Finite Group Databasebeta

← #25200240

Subgroups — #25200240

Order 11008.

700 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#19140392C211yesmaximal, characteristic
2#19137277C211yesmaximal, characteristic
3#19136018C211yesmaximal, characteristic
4#19135799C211yesmaximal, characteristic
5#19135799C211yesmaximal, characteristic
6#19135605C211yesmaximal, characteristic
7#19135456C211yesmaximal, characteristic, complemented
8#19135328C211yesmaximal, characteristic, complemented
9#19135285C211yesmaximal, characteristic, complemented
10#19135285C211yesmaximal, characteristic, complemented
11#19135237C211yesmaximal, characteristic, complemented
12#19135167C211yesmaximal, characteristic, complemented
13#19134935C211yesmaximal, characteristic, complemented
14#19134852C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063259C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29#14582837—21no—
30#14582830—21no—
31#14582827—21no—
32#14582827—21no—
33#14582805C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582794—21no—
40#14582793—21no—
41#14582787—21no—
42#14582780—21no—
43#14582759C2211yescharacteristic
44#14582759C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C2×Dic172—22no—
62C2×Dic172—22no—
63C2×Dic172—41no—
64#13063304—22no—
65#13063304—22no—
66#13063304—41no—
67#13063304—41no—
68C4×Dic86—41no—
69C4×Dic86—41no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88#13063259—22no—
89#13063259—22no—
90#13063259—41no—
91#13063250—22no—
92#13063250—22no—
93#13063250—22no—
94#13063250—22no—
95#13063250—41no—
96#13063250—41no—
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⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C23×C4×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114#117×C43—41no—
115#117×C43—41no—
116C2×C4⋊C4×C43D411yescharacteristic
117C2×C4⋊C4×C43D411yescharacteristic
118C2×C22⋊C4×C43D411yescharacteristic
119C2×C22⋊C4×C43D411yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C22⋊C8×C43—22no—
123C22⋊C8×C43—22no—
124#97×C43—41no—
125C4×C8×C43—41no—
126C24×C43C2×D411yescharacteristic
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86#4112yes—
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—21no—
168C2×C8×C43—21no—
169C2×C8×C43#4112yes—
170C2×C8×C43#4112yes—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C22⋊Dic43—24no—
180C22⋊Dic43—42no—
181C22⋊Dic43—81no—
182C22⋊Dic43—81no—
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⋊Dic43#4112yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—81no—
199Dic43⋊C4—81no—
200Dic43⋊C4—81no—
201C4×Dic43—42no—
202C4×Dic43—81no—
203Dic172—44no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43C22×D411yescharacteristic
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
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—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—41no—
240C2×Dic43—41no—
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—
261Dic86—22no—
262Dic86—22no—
263Dic86—41no—
264Dic86—41no—
265Dic86—41no—
266Dic86—41no—
267Dic86—41no—
268Dic86—41no—
269C8×C43—22no—
270C8×C43—22no—
271C8×C43—41no—
272C8×C43—41no—
273#29470—431nomaximal, Sylow
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43#52511yescharacteristic
282C22×C43#53211yescharacteristic
283C22×C43#53411yescharacteristic
284C22×C43#57611yescharacteristic
285C22×C43#57811yescharacteristic
286C22×C43#57811yescharacteristic
287C22×C43#57811yescharacteristic
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43#55111yescharacteristic
294C4×C43#55311yescharacteristic
295C4×C43#55311yescharacteristic
296C4×C43#55911yescharacteristic
297Dic43—42no—
298Dic43—42no—
299Dic43—81no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303Dic43—81no—
304Dic43—81no—
305#2625—431no—
306#2323—431no—
307#2075—431no—
308#2036—431no—
309#2036—431no—
310#2001—431no—
311#1969—431no—
312#1942—431no—
313#1935—431no—
314#1935—431no—
315#1928—431no—
316#1918—431no—
317#1878—431no—
318#1863—431no—
319#1750D4311yescharacteristic
320C2×C43—81no—
321C2×C43#260211yescharacteristic
322C2×C43#312411yescharacteristic
323C2×C43#312711yescharacteristic
324C2×C43#317511yescharacteristic
325C2×C43#317711yescharacteristic
326C2×C43#320211yescharacteristic
327C2×C43#320311yescharacteristic
328C22×Q16—431no—
329C2×C22⋊Q8—431no—
330C2×C22⋊Q8—431no—
331C2×C4×Q8—431no—
332C2×#117C2×D4311yescharacteristic
333C2×#107—431no—
334C2×#107—431no—
335C2×#107—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×C22⋊C8C2×D4311yescharacteristic
343C2×C22⋊C8C2×D4311yescharacteristic
344C2×#97C2×D4311yescharacteristic
345C2×C4×C8C2×D4311yescharacteristic
346#400—861no—
347#398—861no—
348#397—861no—
349#397—861no—
350#391—431no—
351#391—431no—
352#391—431no—
353#389—431no—
354#389—431no—
355#389—431no—
356#389—861no—
357#388—861no—
358#388—861no—
359#387—861no—
360#380—431no—
361#380—431no—
362C4×C4⋊C4—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#336C2×D4311yescharacteristic
370#336C2×D4311yescharacteristic
371C43#2947011yescharacteristic, complemented, Sylow
372C22×Q8—431no—
373C22×Q8—431no—
374C23×C4C22×D4311yescharacteristic
375C2×Q16—862no—
376C2×Q16—862no—
377C2×Q16—1721no—
378C22×C8C22×D4311yescharacteristic
379C22×C8C22×D4311yescharacteristic
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C22⋊Q8—1721no—
385C22⋊Q8—1721no—
386C4×Q8—1721no—
387C4×Q8—1721no—
388#117—41no—
389#117—41no—
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—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4D17211yescharacteristic
403C2×C4⋊C4D17211yescharacteristic
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4D17211yescharacteristic
409C2×C22⋊C4D17211yescharacteristic
410C2×C42—861no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413C2×C42C22×D4311yescharacteristic
414#107—862no—
415#107—862no—
416#107—1721no—
417#103—862no—
418#103—862no—
419#103—862no—
420#103—862no—
421#103—1721no—
422#103—1721no—
423C22⋊C8—22no—
424C22⋊C8—22no—
425#97—41no—
426C4×C8—41no—
427#95—861no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439C24C2×D17211yescharacteristic
440C2×Q8—432no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4C2×D17211yescharacteristic
467C22×C4C2×D17211yescharacteristic
468C22×C4C2×D17211yescharacteristic
469C22×C4C2×D17211yescharacteristic
470C22×C4C2×D17211yescharacteristic
471C22×C4C23×D4311yescharacteristic
472Q16—1724no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8#1062189812yes—
484C2×C8#1062189812yes—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—432no—
488C4⋊C4—864no—
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—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—3441no—
501C4⋊C4—3441no—
502C4⋊C4—3441no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—864no—
508C22⋊C4—3441no—
509C22⋊C4—3441no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—3441no—
516C42—1722no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23C22×D17211yescharacteristic
525Q8—862no—
526Q8—862no—
527Q8—1721no—
528Q8—1721no—
529Q8—1721no—
530Q8—1721no—
531Q8—1721no—
532Q8—1721no—
533C2×C4—21no—
534C2×C4—21no—
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—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—862no—
553C2×C4—862no—
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—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×C4C2×#1062189811yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C2×C4#1306337011yescharacteristic
581C2×C4#1306337011yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1458341111yescharacteristic
594C22#1458344911yescharacteristic
595C22#1458346111yescharacteristic
596C22#1458370411yescharacteristic
597C22#1458371611yescharacteristic
598C22#1458371611yescharacteristic
599C22#1458371611yescharacteristic
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—3441no—
606C4—3441no—
607C4—3441no—
608C4—3441no—
609C4—3441no—
610C4—3441no—
611C4—1722no—
612C4—1722no—
613C4#1458357811yescharacteristic
614C4#1458359811yescharacteristic
615C4#1458359911yescharacteristic
616C4#1458363211yescharacteristic
617C2—81no—
618C2#1914020111yescharacteristic
619C2#1914485911yescharacteristic
620C2#1914489611yescharacteristic
621C2#1914523411yescharacteristic
622C2#1914525411yescharacteristic
623C2#1914549011yescharacteristic
624C2#1914549711yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1750C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1750D43
hypocenterC43#29470
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
7. #19135456C2semidirect
8. #19135328C2semidirect
9. #19135285C2semidirect
10. #19135285C2semidirect
11. #19135237C2semidirect
12. #19135167C2semidirect
13. #19134935C2semidirect
14. #19134852C2semidirect
371. C43#29470semidirect

Maximal subgroups

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

subgroupindex
#191403922
#191372772
#191360182
#191357992
#191356052
#191354562
#191353282
#191352852
#191352372
#191351672
#191349352
#191348522
C43×#17502
#2947043