Finite Group Databasebeta

← #25196592

Subgroups — #25196592

Order 11008.

784 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
1#19142905C211yesmaximal, characteristic
2C4×#13063304C211yesmaximal, characteristic
3#19136164C211yesmaximal, characteristic, complemented
4#19136142C211yesmaximal, characteristic, complemented
5#19135934C211yesmaximal, characteristic, complemented
6#19135747C211yesmaximal, characteristic, complemented
7#19135181C211yesmaximal, characteristic, complemented
8#19135167C211yesmaximal, characteristic, complemented
9#19135018C211yesmaximal, characteristic
10#19135018C211yesmaximal, characteristic
11#19134866C211yesmaximal, characteristic, complemented
12#19134852C211yesmaximal, characteristic, complemented
13#19134624C211yesmaximal, characteristic
14#19134620C211yesmaximal, characteristic
15C2×C43×#336C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27#14582805C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582797C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582783—21no—
32#14582783—21no—
33#14582783—21no—
34#14582772—21no—
35#14582772—21no—
36#14582772—21no—
37#14582765C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582759C2211yescharacteristic
41C4×Dic43⋊C4—21no—
42C4×C4⋊Dic43C2211yescharacteristic
43C4×C22⋊Dic43—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C23×C8×C43C2211yescharacteristic
53C23×C8×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C43×#336C2211yescharacteristic
56C43×#336C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60#13063317—41no—
61#13063317—41no—
62#13063304—22no—
63#13063304Q814yes—
64C4×Dic86—41no—
65C4×Dic86—41no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
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×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063259—22no—
87#13063259—41no—
88#13063257—22no—
89#13063257—41no—
90#13063250—22no—
91#13063250—22no—
92#13063250—41no—
93#13063250—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
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—
105C23×C4×C43D411yescharacteristic
106C23×C4×C43D411yescharacteristic
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43—22no—
109C22×C8×C43—22no—
110C22×C8×C43—22no—
111C22×C8×C43—22no—
112C22×C8×C43—41no—
113C22×C8×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C2×C42×C43—41no—
119C2×C42×C43—41no—
120C2×C42×C43D411yescharacteristic
121C2×C42×C43D411yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
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—22no—
131C22×C4×C43—22no—
132C22×C4×C43—41no—
133C22×C4×C43—41no—
134C22×C4×C43—41no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×Q812yes—
141C22×C4×C43#4112yes—
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
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—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—44no—
168C2×C8×C43—44no—
169C2×C8×C43#4112yes—
170C2×C8×C43#4112yes—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—41no—
176C42×C43—41no—
177C22⋊Dic43—24no—
178C22⋊Dic43—42no—
179C22⋊Dic43—42no—
180C22⋊Dic43—42no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×Q812yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—42no—
202C4×Dic43—42no—
203C4×Dic43—42no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43C22⋊Q812yes—
209C23×C43#13512yes—
210C23×C43#13712yes—
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×C43C22⋊Q812yes—
232C2×C4×C43#13512yes—
233C2×C4×C43C22×Q811yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
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—
267C8×C43—22no—
268C8×C43—22no—
269C8×C43—41no—
270C8×C43—41no—
271#29158—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43#47914yes—
279C22×C43C2×C22⋊Q811yescharacteristic
280C22×C43#53211yescharacteristic
281C22×C43#53411yescharacteristic
282C22×C43C2×#13511yescharacteristic
283C22×C43C2×#13511yescharacteristic
284C22×C43C2×#13711yescharacteristic
285C22×C43#57511yescharacteristic
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43#55111yescharacteristic
292C4×C43#55111yescharacteristic
293C4×C43#55411yescharacteristic
294C4×C43#55411yescharacteristic
295Dic43—42no—
296Dic43—42no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303#2851—431no—
304C4×C22⋊Q8—431no—
305#2101—431no—
306#2097—431no—
307#2059—431no—
308#2026—431no—
309#1920—431no—
310#1918—431no—
311#1892—431no—
312#1892—431no—
313#1865—431no—
314#1863—431no—
315#1808—431no—
316#1807—431no—
317C2×#336D4311yescharacteristic
318C2×C43—24no—
319C2×C43#256411yescharacteristic
320C2×C43C2×#47911yescharacteristic
321C2×C43#307611yescharacteristic
322C2×C43#316811yescharacteristic
323C2×C43#318111yescharacteristic
324C2×C43#319011yescharacteristic
325C2×C43#319111yescharacteristic
326C23×C8C2×D4311yescharacteristic
327C23×C8C2×D4311yescharacteristic
328C2×#125—431no—
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#389—431no—
343#389—431no—
344#387—861no—
345#387—861no—
346#387—861no—
347#385—861no—
348#385—861no—
349#385—861no—
350#382—431no—
351#380—431no—
352#380—431no—
353#380—431no—
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#336C2×D4311yescharacteristic
366#336C2×D4311yescharacteristic
367#336C2×D4311yescharacteristic
368#336C2×D4311yescharacteristic
369C43#2915811yescharacteristic, complemented, Sylow
370C22×Q8—431no—
371C23×C4D17211yescharacteristic
372C23×C4D17211yescharacteristic
373C23×C4C22×D4311yescharacteristic
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—41no—
379C22×C8—41no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C22×C8C22×D4311yescharacteristic
383C22×C8C22×D4311yescharacteristic
384#125—1721no—
385#125—1721no—
386C22⋊Q8—434no—
387C22⋊Q8—862no—
388C4×Q8—1721no—
389C4×Q8—1721no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
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⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—41no—
409C2×C42—41no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42D17211yescharacteristic
413C2×C42D17211yescharacteristic
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—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435C24C2×D17211yescharacteristic
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—22no—
448C22×C4—22no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4C2×D17211yescharacteristic
461C22×C4C2×D17211yescharacteristic
462C22×C4C2×D17211yescharacteristic
463C22×C4C2×D17211yescharacteristic
464C22×C4C2×D17211yescharacteristic
465C22×C4#1062190012yes—
466C22×C4Q8×D4312yes—
467C22×C4C23×D4311yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—44no—
479C2×C8—44no—
480C2×C8#1062189812yes—
481C2×C8#1062189812yes—
482C4⋊C4—432no—
483C4⋊C4—864no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4—1722no—
502C4⋊C4—1722no—
503C22⋊C4—864no—
504C22⋊C4—1722no—
505C22⋊C4—1722no—
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#1306330512yes—
520C23#1306334712yes—
521C23#1306335812yes—
522C23C22×D17211yescharacteristic
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—862no—
547C2×C4—862no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
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#1306330512yes—
571C2×C4#1306334712yes—
572C2×C4C2×Q8×D4311yescharacteristic
573C2×C4C2×#1062190011yescharacteristic
574C2×C4C2×#1062189811yescharacteristic
575C2×C4C2×#1062189811yescharacteristic
576C2×C4#1306337011yescharacteristic
577C2×C4#1306337011yescharacteristic
578C8—22no—
579C8—22no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22#1458320714yes—
589C22C2×#1306330511yescharacteristic
590C22#1458344911yescharacteristic
591C22#1458346111yescharacteristic
592C22C2×#1306334711yescharacteristic
593C22C2×#1306334711yescharacteristic
594C22C2×#1306335811yescharacteristic
595C22#1458369911yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—3441no—
602C4—3441no—
603C4—3441no—
604C4—3441no—
605C4—3441no—
606C4—3441no—
607C4—1722no—
608C4—1722no—
609C4#1458357511yescharacteristic
610C4#1458357511yescharacteristic
611C4#1458360411yescharacteristic
612C4#1458360411yescharacteristic
613C2—24no—
614C2#1913977511yescharacteristic
615C2C2×#1458320711yescharacteristic
616C2#1914438511yescharacteristic
617C2#1914516511yescharacteristic
618C2#1914530411yescharacteristic
619C2#1914537811yescharacteristic
620C2#1914538811yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#336C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenterC2×#336D43
hypocenterC43#29158
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #19136164C2semidirect
4. #19136142C2semidirect
5. #19135934C2semidirect
6. #19135747C2semidirect
7. #19135181C2semidirect
8. #19135167C2semidirect
11. #19134866C2semidirect
12. #19134852C2semidirect
369. C43#29158semidirect

Maximal subgroups

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

subgroupindex
#191429052
C4×#130633042
#191361642
#191361422
#191359342
#191357472
#191351812
#191351672
#191350182
#191348662
#191348522
#191346242
#191346202
C2×C43×#3362
#2915843