Finite Group Databasebeta

← #24988446

Subgroups — #24988446

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147985C211yesmaximal, characteristic
2#19133253C211yesmaximal, characteristic, complemented
3#19133245C211yesmaximal, characteristic, complemented
4#19132997C211yesmaximal, characteristic, complemented
5#19132993C211yesmaximal, characteristic, complemented
6#19132909C211yesmaximal, characteristic, complemented
7C43×#1798C211yesmaximal, characteristic, complemented
8#14583520—21no—
9#14583520—21no—
10#14583511—21no—
11#14583504—21no—
12#14583496—21no—
13#14583496C412yes—
14#14583487—21no—
15#14583487C412yes—
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583427—22no—
19#14583427—22no—
20#14583410—21no—
21C4×#10621898—21no—
22#14582952C2211yescharacteristic
23#14582952C2211yescharacteristic
24#14582647—21no—
25#14582646—21no—
26#14582644—21no—
27#14582642—21no—
28#14582629—22no—
29#14582626—22no—
30#14582625—21no—
31#14582623—21no—
32C2×#117×C43C2211yescharacteristic
33C2×C4⋊C8×C43C2211yescharacteristic
34C2×C4⋊C8×C43C2211yescharacteristic
35C2×C22⋊C8×C43—21no—
36C43×#336—21no—
37C2×#10621898—21no—
38#13063325D411yescharacteristic
39#13063325D411yescharacteristic
40#13063325D411yescharacteristic
41#13063322D411yescharacteristic
42#13063320—22no—
43#13063320—22no—
44#13063318—22no—
45#13063318—22no—
46#13063317—21no—
47#13063315—22no—
48#13063315—22no—
49#13063313—21no—
50#13063311—22no—
51#13063311—22no—
52#13063310—22no—
53#13063310—22no—
54#13063308—22no—
55#13063307—22no—
56#13063307—22no—
57#13063304—21no—
58#13063304—21no—
59#13063304—21no—
60#13063304C2×C412yes—
61#13063303—22no—
62#13063303—22no—
63#13063299—21no—
64#13063299—21no—
65#13063299—21no—
66#13063299C2×C412yes—
67#13063298—22no—
68#13063298—22no—
69#13063294—22no—
70C4×Dic86—21no—
71C4×Dic86—21no—
72C4×Dic86—21no—
73C4×Dic86D412yes—
74C4×D172—21no—
75C4×D172—21no—
76C4×D172—21no—
77C4×D172D412yes—
78C4×C22⋊D43—22no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—22no—
81C4×C22⋊D43—22no—
82#13063284—21no—
83#13063282—22no—
84C42×D43—22no—
85C4⋊(C43⋊C8)—21no—
86C4⋊(C43⋊C8)—21no—
87C22⋊(C43⋊C8)—21no—
88C22⋊(C43⋊C8)—21no—
89C4×C43⋊C8—21no—
90C4×C43⋊C8—21no—
91C23×C4×C43D411yescharacteristic
92C22×C8×C43—21no—
93C22×C8×C43—21no—
94#117×C43—21no—
95#117×C43—21no—
96#117×C43—21no—
97#117×C43—21no—
98C2×C4⋊C4×C43C2×C411yescharacteristic
99C2×C4⋊C4×C43D411yescharacteristic
100C2×C22⋊C4×C43C2×C411yescharacteristic
101C2×C22⋊C4×C43D411yescharacteristic
102C2×C42×C43D411yescharacteristic
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43—21no—
105C4⋊C8×C43—21no—
106C4⋊C8×C43—21no—
107C4⋊C8×C43—21no—
108C22⋊C8×C43—42no—
109C24×C43C22⋊C411yescharacteristic
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43C22⋊C411yescharacteristic
117C22×C4×C43C22⋊C411yescharacteristic
118C22×C4×C43C22⋊C411yescharacteristic
119C22×C4×C43C22×C411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C2×C22⋊D43—22no—
123C2×C22⋊D43—22no—
124C2×C22⋊D43—22no—
125#10621898—41no—
126#10621898—41no—
127#10621898—41no—
128#10621898—41no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172C22⋊C412yes—
132C2×C4×D43—22no—
133C2×C4×D43—22no—
134C2×C4×D43—22no—
135C2×Dic86—21no—
136C2×Dic86—21no—
137C2×Dic86C22⋊C412yes—
138C2×C8×C43—41no—
139C2×C8×C43—41no—
140C2×C8×C43—41no—
141C2×C8×C43—41no—
142C2×C8×C43—41no—
143C2×C8×C43—41no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C22⋊C4×C43—21no—
149C22⋊C4×C43—21no—
150C22⋊C4×C43—21no—
151C22⋊C4×C43—21no—
152C42×C43—21no—
153C42×C43—21no—
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C22⋊Dic43—22no—
159C22⋊Dic43—22no—
160C22⋊Dic43—22no—
161(C2×D43)⋊C4—22no—
162(C2×D43)⋊C4—22no—
163(C2×D43)⋊C4—22no—
164(C2×D43)⋊C4—22no—
165(C2×D43)⋊C4—22no—
166(C2×D43)⋊C4—22no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43C22⋊C412yes—
172C4⋊Dic43C22⋊C412yes—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175Dic43⋊C4—22no—
176Dic43⋊C4—22no—
177Dic43⋊C4—22no—
178Dic43⋊C4—22no—
179C4×Dic43—22no—
180C4×Dic43—22no—
181C4×Dic43—22no—
182C2×C43⋊C8—41no—
183C2×C43⋊C8—41no—
184C23×C43—21no—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43C2×C22⋊C411yescharacteristic
190C22×D43—22no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43C2×C22⋊C411yescharacteristic
205C2×C4×C43C2×C22⋊C411yescharacteristic
206C2×C4×C43#12011yescharacteristic
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#13511yescharacteristic
211C2×C4×C43#13511yescharacteristic
212C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
213C2×C4×C43#13711yescharacteristic
214C22⋊D43—42no—
215C22⋊D43—42no—
216C22⋊D43—82no—
217C22⋊D43—82no—
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—22no—
221D172—42no—
222D172—41no—
223D172—41no—
224D172—81no—
225C4×D43—42no—
226C4×D43—42no—
227C4×D43—82no—
228C4×D43—82no—
229Dic86—41no—
230Dic86—41no—
231Dic86—42no—
232Dic86—81no—
233C8×C43—81no—
234C8×C43—81no—
235C43⋊C8—81no—
236C43⋊C8—81no—
237#8411—431nomaximal, Sylow
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—42no—
241C22×C43—41no—
242C22×C43—41no—
243C22×C43—41no—
244C22×C43—81no—
245C22×C43#37911yescharacteristic
246C22×C43#41611yescharacteristic
247C22×C43#41711yescharacteristic
248C2×D43—42no—
249C2×D43—42no—
250C2×D43—42no—
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43#44911yescharacteristic
259C4×C43#44911yescharacteristic
260C4×C43#45211yescharacteristic
261C4×C43#45211yescharacteristic
262Dic43—42no—
263Dic43—42no—
264Dic43—42no—
265#3455—431no—
266#1798D4311yescharacteristic, complemented
267#1542—431no—
268#1540—431no—
269#1481—431no—
270#1480—431no—
271#1458—431no—
272C2×C43—21no—
273C2×C43—21no—
274C2×C43—81no—
275C2×C43#178811yescharacteristic
276C2×C43#179111yescharacteristic
277C2×C43#179411yescharacteristic
278D43—82no—
279#542—861no—
280#542—861no—
281#541—861no—
282#540—861no—
283#539—432no—
284#539—861no—
285#538—432no—
286#538—861no—
287#533—431no—
288#532—431no—
289#529—862no—
290#529—862no—
291#525—861no—
292C4×#41—861no—
293C2×#117C2×D4311yescharacteristic
294#431—431no—
295#431—431no—
296C2×C4⋊C8C2×D4311yescharacteristic
297C2×C4⋊C8C2×D4311yescharacteristic
298C2×C22⋊C8—21no—
299#336—21no—
300#333—861no—
301#332—861no—
302#332—861no—
303#331—861no—
304Q8⋊C8—862no—
305D4⋊C8—862no—
306#324—861no—
307#323—861no—
308C43#841111yescharacteristic, complemented, Sylow
309C2×#41—861no—
310C23×C4C22⋊D4311yescharacteristic
311C22×C8—21no—
312C22×C8—21no—
313C4⋊Q8—431no—
314C4⋊Q8—431no—
315C4⋊Q8—431no—
316#127—431no—
317#126—862no—
318#126—862no—
319#126—862no—
320#126—862no—
321#125—862no—
322#125—862no—
323#125—861no—
324#124—862no—
325#124—862no—
326#124—861no—
327#123—862no—
328#123—862no—
329#123—862no—
330#123—862no—
331#123—862no—
332C22⋊Q8—432no—
333C22⋊Q8—862no—
334C22⋊Q8—862no—
335C22⋊Q8—861no—
336C22⋊Q8—861no—
337C22⋊Q8—861no—
338#121—432no—
339#121—862no—
340#121—862no—
341#121—861no—
342#121—861no—
343#121—861no—
344#120—862no—
345C4×Q8—432no—
346C4×Q8—861no—
347C4×Q8—861no—
348C4×Q8—861no—
349C4×D4—432no—
350C4×D4—861no—
351C4×D4—861no—
352C4×D4—862no—
353C4×D4—862no—
354C4×D4—862no—
355C4×D4—862no—
356C4×D4—861no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—862no—
362#117—861no—
363C2×C4⋊C4C4×D4311yescharacteristic
364C2×C4⋊C4D17211yescharacteristic
365C2×C22⋊C4C4×D4311yescharacteristic
366C2×C22⋊C4D17211yescharacteristic
367C2×C42—862no—
368C2×C42C22⋊D4311yescharacteristic
369C2×C42C22×D4311yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—861no—
375C4⋊C8—861no—
376C22⋊C8—42no—
377C22⋊C8—861no—
378C22⋊C8—861no—
379C4×C8—861no—
380C4×C8—861no—
381C24(C2×D43)⋊C411yescharacteristic
382#41—1721no—
383#41—1721no—
384#41—1721no—
385#41—1721no—
386C2×Q8—432no—
387C2×Q8—861no—
388C2×Q8—861no—
389C2×D4—432no—
390C2×D4—862no—
391C2×D4—862no—
392C2×D4—862no—
393C2×D4—861no—
394C2×D4—861no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—862no—
402C22×C4—862no—
403C22×C4—862no—
404C22×C4(C2×D43)⋊C411yescharacteristic
405C22×C4(C2×D43)⋊C411yescharacteristic
406C22×C4(C2×D43)⋊C411yescharacteristic
407C22×C4C2×C4×D4311yescharacteristic
408C22×C4C2×D17211yescharacteristic
409C22×C4C2×C22⋊D4311yescharacteristic
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—1721no—
417C2×C8—1721no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—432no—
423C4⋊C4—432no—
424C4⋊C4—862no—
425C4⋊C4—862no—
426C4⋊C4—862no—
427C4⋊C4—862no—
428C4⋊C4—862no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C4⋊C4—862no—
433C4⋊C4—861no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—862no—
439C22⋊C4—862no—
440C22⋊C4—862no—
441C22⋊C4—862no—
442C22⋊C4—862no—
443C22⋊C4—862no—
444C22⋊C4—862no—
445C22⋊C4—862no—
446C22⋊C4—862no—
447C42—21no—
448C42—21no—
449C42—862no—
450C42—862no—
451C42—862no—
452C42D4×D4311yescharacteristic
453C42D4×D4311yescharacteristic
454C42D4×D4311yescharacteristic
455C42D4×D4311yescharacteristic
456C23—21no—
457C23—21no—
458C23—21no—
459C23—41no—
460C23—41no—
461C23—862no—
462C23C2×(C2×D43)⋊C411yescharacteristic
463Q8—3441no—
464Q8—1722no—
465Q8—1721no—
466Q8—1721no—
467D4—3441no—
468D4—3442no—
469D4—3442no—
470D4—1722no—
471D4—1722no—
472D4—1722no—
473D4—1721no—
474D4—1721no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—862no—
489C2×C4—862no—
490C2×C4—862no—
491C2×C4—3442no—
492C2×C4—3442no—
493C2×C4—1722no—
494C2×C4—1722no—
495C2×C4C22⋊C4×D4311yescharacteristic
496C2×C4C22⋊C4×D4311yescharacteristic
497C2×C4#1306329311yescharacteristic
498C2×C4#1306329311yescharacteristic
499C2×C4#1306329511yescharacteristic
500C2×C4#1306329511yescharacteristic
501C2×C4#1306334511yescharacteristic
502C2×C4#1306334511yescharacteristic
503C2×C4#1306335111yescharacteristic
504C2×C4#1306335611yescharacteristic
505C8—81no—
506C8—81no—
507C8—3441no—
508C8—3441no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—81no—
516C22—1722no—
517C22—1722no—
518C22—1722no—
519C22#1458275411yescharacteristic
520C22#1458289311yescharacteristic
521C22#1458289811yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—1722no—
530C4—1722no—
531C4—1722no—
532C4#1458304211yescharacteristic
533C4#1458304211yescharacteristic
534C4#1458305911yescharacteristic
535C4#1458305911yescharacteristic
536C2—21no—
537C2—21no—
538C2—81no—
539C2—3442no—
540C2#1913453311yescharacteristic
541C2#1913454511yescharacteristic
542C2#1913455811yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1798C2
socleC22×C43#379
prime radical#19147985C2
cosocleC2×C42×C43C23
hypercenter#1798D43
hypocenterC43#8411
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #19133253C2semidirect
3. #19133245C2semidirect
4. #19132997C2semidirect
5. #19132993C2semidirect
6. #19132909C2semidirect
7. C43×#1798C2semidirect
266. #1798D43semidirect
308. C43#8411semidirect

Maximal subgroups

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

subgroupindex
#191479852
#191332532
#191332452
#191329972
#191329932
#191329092
C43×#17982
#841143