Finite Group Databasebeta

← #25063820

Subgroups — #25063820

Order 11008.

1030 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148672C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19136958C211yesmaximal, characteristic, complemented
4#19133121C211yesmaximal, characteristic, complemented
5#19133117C212yesmaximal, complemented
6#19133101C212yesmaximal, complemented
7#19133090C211yesmaximal, characteristic, complemented
8#19133088C212yesmaximal, complemented
9#19133079C211yesmaximal, characteristic, complemented
10#19133078C212yesmaximal, complemented
11C43×#1505C211yesmaximal, characteristic, complemented
12#14583635C411yescharacteristic, complemented
13#14583632C412yescomplemented
14#14583629C411yescharacteristic, complemented
15#14583610C411yescharacteristic, complemented
16#14583608C412yescomplemented
17#14583569C411yescharacteristic, complemented
18#14583555—21no—
19#14583549—21no—
20#14583548—22no—
21#14583514—21no—
22#14583513—22no—
23#14583444C2212yes—
24#14583433C2211yescharacteristic
25#14583430C2212yes—
26#14583378—21no—
27C2×C4×Dic86—21no—
28C2×C4×Dic86C2211yescharacteristic
29#14583027—22no—
30#14583026—21no—
31#14583023—21no—
32#14582953C2212yes—
33#14582952C2211yescharacteristic
34#14582949C2212yes—
35C4×C4⋊Dic43—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37#14582750—22no—
38#14582750C2212yes—
39#14582744C2212yes—
40#14582637C2212yes—
41#14582635C2211yescharacteristic
42#14582635C2211yescharacteristic
43#14582634C2212yes—
44#14582633C2212yes—
45#14582633C2212yes—
46#14582632C2211yescharacteristic
47#14582632C2211yescharacteristic
48C43×#532C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#376C2211yescharacteristic
51C43×#327C2212yes—
52C43×#327C2212yes—
53C2×#10621900—22no—
54C2×#10621900—21no—
55C22×Dic86D411yescharacteristic
56#13063324—21no—
57#13063324C2×C412yes—
58#13063323—22no—
59#13063321C2×C412yes—
60#13063319—21no—
61#13063318—22no—
62#13063317C2×C411yescharacteristic
63#13063316C2×C412yes—
64#13063313C2×C411yescharacteristic
65#13063312—21no—
66#13063312C2×C412yes—
67#13063311—22no—
68#13063311—22no—
69#13063308—21no—
70#13063308—22no—
71#13063307—22no—
72#13063306—22no—
73#13063306—22no—
74#13063305—21no—
75#13063304—22no—
76#13063304C2311yescharacteristic
77#13063302—22no—
78#13063302—22no—
79#13063301—22no—
80#13063299C2311yescharacteristic
81#13063297—22no—
82#13063297—22no—
83#13063296—21no—
84C4×Dic86—28no—
85C4×Dic86C2×C411yescharacteristic
86C4×Dic86C2×C411yescharacteristic
87C4×Dic86C2×C412yes—
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86D411yescharacteristic
90C4×Dic86D412yes—
91C4×Dic86D411yescharacteristic
92#13063290—21no—
93#13063290C2×C412yes—
94C4×D172C2×C411yescharacteristic
95D4×Dic43—22no—
96D4×Dic43—21no—
97D4×Dic43C2×C412yes—
98D4×Dic43C2×C412yes—
99#13063287C2×C412yes—
100C4×C22⋊D43—21no—
101C4×C22⋊D43—22no—
102(C22⋊D43)⋊C4—22no—
103#13063282—21no—
104#13063281—22no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43D411yescharacteristic
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4—22no—
109C2×Dic43⋊C4D412yes—
110C4⋊C4×D43—21no—
111C2×C4×Dic43—22no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—22no—
114C2×C4×Dic43C2312yes—
115C4⋊(C43⋊C8)—21no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)C2311yescharacteristic
119C22⋊(C43⋊C8)C2311yescharacteristic
120#13063235—22no—
121C4×C43⋊C8—21no—
122C8×Dic43—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C2×#41×C43—21no—
126C4⋊Q8×C43C2×C411yescharacteristic
127#127×C43C2×C411yescharacteristic
128#124×C43—21no—
129#121×C43—21no—
130#121×C43C2312yes—
131C4×D4×C43—21no—
132C4×D4×C43C2×C412yes—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2312yes—
137#97×C43—21no—
138#95×C43—21no—
139#95×C43C2311yescharacteristic
140#95×C43C2311yescharacteristic
141#41×C43—81no—
142#41×C43—81no—
143C2×Q8×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—22no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—22no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—21no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43C2×D412yes—
161C22×Dic43C2×D412yes—
162#10621900—44no—
163#10621900—82no—
164#10621900—82no—
165C2×D172C22×C411yescharacteristic
166C2×C4×D43—21no—
167C2×C4×D43—22no—
168C2×Dic86—24no—
169C2×Dic86—22no—
170C2×Dic86C22⋊C412yes—
171C2×Dic86C22⋊C411yescharacteristic
172C2×Dic86C22⋊C411yescharacteristic
173C2×Dic86C22×C411yescharacteristic
174C2×C8×C43—22no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C22×C412yes—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C42×C43—24no—
180C42×C43C22×C411yescharacteristic
181C42×C43C22×C411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C22⋊Dic43—22no—
185C22⋊Dic43—22no—
186C22⋊Dic43—22no—
187C22⋊Dic43—22no—
188C22⋊Dic43—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—22no—
194C4⋊Dic43—24no—
195C4⋊Dic43—22no—
196C4⋊Dic43C22⋊C411yescharacteristic
197C4⋊Dic43C22⋊C411yescharacteristic
198C4⋊Dic43C22⋊C412yes—
199C4⋊Dic43C22×C411yescharacteristic
200C4⋊Dic43C22×C411yescharacteristic
201Dic43⋊C4—28no—
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4C22⋊C412yes—
210Dic43⋊C4C22⋊C412yes—
211Dic43⋊C4C22⋊C412yes—
212Dic43⋊C4C22⋊C412yes—
213C4×Dic43—28no—
214C4×Dic43—21no—
215C4×Dic43—22no—
216C4×Dic43—82no—
217C4×Dic43—81no—
218C4×Dic43C22×C412yes—
219C4×Dic43C22×C412yes—
220C4×Dic43C2×D412yes—
221C4×Dic43C2×D412yes—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C23×C43—22no—
225C23×C43C22×D411yescharacteristic
226C22×D43—21no—
227Q8×C43—81no—
228D4×C43—42no—
229D4×C43—42no—
230D4×C43—42no—
231D4×C43—42no—
232D4×C43—81no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—82no—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C22⋊D43—41no—
252C22⋊D43—41no—
253C22⋊D43—44no—
254C22⋊D43—82no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—24no—
258C2×Dic43—24no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—44no—
265C2×Dic43—82no—
266C2×Dic43C2×C22⋊C412yes—
267C2×Dic43C2×C22⋊C412yes—
268C2×Dic43C2×C22⋊C412yes—
269C2×Dic43C2×C22⋊C412yes—
270D172—41no—
271C4×D43—42no—
272C4×D43—82no—
273Dic86—22no—
274Dic86—24no—
275Dic86—41no—
276Dic86—82no—
277Dic86#10414yes—
278C8×C43—42no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#17550—431nomaximal, Sylow
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43C22×C22⋊C411yescharacteristic
288C22×C43#57611yescharacteristic
289C22×C43#57711yescharacteristic
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—41no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—42no—
299C4×C43—42no—
300C4×C43—42no—
301C4×C43C2×#10412yes—
302Dic43—22no—
303Dic43—22no—
304Dic43—22no—
305Dic43—44no—
306Dic43—41no—
307Dic43—41no—
308Dic43—41no—
309Dic43C2×#10414yes—
310#3522—431no—
311#2984—431no—
312#2276—431no—
313#1509—431no—
314#1509—432no—
315#1505—432no—
316#1505D4311yescharacteristic, complemented
317#1502—432no—
318#1502—431no—
319#1500—431no—
320#1500—432no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43—82no—
324C2×C43#288411yescharacteristic
325C2×C43#289711yescharacteristic
326C2×C43C22×#10411yescharacteristic
327D43—81no—
328#559—431no—
329#559—432no—
330Q82—431no—
331#554—431no—
332#554—432no—
333#550—431no—
334#548—861no—
335#547—861no—
336#547—862no—
337#542—861no—
338#542—862no—
339#532—432no—
340#532C2×D4311yescharacteristic
341#529—432no—
342#529—431no—
343#520—861no—
344C2×C4×Q8—431no—
345C2×C4×Q8—861no—
346#446—862no—
347#446—861no—
348C8×Q8—861no—
349#432—432no—
350#432C2×D4311yescharacteristic
351#431—431no—
352#431—432no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—432no—
355C4×C4⋊C4—862no—
356C4×C4⋊C4—861no—
357#376—432no—
358#376C2×D4311yescharacteristic
359#328—432no—
360#328—431no—
361#328—431no—
362#327—432no—
363#327—432no—
364#327—432no—
365#327—431no—
366#327—431no—
367#327C2×D4312yes—
368#327C2×D4312yes—
369C43#1755011yescharacteristic, complemented, Sylow
370C2×#41—21no—
371C2×#41—862no—
372C2×#41—861no—
373C22×Q8—431no—
374C4⋊Q8—432no—
375C4⋊Q8—861no—
376C4⋊Q8—862no—
377C4⋊Q8C4×D4311yescharacteristic
378#127—432no—
379#127C4×D4311yescharacteristic
380#126—862no—
381#126—861no—
382#125—432no—
383#125—431no—
384#124—21no—
385#124—432no—
386#124—431no—
387#124—862no—
388#124—862no—
389#124—861no—
390#123—862no—
391#123—862no—
392#123—862no—
393#123—862no—
394#123—861no—
395C22⋊Q8—431no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—861no—
399C22⋊Q8—862no—
400C22⋊Q8—862no—
401#121—21no—
402#121—431no—
403#121—861no—
404#121—862no—
405#121—862no—
406#121C22×D4312yes—
407C4×Q8—431no—
408C4×Q8—431no—
409C4×Q8—432no—
410C4×Q8—431no—
411C4×Q8—432no—
412C4×Q8—431no—
413C4×Q8—432no—
414C4×Q8—431no—
415C4×Q8—868no—
416C4×Q8—861no—
417C4×D4—21no—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—432no—
421C4×D4—431no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—861no—
425C4×D4—862no—
426C4×D4—861no—
427C4×D4C4×D4312yes—
428#117—862no—
429#117—861no—
430C2×C4⋊C4—432no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—861no—
436C2×C42—21no—
437C2×C42—432no—
438C2×C42—862no—
439C2×C42—862no—
440C2×C42—861no—
441C2×C42C22×D4311yescharacteristic
442C4⋊C8—21no—
443C4⋊C8—862no—
444C4⋊C8—862no—
445C4⋊C8—861no—
446C22⋊C8—431no—
447C22⋊C8—431no—
448C22⋊C8C22×D4312yes—
449#97—21no—
450#97—862no—
451C4×C8—862no—
452C4×C8—861no—
453#95—21no—
454#95—432no—
455#95—862no—
456#95C22×D4311yescharacteristic
457#95C22×D4311yescharacteristic
458#41—81no—
459#41—81no—
460#41—3442no—
461#41—3442no—
462#41—1724no—
463C2×Q8—21no—
464C2×Q8—431no—
465C2×Q8—432no—
466C2×Q8—431no—
467C2×Q8—431no—
468C2×Q8—862no—
469C2×Q8—864no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—431no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—861no—
477C2×D4C2×C4×D4312yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—432no—
482C22×C4—432no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—861no—
488C22×C4D4×D4311yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4C23×D4311yescharacteristic
491C2×C8—22no—
492C2×C8—861no—
493C2×C8—861no—
494C4⋊C4—21no—
495C4⋊C4—432no—
496C4⋊C4—431no—
497C4⋊C4—432no—
498C4⋊C4—431no—
499C4⋊C4—432no—
500C4⋊C4—432no—
501C4⋊C4—432no—
502C4⋊C4—431no—
503C4⋊C4—431no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—868no—
509C4⋊C4—864no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4C2×C4×D4312yes—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C22⋊C4—861no—
525C22⋊C4—861no—
526C22⋊C4—861no—
527C42—24no—
528C42—432no—
529C42—432no—
530C42—432no—
531C42—432no—
532C42—862no—
533C42—868no—
534C42—861no—
535C42—3441no—
536C42—3442no—
537C42C2×C4×D4311yescharacteristic
538C42C2×C4×D4311yescharacteristic
539C42D4×D4311yescharacteristic
540C42D4×D4311yescharacteristic
541C23—22no—
542C23—861no—
543C23C2×D4×D4311yescharacteristic
544Q8—81no—
545Q8—434no—
546Q8—864no—
547Q8—862no—
548Q8—3442no—
549Q8—1721no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—81no—
555D4—3442no—
556D4—1721no—
557D4—1724no—
558D4—1721no—
559D4—1721no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—432no—
576C2×C4—864no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—864no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—3442no—
584C2×C4—3442no—
585C2×C4—1724no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4C22⋊C4×D4311yescharacteristic
590C2×C4C22⋊C4×D4311yescharacteristic
591C2×C4C22⋊C4×D4311yescharacteristic
592C2×C4C22⋊C4×D4311yescharacteristic
593C2×C4C22×C4×D4311yescharacteristic
594C2×C4C2×D4×D4311yescharacteristic
595C8—42no—
596C8—1721no—
597C8—1721no—
598C22—21no—
599C22—21no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—1721no—
604C22—1721no—
605C22—1721no—
606C22C2×C22⋊C4×D4311yescharacteristic
607C22#1458370311yescharacteristic
608C22#1458370911yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—21no—
614C4—42no—
615C4—42no—
616C4—42no—
617C4—434no—
618C4—862no—
619C4—862no—
620C4—862no—
621C4—1724no—
622C4—1721no—
623C4—1721no—
624C4—1721no—
625C4#104×D4312yes—
626C2—21no—
627C2—21no—
628C2—82no—
629C2—3441no—
630C2#1914305711yescharacteristic
631C2#1914312011yescharacteristic
632C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1505C2
socleC22×C43C22×C22⋊C4
prime radical#19148672C2
cosocleC22×C4×C43C24
hypercenter#1505D43
hypocenterC43#17550
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19136958C2semidirect
4. #19133121C2semidirect
5. #19133117C2semidirect
6. #19133101C2semidirect
7. #19133090C2semidirect
8. #19133088C2semidirect
9. #19133079C2semidirect
10. #19133078C2semidirect
11. C43×#1505C2semidirect
12. #14583635C4semidirect
13. #14583632C4semidirect
14. #14583629C4semidirect
15. #14583610C4semidirect
16. #14583608C4semidirect
17. #14583569C4semidirect
316. #1505D43semidirect
369. C43#17550semidirect

Maximal subgroups

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

subgroupindex
#191486722
#191436852
#191369582
#191331212
#191331172
#191331012
#191330902
#191330882
#191330792
#191330782
C43×#15052
#1755043