Finite Group Databasebeta

← #25110455

Subgroups — #25110455

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583292C211yesmaximal, characteristic
2#19137311C211yesmaximal, characteristic, complemented
3#19137309C211yesmaximal, characteristic
4#19135403C211yesmaximal, characteristic
5#19135395C211yesmaximal, characteristic, complemented
6#19134950C211yesmaximal, characteristic
7#19134949C211yesmaximal, characteristic
8#19134939C211yesmaximal, characteristic, complemented
9#19134938C211yesmaximal, characteristic, complemented
10#19134934C211yesmaximal, characteristic, complemented
11#19134930C211yesmaximal, characteristic
12#19134926C211yesmaximal, characteristic
13#19134727C211yesmaximal, characteristic, complemented
14#19134345C211yesmaximal, characteristic, complemented
15C43×#1878C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063323C2211yescharacteristic
20C2×#13063314C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24#14583292C418yescomplemented
25C2×#13063250C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582788—21no—
37#14582788—21no—
38#14582783—21no—
39#14582783—21no—
40#14582780—21no—
41#14582780—21no—
42#14582773—21no—
43#14582773—21no—
44#14582768C2211yescharacteristic
45#14582764C2211yescharacteristic
46#14582745C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×Q16×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×#10621885—41no—
64C2×#10621885—41no—
65C2×#10621885C2×C414yescomplemented
66C2×#10621873—41no—
67C2×#10621873—41no—
68C2×#10621873C2×C414yes—
69C2×#10621884—41no—
70C2×#10621884—41no—
71C2×#10621884C2×C414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063323—22no—
75#13063323C2×C414yescomplemented
76#13063314—22no—
77#13063314C2×C414yes—
78Q8×Dic43—41no—
79Q8×Dic43—41no—
80C4×Dic86—41no—
81C4×Dic86—41no—
82#13063287—41no—
83#13063287—41no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063250—41no—
102#13063249—41no—
103#13063249—41no—
104#13063248—41no—
105#13063247—41no—
106#13063245—41no—
107#13063235C2×C414yescomplemented
108C8×Dic43—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C22×Q8×C43C2311yescharacteristic
121C2×Q16×C43—41no—
122C2×Q16×C43—41no—
123C2×Q16×C43C2×C414yescomplemented
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×Q8×C43—41no—
127C4×Q8×C43—41no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#103×C43—41no—
134#103×C43—41no—
135#95×C43—21no—
136#95×C43—21no—
137C23×D43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C22×C412yes—
149C2×Q8×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172C22×C412yes—
170C2×C4×D43—42no—
171C2×C4×D43—81no—
172C2×C4×D43—81no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86C22×C412yes—
179Q16×C43—44no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43C22×C412yes—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—42no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—42no—
194#10621885—44no—
195#10621884—44no—
196(C2×D43)⋊C4—24no—
197(C2×D43)⋊C4—24no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—81no—
200(C2×D43)⋊C4—81no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—42no—
206Dic43⋊C4—24no—
207Dic43⋊C4—24no—
208Dic43⋊C4—42no—
209Dic43⋊C4—81no—
210Dic43⋊C4—81no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—42no—
214C4×Dic43—42no—
215C4×Dic43C22×C412yes—
216C4×Dic43#4112yes—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8C22×C412yes—
223#10621873—44no—
224C23×C43C22×D411yescharacteristic
225C22×D43—22no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238Q8×C43—41no—
239Q8×C43—41no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43C23×C411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×C4×C43H(5,𝔽2)11yescharacteristic
262C2×C4×C43H(5,𝔽2)11yescharacteristic
263C2×C4×C43H(5,𝔽2)11yescharacteristic
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43C4×D412yes—
284C2×Dic43C4×D412yes—
285D172—22no—
286D172—22no—
287D172—41no—
288D172—41no—
289C4×D43—84no—
290Dic86—22no—
291Dic86—22no—
292Dic86—41no—
293Dic86—41no—
294C8×C43—22no—
295C8×C43—41no—
296C43⋊C8—22no—
297C43⋊C8—41no—
298#22278—431nomaximal, Sylow
299C22×C43C2×C4×D411yescharacteristic
300C22×C43#53511yescharacteristic
301C22×C43#53511yescharacteristic
302C22×C43#57711yescharacteristic
303C22×C43#57711yescharacteristic
304C22×C43#57811yescharacteristic
305C22×C43#57811yescharacteristic
306C2×D43—42no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C4×C43—42no—
314C4×C43—42no—
315C4×C43—41no—
316C4×C43—41no—
317C4×C43—81no—
318C4×C43—81no—
319C4×C43#51811yescharacteristic
320C4×C43#51811yescharacteristic
321C4×C43#54011yescharacteristic
322C4×C43#54011yescharacteristic
323Dic43—22no—
324Dic43—22no—
325Dic43—42no—
326Dic43—41no—
327Dic43—41no—
328Dic43—81no—
329Dic43—81no—
330C2×#497—431no—
331#2327—431no—
332#2326—431no—
333#1958—431no—
334#1956—431no—
335#1880—431no—
336#1880—431no—
337#1878—431no—
338#1878—431no—
339#1878—431no—
340#1878D4311yescharacteristic, complemented
341#1877—431no—
342#1877—431no—
343#1836—431no—
344#1746—431no—
345C2×C43#232811yescharacteristic
346C2×C43#294711yescharacteristic
347C2×C43#294711yescharacteristic
348C2×C43#322211yescharacteristic
349C2×C43#322311yescharacteristic
350C2×C43#322511yescharacteristic
351C2×C43#322511yescharacteristic
352D43—82no—
353C22×Q16—431no—
354C22×Q16C2×D4311yescharacteristic
355C22×SD16—431no—
356C22×SD16—431no—
357C2×C4⋊Q8—431no—
358C2×#124—431no—
359C2×C4×Q8—431no—
360C2×C4×Q8—431no—
361C2×C4×Q8C2×D4311yescharacteristic
362C2×C4×D4—431no—
363#497—438no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103C2×D4311yescharacteristic
369C2×#103C2×D4311yescharacteristic
370C2×#102—431no—
371C2×#102—431no—
372C2×#97—431no—
373C2×C4×C8—431no—
374#391—431no—
375#391—431no—
376#391C2×D4311yescharacteristic
377#390—431no—
378#388—861no—
379#388—861no—
380#387—861no—
381#387—861no—
382#387—861no—
383#387—861no—
384#385—861no—
385#385—861no—
386#384—431no—
387#382—431no—
388#376—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#340C2×D4311yescharacteristic
393#336—431no—
394#336—431no—
395#336—431no—
396#336C2×D4311yescharacteristic
397C43#2227811yescharacteristic, complemented, Sylow
398C22×Q8—431no—
399C22×Q8C22×D4311yescharacteristic
400C22×Q8C22×D4311yescharacteristic
401C22×D4—431no—
402C23×C4—861no—
403C2×Q16—41no—
404C2×Q16—41no—
405C2×Q16—434no—
406C2×Q16—1721no—
407C2×Q16—1721no—
408C2×Q16C4×D4314yescomplemented
409C2×SD16—434no—
410C2×SD16—434no—
411C2×SD16—1721no—
412C2×SD16—1721no—
413C2×SD16—1721no—
414C2×SD16—1721no—
415C22×C8—431no—
416C22×C8—431no—
417C22×C8C22×D4311yescharacteristic
418C22×C8C22×D4311yescharacteristic
419C4⋊Q8—434no—
420C4⋊Q8—862no—
421#124—434no—
422#124—862no—
423C4×Q8—41no—
424C4×Q8—41no—
425C4×Q8—1721no—
426C4×Q8—1721no—
427C4×Q8—1721no—
428C4×Q8—1721no—
429C4×D4—1721no—
430C4×D4—1721no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C4⋊C4C22×D4311yescharacteristic
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C42—21no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453#103—41no—
454#103—41no—
455#103—1721no—
456#103—1721no—
457#103—1721no—
458#103—1721no—
459#102—1721no—
460#102—1721no—
461#97—434no—
462C4×C8—862no—
463#95—21no—
464#95—21no—
465#95—431no—
466#95—431no—
467#95—431no—
468#95—431no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475C24—861no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—432no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8C2×C4×D4312yes—
493C2×Q8C2×C4×D4312yes—
494C2×D4—432no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—861no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—3441no—
512C22×C4—3441no—
513C22×C4—1722no—
514C22×C4D4×D4311yescharacteristic
515C22×C4D4×D4311yescharacteristic
516C22×C4C23×D4311yescharacteristic
517Q16—44no—
518Q16—1724no—
519SD16—1724no—
520SD16—1724no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—432no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8C2×C4×D4312yes—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—864no—
539C4⋊C4—864no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C4⋊C4—861no—
543C4⋊C4—861no—
544C4⋊C4—3441no—
545C4⋊C4—3441no—
546C4⋊C4—1722no—
547C4⋊C4—1722no—
548C22⋊C4—864no—
549C22⋊C4—864no—
550C22⋊C4—3441no—
551C22⋊C4—3441no—
552C22⋊C4—1722no—
553C42—21no—
554C42—21no—
555C42—42no—
556C42—432no—
557C42—432no—
558C42—861no—
559C42—861no—
560C42—1722no—
561C42—1722no—
562C23—862no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23C2×D4×D4311yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—862no—
579Q8—862no—
580Q8—1721no—
581Q8—1721no—
582D4—862no—
583D4—862no—
584D4—1721no—
585D4—1721no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—432no—
605C2×C4—432no—
606C2×C4—861no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—3444no—
618C2×C4—1721no—
619C2×C4—1721no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4C22×C4×D4311yescharacteristic
627C2×C4#41×D4311yescharacteristic
628C2×C4#1306337011yescharacteristic
629C2×C4#1306337011yescharacteristic
630C2×C4#1306337011yescharacteristic
631C2×C4#1306337111yescharacteristic
632C8—22no—
633C8—41no—
634C8—862no—
635C8—1721no—
636C22—3441no—
637C22—3441no—
638C22—3441no—
639C22—3441no—
640C22—1722no—
641C22—1722no—
642C22—1722no—
643C22C4×D4×D4311yescharacteristic
644C22#1458346411yescharacteristic
645C22#1458346511yescharacteristic
646C22#1458370611yescharacteristic
647C22#1458370811yescharacteristic
648C22#1458371211yescharacteristic
649C22#1458371511yescharacteristic
650C4—42no—
651C4—42no—
652C4—41no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—862no—
657C4—862no—
658C4—3441no—
659C4—3441no—
660C4—1722no—
661C4—1721no—
662C4—1721no—
663C4#1458337111yescharacteristic
664C4#1458337211yescharacteristic
665C4#1458349911yescharacteristic
666C4#1458350111yescharacteristic
667C2—3442no—
668C2#1913731611yescharacteristic
669C2#1914343311yescharacteristic
670C2#1914343711yescharacteristic
671C2#1914566411yescharacteristic
672C2#1914567711yescharacteristic
673C2#1914570811yescharacteristic
674C2#1914571011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1878C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1878D43
hypocenterC43#22278
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. #19137311C2semidirect
5. #19135395C2semidirect
8. #19134939C2semidirect
9. #19134938C2semidirect
10. #19134934C2semidirect
13. #19134727C2semidirect
14. #19134345C2semidirect
15. C43×#1878C2semidirect
24. #14583292C4semidirect
65. C2×#10621885C2×C4semidirect
75. #13063323C2×C4semidirect
107. #13063235C2×C4semidirect
123. C2×Q16×C43C2×C4semidirect
340. #1878D43semidirect
397. C43#22278semidirect
408. C2×Q16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832922
#191373112
#191373092
#191354032
#191353952
#191349502
#191349492
#191349392
#191349382
#191349342
#191349302
#191349262
#191347272
#191343452
C43×#18782
#2227843