Finite Group Databasebeta

← #25132308

Subgroups — #25132308

Order 11008.

1410 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D43C211yesmaximal, characteristic, complemented
2C2×#14583140C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D43C211yesmaximal, characteristic
4#19137956C212yesmaximal
5#19135916C212yesmaximal, complemented
6#19135603C212yesmaximal, complemented
7#19135457C211yesmaximal, characteristic, complemented
8#19135454C211yesmaximal, characteristic, complemented
9#19134621C211yesmaximal, characteristic, complemented
10#19134528C212yesmaximal, complemented
11C2×C43×#467C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2212yes—
13C22×Dic172C2211yescharacteristic
14C22×#10621885C2212yes—
15C2×Q16×D43—24no—
16C2×Q16×D43—24no—
17C2×Q16×D43—24no—
18C22×C8×D43C2211yescharacteristic
19C2×#13063304C2212yes—
20C2×C4×C22⋊D43C2211yescharacteristic
21#14583140—24no—
22C8×C22⋊D43—24no—
23C2×#13063259C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063250C2212yes—
26C2×#13063249C2212yes—
27C2×#13063248C2212yes—
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582819—22no—
32#14582811—22no—
33#14582806C2212yes—
34#14582804C2212yes—
35#14582775—22no—
36#14582770—22no—
37#14582756C2212yes—
38#14582661C2212yes—
39C22×Q16×C43C2211yescharacteristic
40C23×C8×C43C2211yescharacteristic
41C2×C22⋊Q8×C43C2212yes—
42C43×#467—24no—
43C2×#107×C43C2211yescharacteristic
44C2×#103×C43C2212yes—
45C22×Dic86—22no—
46C22×Dic86C2312yes—
47C2×Q8×D43—24no—
48C2×Q8×D43—24no—
49C2×Q8×D43—24no—
50C2×Q8×D43—24no—
51C2×Q8×D43—42no—
52C2×Q8×D43—42no—
53C22×C22⋊D43D411yescharacteristic
54C22×C4×D43—22no—
55C22×C4×D43C2311yescharacteristic
56C2×Dic172—22no—
57C2×Dic172—22no—
58C2×Dic172D414yescomplemented
59C2×#10621885—24no—
60C2×#10621885—24no—
61C2×#10621885—24no—
62Q16×D43—232no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C2×C8×D43—22no—
66C2×C8×D43—22no—
67C2×C8×D43D414yes—
68#13063304—24no—
69#13063304—42no—
70C4×C22⋊D43—22no—
71C4×C22⋊D43—22no—
72C2×C4⋊Dic43C2312yes—
73C2×Dic43⋊C4—22no—
74C2×Dic43⋊C4D411yescharacteristic
75C2×C22⋊Dic43—22no—
76C2×C22⋊Dic43D411yescharacteristic
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4D411yescharacteristic
79C2×C4×Dic43C2311yescharacteristic
80#13063259—22no—
81Dic43⋊C8—22no—
82#13063250—24no—
83#13063249—42no—
84#13063248—42no—
85C22⋊(C43⋊C8)—22no—
86(C2×D43)⋊C8—22no—
87C8×Dic43—22no—
88C43⋊#95—22no—
89C43⋊#95—22no—
90C43⋊#95—22no—
91C43⋊#95—22no—
92C43⋊#95—22no—
93C22×Q8×C43C2312yes—
94C23×C4×C43C2311yescharacteristic
95C2×Q16×C43—22no—
96C2×Q16×C43—22no—
97C2×Q16×C43D414yescomplemented
98C22×C8×C43—22no—
99C22×C8×C43—22no—
100C22×C8×C43—22no—
101C22×C8×C43C2311yescharacteristic
102C22×C8×C43C2311yescharacteristic
103C22⋊Q8×C43—24no—
104C22⋊Q8×C43—42no—
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43C2312yes—
107C2×C22⋊C4×C43—22no—
108#107×C43—22no—
109#103×C43—24no—
110C24×C43C2×D411yescharacteristic
111C23×D43C2×D411yescharacteristic
112C2×Q8×C43—22no—
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43C2×D414yes—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—22no—
129C2×C22⋊D43—22no—
130C2×C22⋊D43Q1614yescomplemented
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136Q8×D43—216no—
137Q8×D43—48no—
138Q8×D43—48no—
139Q8×D43—48no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—44no—
145C2×C4×D43—44no—
146C2×C4×D43—44no—
147C2×C4×D43C2×D412yes—
148C2×C4×D43#4112yes—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C2×Dic86—22no—
152C2×Dic86—22no—
153C2×Dic86—22no—
154C2×Dic86—44no—
155C2×Dic86—44no—
156C2×Dic86—44no—
157C2×Dic86C2×D414yes—
158Q16×C43—28no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—44no—
163C2×C8×C43C2×D412yes—
164C2×C8×C43C2×D412yes—
165C2×C8×C43C2×D412yes—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—44no—
169C22⋊C4×C43—44no—
170C22⋊Dic43—22no—
171C22⋊Dic43—44no—
172#10621885—216no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—44no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177Dic43⋊C4—22no—
178Dic43⋊C4—44no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8C2×D412yes—
187Dic172—28no—
188C8×D43—28no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43C2×Q1612yescomplemented
196C23×C43C22×D411yescharacteristic
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43#12112yes—
202C22×D43C2×Q1612yes—
203C22×D43#13512yes—
204Q8×C43—24no—
205Q8×C43—24no—
206Q8×C43—42no—
207Q8×C43—42no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—24no—
211C2×C4×C43—21no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C43H(5,𝔽2)11yescharacteristic
227C22⋊D43—28no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—24no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43#12112yes—
242C2×Dic43C2×Q1612yescomplemented
243C4×D43—22no—
244C4×D43—22no—
245C4×D43—22no—
246C4×D43—22no—
247C4×D43—416no—
248Dic86—24no—
249Dic86—24no—
250Dic86—416no—
251Dic86—42no—
252Dic86—42no—
253C8×C43—41no—
254C8×C43#12014yes—
255C43⋊C8—22no—
256C43⋊C8—41no—
257#24268—431nomaximal, Sylow
258C22×C43—22no—
259C22×C43—22no—
260C22×C43—22no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43C2×#12111yescharacteristic
266C22×C43D4211yescharacteristic
267C22×C43D4211yescharacteristic
268C22×C43C22×Q1611yescharacteristic
269C22×C43C2×#13511yescharacteristic
270C22×C43#57811yescharacteristic
271C22×C43#57811yescharacteristic
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—22no—
276C2×D43—22no—
277C2×D43—22no—
278C2×D43#46714yescomplemented
279C4×C43—44no—
280C4×C43—41no—
281C4×C43—82no—
282C4×C43C2×#12011yescharacteristic
283C4×C43#53511yescharacteristic
284C4×C43#54611yescharacteristic
285C4×C43#54611yescharacteristic
286Dic43—22no—
287Dic43—22no—
288Dic43—44no—
289Dic43—41no—
290Dic43—82no—
291C23×Q16—431no—
292C2×#467—431no—
293C2×#467D4311yescharacteristic, complemented
294C2×C8×D4—431no—
295#2409—432no—
296#2056—432no—
297#2001—432no—
298#1969—431no—
299#1969—431no—
300#1808—431no—
301#1787—432no—
302C2×C43—42no—
303C2×C43#240811yescharacteristic
304C2×C43C2×#46711yescharacteristic
305C2×C43#305911yescharacteristic
306C2×C43#328511yescharacteristic
307C2×C43#328511yescharacteristic
308C2×C43D4×Q1611yescharacteristic
309C2×C43D4×Q1611yescharacteristic
310D43—24no—
311C23×Q8—432no—
312C22×Q16—432no—
313C22×Q16—431no—
314C22×Q16—864no—
315C22×Q16—864no—
316C22×Q16—864no—
317C22×Q16C2×D4311yescharacteristic
318C23×C8—431no—
319C23×C8C2×D4311yescharacteristic
320C2×C22⋊Q8—432no—
321C2×C22⋊Q8C2×D4312yes—
322C2×C4×D4—431no—
323#467—24no—
324#467—864no—
325C8×D4—864no—
326C2×#107—431no—
327C2×#107C2×D4311yescharacteristic
328C2×C4⋊C8—431no—
329C2×#103—432no—
330C2×#103—432no—
331C2×#103—432no—
332C2×#103C2×D4312yes—
333C2×C22⋊C8—431no—
334C2×C22⋊C8—431no—
335C2×C4×C8—431no—
336#395—862no—
337#393—862no—
338#391—432no—
339#391—432no—
340#386—862no—
341#385—862no—
342#380—432no—
343#340—432no—
344C43#2426811yescharacteristic, complemented, Sylow
345C22×Q8—432no—
346C22×Q8—862no—
347C22×Q8—864no—
348C22×Q8—864no—
349C22×Q8—864no—
350C22×Q8—864no—
351C22×Q8—1722no—
352C22×Q8—1722no—
353C22×Q8C22×D4312yes—
354C22×D4—431no—
355C23×C4—431no—
356C23×C4—862no—
357C23×C4C22×D4311yescharacteristic
358C2×Q16—22no—
359C2×Q16—22no—
360C2×Q16—434no—
361C2×Q16—864no—
362C2×Q16—8632no—
363C2×Q16—864no—
364C2×Q16—864no—
365C2×Q16—862no—
366C2×Q16—862no—
367C2×Q16C22⋊D4314yescomplemented
368C22×C8—22no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—431no—
372C22×C8—434no—
373C22×C8—431no—
374C22×C8—862no—
375C22×C8—862no—
376C22×C8C22×D4311yescharacteristic
377C22×C8C22×D4311yescharacteristic
378C22⋊Q8—24no—
379C22⋊Q8—42no—
380C22⋊Q8—864no—
381C22⋊Q8—1722no—
382C4×D4—862no—
383C4×D4—862no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—432no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4C22×D4312yes—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—431no—
391C2×C22⋊C4—431no—
392C2×C22⋊C4—862no—
393C2×C22⋊C4—862no—
394C2×C42—431no—
395#107—22no—
396#107—862no—
397C4⋊C8—862no—
398#103—24no—
399#103—864no—
400#103—1722no—
401#103—1722no—
402C22⋊C8—862no—
403C22⋊C8—862no—
404C4×C8—862no—
405#95—862no—
406#95—862no—
407#95—862no—
408#95—862no—
409#95—862no—
410C24—431no—
411C24D4×D4311yescharacteristic
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—434no—
418C2×Q8—862no—
419C2×Q8—8616no—
420C2×Q8—862no—
421C2×Q8—862no—
422C2×Q8—862no—
423C2×Q8—862no—
424C2×Q8—1724no—
425C2×Q8—1724no—
426C2×Q8—1724no—
427C2×Q8—1728no—
428C2×Q8—1728no—
429C2×Q8—1728no—
430C2×Q8C2×C22⋊D4314yes—
431C2×D4—434no—
432C2×D4—862no—
433C2×D4—862no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—432no—
445C22×C4—432no—
446C22×C4—431no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—1724no—
454C22×C4—1724no—
455C22×C4—1724no—
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458Q16—28no—
459Q16—8616no—
460Q16—868no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—44no—
465C2×C8—432no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—868no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8D4×D4312yes—
473C2×C8D4×D4312yes—
474C2×C8C2×C22⋊D4312yes—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—44no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—1724no—
482C22⋊C4—44no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C22⋊C4—1724no—
486C22⋊C4—1724no—
487C42—861no—
488C42—861no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—432no—
496C23—432no—
497C23—432no—
498C23—861no—
499C23—861no—
500C23—861no—
501C23—861no—
502C23Q16×D4312yescomplemented
503C23C2×D4×D4311yescharacteristic
504Q8—24no—
505Q8—24no—
506Q8—42no—
507Q8—42no—
508Q8—864no—
509Q8—864no—
510Q8—17216no—
511Q8—1722no—
512Q8—1722no—
513D4—868no—
514C2×C4—21no—
515C2×C4—24no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—432no—
528C2×C4—432no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—864no—
541C2×C4—17216no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4C22×C22⋊D4311yescharacteristic
550C2×C4#41×D4311yescharacteristic
551C2×C4#1306337011yescharacteristic
552C2×C4#1306337111yescharacteristic
553C8—41no—
554C8—862no—
555C8—1721no—
556C8#1306329314yes—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—434no—
565C22—862no—
566C22—862no—
567C22—862no—
568C22—862no—
569C22—862no—
570C22—862no—
571C22#121×D4311yescharacteristic
572C22D4×C22⋊D4311yescharacteristic
573C22#1458353311yescharacteristic
574C22C2×Q16×D4311yescharacteristic
575C22#135×D4311yescharacteristic
576C22#1458371211yescharacteristic
577C22#1458371311yescharacteristic
578C4—41no—
579C4—44no—
580C4—82no—
581C4—862no—
582C4—862no—
583C4—3442no—
584C4—1721no—
585C4—1724no—
586C4C2×#1306329311yescharacteristic
587C4#1458346511yescharacteristic
588C4#1458353711yescharacteristic
589C4#1458354611yescharacteristic
590C2—42no—
591C2—864no—
592C2#1913794711yescharacteristic
593C2#467×D4311yescharacteristic
594C2#1914424511yescharacteristic
595C2#1914633011yescharacteristic
596C2#1914633911yescharacteristic
597C2Q16×C22⋊D4311yescharacteristic
598C2#1914634411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#467C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#467D43
hypocenterC43#24268
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×Q16×D43C2semidirect
2. C2×#14583140C2semidirect
5. #19135916C2semidirect
6. #19135603C2semidirect
7. #19135457C2semidirect
8. #19135454C2semidirect
9. #19134621C2semidirect
10. #19134528C2semidirect
11. C2×C43×#467C2semidirect
58. C2×Dic172D4semidirect
97. C2×Q16×C43D4semidirect
130. C2×C22⋊D43Q16semidirect
195. C23×C43C2×Q16semidirect
242. C2×Dic43C2×Q16semidirect
278. C2×D43#467semidirect
293. C2×#467D43semidirect
344. C43#24268semidirect
367. C2×Q16C22⋊D43semidirect
502. C23Q16×D43semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×D432
C2×#145831402
C2×C8×C22⋊D432
#191379562
#191359162
#191356032
#191354572
#191354542
#191346212
#191345282
C2×C43×#4672
#2426843