Finite Group Databasebeta

← #25066183

Subgroups — #25066183

Order 11008.

748 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143558C211yesmaximal, characteristic, complemented
2C4×#13063349C211yesmaximal, characteristic
3C8×D4×D43C211yesmaximal, characteristic, complemented
4#19133457C211yesmaximal, characteristic, complemented
5#19133454C211yesmaximal, characteristic, complemented
6#19133452C211yesmaximal, characteristic, complemented
7#19133430C211yesmaximal, characteristic, complemented
8#19133428C211yesmaximal, characteristic, complemented
9#19133427C211yesmaximal, characteristic, complemented
10#19133425C211yesmaximal, characteristic, complemented
11#19133344C211yesmaximal, characteristic, complemented
12#19132984C211yesmaximal, characteristic, complemented
13#19132979C211yesmaximal, characteristic, complemented
14#19132883C211yesmaximal, characteristic, complemented
15C43×#1586C211yesmaximal, characteristic, complemented
16C2×#13063349C411yescharacteristic
17C22×C8×D43—21no—
18C4×#10621900C2211yescharacteristic
19C4×D4×D43C2211yescharacteristic
20#14583029C2211yescharacteristic, complemented
21#14583026C2211yescharacteristic, complemented
22#14583011C411yescharacteristic
23#14583008C411yescharacteristic
24#14582998C411yescharacteristic
25#14582996C411yescharacteristic
26C4×#10621873C2211yescharacteristic
27C4×#10621883C2211yescharacteristic
28C4×#10621882C2211yescharacteristic
29#14582977C2211yescharacteristic, complemented
30#14582973—21no—
31#14582968—21no—
32C8×D172C2211yescharacteristic
33D4×C43⋊C8C2211yescharacteristic
34#14582964C2211yescharacteristic
35C8×C22⋊D43—21no—
36(C22⋊D43)⋊C8—21no—
37#14582951C2211yescharacteristic
38#14582950C2211yescharacteristic
39#14582949—21no—
40#14582940C411yescharacteristic
41C4⋊C8×D43C2211yescharacteristic
42#14582902C411yescharacteristic
43#14582897C411yescharacteristic
44C22⋊C8×D43—21no—
45M16×Dic43—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic, complemented
49#14582651C2211yescharacteristic, complemented
50#14582649C2211yescharacteristic, complemented
51#14582631C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53#14582628C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic, complemented
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic, complemented
58#14582621C2211yescharacteristic, complemented
59#14582621C2211yescharacteristic, complemented
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic, complemented
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×#10621900C2×C411yescharacteristic
68C2×D4×D43C2×C411yescharacteristic
69C22×C4×D43—21no—
70#13063349—24no—
71C2×#10621873C2×C411yescharacteristic
72C2×#10621883C2×C411yescharacteristic
73C2×#10621882C2×C411yescharacteristic
74C2×#10621877—21no—
75C2×#10621872C2×C411yescharacteristic
76C2×#10621872C2×C411yescharacteristic
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79C2×C8×D43—21no—
80C2×C8×D43—21no—
81C2×C8×D43—44no—
82C2×C8×D43D411yescharacteristic
83C2×C8×D43D411yescharacteristic
84C4×Dic86C2311yescharacteristic
85#13063290C2×C411yescharacteristic
86C4×D172C2311yescharacteristic
87D4×Dic43C2×C411yescharacteristic
88D4×Dic43C2×C411yescharacteristic
89#13063287C2×C411yescharacteristic
90C4×C22⋊D43—21no—
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93(C22⋊D43)⋊C4—21no—
94#13063283C2×C411yescharacteristic
95#13063281—21no—
96C4⋊C4×D43C2×C411yescharacteristic
97C22⋊C4×D43—21no—
98C2×C4×Dic43—21no—
99C42×D43C2311yescharacteristic
100#13063258C2×C411yescharacteristic
101#13063257C2×C411yescharacteristic
102#13063256C2×C411yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111#13063247C2×C411yescharacteristic
112#13063246C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114#13063245C2×C411yescharacteristic
115C22⋊(C43⋊C8)—21no—
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123#13063235C2×C411yescharacteristic
124#13063235C2×C411yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43D411yescharacteristic
130C8×Dic43D411yescharacteristic
131C2×D8×C43C2×C411yescharacteristic
132C2×M16×C43—21no—
133C22×C8×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43C2×C411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43C2×C411yescharacteristic
140#102×C43C2×C411yescharacteristic
141C22⋊C8×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C2×D4×C43C22×C411yescharacteristic
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156#10621900—22no—
157#10621900—22no—
158D4×D43—22no—
159D4×D43M1614yescomplemented
160C2×D172C22×C411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43C22×C411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43#4111yescharacteristic
169C2×Dic86C22×C411yescharacteristic
170D8×C43—22no—
171M16×C43—42no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—42no—
176C2×C8×C43C22×C411yescharacteristic
177C2×C8×C43C22×C411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C42×C43C2411yescharacteristic
185C22⋊Dic43—21no—
186C22⋊Dic43—21no—
187#10621883—22no—
188#10621882—22no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43C22×C411yescharacteristic
193C4⋊Dic43C22×C411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43C22×C411yescharacteristic
201C4×Dic43C2×D411yescharacteristic
202C4×Dic43#4111yescharacteristic
203#10621877—42no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—42no—
208C2×C43⋊C8C22×C411yescharacteristic
209C2×C43⋊C8C22×C411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212#10621873—22no—
213#10621872—22no—
214#10621872—22no—
215C8×D43—22no—
216C8×D43—41no—
217C8×D43—42no—
218C8×D43—42no—
219C8×D43—42no—
220C23×C43—21no—
221C23×C43—21no—
222C22×D43—21no—
223C22×D43—24no—
224C22×D43—42no—
225C22×D43—42no—
226C22×D43C4×D411yescharacteristic
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43C2×M1612yes—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—24no—
241C22⋊D43—42no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43C4×D411yescharacteristic
249C2×Dic43C4×D411yescharacteristic
250C2×Dic43C4×D411yescharacteristic
251D172—21no—
252D172C2×M1612yes—
253C4×D43—21no—
254C4×D43—21no—
255C4×D43—41no—
256C4×D43—42no—
257C4×D43—42no—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43C2×M1612yes—
261C4×D43#13112yes—
262Dic86—21no—
263Dic86—21no—
264C8×C43—21no—
265C8×C43—21no—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—41no—
269C8×C43—41no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—21no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8AGL(1,ℤ/8)12yescomplemented
278#17869—431nomaximal, Sylow
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×C4×D411yescharacteristic
286C2×D43—21no—
287C2×D43—21no—
288C2×D43—22no—
289C2×D43—48no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43#43512yes—
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43C22×M1611yescharacteristic
297C4×C43C2×#13111yescharacteristic
298C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C43#57511yescharacteristic
300Dic43—21no—
301Dic43—21no—
302Dic43—41no—
303Dic43—41no—
304Dic43—41no—
305Dic43#43512yes—
306#2965—431no—
307C4×AGL(1,ℤ/8)—431no—
308C2×C8×D4—431no—
309#1586—431no—
310#1586D4311yescharacteristic, complemented
311#1585—431no—
312#1585—431no—
313#1582—431no—
314#1582—431no—
315#1581—431no—
316#1581—431no—
317#1565—431no—
318#1478—431no—
319#1477—431no—
320#1451—431no—
321C2×C43—42no—
322C2×C43—81no—
323C2×C43C2×#43511yescharacteristic
324C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
325C2×C43#295511yescharacteristic
326D43—22no—
327D43—42no—
328C2×AGL(1,ℤ/8)—431no—
329C23×C8—861no—
330C4×#41—431no—
331C2×C4×D4—431no—
332#446—431no—
333#446—431no—
334#442—431no—
335#442—431no—
336#440—431no—
337#440—431no—
338C4×SD16—431no—
339C4×SD16—431no—
340C4×D8—431no—
341C4×D8C2×D4311yescharacteristic
342#436—431no—
343#436C2×D4311yescharacteristic, complemented
344#435—861no—
345#435—861no—
346C8×D4—431no—
347C8×D4—431no—
348C8×D4—431no—
349C8×D4—861no—
350C8×D4—861no—
351C8×D4C2×D4311yescharacteristic
352#431—431no—
353#431—431no—
354#431—861no—
355#428—431no—
356C2×C4⋊C8—431no—
357#418—431no—
358#417—431no—
359C2×C22⋊C8—861no—
360C4×M16—431no—
361C4×M16—861no—
362C2×C4×C8—431no—
363#335—431no—
364#335—431no—
365#334—431no—
366#334C2×D4311yescharacteristic, complemented
367Q8⋊C8—431no—
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372D4⋊C8—431no—
373D4⋊C8C2×D4311yescharacteristic
374D4⋊C8C2×D4311yescharacteristic, complemented
375#322—431no—
376#322—431no—
377#322—431no—
378#322C2×D4311yescharacteristic, complemented
379C43#1786911yescharacteristic, complemented, Sylow
380C2×#41—431no—
381C22×D4—431no—
382C23×C4—861no—
383AGL(1,ℤ/8)—864no—
384C2×SD16—431no—
385C2×SD16—431no—
386C2×D8—431no—
387C2×D8C4×D4311yescharacteristic
388C2×M16—21no—
389C2×M16—431no—
390C2×M16—431no—
391C2×M16—861no—
392C22×C8—21no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8—861no—
396C22×C8—861no—
397C22×C8—861no—
398C22×C8—861no—
399C22×C8—1724no—
400C4×Q8—431no—
401C4×Q8—431no—
402C4×D4—431no—
403C4×D4—431no—
404C4×D4—431no—
405C4×D4—431no—
406C4×D4—861no—
407C4×D4—861no—
408C4×D4—861no—
409C4×D4—861no—
410C4×D4C22×D4311yescharacteristic
411C4×D4C22×D4311yescharacteristic
412#117—431no—
413#117—861no—
414C2×C4⋊C4—431no—
415C2×C22⋊C4—861no—
416C2×C42—431no—
417C2×C42—861no—
418#107—431no—
419#107C4×D4311yescharacteristic
420#106—431no—
421#106—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8—861no—
427C4⋊C8—861no—
428C4⋊C8C22×D4311yescharacteristic
429C4⋊C8C22×D4311yescharacteristic
430#103—431no—
431#103—431no—
432#102—431no—
433#102—431no—
434#102—431no—
435#102—431no—
436#102C4×D4311yescharacteristic
437#102C4×D4311yescharacteristic
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—861no—
441C22⋊C8—861no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446#97—431no—
447#97—431no—
448#97—861no—
449#97—861no—
450C4×C8—431no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8—861no—
456C4×C8C22×D4311yescharacteristic
457C4×C8C22×D4311yescharacteristic
458C4×C8C22×D4311yescharacteristic
459C24—861no—
460#41—862no—
461#41—862no—
462C2×Q8—431no—
463C2×D4—434no—
464C2×D4—431no—
465C2×D4—862no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4C2×C4×D4311yescharacteristic
469C2×D4C2×C4×D4311yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—1722no—
482C22×C4—1722no—
483SD16—862no—
484SD16—862no—
485D8—22no—
486D8—862no—
487M16—42no—
488M16—862no—
489M16—862no—
490M16—1722no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—42no—
495C2×C8—431no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—431no—
499C2×C8—862no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—1721no—
504C2×C8—1722no—
505C2×C8—1722no—
506C2×C8—1722no—
507C2×C8—1722no—
508C2×C8C2×C4×D4311yescharacteristic
509C2×C8C2×C4×D4311yescharacteristic
510C2×C8D4×D4311yescharacteristic
511C2×C8D4×D4311yescharacteristic
512C4⋊C4—431no—
513C4⋊C4—431no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4C2×C4×D4311yescharacteristic
518C4⋊C4C2×C4×D4311yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—861no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C22⋊C4—861no—
525C22⋊C4—861no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—861no—
530C42—861no—
531C42—861no—
532C42C23×D4311yescharacteristic
533C23—21no—
534C23—21no—
535C23—431no—
536C23—864no—
537C23—861no—
538C23—1722no—
539C23—1722no—
540Q8—861no—
541Q8—861no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—432no—
546D4—864no—
547D4—861no—
548D4—1722no—
549D4M16×D4312yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—431no—
557C2×C4—432no—
558C2×C4—432no—
559C2×C4—431no—
560C2×C4—431no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—1721no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C8—21no—
578C8—21no—
579C8—21no—
580C8—21no—
581C8—41no—
582C8—41no—
583C8—41no—
584C8—432no—
585C8—861no—
586C8—861no—
587C8—861no—
588C8—1721no—
589C8—1721no—
590C8—1721no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—432no—
598C22—861no—
599C22—861no—
600C22—862no—
601C22—1728no—
602C22—1721no—
603C22—1721no—
604C22C4×D4×D4311yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—432no—
609C4—861no—
610C4—861no—
611C4—1721no—
612C4—1721no—
613C4—1721no—
614C4C2×M16×D4311yescharacteristic
615C4#131×D4311yescharacteristic
616C4AGL(1,ℤ/8)×D4311yescharacteristic
617C4#1458369511yescharacteristic
618C2—42no—
619C2—81no—
620C2—862no—
621C2—1722no—
622C2#435×D4311yescharacteristic
623C2#1914340611yescharacteristic
624C2#1914349311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1586C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063349C4
cosocleC42×C43C24
hypercenter#1586D43
hypocenterC43#17869
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
1. #19143558C2semidirect
3. C8×D4×D43C2semidirect
4. #19133457C2semidirect
5. #19133454C2semidirect
6. #19133452C2semidirect
7. #19133430C2semidirect
8. #19133428C2semidirect
9. #19133427C2semidirect
10. #19133425C2semidirect
11. #19133344C2semidirect
12. #19132984C2semidirect
13. #19132979C2semidirect
14. #19132883C2semidirect
15. C43×#1586C2semidirect
20. #14583029C22semidirect
21. #14583026C22semidirect
29. #14582977C22semidirect
48. #14582652C22semidirect
49. #14582651C22semidirect
50. #14582649C22semidirect
51. #14582631C22semidirect
52. #14582629C22semidirect
55. D4⋊(C43⋊C8)C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. #14582621C22semidirect
61. C43×#436C22semidirect
63. C43×#334C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
159. D4×D43M16semidirect
277. C43⋊C8AGL(1,ℤ/8)semidirect
310. #1586D43semidirect
343. #436C2×D43semidirect
366. #334C2×D43semidirect
374. D4⋊C8C2×D43semidirect
378. #322C2×D43semidirect
379. C43#17869semidirect

Maximal subgroups

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

subgroupindex
#191435582
C4×#130633492
C8×D4×D432
#191334572
#191334542
#191334522
#191334302
#191334282
#191334272
#191334252
#191333442
#191329842
#191329792
#191328832
C43×#15862
#1786943