Finite Group Databasebeta

← #25100930

Subgroups — #25100930

Order 11008.

874 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
1C2×#14582999C211yesmaximal, characteristic
2#19137072C211yesmaximal, characteristic, complemented
3#19135475C211yesmaximal, characteristic
4#19135448C211yesmaximal, characteristic
5#19135330C211yesmaximal, characteristic, complemented
6#19135325C211yesmaximal, characteristic, complemented
7#19135295C211yesmaximal, characteristic
8#19135284C211yesmaximal, characteristic, complemented
9#19135281C211yesmaximal, characteristic
10#19135270C211yesmaximal, characteristic, complemented
11#19134493C211yesmaximal, characteristic, complemented
12#19134428C211yesmaximal, characteristic, complemented
13#19134420C211yesmaximal, characteristic
14C4×#13063236C211yesmaximal, characteristic, complemented
15C43×#2293C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14582999C418yescomplemented
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C2×#13063236C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582783—21no—
39#14582783—21no—
40C4×Dic43⋊C4—21no—
41C4×C4⋊Dic43C2211yescharacteristic
42#14582745—21no—
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49C2×C4×D4×C43C2211yescharacteristic
50C2×#117×C43—21no—
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#388—21no—
56C43×#388—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43—21no—
59C43×C43C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C2×#10621883—22no—
62C2×#10621883—22no—
63C2×#10621883C2×C414yes—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C4×Dic86—22no—
69C4×Dic86C2×C414yes—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78#13063258—22no—
79#13063258C2×C414yes—
80#13063256—22no—
81#13063248—22no—
82#13063248—22no—
83#13063248C2×C414yes—
84#13063246—22no—
85#13063246—22no—
86#13063246C2×C414yes—
87#13063236—22no—
88#13063236—22no—
89#13063236—22no—
90#13063236C2×C414yes—
91C4×C43⋊C8—22no—
92C4×C43⋊C8—22no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C22×D4×C43C2311yescharacteristic
101C23×C4×C43—21no—
102C4×D4×C43—22no—
103C4×D4×C43C2×C414yes—
104#117×C43—44no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
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×C42×C43—21no—
116C2×C42×C43D411yescharacteristic
117C2×C42×C43D411yescharacteristic
118C2×C42×C43D411yescharacteristic
119C2×C42×C43D411yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C22×C412yes—
133C22×C4×C43—24no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86C22×C412yes—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43C22×C412yes—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—42no—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—42no—
168C22⋊C4×C43—42no—
169C42×C43—22no—
170C42×C43—22no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—41no—
176C42×C43—41no—
177C42×C43—42no—
178C42×C43C22×C412yes—
179C42×C43#4112yes—
180#10621883—28no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43C22×C412yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190C4×Dic43—24no—
191C4×Dic43—42no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C412yes—
199C2×C43⋊C8C22×C412yes—
200C2×C43⋊C8#4112yes—
201C2×C43⋊C8#4112yes—
202C2×C43⋊C8#4112yes—
203C2×C43⋊C8#4112yes—
204C23×C43—22no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43C22×D411yescharacteristic
212D4×C43—22no—
213D4×C43—22no—
214D4×C43—41no—
215D4×C43—41no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—48no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43C4×D412yes—
241C2×C4×C43C4×D412yes—
242C2×C4×C43AGL(1,ℤ/8)12yes—
243C2×C4×C43#13712yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262Dic86—22no—
263Dic86—22no—
264Dic86—41no—
265Dic86—41no—
266C43⋊C8—22no—
267C43⋊C8—22no—
268C43⋊C8—22no—
269C43⋊C8#11714yescomplemented
270#21288—431nomaximal, Sylow
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43C2×C4×D411yescharacteristic
279C22×C43#53211yescharacteristic
280C22×C43#53211yescharacteristic
281C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C43C2×#13711yescharacteristic
283C22×C43#57511yescharacteristic
284C22×C43#57511yescharacteristic
285C4×C43—22no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—22no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C2×#11711yescharacteristic
295C4×C43C4×#4111yescharacteristic
296C4×C43#52911yescharacteristic
297C4×C43#52911yescharacteristic
298Dic43—42no—
299Dic43—42no—
300Dic43—81no—
301Dic43—81no—
302C2×#440—431no—
303#2295—431no—
304#2293D4311yescharacteristic
305#1973—431no—
306#1968—431no—
307#1943—431no—
308#1942—431no—
309#1936—431no—
310#1935—431no—
311#1934—431no—
312#1933—431no—
313#1776—431no—
314#1763—431no—
315#1762—431no—
316C4×#97—431no—
317C2×C43—82no—
318C2×C43#229311yescharacteristic
319C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
320C2×C43C4×#13711yescharacteristic
321C2×C43#318011yescharacteristic
322C2×C43#318111yescharacteristic
323C2×C43#318211yescharacteristic
324C2×C43#318311yescharacteristic
325C22×SD16—431no—
326C2×C4×Q8—431no—
327C2×C4×D4C2×D4311yescharacteristic
328C2×#117—21no—
329#440—438no—
330C2×#107—431no—
331C2×#107—431no—
332C2×#106—431no—
333C2×#103—431no—
334C2×#103—431no—
335C2×#103—431no—
336C2×#102—431no—
337C2×#102—431no—
338C2×#102—431no—
339C2×#97—431no—
340C2×#97—431no—
341C2×#97—431no—
342C2×#97—431no—
343C2×C4×C8—431no—
344C2×C4×C8—431no—
345#391—431no—
346#391—431no—
347#390C2×D4311yescharacteristic
348#390C2×D4311yescharacteristic
349#389—431no—
350#389—431no—
351#389C2×D4311yescharacteristic
352#389C2×D4311yescharacteristic
353#388—21no—
354#388—21no—
355#387—861no—
356#387—861no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—861no—
359C4×C4⋊C4C2×D4311yescharacteristic
360C4×C22⋊C4—21no—
361#376—861no—
362C43C2×D4311yescharacteristic
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369C43#2128811yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C22×D4C22×D4311yescharacteristic
372C23×C4—21no—
373C2×SD16—434no—
374C2×SD16—862no—
375C2×SD16—862no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8—431no—
380C4×Q8—434no—
381C4×Q8—862no—
382C4×D4—22no—
383C4×D4C4×D4314yes—
384#117—44no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C4⋊C4C22×D4311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402C2×C42—861no—
403C2×C42—861no—
404C2×C42C22⋊D4311yescharacteristic
405C2×C42C22⋊D4311yescharacteristic
406C2×C42C22⋊D4311yescharacteristic
407C2×C42C22⋊D4311yescharacteristic
408C2×C42C22×D4311yescharacteristic
409C2×C42C22×D4311yescharacteristic
410C2×C42C22×D4311yescharacteristic
411#107—434no—
412#107—862no—
413#106—862no—
414#103—434no—
415#103—862no—
416#103—862no—
417#102—434no—
418#102—862no—
419#102—862no—
420#97—434no—
421#97—862no—
422#97—862no—
423#97—862no—
424C4×C8—862no—
425C4×C8—862no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436C24—21no—
437C2×Q8—432no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4C2×C4×D4312yes—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4C2×C22⋊D4311yescharacteristic
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466SD16—868no—
467C2×C8—432no—
468C2×C8—432no—
469C2×C8—432no—
470C2×C8—432no—
471C2×C8—432no—
472C2×C8—432no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—432no—
487C4⋊C4—864no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4C2×C4×D4312yes—
496C22⋊C4—24no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42—42no—
510C42—864no—
511C42—1722no—
512C42C2×C4×D4312yes—
513C42#1062189812yes—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×C22⋊D4311yescharacteristic
522Q8—862no—
523Q8—862no—
524Q8—1721no—
525Q8—1721no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—48no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4C4×C22⋊D4312yes—
567C2×C4C4×C22⋊D4312yes—
568C2×C4#1306335112yes—
569C2×C4#1306335512yes—
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4#41×D4311yescharacteristic
572C2×C4#41×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C8—434no—
577C8—862no—
578C8—862no—
579C8—862no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×C4×C22⋊D4311yescharacteristic
588C22#1458344511yescharacteristic
589C22#1458344511yescharacteristic
590C22C2×#1306335111yescharacteristic
591C22C2×#1306335511yescharacteristic
592C22#1458369711yescharacteristic
593C22#1458369711yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—3441no—
604C4—3441no—
605C4—1722no—
606C4—1722no—
607C4#117×D4311yescharacteristic
608C4#1458336711yescharacteristic
609C4#1458342711yescharacteristic
610C4#1458342711yescharacteristic
611C2—82no—
612C2#1913705411yescharacteristic
613C2C4×#1306335111yescharacteristic
614C2C4×#1306335511yescharacteristic
615C2#1914528711yescharacteristic
616C2#1914530511yescharacteristic
617C2#1914530911yescharacteristic
618C2#1914531811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2293C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#2293D43
hypocenterC43#21288
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. #19137072C2semidirect
5. #19135330C2semidirect
6. #19135325C2semidirect
8. #19135284C2semidirect
10. #19135270C2semidirect
11. #19134493C2semidirect
12. #19134428C2semidirect
14. C4×#13063236C2semidirect
18. #14582999C4semidirect
269. C43⋊C8#117semidirect
369. C43#21288semidirect

Maximal subgroups

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

subgroupindex
C2×#145829992
#191370722
#191354752
#191354482
#191353302
#191353252
#191352952
#191352842
#191352812
#191352702
#191344932
#191344282
#191344202
C4×#130632362
C43×#22932
#2128843