Finite Group Databasebeta

← #25128793

Subgroups — #25128793

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×#14583601C211yesmaximal, characteristic
2C22×#13063249C211yesmaximal, characteristic, complemented
3#19137954C211yesmaximal, characteristic, complemented
4#19135744C212yesmaximal, complemented
5#19135595C212yesmaximal, complemented
6#19135024C211yesmaximal, characteristic, complemented
7#19134931C212yesmaximal, complemented
8#19134904C212yesmaximal, complemented
9#19134885C211yesmaximal, characteristic, complemented
10#19134686C211yesmaximal, characteristic, complemented
11C2×C43×#448C211yesmaximal, characteristic, complemented
12C23×C43⋊C8C2211yescharacteristic
13#14583601—24no—
14#14583601—24no—
15C2×#13063318—21no—
16C2×#13063316C2211yescharacteristic
17C2×#13063309—21no—
18C2×#13063301C2212yes—
19C2×#13063297—21no—
20C2×#13063296C2211yescharacteristic
21C2×D4×Dic43—21no—
22C2×D4×Dic43C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24C2×#13063283C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C2×#13063249—24no—
27C2×#13063249C2212yes—
28C2×#13063249C2212yes—
29C2×#13063246C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31#14582818—21no—
32#14582810—21no—
33#14582806C2212yes—
34#14582778—21no—
35#14582772—21no—
36#14582759C2211yescharacteristic
37#14582662C2212yes—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582653C2212yes—
41C23×Q8×C43C2211yescharacteristic
42C22×SD16×C43C2212yes—
43C2×#121×C43C2211yescharacteristic
44C43×#448—24no—
45C2×#103×C43C2212yes—
46C2×C22⋊C8×C43C2211yescharacteristic
47C22×C22⋊D43—21no—
48C22×C22⋊D43D411yescharacteristic
49C23×Dic43—21no—
50C23×Dic43—21no—
51C22×C4×D43C2311yescharacteristic
52C22×C43⋊C8—22no—
53C22×C43⋊C8—42no—
54C22×C43⋊C8C2312yes—
55#13063318—28no—
56#13063316—22no—
57#13063316—22no—
58#13063309—28no—
59#13063301—24no—
60#13063301—42no—
61#13063297—28no—
62#13063296—22no—
63#13063296—22no—
64D4×Dic43—28no—
65D4×Dic43—22no—
66D4×Dic43—22no—
67C4×C22⋊D43—22no—
68C4×C22⋊D43—22no—
69#13063283—22no—
70#13063283—22no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43D414yes—
75C2×C4⋊Dic43C2312yes—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43D411yescharacteristic
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90#13063249—24no—
91#13063249—24no—
92#13063246—42no—
93(C2×D43)⋊C8—42no—
94C43⋊#95—21no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C22×Q8×C43—21no—
98C22×Q8×C43—24no—
99C22×Q8×C43—22no—
100C22×Q8×C43—22no—
101C22×Q8×C43—42no—
102C22×Q8×C43C2312yes—
103C22×D4×C43—21no—
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C23×C4×C43C2311yescharacteristic
107C2×SD16×C43—24no—
108C2×SD16×C43—24no—
109C2×SD16×C43—42no—
110C22×C8×C43C2312yes—
111#121×C43—22no—
112#121×C43D414yes—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115#103×C43—24no—
116C22⋊C8×C43—22no—
117C24×C43—21no—
118C24×C43C2×D411yescharacteristic
119C23×D43C2×D411yescharacteristic
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—21no—
132C2×D4×C43—24no—
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43—42no—
136C2×D4×C43—42no—
137C2×D4×C43C2×D412yes—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—21no—
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×C43C2411yescharacteristic
148C2×C22⋊D43—24no—
149C2×C22⋊D43—22no—
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43—82no—
153C22×Dic43—24no—
154C22×Dic43—24no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—22no—
158C22×Dic43—82no—
159C22×Dic43—82no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167SD16×C43—48no—
168C2×C8×C43—22no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C2×D412yes—
173C22⋊C4×C43—24no—
174C22⋊Dic43—24no—
175C22⋊Dic43—24no—
176C22⋊Dic43—22no—
177C22⋊Dic43—42no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—22no—
180(C2×D43)⋊C4—44no—
181C4⋊Dic43—24no—
182C4⋊Dic43—24no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43C2×D412yes—
188C4⋊Dic43C2×D412yes—
189Dic43⋊C4—24no—
190Dic43⋊C4—22no—
191Dic43⋊C4—44no—
192C4×Dic43—24no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—44no—
199C23×C43—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—42no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—42no—
206C23×C43#12012yes—
207C23×C43#13512yes—
208C23×C43#13712yes—
209C23×C43C22×D411yescharacteristic
210C22×D43—21no—
211C22×D43—22no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—22no—
215Q8×C43—24no—
216Q8×C43—24no—
217Q8×C43—48no—
218Q8×C43—42no—
219Q8×C43—42no—
220D4×C43—24no—
221D4×C43—48no—
222D4×C43—41no—
223D4×C43—41no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—24no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—48no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43#12012yes—
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C2×#4112yes—
239C2×C4×C43H(5,𝔽2)12yes—
240C22⋊D43—44no—
241C22⋊D43—84no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—84no—
257C2×Dic43—84no—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—42no—
261C8×C43—42no—
262C43⋊C8—42no—
263#23964—431nomaximal, Sylow
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—24no—
267C22×C43—24no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—82no—
272C22×C43—82no—
273C22×C43#45214yes—
274C22×C43C2×#12011yescharacteristic
275C22×C43#54612yes—
276C22×C43C2×#13511yescharacteristic
277C22×C43C2×#13711yescharacteristic
278C22×C43#57712yes—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—42no—
283C2×D43—42no—
284C4×C43—22no—
285C4×C43—44no—
286C4×C43—42no—
287C4×C43#52511yescharacteristic
288C4×C43#53511yescharacteristic
289C4×C43#54612yes—
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43—42no—
294Dic43—42no—
295Dic43—82no—
296C2×#553—431no—
297C2×#448D4311yescharacteristic, complemented
298C22×#103—431no—
299#2409—431no—
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—82no—
309C2×C43#240411yescharacteristic
310C2×C43C2×#45211yescharacteristic
311C2×C43#300911yescharacteristic
312C2×C43#330112yes—
313C2×C43#332012yes—
314D43—81no—
315C23×Q8C2×D4311yescharacteristic
316C22×SD16C2×D4312yes—
317C23×C8—431no—
318#553—864no—
319#553—864no—
320C2×#126—861no—
321C2×#125—431no—
322C2×#123—861no—
323C2×C22⋊Q8—432no—
324C2×#121—431no—
325C2×#121—861no—
326C2×#121C2×D4311yescharacteristic
327C2×C4×D4—431no—
328C2×C4×D4—431no—
329C2×C4×D4—861no—
330C2×#117—431no—
331C22×C4⋊C4—431no—
332#448—24no—
333C2×#103—432no—
334C2×#103—432no—
335C2×#103—864no—
336C2×#103C2×D4312yes—
337C2×#102—432no—
338C2×C22⋊C8—432no—
339C2×C22⋊C8C2×D4311yescharacteristic
340#395—861no—
341#393—861no—
342#391—432no—
343#386—861no—
344#385—861no—
345#380—431no—
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—21no—
358C22×D4—431no—
359C22×D4—861no—
360C22×D4C22×D4311yescharacteristic
361C23×C4—21no—
362C23×C4—431no—
363C23×C4—861no—
364C23×C4—861no—
365C23×C4C22×D4311yescharacteristic
366C2×SD16—24no—
367C2×SD16—24no—
368C2×SD16—42no—
369C22×C8—432no—
370C22×C8—862no—
371C22×C8—1722no—
372C22×C8C22×D4312yes—
373#126—868no—
374#125—862no—
375#125—862no—
376#123—868no—
377C22⋊Q8—864no—
378C22⋊Q8—1722no—
379#121—22no—
380#121—862no—
381#121—868no—
382#121—862no—
383#121C22⋊D4314yes—
384C4×D4—862no—
385C4×D4—868no—
386C4×D4—862no—
387C4×D4—862no—
388C4×D4—862no—
389#117—862no—
390#117—862no—
391C2×C4⋊C4—434no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—432no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—431no—
404C2×C22⋊C4—431no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—862no—
409C2×C22⋊C4—861no—
410C2×C42—431no—
411C2×C42—861no—
412#103—24no—
413#103—864no—
414#103—864no—
415#102—1722no—
416C22⋊C8—22no—
417C22⋊C8—1722no—
418#95—862no—
419#95—862no—
420#95—861no—
421C24—21no—
422C24—431no—
423C24D4×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—24no—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—864no—
442C2×D4—862no—
443C2×D4—862no—
444C2×D4—862no—
445C2×D4—3442no—
446C2×D4C2×C22⋊D4312yes—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—44no—
452C22×C4—42no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—864no—
457C22×C4—864no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—3442no—
466C22×C4—3442no—
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4312yes—
469C22×C4C2×C22⋊D4312yes—
470C22×C4C23×D4311yescharacteristic
471SD16—48no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—862no—
476C2×C8—862no—
477C2×C8—862no—
478C2×C8—1724no—
479C4⋊C4—21no—
480C4⋊C4—432no—
481C4⋊C4—432no—
482C4⋊C4—864no—
483C4⋊C4—864no—
484C4⋊C4—864no—
485C4⋊C4—862no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—862no—
489C4⋊C4—862no—
490C4⋊C4—1724no—
491C4⋊C4C2×C22⋊D4312yes—
492C22⋊C4—24no—
493C22⋊C4—864no—
494C22⋊C4—864no—
495C22⋊C4—864no—
496C22⋊C4—862no—
497C22⋊C4—862no—
498C22⋊C4—1724no—
499C22⋊C4—1722no—
500C42—864no—
501C42—861no—
502C42—861no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—41no—
507C23—41no—
508C23—42no—
509C23—42no—
510C23—861no—
511C23—861no—
512C23—861no—
513C23—862no—
514C23—862no—
515C23#1306329312yes—
516C23#1306334612yes—
517C23#1306335412yes—
518C23C2×D4×D4311yescharacteristic
519Q8—24no—
520Q8—24no—
521Q8—48no—
522Q8—42no—
523Q8—42no—
524D4—24no—
525D4—48no—
526D4—41no—
527D4—41no—
528D4—3444no—
529D4—1724no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—48no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—861no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—862no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—3444no—
551C2×C4—3444no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1722no—
560C2×C4#1306329312yes—
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4C22×C22⋊D4311yescharacteristic
563C2×C4C2×#1062190012yes—
564C2×C4#1306337012yes—
565C8—42no—
566C8—1722no—
567C22—24no—
568C22—24no—
569C22—22no—
570C22—22no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—82no—
575C22—82no—
576C22—1722no—
577C22—1722no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22#1458305814yes—
582C22C2×#1306329311yescharacteristic
583C22#1458353612yes—
584C22C2×#1306334611yescharacteristic
585C22C2×#1306335411yescharacteristic
586C22#1458370812yes—
587C4—22no—
588C4—44no—
589C4—42no—
590C4—3442no—
591C4—1721no—
592C4—1721no—
593C4—1721no—
594C4—1722no—
595C4—1722no—
596C4#1458340511yescharacteristic
597C4#1458346411yescharacteristic
598C4#1458354312yes—
599C2—24no—
600C2—82no—
601C2—3441no—
602C2#1913791111yescharacteristic
603C2C2×#1458305811yescharacteristic
604C2#1914387111yescharacteristic
605C2#1914650112yes—
606C2#1914677012yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#448C2
socleC23×C43C22×D4
prime radicalC2×#14583601C2
hypercenterC2×#448D43
hypocenterC43#23964
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
2. C22×#13063249C2semidirect
3. #19137954C2semidirect
4. #19135744C2semidirect
5. #19135595C2semidirect
6. #19135024C2semidirect
7. #19134931C2semidirect
8. #19134904C2semidirect
9. #19134885C2semidirect
10. #19134686C2semidirect
11. C2×C43×#448C2semidirect
297. C2×#448D43semidirect
350. C43#23964semidirect

Maximal subgroups

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

subgroupindex
C2×#145836012
C22×#130632492
#191379542
#191357442
#191355952
#191350242
#191349312
#191349042
#191348852
#191346862
C2×C43×#4482
#2396443