Finite Group Databasebeta

← #25063822

Subgroups — #25063822

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#19148678C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19136959C211yesmaximal, characteristic, complemented
4#19133119C212yesmaximal, complemented
5#19133104C211yesmaximal, characteristic, complemented
6#19133101C212yesmaximal, complemented
7#19133089C211yesmaximal, characteristic, complemented
8#19133088C212yesmaximal, complemented
9#19133081C211yesmaximal, characteristic, complemented
10#19133080C212yesmaximal, complemented
11C43×#1509C211yesmaximal, characteristic, complemented
12#14583634C411yescharacteristic, complemented
13#14583631C412yescomplemented
14Q8×Dic86C411yescharacteristic, complemented
15#14583606C411yescharacteristic, complemented
16#14583605C412yescomplemented
17#14583570C411yescharacteristic, complemented
18#14583558—21no—
19#14583553—21no—
20#14583547—22no—
21#14583520—21no—
22#14583515—22no—
23#14583449C2211yescharacteristic
24#14583444C2212yes—
25#14583435C2212yes—
26#14583379—21no—
27C2×C4×Dic86C2211yescharacteristic
28C2×#13063290—21no—
29#14583027—22no—
30#14583026—21no—
31#14583023—21no—
32#14582953C2212yes—
33#14582952C2211yescharacteristic
34#14582949C2212yes—
35C4⋊C4×Dic43—21no—
36C4×Dic43⋊C4—22no—
37#14582750C2212yes—
38#14582745C2211yescharacteristic
39#14582744C2212yes—
40#14582636C2211yescharacteristic
41#14582636C2211yescharacteristic
42#14582634C2212yes—
43#14582634C2212yes—
44#14582633C2211yescharacteristic
45#14582633C2211yescharacteristic
46#14582632C2212yes—
47#14582632C2212yes—
48C43×#529C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C43×#328C2212yes—
52C43×#327C2212yes—
53C2×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621900—22no—
56C22×Dic86D411yescharacteristic
57#13063325—21no—
58#13063325C2×C411yescharacteristic
59#13063324—22no—
60#13063324C2×C412yes—
61#13063322C2×C411yescharacteristic
62#13063321C2×C412yes—
63#13063320—22no—
64#13063316C2×C412yes—
65#13063314C2×C412yes—
66#13063313—21no—
67#13063313—21no—
68#13063311—22no—
69#13063311—22no—
70#13063310—22no—
71#13063309—22no—
72#13063309—22no—
73#13063307—22no—
74#13063305—22no—
75#13063304—21no—
76#13063303—22no—
77#13063303—22no—
78#13063302—22no—
79#13063299—21no—
80#13063299—21no—
81#13063299C2312yes—
82#13063298—22no—
83#13063297—22no—
84Q8×Dic43C2×C412yes—
85C4×Dic86—21no—
86C4×Dic86C2×C411yescharacteristic
87C4×Dic86C2×C412yes—
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86D411yescharacteristic
90C4×Dic86D412yes—
91C4×Dic86D411yescharacteristic
92#13063290—28no—
93C4×D172—21no—
94C4×D172—21no—
95C4×D172C2×C412yes—
96D4×Dic43C2×C412yes—
97#13063287C2×C412yes—
98#13063287C2×C412yes—
99(C22⋊D43)⋊C4—22no—
100(C22⋊D43)⋊C4—22no—
101(C22⋊D43)⋊C4—22no—
102#13063283—22no—
103C2×C4⋊Dic43—21no—
104C2×C4⋊Dic43D411yescharacteristic
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4D412yes—
107C4⋊C4×D43—22no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—22no—
110C2×C4×Dic43—22no—
111C2×C4×Dic43C2312yes—
112C4⋊(C43⋊C8)—21no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115C22⋊(C43⋊C8)C2311yescharacteristic
116C22⋊(C43⋊C8)C2311yescharacteristic
117#13063235—22no—
118C4×C43⋊C8—21no—
119C8×Dic43—22no—
120C43⋊#95—21no—
121C43⋊#95—22no—
122C43⋊#95C2311yescharacteristic
123C43⋊#95C2311yescharacteristic
124#126×C43—21no—
125#125×C43C2×C411yescharacteristic
126#124×C43C2×C411yescharacteristic
127#123×C43—21no—
128C22⋊Q8×C43C2311yescharacteristic
129#121×C43C2311yescharacteristic
130C4×Q8×C43C2×C411yescharacteristic
131C4×D4×C43—21no—
132C4×D4×C43C2×C411yescharacteristic
133#117×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C22⋊C8×C43C2312yes—
139#97×C43—21no—
140#95×C43C2312yes—
141C2×Q8×C43C22×C411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43C22×C411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—22no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—22no—
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C22×Dic43—22no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D412yes—
156C22×Dic43C2×D412yes—
157#10621900—82no—
158#10621900—82no—
159#10621898—44no—
160#10621898—81no—
161#10621898—81no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172C22×C412yes—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×Dic86—24no—
169C2×Dic86—21no—
170C2×Dic86—22no—
171C2×Dic86C22⋊C412yes—
172C2×Dic86C22⋊C411yescharacteristic
173C2×Dic86C22⋊C411yescharacteristic
174C2×C8×C43—22no—
175C4⋊C4×C43—24no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C22×C411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C42×C43—81no—
189C42×C43C22×C411yescharacteristic
190C42×C43C22×C411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C22⋊Dic43—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43C22⋊C411yescharacteristic
204C4⋊Dic43C22⋊C411yescharacteristic
205C4⋊Dic43C22⋊C412yes—
206C4⋊Dic43C22×C412yes—
207Dic43⋊C4—28no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4C22⋊C412yes—
211Dic43⋊C4C22⋊C412yes—
212Dic43⋊C4C22⋊C412yes—
213Dic43⋊C4C22⋊C412yes—
214C4×Dic43—28no—
215C4×Dic43—24no—
216C4×Dic43—22no—
217C4×Dic43—82no—
218C4×Dic43C22×C412yes—
219C4×Dic43C22×C412yes—
220C4×Dic43C2×D412yes—
221C4×Dic43C2×D412yes—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C23×C43—21no—
225C23×C43C22×D411yescharacteristic
226C22×D43—22no—
227Q8×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—24no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C22⋊D43—42no—
249C22⋊D43—42no—
250C22⋊D43—44no—
251C22⋊D43—82no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—24no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—82no—
263C2×Dic43C2×C22⋊C412yes—
264C2×Dic43C2×C22⋊C412yes—
265C2×Dic43C2×C22⋊C412yes—
266C2×Dic43C2×C22⋊C412yes—
267D172—42no—
268D172—42no—
269D172—81no—
270C4×D43—44no—
271C4×D43—82no—
272C4×D43—82no—
273Dic86—22no—
274Dic86—24no—
275Dic86—82no—
276Dic86—81no—
277Dic86#10414yes—
278C8×C43—42no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#17550—431nomaximal, Sylow
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43C22×C22⋊C411yescharacteristic
288C22×C43#57611yescharacteristic
289C22×C43#57711yescharacteristic
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—44no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43C2×#10412yes—
303Dic43—22no—
304Dic43—22no—
305Dic43—22no—
306Dic43—42no—
307Dic43—42no—
308Dic43—42no—
309Dic43C2×#10414yes—
310#3522—431no—
311#2984—431no—
312#2276—431no—
313#1509—432no—
314#1509D4311yescharacteristic, complemented
315#1505—431no—
316#1505—432no—
317#1502—431no—
318#1502—432no—
319#1500—432no—
320#1500—431no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43—81no—
324C2×C43#288411yescharacteristic
325C2×C43#289711yescharacteristic
326C2×C43C22×#10411yescharacteristic
327D43—82no—
328#559—432no—
329#559—431no—
330Q82—431no—
331#554—432no—
332#554—431no—
333#550—431no—
334#548—861no—
335#547—861no—
336#547—862no—
337#542—861no—
338#542—862no—
339#532—432no—
340#532—431no—
341#529—432no—
342#529C2×D4311yescharacteristic
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—432no—
354C4×C4⋊C4—862no—
355C4×C4⋊C4—861no—
356C4×C4⋊C4C2×D4311yescharacteristic
357#376—431no—
358#376—432no—
359#328—431no—
360#328—431no—
361#328C2×D4312yes—
362#327—431no—
363#327—431no—
364#327—432no—
365#327—432no—
366#327—432no—
367#327—432no—
368#327C2×D4312yes—
369C43#1755011yescharacteristic, complemented, Sylow
370C2×#41—861no—
371C2×#41—862no—
372C2×#41—861no—
373C22×Q8—431no—
374C4⋊Q8—432no—
375C4⋊Q8—431no—
376C4⋊Q8—861no—
377C4⋊Q8—862no—
378#127—432no—
379#127—431no—
380#126—21no—
381#126—862no—
382#125—432no—
383#125C4×D4311yescharacteristic
384#124—432no—
385#124—861no—
386#124—862no—
387#124—862no—
388#124—861no—
389#124C4×D4311yescharacteristic
390#123—21no—
391#123—862no—
392#123—862no—
393#123—862no—
394#123—862no—
395C22⋊Q8—862no—
396C22⋊Q8—862no—
397C22⋊Q8—862no—
398C22⋊Q8—862no—
399C22⋊Q8—861no—
400C22⋊Q8C22×D4311yescharacteristic
401#121—432no—
402#121—862no—
403#121—861no—
404#121—862no—
405#121—861no—
406#121C22×D4311yescharacteristic
407C4×Q8—431no—
408C4×Q8—431no—
409C4×Q8—432no—
410C4×Q8—431no—
411C4×Q8—432no—
412C4×Q8—431no—
413C4×Q8—432no—
414C4×Q8—861no—
415C4×Q8—868no—
416C4×Q8C4×D4311yescharacteristic
417C4×D4—21no—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—432no—
421C4×D4—432no—
422C4×D4—861no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—861no—
427C4×D4C4×D4311yescharacteristic
428#117—21no—
429#117—862no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—432no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—861no—
435C2×C4⋊C4—862no—
436C2×C42—21no—
437C2×C42—432no—
438C2×C42—862no—
439C2×C42—861no—
440C2×C42—862no—
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—431no—
454#95—431no—
455#95—862no—
456#95—861no—
457#95C22×D4312yes—
458#41—3441no—
459#41—3441no—
460#41—3442no—
461#41—3442no—
462#41—1724no—
463C2×Q8—431no—
464C2×Q8—432no—
465C2×Q8—431no—
466C2×Q8—862no—
467C2×Q8—864no—
468C2×Q8—861no—
469C2×Q8C2×C4×D4311yescharacteristic
470C2×D4—21no—
471C2×D4—432no—
472C2×D4—862no—
473C2×D4—862no—
474C2×D4—862no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4C2×C4×D4311yescharacteristic
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—432no—
481C22×C4—432no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—862no—
488C22×C4D4×D4311yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4C23×D4311yescharacteristic
491C2×C8—22no—
492C2×C8—861no—
493C2×C8—861no—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—432no—
500C4⋊C4—431no—
501C4⋊C4—432no—
502C4⋊C4—431no—
503C4⋊C4—432no—
504C4⋊C4—432no—
505C4⋊C4—432no—
506C4⋊C4—432no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—868no—
512C4⋊C4—861no—
513C4⋊C4C2×C4×D4311yescharacteristic
514C4⋊C4C2×C4×D4311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C42—21no—
528C42—81no—
529C42—432no—
530C42—432no—
531C42—432no—
532C42—432no—
533C42—862no—
534C42—864no—
535C42—868no—
536C42—3442no—
537C42C2×C4×D4311yescharacteristic
538C42C2×C4×D4311yescharacteristic
539C42D4×D4311yescharacteristic
540C42D4×D4311yescharacteristic
541C23—21no—
542C23—862no—
543C23C2×D4×D4311yescharacteristic
544Q8—41no—
545Q8—434no—
546Q8—864no—
547Q8—862no—
548Q8—3441no—
549Q8—3442no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—3441no—
554D4—3442no—
555D4—1722no—
556D4—1724no—
557D4—1722no—
558D4—1722no—
559D4—1722no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—432no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—864no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—3442no—
582C2×C4—3442no—
583C2×C4—3442no—
584C2×C4—1724no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
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—41no—
601C22—41no—
602C22—41no—
603C22—1722no—
604C22—1722no—
605C22—1722no—
606C22C2×C22⋊C4×D4311yescharacteristic
607C22#1458370311yescharacteristic
608C22#1458370811yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—21no—
614C4—44no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—434no—
619C4—862no—
620C4—862no—
621C4—862no—
622C4—1722no—
623C4—1722no—
624C4—1722no—
625C4#104×D4312yes—
626C2—21no—
627C2—21no—
628C2—81no—
629C2—3442no—
630C2#1914305711yescharacteristic
631C2#1914311911yescharacteristic
632C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#19148678C2
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17550
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19136959C2semidirect
4. #19133119C2semidirect
5. #19133104C2semidirect
6. #19133101C2semidirect
7. #19133089C2semidirect
8. #19133088C2semidirect
9. #19133081C2semidirect
10. #19133080C2semidirect
11. C43×#1509C2semidirect
12. #14583634C4semidirect
13. #14583631C4semidirect
14. Q8×Dic86C4semidirect
15. #14583606C4semidirect
16. #14583605C4semidirect
17. #14583570C4semidirect
314. #1509D43semidirect
369. C43#17550semidirect

Maximal subgroups

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

subgroupindex
#191486782
#191436852
#191369592
#191331192
#191331042
#191331012
#191330892
#191330882
#191330812
#191330802
C43×#15092
#1755043