Finite Group Databasebeta

← #25129583

Subgroups — #25129583

Order 11008.

1344 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×#14583555C211yesmaximal, characteristic
2C2×#14583215C211yesmaximal, characteristic, complemented
3C22×#13063250C211yesmaximal, characteristic, complemented
4#19138913C211yesmaximal, characteristic, complemented
5#19135835C212yesmaximal, complemented
6#19135794C212yesmaximal, complemented
7#19134887C211yesmaximal, characteristic, complemented
8#19134864C212yesmaximal, complemented
9#19134532C212yesmaximal, complemented
10#19134529C211yesmaximal, characteristic, complemented
11C43×#1893C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13C23×Dic86C2211yescharacteristic
14#14583555—24no—
15#14583555—24no—
16C2×#13063312C2211yescharacteristic
17C2×#13063311—21no—
18C2×#13063305C2211yescharacteristic
19C2×#13063302—21no—
20C2×#13063297—21no—
21C2×#13063290C2211yescharacteristic
22C2×D4×Dic43—21no—
23C2×C4×C22⋊D43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25#14583215—24no—
26C2×#13063256C2212yes—
27C2×#13063250—24no—
28C2×#13063250C2212yes—
29C2×#13063250C2212yes—
30C2×#13063248C2212yes—
31C2×#13063248C2212yes—
32C2×#13063246C2212yes—
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×(C2×D43)⋊C8C2212yes—
35#14582839—21no—
36#14582836—21no—
37#14582798C2212yes—
38#14582776—21no—
39#14582774—21no—
40#14582756C2212yes—
41#14582653C2212yes—
42C23×C8×C43C2211yescharacteristic
43C2×#121×C43C2211yescharacteristic
44C2×#102×C43C2212yes—
45C43×#380C2211yescharacteristic
46C43×#340C2212yes—
47C2×#10621900—22no—
48C2×#10621900—22no—
49C2×#10621900—24no—
50C2×#10621900—42no—
51C22×Dic86—24no—
52C22×Dic86—22no—
53C22×Dic86—21no—
54C22×Dic86—42no—
55C22×Dic86D414yes—
56C22×Dic86C2311yescharacteristic
57C22×Dic86C2311yescharacteristic
58C22×C22⋊D43—21no—
59C22×C22⋊D43D411yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8C2312yes—
65#13063312—22no—
66#13063312—22no—
67#13063311—28no—
68#13063305—22no—
69#13063305—22no—
70#13063302—28no—
71#13063297—28no—
72#13063290—22no—
73#13063290—22no—
74D4×Dic43—28no—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43C2312yes—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4D411yescharacteristic
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43D411yescharacteristic
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063256—24no—
94#13063250—24no—
95#13063250—24no—
96#13063248—24no—
97#13063248—42no—
98#13063246—24no—
99C22⋊(C43⋊C8)—22no—
100(C2×D43)⋊C8—42no—
101C43⋊#95—22no—
102C43⋊#95—22no—
103C22×D4×C43—21no—
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43C2311yescharacteristic
106C22×C8×C43—22no—
107C22×C8×C43—42no—
108C22×C8×C43C2312yes—
109#121×C43—22no—
110#121×C43D414yes—
111C2×C4⋊C4×C43C2312yes—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115#102×C43—42no—
116#95×C43—21no—
117C24×C43—21no—
118C24×C43C2×D411yescharacteristic
119C23×D43C2×D411yescharacteristic
120C2×D4×C43—21no—
121C2×D4×C43—24no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—42no—
125C2×D4×C43—42no—
126C2×D4×C43C2×D412yes—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43—24no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43—22no—
139C2×C22⋊D43—44no—
140C22×Dic43—24no—
141C22×Dic43—24no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—22no—
145C22×Dic43—44no—
146C22×Dic43—44no—
147C22×Dic43—42no—
148C22×Dic43—82no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152#10621900—48no—
153#10621900—44no—
154#10621900—44no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×Dic86—21no—
160C2×Dic86—22no—
161C2×Dic86—22no—
162C2×Dic86—22no—
163C2×Dic86—28no—
164C2×Dic86—24no—
165C2×Dic86—21no—
166C2×Dic86—44no—
167C2×Dic86—48no—
168C2×Dic86—44no—
169C2×Dic86C2×D412yes—
170C2×Dic86C2×D412yes—
171C2×Dic86#4114yes—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C2×C8×C43—44no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43C2×D412yes—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—42no—
182C22⋊Dic43—24no—
183C22⋊Dic43—24no—
184C22⋊Dic43—22no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—82no—
188C4⋊Dic43—24no—
189C4⋊Dic43—22no—
190C4⋊Dic43—22no—
191C4⋊Dic43—42no—
192C4⋊Dic43—82no—
193Dic43⋊C4—24no—
194Dic43⋊C4—22no—
195C4×Dic43—24no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43—22no—
204C23×C43—42no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—42no—
208C23×C43#12012yes—
209C23×C43#13512yes—
210C23×C43#13712yes—
211C23×C43C22×D411yescharacteristic
212C22×D43—21no—
213C22×D43—22no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—22no—
217D4×C43—24no—
218D4×C43—48no—
219D4×C43—41no—
220D4×C43—41no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—24no—
225C2×C4×C43—22no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43#12012yes—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4112yes—
235C2×C4×C43H(5,𝔽2)12yes—
236C22⋊D43—48no—
237C22⋊D43—44no—
238C2×Dic43—22no—
239C2×Dic43—24no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—48no—
249C2×Dic43—48no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—84no—
255C4×D43—41no—
256C4×D43—41no—
257C4×D43—42no—
258Dic86—22no—
259Dic86—24no—
260Dic86—22no—
261Dic86—22no—
262Dic86—48no—
263Dic86—42no—
264Dic86#12314yes—
265C8×C43—42no—
266C43⋊C8—42no—
267#24036—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—24no—
271C22×C43—24no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—82no—
276C22×C43—82no—
277C22×C43#45214yes—
278C22×C43C2×#12011yescharacteristic
279C22×C43#54612yes—
280C22×C43C2×#13511yescharacteristic
281C22×C43C2×#13711yescharacteristic
282C22×C43#57712yes—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—42no—
287C2×D43—42no—
288C4×C43—22no—
289C4×C43—42no—
290C4×C43—82no—
291C4×C43C2×#12311yescharacteristic
292C4×C43#53411yescharacteristic
293C4×C43#54612yes—
294Dic43—24no—
295Dic43—42no—
296Dic43—41no—
297Dic43—41no—
298Dic43—41no—
299Dic43—82no—
300C2×#548—431no—
301C2×#481—431no—
302C22×#103—431no—
303#2487—431no—
304#2042—432no—
305#2035—432no—
306#1893D4311yescharacteristic, complemented
307#1869—431no—
308#1865—432no—
309#1788—432no—
310#1787—431no—
311C2×C43—24no—
312C2×C43—82no—
313C2×C43#240511yescharacteristic
314C2×C43C2×#45211yescharacteristic
315C2×C43#301011yescharacteristic
316C2×C43#330112yes—
317C2×C43#331612yes—
318D43—81no—
319C22×#41—431no—
320C23×Q8—431no—
321C23×C8C2×D4311yescharacteristic
322#548—864no—
323#548—864no—
324C2×#124—431no—
325C2×#124—861no—
326C2×C22⋊Q8—431no—
327C2×C22⋊Q8—861no—
328C2×#121—861no—
329C2×#121C2×D4311yescharacteristic
330C2×C4×Q8—431no—
331C2×C4×D4—431no—
332C2×C4×D4—861no—
333C22×C4⋊C4—431no—
334#481—864no—
335C2×#106—432no—
336C2×#103—432no—
337C2×#103—432no—
338C2×#103—432no—
339C2×#103—432no—
340C2×#103—864no—
341C2×#102—432no—
342C2×#102C2×D4312yes—
343C2×C22⋊C8—431no—
344C2×C22⋊C8—432no—
345#400—861no—
346#399—861no—
347#389—432no—
348#386—861no—
349#385—861no—
350#380—432no—
351#380C2×D4311yescharacteristic
352#340C2×D4312yes—
353#336—432no—
354C43#2403611yescharacteristic, complemented, Sylow
355C2×#41—862no—
356C2×#41—862no—
357C2×#41—864no—
358C2×#41—1722no—
359C22×Q8—434no—
360C22×Q8—431no—
361C22×Q8—431no—
362C22×Q8—864no—
363C22×Q8—862no—
364C22×Q8—861no—
365C22×Q8—1722no—
366C22×D4—21no—
367C22×D4—431no—
368C22×D4—861no—
369C22×D4C22×D4311yescharacteristic
370C23×C4—431no—
371C23×C4—861no—
372C23×C4—861no—
373C23×C4—861no—
374C23×C4C22×D4311yescharacteristic
375C22×C8—22no—
376C22×C8—42no—
377C22×C8—432no—
378C22×C8C22×D4312yes—
379#124—868no—
380#124—862no—
381#124—862no—
382C22⋊Q8—868no—
383C22⋊Q8—862no—
384C22⋊Q8—862no—
385#121—22no—
386#121—868no—
387#121D17214yes—
388C4×Q8—862no—
389C4×Q8—862no—
390C4×D4—868no—
391C4×D4—862no—
392C4×D4—862no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—432no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—862no—
398C2×C4⋊C4—862no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4312yes—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—431no—
406C2×C22⋊C4—431no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—862no—
411C2×C42—431no—
412C2×C42—861no—
413#106—864no—
414#103—864no—
415#103—864no—
416#103—864no—
417#103—1722no—
418#102—42no—
419#102—864no—
420C22⋊C8—862no—
421C22⋊C8—1722no—
422#95—21no—
423#95—862no—
424#95—862no—
425C24—21no—
426C24—431no—
427C24D4×D4311yescharacteristic
428#41—1728no—
429#41—1724no—
430#41—1724no—
431C2×Q8—432no—
432C2×Q8—432no—
433C2×Q8—434no—
434C2×Q8—868no—
435C2×Q8—864no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—862no—
439C2×Q8—862no—
440C2×Q8—862no—
441C2×Q8—1724no—
442C2×Q8—1724no—
443C2×Q8—1728no—
444C2×D4—24no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—864no—
451C2×D4—862no—
452C2×D4—862no—
453C2×D4—862no—
454C2×D4—1724no—
455C2×D4C2×D17212yes—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—861no—
464C22×C4—864no—
465C22×C4—864no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—3442no—
473C22×C4—1724no—
474C22×C4—1724no—
475C22×C4—1722no—
476C22×C4C2×D17212yes—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4312yes—
479C22×C4C23×D4311yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—44no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8—862no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—864no—
491C4⋊C4—864no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—3442no—
496C4⋊C4—1722no—
497C4⋊C4C2×D17212yes—
498C22⋊C4—24no—
499C22⋊C4—42no—
500C22⋊C4—864no—
501C22⋊C4—864no—
502C22⋊C4—864no—
503C22⋊C4—862no—
504C22⋊C4—862no—
505C22⋊C4—3442no—
506C42—864no—
507C42—861no—
508C42—861no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23—861no—
517C23—861no—
518C23—861no—
519C23—862no—
520C23—862no—
521C23#1306329512yes—
522C23#1306334412yes—
523C23#1306335412yes—
524C23C2×D4×D4311yescharacteristic
525Q8—434no—
526Q8—862no—
527Q8—864no—
528Q8—862no—
529Q8—862no—
530Q8—1728no—
531Q8—1722no—
532D4—24no—
533D4—48no—
534D4—41no—
535D4—41no—
536D4—1728no—
537D4—1724no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—862no—
549C2×C4—864no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—862no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—3444no—
559C2×C4—1728no—
560C2×C4—1728no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1722no—
568C2×C4#1306329512yes—
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4C22×D17211yescharacteristic
571C2×C4#41×D4312yes—
572C2×C4#1306337012yes—
573C8—42no—
574C8—1722no—
575C22—24no—
576C22—22no—
577C22—22no—
578C22—24no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—82no—
583C22—82no—
584C22—1722no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1722no—
589C22#1458306214yes—
590C22C2×#1306329511yescharacteristic
591C22#1458353812yes—
592C22C2×#1306334411yescharacteristic
593C22C2×#1306335411yescharacteristic
594C22#1458370612yes—
595C4—22no—
596C4—42no—
597C4—82no—
598C4—864no—
599C4—3442no—
600C4—1721no—
601C4—1721no—
602C4—1722no—
603C4—1721no—
604C4#123×D4311yescharacteristic
605C4#1458345911yescharacteristic
606C4#1458354412yes—
607C2—24no—
608C2—82no—
609C2—3441no—
610C2#1913792111yescharacteristic
611C2C2×#1458306211yescharacteristic
612C2#1914388411yescharacteristic
613C2#1914650312yes—
614C2#1914671212yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#14583555C2
hypercenter#1893D43
hypocenterC43#24036
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#14583215C2semidirect
3. C22×#13063250C2semidirect
4. #19138913C2semidirect
5. #19135835C2semidirect
6. #19135794C2semidirect
7. #19134887C2semidirect
8. #19134864C2semidirect
9. #19134532C2semidirect
10. #19134529C2semidirect
11. C43×#1893C2semidirect
306. #1893D43semidirect
354. C43#24036semidirect

Maximal subgroups

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

subgroupindex
C2×#145835552
C2×#145832152
C22×#130632502
#191389132
#191358352
#191357942
#191348872
#191348642
#191345322
#191345292
C43×#18932
#2403643