Finite Group Databasebeta

← #25128799

Subgroups — #25128799

Order 11008.

1304 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583595C211yesmaximal, characteristic
2C2×#14583038C211yesmaximal, characteristic, complemented
3C22×#13063249C211yesmaximal, characteristic, complemented
4#19135746C212yesmaximal, complemented
5#19135596C212yesmaximal, complemented
6#19135021C211yesmaximal, characteristic, complemented
7#19134932C212yesmaximal, complemented
8#19134908C212yesmaximal, complemented
9#19134888C211yesmaximal, characteristic, complemented
10#19134683C211yesmaximal, characteristic, complemented
11C43×#2409C211yesmaximal, characteristic, complemented
12C22×#10621884C2212yes—
13C23×C43⋊C8C2211yescharacteristic
14#14583595—24no—
15#14583595—24no—
16C2×#13063320—21no—
17C2×#13063317C2211yescharacteristic
18C2×#13063307—21no—
19C2×#13063299C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063297—21no—
22C2×C4×D172C2211yescharacteristic
23C2×(C22⋊D43)⋊C4—21no—
24C2×#13063284C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26#14583038—24no—
27C2×#13063249—24no—
28C2×#13063249C2212yes—
29C2×#13063249C2212yes—
30C2×#13063249C2212yes—
31C2×#13063245C2212yes—
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2212yes—
34#14582661C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37#14582654C2212yes—
38C23×Q8×C43C2211yescharacteristic
39C2×C22⋊Q8×C43C2212yes—
40C2×C4×D4×C43C2211yescharacteristic
41C43×#395—21no—
42C43×#393—21no—
43C43×#391C2212yes—
44C43×#386—21no—
45C43×#385—21no—
46C43×#380C2211yescharacteristic
47C22×D172C2311yescharacteristic
48C22×C22⋊D43—21no—
49C22×C22⋊D43—21no—
50C23×Dic43—21no—
51C22×C4×D43—21no—
52C2×#10621884—24no—
53C2×#10621884—24no—
54C2×#10621884—42no—
55C22×C43⋊C8—22no—
56C22×C43⋊C8—42no—
57C22×C43⋊C8C2312yes—
58C22×C43⋊C8C2312yes—
59#13063320—28no—
60#13063317—22no—
61#13063317—22no—
62#13063307—28no—
63#13063299—22no—
64#13063299—22no—
65#13063299—22no—
66#13063299D414yes—
67#13063297—28no—
68C4×D172—22no—
69C4×D172—22no—
70(C22⋊D43)⋊C4—28no—
71#13063284—22no—
72#13063284—22no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43D414yes—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—21no—
86#13063249—24no—
87#13063249—24no—
88#13063249—24no—
89#13063245—42no—
90C22⋊(C43⋊C8)—22no—
91C22⋊(C43⋊C8)—42no—
92C22×Q8×C43—21no—
93C22×Q8×C43—24no—
94C22×Q8×C43—22no—
95C22×Q8×C43—22no—
96C22×Q8×C43—42no—
97C22×Q8×C43C2312yes—
98C22×D4×C43D411yescharacteristic
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101C23×C4×C43C2311yescharacteristic
102C22⋊Q8×C43—24no—
103C22⋊Q8×C43—42no—
104C4×D4×C43—22no—
105C4×D4×C43—22no—
106C2×C4⋊C4×C43—22no—
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C4⋊C4×C43C2312yes—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C42×C43C2311yescharacteristic
114#95×C43—21no—
115#95×C43—22no—
116#95×C43—22no—
117C24×C43C2×D411yescharacteristic
118C24×C43C2×D411yescharacteristic
119C23×D43—21no—
120C2×Q8×C43—22no—
121C2×Q8×C43—28no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—44no—
127C2×Q8×C43—48no—
128C2×Q8×C43—44no—
129C2×Q8×C43—42no—
130C2×Q8×C43#4114yes—
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—44no—
143C22×C4×C43—42no—
144C22×C4×C43C2×D412yes—
145C22×C4×C43C2×D412yes—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—24no—
152C2×C22⋊D43—24no—
153C2×C22⋊D43—42no—
154C2×C22⋊D43—42no—
155C2×C22⋊D43—82no—
156C22×Dic43—24no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—82no—
161C2×D172—21no—
162C2×D172—22no—
163C2×D172—22no—
164C2×D172C2×D412yes—
165C2×C4×D43—24no—
166C2×C4×D43—82no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—44no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—44no—
174C22⋊C4×C43—42no—
175C42×C43—21no—
176C42×C43—21no—
177C22⋊Dic43—24no—
178#10621884—48no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—24no—
182C4⋊Dic43—24no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43C2×D412yes—
187C4⋊Dic43C2×D412yes—
188C4⋊Dic43C2×D412yes—
189Dic43⋊C4—24no—
190Dic43⋊C4—24no—
191C4×Dic43—24no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—44no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—21no—
202C23×C43—22no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—22no—
206C23×C43#12012yes—
207C23×C43#13512yes—
208C23×C43#13712yes—
209C23×C43C22×D411yescharacteristic
210C22×D43—22no—
211C22×D43—42no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—42no—
215Q8×C43—24no—
216Q8×C43—24no—
217Q8×C43—48no—
218Q8×C43—42no—
219Q8×C43—42no—
220D4×C43—44no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—24no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—48no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43#12012yes—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4112yes—
246C2×C4×C43H(5,𝔽2)12yes—
247C22⋊D43—48no—
248C22⋊D43—84no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—84no—
257D172—24no—
258D172—41no—
259D172—41no—
260C4×D43—84no—
261C43⋊C8—42no—
262C43⋊C8—42no—
263#23964—431nomaximal, Sylow
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—24no—
267C22×C43—24no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43#45214yes—
274C22×C43C2×#12011yescharacteristic
275C22×C43#54612yes—
276C22×C43C2×#13511yescharacteristic
277C22×C43C2×#13711yescharacteristic
278C22×C43#57712yes—
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—42no—
282C2×D43—82no—
283C2×D43—82no—
284C4×C43—22no—
285C4×C43—41no—
286C4×C43—44no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—82no—
290C4×C43#52511yescharacteristic
291C4×C43#53511yescharacteristic
292C4×C43#54612yes—
293Dic43—42no—
294Dic43—42no—
295Dic43—42no—
296C2×#553—431no—
297C2×#448—431no—
298C22×#103—431no—
299#2409D4311yescharacteristic, complemented
300#2026—432no—
301#2000—432no—
302#1893—431no—
303#1877—432no—
304#1873—432no—
305#1869—431no—
306#1824—431no—
307C2×C43—24no—
308C2×C43—81no—
309C2×C43#240411yescharacteristic
310C2×C43C2×#45211yescharacteristic
311C2×C43#300911yescharacteristic
312C2×C43#330112yes—
313C2×C43#332012yes—
314D43—82no—
315C23×Q8C2×D4311yescharacteristic
316C22×SD16—432no—
317C23×C8—431no—
318#553—864no—
319#553—864no—
320C2×#126—861no—
321C2×#125—431no—
322C2×#123—861no—
323C2×C22⋊Q8C2×D4312yes—
324C2×#121—431no—
325C2×#121—431no—
326C2×#121—861no—
327C2×C4×D4—431no—
328C2×C4×D4—861no—
329C2×C4×D4C2×D4311yescharacteristic
330C2×#117—431no—
331C22×C4⋊C4—431no—
332#448—864no—
333C2×#103—432no—
334C2×#103—432no—
335C2×#103—432no—
336C2×#103—864no—
337C2×#102—432no—
338C2×C22⋊C8—431no—
339C2×C22⋊C8—432no—
340#395—21no—
341#393—21no—
342#391C2×D4312yes—
343#386—21no—
344#385—21no—
345#380C2×D4311yescharacteristic
346#340—432no—
347#340—432no—
348#340—432no—
349#336—432no—
350C43#2396411yescharacteristic, complemented, Sylow
351C22×Q8—21no—
352C22×Q8—24no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—42no—
356C22×Q8C22×D4312yes—
357C22×D4—431no—
358C22×D4—861no—
359C22×D4—861no—
360C22×D4C22⋊D4311yescharacteristic
361C23×C4—21no—
362C23×C4—861no—
363C23×C4—861no—
364C23×C4C22×D4311yescharacteristic
365C23×C4C22×D4311yescharacteristic
366C2×SD16—864no—
367C2×SD16—864no—
368C2×SD16—1722no—
369C22×C8—432no—
370C22×C8—432no—
371C22×C8—862no—
372C22×C8—1722no—
373#126—868no—
374#125—862no—
375#125—862no—
376#123—868no—
377C22⋊Q8—24no—
378C22⋊Q8—42no—
379#121—434no—
380#121—862no—
381#121—862no—
382#121—868no—
383#121—862no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—862no—
387C4×D4—862no—
388C4×D4—868no—
389#117—862no—
390#117—862no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—434no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22⋊D4311yescharacteristic
401C2×C4⋊C4C22×D4312yes—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4C22⋊D4311yescharacteristic
409C2×C22⋊C4C22⋊D4311yescharacteristic
410C2×C42—861no—
411C2×C42C22×D4311yescharacteristic
412#103—864no—
413#103—864no—
414#103—864no—
415#102—1722no—
416C22⋊C8—862no—
417C22⋊C8—1722no—
418#95—21no—
419#95—22no—
420#95—22no—
421C24—861no—
422C24C2×C22⋊D4311yescharacteristic
423C24C2×C22⋊D4311yescharacteristic
424C2×Q8—22no—
425C2×Q8—28no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—44no—
431C2×Q8—48no—
432C2×Q8—44no—
433C2×Q8—42no—
434C2×Q8#1062190014yes—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—432no—
439C2×D4—864no—
440C2×D4—864no—
441C2×D4—861no—
442C2×D4—862no—
443C2×D4—862no—
444C2×D4—3442no—
445C2×D4—1722no—
446C2×D4—1722no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—44no—
456C22×C4—42no—
457C22×C4—864no—
458C22×C4—864no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—3442no—
463C22×C4—3442no—
464C22×C4D4×D4312yes—
465C22×C4D4×D4312yes—
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C2×C22⋊D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C2×C22⋊D4311yescharacteristic
470C22×C4C23×D4311yescharacteristic
471SD16—1728no—
472C2×C8—862no—
473C2×C8—862no—
474C2×C8—862no—
475C2×C8—862no—
476C2×C8—862no—
477C2×C8—862no—
478C2×C8—1724no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—44no—
483C4⋊C4—432no—
484C4⋊C4—432no—
485C4⋊C4—432no—
486C4⋊C4—864no—
487C4⋊C4—864no—
488C4⋊C4—864no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—44no—
495C22⋊C4—42no—
496C22⋊C4—864no—
497C22⋊C4—864no—
498C22⋊C4—864no—
499C22⋊C4—864no—
500C42—21no—
501C42—21no—
502C42—864no—
503C23—22no—
504C23—22no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—22no—
509C23—22no—
510C23—862no—
511C23—1721no—
512C23—1721no—
513C23—1722no—
514C23—1722no—
515C23#1306329312yes—
516C23#1306334512yes—
517C23#1306335612yes—
518C23C22×C22⋊D4311yescharacteristic
519Q8—24no—
520Q8—24no—
521Q8—48no—
522Q8—42no—
523Q8—42no—
524D4—44no—
525D4—864no—
526D4—3444no—
527D4—1728no—
528D4—1721no—
529D4—1721no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—3444no—
555C2×C4—3444no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4#1306329312yes—
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C2×D4×D4311yescharacteristic
563C2×C4C2×#1062190012yes—
564C2×C4#1306337012yes—
565C8—1722no—
566C8—1722no—
567C22—24no—
568C22—24no—
569C22—22no—
570C22—22no—
571C22—42no—
572C22—42no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—3442no—
577C22—3442no—
578C22—1722no—
579C22—1722no—
580C22—1722no—
581C22#1458305914yes—
582C22C2×#1306329311yescharacteristic
583C22#1458354312yes—
584C22C2×#1306334511yescharacteristic
585C22C2×#1306335611yescharacteristic
586C22#1458370712yes—
587C4—22no—
588C4—41no—
589C4—44no—
590C4—41no—
591C4—41no—
592C4—82no—
593C4—1722no—
594C4—1722no—
595C4—1722no—
596C4#1458340511yescharacteristic
597C4#1458346411yescharacteristic
598C4#1458353612yes—
599C2—24no—
600C2—81no—
601C2—3442no—
602C2#1913791111yescharacteristic
603C2C2×#1458305911yescharacteristic
604C2#1914387011yescharacteristic
605C2#1914649712yes—
606C2#1914676612yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2409C2
socleC23×C43C22×D4
prime radicalC2×#14583595C2
hypercenter#2409D43
hypocenterC43#23964
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
2. C2×#14583038C2semidirect
3. C22×#13063249C2semidirect
4. #19135746C2semidirect
5. #19135596C2semidirect
6. #19135021C2semidirect
7. #19134932C2semidirect
8. #19134908C2semidirect
9. #19134888C2semidirect
10. #19134683C2semidirect
11. C43×#2409C2semidirect
299. #2409D43semidirect
350. C43#23964semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
C2×#145830382
C22×#130632492
#191357462
#191355962
#191350212
#191349322
#191349082
#191348882
#191346832
C43×#24092
#2396443