Finite Group Databasebeta

← #25126323

Subgroups — #25126323

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063355C211yesmaximal, characteristic
2C2×#14583004C211yesmaximal, characteristic, complemented
3#19143246C211yesmaximal, characteristic
4#19136108C211yesmaximal, characteristic, complemented
5#19136043C211yesmaximal, characteristic
6#19135962C211yesmaximal, characteristic, complemented
7#19135959C211yesmaximal, characteristic, complemented
8#19135892C211yesmaximal, characteristic
9#19135891C211yesmaximal, characteristic
10#19135862C211yesmaximal, characteristic, complemented
11#19135713C211yesmaximal, characteristic
12#19134502C211yesmaximal, characteristic, complemented
13C4×#13063243C211yesmaximal, characteristic, complemented
14C4×#13063244C211yesmaximal, characteristic, complemented
15C4×#137×C43C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19#14583004—22no—
20#14583004—22no—
21#14583004—21no—
22#14582999—21no—
23C4×#10621885—21no—
24C4×#10621883—21no—
25#14582960—22no—
26#14582956—22no—
27C2×#13063260C2211yescharacteristic
28C2×#13063260C2211yescharacteristic
29#14582942C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31#14582926C2211yescharacteristic
32#14582926C2211yescharacteristic
33#14582907C2211yescharacteristic
34#14582900C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063244C2211yescharacteristic
38C2×#13063244C2211yescharacteristic
39C2×#13063243C2211yescharacteristic
40C2×#13063243C2211yescharacteristic
41#14582866C2211yescharacteristic
42#14582866C2211yescharacteristic
43C4×#10621877C2211yescharacteristic
44C4×#10621877C2211yescharacteristic
45C2×#13063236C2211yescharacteristic
46#14582668C2211yescharacteristic
47#14582668C2211yescharacteristic
48#14582667C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582663C2211yescharacteristic
51#14582663C2211yescharacteristic
52C2×#137×C43C2211yescharacteristic
53C4×#41×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C43×#441—21no—
56C43×#440—21no—
57C4×Q16×C43—21no—
58C4×SD16×C43—21no—
59C43×#428C2211yescharacteristic
60C43×#419C2211yescharacteristic
61C43×#417C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64#13063355—22no—
65#13063355—22no—
66C2×#10621885—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621883—21no—
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C4×Dic86—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×C4×Dic43—21no—
84#13063260—22no—
85#13063260—22no—
86#13063258—21no—
87#13063256—21no—
88#13063256—22no—
89C4⋊(C43⋊C8)—22no—
90C4⋊(C43⋊C8)—22no—
91#13063249—21no—
92#13063249—22no—
93#13063248—21no—
94#13063248—21no—
95#13063248—22no—
96#13063246—21no—
97#13063244—22no—
98#13063244—22no—
99#13063243—22no—
100#13063243—22no—
101C22⋊(C43⋊C8)—22no—
102C22⋊(C43⋊C8)—22no—
103#13063236—21no—
104#13063236—21no—
105#13063236D412yes—
106#13063236D412yes—
107C4×C43⋊C8—21no—
108C4×C43⋊C8—21no—
109C2×#41×C43C2311yescharacteristic
110C22×Q8×C43C2311yescharacteristic
111#137×C43—22no—
112#137×C43—22no—
113C2×Q16×C43—21no—
114C2×SD16×C43—21no—
115C2×M16×C43C2311yescharacteristic
116C2×M16×C43C2311yescharacteristic
117C4×Q8×C43—21no—
118C4×Q8×C43—21no—
119C4×Q8×C43—21no—
120C4×Q8×C43—21no—
121C4×Q8×C43D411yescharacteristic
122C4×Q8×C43D411yescharacteristic
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125C4×D4×C43D411yescharacteristic
126C4×D4×C43D411yescharacteristic
127#117×C43—21no—
128#117×C43C2311yescharacteristic
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#102×C43—21no—
140#97×C43—21no—
141C4×C8×C43—21no—
142#41×C43—21no—
143#41×C43—21no—
144#41×C43—21no—
145#41×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43#4112yes—
153C2×D4×C43—21no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C22×Dic43—21no—
164C22×Dic43—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86#4112yes—
171Q16×C43—24no—
172SD16×C43—24no—
173M16×C43—21no—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43#4112yes—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43—41no—
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—41no—
194C42×C43—41no—
195C42×C43C2×D411yescharacteristic
196C42×C43C2×D411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199#10621885—28no—
200#10621885—24no—
201#10621883—24no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206C4×Dic43—41no—
207C4×Dic43—41no—
208#10621877—21no—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877—21no—
215#10621877#4112yes—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8C2×D412yes—
225C2×C43⋊C8C2×D412yes—
226C23×C43—21no—
227C23×C43C2×#4111yescharacteristic
228Q8×C43—22no—
229Q8×C43—21no—
230Q8×C43—22no—
231Q8×C43—21no—
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—41no—
237D4×C43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—22no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—81no—
250C2×C4×C43—81no—
251C2×C4×C43—81no—
252C2×C4×C43#12111yescharacteristic
253C2×C4×C43#12111yescharacteristic
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43#12111yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×Dic43—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—81no—
267Dic86—22no—
268Dic86—22no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—22no—
272C8×C43—41no—
273C43⋊C8—22no—
274C43⋊C8—22no—
275C43⋊C8—22no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#23720—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×#12111yescharacteristic
286C22×C43#52911yescharacteristic
287C22×C43#52911yescharacteristic
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—42no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43#52511yescharacteristic
298C4×C43#52511yescharacteristic
299C4×C43#52511yescharacteristic
300C4×C43#53211yescharacteristic
301Dic43—42no—
302Dic43—81no—
303C4×#137—431no—
304C4×#137D4311yescharacteristic
305C2×#441—431no—
306#2923—431no—
307#2090—431no—
308#2079—431no—
309#2064—431no—
310#2064—431no—
311#2052—431no—
312#2052—431no—
313#2047—431no—
314#2020—431no—
315#1778—431no—
316C4×#101—431no—
317C4×#101—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—81no—
321C2×C43#239211yescharacteristic
322C2×C43#306911yescharacteristic
323C2×C43#306911yescharacteristic
324C2×#137—431no—
325C2×#137C2×D4311yescharacteristic
326C22×Q16—431no—
327C4×#41C2×D4311yescharacteristic
328C2×C4×Q8—431no—
329C2×C4×Q8C2×D4311yescharacteristic
330#441—21no—
331#441—862no—
332#441—862no—
333#441—861no—
334#440—21no—
335#440—861no—
336C4×Q16—21no—
337C4×Q16—861no—
338C4×SD16—21no—
339C4×SD16—861no—
340#433—862no—
341#432—862no—
342C2×#108—431no—
343C2×#108—431no—
344#428—431no—
345#428C2×D4311yescharacteristic
346C2×#106—431no—
347#424—431no—
348#424—431no—
349#419—431no—
350#419C2×D4311yescharacteristic
351#417—431no—
352#417C2×D4311yescharacteristic
353C2×#103—431no—
354C2×#103—431no—
355C2×#101—431no—
356C2×#101—431no—
357C2×#101—431no—
358C2×#101—431no—
359#408—431no—
360#408—431no—
361C4×M16—431no—
362C4×M16—431no—
363C4×M16C2×D4311yescharacteristic
364C2×#97—431no—
365#343—431no—
366#343—431no—
367#343—431no—
368#343—431no—
369#341—431no—
370#341—431no—
371C43#2372011yescharacteristic, complemented, Sylow
372C2×#41C22×D4311yescharacteristic
373C22×Q8—431no—
374C22×Q8C22×D4311yescharacteristic
375#137—22no—
376#137—22no—
377#137—862no—
378#137—862no—
379C2×Q16—21no—
380C2×Q16—862no—
381C2×Q16—862no—
382C2×Q16—862no—
383C2×Q16—861no—
384C2×SD16—21no—
385C2×SD16—861no—
386C2×M16—431no—
387C2×M16—431no—
388C2×M16—431no—
389C2×M16—431no—
390C2×M16C22×D4311yescharacteristic
391C2×M16C22×D4311yescharacteristic
392C22×C8—431no—
393C22×C8—431no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—861no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8C22⋊D4311yescharacteristic
403C4×Q8C22⋊D4311yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4C22⋊D4311yescharacteristic
407C4×D4C22⋊D4311yescharacteristic
408#117—21no—
409#117C22×D4311yescharacteristic
410C2×C4⋊C4—21no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418#108—862no—
419#108—862no—
420#107—21no—
421#107—861no—
422#106—21no—
423#106—862no—
424#106—861no—
425C4⋊C8—862no—
426C4⋊C8—862no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—862no—
431#103—862no—
432#103—861no—
433#103—861no—
434#103—861no—
435#102—21no—
436#102—861no—
437#101—862no—
438#101—862no—
439#101—862no—
440#101—862no—
441C22⋊C8—862no—
442C22⋊C8—862no—
443#97—21no—
444#97—432no—
445#97—432no—
446#97—861no—
447#97—861no—
448C4×C8—21no—
449C4×C8—861no—
450C4×C8—861no—
451#41—21no—
452#41—21no—
453#41—21no—
454#41—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—432no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8#1062189812yes—
467C2×Q8C2×C22⋊D4311yescharacteristic
468C2×D4—21no—
469C2×D4C2×C22⋊D4311yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4#1062190011yescharacteristic
478C22×C4#1062190011yescharacteristic
479C22×C4C23×D4311yescharacteristic
480Q16—24no—
481Q16—868no—
482Q16—864no—
483SD16—24no—
484SD16—864no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—432no—
489M16—861no—
490M16—861no—
491M16—861no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16—861no—
496M16#1062189812yes—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—432no—
500C2×C8—432no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—1721no—
518C4⋊C4—1721no—
519C4⋊C4C2×C22⋊D4311yescharacteristic
520C4⋊C4C2×C22⋊D4311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—41no—
528C42—41no—
529C42—1721no—
530C42—1721no—
531C42D4×D4311yescharacteristic
532C42D4×D4311yescharacteristic
533C42C2×C22⋊D4311yescharacteristic
534C42C2×C22⋊D4311yescharacteristic
535C23—21no—
536C23C2×#1062190011yescharacteristic
537Q8—21no—
538Q8—22no—
539Q8—22no—
540Q8—21no—
541Q8—41no—
542Q8—41no—
543Q8—862no—
544Q8—862no—
545Q8—1721no—
546Q8—1721no—
547D4—21no—
548D4—21no—
549D4—41no—
550D4—41no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—862no—
566C2×C4—3441no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4#1306329711yescharacteristic
571C2×C4#1306329711yescharacteristic
572C2×C4#1306329711yescharacteristic
573C2×C4#1306329711yescharacteristic
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C22×C22⋊D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4C2×#1062189811yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C8—22no—
581C8—41no—
582C8—862no—
583C8—862no—
584C8—862no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#1306329711yescharacteristic
594C22#1458342911yescharacteristic
595C22#1458343111yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—3441no—
606C4—1722no—
607C4#1458340611yescharacteristic
608C4#1458340811yescharacteristic
609C4#1458341011yescharacteristic
610C4#1458344611yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2#1913783711yescharacteristic
615C2#1914432911yescharacteristic
616C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#137×C43C2
socleC22×C43C2×#121
prime radicalC2×#41×C43C23
hypercenterC4×#137D43
hypocenterC43#23720
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. C2×#14583004C2semidirect
4. #19136108C2semidirect
6. #19135962C2semidirect
7. #19135959C2semidirect
10. #19135862C2semidirect
12. #19134502C2semidirect
13. C4×#13063243C2semidirect
14. C4×#13063244C2semidirect
371. C43#23720semidirect

Maximal subgroups

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

subgroupindex
C4×#130633552
C2×#145830042
#191432462
#191361082
#191360432
#191359622
#191359592
#191358922
#191358912
#191358622
#191357132
#191345022
C4×#130632432
C4×#130632442
C4×#137×C432
#2372043