Finite Group Databasebeta

← #24993644

Subgroups — #24993644

Order 11008.

678 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143855C211yesmaximal, characteristic
2#19143044C211yesmaximal, characteristic
3#19133166C211yesmaximal, characteristic, complemented
4#19132958C211yesmaximal, characteristic, complemented
5#19132501C211yesmaximal, characteristic, complemented
6#19132483C211yesmaximal, characteristic, complemented
7C43×#1788C211yesmaximal, characteristic
8C2×#13063355C411yescharacteristic, complemented
9C2×#13063355C411yescharacteristic, complemented
10C2×#13063332—21no—
11C2×#13063304C2211yescharacteristic
12#14583061—21no—
13#14583061—21no—
14#14583055—21no—
15#14583050—21no—
16#14582900C411yescharacteristic, complemented
17#14582900C411yescharacteristic, complemented
18#14582866—22no—
19#14582866—21no—
20#14582863—21no—
21#14582863C2211yescharacteristic
22#14582863C2211yescharacteristic
23C2×C22⋊(C43⋊C8)—21no—
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25#14582635—21no—
26#14582635—21no—
27#14582624—22no—
28C22×#41×C43C2211yescharacteristic
29C2×#103×C43—21no—
30C2×#102×C43—21no—
31C2×C22⋊C8×C43C2211yescharacteristic
32C43×#380C2211yescharacteristic
33C22×Dic86C2×C411yescharacteristic
34#13063355—42no—
35#13063355—42no—
36C2×#10621885—21no—
37C2×#10621885—21no—
38C2×#10621883—21no—
39C2×#10621883—21no—
40#13063332—42no—
41#13063332—42no—
42C2×#10621877—22no—
43C2×#10621877—21no—
44C2×#10621877C2×C411yescharacteristic
45C2×#10621877C2×C411yescharacteristic
46C22×C43⋊C8—22no—
47C22×C43⋊C8—21no—
48#13063304—21no—
49#13063304—21no—
50#13063304—21no—
51#13063304—21no—
52C2×C4⋊Dic43C2×C411yescharacteristic
53C2×Dic43⋊C4—21no—
54C2×C22⋊Dic43—21no—
55#13063249—21no—
56#13063249—21no—
57#13063246—21no—
58#13063246—21no—
59C22⋊(C43⋊C8)—22no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)—21no—
63C22⋊(C43⋊C8)—21no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)D411yescharacteristic
66C22⋊(C43⋊C8)D411yescharacteristic
67C22⋊(C43⋊C8)D412yes—
68C2×#41×C43—21no—
69C2×#41×C43—21no—
70C2×#41×C43—42no—
71C2×#41×C43—42no—
72C2×#41×C43C2×C411yescharacteristic
73C2×#41×C43C2×C411yescharacteristic
74C2×#41×C43D411yescharacteristic
75C2×#41×C43D411yescharacteristic
76C22×Q8×C43D411yescharacteristic
77C22×D4×C43—21no—
78C22×D4×C43D411yescharacteristic
79C23×C4×C43—21no—
80C23×C4×C43C2311yescharacteristic
81C22×C8×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84#103×C43—42no—
85#102×C43—42no—
86C22⋊C8×C43—21no—
87C22⋊C8×C43—21no—
88#95×C43—21no—
89C24×C43—21no—
90C24×C43#4111yescharacteristic
91#41×C43—22no—
92#41×C43—22no—
93#41×C43—22no—
94#41×C43—22no—
95#41×C43—41no—
96#41×C43—41no—
97#41×C43—41no—
98#41×C43—41no—
99#41×C43—44no—
100#41×C43—44no—
101C2×Q8×C43—21no—
102C2×Q8×C43—22no—
103C2×Q8×C43—41no—
104C2×Q8×C43C22⋊C411yescharacteristic
105C2×Q8×C43C22⋊C411yescharacteristic
106C2×D4×C43—21no—
107C2×D4×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43—22no—
112C2×D4×C43—41no—
113C2×D4×C43—44no—
114C2×D4×C43C22⋊C411yescharacteristic
115C2×D4×C43C22⋊C411yescharacteristic
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—44no—
124C22×C4×C43—41no—
125C22×C4×C43C22×C411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43#4111yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C2×Dic86—21no—
134C2×Dic86—21no—
135C2×Dic86—41no—
136C2×Dic86—41no—
137C2×C8×C43—41no—
138C2×C8×C43—41no—
139C2×C8×C43—41no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43—41no—
142C22⋊C4×C43—81no—
143C22⋊Dic43—41no—
144C22⋊Dic43—41no—
145#10621885—42no—
146#10621885—42no—
147#10621883—42no—
148#10621883—42no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153#10621877—44no—
154#10621877—41no—
155#10621877—41no—
156#10621877—41no—
157#10621877—41no—
158C2×C43⋊C8—21no—
159C2×C43⋊C8—21no—
160C2×C43⋊C8—21no—
161C2×C43⋊C8—22no—
162C2×C43⋊C8—21no—
163C2×C43⋊C8—44no—
164C2×C43⋊C8—41no—
165C2×C43⋊C8—41no—
166C23×C43—21no—
167C23×C43—21no—
168C23×C43—21no—
169C23×C43—21no—
170C23×C43—41no—
171C23×C43—41no—
172C23×C43—42no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43—81no—
176C23×C43C4×D411yescharacteristic
177C23×C43#12111yescharacteristic
178C23×C43#12311yescharacteristic
179Q8×C43—21no—
180Q8×C43—21no—
181Q8×C43—21no—
182Q8×C43—42no—
183Q8×C43#9912yes—
184D4×C43—24no—
185D4×C43—21no—
186D4×C43—21no—
187D4×C43—21no—
188D4×C43—42no—
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—42no—
192D4×C43#9912yes—
193C2×C4×C43—24no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—81no—
210C2×C4×C43—81no—
211C2×C4×C43—81no—
212C2×C4×C43C2×C22⋊C411yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×Dic43—42no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—81no—
220Dic86—41no—
221Dic86—41no—
222Dic86—81no—
223C8×C43—81no—
224C43⋊C8—41no—
225C43⋊C8—42no—
226C43⋊C8—41no—
227C43⋊C8—41no—
228C43⋊C8—41no—
229#9345—431nomaximal, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—22no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—41no—
240C22×C43—41no—
241C22×C43—41no—
242C22×C43—41no—
243C22×C43—41no—
244C22×C43—81no—
245C22×C43—81no—
246C22×C43—82no—
247C22×C43—82no—
248C22×C43#38611yescharacteristic
249C22×C43#47111yescharacteristic
250C22×C43#47311yescharacteristic
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—22no—
255C4×C43—41no—
256C4×C43—161no—
257C4×C43C2×#9911yescharacteristic
258C4×C43C2×#9911yescharacteristic
259Dic43—81no—
260Dic43—81no—
261#3007—431no—
262#2880—431no—
263#1788D4311yescharacteristic
264#1520—431no—
265#1472—431no—
266#1305—431no—
267#1298—431no—
268C2×C43—21no—
269C2×C43—21no—
270C2×C43—41no—
271C2×C43—41no—
272C2×C43—42no—
273C2×C43—81no—
274C2×C43#188111yescharacteristic
275C2×C43#189811yescharacteristic
276C2×C43#190811yescharacteristic
277C22×#41C2×D4311yescharacteristic
278C2×#137—431no—
279C2×#137—431no—
280C2×#131—861no—
281C2×C22⋊Q8—431no—
282#452—861no—
283#452—861no—
284#451—861no—
285#450—861no—
286#417—431no—
287#417—431no—
288C2×#103—21no—
289C2×#102—21no—
290#408—862no—
291#408—861no—
292#407—431no—
293#407—431no—
294#407—861no—
295C2×C22⋊C8—431no—
296C2×C22⋊C8—861no—
297C2×C22⋊C8C2×D4311yescharacteristic
298#380C2×D4311yescharacteristic
299#328—861no—
300#328—861no—
301#324—862no—
302C43#934511yescharacteristic, complemented, Sylow
303C2×#41—21no—
304C2×#41—21no—
305C2×#41—42no—
306C2×#41—42no—
307C2×#41C4×D4311yescharacteristic
308C2×#41C4×D4311yescharacteristic
309C2×#41D17211yescharacteristic
310C2×#41D17211yescharacteristic
311C22×Q8—431no—
312C22×Q8C22⋊D4311yescharacteristic
313C22×D4—21no—
314C22×D4C22⋊D4311yescharacteristic
315C23×C4—21no—
316C23×C4C22×D4311yescharacteristic
317#137—1722no—
318#137—1722no—
319C2×Q16—861no—
320C2×Q16—861no—
321C2×SD16—861no—
322C2×SD16—861no—
323#131—1722no—
324#131—1722no—
325C2×M16—431no—
326C2×M16—431no—
327C2×M16—862no—
328C2×M16—861no—
329C22×C8—21no—
330C22×C8—862no—
331C22×C8—861no—
332C22⋊Q8—861no—
333C22⋊Q8—861no—
334C22⋊Q8—861no—
335C22⋊Q8—861no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—431no—
338C2×C4⋊C4—861no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—861no—
341#103—42no—
342#103—861no—
343#103—861no—
344#102—42no—
345#102—861no—
346#102—861no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—432no—
350C22⋊C8—431no—
351C22⋊C8—431no—
352C22⋊C8—862no—
353C22⋊C8—862no—
354C22⋊C8—861no—
355C22⋊C8—861no—
356C22⋊C8—861no—
357C22⋊C8—861no—
358#95—21no—
359C24—21no—
360C24#1062190011yescharacteristic
361#41—22no—
362#41—22no—
363#41—22no—
364#41—22no—
365#41—41no—
366#41—41no—
367#41—41no—
368#41—41no—
369#41—44no—
370#41—44no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—41no—
374C2×Q8—861no—
375C2×Q8—861no—
376C2×Q8—1721no—
377C2×Q8—1721no—
378C2×Q8(C2×D43)⋊C411yescharacteristic
379C2×Q8(C2×D43)⋊C411yescharacteristic
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—44no—
388C2×D4(C2×D43)⋊C411yescharacteristic
389C2×D4(C2×D43)⋊C411yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—44no—
398C22×C4—41no—
399C22×C4—861no—
400C22×C4—861no—
401C22×C4C2×C4×D4311yescharacteristic
402C22×C4C2×D17211yescharacteristic
403C22×C4D4×D4311yescharacteristic
404C22×C4D4×D4311yescharacteristic
405C22×C4#1062190011yescharacteristic
406C22×C4C2×C22⋊D4311yescharacteristic
407Q16—1722no—
408Q16—1722no—
409SD16—1722no—
410SD16—1722no—
411M16—1724no—
412M16—1721no—
413M16—1721no—
414M16—1721no—
415M16—1721no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—861no—
420C2×C8—861no—
421C2×C8—861no—
422C2×C8—862no—
423C2×C8—861no—
424C2×C8—1724no—
425C2×C8—1721no—
426C2×C8—1721no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C22⋊C4—81no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—41no—
441C23—41no—
442C23—42no—
443C23—41no—
444C23—41no—
445C23—81no—
446C23(C22⋊D43)⋊C411yescharacteristic
447C23#1306329711yescharacteristic
448C23#1306330911yescharacteristic
449Q8—21no—
450Q8—21no—
451Q8—21no—
452Q8—42no—
453Q8—3441no—
454Q8—1721no—
455Q8—1721no—
456Q8#1306323912yes—
457D4—24no—
458D4—21no—
459D4—21no—
460D4—21no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—42no—
465D4#1306323912yes—
466C2×C4—24no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—3441no—
486C2×C4—1722no—
487C2×C4—1721no—
488C2×C4—1721no—
489C2×C4C2×(C2×D43)⋊C411yescharacteristic
490C2×C4(C22⋊D43)⋊C411yescharacteristic
491C2×C4#1306329511yescharacteristic
492C2×C4#1306329711yescharacteristic
493C8—81no—
494C8—1721no—
495C8—1722no—
496C8—1721no—
497C8—1721no—
498C8—1721no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—22no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—81no—
514C22—81no—
515C22—82no—
516C22—82no—
517C22#1458277611yescharacteristic
518C22#1458316011yescharacteristic
519C22#1458317211yescharacteristic
520C4—21no—
521C4—21no—
522C4—22no—
523C4—21no—
524C4—41no—
525C4—161no—
526C4—3441no—
527C4—3441no—
528C4C2×#1306323911yescharacteristic
529C4C2×#1306323911yescharacteristic
530C2—21no—
531C2—21no—
532C2—41no—
533C2—41no—
534C2—42no—
535C2—81no—
536C2#1913495511yescharacteristic
537C2#1913504611yescharacteristic
538C2#1913510811yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1788C2
socleC22×C43#386
prime radicalC22×#41×C43C22
cosocleC23×C4×C43C23
hypercenter#1788D43
hypocenterC43#9345
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
3. #19133166C2semidirect
4. #19132958C2semidirect
5. #19132501C2semidirect
6. #19132483C2semidirect
8. C2×#13063355C4semidirect
9. C2×#13063355C4semidirect
16. #14582900C4semidirect
17. #14582900C4semidirect
302. C43#9345semidirect

Maximal subgroups

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

subgroupindex
#191438552
#191430442
#191331662
#191329582
#191325012
#191324832
C43×#17882
#934543