Finite Group Databasebeta

← #25113102

Subgroups — #25113102

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148159C211yesmaximal, characteristic
2#19143330C211yesmaximal, characteristic, complemented
3#19137056C211yesmaximal, characteristic, complemented
4#19135571C211yesmaximal, characteristic, complemented
5#19135538C211yesmaximal, characteristic, complemented
6#19135040C212yesmaximal, complemented
7#19134894C212yesmaximal, complemented
8#19134693C212yesmaximal, complemented
9C4×#13063252C211yesmaximal, characteristic, complemented
10#19134303C212yesmaximal, complemented
11C43×#1806C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583622C411yescharacteristic, complemented
14#14583614C411yescharacteristic, complemented
15#14583609C411yescharacteristic, complemented
16#14583599C412yescomplemented
17#14583590C412yescomplemented
18#14583589—21no—
19#14583578—22no—
20#14583554C411yescharacteristic, complemented
21#14583545—21no—
22#14583456C2211yescharacteristic
23#14583433—21no—
24#14583427—22no—
25#14583406C2212yes—
26C4×#10621898—21no—
27C2×C4×D172C2211yescharacteristic
28C2×#13063282C2212yes—
29#117×D43C2212yes—
30#14582976—21no—
31#14582969—22no—
32#14582964—21no—
33C2×#13063252C2211yescharacteristic
34C2×#13063252C2211yescharacteristic
35#14582862C2212yes—
36C4×#10621877C2211yescharacteristic
37#14582800—21no—
38#14582795—21no—
39#14582788—22no—
40C4×(C2×D43)⋊C4C2212yes—
41C42×Dic43C2211yescharacteristic
42#14582660C2212yes—
43#14582660C2212yes—
44#14582659C2212yes—
45#14582659C2212yes—
46#14582658C2211yescharacteristic
47#14582658C2211yescharacteristic
48C4×#41×C43C2211yescharacteristic
49C43×#423C2211yescharacteristic
50C2×#104×C43C2212yes—
51C4×C4⋊C4×C43C2211yescharacteristic
52C43×#339C2212yes—
53C2×#10621898—21no—
54C22×D172D411yescharacteristic
55C22×C4×D43C2312yes—
56C2×#10621877C2311yescharacteristic
57C2×#10621877C2311yescharacteristic
58C2×#10621872—22no—
59M16×D43—24no—
60M16×D43—42no—
61C2×C8×D43—22no—
62#13063325C2×C411yescharacteristic
63#13063325C2×C411yescharacteristic
64#13063320—22no—
65#13063319—22no—
66#13063318—22no—
67#13063317—21no—
68#13063317C2×C412yes—
69#13063315—22no—
70#13063313—21no—
71#13063311—22no—
72#13063310—22no—
73#13063308—22no—
74#13063307—22no—
75#13063306—22no—
76#13063304—21no—
77#13063304—21no—
78#13063304—21no—
79#13063303—22no—
80#13063301C2×C412yes—
81#13063301C2×C412yes—
82#13063299—21no—
83#13063298—22no—
84#13063296C2×C412yes—
85#13063296C2×C412yes—
86#13063293—22no—
87C4×Dic86—21no—
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×D172—21no—
91C4×D172C2×C411yescharacteristic
92C4×D172C2×C412yes—
93C4×D172C2×C411yescharacteristic
94C4×D172D411yescharacteristic
95C4×D172D412yes—
96C4×D172D411yescharacteristic
97C4×C22⋊D43—22no—
98C4×C22⋊D43—22no—
99C4×C22⋊D43—22no—
100#13063284—21no—
101#13063284C2312yes—
102#13063283C2×C412yes—
103#13063283C2×C412yes—
104#13063282—22no—
105#13063282—22no—
106#13063282—24no—
107#13063282—42no—
108#13063281—22no—
109C2×C4⋊Dic43D411yescharacteristic
110C2×Dic43⋊C4—22no—
111C4⋊C4×D43C2×C412yes—
112C4⋊C4×D43C2×C412yes—
113C2×(C2×D43)⋊C4—22no—
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4D412yes—
116C22⋊C4×D43—22no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43C2311yescharacteristic
120C2×C4×Dic43C2311yescharacteristic
121C42×D43—22no—
122#13063252—22no—
123#13063252—22no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126#13063236—21no—
127C4×C43⋊C8—21no—
128C43⋊#95—22no—
129C2×#41×C43C2311yescharacteristic
130C2×M16×C43C2312yes—
131C4×Q8×C43C2×C411yescharacteristic
132C4×Q8×C43C2×C411yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43C2×C411yescharacteristic
136C4×D4×C43C2×C411yescharacteristic
137#117×C43—21no—
138#117×C43C2311yescharacteristic
139C2×C4⋊C4×C43—21no—
140C2×C42×C43—21no—
141C2×C42×C43C2312yes—
142C2×C42×C43C2311yescharacteristic
143C4⋊C8×C43—21no—
144C4⋊C8×C43—21no—
145#104×C43—42no—
146#95×C43—21no—
147C23×D43C2×D412yes—
148#41×C43—21no—
149#41×C43—21no—
150#41×C43—21no—
151#41×C43—21no—
152C2×Q8×C43C22×C411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43C22×C411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—22no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43C2×D412yes—
167#10621898—44no—
168C2×D172—42no—
169C2×D172C22⋊C411yescharacteristic
170C2×D172C22⋊C411yescharacteristic
171C2×D172C22⋊C412yes—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43C22×C412yes—
179C2×C4×D43C22×C412yes—
180C2×C4×D43C2×D412yes—
181C2×C4×D43C2×D412yes—
182C2×Dic86—21no—
183C2×Dic86—21no—
184M16×C43—22no—
185M16×C43—22no—
186C2×C8×C43—22no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—42no—
190C4⋊C4×C43C22×C411yescharacteristic
191C4⋊C4×C43C22×C411yescharacteristic
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—22no—
199C42×C43—22no—
200C42×C43C22×C411yescharacteristic
201C42×C43C22×C411yescharacteristic
202C42×C43C2×D411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C22⋊Dic43—22no—
205C22⋊Dic43—22no—
206C22⋊Dic43—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211(C2×D43)⋊C4—44no—
212(C2×D43)⋊C4—44no—
213(C2×D43)⋊C4C22⋊C412yes—
214(C2×D43)⋊C4C22⋊C412yes—
215(C2×D43)⋊C4C22⋊C412yes—
216(C2×D43)⋊C4C22⋊C412yes—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43C22⋊C411yescharacteristic
220C4⋊Dic43C22⋊C411yescharacteristic
221C4⋊Dic43C22⋊C412yes—
222C4⋊Dic43C22×C412yes—
223C4⋊Dic43C22×C412yes—
224Dic43⋊C4—22no—
225Dic43⋊C4—22no—
226Dic43⋊C4—22no—
227Dic43⋊C4—22no—
228Dic43⋊C4—22no—
229Dic43⋊C4—22no—
230Dic43⋊C4—44no—
231C4×Dic43—22no—
232C4×Dic43—21no—
233C4×Dic43—22no—
234C4×Dic43—22no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—42no—
238C4×Dic43—42no—
239C4×Dic43#4112yescomplemented
240#10621877—21no—
241#10621877—21no—
242#10621877—21no—
243#10621877#4112yescomplemented
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246#10621872—44no—
247C8×D43—44no—
248C23×C43—21no—
249C23×C43C22×D411yescharacteristic
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—42no—
253C22×D43—42no—
254C22×D43C2×C22⋊C412yes—
255C22×D43C2×C22⋊C412yes—
256Q8×C43—21no—
257Q8×C43—21no—
258D4×C43—21no—
259D4×C43—21no—
260D4×C43—41no—
261D4×C43—41no—
262C2×C4×C43—22no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—42no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—81no—
274C2×C4×C43C2×C22⋊C411yescharacteristic
275C2×C4×C43C2×C22⋊C411yescharacteristic
276C2×C4×C43C2×C22⋊C411yescharacteristic
277C2×C4×C43C2×C22⋊C411yescharacteristic
278C2×C4×C43C23×C411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43H(5,𝔽2)11yescharacteristic
283C2×C4×C432−1+411yescharacteristic
284C22⋊D43—44no—
285C22⋊D43—82no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43C2×C22⋊C412yes—
297C2×Dic43C2×C22⋊C412yes—
298D172—22no—
299D172—22no—
300D172—42no—
301C4×D43—22no—
302C4×D43—22no—
303C4×D43—22no—
304C4×D43—22no—
305C4×D43—22no—
306C4×D43—22no—
307C4×D43—22no—
308C4×D43—22no—
309C4×D43—44no—
310C4×D43—82no—
311Dic86—42no—
312Dic86—81no—
313C8×C43—42no—
314C43⋊C8—22no—
315C43⋊C8—41no—
316#22507—431nomaximal, Sylow
317C22×C43—21no—
318C22×C43—21no—
319C22×C43—41no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43C22×C22⋊C411yescharacteristic
323C22×C43#54611yescharacteristic
324C22×C43#54711yescharacteristic
325C2×D43—22no—
326C2×D43—22no—
327C2×D43—22no—
328C2×D43—22no—
329C2×D43—22no—
330C2×D43—22no—
331C2×D43—82no—
332C2×D43—82no—
333C4×C43—21no—
334C4×C43—21no—
335C4×C43—21no—
336C4×C43—41no—
337C4×C43—41no—
338C4×C43—41no—
339C4×C43—82no—
340C4×C43#42112yes—
341C4×C43C4×#4111yescharacteristic
342C4×C43#52011yescharacteristic
343C4×C43#54611yescharacteristic
344C4×C43#54711yescharacteristic
345Dic43—22no—
346Dic43—22no—
347Dic43—42no—
348Dic43—42no—
349Dic43—42no—
350Dic43—42no—
351#3475—431no—
352D4×M16—431no—
353#2293—431no—
354#1994—431no—
355#1986—431no—
356#1897—432no—
357#1871—432no—
358#1826—432no—
359#1806D4311yescharacteristic, complemented
360C4×#104—431no—
361#1733—432no—
362C2×C43—21no—
363C2×C43—21no—
364C2×C43—81no—
365C2×C43#233911yescharacteristic
366C2×C43C2×#42111yescharacteristic
367C2×C43#290111yescharacteristic
368D43—42no—
369D43—42no—
370C22×M16—432no—
371#556—431no—
372#555—431no—
373#554—431no—
374#553—432no—
375#552—432no—
376#552—861no—
377#551—862no—
378#547—431no—
379#546—861no—
380#533—431no—
381#529—861no—
382#529—862no—
383#525—432no—
384C4×#41—861no—
385C4×#41C2×D4311yescharacteristic
386C2×C4×D4—431no—
387C2×#117—432no—
388C2×#117—432no—
389#436—861no—
390#435—862no—
391C8×D4—861no—
392#423C2×D4311yescharacteristic
393C2×#104—431no—
394C2×#104—431no—
395C2×#104C2×D4312yes—
396#407—432no—
397C4×M16—431no—
398#390—861no—
399#389—861no—
400#388—862no—
401C4×C4⋊C4C2×D4311yescharacteristic
402C4×C22⋊C4—432no—
403C43—431no—
404#339—432no—
405#339—432no—
406#339—431no—
407#339—431no—
408#339—432no—
409#339—432no—
410#339C2×D4312yes—
411C43#2250711yescharacteristic, complemented, Sylow
412C2×#41—861no—
413C2×#41C22×D4311yescharacteristic
414C22×D4—431no—
415C23×C4—432no—
416C2×M16—431no—
417C2×M16—431no—
418C2×M16—862no—
419C2×M16—864no—
420C2×M16—1722no—
421C2×M16C22×D4312yes—
422C22×C8—862no—
423C4⋊Q8—431no—
424C4⋊Q8—431no—
425#126—862no—
426#126—862no—
427#126—862no—
428#125—432no—
429#125—861no—
430#125—862no—
431#124—861no—
432#124—862no—
433#123—862no—
434#123—862no—
435#123—862no—
436#123—862no—
437C22⋊Q8—432no—
438C22⋊Q8—432no—
439C22⋊Q8—862no—
440C22⋊Q8—861no—
441C22⋊Q8—861no—
442C22⋊Q8—861no—
443#121—432no—
444#121—432no—
445#121—862no—
446#121—861no—
447#120—862no—
448C4×Q8—861no—
449C4×Q8—861no—
450C4×Q8—861no—
451C4×Q8C4×D4311yescharacteristic
452C4×Q8C4×D4311yescharacteristic
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—431no—
456C4×D4—432no—
457C4×D4—431no—
458C4×D4—431no—
459C4×D4—431no—
460C4×D4—432no—
461C4×D4—861no—
462C4×D4—862no—
463C4×D4—862no—
464C4×D4—862no—
465C4×D4C4×D4311yescharacteristic
466C4×D4C4×D4311yescharacteristic
467#117—21no—
468#117—432no—
469#117—432no—
470#117—432no—
471#117—864no—
472#117—862no—
473#117—862no—
474#117—862no—
475#117—861no—
476#117—1722no—
477#117C22×D4311yescharacteristic
478C2×C4⋊C4—21no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—432no—
481C2×C4⋊C4—432no—
482C2×C4⋊C4—862no—
483C2×C22⋊C4—432no—
484C2×C22⋊C4—862no—
485C2×C22⋊C4—862no—
486C2×C22⋊C4—862no—
487C2×C42—21no—
488C2×C42—431no—
489C2×C42—431no—
490C2×C42—862no—
491C2×C42—861no—
492C2×C42—861no—
493C2×C42C22×D4312yes—
494C2×C42C22×D4311yescharacteristic
495C4⋊C8—21no—
496C4⋊C8—21no—
497#104—42no—
498#104—862no—
499#104—862no—
500C22⋊C8—862no—
501C22⋊C8—862no—
502#97—861no—
503C4×C8—861no—
504#95—21no—
505#95—862no—
506C24—432no—
507#41—21no—
508#41—21no—
509#41—21no—
510#41—21no—
511#41—1724no—
512C2×Q8—861no—
513C2×Q8—861no—
514C2×Q8C2×C4×D4311yescharacteristic
515C2×D4—21no—
516C2×D4—431no—
517C2×D4—431no—
518C2×D4—432no—
519C2×D4—862no—
520C2×D4—862no—
521C2×D4—1722no—
522C2×D4C2×C4×D4311yescharacteristic
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—432no—
528C22×C4—432no—
529C22×C4—432no—
530C22×C4—432no—
531C22×C4—432no—
532C22×C4—862no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4D4×D4311yescharacteristic
541C22×C4D4×D4311yescharacteristic
542C22×C4C23×D4311yescharacteristic
543M16—22no—
544M16—22no—
545M16—432no—
546M16—861no—
547M16—861no—
548M16—861no—
549M16—1724no—
550C2×C8—22no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—1724no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—431no—
558C4⋊C4—431no—
559C4⋊C4—432no—
560C4⋊C4—432no—
561C4⋊C4—432no—
562C4⋊C4—862no—
563C4⋊C4—862no—
564C4⋊C4—862no—
565C4⋊C4—862no—
566C4⋊C4—861no—
567C4⋊C4—862no—
568C4⋊C4—862no—
569C4⋊C4—861no—
570C4⋊C4—1724no—
571C4⋊C4C2×C4×D4311yescharacteristic
572C4⋊C4C2×C4×D4311yescharacteristic
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—432no—
577C22⋊C4—432no—
578C22⋊C4—432no—
579C22⋊C4—432no—
580C22⋊C4—862no—
581C22⋊C4—862no—
582C22⋊C4—862no—
583C22⋊C4—862no—
584C22⋊C4—862no—
585C22⋊C4—862no—
586C22⋊C4—862no—
587C22⋊C4—1724no—
588C22⋊C4—1724no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—22no—
593C42—22no—
594C42—432no—
595C42—862no—
596C42—862no—
597C42—862no—
598C42—861no—
599C42—861no—
600C42—861no—
601C42—1722no—
602C42—1722no—
603C42C2×C4×D4311yescharacteristic
604C42C2×C4×D4311yescharacteristic
605C42D4×D4311yescharacteristic
606C42D4×D4311yescharacteristic
607C23—21no—
608C23—432no—
609C23—432no—
610C23—862no—
611C23—862no—
612C23—1722no—
613C23—1722no—
614C23C2×D4×D4311yescharacteristic
615Q8—21no—
616Q8—21no—
617Q8—3441no—
618Q8—1722no—
619D4—21no—
620D4—21no—
621D4—41no—
622D4—41no—
623D4—862no—
624D4—862no—
625D4—3442no—
626D4—1722no—
627D4—1724no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—81no—
640C2×C4—432no—
641C2×C4—432no—
642C2×C4—862no—
643C2×C4—862no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—862no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—3442no—
657C2×C4—1724no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4C22⋊C4×D4311yescharacteristic
663C2×C4C22⋊C4×D4311yescharacteristic
664C2×C4C22⋊C4×D4311yescharacteristic
665C2×C4C22⋊C4×D4311yescharacteristic
666C2×C4C22×C4×D4311yescharacteristic
667C2×C4C2×D4×D4311yescharacteristic
668C2×C4#41×D4311yescharacteristic
669C2×C4#41×D4311yescharacteristic
670C2×C4#1306337011yescharacteristic
671C2×C4#1306337311yescharacteristic
672C8—42no—
673C8—862no—
674C8—1721no—
675C22—21no—
676C22—21no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—862no—
681C22—862no—
682C22—862no—
683C22—862no—
684C22—862no—
685C22—862no—
686C22—3442no—
687C22—3442no—
688C22C2×C22⋊C4×D4311yescharacteristic
689C22#1458354611yescharacteristic
690C22#1458355111yescharacteristic
691C4—21no—
692C4—21no—
693C4—21no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—82no—
698C4—862no—
699C4—862no—
700C4—1722no—
701C4—1722no—
702C4—1722no—
703C4—1722no—
704C4#1458291412yes—
705C4#1458336711yescharacteristic
706C4#1458338011yescharacteristic
707C4#1458354611yescharacteristic
708C4#1458355111yescharacteristic
709C2—21no—
710C2—21no—
711C2—81no—
712C2—1722no—
713C2—1722no—
714C2#1913742311yescharacteristic
715C2C2×#1458291411yescharacteristic
716C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radical#19148159C2
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#22507
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143330C2semidirect
3. #19137056C2semidirect
4. #19135571C2semidirect
5. #19135538C2semidirect
6. #19135040C2semidirect
7. #19134894C2semidirect
8. #19134693C2semidirect
9. C4×#13063252C2semidirect
10. #19134303C2semidirect
11. C43×#1806C2semidirect
13. #14583622C4semidirect
14. #14583614C4semidirect
15. #14583609C4semidirect
16. #14583599C4semidirect
17. #14583590C4semidirect
20. #14583554C4semidirect
239. C4×Dic43#41semidirect
243. #10621877#41semidirect
359. #1806D43semidirect
411. C43#22507semidirect

Maximal subgroups

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

subgroupindex
#191481592
#191433302
#191370562
#191355712
#191355382
#191350402
#191348942
#191346932
C4×#130632522
#191343032
C43×#18062
#2250743