Finite Group Databasebeta

← #25159602

Subgroups — #25159602

Order 11008.

864 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583177C211yesmaximal, characteristic
2#19138428C211yesmaximal, characteristic, complemented
3#19137500C211yesmaximal, characteristic
4#19136141C211yesmaximal, characteristic, complemented
5#19136080C211yesmaximal, characteristic, complemented
6#19135988C211yesmaximal, characteristic, complemented
7#19135926C211yesmaximal, characteristic, complemented
8#19135328C211yesmaximal, characteristic, complemented
9#19135152C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic
11#19134931C211yesmaximal, characteristic
12#19134856C211yesmaximal, characteristic
13#19134849C211yesmaximal, characteristic, complemented
14#19134844C211yesmaximal, characteristic
15C2×C4×SD16×C43C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583177—24no—
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29#14582832—21no—
30#14582819—21no—
31#14582806C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582805—21no—
34#14582798C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582783—21no—
39#14582772—21no—
40#14582771—21no—
41#14582764C2211yescharacteristic
42#14582757—21no—
43C4×Dic43⋊C4C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C4×SD16×C43—24no—
57C2×#106×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C22×Dic86—21no—
62C23×Dic43—21no—
63C23×Dic43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063324—22no—
67#13063324—41no—
68D4×Dic43—22no—
69D4×Dic43—22no—
70D4×Dic43—22no—
71D4×Dic43—41no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063259—22no—
88#13063259—22no—
89#13063258—22no—
90#13063256—41no—
91Dic43⋊C8—22no—
92#13063249—22no—
93#13063249—41no—
94#13063246—22no—
95#13063246—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43Q814yescomplemented
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C4×Q8×C43—22no—
117C4×Q8×C43—41no—
118C4×D4×C43—22no—
119C4×D4×C43—41no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#106×C43—22no—
127#103×C43—22no—
128#102×C43D414yes—
129C4×C8×C43—22no—
130C24×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43C2×Q812yes—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43C2×D412yes—
141C2×D4×C43C2×Q812yes—
142C2×D4×C43#4112yes—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—24no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—81no—
160C22×Dic43—81no—
161C22×Dic43—81no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C2×Dic86—42no—
167C2×Dic86—42no—
168C2×Dic86—81no—
169SD16×C43—28no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C2×D412yes—
175C2×C8×C43C2×Q812yes—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43C2×D412yes—
181C22⋊C4×C43—42no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—42no—
185C22⋊Dic43—24no—
186C22⋊Dic43—42no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—81no—
195C4⋊Dic43#4112yes—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—42no—
199Dic43⋊C4—81no—
200Dic43⋊C4—81no—
201Dic43⋊C4—81no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43C22×D411yescharacteristic
220Q8×C43—22no—
221Q8×C43—22no—
222Q8×C43—41no—
223Q8×C43—41no—
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—22no—
227D4×C43C22⋊Q814yes—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—84no—
243C2×C4×C43#13712yes—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—84no—
274C2×Dic43—84no—
275C2×Dic43#13512yes—
276Dic86—84no—
277C8×C43—22no—
278C8×C43—22no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#26372—431nomaximal, Sylow
282C22×C43—24no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43#52511yescharacteristic
290C22×C43D4211yescharacteristic
291C22×C43D4×Q811yescharacteristic
292C22×C43C2×#13511yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43#57611yescharacteristic
295C22×C43#57711yescharacteristic
296C4×C43—22no—
297C4×C43—42no—
298C4×C43—42no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43C2×C22⋊Q811yescharacteristic
302C4×C43#53911yescharacteristic
303C4×C43#54711yescharacteristic
304C4×C43#55411yescharacteristic
305Dic43—22no—
306Dic43—41no—
307Dic43—41no—
308Dic43—42no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312Dic43—81no—
313C2×#474—431no—
314C2×C4×SD16D4311yescharacteristic
315#2451—431no—
316#2349—431no—
317#2097—431no—
318#2085—431no—
319#2068—431no—
320#2058—431no—
321#1942—431no—
322#1916—431no—
323#1877—431no—
324#1877—431no—
325#1864—431no—
326#1863—431no—
327#1862—431no—
328C2×C43—44no—
329C2×C43#244911yescharacteristic
330C2×C43#310711yescharacteristic
331C2×C43#311811yescharacteristic
332C2×C43#326611yescharacteristic
333C2×C43#328011yescharacteristic
334C2×C43#338111yescharacteristic
335C2×C43#338511yescharacteristic
336C22×SD16C2×D4311yescharacteristic
337C2×C4⋊Q8—431no—
338C2×C4×Q8C2×D4311yescharacteristic
339C2×C4×D4—431no—
340C2×C4×D4—431no—
341C2×C4×D4C2×D4311yescharacteristic
342#474—864no—
343C4×SD16—24no—
344C2×#107—431no—
345C2×#107—431no—
346C2×#107—431no—
347C2×#106—431no—
348C2×#106C2×D4311yescharacteristic
349C2×C4⋊C8—431no—
350C2×#103—431no—
351C2×#103—431no—
352C2×#103C2×D4311yescharacteristic
353C2×#102—431no—
354C2×#102—431no—
355C2×#102C2×D4311yescharacteristic
356C2×C4×C8C2×D4311yescharacteristic
357#398—861no—
358#395—861no—
359#391—431no—
360#391—431no—
361#391—861no—
362#389—431no—
363#389—431no—
364#389—431no—
365#389—431no—
366#387—861no—
367#385—861no—
368#385—861no—
369#382—431no—
370#380—861no—
371C4×C4⋊C4—431no—
372C2×#95—861no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#336—431no—
378#336—431no—
379#336—431no—
380#336—431no—
381C43#2637211yescharacteristic, complemented, Sylow
382C22×Q8—861no—
383C22×Q8C22×D4311yescharacteristic
384C22×D4C22×D4311yescharacteristic
385C23×C4—21no—
386C23×C4—861no—
387C23×C4—861no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16Dic8614yescomplemented
391C22×C8—431no—
392C22×C8—431no—
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395C4⋊Q8—862no—
396C4⋊Q8—1721no—
397C4×Q8—22no—
398C4×Q8—41no—
399C4×D4—22no—
400C4×D4—41no—
401C4×D4—862no—
402C4×D4—862no—
403C4×D4—862no—
404C4×D4—1721no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C42—21no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42C22×D4311yescharacteristic
426#107—862no—
427#107—862no—
428#107—862no—
429#106—22no—
430#106—1721no—
431C4⋊C8—862no—
432#103—22no—
433#103—862no—
434#103—1721no—
435#102—862no—
436#102—862no—
437#102C22⋊D4314yes—
438C4×C8—22no—
439#95—431no—
440#95—431no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451C24—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—3441no—
458C2×Q8—1722no—
459C2×Q8—1722no—
460C2×Q8C2×Dic8612yes—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4C2×Dic8612yes—
465C2×D4#1062189812yes—
466C2×D4C2×C22⋊D4312yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—864no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—3441no—
483C22×C4—3441no—
484C22×C4—3441no—
485C22×C4—1722no—
486C22×C4—1722no—
487C22×C4D4×D4311yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4C23×D4311yescharacteristic
490SD16—28no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8C2×Dic8612yes—
502C2×C8C2×C22⋊D4312yes—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—432no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—3441no—
518C4⋊C4—3441no—
519C4⋊C4—3441no—
520C4⋊C4—3441no—
521C4⋊C4—1722no—
522C4⋊C4C2×C22⋊D4312yes—
523C22⋊C4—42no—
524C22⋊C4—864no—
525C22⋊C4—1722no—
526C42—21no—
527C42—21no—
528C42—42no—
529C42—861no—
530C42—861no—
531C42—861no—
532C42—861no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23C2×D4×D4311yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—3444no—
546D4—22no—
547D4—22no—
548D4—22no—
549D4#1306330414yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4—432no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—862no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—3444no—
579C2×C4—3444no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4#1306335412yes—
592C2×C4C22×C22⋊D4311yescharacteristic
593C2×C4C22×Dic8611yescharacteristic
594C2×C4#41×D4311yescharacteristic
595C2×C4C2×#1062189811yescharacteristic
596C2×C4#1306337011yescharacteristic
597C2×C4#1306337211yescharacteristic
598C8—22no—
599C8—22no—
600C8—1721no—
601C8—1721no—
602C22—24no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22#1458340811yescharacteristic
610C22D4×C22⋊D4311yescharacteristic
611C22D4×Dic8611yescharacteristic
612C22#135×D4311yescharacteristic
613C22C2×#1306335411yescharacteristic
614C22#1458370111yescharacteristic
615C22#1458370511yescharacteristic
616C4—22no—
617C4—41no—
618C4—42no—
619C4—42no—
620C4—81no—
621C4—862no—
622C4—3441no—
623C4—3441no—
624C4—3441no—
625C4—1721no—
626C4—1722no—
627C4—1721no—
628C4—1721no—
629C4C2×#1306330411yescharacteristic
630C4#1458349111yescharacteristic
631C4#1458354811yescharacteristic
632C4#1458360811yescharacteristic
633C2—44no—
634C2#1913839811yescharacteristic
635C2#1914466211yescharacteristic
636C2#1914478511yescharacteristic
637C2#1914610511yescharacteristic
638C2#1914627411yescharacteristic
639C2#1914747111yescharacteristic
640C2#1914750311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×C4×SD16D43
hypocenterC43#26372
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. #19138428C2semidirect
4. #19136141C2semidirect
5. #19136080C2semidirect
6. #19135988C2semidirect
7. #19135926C2semidirect
8. #19135328C2semidirect
9. #19135152C2semidirect
13. #19134849C2semidirect
113. C2×SD16×C43Q8semidirect
381. C43#26372semidirect
390. C2×SD16Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145831772
#191384282
#191375002
#191361412
#191360802
#191359882
#191359262
#191353282
#191351522
#191349312
#191348562
#191348492
#191348442
C2×C4×SD16×C432
#2637243