Finite Group Databasebeta

← #25104728

Subgroups — #25104728

Order 11008.

886 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583257C211yesmaximal, characteristic
2#19137166C211yesmaximal, characteristic, complemented
3#19137142C211yesmaximal, characteristic
4#19135566C211yesmaximal, characteristic, complemented
5#19135410C211yesmaximal, characteristic
6#19135281C211yesmaximal, characteristic
7#19135271C211yesmaximal, characteristic, complemented
8#19135270C211yesmaximal, characteristic, complemented
9#19134727C211yesmaximal, characteristic, complemented
10#19134424C211yesmaximal, characteristic, complemented
11#19134424C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic
13#19134422C211yesmaximal, characteristic
14C4×#13063235C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×#13063290—21no—
19C2×#13063290C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21#14583257C418yescomplemented
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582803—21no—
35#14582797C2211yescharacteristic
36#14582794—21no—
37#14582787—21no—
38#14582787—21no—
39#14582768C2211yescharacteristic
40#14582764C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43#14582750—21no—
44C22⋊C4×Dic43—21no—
45C22⋊C4×Dic43—21no—
46C42×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86—21no—
61C22×Dic86C2311yescharacteristic
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063324—22no—
66#13063324C2×C414yescomplemented
67#13063312—22no—
68#13063312C2×C414yes—
69#13063290—22no—
70#13063290—22no—
71#13063290—44no—
72D4×Dic43—22no—
73D4×Dic43—22no—
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⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063250—22no—
95#13063250C2×C414yescomplemented
96#13063248—22no—
97#13063248C2×C414yescomplemented
98#13063246—22no—
99#13063246C2×C414yes—
100#13063235—22no—
101#13063235—22no—
102#13063235—22no—
103#13063235C2×C414yescomplemented
104C4×C43⋊C8—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×D4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#102×C43—22no—
123#102×C43C2×C414yes—
124C4×C8×C43—22no—
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—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—24no—
156C2×Dic86—42no—
157C2×Dic86—42no—
158C2×Dic86C22×C412yes—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C412yes—
164C2×C8×C43#4112yes—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43C22×C412yes—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—42no—
174C42×C43—21no—
175C42×C43—21no—
176C22⋊Dic43—24no—
177C22⋊Dic43—24no—
178C22⋊Dic43—42no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C22×C412yes—
185Dic43⋊C4—24no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—41no—
193C4×Dic43—41no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43C22×C412yes—
198C4×Dic43#4112yes—
199C4×Dic43#4112yes—
200C4×Dic43#4112yes—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C22×C412yes—
206C2×C43⋊C8#4112yes—
207C23×C43—22no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43C22×D411yescharacteristic
215D4×C43—22no—
216D4×C43—22no—
217D4×C43—41no—
218D4×C43—41no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43AGL(1,ℤ/8)12yes—
233C2×C4×C43#13712yes—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—41no—
251C2×Dic43—41no—
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—84no—
261C2×Dic43C4×D412yes—
262C2×Dic43C4×D412yes—
263C2×Dic43#12412yes—
264C2×Dic43#12412yes—
265Dic86—22no—
266Dic86—22no—
267Dic86—48no—
268Dic86—41no—
269Dic86—41no—
270C8×C43—22no—
271C8×C43—22no—
272C43⋊C8—22no—
273C43⋊C8—22no—
274#21655—431nomaximal, Sylow
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43C2×C4×D411yescharacteristic
283C22×C43C2×#12411yescharacteristic
284C22×C43#53211yescharacteristic
285C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C43C2×#13711yescharacteristic
287C22×C43#57511yescharacteristic
288C22×C43#57511yescharacteristic
289C4×C43—22no—
290C4×C43—22no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C4×#4111yescharacteristic
295C4×C43C4×#4111yescharacteristic
296C4×C43#52911yescharacteristic
297C4×C43#52911yescharacteristic
298Dic43—22no—
299Dic43—22no—
300Dic43—22no—
301Dic43—22no—
302Dic43—42no—
303Dic43—42no—
304Dic43—81no—
305Dic43—81no—
306C2×#489—431no—
307C4×C4⋊Q8—431no—
308C4×#124—431no—
309#1993—431no—
310#1959—431no—
311#1934—431no—
312#1934D4311yescharacteristic
313#1933—431no—
314#1933—431no—
315#1836—431no—
316#1763—431no—
317#1763—431no—
318#1762—431no—
319#1762—431no—
320C4×#97—431no—
321C2×C43—82no—
322C2×C43C4×#12411yescharacteristic
323C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
324C2×C43C4×#13711yescharacteristic
325C2×C43#314011yescharacteristic
326C2×C43#314111yescharacteristic
327C2×C43#318011yescharacteristic
328C2×C43#318111yescharacteristic
329C2×C4⋊Q8—431no—
330C2×#124—431no—
331C2×C4×Q8—431no—
332C2×C4×Q8—861no—
333C2×C4×D4—431no—
334#489—438no—
335C2×#103—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#102—431no—
340C2×#102—431no—
341C2×#102C2×D4311yescharacteristic
342C2×#102C2×D4311yescharacteristic
343C2×#97—431no—
344C2×#97—431no—
345C2×#97—431no—
346C2×#97—431no—
347C2×C4×C8—431no—
348C2×C4×C8C2×D4311yescharacteristic
349#391—431no—
350#391—861no—
351#390C2×D4311yescharacteristic
352#389—431no—
353#389—861no—
354#389C2×D4311yescharacteristic
355#388—861no—
356#388—861no—
357#384—431no—
358#382—431no—
359C4×C4⋊C4—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—861no—
362C4×C22⋊C4—861no—
363C4×C22⋊C4—861no—
364C43—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340C2×D4311yescharacteristic
372#340C2×D4311yescharacteristic
373C43#2165511yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C22×Q8—861no—
376C22×D4C22×D4311yescharacteristic
377C23×C4—861no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C4⋊Q8—434no—
383C4⋊Q8—862no—
384#124—434no—
385#124—862no—
386C4×Q8—862no—
387C4×Q8—862no—
388C4×Q8—1724no—
389C4×D4—862no—
390C4×D4—862no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418#103—434no—
419#103—434no—
420#103—862no—
421#103—862no—
422#102—22no—
423#102—434no—
424#102—862no—
425#102C4×D4314yes—
426#97—434no—
427#97—862no—
428#97—862no—
429#97—862no—
430C4×C8—22no—
431C4×C8—862no—
432#95—21no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440C24—21no—
441C2×Q8—432no—
442C2×Q8—864no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—1722no—
449C2×Q8—1722no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4C2×C4×D4312yes—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4—1722no—
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4C23×D4311yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—432no—
478C2×C8—432no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8C2×C4×D4312yes—
484C2×C8#1062190012yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—432no—
492C4⋊C4—864no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4C2×C4×D4312yes—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—864no—
506C22⋊C4—864no—
507C22⋊C4—1722no—
508C42—21no—
509C42—21no—
510C42—432no—
511C42—432no—
512C42—432no—
513C42—432no—
514C42—862no—
515C42—862no—
516C42—1721no—
517C42—1721no—
518C42—1722no—
519C42—1722no—
520C42—1722no—
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C2×D4×D4311yescharacteristic
529Q8—862no—
530Q8—862no—
531Q8—1728no—
532Q8—1721no—
533Q8—1721no—
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—3444no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4#1306334912yes—
577C2×C4#1306335412yes—
578C2×C4C22×C4×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C2×C4#41×D4311yescharacteristic
582C2×C4#41×D4311yescharacteristic
583C2×C4C2×#1062190011yescharacteristic
584C8—22no—
585C8—22no—
586C8—862no—
587C8—862no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22C4×D4×D4311yescharacteristic
596C22#124×D4311yescharacteristic
597C22#1458344411yescharacteristic
598C22C2×#1306334911yescharacteristic
599C22C2×#1306335411yescharacteristic
600C22#1458369611yescharacteristic
601C22#1458369611yescharacteristic
602C4—22no—
603C4—22no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—862no—
608C4—862no—
609C4—862no—
610C4—862no—
611C4—3441no—
612C4—3441no—
613C4—1722no—
614C4—1722no—
615C4C4×#1062190011yescharacteristic
616C4#1458336711yescharacteristic
617C4#1458342611yescharacteristic
618C4#1458343211yescharacteristic
619C2—82no—
620C2#1913713611yescharacteristic
621C2C4×#1306334911yescharacteristic
622C2C4×#1306335411yescharacteristic
623C2#1914497811yescharacteristic
624C2#1914498511yescharacteristic
625C2#1914528811yescharacteristic
626C2#1914529711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1934D43
hypocenterC43#21655
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #19137166C2semidirect
4. #19135566C2semidirect
7. #19135271C2semidirect
8. #19135270C2semidirect
9. #19134727C2semidirect
10. #19134424C2semidirect
11. #19134424C2semidirect
14. C4×#13063235C2semidirect
21. #14583257C4semidirect
66. #13063324C2×C4semidirect
95. #13063250C2×C4semidirect
97. #13063248C2×C4semidirect
103. #13063235C2×C4semidirect
373. C43#21655semidirect

Maximal subgroups

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

subgroupindex
C2×#145832572
#191371662
#191371422
#191355662
#191354102
#191352812
#191352712
#191352702
#191347272
#191344242
#191344222
C4×#130632352
C43×#19342
#2165543