Finite Group Databasebeta

← #25164702

Subgroups — #25164702

Order 11008.

748 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138938C211yesmaximal, characteristic
2#19137600C211yesmaximal, characteristic
3#19135916C211yesmaximal, characteristic, complemented
4#19135792C211yesmaximal, characteristic
5#19135745C211yesmaximal, characteristic, complemented
6#19135603C211yesmaximal, characteristic
7#19135549C211yesmaximal, characteristic, complemented
8#19135268C211yesmaximal, characteristic, complemented
9#19135231C211yesmaximal, characteristic, complemented
10#19135204C211yesmaximal, characteristic
11#19135179C211yesmaximal, characteristic, complemented
12#19134933C211yesmaximal, characteristic, complemented
13#19134681C211yesmaximal, characteristic
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1872C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582837—21no—
29#14582824—21no—
30#14582806C2211yescharacteristic
31#14582806C2211yescharacteristic
32#14582804C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582794—21no—
35#14582793—21no—
36#14582780—21no—
37#14582772—21no—
38#14582764—21no—
39#14582759C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C22⋊Dic43—21no—
43C4×C22⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C22⋊Q8×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621885—22no—
61C2×#10621885—41no—
62C2×#10621885—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063316—22no—
66#13063316—41no—
67#13063304—22no—
68#13063304—22no—
69#13063290—22no—
70#13063290—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—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#13063257—22no—
89Dic43⋊C8—41no—
90#13063250—22no—
91#13063250—41no—
92#13063249—22no—
93#13063248—22no—
94C22⋊(C43⋊C8)—41no—
95C8×Dic43—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C23×C4×C43—21no—
110C23×C4×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—41no—
115C2×C4⋊C4×C43—22no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—41no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123#103×C43—22no—
124#103×C43—41no—
125C22⋊C8×C43—41no—
126C24×C43C2×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—
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×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—81no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86#4112yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43#4112yes—
175C4⋊C4×C43#4112yes—
176C22⋊C4×C43—42no—
177C22⋊Dic43—24no—
178C22⋊Dic43—22no—
179C22⋊Dic43—22no—
180C22⋊Dic43—42no—
181#10621885—44no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188C4⋊Dic43#4112yes—
189Dic43⋊C4—24no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—81no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43#13512yes—
213C23×C43C22×D411yescharacteristic
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
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×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—84no—
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—21no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
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#13712yes—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272C8×C43—41no—
273C8×C43—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#26725—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43#52511yescharacteristic
285C22×C43#54611yescharacteristic
286C22×C43#54611yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43C2×#13711yescharacteristic
289C22×C43#57711yescharacteristic
290C22×C43#57811yescharacteristic
291C4×C43—42no—
292C4×C43—41no—
293C4×C43—42no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43#52911yescharacteristic
297C4×C43#53811yescharacteristic
298C4×C43#55511yescharacteristic
299C4×C43#55911yescharacteristic
300Dic43—22no—
301Dic43—41no—
302Dic43—42no—
303Dic43—42no—
304Dic43—41no—
305Dic43—41no—
306Dic43—81no—
307Dic43—81no—
308#2489—431no—
309#2360—431no—
310#2056—431no—
311#2035—431no—
312#2026—431no—
313#2001—431no—
314#1989—431no—
315#1933—431no—
316#1927—431no—
317#1923—431no—
318#1920—431no—
319#1878—431no—
320#1872D4311yescharacteristic
321#1823—431no—
322C4×#103—431no—
323C2×C43—42no—
324C2×C43#245911yescharacteristic
325C2×C43#310811yescharacteristic
326C2×C43#312011yescharacteristic
327C2×C43#329611yescharacteristic
328C2×C43#330011yescharacteristic
329C2×C43#331211yescharacteristic
330C2×C43#333111yescharacteristic
331C22×Q16—431no—
332C2×#125—431no—
333C2×C22⋊Q8—431no—
334C2×C22⋊Q8C2×D4311yescharacteristic
335C2×C4×Q8—431no—
336C22×C4⋊C4C2×D4311yescharacteristic
337C2×#106—431no—
338C2×C4⋊C8—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103C2×D4311yescharacteristic
344C2×#103C2×D4311yescharacteristic
345C2×C22⋊C8—431no—
346C2×C22⋊C8C2×D4311yescharacteristic
347C2×C4×C8—431no—
348#400—861no—
349#397—861no—
350#391—431no—
351#391—431no—
352#391—431no—
353#389—431no—
354#389—861no—
355#388—861no—
356#387—861no—
357#385—861no—
358#382—861no—
359#380—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—431no—
362C4×C22⋊C4—431no—
363C4×C22⋊C4—861no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340C2×D4311yescharacteristic
371#340C2×D4311yescharacteristic
372#336—431no—
373#336—431no—
374C43#2672511yescharacteristic, complemented, Sylow
375C22×Q8—431no—
376C22×Q8C22×D4311yescharacteristic
377C23×C4—21no—
378C23×C4C22×D4311yescharacteristic
379C2×Q16—862no—
380C2×Q16—1721no—
381C2×Q16—1721no—
382C22×C8—431no—
383C22×C8—431no—
384C22×C8C22×D4311yescharacteristic
385C22×C8C22×D4311yescharacteristic
386#125—862no—
387#125—1721no—
388C22⋊Q8—22no—
389C22⋊Q8—41no—
390C22⋊Q8—862no—
391C22⋊Q8—862no—
392C4×Q8—862no—
393C4×Q8—1721no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—431no—
411C2×C22⋊C4—431no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418C2×C42—861no—
419#106—862no—
420C4⋊C8—1721no—
421#103—22no—
422#103—41no—
423#103—862no—
424#103—862no—
425#103—862no—
426#103—1721no—
427C22⋊C8—41no—
428C22⋊C8—1721no—
429C4×C8—1721no—
430#95—431no—
431#95—431no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442C24D4×D4311yescharacteristic
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—432no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
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—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—81no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478Q16—1724no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—861no—
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—42no—
496C4⋊C4—42no—
497C4⋊C4—432no—
498C4⋊C4—864no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—3441no—
505C4⋊C4—1722no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C4⋊C4#1062189812yes—
509C4⋊C4#1062190012yes—
510C22⋊C4—42no—
511C22⋊C4—862no—
512C22⋊C4—864no—
513C22⋊C4—862no—
514C22⋊C4—1722no—
515C42—861no—
516C42—861no—
517C42—861no—
518C42—861no—
519C42—3441no—
520C42—1722no—
521C42—1722no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23#1306334612yes—
529C23C2×D4×D4311yescharacteristic
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534Q8—862no—
535Q8—862no—
536Q8—1721no—
537Q8—1721no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—21no—
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—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—84no—
558C2×C4—432no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—862no—
562C2×C4—862no—
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—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—1721no—
582C2×C4#41×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C2×C4C2×#1062190011yescharacteristic
585C2×C4C2×#1062189811yescharacteristic
586C2×C4#1306337011yescharacteristic
587C2×C4#1306337011yescharacteristic
588C8—41no—
589C8—41no—
590C8—1721no—
591C8—1721no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22#1458340711yescharacteristic
600C22#1458353611yescharacteristic
601C22#1458353911yescharacteristic
602C22C2×#1306334611yescharacteristic
603C22#137×D4311yescharacteristic
604C22#1458370911yescharacteristic
605C22#1458371211yescharacteristic
606C4—42no—
607C4—42no—
608C4—41no—
609C4—81no—
610C4—81no—
611C4—862no—
612C4—3441no—
613C4—3441no—
614C4—1722no—
615C4—1721no—
616C4—1721no—
617C4—1722no—
618C4—1721no—
619C4#1458343111yescharacteristic
620C4#1458348111yescharacteristic
621C4#1458361311yescharacteristic
622C4#1458363211yescharacteristic
623C2—42no—
624C2#1913853111yescharacteristic
625C2#1914467811yescharacteristic
626C2#1914480411yescharacteristic
627C2#1914643411yescharacteristic
628C2#1914647811yescharacteristic
629C2#1914663911yescharacteristic
630C2#1914690711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1872D43
hypocenterC43#26725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. #19135916C2semidirect
5. #19135745C2semidirect
7. #19135549C2semidirect
8. #19135268C2semidirect
9. #19135231C2semidirect
11. #19135179C2semidirect
12. #19134933C2semidirect
14. #19134414C2semidirect
374. C43#26725semidirect

Maximal subgroups

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

subgroupindex
#191389382
#191376002
#191359162
#191357922
#191357452
#191356032
#191355492
#191352682
#191352312
#191352042
#191351792
#191349332
#191346812
#191344142
C43×#18722
#2672543