Finite Group Databasebeta

← #25169277

Subgroups — #25169277

Order 11008.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139030C211yesmaximal, characteristic, complemented
2#19137615C211yesmaximal, 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#19135183C211yesmaximal, characteristic, complemented
10#19135175C211yesmaximal, characteristic, complemented
11#19134854C211yesmaximal, characteristic, complemented
12#19134787C211yesmaximal, characteristic, complemented
13#19134682C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2034C211yesmaximal, characteristic
16C2×D4×Dic43—21no—
17C2×D4×Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582840—21no—
28#14582822—21no—
29#14582802C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582793—21no—
34#14582792—21no—
35#14582784—21no—
36#14582779—21no—
37#14582774—21no—
38#14582768C2211yescharacteristic
39#14582759C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
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—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63D4×Dic43—22no—
64D4×Dic43—41no—
65D4×Dic43—44no—
66C2×C4⋊Dic43—22no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—41no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43D411yescharacteristic
83C2×C22⋊Dic43D411yescharacteristic
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063256—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—42no—
130C2×D4×C43—42no—
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—42no—
150C22×Dic43—42no—
151C22×Dic43—81no—
152C22×Dic43—81no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43#4112yes—
169C22⋊C4×C43—24no—
170C22⋊C4×C43—81no—
171C22⋊Dic43—41no—
172C22⋊Dic43—42no—
173C22⋊Dic43—42no—
174C22⋊Dic43—81no—
175C22⋊Dic43—81no—
176C22⋊Dic43SD1614yes—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—42no—
185C4⋊Dic43—42no—
186C4⋊Dic43—42no—
187C4⋊Dic43#4112yes—
188Dic43⋊C4—81no—
189Dic43⋊C4—81no—
190Dic43⋊C4—81no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—42no—
196C4×Dic43—81no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8#4112yes—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—22no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C2×SD1612yes—
217C23×C43C22×D411yescharacteristic
218D4×C43—22no—
219D4×C43—22no—
220D4×C43—48no—
221D4×C43—41no—
222D4×C43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
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×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C432−1+411yescharacteristic
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
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—41no—
266C2×Dic43—41no—
267C2×Dic43—84no—
268C2×Dic43—84no—
269C2×Dic43C2×SD1612yes—
270C2×Dic43C2×SD1612yes—
271C8×C43—41no—
272C8×C43—41no—
273C43⋊C8—22no—
274C43⋊C8—41no—
275#27032—431nomaximal, Sylow
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43#52511yescharacteristic
291C22×C43#54611yescharacteristic
292C22×C43#54711yescharacteristic
293C22×C43C22×SD1611yescharacteristic
294C22×C43#57511yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57711yescharacteristic
297C4×C43—42no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43#52911yescharacteristic
302C4×C43#53911yescharacteristic
303C4×C43#55311yescharacteristic
304C4×C43#55611yescharacteristic
305Dic43—22no—
306Dic43—22no—
307Dic43—41no—
308Dic43—42no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312Dic43—81no—
313#2497—431no—
314#2361—431no—
315#2071—431no—
316#2065—431no—
317#2034—431no—
318#2034D4311yescharacteristic
319#1948—431no—
320#1941—431no—
321#1923—431no—
322#1920—431no—
323#1919—431no—
324#1864—431no—
325#1853—431no—
326#1823—431no—
327C4×#102—431no—
328C2×C43—42no—
329C2×C43—82no—
330C2×C43#246611yescharacteristic
331C2×C43#310111yescharacteristic
332C2×C43#311911yescharacteristic
333C2×C43#329511yescharacteristic
334C2×C43#332111yescharacteristic
335C2×C43#333511yescharacteristic
336C2×C43#335511yescharacteristic
337C2×#121C2×D4311yescharacteristic
338C2×C4×D4—431no—
339C2×C4×D4—861no—
340C22×C4⋊C4—431no—
341C2×#106—431no—
342C2×#106—431no—
343C2×#106—431no—
344C2×#106C2×D4311yescharacteristic
345C2×C4⋊C8—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×#102C2×D4311yescharacteristic
349C2×#102C2×D4311yescharacteristic
350C2×C22⋊C8—431no—
351C2×C22⋊C8C2×D4311yescharacteristic
352C2×C4×C8—431no—
353#400—861no—
354#396—861no—
355#390—431no—
356#389—431no—
357#389—431no—
358#389—431no—
359#388—861no—
360#388—861no—
361#387—861no—
362#386—861no—
363#385—861no—
364#384—431no—
365#380—431no—
366#380C2×D4311yescharacteristic
367C4×C4⋊C4—431no—
368C4×C4⋊C4—431no—
369C4×C22⋊C4—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340C2×D4311yescharacteristic
378#336—431no—
379#336—431no—
380C43#2703211yescharacteristic, complemented, Sylow
381C22×D4—21no—
382C22×D4C22×D4311yescharacteristic
383C23×C4—861no—
384C23×C4—861no—
385C23×C4C22×D4311yescharacteristic
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390#121—22no—
391#121—22no—
392C4×D4—862no—
393C4×D4—1721no—
394C4×D4—1724no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—1721no—
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—431no—
413C2×C22⋊C4—431no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C42—431no—
419C2×C42—431no—
420C2×C42—861no—
421C2×C42—861no—
422#106—22no—
423#106—862no—
424#106—862no—
425#106—1721no—
426C4⋊C8—862no—
427#102—22no—
428#102—41no—
429#102—862no—
430#102—862no—
431C22⋊C8—41no—
432C22⋊C8—862no—
433C4×C8—1721no—
434#95—21no—
435#95—431no—
436#95—431no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443C24—21no—
444C24D4×D4311yescharacteristic
445C2×D4—24no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4#1062190012yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—3441no—
472C22×C4—3441no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4D4×D4311yescharacteristic
478C22×C4C23×D4311yescharacteristic
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—432no—
486C2×C8—861no—
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—21no—
496C4⋊C4—432no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—3441no—
505C4⋊C4—3441no—
506C4⋊C4—3441no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4#1062190012yes—
511C22⋊C4—24no—
512C22⋊C4—81no—
513C22⋊C4—434no—
514C22⋊C4—3441no—
515C22⋊C4—3441no—
516C22⋊C4—1722no—
517C22⋊C4—1721no—
518C22⋊C4—1722no—
519C42—861no—
520C42—861no—
521C42—861no—
522C42—861no—
523C42—3441no—
524C42—1722no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—22no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23SD16×D4312yes—
539C23C2×D4×D4311yescharacteristic
540D4—22no—
541D4—22no—
542D4—48no—
543D4—41no—
544D4—41no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—432no—
562C2×C4—432no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—862no—
573C2×C4—861no—
574C2×C4—3444no—
575C2×C4—3444no—
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—1721no—
586C2×C4—1721no—
587C2×C4#41×D4311yescharacteristic
588C2×C4#41×D4311yescharacteristic
589C2×C4C2×#1062190011yescharacteristic
590C2×C4C2×#1062190011yescharacteristic
591C2×C4#1306337011yescharacteristic
592C2×C4#1306337211yescharacteristic
593C8—41no—
594C8—41no—
595C8—862no—
596C8—1721no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22#1458340511yescharacteristic
612C22#1458353811yescharacteristic
613C22#1458354711yescharacteristic
614C22C2×SD16×D4311yescharacteristic
615C22#1458369511yescharacteristic
616C22#1458370111yescharacteristic
617C22#1458370911yescharacteristic
618C4—41no—
619C4—42no—
620C4—81no—
621C4—81no—
622C4—862no—
623C4—862no—
624C4—3441no—
625C4—3441no—
626C4—3441no—
627C4—1721no—
628C4—1722no—
629C4—1721no—
630C4#1458342611yescharacteristic
631C4#1458349411yescharacteristic
632C4#1458359611yescharacteristic
633C4#1458361811yescharacteristic
634C2—42no—
635C2—82no—
636C2#1913862411yescharacteristic
637C2#1914459811yescharacteristic
638C2#1914478711yescharacteristic
639C2#1914641411yescharacteristic
640C2#1914677611yescharacteristic
641C2#1914695011yescharacteristic
642C2#1914719411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2034C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2034D43
hypocenterC43#27032
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. #19139030C2semidirect
3. #19136001C2semidirect
4. #19135965C2semidirect
6. #19135355C2semidirect
7. #19135322C2semidirect
8. #19135198C2semidirect
9. #19135183C2semidirect
10. #19135175C2semidirect
11. #19134854C2semidirect
12. #19134787C2semidirect
13. #19134682C2semidirect
14. #102×Dic43C2semidirect
380. C43#27032semidirect

Maximal subgroups

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

subgroupindex
#191390302
#191376152
#191360012
#191359652
#191357812
#191353552
#191353222
#191351982
#191351832
#191351752
#191348542
#191347872
#191346822
#102×Dic432
C43×#20342
#2703243