Finite Group Databasebeta

← #25097478

Subgroups — #25097478

Order 11008.

1422 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583379C211yesmaximal, characteristic
2#19143184C211yesmaximal, characteristic, complemented
3C2×#14582917C211yesmaximal, characteristic
4#19143115C211yesmaximal, characteristic
5#19137218C211yesmaximal, characteristic, complemented
6#19134829C214yesmaximal, complemented
7#19134822C214yesmaximal, complemented
8C2×#14582667C211yesmaximal, characteristic, complemented
9C43×#1733C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12#14583379—22no—
13#14583379—22no—
14#14583379—22no—
15#14583379C2214yes—
16C2×C4×Dic86—21no—
17C2×C4×D172—21no—
18C2×(C22⋊D43)⋊C4—22no—
19C2×#13063284C2211yescharacteristic
20C2×#13063283—21no—
21C22×C4⋊Dic43C2211yescharacteristic
22C2×C4⋊C4×D43—21no—
23#14582942C2212yescomplemented
24#14582942C2212yescomplemented
25#14582939—21no—
26#14582939—21no—
27#14582935—22no—
28#14582917C418yescomplemented
29C2×#13063253C2214yes—
30#14582909—21no—
31#14582905—21no—
32#14582901C2212yes—
33#14582901C2212yes—
34#14582896—22no—
35#14582798—22no—
36#14582774—22no—
37#14582769C2212yescomplemented
38#14582765C2212yescomplemented
39#14582667C2214yescomplemented
40C22×M16×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C43×#339C2214yescomplemented
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898C2×C414yes—
49C2×#10621898D412yes—
50C2×#10621898Q814yes—
51C2×#10621898C2312yes—
52C22×Dic86D411yescharacteristic
53C22×D172D411yescharacteristic
54C22×C22⋊D43—21no—
55C23×Dic43D412yes—
56C22×C4×D43—21no—
57C22×C4×D43—22no—
58C2×#10621877—21no—
59C2×#10621877—22no—
60C2×#10621877C2×C414yescomplemented
61C2×#10621877C2312yes—
62C22×C43⋊C8—21no—
63C4×Dic86—24no—
64C4×Dic86—24no—
65C4×D172—24no—
66C4×D172—24no—
67(C22⋊D43)⋊C4—28no—
68(C22⋊D43)⋊C4—28no—
69#13063284—21no—
70#13063284—21no—
71#13063284—21no—
72#13063284—21no—
73#13063283—24no—
74#13063283—24no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—24no—
80C2×C4⋊Dic43D412yes—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2312yes—
84C2×Dic43⋊C4—22no—
85C4⋊C4×D43—24no—
86C4⋊C4×D43—24no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—22no—
89C2×C4×Dic43—22no—
90C2×C4×Dic43—21no—
91#13063258—22no—
92#13063258—22no—
93#13063256—22no—
94#13063256—22no—
95#13063253C2×C4116yescomplemented
96#13063250—22no—
97#13063250—22no—
98#13063247—22no—
99#13063247—22no—
100C43⋊#95—24no—
101C23×C4×C43C2311yescharacteristic
102C2×M16×C43—21no—
103C2×M16×C43—22no—
104C2×M16×C43—22no—
105C2×M16×C43C2312yes—
106C22×C8×C43—21no—
107#117×C43—21no—
108#117×C43—21no—
109#117×C43—22no—
110#117×C43C2×C414yescomplemented
111#117×C43D412yes—
112#117×C43C2312yes—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43C2312yes—
120C24×C43C2×D411yescharacteristic
121C23×D43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43C22×C412yes—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×Q812yes—
132C22×C4×C43#4112yes—
133C22×C4×C43#4112yes—
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43—24no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—24no—
138C2×C22⋊D43—22no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—82no—
145C22×Dic43C2×D414yes—
146#10621898—24no—
147#10621898—24no—
148#10621898—24no—
149#10621898—24no—
150#10621898—24no—
151#10621898—22no—
152#10621898—22no—
153#10621898C4⋊C418yescomplemented
154#10621898C22×C414yes—
155#10621898C2×Q814yes—
156C2×D172—21no—
157C2×D172—22no—
158C2×D172C4⋊C414yescomplemented
159C2×D172C2×D412yes—
160C2×C4×D43—24no—
161C2×C4×D43—22no—
162C2×C4×D43—24no—
163C2×C4×D43—22no—
164C2×C4×D43—28no—
165C2×C4×D43—84no—
166C2×Dic86—21no—
167C2×Dic86—22no—
168C2×Dic86C4⋊C414yescomplemented
169C2×Dic86C2×D412yes—
170M16×C43—22no—
171M16×C43—22no—
172M16×C43—42no—
173C2×C8×C43—22no—
174C2×C8×C43—42no—
175C4⋊C4×C43—24no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C2×D412yes—
179C4⋊C4×C43C2×D412yes—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C42×C43—22no—
184C42×C43—22no—
185C42×C43—22no—
186C42×C43C22×C414yescomplemented
187C22⋊Dic43—41no—
188C22⋊Dic43—41no—
189(C2×D43)⋊C4—28no—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—22no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—84no—
199Dic43⋊C4—28no—
200C4×Dic43—28no—
201C4×Dic43—41no—
202C4×Dic43—41no—
203#10621877—24no—
204#10621877—22no—
205#10621877C22×C414yescomplemented
206C2×C43⋊C8—24no—
207C2×C43⋊C8—22no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43C4×D412yes—
211C23×C43#12011yescharacteristic
212C23×C43#12011yescharacteristic
213C23×C43C22⋊Q812yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—22no—
216C22×D43—24no—
217C22×D43—42no—
218C22×D43—42no—
219C2×C4×C43—24no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43C2×C4⋊C412yes—
227C2×C4×C43C2×C4⋊C412yes—
228C2×C4×C43C4×D412yes—
229C2×C4×C43C4×D412yes—
230C2×C4×C43C4×D412yes—
231C2×C4×C43#12011yescharacteristic
232C2×C4×C43#12011yescharacteristic
233C2×C4×C43C22⋊Q812yes—
234C2×C4×C43C22⋊Q812yes—
235C2×C4×C43C22⋊Q812yes—
236C2×C4×C43#12312yes—
237C2×C4×C43#12312yes—
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C22⋊D43—24no—
245C22⋊D43—24no—
246C22⋊D43—28no—
247C2×Dic43—22no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—44no—
251C2×Dic43—44no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—82no—
257D172—22no—
258D172—24no—
259D172C2×C4⋊C414yes—
260C4×D43—24no—
261C4×D43—24no—
262C4×D43—28no—
263C4×D43—88no—
264Dic86—22no—
265Dic86—24no—
266Dic86C2×C4⋊C414yes—
267C8×C43—42no—
268C43⋊C8—24no—
269#20864—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43#38512yes—
279C22×C43#38512yes—
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C2×#12011yescharacteristic
282C22×C43C2×C22⋊Q811yescharacteristic
283C2×D43—24no—
284C2×D43—48no—
285C2×D43—42no—
286C2×D43—42no—
287C4×C43—44no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43#38512yes—
291C4×C43#38512yes—
292C4×C43C22×C4⋊C411yescharacteristic
293C4×C43C2×C4×D411yescharacteristic
294C4×C43C2×C22⋊Q811yescharacteristic
295C4×C43C2×#12311yescharacteristic
296Dic43—24no—
297Dic43—44no—
298Dic43—81no—
299Dic43—81no—
300C2×#520—431no—
301#2911—431no—
302C2×#421—431no—
303#2896—431no—
304#2317—431no—
305#1860—434no—
306#1859—434no—
307C2×#343—431no—
308#1733D4311yescharacteristic, complemented
309C2×C43—21no—
310C2×C43—22no—
311C2×C43—21no—
312C2×C43—22no—
313C2×C43C2×#38511yescharacteristic
314C2×C43#301911yescharacteristic
315C2×C43#302011yescharacteristic
316D43—44no—
317C22×#41—431no—
318C22×M16—431no—
319C22×M16C2×D4311yescharacteristic
320#520—434no—
321#520—862no—
322#520—862no—
323#520—862no—
324C2×C4×Q8—861no—
325C2×C4×D4—861no—
326C2×C4×D4—862no—
327C2×#117—431no—
328C2×#117—861no—
329C2×#117C2×D4311yescharacteristic
330C2×#117C2×D4311yescharacteristic
331C22×C4⋊C4—431no—
332C22×C4⋊C4—861no—
333#428—432no—
334#428—432no—
335#428—861no—
336#428—861no—
337#427—862no—
338#421—438no—
339C2×#104—434no—
340#419—861no—
341#418—861no—
342#417—432no—
343#417—432no—
344#416—862no—
345#389—862no—
346#385—862no—
347#384—432no—
348#382—432no—
349#343—434no—
350#339C2×D4314yescomplemented
351C43#2086411yescharacteristic, complemented, Sylow
352C2×#41—434no—
353C2×#41—432no—
354C2×#41—434no—
355C2×#41—432no—
356C2×#41—861no—
357C2×#41—862no—
358C2×#41—861no—
359C2×#41—862no—
360C22×Q8—431no—
361C22×D4—431no—
362C22×D4—861no—
363C23×C4—432no—
364C23×C4—862no—
365C23×C4—861no—
366C23×C4C22×D4311yescharacteristic
367C2×M16—21no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—434no—
371C2×M16—432no—
372C2×M16—861no—
373C2×M16—862no—
374C2×M16C22×D4312yes—
375C22×C8—21no—
376C22×C8—861no—
377C4×Q8—864no—
378C4×Q8—864no—
379C4×D4—864no—
380C4×D4—864no—
381C4×D4—868no—
382C4×D4—868no—
383#117—21no—
384#117—21no—
385#117—22no—
386#117—864no—
387#117—864no—
388#117—861no—
389#117—861no—
390#117—861no—
391#117—861no—
392#117C4×D4314yescomplemented
393#117D17212yes—
394#117C22×D4312yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—432no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—864no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—864no—
407C2×C4⋊C4—864no—
408C2×C4⋊C4D17211yescharacteristic
409C2×C4⋊C4D17211yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—861no—
414C2×C42—21no—
415C2×C42—862no—
416C2×C42—861no—
417C2×C42C22×D4312yes—
418#107—862no—
419#107—862no—
420#106—862no—
421#106—862no—
422#104—4316no—
423#103—862no—
424#103—862no—
425#102—862no—
426#102—862no—
427#95—864no—
428C24—861no—
429C24D4×D4311yescharacteristic
430#41—438no—
431#41—434no—
432#41—434no—
433#41—864no—
434#41—864no—
435#41—864no—
436#41—864no—
437#41—864no—
438#41—862no—
439#41—862no—
440C2×Q8—434no—
441C2×Q8—432no—
442C2×Q8—861no—
443C2×Q8—862no—
444C2×D4—434no—
445C2×D4—432no—
446C2×D4—864no—
447C2×D4—862no—
448C2×D4—864no—
449C2×D4—862no—
450C2×D4—861no—
451C2×D4—862no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—434no—
456C22×C4—868no—
457C22×C4—861no—
458C22×C4—864no—
459C22×C4—862no—
460C22×C4—864no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—3444no—
467C22×C4—3442no—
468C22×C4C2×C4×D4312yes—
469C22×C4C2×D17211yescharacteristic
470C22×C4C2×D17211yescharacteristic
471C22×C4#1062189812yes—
472C22×C4D4×D4311yescharacteristic
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4#1062190012yes—
476C22×C4Q8×D4312yes—
477C22×C4C23×D4311yescharacteristic
478M16—22no—
479M16—22no—
480M16—42no—
481M16—434no—
482M16—864no—
483M16—862no—
484C2×C8—22no—
485C2×C8—42no—
486C2×C8—864no—
487C2×C8—862no—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—868no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—3444no—
501C4⋊C4C2×D17212yes—
502C4⋊C4C2×D17212yes—
503C22⋊C4—24no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—868no—
507C22⋊C4—1721no—
508C22⋊C4—1721no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—868no—
513C42—1721no—
514C42—1721no—
515C42C2×C4×D4314yescomplemented
516C23—41no—
517C23—41no—
518C23—862no—
519C23—864no—
520C23—1722no—
521C23—1722no—
522C23(C22⋊D43)⋊C412yes—
523C23#1306329511yescharacteristic
524C23#1306329511yescharacteristic
525C23#1306330312yes—
526C23C2×D4×D4311yescharacteristic
527Q8—434no—
528Q8—862no—
529Q8—864no—
530D4—434no—
531D4—864no—
532D4—864no—
533D4—868no—
534D4—862no—
535D4—864no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—862no—
544C2×C4—864no—
545C2×C4—864no—
546C2×C4—864no—
547C2×C4—868no—
548C2×C4—864no—
549C2×C4—3448no—
550C2×C4—3442no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1724no—
556C2×C4—1724no—
557C2×C4C4⋊C4×D4312yes—
558C2×C4C4⋊C4×D4312yes—
559C2×C4(C22⋊D43)⋊C412yes—
560C2×C4C4×D17212yes—
561C2×C4C4×D17212yes—
562C2×C4#1306329511yescharacteristic
563C2×C4#1306329511yescharacteristic
564C2×C4#1306330312yes—
565C2×C4#1306330512yes—
566C2×C4#1306330512yes—
567C2×C4#1306330712yes—
568C2×C4#1306330712yes—
569C2×C4C22×C4×D4311yescharacteristic
570C2×C4C2×D4×D4311yescharacteristic
571C2×C4C22×D17211yescharacteristic
572C2×C4C2×Q8×D4311yescharacteristic
573C2×C4C2×#1062190011yescharacteristic
574C2×C4C2×#1062189811yescharacteristic
575C8—42no—
576C8—864no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—42no—
584C22—42no—
585C22—864no—
586C22—1728no—
587C22—1722no—
588C22—1722no—
589C22#1458277312yes—
590C22#1458277312yes—
591C22C2×(C22⋊D43)⋊C411yescharacteristic
592C22C2×#1306329511yescharacteristic
593C22C2×#1306330311yescharacteristic
594C4—44no—
595C4—42no—
596C4—42no—
597C4—864no—
598C4—3441no—
599C4—3441no—
600C4—1724no—
601C4#1458277312yes—
602C4#1458277312yes—
603C4C2×C4⋊C4×D4311yescharacteristic
604C4C2×C4×D17211yescharacteristic
605C4C2×#1306330511yescharacteristic
606C4C2×#1306330711yescharacteristic
607C2—21no—
608C2—22no—
609C2—21no—
610C2—22no—
611C2—1724no—
612C2C2×#1458277311yescharacteristic
613C2#1914395411yescharacteristic
614C2#1914396111yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1733C2
socleC22×C43C2×#120
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1733D43
hypocenterC43#20864
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
2. #19143184C2semidirect
5. #19137218C2semidirect
6. #19134829C2semidirect
7. #19134822C2semidirect
8. C2×#14582667C2semidirect
9. C43×#1733C2semidirect
23. #14582942C22semidirect
24. #14582942C22semidirect
28. #14582917C4semidirect
37. #14582769C22semidirect
38. #14582765C22semidirect
39. #14582667C22semidirect
43. C43×#339C22semidirect
60. C2×#10621877C2×C4semidirect
95. #13063253C2×C4semidirect
110. #117×C43C2×C4semidirect
153. #10621898C4⋊C4semidirect
158. C2×D172C4⋊C4semidirect
168. C2×Dic86C4⋊C4semidirect
186. C42×C43C22×C4semidirect
205. #10621877C22×C4semidirect
308. #1733D43semidirect
350. #339C2×D43semidirect
351. C43#20864semidirect
392. #117C4×D43semidirect
515. C42C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833792
#191431842
C2×#145829172
#191431152
#191372182
#191348292
#191348222
C2×#145826672
C43×#17332
#2086443