Finite Group Databasebeta

← #25159698

Subgroups — #25159698

Order 11008.

848 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583199C211yesmaximal, characteristic
2C2×C4×#10621883C211yesmaximal, characteristic
3#19138456C211yesmaximal, characteristic, complemented
4#19136146C211yesmaximal, characteristic, complemented
5#19136077C211yesmaximal, characteristic, complemented
6#19135973C211yesmaximal, characteristic, complemented
7#19135933C211yesmaximal, characteristic, complemented
8#19135320C211yesmaximal, characteristic, complemented
9#19135154C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic
11#19134929C211yesmaximal, characteristic
12#19134856C211yesmaximal, characteristic
13#19134848C211yesmaximal, characteristic, complemented
14#19134842C211yesmaximal, characteristic
15C43×#2349C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19#14583199—24no—
20C4×#10621883—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582840—21no—
35#14582830—21no—
36#14582805C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582794—21no—
41#14582781—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#385—21no—
56C43×#385—21no—
57C43×#382C2211yescharacteristic
58C43×#380—21no—
59C4×C4⋊C4×C43C2211yescharacteristic
60C2×#95×C43—21no—
61C22×Dic86C2311yescharacteristic
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883Q814yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063317—22no—
70#13063317—41no—
71C4×Dic86—22no—
72C4×Dic86—41no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C4×Dic43—21no—
82#13063258—22no—
83#13063258—41no—
84#13063256—22no—
85#13063256—22no—
86#13063256—22no—
87C4⋊(C43⋊C8)—22no—
88#13063248—22no—
89#13063248—22no—
90#13063248—41no—
91#13063246—22no—
92#13063246—22no—
93#13063246D414yes—
94C4×C43⋊C8—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C22×D4×C43C2311yescharacteristic
102C23×C4×C43—21no—
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43—41no—
110C4×D4×C43—41no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43D411yescharacteristic
129#95×C43D411yescharacteristic
130C24×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43C2×D412yes—
135C2×D4×C43C2×Q812yes—
136C2×D4×C43#4112yes—
137C22×C4×C43—24no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—42no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—81no—
146C22×C4×C43—81no—
147C22×C4×C43—81no—
148C22×C4×C43—81no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86C2×Q812yes—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—81no—
174C4⋊C4×C43—81no—
175C4⋊C4×C43#4112yes—
176C22⋊C4×C43—24no—
177C22⋊C4×C43—42no—
178C22⋊C4×C43—42no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185#10621883—28no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C2×D412yes—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197C4×Dic43—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C2×D412yes—
209C2×C43⋊C8C2×Q812yes—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43C22×D411yescharacteristic
218D4×C43—22no—
219D4×C43—22no—
220D4×C43—22no—
221D4×C43C22⋊Q814yes—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—84no—
249C2×C4×C43—84no—
250C2×C4×C43—84no—
251C2×C4×C43#13512yes—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×Q811yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C432−1+411yescharacteristic
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270Dic86—22no—
271Dic86—22no—
272Dic86—41no—
273Dic86—41no—
274C43⋊C8—22no—
275C43⋊C8—22no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#26378—431nomaximal, Sylow
279C22×C43—24no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43#52511yescharacteristic
287C22×C43D4211yescharacteristic
288C22×C43D4×Q811yescharacteristic
289C22×C43C2×#13511yescharacteristic
290C22×C43#57511yescharacteristic
291C22×C43#57711yescharacteristic
292C22×C43#57711yescharacteristic
293C4×C43—22no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43C2×C22⋊Q811yescharacteristic
303C4×C43#53911yescharacteristic
304C4×C43#54711yescharacteristic
305C4×C43#55411yescharacteristic
306Dic43—42no—
307Dic43—42no—
308Dic43—81no—
309Dic43—81no—
310C2×#478—431no—
311C2×C4×SD16—431no—
312#2453—431no—
313#2349D4311yescharacteristic
314#2097—431no—
315#2085—431no—
316#2066—431no—
317#2059—431no—
318#1941—431no—
319#1916—431no—
320#1877—431no—
321#1877—431no—
322#1864—431no—
323#1863—431no—
324#1862—431no—
325C2×C43—44no—
326C2×C43#244911yescharacteristic
327C2×C43#310211yescharacteristic
328C2×C43#312311yescharacteristic
329C2×C43#326711yescharacteristic
330C2×C43#328211yescharacteristic
331C2×C43#338111yescharacteristic
332C2×C43#338811yescharacteristic
333C22×SD16—431no—
334C2×#125—431no—
335C2×C4×Q8—431no—
336C2×C4×D4C2×D4311yescharacteristic
337C2×C4×D4C2×D4311yescharacteristic
338C2×C4×D4C2×D4311yescharacteristic
339#478—864no—
340C4×SD16—864no—
341C2×#107—431no—
342C2×#107—431no—
343C2×#106—431no—
344C2×#106—431no—
345C2×#106—431no—
346C2×C4⋊C8—431no—
347C2×#103—431no—
348C2×#103—431no—
349C2×#103—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×C4×C8—431no—
354#400—861no—
355#398—861no—
356#391—431no—
357#391—431no—
358#389—431no—
359#389—431no—
360#389—861no—
361#389C2×D4311yescharacteristic
362#389C2×D4311yescharacteristic
363#387—861no—
364#385—21no—
365#385—21no—
366#382C2×D4311yescharacteristic
367#380—21no—
368C4×C4⋊C4C2×D4311yescharacteristic
369C2×#95—21no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#336—431no—
375#336—431no—
376#336—431no—
377#336—431no—
378C43#2637811yescharacteristic, complemented, Sylow
379C22×Q8—431no—
380C22×D4C22×D4311yescharacteristic
381C23×C4—21no—
382C23×C4—21no—
383C23×C4—21no—
384C2×SD16—434no—
385C2×SD16—862no—
386C2×SD16—862no—
387C22×C8—431no—
388C22×C8—431no—
389C22×C8—431no—
390C22×C8—431no—
391#125—862no—
392#125—1721no—
393C4×Q8—862no—
394C4×Q8—1721no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—41no—
400C4×D4—41no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4C22⋊D4311yescharacteristic
412C2×C4⋊C4C22⋊D4311yescharacteristic
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42—861no—
420C2×C42C22×D4311yescharacteristic
421C2×C42C22×D4311yescharacteristic
422C2×C42C22×D4311yescharacteristic
423#107—862no—
424#107—1721no—
425#106—862no—
426#106—862no—
427#106—862no—
428C4⋊C8—862no—
429#103—862no—
430#103—862no—
431#103—1721no—
432#102—434no—
433#102—862no—
434#102—862no—
435C4×C8—862no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95C22⋊D4311yescharacteristic
447#95C22⋊D4311yescharacteristic
448C24—21no—
449C2×Q8—432no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4#1062189812yes—
459C2×D4D4×D4312yes—
460C2×D4Q8×D4312yes—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—81no—
470C22×C4—81no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4C2×C22⋊D4311yescharacteristic
478C22×C4C2×C22⋊D4311yescharacteristic
479C22×C4C2×C22⋊D4311yescharacteristic
480C22×C4C2×C22⋊D4311yescharacteristic
481C22×C4C2×C22⋊D4311yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484SD16—868no—
485C2×C8—432no—
486C2×C8—432no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—81no—
505C4⋊C4—81no—
506C4⋊C4—432no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4#1062189812yes—
518C22⋊C4—24no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—1722no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23C22×C22⋊D4311yescharacteristic
536Q8—862no—
537Q8—862no—
538Q8—1721no—
539Q8—1721no—
540D4—22no—
541D4—22no—
542D4—22no—
543D4#1306330314yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—84no—
571C2×C4—84no—
572C2×C4—84no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4#1306334512yes—
586C2×C4C2×D4×D4311yescharacteristic
587C2×C4C2×Q8×D4311yescharacteristic
588C2×C4C2×#1062189811yescharacteristic
589C2×C4C2×#1062189811yescharacteristic
590C2×C4#1306337011yescharacteristic
591C2×C4#1306337311yescharacteristic
592C8—862no—
593C8—862no—
594C8—1721no—
595C8—1721no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22#1458341011yescharacteristic
604C22D4×C22⋊D4311yescharacteristic
605C22Q8×C22⋊D4311yescharacteristic
606C22C2×#1306334511yescharacteristic
607C22#1458369711yescharacteristic
608C22#1458371011yescharacteristic
609C22#1458371011yescharacteristic
610C4—22no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4—3441no—
620C4—3441no—
621C4—1722no—
622C4—1722no—
623C4C2×#1306330311yescharacteristic
624C4#1458349611yescharacteristic
625C4#1458355011yescharacteristic
626C4#1458360411yescharacteristic
627C2—44no—
628C2#1913840411yescharacteristic
629C2#1914461311yescharacteristic
630C2#1914484711yescharacteristic
631C2#1914611611yescharacteristic
632C2#1914629811yescharacteristic
633C2#1914747011yescharacteristic
634C2#1914754011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2349C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2349D43
hypocenterC43#26378
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #19138456C2semidirect
4. #19136146C2semidirect
5. #19136077C2semidirect
6. #19135973C2semidirect
7. #19135933C2semidirect
8. #19135320C2semidirect
9. #19135154C2semidirect
13. #19134848C2semidirect
378. C43#26378semidirect

Maximal subgroups

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

subgroupindex
C2×#145831992
C2×C4×#106218832
#191384562
#191361462
#191360772
#191359732
#191359332
#191353202
#191351542
#191349292
#191348562
#191348482
#191348422
C43×#23492
#2637843