Finite Group Databasebeta

← #25159712

Subgroups — #25159712

Order 11008.

828 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×#14583209C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic
3#19138461C211yesmaximal, characteristic
4#19137509C211yesmaximal, characteristic, complemented
5#19136121C211yesmaximal, characteristic
6#19136074C211yesmaximal, characteristic, complemented
7#19135979C211yesmaximal, characteristic
8#19135936C211yesmaximal, characteristic, complemented
9#19135325C211yesmaximal, characteristic, complemented
10#19135150C211yesmaximal, characteristic, complemented
11#19134947C211yesmaximal, characteristic
12#19134947C211yesmaximal, characteristic
13#19134852C211yesmaximal, characteristic, complemented
14#19134850C211yesmaximal, characteristic, complemented
15C43×#1864C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21#14583209—24no—
22C4×#10621883—24no—
23C2×#13063259C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582835—21no—
34#14582822—21no—
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582798C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582796—21no—
41#14582794—21no—
42#14582772—21no—
43#14582768—21no—
44#14582768C2211yescharacteristic
45#14582759—21no—
46C4×Dic43⋊C4C2211yescharacteristic
47#14582750—21no—
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883Q814yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063316—22no—
68#13063316—41no—
69C4×Dic86—22no—
70C4×Dic86—41no—
71#13063290—22no—
72#13063290—22no—
73#13063290—22no—
74#13063290—41no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4D411yescharacteristic
89C2×Dic43⋊C4D411yescharacteristic
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99#13063259—41no—
100#13063258—22no—
101#13063258—22no—
102#13063256—22no—
103Dic43⋊C8—22no—
104#13063250—22no—
105#13063250—22no—
106#13063248D414yes—
107#13063246—22no—
108C4×C43⋊C8—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95D411yescharacteristic
113C43⋊#95D411yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C23×C4×C43—21no—
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C4×D4×C43—22no—
119C4×D4×C43—41no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#106×C43—22no—
127#102×C43—22no—
128#102×C43—41no—
129#95×C43—21no—
130C24×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43C2×Q812yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—42no—
141C22×C4×C43—42no—
142C22×C4×C43—81no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D412yes—
158C2×Dic86C2×Q812yes—
159C2×Dic86#4112yes—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—81no—
171C4⋊C4×C43C2×D412yes—
172C4⋊C4×C43#4112yes—
173C22⋊C4×C43—42no—
174C42×C43—21no—
175C42×C43—21no—
176C22⋊Dic43—42no—
177C22⋊Dic43—81no—
178C22⋊Dic43—81no—
179C22⋊Dic43—81no—
180#10621883—28no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188C4⋊Dic43—81no—
189C4⋊Dic43—81no—
190Dic43⋊C4—24no—
191Dic43⋊C4—22no—
192Dic43⋊C4—22no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—81no—
198Dic43⋊C4—81no—
199C4×Dic43—24no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—42no—
205C4×Dic43—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8C2×D412yes—
211C2×C43⋊C8C2×Q812yes—
212C23×C43—22no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43C22×D411yescharacteristic
220D4×C43—22no—
221D4×C43—22no—
222D4×C43—41no—
223D4×C43—41no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
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—84no—
239C2×C4×C43#13712yes—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C432−1+411yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
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#13512yes—
270Dic86—22no—
271Dic86—22no—
272Dic86—22no—
273Dic86C22⋊Q814yes—
274C8×C43—41no—
275C8×C43—41no—
276C43⋊C8—22no—
277C43⋊C8—22no—
278#26379—431nomaximal, Sylow
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43#52511yescharacteristic
287C22×C43D4211yescharacteristic
288C22×C43D4×Q811yescharacteristic
289C22×C43C2×#13511yescharacteristic
290C22×C43C2×#13711yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57711yescharacteristic
293C4×C43—22no—
294C4×C43—42no—
295C4×C43—42no—
296C4×C43—41no—
297C4×C43—81no—
298C4×C43C2×C22⋊Q811yescharacteristic
299C4×C43#53911yescharacteristic
300C4×C43#54711yescharacteristic
301C4×C43#55411yescharacteristic
302Dic43—22no—
303Dic43—24no—
304Dic43—41no—
305Dic43—41no—
306Dic43—41no—
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310C2×#479—431no—
311C2×C4×SD16—431no—
312#2454—431no—
313Q8×C4⋊C4—431no—
314#2093—431no—
315#2084—431no—
316#2067—431no—
317#2059—431no—
318#1942—431no—
319#1916—431no—
320#1880—431no—
321#1880—431no—
322#1864D4311yescharacteristic
323#1863—431no—
324#1863—431no—
325C2×C43—82no—
326C2×C43#244911yescharacteristic
327C2×C43#310811yescharacteristic
328C2×C43#311911yescharacteristic
329C2×C43#326611yescharacteristic
330C2×C43#328711yescharacteristic
331C2×C43#338111yescharacteristic
332C2×C43#338511yescharacteristic
333C22×SD16—431no—
334C2×#125—431no—
335C2×C4×Q8—431no—
336C2×C4×Q8—431no—
337C2×C4×Q8—431no—
338C2×C4×D4C2×D4311yescharacteristic
339#479—864no—
340C4×SD16—864no—
341C2×#107—431no—
342C2×#107—431no—
343C2×#107—431no—
344C2×#106—431no—
345C2×#106C2×D4311yescharacteristic
346C2×C4⋊C8—431no—
347C2×#103—431no—
348C2×#103—431no—
349C2×#103—431no—
350C2×#102—431no—
351C2×#102C2×D4311yescharacteristic
352C2×#102C2×D4311yescharacteristic
353C2×C4×C8—431no—
354#399—861no—
355#396—861no—
356#390—431no—
357#390—431no—
358#389—431no—
359#389—431no—
360#389—431no—
361#389—861no—
362#389—861no—
363#389C2×D4311yescharacteristic
364#385—861no—
365#384—431no—
366#384—861no—
367#380—861no—
368C4×C4⋊C4—431no—
369C4×C4⋊C4—861no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340C2×D4311yescharacteristic
374#336—431no—
375#336—431no—
376#336—431no—
377#336C2×D4311yescharacteristic
378C43#2637911yescharacteristic, complemented, Sylow
379C22×Q8—431no—
380C22×D4C22×D4311yescharacteristic
381C23×C4—21no—
382C2×SD16—434no—
383C2×SD16—862no—
384C2×SD16—862no—
385C22×C8—431no—
386C22×C8—431no—
387C22×C8C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389#125—862no—
390#125—1721no—
391C4×Q8—862no—
392C4×Q8—862no—
393C4×Q8—862no—
394C4×Q8—862no—
395C4×Q8—1721no—
396C4×Q8—1721no—
397C4×D4—22no—
398C4×D4—41no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—861no—
426C2×C42—861no—
427C2×C42—861no—
428C2×C42C22×D4311yescharacteristic
429#107—862no—
430#107—862no—
431#107—1721no—
432#106—22no—
433#106—862no—
434C4⋊C8—862no—
435#103—434no—
436#103—862no—
437#103—862no—
438#102—22no—
439#102—41no—
440#102—862no—
441C4×C8—862no—
442#95—21no—
443#95—431no—
444#95—431no—
445#95—861no—
446#95—861no—
447#95—861no—
448C24—21no—
449C2×Q8—432no—
450C2×Q8—432no—
451C2×Q8—432no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4Q8×D4312yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—81no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—868no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—432no—
486C2×C8—432no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—81no—
496C4⋊C4—862no—
497C4⋊C4—864no—
498C4⋊C4—862no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—3441no—
506C4⋊C4—3441no—
507C4⋊C4—3441no—
508C4⋊C4—3441no—
509C4⋊C4—1722no—
510C4⋊C4—1722no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4—1722no—
514C4⋊C4#1062189812yes—
515C4⋊C4D4×D4312yes—
516C22⋊C4—42no—
517C22⋊C4—3441no—
518C22⋊C4—3441no—
519C22⋊C4—3441no—
520C22⋊C4—1722no—
521C42—21no—
522C42—21no—
523C42—864no—
524C42—861no—
525C42—861no—
526C42—861no—
527C42—861no—
528C42—1722no—
529C42—1722no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23C2×D4×D4311yescharacteristic
538Q8—434no—
539Q8—862no—
540Q8—862no—
541Q8—862no—
542D4—22no—
543D4—22no—
544D4—41no—
545D4—41no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4—432no—
562C2×C4—862no—
563C2×C4—861no—
564C2×C4—862no—
565C2×C4—861no—
566C2×C4—862no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
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#1306335412yes—
586C2×C4C2×D4×D4311yescharacteristic
587C2×C4C2×Q8×D4311yescharacteristic
588C2×C4#41×D4311yescharacteristic
589C2×C4C2×#1062189811yescharacteristic
590C2×C4#1306337011yescharacteristic
591C2×C4#1306337211yescharacteristic
592C8—41no—
593C8—41no—
594C8—862no—
595C8—862no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#1458340811yescharacteristic
604C22#1458353111yescharacteristic
605C22#1458356211yescharacteristic
606C22#135×D4311yescharacteristic
607C22C2×#1306335411yescharacteristic
608C22#1458370311yescharacteristic
609C22#1458370911yescharacteristic
610C4—22no—
611C4—42no—
612C4—41no—
613C4—42no—
614C4—81no—
615C4—864no—
616C4—862no—
617C4—3441no—
618C4—3441no—
619C4—3441no—
620C4—1721no—
621C4—1721no—
622C4—1721no—
623C4C22⋊Q8×D4311yescharacteristic
624C4#1458349211yescharacteristic
625C4#1458355411yescharacteristic
626C4#1458360411yescharacteristic
627C2—82no—
628C2#1913840311yescharacteristic
629C2#1914467311yescharacteristic
630C2#1914479811yescharacteristic
631C2#1914610911yescharacteristic
632C2#1914634811yescharacteristic
633C2#1914746511yescharacteristic
634C2#1914750911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1864C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1864D43
hypocenterC43#26379
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
1. C2×#14583209C2semidirect
4. #19137509C2semidirect
6. #19136074C2semidirect
8. #19135936C2semidirect
9. #19135325C2semidirect
10. #19135150C2semidirect
13. #19134852C2semidirect
14. #19134850C2semidirect
378. C43#26379semidirect

Maximal subgroups

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

subgroupindex
C2×#145832092
C2×C4×#106218832
#191384612
#191375092
#191361212
#191360742
#191359792
#191359362
#191353252
#191351502
#191349472
#191348522
#191348502
C43×#18642
#2637943