Finite Group Databasebeta

← #24991723

Subgroups — #24991723

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583038C211yesmaximal, characteristic
2#19137298C211yesmaximal, characteristic
3#19134530C211yesmaximal, characteristic, complemented
4C2×#14582632C211yesmaximal, characteristic
5#19132474C211yesmaximal, characteristic, complemented
6#19132438C211yesmaximal, characteristic, complemented
7C43×#1446C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063299C2211yescharacteristic
10C2×C4×C22⋊D43—21no—
11#14583038—22no—
12#14583038C414yescomplemented
13C2×#13063249—21no—
14C2×#13063249—21no—
15C2×#13063249—21no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18#14582791—21no—
19#14582784—21no—
20#14582778—21no—
21#14582777—21no—
22#14582773—21no—
23#14582759C2211yescharacteristic
24#14582632—22no—
25C23×Q8×C43C2211yescharacteristic
26C2×#95×C43—21no—
27C2×#95×C43—21no—
28C2×#95×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C22×D172D411yescharacteristic
31C22×C22⋊D43—21no—
32C22×C4×D43—21no—
33C2×#10621884—24no—
34C2×#10621884—42no—
35C2×#10621884—42no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38#13063299—21no—
39#13063299—21no—
40#13063299C2×C412yes—
41#13063299D412yes—
42C4×C22⋊D43—42no—
43C4×C22⋊D43—42no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×C4⋊Dic43D411yescharacteristic
46C2×C4⋊Dic43D411yescharacteristic
47C2×Dic43⋊C4—21no—
48C2×C22⋊Dic43—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×C4×Dic43—21no—
54#13063249—24no—
55#13063249—42no—
56#13063249—42no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)C2×C412yescomplemented
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C22×Q8×C43—21no—
65C22×Q8×C43—21no—
66C22×Q8×C43—21no—
67C22×Q8×C43—21no—
68C22×Q8×C43—21no—
69C22×Q8×C43—42no—
70C22×Q8×C43—42no—
71C22×Q8×C43C2×C412yescomplemented
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43D411yescharacteristic
75C23×C4×C43D411yescharacteristic
76C23×C4×C43C2311yescharacteristic
77#95×C43—21no—
78#95×C43—21no—
79#95×C43—21no—
80#95×C43—21no—
81#95×C43—42no—
82#95×C43—42no—
83C24×C43C2×D411yescharacteristic
84C23×D43—21no—
85C2×Q8×C43—22no—
86C2×Q8×C43—22no—
87C2×Q8×C43—22no—
88C2×Q8×C43—22no—
89C2×Q8×C43—22no—
90C2×Q8×C43—22no—
91C2×Q8×C43—44no—
92C2×Q8×C43—41no—
93C2×Q8×C43—41no—
94C2×Q8×C43—41no—
95C2×Q8×C43—41no—
96C2×Q8×C43—44no—
97C2×Q8×C43—44no—
98C2×Q8×C43—44no—
99C2×Q8×C43—41no—
100C2×Q8×C43—41no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—41no—
111C22×C4×C43—41no—
112C22×C4×C43—41no—
113C22×C4×C43—41no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43SD1612yescomplemented
127C22×C4×C43C22×C411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C22×C4×C43#4111yescharacteristic
133C2×C22⋊D43—22no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—41no—
136C2×C22⋊D43—41no—
137C2×C22⋊D43—41no—
138C2×C22⋊D43—41no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C2×D172—21no—
143C2×D172—41no—
144C2×D172—41no—
145C2×D172C22⋊C412yes—
146C2×C4×D43—42no—
147C2×C4×D43—81no—
148C2×C4×D43—81no—
149C22⋊Dic43—41no—
150C22⋊Dic43—41no—
151#10621884—48no—
152(C2×D43)⋊C4—22no—
153(C2×D43)⋊C4—22no—
154(C2×D43)⋊C4—42no—
155(C2×D43)⋊C4—81no—
156(C2×D43)⋊C4—81no—
157C4⋊Dic43—21no—
158C4⋊Dic43—41no—
159C4⋊Dic43—41no—
160C4⋊Dic43C22⋊C412yes—
161Dic43⋊C4—42no—
162C4×Dic43—42no—
163C2×C43⋊C8—22no—
164C2×C43⋊C8—41no—
165C2×C43⋊C8—41no—
166C2×C43⋊C8—41no—
167C2×C43⋊C8—41no—
168C2×C43⋊C8—41no—
169C23×C43—21no—
170C23×C43—21no—
171C23×C43—21no—
172C23×C43—21no—
173C23×C43C4×D411yescharacteristic
174C23×C43#12011yescharacteristic
175C23×C43#12111yescharacteristic
176C23×C43C2×SD1611yescharacteristic
177C23×C43#13511yescharacteristic
178C23×C43AGL(1,ℤ/8)11yescharacteristic
179C23×C43#13711yescharacteristic
180C22×D43—22no—
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—41no—
187Q8×C43—24no—
188Q8×C43—24no—
189Q8×C43—42no—
190Q8×C43—42no—
191Q8×C43—42no—
192Q8×C43—42no—
193Q8×C43—42no—
194Q8×C43—42no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—24no—
200C2×C4×C43—22no—
201C2×C4×C43—41no—
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—41no—
210C2×C4×C43—41no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—81no—
222C2×C4×C43—81no—
223C2×C4×C43—81no—
224C2×C4×C43—81no—
225C2×C4×C43—81no—
226C2×C4×C43—81no—
227C2×C4×C43C2×C22⋊C411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12311yescharacteristic
231C22⋊D43—42no—
232C22⋊D43—42no—
233C22⋊D43—42no—
234C22⋊D43—42no—
235C2×Dic43—22no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244D172—42no—
245D172—81no—
246C4×D43—84no—
247C43⋊C8—42no—
248C43⋊C8—81no—
249#9039—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43#38611yescharacteristic
263C22×C43C4×SD1611yescharacteristic
264C22×C43#44011yescharacteristic
265C22×C43#45011yescharacteristic
266C22×C43#45211yescharacteristic
267C22×C43#45511yescharacteristic
268C22×C43#45611yescharacteristic
269C22×C43B(4,𝔽2)11yescharacteristic
270C22×C43B(4,𝔽2)11yescharacteristic
271C22×C43#46111yescharacteristic
272C22×C43#46311yescharacteristic
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—42no—
285C4×C43—44no—
286C4×C43—82no—
287C4×C43—81no—
288Dic43—42no—
289Dic43—81no—
290Dic43—81no—
291C2×#448—431no—
292#2325—431no—
293#1787—431no—
294C2×#327—431no—
295#1446D4311yescharacteristic, complemented
296#1294—431no—
297#1280—431no—
298C2×C43—21no—
299C2×C43—21no—
300C2×C43—21no—
301C2×C43—21no—
302C2×C43#160111yescharacteristic
303C2×C43#160311yescharacteristic
304C2×C43#160411yescharacteristic
305C2×C43#160611yescharacteristic
306C2×C43#187711yescharacteristic
307C2×C43#188211yescharacteristic
308C2×C43#188911yescharacteristic
309D43—82no—
310C23×Q8C2×D4311yescharacteristic
311C22×SD16—861no—
312C2×#121—431no—
313C2×C4×D4—861no—
314#448—434no—
315#448—862no—
316C2×#103—861no—
317C2×#103—861no—
318C2×#103—861no—
319C2×C22⋊C8—431no—
320C2×C22⋊C8—431no—
321#388—861no—
322#387—861no—
323#386—861no—
324#386—861no—
325#385—861no—
326#380—431no—
327C2×#95—21no—
328C2×#95—21no—
329C2×#95C2×D4311yescharacteristic
330C2×#95C2×D4311yescharacteristic
331#327—862no—
332C43#903911yescharacteristic, complemented, Sylow
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—42no—
339C22×Q8—42no—
340C22×Q8C4×D4312yescomplemented
341C22×D4—431no—
342C22×D4—861no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—861no—
346C23×C4C22⋊D4311yescharacteristic
347C23×C4C22⋊D4311yescharacteristic
348C23×C4C22×D4311yescharacteristic
349C2×SD16—864no—
350C2×SD16—1722no—
351C2×SD16—1722no—
352C22×C8—861no—
353C22×C8—861no—
354#121—432no—
355#121—432no—
356#121—861no—
357#121—861no—
358C4×D4—1722no—
359C4×D4—1722no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—861no—
364C2×C22⋊C4—861no—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C42—861no—
370#103—864no—
371#103—1722no—
372#103—1722no—
373C22⋊C8—432no—
374C22⋊C8—861no—
375C22⋊C8—861no—
376C22⋊C8—861no—
377#95—21no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—42no—
382#95—42no—
383#95—861no—
384#95—861no—
385#95—861no—
386C24—861no—
387C24C2×C22⋊D4311yescharacteristic
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—44no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—44no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×D4—432no—
405C2×D4—862no—
406C2×D4—862no—
407C2×D4—861no—
408C2×D4—1721no—
409C2×D4—1721no—
410C2×D4—1721no—
411C2×D4—1721no—
412C2×D4—1721no—
413C2×D4—1721no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—3441no—
443C22×C4—3441no—
444C22×C4—1722no—
445C22×C4#1062188412yescomplemented
446C22×C4C2×C4×D4311yescharacteristic
447C22×C4#1062189811yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4#1062190011yescharacteristic
452SD16—1728no—
453C2×C8—862no—
454C2×C8—1721no—
455C2×C8—1721no—
456C2×C8—1721no—
457C2×C8—1721no—
458C2×C8—1721no—
459C4⋊C4—432no—
460C4⋊C4—861no—
461C4⋊C4—1721no—
462C4⋊C4—1721no—
463C4⋊C4—1722no—
464C22⋊C4—862no—
465C22⋊C4—862no—
466C22⋊C4—3441no—
467C22⋊C4—3441no—
468C22⋊C4—1722no—
469C22⋊C4—1721no—
470C22⋊C4—1721no—
471C42—1722no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—862no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23—1721no—
482C23—1721no—
483C23C4×C22⋊D4311yescharacteristic
484C23#1306329311yescharacteristic
485C23#1306329611yescharacteristic
486C23C2×#1062188411yescharacteristic
487C23#1306334511yescharacteristic
488C23#1306335011yescharacteristic
489C23#1306335611yescharacteristic
490Q8—24no—
491Q8—24no—
492Q8—42no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496Q8—42no—
497Q8—42no—
498D4—3441no—
499D4—1722no—
500D4—1722no—
501D4—1722no—
502D4—1722no—
503D4—1722no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—862no—
537C2×C4—3444no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C22⋊C4×D4311yescharacteristic
547C2×C4(C22⋊D43)⋊C411yescharacteristic
548C2×C4#1306329811yescharacteristic
549C2×C4#1306330711yescharacteristic
550C8—3441no—
551C8—1722no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—3441no—
565C22—3441no—
566C22—3441no—
567C22—3441no—
568C22—1722no—
569C22—1722no—
570C22—1722no—
571C22#1458277511yescharacteristic
572C22C4×#1062188411yescharacteristic
573C22#1458299711yescharacteristic
574C22#1458304911yescharacteristic
575C22#1458305911yescharacteristic
576C22#1458307611yescharacteristic
577C22#1458308111yescharacteristic
578C22#1458308511yescharacteristic
579C22#1458308511yescharacteristic
580C22#1458310111yescharacteristic
581C22#1458311111yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—44no—
587C4—42no—
588C4—82no—
589C4—81no—
590C4—3441no—
591C4—3441no—
592C4—1722no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—3442no—
598C2#1913354611yescharacteristic
599C2#1913355611yescharacteristic
600C2#1913356311yescharacteristic
601C2#1913357311yescharacteristic
602C2#1913493211yescharacteristic
603C2#1913496711yescharacteristic
604C2#1913500011yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1446C2
socleC23×C43#120
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1446D43
hypocenterC43#9039
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1446

Complements

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

NH ≅ G/Ntype
3. #19134530C2semidirect
5. #19132474C2semidirect
6. #19132438C2semidirect
7. C43×#1446C2semidirect
12. #14583038C4semidirect
60. C22⋊(C43⋊C8)C2×C4semidirect
71. C22×Q8×C43C2×C4semidirect
126. C22×C4×C43SD16semidirect
295. #1446D43semidirect
332. C43#9039semidirect
340. C22×Q8C4×D43semidirect
445. C22×C4#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145830382
#191372982
#191345302
C2×#145826322
#191324742
#191324382
C43×#14462
#903943