Finite Group Databasebeta

← #25169382

Subgroups — #25169382

Order 11008.

762 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139019C211yesmaximal, characteristic, complemented
2#19137637C211yesmaximal, characteristic
3#19136001C211yesmaximal, characteristic, complemented
4#19135965C211yesmaximal, characteristic, complemented
5#19135781C211yesmaximal, characteristic
6#19135355C211yesmaximal, characteristic, complemented
7#19135322C211yesmaximal, characteristic, complemented
8#19135198C211yesmaximal, characteristic, complemented
9#19135190C211yesmaximal, characteristic, complemented
10#19135182C211yesmaximal, characteristic, complemented
11#19134840C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134691C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2034C211yesmaximal, characteristic
16C2×#13063318—21no—
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582841—21no—
28#14582827—21no—
29#14582802—21no—
30#14582802C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582792—21no—
35#14582781—21no—
36#14582779—21no—
37#14582768C2211yescharacteristic
38#14582759C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C22⋊C4×Dic43—21no—
42C4×C22⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063318—44no—
63D4×Dic43—22no—
64D4×Dic43—41no—
65#13063284—22no—
66#13063284—41no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43D411yescharacteristic
82C2×C22⋊Dic43D411yescharacteristic
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063258—22no—
89#13063256—22no—
90#13063256—41no—
91Dic43⋊C8—22no—
92#13063246—22no—
93#13063246—22no—
94C22⋊(C43⋊C8)—22no—
95C8×Dic43—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C22×D4×C43—21no—
105C22×D4×C43C2311yescharacteristic
106C23×C4×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#121×C43—22no—
110#121×C43—22no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116#106×C43—22no—
117#102×C43—22no—
118#102×C43—41no—
119C22⋊C8×C43—41no—
120#95×C43—21no—
121C24×C43—21no—
122C24×C43C2×D411yescharacteristic
123C2×D4×C43—24no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—81no—
130C2×D4×C43—81no—
131C2×D4×C43#4112yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43—81no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43#4112yes—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—42no—
168C22⋊Dic43—22no—
169C22⋊Dic43—22no—
170C22⋊Dic43—42no—
171C22⋊Dic43—42no—
172C22⋊Dic43—42no—
173C22⋊Dic43—42no—
174C22⋊Dic43—81no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—42no—
183C4⋊Dic43—81no—
184C4⋊Dic43#4112yes—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C4×Dic43—81no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8#4112yes—
201C23×C43—22no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43C22×D411yescharacteristic
216D4×C43—22no—
217D4×C43—22no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—84no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
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×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—84no—
266C2×Dic43#13512yes—
267C2×Dic43AGL(1,ℤ/8)12yes—
268C8×C43—41no—
269C8×C43—41no—
270C43⋊C8—22no—
271C43⋊C8—41no—
272#27039—431nomaximal, Sylow
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—42no—
277C22×C43—41no—
278C22×C43—42no—
279C22×C43—41no—
280C22×C43—42no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43#52511yescharacteristic
288C22×C43#54611yescharacteristic
289C22×C43#54711yescharacteristic
290C22×C43C2×#13511yescharacteristic
291C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57711yescharacteristic
294C4×C43—42no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43#52911yescharacteristic
299C4×C43#53911yescharacteristic
300C4×C43#55311yescharacteristic
301C4×C43#55611yescharacteristic
302Dic43—22no—
303Dic43—22no—
304Dic43—41no—
305Dic43—41no—
306Dic43—42no—
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310#2496—431no—
311#2363—431no—
312#2071—431no—
313#2065—431no—
314#2034—431no—
315#2034D4311yescharacteristic
316#1948—431no—
317#1941—431no—
318#1923—431no—
319#1921—431no—
320#1920—431no—
321#1862—431no—
322#1854—431no—
323#1825—431no—
324C4×#102—431no—
325C2×C43—81no—
326C2×C43—82no—
327C2×C43#246611yescharacteristic
328C2×C43#310611yescharacteristic
329C2×C43#312311yescharacteristic
330C2×C43#330411yescharacteristic
331C2×C43#330611yescharacteristic
332C2×C43#333711yescharacteristic
333C2×C43#335411yescharacteristic
334C2×#126—861no—
335C2×#121C2×D4311yescharacteristic
336C2×C4×D4—431no—
337C2×#117—431no—
338C2×#107—431no—
339C2×#106—431no—
340C2×#106—431no—
341C2×#106C2×D4311yescharacteristic
342C2×C4⋊C8—431no—
343C2×#102—431no—
344C2×#102—431no—
345C2×#102C2×D4311yescharacteristic
346C2×#102C2×D4311yescharacteristic
347C2×C22⋊C8—431no—
348C2×C22⋊C8C2×D4311yescharacteristic
349C2×C4×C8—431no—
350#400—861no—
351#397—861no—
352#390—431no—
353#390—861no—
354#389—431no—
355#389—431no—
356#389—431no—
357#388—861no—
358#387—861no—
359#386—861no—
360#384—431no—
361#380—431no—
362#380C2×D4311yescharacteristic
363C4×C4⋊C4—431no—
364C4×C4⋊C4—431no—
365C4×C22⋊C4—431no—
366C4×C22⋊C4—861no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340C2×D4311yescharacteristic
375#336—431no—
376#336—431no—
377C43#2703911yescharacteristic, complemented, Sylow
378C22×D4—21no—
379C22×D4C22×D4311yescharacteristic
380C23×C4—861no—
381C23×C4C22×D4311yescharacteristic
382C22×C8—431no—
383C22×C8—431no—
384C22×C8C22×D4311yescharacteristic
385C22×C8C22×D4311yescharacteristic
386#126—1724no—
387#121—22no—
388#121—22no—
389C4×D4—862no—
390C4×D4—1721no—
391#117—862no—
392#117—1721no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—431no—
408C2×C22⋊C4—431no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42—861no—
419#107—862no—
420#106—22no—
421#106—862no—
422#106—1721no—
423C4⋊C8—862no—
424#102—22no—
425#102—41no—
426#102—862no—
427#102—862no—
428C22⋊C8—41no—
429C22⋊C8—862no—
430C4×C8—1721no—
431#95—21no—
432#95—431no—
433#95—431no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440C24—21no—
441C24D4×D4311yescharacteristic
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—81no—
449C2×D4—81no—
450C2×D4#1062190012yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—3441no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4D4×D4311yescharacteristic
472C22×C4C23×D4311yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—432no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—432no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—3441no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4—1722no—
503C4⋊C4#1062190012yes—
504C22⋊C4—24no—
505C22⋊C4—42no—
506C22⋊C4—862no—
507C22⋊C4—862no—
508C22⋊C4—3441no—
509C22⋊C4—1722no—
510C22⋊C4—1722no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C42—861no—
514C42—861no—
515C42—861no—
516C42—861no—
517C42—3441no—
518C42—1722no—
519C42—1722no—
520C23—22no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C2×D4×D4311yescharacteristic
535D4—22no—
536D4—22no—
537D4—41no—
538D4—41no—
539D4—84no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
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—41no—
555C2×C4—41no—
556C2×C4—432no—
557C2×C4—432no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—862no—
568C2×C4—861no—
569C2×C4—3444no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4#41×D4311yescharacteristic
582C2×C4#41×D4311yescharacteristic
583C2×C4C2×#1062190011yescharacteristic
584C2×C4C2×#1062190011yescharacteristic
585C2×C4#1306337011yescharacteristic
586C2×C4#1306337211yescharacteristic
587C8—41no—
588C8—41no—
589C8—862no—
590C8—1721no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—42no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22#1458340511yescharacteristic
606C22#1458353811yescharacteristic
607C22#1458354711yescharacteristic
608C22#135×D4311yescharacteristic
609C22AGL(1,ℤ/8)×D4311yescharacteristic
610C22#1458370511yescharacteristic
611C22#1458370911yescharacteristic
612C4—41no—
613C4—42no—
614C4—81no—
615C4—81no—
616C4—862no—
617C4—862no—
618C4—3441no—
619C4—3441no—
620C4—3441no—
621C4—1721no—
622C4—1722no—
623C4—1721no—
624C4#1458342611yescharacteristic
625C4#1458349411yescharacteristic
626C4#1458359611yescharacteristic
627C4#1458361811yescharacteristic
628C2—81no—
629C2—82no—
630C2#1913862411yescharacteristic
631C2#1914464811yescharacteristic
632C2#1914484111yescharacteristic
633C2#1914652911yescharacteristic
634C2#1914655111yescharacteristic
635C2#1914696711yescharacteristic
636C2#1914718311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2034C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2034D43
hypocenterC43#27039
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
1. #19139019C2semidirect
3. #19136001C2semidirect
4. #19135965C2semidirect
6. #19135355C2semidirect
7. #19135322C2semidirect
8. #19135198C2semidirect
9. #19135190C2semidirect
10. #19135182C2semidirect
11. #19134840C2semidirect
12. #19134792C2semidirect
13. #19134691C2semidirect
14. #102×Dic43C2semidirect
377. C43#27039semidirect

Maximal subgroups

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

subgroupindex
#191390192
#191376372
#191360012
#191359652
#191357812
#191353552
#191353222
#191351982
#191351902
#191351822
#191348402
#191347922
#191346912
#102×Dic432
C43×#20342
#2703943