Finite Group Databasebeta

← #25196668

Subgroups — #25196668

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063304C211yesmaximal, characteristic
2#19136162C211yesmaximal, characteristic, complemented
3#19136146C211yesmaximal, characteristic, complemented
4#19135930C211yesmaximal, characteristic, complemented
5#19135743C211yesmaximal, characteristic, complemented
6#19135184C211yesmaximal, characteristic, complemented
7#19135170C211yesmaximal, characteristic, complemented
8#19135026C211yesmaximal, characteristic
9#19135026C211yesmaximal, characteristic
10#19134862C211yesmaximal, characteristic, complemented
11#19134848C211yesmaximal, characteristic, complemented
12#19134626C211yesmaximal, characteristic
13#19134626C211yesmaximal, characteristic
14#19134289C211yesmaximal, characteristic
15C43×#2851C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28#14582805C2211yescharacteristic
29#14582797C2211yescharacteristic
30#14582783—21no—
31#14582772—21no—
32#14582759C2211yescharacteristic
33C4×Dic43⋊C4—21no—
34C4×C4⋊Dic43C2211yescharacteristic
35C4×C22⋊Dic43—21no—
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#125×C43C2211yescharacteristic
49C22×C42×C43C2211yescharacteristic
50C43×#389C2211yescharacteristic
51C43×#389C2211yescharacteristic
52C43×#387—21no—
53C43×#387—21no—
54C43×#385—21no—
55C43×#385—21no—
56C43×#382C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621877—22no—
61C2×#10621877—22no—
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877—41no—
65C2×#10621877—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063304—22no—
71#13063304Q814yes—
72C4×Dic86—41no—
73C4×Dic86—41no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84#13063258—22no—
85#13063258—41no—
86#13063256—22no—
87#13063256—41no—
88#13063248—22no—
89#13063248—22no—
90#13063248—41no—
91#13063248—41no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C23×C4×C43D411yescharacteristic
98C23×C4×C43D411yescharacteristic
99C23×C4×C43C2311yescharacteristic
100#125×C43—41no—
101#125×C43—41no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C42×C43—41no—
113C2×C42×C43—41no—
114C2×C42×C43D411yescharacteristic
115C2×C42×C43D411yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124C24×C43C2×D411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—22no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—41no—
135C22×C4×C43—41no—
136C22×C4×C43—41no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×Q812yes—
145C22×C4×C43#4112yes—
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86C2×Q812yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×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—42no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43—42no—
169C22⋊C4×C43—42no—
170C22⋊C4×C43—42no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—41no—
176C42×C43—41no—
177C22⋊Dic43—24no—
178C22⋊Dic43—42no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C2×Q812yes—
185Dic43⋊C4—24no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188C4×Dic43—42no—
189C4×Dic43—42no—
190#10621877—44no—
191#10621877—44no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8#4112yes—
203C2×C43⋊C8#4112yes—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43C22⋊Q812yes—
211C23×C43C22×D411yescharacteristic
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—21no—
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—21no—
228C2×C4×C43—21no—
229C2×C4×C43—44no—
230C2×C4×C43—44no—
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×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43C22⋊Q812yes—
244C2×C4×C43#13712yes—
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—41no—
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—
263Dic86—22no—
264Dic86—22no—
265Dic86—41no—
266Dic86—41no—
267C43⋊C8—22no—
268C43⋊C8—22no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#29164—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43C2×C22⋊Q811yescharacteristic
280C22×C43#53211yescharacteristic
281C22×C43#53411yescharacteristic
282C22×C43C2×#13711yescharacteristic
283C22×C43#57511yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57511yescharacteristic
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#55111yescharacteristic
296C4×C43#55111yescharacteristic
297C4×C43#55411yescharacteristic
298C4×C43#55411yescharacteristic
299Dic43—42no—
300Dic43—42no—
301Dic43—81no—
302Dic43—81no—
303#2851D4311yescharacteristic
304C4×C22⋊Q8—431no—
305#2101—431no—
306#2097—431no—
307#2059—431no—
308#2026—431no—
309#1921—431no—
310#1919—431no—
311#1894—431no—
312#1894—431no—
313#1865—431no—
314#1863—431no—
315#1809—431no—
316#1809—431no—
317#1728—431no—
318C2×C43—42no—
319C2×C43#256411yescharacteristic
320C2×C43#307811yescharacteristic
321C2×C43#308011yescharacteristic
322C2×C43#317211yescharacteristic
323C2×C43#318311yescharacteristic
324C2×C43#319611yescharacteristic
325C2×C43#319711yescharacteristic
326C22×M16—431no—
327C22×M16—431no—
328C2×#125C2×D4311yescharacteristic
329C2×C22⋊Q8—431no—
330C2×C4×Q8—431no—
331C22×C42C2×D4311yescharacteristic
332C2×#107—431no—
333C2×#107—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340#391—431no—
341#389—431no—
342#389C2×D4311yescharacteristic
343#389C2×D4311yescharacteristic
344#387—21no—
345#387—21no—
346#387—861no—
347#385—21no—
348#385—21no—
349#385—861no—
350#382C2×D4311yescharacteristic
351#380—431no—
352#380C2×D4311yescharacteristic
353#380C2×D4311yescharacteristic
354C4×C4⋊C4—431no—
355C4×C4⋊C4—861no—
356C4×C22⋊C4—861no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#336—431no—
366#336—431no—
367#336—431no—
368#336—431no—
369C43#2916411yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C23×C4C22⋊D4311yescharacteristic
372C23×C4C22⋊D4311yescharacteristic
373C23×C4C22×D4311yescharacteristic
374C2×M16—862no—
375C2×M16—862no—
376C2×M16—862no—
377C2×M16—862no—
378C2×M16—1721no—
379C2×M16—1721no—
380C22×C8—431no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8—431no—
384#125—41no—
385#125—41no—
386C22⋊Q8—434no—
387C22⋊Q8—862no—
388C4×Q8—1721no—
389C4×Q8—1721no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—41no—
409C2×C42—41no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42C22⋊D4311yescharacteristic
413C2×C42C22⋊D4311yescharacteristic
414C2×C42C22×D4311yescharacteristic
415C2×C42C22×D4311yescharacteristic
416#107—862no—
417#107—1721no—
418#106—862no—
419#106—1721no—
420#103—862no—
421#103—862no—
422#103—1721no—
423#103—1721no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435C24C2×C22⋊D4311yescharacteristic
436C2×Q8—432no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4Q8×D4312yes—
461C22×C4#1062190212yes—
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C23×D4311yescharacteristic
468M16—1724no—
469M16—1724no—
470C2×C8—432no—
471C2×C8—432no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—432no—
495C4⋊C4—864no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—1722no—
502C4⋊C4—1722no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—864no—
506C22⋊C4—1722no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—41no—
512C42—41no—
513C42—1722no—
514C42—1722no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23#1306330112yes—
522C23C22×C22⋊D4311yescharacteristic
523Q8—862no—
524Q8—862no—
525Q8—1721no—
526Q8—1721no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—44no—
545C2×C4—44no—
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—41no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4#1306330112yes—
571C2×C4#1306335512yes—
572C2×C4C2×Q8×D4311yescharacteristic
573C2×C4#41×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C2×C4C2×#1062190211yescharacteristic
576C2×C4#1306337011yescharacteristic
577C2×C4#1306337011yescharacteristic
578C8—862no—
579C8—862no—
580C8—1721no—
581C8—1721no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22C2×#1306330111yescharacteristic
590C22#1458344511yescharacteristic
591C22#1458345811yescharacteristic
592C22C2×#1306335511yescharacteristic
593C22#1458369711yescharacteristic
594C22#1458369711yescharacteristic
595C22#1458369711yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—3441no—
606C4—3441no—
607C4—1722no—
608C4—1722no—
609C4#1458357611yescharacteristic
610C4#1458357611yescharacteristic
611C4#1458360311yescharacteristic
612C4#1458360311yescharacteristic
613C2—42no—
614C2#1913977711yescharacteristic
615C2#1914439611yescharacteristic
616C2#1914441311yescharacteristic
617C2#1914520211yescharacteristic
618C2#1914531811yescharacteristic
619C2#1914542111yescharacteristic
620C2#1914543211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2851C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2851D43
hypocenterC43#29164
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
2. #19136162C2semidirect
3. #19136146C2semidirect
4. #19135930C2semidirect
5. #19135743C2semidirect
6. #19135184C2semidirect
7. #19135170C2semidirect
10. #19134862C2semidirect
11. #19134848C2semidirect
369. C43#29164semidirect

Maximal subgroups

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

subgroupindex
C4×#130633042
#191361622
#191361462
#191359302
#191357432
#191351842
#191351702
#191350262
#191348622
#191348482
#191346262
#191342892
C43×#28512
#2916443