Finite Group Databasebeta

← #25151851

Subgroups — #25151851

Order 11008.

1674 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583294C211yesmaximal, characteristic, complemented
2C2×#14583104C211yesmaximal, characteristic, complemented
3C2×#14583061C212yesmaximal, complemented
4C2×#14583050C212yesmaximal, complemented
5#19139548C211yesmaximal, characteristic, complemented
6#19135603C212yesmaximal, complemented
7#19135598C212yesmaximal, complemented
8#19135528C211yesmaximal, characteristic, complemented
9#19135394C211yesmaximal, characteristic, complemented
10#19134420C211yesmaximal, characteristic, complemented
11C2×C43×#546C211yesmaximal, characteristic
12C22×#10621885C2212yescomplemented
13C22×#10621883C2212yes—
14C22×#10621883C2212yes—
15C2×#13063325C2211yescharacteristic, complemented
16C2×#13063304C2212yes—
17C2×#13063304C2212yescomplemented
18#14583294—24no—
19#14583104—24no—
20#14583061—28no—
21#14583050—28no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
23C2×#13063249C2212yescomplemented
24C2×#13063248C2212yescomplemented
25C2×#13063246C2212yes—
26C2×#13063246C2212yes—
27C2×C22⋊(C43⋊C8)C2212yes—
28C2×C22⋊(C43⋊C8)C2212yescomplemented
29C2×#13063236C2211yescharacteristic, complemented
30#14582835—21no—
31#14582835—21no—
32#14582802—21no—
33#14582768—21no—
34C4×C4⋊Dic43C2211yescharacteristic, complemented
35#14582661C2212yescomplemented
36C22×#41×C43C2211yescharacteristic
37C23×D4×C43C2211yescharacteristic
38C43×#546—24no—
39C43×#546—24no—
40C2×#124×C43C2211yescharacteristic
41C2×#123×C43—21no—
42C2×C22⋊Q8×C43C2211yescharacteristic
43C2×#121×C43—21no—
44C2×#121×C43C2211yescharacteristic
45C2×#120×C43—21no—
46C2×C4×D4×C43C2211yescharacteristic
47C2×C4×D4×C43C2211yescharacteristic
48C22×C22⋊C4×C43—21no—
49C22×Dic86C2312yes—
50C2×#10621885—24no—
51C2×#10621885—24no—
52C2×#10621885—42no—
53C2×#10621883—24no—
54C2×#10621883—24no—
55C2×#10621883—24no—
56C2×#10621883—24no—
57C2×#10621883—24no—
58C2×#10621883—42no—
59C22×C43⋊C8C2312yes—
60C22×C43⋊C8C2312yes—
61#13063325—22no—
62#13063325—22no—
63#13063304—24no—
64#13063304—24no—
65#13063304—42no—
66#13063304—42no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2312yes—
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—22no—
72C2×C22⋊Dic43—22no—
73C2×C22⋊Dic43—22no—
74C2×C4×Dic43—21no—
75C4⋊(C43⋊C8)—22no—
76#13063249—24no—
77#13063248—24no—
78#13063246—24no—
79#13063246D418yescomplemented
80C22⋊(C43⋊C8)—24no—
81C22⋊(C43⋊C8)—24no—
82#13063236—22no—
83C43⋊#95—21no—
84C25×C43—21no—
85C2×#41×C43—22no—
86C2×#41×C43—22no—
87C2×#41×C43—24no—
88C2×#41×C43—42no—
89C22×Q8×C43C2311yescharacteristic
90C22×D4×C43—21no—
91C22×D4×C43—21no—
92C22×D4×C43—22no—
93C22×D4×C43—22no—
94C22×D4×C43—24no—
95C22×D4×C43—21no—
96C22×D4×C43—42no—
97C22×D4×C43D411yescharacteristic
98C22×D4×C43C2311yescharacteristic
99C22×D4×C43C2311yescharacteristic
100C23×C4×C43—21no—
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104#124×C43—22no—
105#124×C43D414yes—
106#123×C43—28no—
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43—22no—
109#121×C43—28no—
110#121×C43—22no—
111#121×C43—22no—
112#120×C43—28no—
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C4×D4×C43—22no—
116C4×D4×C43D414yes—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43D411yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—28no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43C2311yescharacteristic
129C24×C43—21no—
130C24×C43—24no—
131C24×C43—21no—
132C24×C43—44no—
133C24×C43—42no—
134C24×C43—42no—
135C24×C43—82no—
136C24×C43C2×D411yescharacteristic
137C24×C43C2×D411yescharacteristic
138#41×C43—48no—
139#41×C43—44no—
140#41×C43—44no—
141C2×Q8×C43—21no—
142C2×Q8×C43—22no—
143C2×Q8×C43—22no—
144C2×Q8×C43C2×D412yes—
145C2×D4×C43—24no—
146C2×D4×C43—24no—
147C2×D4×C43—24no—
148C2×D4×C43—22no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—22no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C2×D4×C43—41no—
156C2×D4×C43—44no—
157C2×D4×C43—44no—
158C2×D4×C43—48no—
159C2×D4×C43—44no—
160C2×D4×C43—44no—
161C2×D4×C43—82no—
162C2×D4×C43C2×D414yes—
163C2×D4×C43C2×D412yes—
164C2×D4×C43C2×D412yes—
165C22×C4×C43—24no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—24no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—44no—
178C22×C4×C43—82no—
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2411yescharacteristic
184C22×Dic43—22no—
185C22×Dic43—22no—
186C2×Dic86—22no—
187C2×Dic86—22no—
188C2×Dic86—22no—
189C2×Dic86—22no—
190C2×Dic86—22no—
191C2×Dic86—22no—
192C4⋊C4×C43—24no—
193C4⋊C4×C43—22no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C2×D412yes—
196C22⋊C4×C43—24no—
197C22⋊C4×C43—24no—
198C22⋊C4×C43—22no—
199C22⋊C4×C43—24no—
200C22⋊C4×C43—24no—
201C22⋊C4×C43—24no—
202C22⋊C4×C43—22no—
203C42×C43C2×D412yes—
204C42×C43C2×D412yes—
205C22⋊Dic43—44no—
206C22⋊Dic43—44no—
207#10621885—48no—
208#10621883—48no—
209#10621883—48no—
210C4⋊Dic43—22no—
211C4⋊Dic43—42no—
212C4⋊Dic43—42no—
213C4⋊Dic43C2×D414yes—
214Dic43⋊C4—44no—
215Dic43⋊C4—44no—
216C4×Dic43—42no—
217C2×C43⋊C8—22no—
218C2×C43⋊C8—22no—
219C2×C43⋊C8—22no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8C2×D414yes—
223C23×C43—21no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—24no—
227C23×C43—21no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—21no—
231C23×C43—22no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—22no—
235C23×C43—48no—
236C23×C43—48no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—42no—
240C23×C43—42no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—42no—
244C23×C43—88no—
245C23×C43—84no—
246C23×C43—88no—
247C23×C43#13712yes—
248C23×C43C22×D411yescharacteristic
249Q8×C43—24no—
250Q8×C43—41no—
251Q8×C43—41no—
252D4×C43—22no—
253D4×C43—24no—
254D4×C43—24no—
255D4×C43—44no—
256D4×C43—48no—
257D4×C43—48no—
258D4×C43—41no—
259D4×C43—41no—
260D4×C43—84no—
261D4×C43#12714yes—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—21no—
267C2×C4×C43—22no—
268C2×C4×C43—21no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—48no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—84no—
281C2×C4×C43#12012yes—
282C2×C4×C43#12012yes—
283C2×C4×C43C22×D412yes—
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43H(5,𝔽2)12yes—
287C2×Dic43—24no—
288C2×Dic43—42no—
289C2×Dic43—42no—
290C2×Dic43—42no—
291C2×Dic43—42no—
292C2×Dic43—42no—
293Dic86—42no—
294Dic86—42no—
295Dic86—42no—
296Dic86—42no—
297C43⋊C8—24no—
298C43⋊C8—42no—
299#25769—431nomaximal, Sylow
300C22×C43—24no—
301C22×C43—22no—
302C22×C43—24no—
303C22×C43—41no—
304C22×C43—42no—
305C22×C43—41no—
306C22×C43—42no—
307C22×C43—44no—
308C22×C43—42no—
309C22×C43—44no—
310C22×C43—41no—
311C22×C43—42no—
312C22×C43—41no—
313C22×C43—42no—
314C22×C43—41no—
315C22×C43—42no—
316C22×C43—42no—
317C22×C43—42no—
318C22×C43—816no—
319C22×C43—82no—
320C22×C43—82no—
321C22×C43C2×#12011yescharacteristic
322C22×C43D4212yes—
323C22×C43C2×#13711yescharacteristic
324C22×C43#57511yescharacteristic
325C22×C43#57712yes—
326C4×C43—22no—
327C4×C43—22no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43—42no—
331C4×C43—42no—
332C4×C43C2×#12711yescharacteristic
333C4×C43#53511yescharacteristic
334C4×C43D4212yes—
335Dic43—44no—
336Dic43—82no—
337C2×#546D4311yescharacteristic
338C2×#497—431no—
339C2×#461—431no—
340C2×#452—432no—
341C2×#450—432no—
342#2542—431no—
343#2001—432no—
344#2000—432no—
345#1983—431no—
346#1955—431no—
347#1762—431no—
348C2×C43—42no—
349C2×C43—44no—
350C2×C43—81no—
351C2×C43—82no—
352C2×C43#243311yescharacteristic
353C2×C43#300711yescharacteristic
354C2×C43#300911yescharacteristic
355C2×C43#326612yes—
356C2×C43#326712yes—
357C22×#41C2×D4311yescharacteristic
358C23×D4C2×D4311yescharacteristic
359C22×Q16—432no—
360C22×SD16—432no—
361C22×SD16—432no—
362#546—24no—
363#546—24no—
364C2×C4⋊Q8—431no—
365C2×#124C2×D4311yescharacteristic
366C2×#123—21no—
367C2×C22⋊Q8—432no—
368C2×C22⋊Q8—432no—
369C2×C22⋊Q8C2×D4311yescharacteristic
370C2×#121—21no—
371C2×#121C2×D4311yescharacteristic
372C2×#120—21no—
373C2×C4×D4C2×D4311yescharacteristic
374C2×C4×D4C2×D4311yescharacteristic
375C22×C22⋊C4—21no—
376#497—864no—
377#461—864no—
378#452—868no—
379#450—868no—
380C2×C4⋊C8—431no—
381C2×#103—432no—
382C2×#103—432no—
383C2×#102—432no—
384C2×#102—432no—
385C2×C22⋊C8—432no—
386C2×C22⋊C8—432no—
387C2×#97—431no—
388#399—861no—
389#399—861no—
390#390—861no—
391#384—861no—
392C4×C4⋊C4—431no—
393#340—432no—
394C43#2576911yescharacteristic, complemented, Sylow
395C25—21no—
396C2×#41—22no—
397C2×#41—22no—
398C2×#41—24no—
399C2×#41—42no—
400C22×Q8—432no—
401C22×Q8C22×D4311yescharacteristic
402C22×D4—21no—
403C22×D4—21no—
404C22×D4—22no—
405C22×D4—22no—
406C22×D4—24no—
407C22×D4—21no—
408C22×D4—42no—
409C22×D4C22⋊D4311yescharacteristic
410C22×D4C22×D4311yescharacteristic
411C22×D4C22×D4311yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4C22×D4311yescharacteristic
415C23×C4C22×D4311yescharacteristic
416C2×Q16—864no—
417C2×Q16—864no—
418C2×Q16—1722no—
419C2×SD16—864no—
420C2×SD16—864no—
421C2×SD16—864no—
422C2×SD16—864no—
423C2×SD16—864no—
424C2×SD16—1722no—
425C22×C8—432no—
426C22×C8—432no—
427C4⋊Q8—862no—
428C4⋊Q8—862no—
429#124—22no—
430#124C22⋊D4314yes—
431#123—28no—
432C22⋊Q8—22no—
433C22⋊Q8—22no—
434C22⋊Q8—864no—
435C22⋊Q8—864no—
436C22⋊Q8—1722no—
437C22⋊Q8—1722no—
438#121—28no—
439#121—22no—
440#121—22no—
441#120—28no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—22no—
445C4×D4C22⋊D4314yes—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—432no—
448C2×C4⋊C4—862no—
449C2×C4⋊C4—862no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4C22⋊D4311yescharacteristic
453C2×C4⋊C4C22×D4311yescharacteristic
454C2×C22⋊C4—28no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—862no—
461C2×C22⋊C4—862no—
462C2×C22⋊C4C22⋊D4311yescharacteristic
463C2×C22⋊C4C22⋊D4311yescharacteristic
464C2×C42—861no—
465C2×C42C22×D4311yescharacteristic
466C4⋊C8—862no—
467#103—864no—
468#103—864no—
469#102—438no—
470#102—864no—
471C22⋊C8—864no—
472C22⋊C8—864no—
473#97—862no—
474#95—861no—
475C24—21no—
476C24—24no—
477C24—21no—
478C24—44no—
479C24—42no—
480C24—42no—
481C24—82no—
482C24C2×C22⋊D4311yescharacteristic
483C24C2×C22⋊D4311yescharacteristic
484#41—48no—
485#41—44no—
486#41—44no—
487C2×Q8—21no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—862no—
491C2×Q8—862no—
492C2×Q8—862no—
493C2×Q8—862no—
494C2×Q8—862no—
495C2×Q8—862no—
496C2×Q8C2×C22⋊D4312yes—
497C2×D4—24no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—24no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—41no—
508C2×D4—44no—
509C2×D4—48no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—82no—
514C2×D4D4×D4314yes—
515C2×D4C2×C22⋊D4312yes—
516C2×D4C2×C22⋊D4312yes—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—44no—
530C22×C4—82no—
531C22×C4—862no—
532C22×C4—862no—
533C22×C4C2×C22⋊D4311yescharacteristic
534C22×C4C2×C22⋊D4311yescharacteristic
535C22×C4C2×C22⋊D4311yescharacteristic
536C22×C4C2×C22⋊D4311yescharacteristic
537C22×C4C23×D4311yescharacteristic
538Q16—1728no—
539SD16—1728no—
540SD16—1728no—
541C2×C8—434no—
542C2×C8—862no—
543C2×C8—862no—
544C2×C8—862no—
545C2×C8—862no—
546C2×C8—862no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—434no—
551C4⋊C4—862no—
552C4⋊C4—1724no—
553C4⋊C4—1724no—
554C4⋊C4—1722no—
555C4⋊C4—1722no—
556C4⋊C4C2×C22⋊D4312yes—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—22no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—22no—
564C22⋊C4—1724no—
565C22⋊C4—1724no—
566C42—1722no—
567C42C2×C22⋊D4312yes—
568C42C2×C22⋊D4312yes—
569C23—21no—
570C23—22no—
571C23—21no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—22no—
580C23—22no—
581C23—48no—
582C23—48no—
583C23—41no—
584C23—41no—
585C23—42no—
586C23—41no—
587C23—41no—
588C23—42no—
589C23—42no—
590C23—88no—
591C23—84no—
592C23—88no—
593C23#1306335512yes—
594C23C22×C22⋊D4311yescharacteristic
595Q8—24no—
596Q8—41no—
597Q8—41no—
598Q8—1722no—
599Q8—1722no—
600Q8—1722no—
601Q8—1722no—
602D4—22no—
603D4—24no—
604D4—24no—
605D4—44no—
606D4—48no—
607D4—48no—
608D4—41no—
609D4—41no—
610D4—84no—
611D4#1306332114yes—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—48no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—84no—
631C2×C4—864no—
632C2×C4—1722no—
633C2×C4—1722no—
634C2×C4—1722no—
635C2×C4—1722no—
636C2×C4—1722no—
637C2×C4#1306329412yes—
638C2×C4#1306329412yes—
639C2×C4C2×D4×D4312yes—
640C2×C4C22×C22⋊D4311yescharacteristic
641C2×C4C22×C22⋊D4311yescharacteristic
642C2×C4#1306337012yes—
643C8—864no—
644C8—1722no—
645C22—24no—
646C22—22no—
647C22—24no—
648C22—44no—
649C22—42no—
650C22—44no—
651C22—42no—
652C22—41no—
653C22—42no—
654C22—41no—
655C22—42no—
656C22—42no—
657C22—41no—
658C22—42no—
659C22—41no—
660C22—42no—
661C22—41no—
662C22—42no—
663C22—816no—
664C22—82no—
665C22—82no—
666C22C2×#1306329411yescharacteristic
667C22D4×C22⋊D4312yes—
668C22C2×#1306335511yescharacteristic
669C22#1458369711yescharacteristic
670C22#1458371012yes—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—42no—
676C4—42no—
677C4—3442no—
678C4—1724no—
679C4C2×#1306332111yescharacteristic
680C4#1458346611yescharacteristic
681C4D4×C22⋊D4312yes—
682C2—42no—
683C2—44no—
684C2—81no—
685C2—82no—
686C2#1913822811yescharacteristic
687C2#1914385511yescharacteristic
688C2#1914387211yescharacteristic
689C2#1914610112yes—
690C2#1914611612yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#546C2
socleC23×C43C22×D4
hypercenterC2×#546D43
hypocenterC43#25769
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#14583294C2semidirect
2. C2×#14583104C2semidirect
3. C2×#14583061C2semidirect
4. C2×#14583050C2semidirect
5. #19139548C2semidirect
6. #19135603C2semidirect
7. #19135598C2semidirect
8. #19135528C2semidirect
9. #19135394C2semidirect
10. #19134420C2semidirect
12. C22×#10621885C22semidirect
15. C2×#13063325C22semidirect
17. C2×#13063304C22semidirect
22. C2×C4⋊(C43⋊C8)C22semidirect
23. C2×#13063249C22semidirect
24. C2×#13063248C22semidirect
28. C2×C22⋊(C43⋊C8)C22semidirect
29. C2×#13063236C22semidirect
34. C4×C4⋊Dic43C22semidirect
35. #14582661C22semidirect
79. #13063246D4semidirect
394. C43#25769semidirect

Maximal subgroups

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

subgroupindex
C2×#145832942
C2×#145831042
C2×#145830612
C2×#145830502
#191395482
#191356032
#191355982
#191355282
#191353942
#191344202
C2×C43×#5462
#2576943