C43#12111yescharacteristic
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43C2×D812yes—
198C2×C4×C43#13512yes—
199C2×C4×C43C22×D411yescharacteristic
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C2×#4111yescharacteristic
202C22⋊D43—24no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206D172—21no—
207D172C2×D812yes—
208C4×D43—24no—
209C4×D43—41no—
210C4×D43—41no—
211C4×D43—81no—
212Dic86—21no—
213Dic86C2×D812yes—
214C8×C43—22no—
215C8×C43—22no—
216C43⋊C8—41no—
217C43⋊C8—41no—
218C43⋊C8—42no—
219C43⋊C8—42no—
220#19416—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43#46612yes—
227C22×C43C2×#12111yescharacteristic
228C2×D43—22no—
229C2×D43—41no—
230C2×D43—41no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—81no—
235C4×C43—82no—
236C4×C43#46612yes—
237C4×C43C22×D811yescharacteristic
238C4×C43C2×#13511yescharacteristic
239C4×C43#57711yescharacteristic
240C4×C43#57811yescharacteristic
241Dic43—22no—
242Dic43—41no—
243Dic43—41no—
244#3226D4311yescharacteristic, complemented
245#3039—431no—
246#3035—431no—
247#2988—431no—
248#1682—432no—
249#1681—432no—
250#1674—432no—
251#1673—432no—
252#1571—431no—
253#1547—431no—
254C2×#332—431no—
255C2×C43—22no—
256C2×C43—161no—
257C2×C43#304611yescharacteristic
258C2×C43C2×#46611yescharacteristic
259C2×C43#306911yescharacteristic
260D43—42no—
261C2×#137—861no—
262C2×#135—861no—
263#532C2×D4311yescharacteristic
264C2×C4⋊Q8C2×D4311yescharacteristic
265C4×#41—431no—
266#500C2×D4312yes—
267#486C2×D4312yes—
268#480—22no—
269#474—21no—
270#474—21no—
271#464—861no—
272#463—861no—
273#462—431no—
274#462—432no—
275#462—861no—
276#461—431no—
277#461—432no—
278#461—861no—
279#460—431no—
280#459—431no—
281C8×Q8—432no—
282C8×D4—432no—
283C8×D4—862no—
284#431—861no—
285#431C2×D4311yescharacteristic
286#423—431no—
287C2×C4⋊C8—431no—
288C2×C4⋊C8—431no—
289C2×C4⋊C8—861no—
290#419—861no—
291#416—861no—
292#335—432no—
293#335—432no—
294#332—432no—
295#332—432no—
296#332—432no—
297#331—432no—
298C43#1941611yescharacteristic, complemented, Sylow
299C2×#41—21no—
300C2×#41—431no—
301C22×Q8—21no—
302#137—1724no—
303#135—1724no—
304C2×Q16—861no—
305C2×Q16—862no—
306C2×SD16—861no—
307C2×SD16—861no—
308C2×SD16—862no—
309C2×D8—861no—
310C2×M16—861no—
311C22×C8—861no—
312C22×C8—861no—
313C22×C8—862no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8C22×D4312yes—
318C4⋊Q8C22×D4311yescharacteristic
319#127C22×D4311yescharacteristic
320#124—21no—
321#121—21no—
322#121—21no—
323C4×Q8—431no—
324C4×Q8—431no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—431no—
328C4×D4—431no—
329C4×D4—861no—
330C4×D4—861no—
331#117—431no—
332#117—861no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C42—861no—
336C2×C42C22×D4311yescharacteristic
337#107—22no—
338#107—22no—
339C4⋊C8—432no—
340C4⋊C8—432no—
341C4⋊C8—431no—
342C4⋊C8—431no—
343C4⋊C8—862no—
344C4⋊C8—861no—
345C4⋊C8—861no—
346C4⋊C8—861no—
347C4⋊C8C22⋊D4311yescharacteristic
348C4⋊C8C22⋊D4311yescharacteristic
349#103—861no—
350#103—861no—
351#103—862no—
352#103—862no—
353#102—22no—
354#102—22no—
355#102—861no—
356#102—861no—
357C22⋊C8—862no—
358C22⋊C8C22⋊D4312yes—
359C4×C8—862no—
360C4×C8C22×D4312yes—
361#41—42no—
362#41—42no—
363#41—434no—
364#41—862no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—41no—
368C2×Q8—42no—
369C2×Q8—42no—
370C2×Q8—431no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—41no—
375C2×D4—431no—
376C2×D4—861no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—861no—
380C22×C4—861no—
381C22×C4—861no—
382C22×C4D4×D4311yescharacteristic
383C22×C4#1062190011yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385Q16—1722no—
386Q16—1724no—
387SD16—1722no—
388SD16—1722no—
389SD16—1724no—
390D8—1722no—
391M16—1722no—
392C2×C8—861no—
393C2×C8—861no—
394C2×C8—862no—
395C2×C8—862no—
396C2×C8—3442no—
397C2×C8—3441no—
398C2×C8—1722no—
399C2×C8C2×C22⋊D4312yes—
400C2×C8C2×C22⋊D4312yes—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—431no—
408C4⋊C4—431no—
409C4⋊C4—861no—
410C4⋊C4—861no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—861no—
414C22⋊C4—861no—
415C22⋊C4—861no—
416C42—861no—
417C42—861no—
418C42—861no—
419C42D4×D4311yescharacteristic
420C42#1062190011yescharacteristic
421C42C2×C22⋊D4311yescharacteristic
422C42C23×D4311yescharacteristic
423C23—41no—
424C23—861no—
425C23#1306329611yescharacteristic
426Q8—42no—
427Q8—41no—
428Q8—42no—
429Q8—41no—
430Q8—82no—
431Q8—432no—
432Q8—861no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4—432no—
440D4—864no—
441D4—861no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—861no—
450C2×C4—864no—
451C2×C4—861no—
452C2×C4—861no—
453C2×C4—3441no—
454C2×C4—1721no—
455C2×C4—1721no—
456C2×C4#1306329611yescharacteristic
457C2×C4#1306329611yescharacteristic
458C2×C4#1306329611yescharacteristic
459C2×C4D8×D4312yes—
460C2×C4#1306334412yes—
461C2×C4C2×D4×D4311yescharacteristic
462C2×C4C22×C22⋊D4311yescharacteristic
463C2×C4C2×#1062190011yescharacteristic
464C8—22no—
465C8—22no—
466C8—1721no—
467C8—1721no—
468C8—1722no—
469C8—1722no—
470C22—21no—
471C22—21no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—862no—
476C22—1721no—
477C22—1721no—
478C22#1458313212yes—
479C22C2×#1306329611yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—81no—
484C4—82no—
485C4—862no—
486C4—1721no—
487C4—1721no—
488C4#1458313212yes—
489C4C2×D8×D4311yescharacteristic
490C4C2×#1306334411yescharacteristic
491C4#1458370711yescharacteristic
492C4#1458371411yescharacteristic
493C2—22no—
494C2—161no—
495C2—1722no—
496C2#1914414111yescharacteristic
497C2C2×#1458313211yescharacteristic
498C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3226C2
socleC22×C43C2×#121
prime radical#19144044C2
hypercenter#3226D43
hypocenterC43#19416
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
1. #19144078C2semidirect
3. #19143703C2semidirect
4. #19134036C2semidirect
5. #19134029C2semidirect
6. #19133986C2semidirect
7. #19133981C2semidirect
8. #19133370C2semidirect
9. #19133272C2semidirect
10. C2×#14582645C2semidirect
11. C43×#3226C2semidirect
244. #3226D43semidirect
298. C43#19416semidirect

Maximal subgroups

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

subgroupindex
#191440782
#191440442
#191437032
#191340362
#191340292
#191339862
#191339812
#191333702
#191332722
C2×#145826452
C43×#32262
#1941643