Finite Group Databasebeta

← #25064548

Subgroups — #25064548

Order 11008.

1036 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583455C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic
3C4×M16×D43C211yesmaximal, characteristic
4#19133208C214yesmaximal, complemented
5#19133198C211yesmaximal, characteristic, complemented
6#19133197C211yesmaximal, characteristic, complemented
7#19133196C211yesmaximal, characteristic, complemented
8#19133188C214yesmaximal, complemented
9C43×#1528C211yesmaximal, characteristic, complemented
10C2×M16×D43—21no—
11#14583455—21no—
12#14583455—21no—
13#14583455—21no—
14#14583455—21no—
15#14583455C412yes—
16#14583455C412yes—
17#14583455C2212yes—
18#14583455C2212yes—
19C2×#13063324C411yescharacteristic
20C2×#13063324C411yescharacteristic
21C2×#13063317C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063303—21no—
24C2×#13063290—21no—
25C2×#13063290—21no—
26C2×#13063283C411yescharacteristic
27C2×#13063283C411yescharacteristic
28C2×C42×D43C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582954C2212yes—
31#14582951—21no—
32#14582949—21no—
33#14582921—21no—
34#14582861—21no—
35C4×#10621877C2211yescharacteristic
36#14582851C2212yes—
37#14582851C2212yes—
38M16×Dic43—21no—
39C4×#10621872—21no—
40#97×D43C2212yes—
41C4×C8×D43—21no—
42#14582641C2214yescomplemented
43#14582640C2214yescomplemented
44#14582640C2214yescomplemented
45C2×#125×C43C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×#330C2214yescomplemented
49C22×Dic86—21no—
50C22×Dic86—21no—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×#10621872—22no—
56C2×#10621872—22no—
57M16×D43—28no—
58C2×C8×D43—22no—
59#13063324—21no—
60#13063324—21no—
61#13063324—21no—
62#13063324—21no—
63#13063324C2×C412yes—
64#13063324C2×C412yes—
65#13063324C2×C412yes—
66#13063324C2×C412yes—
67#13063317—21no—
68#13063317—21no—
69#13063317C2×C412yes—
70#13063317C2312yes—
71#13063303—22no—
72#13063303—22no—
73#13063303—22no—
74#13063303—22no—
75#13063303—22no—
76#13063303—22no—
77#13063303—22no—
78#13063303—22no—
79#13063290—22no—
80#13063290—22no—
81#13063290—22no—
82#13063290—22no—
83#13063290—22no—
84#13063290—22no—
85#13063290—22no—
86#13063290—22no—
87#13063283—21no—
88#13063283—21no—
89#13063283—21no—
90#13063283—21no—
91#13063283C2×C412yes—
92#13063283C2×C412yes—
93#13063283C2×C412yes—
94#13063283C2×C412yes—
95C2×C4⋊Dic43C2×C411yescharacteristic
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43C2311yescharacteristic
115C42×D43C2311yescharacteristic
116C4⋊(C43⋊C8)—21no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120#13063236C2312yes—
121#13063236C2312yes—
122#13063235—22no—
123C4×C43⋊C8—21no—
124C8×Dic43—22no—
125C8×Dic43—22no—
126C2×M16×C43—21no—
127#125×C43—21no—
128#125×C43—21no—
129#125×C43C2×C412yes—
130#125×C43C2312yes—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43C2312yes—
139#97×C43C2312yes—
140C4×C8×C43—21no—
141C23×D43C22⋊C411yescharacteristic
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C22⋊C411yescharacteristic
150C22×Dic43C22⋊C411yescharacteristic
151C22×Dic43C22⋊C411yescharacteristic
152C2×C4×D43—24no—
153C2×C4×D43—24no—
154C2×C4×D43—42no—
155C2×C4×D43C22⋊C411yescharacteristic
156C2×C4×D43C22⋊C411yescharacteristic
157C2×C4×D43C22⋊C411yescharacteristic
158C2×C4×D43C22⋊C411yescharacteristic
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22×C411yescharacteristic
162C2×C4×D43C22×C411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43C2×D411yescharacteristic
167C2×Dic86—22no—
168C2×Dic86—22no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—44no—
172C2×Dic86—44no—
173M16×C43—24no—
174C2×C8×C43—22no—
175C2×C8×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43C22×C412yes—
183C4⋊C4×C43C22×C412yes—
184C42×C43C22×C411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2411yescharacteristic
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C22×C412yes—
195C4⋊Dic43C22×C412yes—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204C4×Dic43—22no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43C22⋊C411yescharacteristic
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22×C411yescharacteristic
215C4×Dic43C22×C411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220#10621877—24no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8—22no—
223#10621872—28no—
224#10621872—44no—
225C8×D43—28no—
226C23×C43C2×C22⋊C411yescharacteristic
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—41no—
230C22×D43C2×C22⋊C411yescharacteristic
231C22×D43C2×C22⋊C411yescharacteristic
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C23×C411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43#10414yes—
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258C4×D43—22no—
259C4×D43—22no—
260C4×D43—22no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43#10114yes—
270Dic86—44no—
271Dic86—44no—
272Dic86—44no—
273Dic86—44no—
274C8×C43—24no—
275C8×C43—42no—
276C43⋊C8—24no—
277C43⋊C8—42no—
278#17648—431nomaximal, Sylow
279C22×C43—21no—
280C22×C43—21no—
281C22×C43C2×#10412yes—
282C22×C43C22×C22⋊C411yescharacteristic
283C2×D43—21no—
284C2×D43—21no—
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—21no—
288C2×D43—44no—
289C2×D43C2×#10112yes—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—42no—
296C4×C43—42no—
297C4×C43C2×#10112yes—
298Dic43—21no—
299Dic43—21no—
300Dic43—42no—
301Dic43—42no—
302Dic43C2×#10112yes—
303Dic43C2×#10412yes—
304Dic43C2×#10412yes—
305Dic43#42112yes—
306C2×#533—431no—
307#2920—431no—
308C2×C4×M16—431no—
309#1531—434no—
310#1528—431no—
311#1528—431no—
312#1528—431no—
313#1528D4311yescharacteristic, complemented
314#1526—434no—
315C2×C43—22no—
316C2×C43C22×#10111yescharacteristic
317C2×C43C22×#10411yescharacteristic
318C2×C43C2×#42111yescharacteristic
319D43—22no—
320D43—41no—
321C22×M16—861no—
322#533—432no—
323#533—432no—
324#533—432no—
325#533—432no—
326#533—861no—
327#533—861no—
328#533—861no—
329#533—861no—
330C2×C4⋊Q8—431no—
331C2×C4⋊Q8—431no—
332C2×#125—431no—
333C2×#125C2×D4311yescharacteristic
334C2×C22⋊Q8—861no—
335C2×C22⋊Q8—861no—
336C2×C4×Q8—861no—
337C2×C4×Q8—861no—
338C2×#117—431no—
339C2×#117—431no—
340C22×C42—431no—
341#432—431no—
342#432—432no—
343#432C2×D4311yescharacteristic
344#431—861no—
345#431—861no—
346#423—861no—
347#407—861no—
348C4×M16—431no—
349C4×M16—432no—
350C4×M16—432no—
351C4×M16—861no—
352C4×M16—861no—
353C4×M16C2×D4311yescharacteristic
354C2×#97—432no—
355C2×C4×C8—861no—
356#330—434no—
357#330—434no—
358#330—434no—
359#330C2×D4314yescomplemented
360C43#1764811yescharacteristic, complemented, Sylow
361C22×Q8—861no—
362C22×Q8—861no—
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—431no—
366C2×M16—21no—
367C2×M16—862no—
368C2×M16—862no—
369C2×M16—868no—
370C2×M16—861no—
371C22×C8—862no—
372C4⋊Q8—432no—
373C4⋊Q8—432no—
374C4⋊Q8—432no—
375C4⋊Q8—432no—
376C4⋊Q8—861no—
377C4⋊Q8—861no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380#125—21no—
381#125—21no—
382#125—432no—
383#125—432no—
384#125—861no—
385#125—861no—
386#125C4×D4312yes—
387#125C22×D4312yes—
388C22⋊Q8—862no—
389C22⋊Q8—862no—
390C22⋊Q8—862no—
391C22⋊Q8—862no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C4×Q8—862no—
397C4×Q8—862no—
398C4×Q8—862no—
399C4×Q8—862no—
400C4×Q8—862no—
401C4×Q8—862no—
402C4×Q8—862no—
403C4×Q8—862no—
404#117—432no—
405#117—432no—
406#117—432no—
407#117—432no—
408#117—861no—
409#117—861no—
410#117—861no—
411#117—861no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4C4×D4311yescharacteristic
421C2×C4⋊C4C4×D4311yescharacteristic
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42C22×D4311yescharacteristic
438C4⋊C8—21no—
439C4⋊C8—862no—
440C4⋊C8—861no—
441C22⋊C8—21no—
442C22⋊C8—862no—
443C22⋊C8—861no—
444#97—432no—
445#97—432no—
446#97—862no—
447#97C22×D4312yes—
448#97C22×D4312yes—
449C4×C8—21no—
450C4×C8—862no—
451C4×C8—862no—
452C4×C8—861no—
453C24—431no—
454C2×Q8—862no—
455C2×Q8—862no—
456C2×Q8—862no—
457C2×Q8—862no—
458C2×Q8—1724no—
459C2×Q8—1724no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—864no—
478C22×C4—864no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—1722no—
482C22×C4C2×C4×D4311yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485M16—24no—
486M16—868no—
487M16—864no—
488M16—1724no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—868no—
492C2×C8—862no—
493C2×C8—862no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—432no—
501C4⋊C4—432no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4C2×C4×D4312yes—
513C4⋊C4C2×C4×D4312yes—
514C22⋊C4—862no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C42—431no—
519C42—431no—
520C42—431no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—862no—
531C42—862no—
532C42—862no—
533C42—862no—
534C42C2×C4×D4311yescharacteristic
535C42D4×D4311yescharacteristic
536C42D4×D4311yescharacteristic
537C42C23×D4311yescharacteristic
538C23—431no—
539C23—431no—
540C23—862no—
541C23—862no—
542C23—1721no—
543C23C22⋊C4×D4311yescharacteristic
544Q8—1724no—
545Q8—1724no—
546Q8—1724no—
547Q8—1724no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—431no—
556C2×C4—431no—
557C2×C4—431no—
558C2×C4—431no—
559C2×C4—434no—
560C2×C4—434no—
561C2×C4—431no—
562C2×C4—431no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4C22⋊C4×D4311yescharacteristic
581C2×C4C22⋊C4×D4311yescharacteristic
582C2×C4C22⋊C4×D4311yescharacteristic
583C2×C4C22×C4×D4311yescharacteristic
584C2×C4C2×D4×D4311yescharacteristic
585C2×C4C2×D4×D4311yescharacteristic
586C8—24no—
587C8—42no—
588C8—864no—
589C8—1722no—
590C22—21no—
591C22—21no—
592C22—432no—
593C22—861no—
594C22—861no—
595C22—861no—
596C22—861no—
597C22—861no—
598C22—1724no—
599C22#104×D4312yes—
600C22C2×C22⋊C4×D4311yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—432no—
609C4—432no—
610C4—432no—
611C4—432no—
612C4—861no—
613C4—861no—
614C4—1722no—
615C4—1722no—
616C4#101×D4312yes—
617C2—22no—
618C2—862no—
619C2—1721no—
620C2C2×#101×D4311yescharacteristic
621C2C2×#104×D4311yescharacteristic
622C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1528C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenter#1528D43
hypocenterC43#17648
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
4. #19133208C2semidirect
5. #19133198C2semidirect
6. #19133197C2semidirect
7. #19133196C2semidirect
8. #19133188C2semidirect
9. C43×#1528C2semidirect
42. #14582641C22semidirect
43. #14582640C22semidirect
44. #14582640C22semidirect
48. C43×#330C22semidirect
313. #1528D43semidirect
359. #330C2×D43semidirect
360. C43#17648semidirect

Maximal subgroups

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

subgroupindex
C2×#145834552
#191432252
C4×M16×D432
#191332082
#191331982
#191331972
#191331962
#191331882
C43×#15282
#1764843