Finite Group Databasebeta

← #25114281

Subgroups — #25114281

Order 11008.

766 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582936C211yesmaximal, characteristic
2#19137487C211yesmaximal, characteristic
3#19137476C211yesmaximal, characteristic
4#19135337C211yesmaximal, characteristic, complemented
5#19135335C211yesmaximal, characteristic, complemented
6#19135189C211yesmaximal, characteristic, complemented
7#19135167C211yesmaximal, characteristic, complemented
8#19135165C211yesmaximal, characteristic, complemented
9#19134688C211yesmaximal, characteristic
10#19134688C211yesmaximal, characteristic
11#19134623C211yesmaximal, characteristic
12#19134493C211yesmaximal, characteristic, complemented
13#19134491C211yesmaximal, characteristic, complemented
14#19134370C211yesmaximal, characteristic
15C43×#1921C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17C2×#13063283C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19#14582936C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×#13063236C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28#14582798C2211yescharacteristic
29#14582797C2211yescharacteristic
30#14582795C2211yescharacteristic
31#14582791—21no—
32#14582790—21no—
33#14582789—21no—
34#14582788—21no—
35#14582766—21no—
36#14582763—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39C4⋊C4×Dic43—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4C2211yescharacteristic
44#14582745—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C4×C4⋊C4×C43C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C2×C8×D43—22no—
64C2×C8×D43—22no—
65C2×C8×D43C2×C414yes—
66#13063283—22no—
67#13063283—22no—
68#13063283C2×C414yes—
69#13063283C2×C414yes—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4D411yescharacteristic
82C2×(C2×D43)⋊C4D411yescharacteristic
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89#13063259C2×C414yes—
90#13063258—22no—
91#13063258—22no—
92#13063256C2×C414yes—
93#13063256C2×C414yes—
94(C2×D43)⋊C8—22no—
95#13063236—22no—
96#13063235—22no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#107×C43C2×C414yes—
117#95×C43—21no—
118#95×C43—21no—
119C23×D43C2×D411yescharacteristic
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43C22×C412yes—
139C2×C4×D43#4112yes—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43C22×C412yes—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—42no—
153C4⋊C4×C43C22×C412yes—
154C4⋊C4×C43C22×C412yes—
155C42×C43—21no—
156C42×C43—21no—
157C42×C43—42no—
158(C2×D43)⋊C4—24no—
159(C2×D43)⋊C4—24no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—81no—
163(C2×D43)⋊C4—81no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—42no—
171C4⋊Dic43C22×C412yes—
172C4⋊Dic43C22×C412yes—
173Dic43⋊C4—81no—
174Dic43⋊C4—81no—
175C4×Dic43—21no—
176C4×Dic43—21no—
177C4×Dic43—24no—
178C4×Dic43—24no—
179C4×Dic43—42no—
180C4×Dic43—81no—
181C4×Dic43—81no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8C22×C412yes—
186C2×C43⋊C8#4112yes—
187C2×C43⋊C8#4112yes—
188C8×D43—28no—
189C23×C43C22×D411yescharacteristic
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43C4×D412yes—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43C23×C411yescharacteristic
216C2×C4×C43C2×#4111yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C432−1+411yescharacteristic
220C2×C4×C432−1+411yescharacteristic
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43C4×D412yes—
242C4×D43—22no—
243C4×D43—22no—
244C4×D43—22no—
245C4×D43—22no—
246C8×C43—22no—
247C8×C43—41no—
248C43⋊C8—41no—
249C43⋊C8#11714yes—
250#22616—431nomaximal, Sylow
251C22×C43C2×C4×D411yescharacteristic
252C22×C43#54711yescharacteristic
253C22×C43#54711yescharacteristic
254C22×C43#57511yescharacteristic
255C22×C43#57511yescharacteristic
256C22×C43#57611yescharacteristic
257C22×C43#57811yescharacteristic
258C2×D43—22no—
259C2×D43—22no—
260C2×D43—22no—
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43C2×#11711yescharacteristic
272C4×C43#51911yescharacteristic
273C4×C43#55211yescharacteristic
274C4×C43#55211yescharacteristic
275Dic43—22no—
276Dic43—41no—
277Dic43—41no—
278Dic43—42no—
279Dic43—42no—
280Dic43—81no—
281Dic43—81no—
282C2×#427—431no—
283#2347—431no—
284#2346—431no—
285#1944—431no—
286#1944—431no—
287#1921—431no—
288#1921D4311yescharacteristic, complemented
289#1918—431no—
290#1918—431no—
291#1825—431no—
292#1825—431no—
293#1808—431no—
294#1776—431no—
295#1776—431no—
296#1752—431no—
297C2×C43#234411yescharacteristic
298C2×C43#294311yescharacteristic
299C2×C43#295111yescharacteristic
300C2×C43#334711yescharacteristic
301C2×C43#334711yescharacteristic
302C2×C43#334911yescharacteristic
303C2×C43#334911yescharacteristic
304D43—42no—
305C23×C8—431no—
306C2×#117—431no—
307C2×#117—431no—
308#427—438no—
309C2×#107—431no—
310C2×#107—431no—
311C2×#107—431no—
312C2×#107C2×D4311yescharacteristic
313C2×#106—431no—
314C2×#106—431no—
315C2×C22⋊C8—431no—
316C2×#97—431no—
317C2×#97—431no—
318#389—431no—
319#389—431no—
320#389—431no—
321#389C2×D4311yescharacteristic
322#388—861no—
323#388—861no—
324#388—861no—
325#388—861no—
326#383—861no—
327#382—861no—
328#380—431no—
329#380—431no—
330C4×C4⋊C4—431no—
331C4×C4⋊C4—431no—
332C4×C4⋊C4—431no—
333C4×C4⋊C4—861no—
334C4×C4⋊C4C2×D4311yescharacteristic
335C4×C22⋊C4—431no—
336#376—861no—
337#340—431no—
338#340—431no—
339#340—431no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340C2×D4311yescharacteristic
345#340C2×D4311yescharacteristic
346#340C2×D4311yescharacteristic
347#336—431no—
348#336C2×D4311yescharacteristic
349C43#2261611yescharacteristic, complemented, Sylow
350C23×C4—431no—
351C22×C8—431no—
352C22×C8—434no—
353C22×C8—431no—
354C22×C8—862no—
355C22×C8—862no—
356C22×C8C22×D4311yescharacteristic
357C22×C8C22×D4311yescharacteristic
358#117—434no—
359#117—434no—
360#117—862no—
361#117—862no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4C22×D4311yescharacteristic
371C2×C4⋊C4C22×D4311yescharacteristic
372C2×C4⋊C4C22×D4311yescharacteristic
373C2×C4⋊C4C22×D4311yescharacteristic
374C2×C22⋊C4—431no—
375C2×C22⋊C4—431no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C42—21no—
381C2×C42—431no—
382C2×C42—861no—
383C2×C42—861no—
384C2×C42—861no—
385C2×C42—861no—
386C2×C42—861no—
387C2×C42C22×D4311yescharacteristic
388#107—434no—
389#107—862no—
390#107—862no—
391#107C4×D4314yes—
392#106—434no—
393#106—434no—
394C22⋊C8—862no—
395#97—862no—
396#97—862no—
397#95—21no—
398#95—21no—
399#95—431no—
400#95—431no—
401#95—861no—
402#95—861no—
403#95—861no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409C24—431no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—431no—
415C22×C4—432no—
416C22×C4—432no—
417C22×C4—431no—
418C22×C4—431no—
419C22×C4—861no—
420C22×C4—861no—
421C22×C4—861no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4D4×D4311yescharacteristic
428C22×C4D4×D4311yescharacteristic
429C22×C4C23×D4311yescharacteristic
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—432no—
436C2×C8—432no—
437C2×C8—432no—
438C2×C8—868no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8C2×C4×D4312yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—42no—
450C4⋊C4—432no—
451C4⋊C4—432no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—3441no—
459C4⋊C4—3441no—
460C4⋊C4—1722no—
461C4⋊C4C2×C4×D4312yes—
462C4⋊C4C2×C4×D4312yes—
463C22⋊C4—864no—
464C22⋊C4—864no—
465C22⋊C4—3441no—
466C22⋊C4—3441no—
467C22⋊C4—1721no—
468C22⋊C4—1721no—
469C42—21no—
470C42—21no—
471C42—42no—
472C42—864no—
473C42—864no—
474C42—861no—
475C42—861no—
476C42—3441no—
477C42—3441no—
478C42—1722no—
479C23—432no—
480C23—861no—
481C23—861no—
482C23—861no—
483C23—861no—
484C23—861no—
485C23—861no—
486C23C2×D4×D4311yescharacteristic
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—432no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—862no—
509C2×C4—862no—
510C2×C4—862no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4C22×C4×D4311yescharacteristic
531C2×C4#41×D4311yescharacteristic
532C2×C4#41×D4311yescharacteristic
533C2×C4#41×D4311yescharacteristic
534C2×C4#1306337211yescharacteristic
535C2×C4#1306337311yescharacteristic
536C8—22no—
537C8—41no—
538C8—434no—
539C8—1721no—
540C22—862no—
541C22—862no—
542C22—862no—
543C22—1721no—
544C22—1721no—
545C22—1721no—
546C22—1721no—
547C22C4×D4×D4311yescharacteristic
548C22#1458354711yescharacteristic
549C22#1458355111yescharacteristic
550C22#1458369511yescharacteristic
551C22#1458369511yescharacteristic
552C22#1458370111yescharacteristic
553C22#1458371211yescharacteristic
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—81no—
559C4—81no—
560C4—862no—
561C4—3441no—
562C4—3441no—
563C4—1722no—
564C4—1722no—
565C4—1721no—
566C4—1721no—
567C4#117×D4311yescharacteristic
568C4#1458337511yescharacteristic
569C4#1458358111yescharacteristic
570C4#1458358511yescharacteristic
571C2—1722no—
572C2#1913746111yescharacteristic
573C2#1914339211yescharacteristic
574C2#1914347011yescharacteristic
575C2#1914708811yescharacteristic
576C2#1914709211yescharacteristic
577C2#1914711811yescharacteristic
578C2#1914712211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1921C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1921D43
hypocenterC43#22616
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. #19135337C2semidirect
5. #19135335C2semidirect
6. #19135189C2semidirect
7. #19135167C2semidirect
8. #19135165C2semidirect
12. #19134493C2semidirect
13. #19134491C2semidirect
15. C43×#1921C2semidirect
19. #14582936C4semidirect
288. #1921D43semidirect
349. C43#22616semidirect

Maximal subgroups

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

subgroupindex
C2×#145829362
#191374872
#191374762
#191353372
#191353352
#191351892
#191351672
#191351652
#191346882
#191346232
#191344932
#191344912
#191343702
C43×#19212
#2261643