Finite Group Databasebeta

← #25138098

Subgroups — #25138098

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×#14583199C211yesmaximal, characteristic, complemented
3#19143261C211yesmaximal, characteristic, complemented
4#19136043C211yesmaximal, characteristic, complemented
5#19136038C211yesmaximal, characteristic, complemented
6#19135884C211yesmaximal, characteristic
7#19135884C211yesmaximal, characteristic
8#19135588C211yesmaximal, characteristic, complemented
9#19135377C211yesmaximal, characteristic, complemented
10#19135372C211yesmaximal, characteristic, complemented
11#19135370C211yesmaximal, characteristic, complemented
12#19135260C211yesmaximal, characteristic, complemented
13#19135260C211yesmaximal, characteristic, complemented
14#19134587C211yesmaximal, characteristic, complemented
15C4×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic
16C2×#13063317C2211yescharacteristic
17#14583206—21no—
18#14583206—21no—
19#14583199—21no—
20#14583199—21no—
21#14583199—21no—
22#14583199—21no—
23#14583199—21no—
24#14583199—21no—
25#14582960—21no—
26#14582960—21no—
27#14582956—21no—
28#14582952—21no—
29C2×#13063260C2211yescharacteristic
30C2×#13063260C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582942C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35#14582923C2211yescharacteristic
36#14582923C2211yescharacteristic
37C2×C4⋊(C43⋊C8)C2211yescharacteristic
38#14582900C2211yescharacteristic
39#14582900C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063242C2211yescharacteristic
43C2×#13063242C2211yescharacteristic
44#14582866C2211yescharacteristic
45#14582866C2211yescharacteristic
46#14582855C2211yescharacteristic
47#14582855C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C43×#442—21no—
60C43×#440—21no—
61C4×SD16×C43—21no—
62C4×D8×C43—21no—
63C43×#428C2211yescharacteristic
64C43×#418C2211yescharacteristic
65C43×#417C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063317—21no—
74#13063317—21no—
75#13063317—21no—
76#13063317—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81#13063260—22no—
82#13063260—22no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)D411yescharacteristic
96C4⋊(C43⋊C8)D411yescharacteristic
97C4⋊(C43⋊C8)D411yescharacteristic
98C4⋊(C43⋊C8)D411yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063242—22no—
108#13063242—22no—
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063236—21no—
114#13063236—21no—
115C4×C43⋊C8—21no—
116C4×C43⋊C8—21no—
117C2×#41×C43C2311yescharacteristic
118C22×D4×C43C2311yescharacteristic
119C23×C4×C43—21no—
120AGL(1,ℤ/8)×C43—22no—
121AGL(1,ℤ/8)×C43—22no—
122C2×SD16×C43—21no—
123C2×D8×C43—21no—
124C2×M16×C43C2311yescharacteristic
125C2×M16×C43C2311yescharacteristic
126C4×Q8×C43D411yescharacteristic
127C4×Q8×C43D411yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43—21no—
134C4×D4×C43D411yescharacteristic
135C4×D4×C43D411yescharacteristic
136#117×C43—21no—
137#117×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C42×C43—21no—
141C2×C42×C43C2311yescharacteristic
142#107×C43—21no—
143#106×C43—21no—
144#103×C43—21no—
145#102×C43—21no—
146#102×C43—21no—
147#102×C43—21no—
148#97×C43—21no—
149C4×C8×C43—21no—
150C24×C43—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×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43#4112yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—82no—
171C22×C4×C43#4111yescharacteristic
172C22×C4×C43#4111yescharacteristic
173C22×C4×C43C2411yescharacteristic
174C22×Dic43—21no—
175C22×Dic43—21no—
176SD16×C43—24no—
177D8×C43—24no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43#4112yes—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—41no—
194C22⋊C4×C43—41no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—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⋊C8—21no—
226C2×C43⋊C8C2×D411yescharacteristic
227C2×C43⋊C8C2×D411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C23×C43—21no—
231C23×C43—22no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—81no—
235C23×C43—81no—
236C23×C43C2×#4111yescharacteristic
237Q8×C43—21no—
238Q8×C43—21no—
239D4×C43—21no—
240D4×C43—22no—
241D4×C43—21no—
242D4×C43—22no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—42no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—81no—
257C2×C4×C43—82no—
258C2×C4×C43—82no—
259C2×C4×C43—81no—
260C2×C4×C43#12111yescharacteristic
261C2×C4×C43#12111yescharacteristic
262C2×C4×C43#12111yescharacteristic
263C2×C4×C43#12111yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C2×C4×C432−1+411yescharacteristic
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—81no—
273C2×Dic43—81no—
274C8×C43—22no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#24724—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—42no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—82no—
292C22×C43—82no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43C2×#12111yescharacteristic
296C22×C43#55211yescharacteristic
297C22×C43#55611yescharacteristic
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43#52511yescharacteristic
307C4×C43#53611yescharacteristic
308C4×C43#54711yescharacteristic
309C4×C43#54811yescharacteristic
310Dic43—81no—
311Dic43—81no—
312#3080—431no—
313C2×#478—431no—
314C4×AGL(1,ℤ/8)D4311yescharacteristic
315#2925—431no—
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—82no—
331C2×C43#241511yescharacteristic
332C2×C43#306711yescharacteristic
333C2×C43#306811yescharacteristic
334C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
335C2×#125—431no—
336C4×#41C2×D4311yescharacteristic
337C2×C4×D4C2×D4311yescharacteristic
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—21no—
347#440—21no—
348C4×SD16—21no—
349C4×D8—21no—
350#433—861no—
351#433—861no—
352#432—861no—
353#431—861no—
354C2×#108—431no—
355C2×#108—431no—
356#428—431no—
357#428—431no—
358#428C2×D4311yescharacteristic
359C2×#107—431no—
360C2×#106—431no—
361#423—431no—
362#423—431no—
363C2×C4⋊C8—431no—
364#418C2×D4311yescharacteristic
365#417—431no—
366#417—431no—
367#417C2×D4311yescharacteristic
368C2×#102—431no—
369C2×#102—431no—
370C2×#100—431no—
371C2×#100—431no—
372#408—431no—
373#408—431no—
374#405—431no—
375#405—431no—
376C4×M16C2×D4311yescharacteristic
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×D4C22×D4311yescharacteristic
388C23×C4—21no—
389AGL(1,ℤ/8)—22no—
390AGL(1,ℤ/8)—22no—
391C2×SD16—21no—
392C2×D8—21no—
393C2×M16—431no—
394C2×M16—431no—
395C2×M16—431no—
396C2×M16—431no—
397C2×M16C22×D4311yescharacteristic
398C2×M16C22×D4311yescharacteristic
399C22×C8—431no—
400C22×C8—431no—
401#125—861no—
402#125—861no—
403#125—861no—
404#125—861no—
405C4×Q8C22⋊D4311yescharacteristic
406C4×Q8C22⋊D4311yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C22⋊D4311yescharacteristic
414C4×D4C22⋊D4311yescharacteristic
415#117—21no—
416#117C22×D4311yescharacteristic
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C42—21no—
424C2×C42C22×D4311yescharacteristic
425#108—862no—
426#108—862no—
427#107—21no—
428#107—861no—
429#107—861no—
430#107—861no—
431#107—861no—
432#106—21no—
433#106—861no—
434#106—861no—
435#106—861no—
436#106—861no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445#103—21no—
446#103—861no—
447#103—861no—
448#102—21no—
449#102—21no—
450#102—21no—
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—861no—
460C22⋊C8—861no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463#97—21no—
464#97—861no—
465#97—861no—
466C4×C8—21no—
467C4×C8—861no—
468C4×C8—861no—
469C24—21no—
470#41—21no—
471#41—21no—
472#41—21no—
473#41—21no—
474C2×Q8C2×C22⋊D4311yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4#1062189812yes—
482C2×D4C2×C22⋊D4311yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—82no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4#1062190011yescharacteristic
493C22×C4#1062190011yescharacteristic
494C22×C4C23×D4311yescharacteristic
495SD16—24no—
496D8—24no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—861no—
501M16—861no—
502M16—861no—
503M16—861no—
504M16—861no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16#1062189812yes—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—431no—
514C2×C8—431no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
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×C22⋊D4311yescharacteristic
536C4⋊C4C2×C22⋊D4311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42C2×C22⋊D4311yescharacteristic
548C42C2×C22⋊D4311yescharacteristic
549C23—21no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—81no—
554C23—81no—
555C23C2×#1062190011yescharacteristic
556Q8—21no—
557Q8—21no—
558D4—22no—
559D4—21no—
560D4—22no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
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—41no—
575C2×C4—81no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4—81no—
579C2×C4—3441no—
580C2×C4—3441no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4#1306329711yescharacteristic
584C2×C4#1306329711yescharacteristic
585C2×C4#1306329711yescharacteristic
586C2×C4#1306329711yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C22×C22⋊D4311yescharacteristic
589C2×C4C2×#1062189811yescharacteristic
590C2×C4C2×#1062189811yescharacteristic
591C2×C4#1306337211yescharacteristic
592C2×C4#1306337211yescharacteristic
593C8—22no—
594C8—41no—
595C8—861no—
596C8—861no—
597C8—861no—
598C8—861no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22C2×#1306329711yescharacteristic
614C22#1458358911yescharacteristic
615C22#1458361911yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—3441no—
625C4—3441no—
626C4#1458341011yescharacteristic
627C4#1458347011yescharacteristic
628C4#1458355411yescharacteristic
629C4#1458355811yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—82no—
634C2#1913802411yescharacteristic
635C2#1914431211yescharacteristic
636C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×AGL(1,ℤ/8)×C43C2
socleC22×C43C2×#121
prime radicalC2×AGL(1,ℤ/8)×C43C22
hypercenterC4×AGL(1,ℤ/8)D43
hypocenterC43#24724
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #19144417C2semidirect
2. C2×#14583199C2semidirect
3. #19143261C2semidirect
4. #19136043C2semidirect
5. #19136038C2semidirect
8. #19135588C2semidirect
9. #19135377C2semidirect
10. #19135372C2semidirect
11. #19135370C2semidirect
12. #19135260C2semidirect
13. #19135260C2semidirect
14. #19134587C2semidirect
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×#145831992
#191432612
#191360432
#191360382
#191358842
#191355882
#191353772
#191353722
#191353702
#191352602
#191345872
C4×AGL(1,ℤ/8)×C432
#2472443