Finite Group Databasebeta

← #24988417

Subgroups — #24988417

Order 11008.

900 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583494C211yesmaximal, characteristic
2#19134913C211yesmaximal, characteristic
3#19134900C211yesmaximal, characteristic, complemented
4C2×#14582635C211yesmaximal, characteristic, complemented
5C2×#14582624C211yesmaximal, characteristic, complemented
6#19132849C211yesmaximal, characteristic, complemented
7C2×C43×#327C211yesmaximal, characteristic
8#14583494—22no—
9#14583494—22no—
10#14583494—22no—
11#14583494C414yescomplemented
12C2×#13063318—21no—
13C2×#13063315—21no—
14C2×#13063306—21no—
15C2×#13063306—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063302—21no—
18C2×D4×Dic43—21no—
19C22×C4⋊Dic43C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C2×#13063250—21no—
22C2×#13063246—21no—
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×C43⋊#95—21no—
25C2×C43⋊#95—21no—
26#14582662—21no—
27#14582661—21no—
28#14582635—22no—
29#14582624—22no—
30C2×#121×C43C2211yescharacteristic
31C2×C22⋊C8×C43C2211yescharacteristic
32C2×#95×C43C2211yescharacteristic
33C43×#327—22no—
34C22×Dic86D411yescharacteristic
35C23×Dic43—21no—
36C23×Dic43—21no—
37C23×Dic43D411yescharacteristic
38C23×Dic43D411yescharacteristic
39C22×C43⋊C8—21no—
40#13063318—24no—
41#13063318—24no—
42#13063315—24no—
43#13063315—24no—
44#13063306—24no—
45#13063306—24no—
46#13063306—24no—
47#13063306—24no—
48#13063304—21no—
49#13063304—21no—
50#13063304C2×C412yes—
51#13063304D412yes—
52#13063302—24no—
53#13063302—24no—
54D4×Dic43—24no—
55D4×Dic43—24no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43—42no—
60C2×C4⋊Dic43D411yescharacteristic
61C2×Dic43⋊C4—21no—
62C2×Dic43⋊C4—21no—
63C2×Dic43⋊C4—21no—
64C2×Dic43⋊C4—21no—
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4C2×C412yes—
69C2×Dic43⋊C4D412yes—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C4×Dic43—21no—
75#13063250—42no—
76#13063246—42no—
77C22⋊(C43⋊C8)—21no—
78C22⋊(C43⋊C8)—21no—
79C43⋊#95—42no—
80C43⋊#95—42no—
81C22×D4×C43—21no—
82C22×D4×C43D411yescharacteristic
83C23×C4×C43—21no—
84C23×C4×C43C2311yescharacteristic
85C22×C8×C43—21no—
86#121×C43—21no—
87#121×C43—21no—
88#121×C43C2×C412yes—
89#121×C43D412yes—
90C2×C4⋊C4×C43D411yescharacteristic
91C2×C22⋊C4×C43—21no—
92C22⋊C8×C43—21no—
93C22⋊C8×C43—21no—
94#95×C43—21no—
95#95×C43—21no—
96C24×C43—21no—
97C24×C43C2×D411yescharacteristic
98C2×D4×C43—21no—
99C2×D4×C43—22no—
100C2×D4×C43—22no—
101C2×D4×C43—41no—
102C2×D4×C43—41no—
103C2×D4×C43—41no—
104C2×D4×C43—41no—
105C2×D4×C43—41no—
106C2×D4×C43—41no—
107C2×D4×C43C22⋊C412yes—
108C22×C4×C43—22no—
109C22×C4×C43—21no—
110C22×C4×C43—41no—
111C22×C4×C43—41no—
112C22×C4×C43—41no—
113C22×C4×C43—41no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43C22×C411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×Dic43—24no—
125C22×Dic43—22no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43—41no—
140C22×Dic43—41no—
141C22×Dic43—41no—
142C22×Dic43—41no—
143C22×Dic43—41no—
144C22×Dic43—81no—
145C22×Dic43—81no—
146C22×Dic43C22⋊C412yes—
147C22×Dic43C22⋊C412yes—
148C2×Dic86—21no—
149C2×Dic86—41no—
150C2×Dic86—41no—
151C2×Dic86C22⋊C412yes—
152C2×C8×C43—41no—
153C2×C8×C43—41no—
154C2×C8×C43—41no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43C22⋊C412yes—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊Dic43—24no—
160C22⋊Dic43—24no—
161C22⋊Dic43—24no—
162C22⋊Dic43—22no—
163C22⋊Dic43—22no—
164C4⋊Dic43—24no—
165C4⋊Dic43—21no—
166C4⋊Dic43—22no—
167C4⋊Dic43—22no—
168C4⋊Dic43—41no—
169C4⋊Dic43—41no—
170C4⋊Dic43C22⋊C412yes—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175Dic43⋊C4—22no—
176Dic43⋊C4—22no—
177Dic43⋊C4—22no—
178Dic43⋊C4—22no—
179C4×Dic43—24no—
180C2×C43⋊C8—41no—
181C2×C43⋊C8—41no—
182C2×C43⋊C8—41no—
183C23×C43—21no—
184C23×C43—21no—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—22no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43C2×C22⋊C411yescharacteristic
195C23×C43#12011yescharacteristic
196C23×C43#12011yescharacteristic
197C23×C43#13511yescharacteristic
198C23×C43#13511yescharacteristic
199C23×C43AGL(1,ℤ/8)11yescharacteristic
200C23×C43#13711yescharacteristic
201D4×C43—42no—
202D4×C43—42no—
203D4×C43—42no—
204D4×C43—42no—
205D4×C43—42no—
206D4×C43—81no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—81no—
222C2×C4×C43—81no—
223C2×C4×C43—81no—
224C2×C4×C43—81no—
225C2×C4×C43C2×C22⋊C411yescharacteristic
226C2×C4×C43C2×C22⋊C411yescharacteristic
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—81no—
250C2×Dic43—84no—
251C2×Dic43—81no—
252C2×Dic43—81no—
253C2×Dic43—81no—
254C2×Dic43—81no—
255Dic86—42no—
256Dic86—81no—
257C8×C43—81no—
258C43⋊C8—81no—
259#8407—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—42no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43#37911yescharacteristic
280C22×C43#41611yescharacteristic
281C22×C43#41711yescharacteristic
282C22×C43#44911yescharacteristic
283C22×C43#44911yescharacteristic
284C22×C43#45211yescharacteristic
285C22×C43#45211yescharacteristic
286C22×C43#45411yescharacteristic
287C22×C43#45611yescharacteristic
288C22×C43B(4,𝔽2)11yescharacteristic
289C22×C43#45811yescharacteristic
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—21no—
294C4×C43—42no—
295C4×C43—82no—
296Dic43—42no—
297Dic43—42no—
298Dic43—42no—
299Dic43—42no—
300Dic43—82no—
301C2×#539—431no—
302#1874—431no—
303#1872—431no—
304C2×#328—431no—
305C2×#327D4311yescharacteristic
306C2×#324—431no—
307#1441—431no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—82no—
313C2×C43#159711yescharacteristic
314C2×C43#160311yescharacteristic
315C2×C43#160911yescharacteristic
316C2×C43#161511yescharacteristic
317C2×C43#178811yescharacteristic
318C2×C43#179011yescharacteristic
319C2×C43#179311yescharacteristic
320#539—434no—
321#539—862no—
322#539—862no—
323#539—862no—
324C2×#126—861no—
325C2×#125—861no—
326C2×#123—861no—
327C2×#123—861no—
328C2×C22⋊Q8—431no—
329C2×C22⋊Q8—861no—
330C2×#121C2×D4311yescharacteristic
331C2×C4×D4—861no—
332C22×C4⋊C4—431no—
333C22×C4⋊C4—431no—
334C2×#103—861no—
335C2×#102—861no—
336C2×C22⋊C8—431no—
337C2×C22⋊C8C2×D4311yescharacteristic
338C2×#95—861no—
339C2×#95—861no—
340C2×#95C2×D4311yescharacteristic
341#340—861no—
342#340—861no—
343#328—862no—
344#327—22no—
345#324—862no—
346C43#840711yescharacteristic, complemented, Sylow
347C22×Q8—431no—
348C22×D4—21no—
349C22×D4D17211yescharacteristic
350C23×C4—21no—
351C23×C4—431no—
352C23×C4—431no—
353C23×C4—861no—
354C23×C4—861no—
355C23×C4C22×D4311yescharacteristic
356C22×C8—21no—
357C22×C8—861no—
358#126—864no—
359#126—864no—
360#125—864no—
361#125—864no—
362#123—864no—
363#123—864no—
364#123—864no—
365#123—864no—
366C22⋊Q8—432no—
367C22⋊Q8—432no—
368C22⋊Q8—864no—
369C22⋊Q8—864no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—21no—
373#121—21no—
374#121C4×D4312yes—
375#121C22⋊D4312yes—
376C4×D4—864no—
377C4×D4—864no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—432no—
380C2×C4⋊C4—432no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—1722no—
392C2×C4⋊C4D17211yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C42—861no—
399#103—1722no—
400#102—1722no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—861no—
404C22⋊C8—861no—
405#95—21no—
406#95—21no—
407#95—1722no—
408#95—1722no—
409C24—21no—
410C24D4×D4311yescharacteristic
411C2×Q8—432no—
412C2×Q8—861no—
413C2×Q8—1721no—
414C2×Q8—1721no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4(C2×D43)⋊C412yes—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—432no—
436C22×C4—432no—
437C22×C4—864no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—862no—
449C22×C4—3441no—
450C22×C4—3441no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4—1721no—
455C22×C4—1721no—
456C22×C4—1721no—
457C22×C4—1721no—
458C22×C4—1721no—
459C22×C4C2×C4×D4311yescharacteristic
460C22×C4C2×D17211yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4D4×D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—1721no—
469C2×C8—1721no—
470C2×C8—1721no—
471C4⋊C4—21no—
472C4⋊C4—432no—
473C4⋊C4—864no—
474C4⋊C4—864no—
475C4⋊C4—864no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—861no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—1721no—
486C4⋊C4—1721no—
487C4⋊C4(C2×D43)⋊C412yes—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—864no—
491C22⋊C4—864no—
492C22⋊C4—864no—
493C22⋊C4—862no—
494C22⋊C4—862no—
495C42—864no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22⋊C4×D4311yescharacteristic
508C23#1306329311yescharacteristic
509C23#1306329511yescharacteristic
510C23#1306334411yescharacteristic
511C23#1306334611yescharacteristic
512C23#1306334911yescharacteristic
513C23#1306335411yescharacteristic
514Q8—3441no—
515Q8—1722no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—81no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—862no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—3441no—
547C2×C4—3441no—
548C2×C4—3441no—
549C2×C4—3441no—
550C2×C4—3441no—
551C2×C4—3444no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1722no—
566C2×C4C22⋊C4×D4311yescharacteristic
567C2×C4C2×(C2×D43)⋊C411yescharacteristic
568C2×C4#1306329311yescharacteristic
569C2×C4#1306329511yescharacteristic
570C8—81no—
571C8—3441no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22#1458275411yescharacteristic
592C22#1458289211yescharacteristic
593C22#1458289711yescharacteristic
594C22#1458304111yescharacteristic
595C22#1458304511yescharacteristic
596C22#1458305811yescharacteristic
597C22#1458306211yescharacteristic
598C22#1458307311yescharacteristic
599C22#1458308311yescharacteristic
600C22#1458308711yescharacteristic
601C22#1458309011yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—82no—
608C4—3442no—
609C4—1722no—
610C4—1722no—
611C4—1722no—
612C4—1722no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—82no—
618C2#1913352511yescharacteristic
619C2#1913355911yescharacteristic
620C2#1913359311yescharacteristic
621C2#1913362711yescharacteristic
622C2#1913453211yescharacteristic
623C2#1913454111yescharacteristic
624C2#1913455511yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#327C2
socleC23×C43#120
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenterC2×#327D43
hypocenterC43#8407
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
3. #19134900C2semidirect
4. C2×#14582635C2semidirect
5. C2×#14582624C2semidirect
6. #19132849C2semidirect
11. #14583494C4semidirect
346. C43#8407semidirect

Maximal subgroups

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

subgroupindex
C2×#145834942
#191349132
#191349002
C2×#145826352
C2×#145826242
#191328492
C2×C43×#3272
#840743