Finite Group Databasebeta

← #25138092

Subgroups — #25138092

Order 11008.

690 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
1#19144417C211yesmaximal, characteristic, complemented
2C2×#14583200C211yesmaximal, characteristic, complemented
3C4×#13063350C211yesmaximal, characteristic
4#19136040C211yesmaximal, characteristic, complemented
5#19136035C211yesmaximal, characteristic, complemented
6#19135886C211yesmaximal, characteristic
7#19135886C211yesmaximal, characteristic
8#19135587C211yesmaximal, characteristic, complemented
9#19135380C211yesmaximal, characteristic, complemented
10#19135375C211yesmaximal, characteristic, complemented
11#19135371C211yesmaximal, characteristic, complemented
12#19135257C211yesmaximal, characteristic, complemented
13#19135257C211yesmaximal, characteristic, complemented
14#19134584C211yesmaximal, characteristic, complemented
15C43×#2925C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583206—21no—
20#14583206—21no—
21#14583200—21no—
22#14583200—21no—
23#14583200—21no—
24#14583200—21no—
25#14583199—21no—
26#14583199—21no—
27#14583009—21no—
28#14582997—21no—
29C4×#10621884—21no—
30C4×#10621882—21no—
31C2×#13063261C2211yescharacteristic
32C2×#13063261C2211yescharacteristic
33#14582942C2211yescharacteristic
34#14582942C2211yescharacteristic
35#14582942C2211yescharacteristic
36C2×#13063259C2211yescharacteristic
37C2×#13063257C2211yescharacteristic
38#14582923C2211yescharacteristic
39#14582903C2211yescharacteristic
40#14582900C2211yescharacteristic
41#14582900C2211yescharacteristic
42#14582900C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45C2×#13063241C2211yescharacteristic
46C2×#13063241C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582667C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C43×#433—21no—
58C43×#433—21no—
59C43×#432—21no—
60C43×#431—21no—
61C43×#423C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C43×#408C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C43×#405C2211yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C4×D43—21no—
69#13063350—22no—
70#13063350—22no—
71C2×#10621884—21no—
72C2×#10621882—21no—
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77#13063317—21no—
78#13063317—21no—
79#13063317—21no—
80#13063317—21no—
81C4×D172—21no—
82C4×D172—21no—
83C4×D172—21no—
84C4×D172—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91#13063261—22no—
92#13063261—22no—
93#13063259—21no—
94#13063259—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063257—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063247—21no—
109#13063247—21no—
110#13063247—21no—
111#13063247—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063245—21no—
116#13063245—21no—
117#13063241—22no—
118#13063241—22no—
119#13063236—21no—
120C4×C43⋊C8—21no—
121C2×#41×C43C2311yescharacteristic
122C2×M16×C43C2311yescharacteristic
123C2×M16×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×Q8×C43D411yescharacteristic
127C4×Q8×C43D411yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43D411yescharacteristic
131C4×D4×C43D411yescharacteristic
132#117×C43—21no—
133#117×C43C2311yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43D411yescharacteristic
139C4⋊C8×C43D411yescharacteristic
140C4⋊C8×C43D411yescharacteristic
141C4⋊C8×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C22⋊C8×C43—21no—
144C22⋊C8×C43—21no—
145C22⋊C8×C43—21no—
146#97×C43—21no—
147#97×C43—21no—
148C4×C8×C43—21no—
149C4×C8×C43—21no—
150C23×D43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43—21no—
154#41×C43—21no—
155C2×Q8×C43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43C2×D411yescharacteristic
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—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172#4112yes—
173C2×C4×D43—41no—
174C2×C4×D43—41no—
175C2×C4×D43—82no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×D411yescharacteristic
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C42×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43C2×D411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C42×C43C2×D411yescharacteristic
203C42×C43C2×D411yescharacteristic
204#10621884—24no—
205#10621882—24no—
206(C2×D43)⋊C4—41no—
207(C2×D43)⋊C4—41no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214Dic43⋊C4—41no—
215Dic43⋊C4—41no—
216Dic43⋊C4—41no—
217Dic43⋊C4—41no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877#4112yes—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C23×C43—21no—
231C23×C43C2×#4111yescharacteristic
232C22×D43—22no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—81no—
236C22×D43—81no—
237Q8×C43—21no—
238Q8×C43—21no—
239D4×C43—21no—
240D4×C43—21no—
241D4×C43—41no—
242D4×C43—41no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—42no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
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×C432−1+411yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—81no—
266C2×Dic43—81no—
267C2×Dic43—81no—
268D172—22no—
269D172—22no—
270D172—41no—
271D172—41no—
272C4×D43—82no—
273C4×D43—82no—
274C8×C43—21no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—21no—
278C8×C43—41no—
279C8×C43—41no—
280C43⋊C8—22no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#24724—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43C2×#12111yescharacteristic
291C22×C43#55211yescharacteristic
292C22×C43#55611yescharacteristic
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—41no—
304C4×C43—41no—
305C4×C43#52511yescharacteristic
306C4×C43#53611yescharacteristic
307C4×C43#54711yescharacteristic
308C4×C43#54811yescharacteristic
309Dic43—81no—
310Dic43—81no—
311Dic43—81no—
312#3080—431no—
313C2×#478—431no—
314C4×AGL(1,ℤ/8)—431no—
315#2925D4311yescharacteristic, complemented
316#2079—431no—
317#2078—431no—
318#2051—431no—
319#2051—431no—
320#1998—431no—
321#1952—431no—
322#1951—431no—
323#1950—431no—
324#1931—431no—
325#1931—431no—
326#1800—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—81no—
330C2×C43#241511yescharacteristic
331C2×C43#306711yescharacteristic
332C2×C43#306811yescharacteristic
333D43—82no—
334C2×AGL(1,ℤ/8)—431no—
335C2×#125—431no—
336C4×#41C2×D4311yescharacteristic
337C2×C4×D4—431no—
338#479—861no—
339#479—861no—
340#478—861no—
341#478—861no—
342#478—861no—
343#478—861no—
344#478—861no—
345#478—861no—
346#442—861no—
347#440—861no—
348C4×SD16—861no—
349C4×D8—861no—
350#433—21no—
351#433—21no—
352#432—21no—
353#431—21no—
354C2×#108—431no—
355C2×#108—431no—
356#428—431no—
357#428—431no—
358#428—431no—
359C2×#107—431no—
360C2×#106—431no—
361#423—431no—
362#423C2×D4311yescharacteristic
363C2×C4⋊C8C2×D4311yescharacteristic
364#418—431no—
365#417—431no—
366#417—431no—
367#417—431no—
368C2×#102—431no—
369C2×#102—431no—
370C2×#100—431no—
371C2×#100—431no—
372#408C2×D4311yescharacteristic
373#408C2×D4311yescharacteristic
374#405C2×D4311yescharacteristic
375#405C2×D4311yescharacteristic
376C4×M16—431no—
377#343—431no—
378#343—431no—
379#343—431no—
380#343—431no—
381#343—431no—
382#343—431no—
383#341—431no—
384#341—431no—
385C43#2472411yescharacteristic, complemented, Sylow
386C2×#41C22×D4311yescharacteristic
387C22×D4—431no—
388C23×C4—861no—
389AGL(1,ℤ/8)—862no—
390AGL(1,ℤ/8)—862no—
391C2×SD16—861no—
392C2×D8—861no—
393C2×M16—431no—
394C2×M16—431no—
395C2×M16—431no—
396C2×M16—431no—
397C2×M16C22×D4311yescharacteristic
398C2×M16C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401#125—861no—
402#125—861no—
403#125—861no—
404#125—861no—
405C4×Q8D17211yescharacteristic
406C4×Q8D17211yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—861no—
410C4×D4—861no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4D17211yescharacteristic
414C4×D4D17211yescharacteristic
415#117—21no—
416#117C22×D4311yescharacteristic
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C42—21no—
424C2×C42C22×D4311yescharacteristic
425#108—862no—
426#108—862no—
427#107—861no—
428#107—861no—
429#107—861no—
430#107—861no—
431#107—861no—
432#106—861no—
433#106—861no—
434#106—861no—
435#106—861no—
436#106—861no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—861no—
440C4⋊C8—861no—
441C4⋊C8C22⋊D4311yescharacteristic
442C4⋊C8C22⋊D4311yescharacteristic
443C4⋊C8C22⋊D4311yescharacteristic
444C4⋊C8C22⋊D4311yescharacteristic
445#103—861no—
446#103—861no—
447#103—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#100—862no—
458#100—862no—
459C22⋊C8—21no—
460C22⋊C8—21no—
461C22⋊C8—21no—
462C22⋊C8—21no—
463#97—21no—
464#97—21no—
465#97—861no—
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—861no—
469C24—861no—
470#41—21no—
471#41—21no—
472#41—21no—
473#41—21no—
474C2×Q8C2×D17211yescharacteristic
475C2×D4—21no—
476C2×D4—432no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4C2×D17211yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—3442no—
490C22×C4—1721no—
491C22×C4—1721no—
492C22×C4#1062189811yescharacteristic
493C22×C4#1062189811yescharacteristic
494C22×C4C23×D4311yescharacteristic
495SD16—864no—
496D8—864no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—432no—
502M16—861no—
503M16—861no—
504M16—861no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16—861no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8C2×C22⋊D4311yescharacteristic
520C2×C8C2×C22⋊D4311yescharacteristic
521C2×C8C2×C22⋊D4311yescharacteristic
522C2×C8C2×C22⋊D4311yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—1721no—
532C4⋊C4—1721no—
533C4⋊C4—1721no—
534C4⋊C4—1721no—
535C4⋊C4C2×D17211yescharacteristic
536C4⋊C4C2×D17211yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—1721no—
541C22⋊C4—1721no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42C2×D17211yescharacteristic
546C42C2×D17211yescharacteristic
547C42C2×C22⋊D4311yescharacteristic
548C42C2×C22⋊D4311yescharacteristic
549C23—21no—
550C23—862no—
551C23—3441no—
552C23—3441no—
553C23—1721no—
554C23—1721no—
555C23C2×#1062189811yescharacteristic
556Q8—21no—
557Q8—21no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—862no—
563D4—862no—
564D4—1721no—
565D4—1721no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—3442no—
576C2×C4—3442no—
577C2×C4—3441no—
578C2×C4—3441no—
579C2×C4—3441no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4#1306329911yescharacteristic
584C2×C4#1306329911yescharacteristic
585C2×C4#1306329911yescharacteristic
586C2×C4#1306329911yescharacteristic
587C2×C4C22×C22⋊D4311yescharacteristic
588C2×C4C22×D17211yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4#41×D4311yescharacteristic
591C2×C4#1306337211yescharacteristic
592C2×C4#1306337211yescharacteristic
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
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×#1306329911yescharacteristic
614C22#1458358811yescharacteristic
615C22#1458361711yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—3441no—
624C4—3441no—
625C4—3441no—
626C4#1458341111yescharacteristic
627C4#1458347511yescharacteristic
628C4#1458354811yescharacteristic
629C4#1458355611yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—3442no—
634C2#1913801811yescharacteristic
635C2#1914431511yescharacteristic
636C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2925C2
socleC22×C43C2×#121
prime radicalC2×#13063350C22
hypercenter#2925D43
hypocenterC43#24724
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2925

Complements

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

NH ≅ G/Ntype
1. #19144417C2semidirect
2. C2×#14583200C2semidirect
4. #19136040C2semidirect
5. #19136035C2semidirect
8. #19135587C2semidirect
9. #19135380C2semidirect
10. #19135375C2semidirect
11. #19135371C2semidirect
12. #19135257C2semidirect
13. #19135257C2semidirect
14. #19134584C2semidirect
15. C43×#2925C2semidirect
315. #2925D43semidirect
385. C43#24724semidirect

Maximal subgroups

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

subgroupindex
#191444172
C2×#145832002
C4×#130633502
#191360402
#191360352
#191358862
#191355872
#191353802
#191353752
#191353712
#191352572
#191345842
C43×#29252
#2472443