Finite Group Databasebeta

← #25126336

Subgroups — #25126336

Order 11008.

776 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063350C211yesmaximal, characteristic
2C2×#14582997C211yesmaximal, characteristic, complemented
3#19143246C211yesmaximal, characteristic, complemented
4#19136103C211yesmaximal, characteristic, complemented
5#19136038C211yesmaximal, characteristic, complemented
6#19135962C211yesmaximal, characteristic, complemented
7#19135952C211yesmaximal, characteristic, complemented
8#19135891C211yesmaximal, characteristic, complemented
9#19135885C211yesmaximal, characteristic
10#19135855C211yesmaximal, characteristic, complemented
11#19135706C211yesmaximal, characteristic
12#19134502C211yesmaximal, characteristic, complemented
13C4×#13063244C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C4×#137×C43C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583009—21no—
20#14582997—22no—
21#14582997—22no—
22#14582997—21no—
23C4×#10621884—21no—
24C4×#10621882—21no—
25#14582960—22no—
26#14582956—22no—
27C2×#13063260C2211yescharacteristic
28C2×#13063260C2211yescharacteristic
29#14582942C2211yescharacteristic
30C2×#13063258C2211yescharacteristic
31#14582926C2211yescharacteristic
32#14582926C2211yescharacteristic
33#14582903C2211yescharacteristic
34#14582900C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063244C2211yescharacteristic
38C2×#13063244C2211yescharacteristic
39C2×#13063241C2211yescharacteristic
40C2×#13063241C2211yescharacteristic
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×D172C2311yescharacteristic
64C22×C4×D43—21no—
65#13063350—22no—
66#13063350—22no—
67C2×#10621884—21no—
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621882—21no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C4×D172—21no—
79C4×D172—21no—
80C4×D172—21no—
81C4×D172—21no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×(C2×D43)⋊C4—21no—
84#13063260—22no—
85#13063260—22no—
86#13063258—21no—
87#13063258—22no—
88#13063256—21no—
89C4⋊(C43⋊C8)—22no—
90C4⋊(C43⋊C8)—22no—
91#13063249—21no—
92#13063249—22no—
93#13063246—21no—
94#13063245—21no—
95#13063245—21no—
96#13063245—22no—
97#13063244—22no—
98#13063244—22no—
99#13063241—22no—
100#13063241—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—
142C23×D43—21no—
143#41×C43—21no—
144#41×C43—21no—
145#41×C43—21no—
146#41×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×Q8×C43#4112yes—
154C2×D4×C43—21no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C22×Dic43—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172#4112yes—
171C2×C4×D43—41no—
172C2×C4×D43—41no—
173C2×C4×D43—82no—
174Q16×C43—24no—
175SD16×C43—24no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43#4112yes—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—41no—
197C42×C43—41no—
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43C2×D411yescharacteristic
202#10621884—28no—
203#10621884—24no—
204#10621882—24no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877#4112yes—
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⋊C8—21no—
225C2×C43⋊C8C2×D412yes—
226C2×C43⋊C8C2×D412yes—
227C23×C43—21no—
228C23×C43C2×#4111yescharacteristic
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—81no—
233C22×D43—81no—
234Q8×C43—22no—
235Q8×C43—21no—
236Q8×C43—22no—
237Q8×C43—21no—
238Q8×C43—41no—
239Q8×C43—41no—
240D4×C43—21no—
241D4×C43—21no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—81no—
256C2×C4×C43—81no—
257C2×C4×C43—81no—
258C2×C4×C43#12111yescharacteristic
259C2×C4×C43#12111yescharacteristic
260C2×C4×C43#12111yescharacteristic
261C2×C4×C43#12111yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×Dic43—41no—
269C2×Dic43—81no—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—82no—
275C4×D43—82no—
276C8×C43—22no—
277C8×C43—41no—
278C43⋊C8—22no—
279C43⋊C8—22no—
280C43⋊C8—22no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#23721—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43C2×#12111yescharacteristic
291C22×C43#52911yescharacteristic
292C22×C43#52911yescharacteristic
293C2×D43—42no—
294C2×D43—82no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—82no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—41no—
303C4×C43—42no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43#52511yescharacteristic
308C4×C43#52511yescharacteristic
309C4×C43#52511yescharacteristic
310C4×C43#53211yescharacteristic
311Dic43—81no—
312C4×#137D4311yescharacteristic, complemented
313C4×AGL(1,ℤ/8)—431no—
314C2×#440—431no—
315#2923—431no—
316#2089—431no—
317#2078—431no—
318#2064—431no—
319#2063—431no—
320#2052—431no—
321#2051—431no—
322#2046—431no—
323#2019—431no—
324#1778—431no—
325C4×#101—431no—
326C4×#100—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—81no—
330C2×C43#239211yescharacteristic
331C2×C43#306811yescharacteristic
332C2×C43#306911yescharacteristic
333D43—82no—
334C2×#137C2×D4311yescharacteristic
335C2×AGL(1,ℤ/8)—431no—
336C22×SD16—431no—
337C4×#41C2×D4311yescharacteristic
338C2×C4×Q8C2×D4311yescharacteristic
339C2×C4×D4—431no—
340#442—861no—
341#441—21no—
342#440—21no—
343#440—862no—
344#440—862no—
345#440—861no—
346C4×Q16—21no—
347C4×SD16—21no—
348C4×SD16—861no—
349C4×D8—861no—
350#433—862no—
351#432—862no—
352C2×#108—431no—
353C2×#108—431no—
354#428—431no—
355#428C2×D4311yescharacteristic
356C2×#107—431no—
357#424—431no—
358#424—431no—
359#419C2×D4311yescharacteristic
360#418—431no—
361#417—431no—
362#417C2×D4311yescharacteristic
363C2×#103—431no—
364C2×#102—431no—
365C2×#101—431no—
366C2×#101—431no—
367C2×#100—431no—
368C2×#100—431no—
369#408—431no—
370#408—431no—
371C4×M16—431no—
372C4×M16—431no—
373C4×M16C2×D4311yescharacteristic
374C2×#97—431no—
375#343—431no—
376#343—431no—
377#343—431no—
378#343—431no—
379#341—431no—
380#341—431no—
381C43#2372111yescharacteristic, complemented, Sylow
382C2×#41C22×D4311yescharacteristic
383C22×Q8C22×D4311yescharacteristic
384C22×D4—431no—
385C23×C4—861no—
386#137—22no—
387#137—22no—
388AGL(1,ℤ/8)—862no—
389AGL(1,ℤ/8)—862no—
390C2×Q16—21no—
391C2×SD16—21no—
392C2×SD16—862no—
393C2×SD16—862no—
394C2×SD16—862no—
395C2×SD16—861no—
396C2×D8—861no—
397C2×M16—431no—
398C2×M16—431no—
399C2×M16—431no—
400C2×M16—431no—
401C2×M16C22×D4311yescharacteristic
402C2×M16C22×D4311yescharacteristic
403C22×C8—431no—
404C22×C8—431no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8C22⋊D4311yescharacteristic
410C4×Q8C22⋊D4311yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—861no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4C22⋊D4311yescharacteristic
418C4×D4C22⋊D4311yescharacteristic
419#117—21no—
420#117C22×D4311yescharacteristic
421C2×C4⋊C4—21no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C22⋊C4—861no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42C22×D4311yescharacteristic
428#108—862no—
429#108—862no—
430#107—21no—
431#107—862no—
432#107—861no—
433#106—21no—
434#106—861no—
435C4⋊C8—862no—
436C4⋊C8—862no—
437#103—21no—
438#103—21no—
439#103—21no—
440#103—862no—
441#103—861no—
442#102—21no—
443#102—862no—
444#102—861no—
445#102—861no—
446#102—861no—
447#101—862no—
448#101—862no—
449#100—862no—
450#100—862no—
451C22⋊C8—862no—
452C22⋊C8—862no—
453#97—21no—
454#97—432no—
455#97—432no—
456#97—861no—
457#97—861no—
458C4×C8—21no—
459C4×C8—861no—
460C4×C8—861no—
461C24—861no—
462#41—21no—
463#41—21no—
464#41—21no—
465#41—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8#1062189812yes—
472C2×Q8C2×C22⋊D4311yescharacteristic
473C2×D4—21no—
474C2×D4—432no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4C2×C22⋊D4311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—861no—
487C22×C4—3442no—
488C22×C4—1721no—
489C22×C4—1721no—
490C22×C4#1062190011yescharacteristic
491C22×C4#1062190011yescharacteristic
492C22×C4C23×D4311yescharacteristic
493Q16—24no—
494SD16—24no—
495SD16—868no—
496SD16—864no—
497D8—864no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—432no—
502M16—861no—
503M16—861no—
504M16—861no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16—861no—
509M16#1062189812yes—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—432no—
513C2×C8—432no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4C2×C22⋊D4311yescharacteristic
531C4⋊C4C2×C22⋊D4311yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—1721no—
536C22⋊C4—1721no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—41no—
541C42—41no—
542C42D4×D4311yescharacteristic
543C42D4×D4311yescharacteristic
544C42C2×C22⋊D4311yescharacteristic
545C42C2×C22⋊D4311yescharacteristic
546C23—21no—
547C23—862no—
548C23—3441no—
549C23—3441no—
550C23—1721no—
551C23—1721no—
552C23C2×#1062190011yescharacteristic
553Q8—21no—
554Q8—22no—
555Q8—22no—
556Q8—21no—
557Q8—41no—
558Q8—41no—
559D4—21no—
560D4—21no—
561D4—41no—
562D4—41no—
563D4—862no—
564D4—862no—
565D4—1721no—
566D4—1721no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—3442no—
582C2×C4—3442no—
583C2×C4—3441no—
584C2×C4—1721no—
585C2×C4#1306329711yescharacteristic
586C2×C4#1306329711yescharacteristic
587C2×C4#1306329711yescharacteristic
588C2×C4#1306329711yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C22×C22⋊D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4C2×#1062189811yescharacteristic
594C2×C4C2×#1062189811yescharacteristic
595C8—22no—
596C8—41no—
597C8—862no—
598C8—862no—
599C8—862no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—3442no—
609C22—3442no—
610C22—3441no—
611C22—3441no—
612C22—1722no—
613C22C2×#1306329711yescharacteristic
614C22#1458342911yescharacteristic
615C22#1458343111yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—3441no—
626C4#1458340611yescharacteristic
627C4#1458340811yescharacteristic
628C4#1458341011yescharacteristic
629C4#1458344611yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—3442no—
634C2#1913783711yescharacteristic
635C2#1914432511yescharacteristic
636C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#137×C43C2
socleC22×C43C2×#121
prime radicalC2×#13063350C22
hypercenterC4×#137D43
hypocenterC43#23721
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×#14582997C2semidirect
3. #19143246C2semidirect
4. #19136103C2semidirect
5. #19136038C2semidirect
6. #19135962C2semidirect
7. #19135952C2semidirect
8. #19135891C2semidirect
10. #19135855C2semidirect
12. #19134502C2semidirect
13. C4×#13063244C2semidirect
14. C4×#13063241C2semidirect
15. C4×#137×C43C2semidirect
312. C4×#137D43semidirect
381. C43#23721semidirect

Maximal subgroups

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

subgroupindex
C4×#130633502
C2×#145829972
#191432462
#191361032
#191360382
#191359622
#191359522
#191358912
#191358852
#191358552
#191357062
#191345022
C4×#130632442
C4×#130632412
C4×#137×C432
#2372143