Finite Group Databasebeta

← #25070537

Subgroups — #25070537

Order 11008.

1084 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145367C211yesmaximal, characteristic, complemented
2#19145352C211yesmaximal, characteristic, complemented
3#19140400C211yesmaximal, characteristic, complemented
4#19133643C214yesmaximal, complemented
5#19133575C214yesmaximal, complemented
6#19133167C211yesmaximal, characteristic, complemented
7#19133163C211yesmaximal, characteristic, complemented
8C2×#14582623C211yesmaximal, characteristic, complemented
9C2×C43×#538C211yesmaximal, characteristic
10C2×#13063304C2211yescharacteristic
11#14583234—21no—
12#14583232C2212yescomplemented
13#14583229—21no—
14#14583215C2212yescomplemented
15#14583138—22no—
16#14583126—22no—
17#14583055—21no—
18#14583054C2212yescomplemented
19#14583050—21no—
20#14583037C2212yescomplemented
21C2×C22⋊(C43⋊C8)C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23#14582835C2212yescomplemented
24#14582822—22no—
25#14582811C2212yescomplemented
26#14582772—21no—
27#14582759C2211yescharacteristic
28#14582755—21no—
29#14582636C2214yescomplemented
30#14582633C2214yescomplemented
31#14582623C2214yescomplemented
32C43×#538—22no—
33C43×#538—22no—
34C43×#538—22no—
35C43×#538C2214yes—
36C2×#126×C43—21no—
37C2×#124×C43—21no—
38C2×#123×C43—21no—
39C2×C22⋊Q8×C43C2211yescharacteristic
40C2×#121×C43—21no—
41C2×#121×C43C2211yescharacteristic
42C2×#120×C43—21no—
43C2×C4×D4×C43—21no—
44C22×C22⋊C4×C43C2211yescharacteristic
45C22×Dic86C2311yescharacteristic
46C2×#10621885—22no—
47C2×#10621883—22no—
48C22×C43⋊C8—21no—
49C22×C43⋊C8—21no—
50#13063304—21no—
51#13063304—21no—
52#13063304—21no—
53#13063304—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43C2311yescharacteristic
56C2×Dic43⋊C4—21no—
57C2×Dic43⋊C4—22no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43—22no—
62#13063258—22no—
63#13063256—22no—
64#13063249—22no—
65#13063248—22no—
66#13063248—22no—
67#13063246—22no—
68C22⋊(C43⋊C8)—21no—
69C22⋊(C43⋊C8)—21no—
70C22⋊(C43⋊C8)C2312yes—
71C22⋊(C43⋊C8)C2312yes—
72C43⋊#95—22no—
73C43⋊#95C2312yes—
74C25×C43D411yescharacteristic
75C22×Q8×C43D411yescharacteristic
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43D411yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43D411yescharacteristic
82C23×C4×C43C2311yescharacteristic
83#126×C43—24no—
84#126×C43—24no—
85#124×C43—24no—
86#124×C43—24no—
87#123×C43—24no—
88#123×C43—24no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43D412yes—
92C22⋊Q8×C43C2312yes—
93#121×C43—24no—
94#121×C43—24no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43D412yes—
98#121×C43C2312yes—
99#120×C43—24no—
100#120×C43—24no—
101C4×D4×C43—24no—
102C4×D4×C43—24no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43D412yes—
117C2×C22⋊C4×C43C2312yes—
118C2×C42×C43—21no—
119C24×C43—21no—
120C24×C43—21no—
121C24×C43—21no—
122C24×C43—22no—
123C24×C43—22no—
124C24×C43—81no—
125C24×C43—81no—
126C24×C43C2×D412yes—
127C24×C43C2×D411yescharacteristic
128C2×Q8×C43—21no—
129C2×Q8×C43—81no—
130C2×Q8×C43C2×D412yes—
131C2×D4×C43—24no—
132C2×D4×C43—24no—
133C2×D4×C43—21no—
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—42no—
137C2×D4×C43—42no—
138C2×D4×C43—81no—
139C2×D4×C43—82no—
140C2×D4×C43—82no—
141C2×D4×C43C2×D412yes—
142C22×C4×C43—24no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—81no—
149C22×C4×C43—81no—
150C22×C4×C43—82no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—22no—
160C22×Dic43—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—81no—
164C4⋊C4×C43—24no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43C2×D412yes—
170C4⋊C4×C43C2×D412yes—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C42×C43—24no—
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185C22⋊Dic43—42no—
186C22⋊Dic43—82no—
187C22⋊Dic43—82no—
188#10621885—82no—
189#10621883—82no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—81no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—82no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8—81no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43—22no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43—81no—
216C23×C43—81no—
217C23×C43—84no—
218C23×C43—84no—
219C23×C43#12011yescharacteristic
220C23×C43#12011yescharacteristic
221C23×C43#13512yes—
222C23×C43#13712yes—
223C23×C43C22×D411yescharacteristic
224Q8×C43—42no—
225Q8×C43—81no—
226D4×C43—42no—
227D4×C43—42no—
228D4×C43—42no—
229D4×C43—44no—
230D4×C43—81no—
231D4×C43—84no—
232D4×C43—84no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—81no—
249C2×C4×C43—84no—
250C2×C4×C43#12011yescharacteristic
251C2×C4×C43#12011yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261Dic86—42no—
262Dic86—42no—
263C43⋊C8—42no—
264C43⋊C8—42no—
265#18297—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—44no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—82no—
282C22×C43—84no—
283C22×C43—84no—
284C22×C43—84no—
285C22×C43#45212yes—
286C22×C43#45212yes—
287C22×C43C2×#12011yescharacteristic
288C22×C43C2×#13511yescharacteristic
289C22×C43C2×#13711yescharacteristic
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—42no—
295C4×C43—42no—
296C4×C43—42no—
297C4×C43—42no—
298Dic43—82no—
299Dic43—81no—
300Dic43—81no—
301C2×#538D4311yescharacteristic
302#3189—431no—
303#3187—431no—
304#2626—431no—
305#1618—434no—
306#1606—434no—
307#1520—431no—
308#1519—431no—
309C2×#323—431no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—22no—
313C2×C43—22no—
314C2×C43—82no—
315C2×C43—82no—
316C2×C43C2×#45211yescharacteristic
317C2×C43#301911yescharacteristic
318C2×C43#302611yescharacteristic
319#538—22no—
320#538—22no—
321#538—22no—
322#538C2×D4314yes—
323C2×#126—21no—
324C2×#124—21no—
325C2×#123—21no—
326C2×C22⋊Q8—431no—
327C2×C22⋊Q8C2×D4311yescharacteristic
328C2×#121—21no—
329C2×#121C2×D4311yescharacteristic
330C2×#120—21no—
331C2×C4×D4—21no—
332C22×C22⋊C4C2×D4311yescharacteristic
333#484—432no—
334#484—861no—
335#483—861no—
336#481—432no—
337#467—862no—
338#465—862no—
339#451—432no—
340#451—861no—
341#450—861no—
342#448—432no—
343C2×C22⋊C8—431no—
344C2×C22⋊C8—431no—
345#399—432no—
346#396—862no—
347#393—432no—
348#385—861no—
349#380—431no—
350#379—861no—
351#328—434no—
352#327—434no—
353#323—434no—
354C43#1829711yescharacteristic, complemented, Sylow
355C25C22⋊D4311yescharacteristic
356C22×Q8—431no—
357C22×Q8C22⋊D4311yescharacteristic
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4C22⋊D4311yescharacteristic
362C23×C4—21no—
363C23×C4C22⋊D4311yescharacteristic
364C23×C4C22×D4311yescharacteristic
365C2×Q16—862no—
366C2×SD16—862no—
367C22×C8—861no—
368C22×C8—861no—
369#126—24no—
370#126—24no—
371#124—24no—
372#124—24no—
373#123—24no—
374#123—24no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379C22⋊Q8—861no—
380C22⋊Q8—861no—
381C22⋊Q8C22⋊D4312yes—
382C22⋊Q8C22×D4312yes—
383#121—24no—
384#121—24no—
385#121—21no—
386#121—21no—
387#121C22⋊D4312yes—
388#121C22×D4312yes—
389#120—24no—
390#120—24no—
391C4×D4—24no—
392C4×D4—24no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4C22⋊D4311yescharacteristic
400C2×C4⋊C4C22⋊D4311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—862no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4C22⋊D4312yes—
415C2×C22⋊C4C22×D4312yes—
416C2×C42—21no—
417#107—862no—
418#106—862no—
419#103—862no—
420#103—862no—
421#103—862no—
422#102—862no—
423C22⋊C8—432no—
424C22⋊C8—432no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427#95—432no—
428#95—862no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—81no—
435C24—81no—
436C24C2×C22⋊D4312yes—
437C24C2×C22⋊D4311yescharacteristic
438C2×Q8—21no—
439C2×Q8—81no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—3441no—
443C2×Q8C2×C22⋊D4312yes—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—21no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—81no—
452C2×D4—82no—
453C2×D4—82no—
454C2×D4C2×C22⋊D4312yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—82no—
464C22×C4—862no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4C2×C22⋊D4312yes—
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C2×C22⋊D4311yescharacteristic
470C22×C4C2×C22⋊D4311yescharacteristic
471C22×C4C2×C22⋊D4311yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473C22×C4C23×D4311yescharacteristic
474Q16—3442no—
475SD16—3442no—
476C2×C8—862no—
477C2×C8—862no—
478C2×C8—3441no—
479C2×C8—3441no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—3442no—
488C4⋊C4—3441no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4C2×C22⋊D4312yes—
492C4⋊C4C2×C22⋊D4312yes—
493C22⋊C4—24no—
494C22⋊C4—24no—
495C22⋊C4—24no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—3442no—
505C22⋊C4—3442no—
506C22⋊C4—1721no—
507C22⋊C4—1721no—
508C22⋊C4—1722no—
509C42—24no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—81no—
526C23—81no—
527C23—84no—
528C23—84no—
529C23#1306329411yescharacteristic
530C23#1306329411yescharacteristic
531C23#1306334512yes—
532C23#1306335512yes—
533C23C22×C22⋊D4311yescharacteristic
534Q8—42no—
535Q8—81no—
536Q8—1722no—
537Q8—1722no—
538D4—42no—
539D4—44no—
540D4—42no—
541D4—42no—
542D4—81no—
543D4—84no—
544D4—84no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—81no—
561C2×C4—84no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1722no—
569C2×C4#1306329411yescharacteristic
570C2×C4#1306329411yescharacteristic
571C2×C4C22×C22⋊D4311yescharacteristic
572C2×C4C22×C22⋊D4311yescharacteristic
573C8—1722no—
574C8—1722no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—42no—
583C22—44no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—82no—
591C22—84no—
592C22—84no—
593C22—84no—
594C22#1458306112yes—
595C22#1458306112yes—
596C22C2×#1306329411yescharacteristic
597C22C2×#1306334511yescharacteristic
598C22C2×#1306335511yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—42no—
604C4—42no—
605C4—42no—
606C4—42no—
607C4—3442no—
608C4—3441no—
609C4—3441no—
610C2—21no—
611C2—21no—
612C2—22no—
613C2—22no—
614C2—82no—
615C2—82no—
616C2C2×#1458306111yescharacteristic
617C2#1914395211yescharacteristic
618C2#1914399211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#538C2
socleC22×C43C2×#120
hypercenterC2×#538D43
hypocenterC43#18297
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #19145367C2semidirect
2. #19145352C2semidirect
3. #19140400C2semidirect
4. #19133643C2semidirect
5. #19133575C2semidirect
6. #19133167C2semidirect
7. #19133163C2semidirect
8. C2×#14582623C2semidirect
12. #14583232C22semidirect
14. #14583215C22semidirect
18. #14583054C22semidirect
20. #14583037C22semidirect
23. #14582835C22semidirect
25. #14582811C22semidirect
29. #14582636C22semidirect
30. #14582633C22semidirect
31. #14582623C22semidirect
354. C43#18297semidirect

Maximal subgroups

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

subgroupindex
#191453672
#191453522
#191404002
#191336432
#191335752
#191331672
#191331632
C2×#145826232
C2×C43×#5382
#1829743