Finite Group Databasebeta

← #25165064

Subgroups — #25165064

Order 11008.

720 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#19138934C211yesmaximal, characteristic
2#19137627C211yesmaximal, characteristic
3#19135796C211yesmaximal, characteristic
4#19135746C211yesmaximal, characteristic, complemented
5#19135602C211yesmaximal, characteristic
6#19135550C211yesmaximal, characteristic, complemented
7#19135282C211yesmaximal, characteristic, complemented
8#19135233C211yesmaximal, characteristic, complemented
9#19135207C211yesmaximal, characteristic
10#19135185C211yesmaximal, characteristic, complemented
11#19134938C211yesmaximal, characteristic, complemented
12#19134904C211yesmaximal, characteristic
13#19134689C211yesmaximal, characteristic
14#19134427C211yesmaximal, characteristic, complemented
15C43×#2056C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29#14582840—21no—
30#14582828—21no—
31#14582806C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582791—21no—
34#14582788—21no—
35#14582788—21no—
36#14582786—21no—
37#14582763—21no—
38#14582756C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41#14582750—21no—
42C4×(C2×D43)⋊C4C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063317—22no—
63#13063317—41no—
64#13063301—22no—
65#13063301—22no—
66#13063301—22no—
67#13063301—41no—
68Q8×Dic43—22no—
69Q8×Dic43—41no—
70#13063283—22no—
71#13063283—41no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
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×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×(C2×D43)⋊C4D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063258—22no—
94#13063249—22no—
95#13063249—22no—
96#13063249—22no—
97#13063249—41no—
98(C2×D43)⋊C8—41no—
99(C2×D43)⋊C8—41no—
100#13063235—41no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C22×Q8×C43C2311yescharacteristic
111C2×Q16×C43—22no—
112C2×Q16×C43—41no—
113C2×Q16×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C4⋊C8×C43—41no—
120#103×C43—22no—
121#103×C43—41no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
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
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159Q16×C43—44no—
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—
170C42×C43—21no—
171C42×C43—21no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—41no—
174(C2×D43)⋊C4—41no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—42no—
184C4⋊Dic43#4112yes—
185C4⋊Dic43#4112yes—
186C4⋊Dic43#4112yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C23×C43C22×D411yescharacteristic
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
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×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—22no—
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—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—41no—
269C8×C43—41no—
270C8×C43—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#26749—431nomaximal, Sylow
274C22×C43#52511yescharacteristic
275C22×C43#54611yescharacteristic
276C22×C43#54611yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57811yescharacteristic
280C22×C43#57811yescharacteristic
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43#52911yescharacteristic
295C4×C43#53811yescharacteristic
296C4×C43#55511yescharacteristic
297C4×C43#55911yescharacteristic
298Dic43—42no—
299Dic43—41no—
300Dic43—41no—
301Dic43—42no—
302Dic43—42no—
303Dic43—41no—
304Dic43—81no—
305#2489—431no—
306#2362—431no—
307#2056D4311yescharacteristic, complemented
308#2036—431no—
309#2026—431no—
310#2001—431no—
311#1989—431no—
312#1935—431no—
313#1928—431no—
314#1924—431no—
315#1921—431no—
316#1878—431no—
317#1873—431no—
318#1825—431no—
319#1763—431no—
320C2×C43#245911yescharacteristic
321C2×C43#311111yescharacteristic
322C2×C43#312711yescharacteristic
323C2×C43#331311yescharacteristic
324C2×C43#331511yescharacteristic
325C2×C43#331511yescharacteristic
326C2×C43#332711yescharacteristic
327D43—81no—
328C22×Q16C2×D4311yescharacteristic
329C2×#125—431no—
330C2×C22⋊Q8—431no—
331C2×C22⋊Q8—431no—
332C2×C4×Q8—431no—
333C2×#117—431no—
334C2×#107—431no—
335C2×C4⋊C8C2×D4311yescharacteristic
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103C2×D4311yescharacteristic
341C2×#103C2×D4311yescharacteristic
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×#97—431no—
345#400—861no—
346#397—861no—
347#391—431no—
348#391C2×D4311yescharacteristic
349#391C2×D4311yescharacteristic
350#389—431no—
351#388—861no—
352#388—861no—
353#388—861no—
354#387—861no—
355#382—861no—
356#380—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4—861no—
360C4×C22⋊C4—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#336—431no—
370#336—431no—
371C43#2674911yescharacteristic, complemented, Sylow
372C22×Q8C22×D4311yescharacteristic
373C22×Q8C22×D4311yescharacteristic
374C23×C4—431no—
375C2×Q16—22no—
376C2×Q16—41no—
377C2×Q16—41no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382#125—862no—
383#125—1721no—
384C22⋊Q8—862no—
385C22⋊Q8—862no—
386C22⋊Q8—862no—
387C22⋊Q8—1721no—
388C4×Q8—862no—
389C4×Q8—1721no—
390#117—862no—
391#117—1721no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
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×C22⋊C4—431no—
405C2×C22⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C42—431no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42C22×D4311yescharacteristic
416#107—862no—
417C4⋊C8—41no—
418#103—22no—
419#103—41no—
420#103—862no—
421#103—862no—
422#103—862no—
423#103—1721no—
424C22⋊C8—1721no—
425C22⋊C8—1721no—
426#97—1721no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—431no—
432#95—431no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439C24—431no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8#1062190012yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4D4×D4311yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4C23×D4311yescharacteristic
472Q16—44no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—861no—
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—432no—
490C4⋊C4—432no—
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⋊C4—1722no—
503C22⋊C4—864no—
504C22⋊C4—1721no—
505C22⋊C4—1721no—
506C22⋊C4—1722no—
507C22⋊C4—1722no—
508C22⋊C4—1722no—
509C42—21no—
510C42—21no—
511C42—861no—
512C42—861no—
513C42—1722no—
514C42—1722no—
515C42—1722no—
516C42—1722no—
517C23—861no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23C2×D4×D4311yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
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—862no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—862no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—862no—
562C2×C4—861no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
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#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C2×C4#1306337011yescharacteristic
581C2×C4#1306337011yescharacteristic
582C8—41no—
583C8—41no—
584C8—1721no—
585C8—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22#1458340911yescharacteristic
594C22#1458353811yescharacteristic
595C22#1458354611yescharacteristic
596C22#1458369611yescharacteristic
597C22#1458369811yescharacteristic
598C22#1458371211yescharacteristic
599C22#1458371511yescharacteristic
600C4—41no—
601C4—41no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—3441no—
607C4—1721no—
608C4—1722no—
609C4—1721no—
610C4—1722no—
611C4—1721no—
612C4—1722no—
613C4#1458342611yescharacteristic
614C4#1458348411yescharacteristic
615C4#1458361111yescharacteristic
616C4#1458363311yescharacteristic
617C2—3441no—
618C2#1913853311yescharacteristic
619C2#1914470311yescharacteristic
620C2#1914489311yescharacteristic
621C2#1914666711yescharacteristic
622C2#1914668611yescharacteristic
623C2#1914669811yescharacteristic
624C2#1914687011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2056C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2056D43
hypocenterC43#26749
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2056

Complements

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

NH ≅ G/Ntype
4. #19135746C2semidirect
6. #19135550C2semidirect
7. #19135282C2semidirect
8. #19135233C2semidirect
10. #19135185C2semidirect
11. #19134938C2semidirect
14. #19134427C2semidirect
15. C43×#2056C2semidirect
307. #2056D43semidirect
371. C43#26749semidirect

Maximal subgroups

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

subgroupindex
#191389342
#191376272
#191357962
#191357462
#191356022
#191355502
#191352822
#191352332
#191352072
#191351852
#191349382
#191349042
#191346892
#191344272
C43×#20562
#2674943