Finite Group Databasebeta

← #24988058

Subgroups — #24988058

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic
2#19134661C211yesmaximal, characteristic
3C2×#14582637C211yesmaximal, characteristic
4C2×#14582636C211yesmaximal, characteristic
5C2×#14582635C211yesmaximal, characteristic
6#19132819C211yesmaximal, characteristic
7C2×C43×#328C211yesmaximal, characteristic
8#14583451—22no—
9#14583451—22no—
10#14583451—22no—
11#14583451—22no—
12C2×#13063324C411yescharacteristic, complemented
13C2×#13063323C411yescharacteristic, complemented
14C2×#13063315—21no—
15C2×#13063304C2211yescharacteristic
16C2×#13063302—21no—
17C2×Q8×Dic43C411yescharacteristic, complemented
18C2×#13063290—21no—
19C2×#13063290C411yescharacteristic, complemented
20C2×#13063281—21no—
21C22×C4×Dic43C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C43⋊#95—21no—
24C2×C43⋊#95—21no—
25C2×C43⋊#95C2211yescharacteristic
26#14582653—21no—
27#14582653—21no—
28#14582637—22no—
29#14582636—22no—
30#14582635—22no—
31C2×C22⋊Q8×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×#95×C43C2211yescharacteristic
34C43×#328—22no—
35C22×Dic86—21no—
36C22×Dic86C2×C411yescharacteristic
37C23×Dic43—21no—
38C23×Dic43D411yescharacteristic
39C23×Dic43D411yescharacteristic
40C22×C43⋊C8—21no—
41#13063324—22no—
42#13063324—22no—
43#13063323—22no—
44#13063323—22no—
45#13063315—24no—
46#13063315—24no—
47#13063304—21no—
48#13063304—21no—
49#13063304D412yes—
50#13063304D412yes—
51#13063302—24no—
52#13063302—24no—
53Q8×Dic43—22no—
54Q8×Dic43—22no—
55#13063290—24no—
56#13063290—24no—
57#13063290—22no—
58#13063290—22no—
59#13063281—24no—
60#13063281—24no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43C2×C411yescharacteristic
63C2×Dic43⋊C4—21no—
64C2×Dic43⋊C4—21no—
65C2×Dic43⋊C4—21no—
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×C22⋊Dic43—21no—
69C2×C4×Dic43—21no—
70C2×C4×Dic43—21no—
71C2×C4×Dic43—21no—
72C2×C4×Dic43—21no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43C2×C411yescharacteristic
76C2×C4×Dic43C2×C411yescharacteristic
77C2×C4×Dic43D411yescharacteristic
78C2×C4×Dic43D411yescharacteristic
79C22⋊(C43⋊C8)—21no—
80C22⋊(C43⋊C8)—21no—
81C43⋊#95—24no—
82C43⋊#95—21no—
83C43⋊#95—21no—
84C43⋊#95—42no—
85C22×Q8×C43C2×C411yescharacteristic
86C23×C4×C43—21no—
87C23×C4×C43C2311yescharacteristic
88C22×C8×C43—21no—
89C22⋊Q8×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43D412yes—
92C22⋊Q8×C43D412yes—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43C2×C411yescharacteristic
95C2×C22⋊C4×C43—21no—
96C22⋊C8×C43—21no—
97C22⋊C8×C43—21no—
98#95×C43—21no—
99#95×C43—21no—
100C24×C43C2×D411yescharacteristic
101C2×Q8×C43—21no—
102C2×Q8×C43—41no—
103C2×Q8×C43—41no—
104C2×Q8×C43C22⋊C412yes—
105C22×C4×C43—22no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
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×C43C22×C411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×Dic43—22no—
123C22×Dic43—22no—
124C22×Dic43—21no—
125C22×Dic43—21no—
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134C22×Dic43—41no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C22×Dic43—41no—
139C22×Dic43C22⋊C411yescharacteristic
140C22×Dic43C22⋊C411yescharacteristic
141C22×Dic43C22⋊C411yescharacteristic
142C22×Dic43C22⋊C411yescharacteristic
143C22×Dic43SD1612yes—
144C22×Dic43Q1612yes—
145C2×Dic86—24no—
146C2×Dic86—21no—
147C2×Dic86—42no—
148C2×Dic86—42no—
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×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43C22⋊C412yes—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161C22⋊Dic43—22no—
162C22⋊Dic43—22no—
163C4⋊Dic43—24no—
164C4⋊Dic43—21no—
165C4⋊Dic43C22⋊C412yes—
166Dic43⋊C4—24no—
167Dic43⋊C4—24no—
168Dic43⋊C4—24no—
169Dic43⋊C4—24no—
170Dic43⋊C4—22no—
171Dic43⋊C4—22no—
172C4×Dic43—24no—
173C4×Dic43—24no—
174C4×Dic43—21no—
175C4×Dic43—21no—
176C4×Dic43—21no—
177C4×Dic43—21no—
178C4×Dic43—21no—
179C4×Dic43—21no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C2×C43⋊C8—41no—
183C2×C43⋊C8—41no—
184C2×C43⋊C8—41no—
185C23×C43—21no—
186C23×C43—21no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43C2×C22⋊C411yescharacteristic
190C23×C43#12011yescharacteristic
191C23×C43#12011yescharacteristic
192C23×C43C2×SD1611yescharacteristic
193C23×C43C2×Q1611yescharacteristic
194C23×C43#13711yescharacteristic
195C23×C43#13711yescharacteristic
196Q8×C43—42no—
197Q8×C43—42no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—81no—
216C2×C4×C43—81no—
217C2×C4×C43—81no—
218C2×C4×C43—81no—
219C2×C4×C43C2×C22⋊C411yescharacteristic
220C2×C4×C43C2×C22⋊C411yescharacteristic
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—21no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—81no—
248C2×Dic43—81no—
249C2×Dic43—81no—
250C2×Dic43—81no—
251C2×Dic43#10312yes—
252C2×Dic43#10312yes—
253C2×Dic43#10412yes—
254Dic86—48no—
255Dic86—42no—
256Dic86—42no—
257C8×C43—81no—
258C43⋊C8—81no—
259#8333—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#37911yescharacteristic
273C22×C43#41011yescharacteristic
274C22×C43#41011yescharacteristic
275C22×C43C2×#10311yescharacteristic
276C22×C43#41911yescharacteristic
277C22×C43C2×#10411yescharacteristic
278C22×C43#42111yescharacteristic
279C22×C43#44811yescharacteristic
280C22×C43#44811yescharacteristic
281C22×C43#45111yescharacteristic
282C22×C43#45111yescharacteristic
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—82no—
290Dic43—22no—
291Dic43—22no—
292Dic43—22no—
293Dic43—42no—
294Dic43—42no—
295Dic43—41no—
296Dic43—82no—
297C2×#533—431no—
298#1817—431no—
299C2×#328—431no—
300C2×#328—431no—
301C2×#328—431no—
302C2×#328D4311yescharacteristic
303#1434—431no—
304C2×C43—21no—
305C2×C43—21no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43#150311yescharacteristic
309C2×C43#150611yescharacteristic
310C2×C43#151511yescharacteristic
311C2×C43#151811yescharacteristic
312C2×C43#178211yescharacteristic
313C2×C43#178711yescharacteristic
314C2×C43#178911yescharacteristic
315#533—862no—
316#533—862no—
317#533—862no—
318#533—862no—
319C2×C4⋊Q8—431no—
320C2×C4⋊Q8—431no—
321C2×#125—861no—
322C2×C22⋊Q8—431no—
323C2×C22⋊Q8—861no—
324C2×C22⋊Q8C2×D4311yescharacteristic
325C2×C4×Q8—431no—
326C2×C4×Q8—431no—
327C2×C4×Q8—861no—
328C2×#117—861no—
329C22×C42—431no—
330C2×C22⋊C8—431no—
331C2×C22⋊C8C2×D4311yescharacteristic
332C2×#95—431no—
333C2×#95—861no—
334C2×#95—861no—
335C2×#95C2×D4311yescharacteristic
336#336—861no—
337#336—861no—
338#328—22no—
339#328—862no—
340#328—862no—
341#328—862no—
342C43#833311yescharacteristic, complemented, Sylow
343C22×Q8—431no—
344C22×Q8—861no—
345C22×Q8C4×D4311yescharacteristic
346C23×C4—21no—
347C23×C4—431no—
348C23×C4—431no—
349C23×C4—861no—
350C23×C4C22×D4311yescharacteristic
351C22×C8—21no—
352C22×C8—861no—
353C4⋊Q8—862no—
354C4⋊Q8—862no—
355C4⋊Q8—862no—
356C4⋊Q8—862no—
357#125—864no—
358#125—864no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—432no—
362C22⋊Q8—432no—
363C22⋊Q8—864no—
364C22⋊Q8—864no—
365C22⋊Q8—861no—
366C22⋊Q8—861no—
367C22⋊Q8D17212yes—
368C22⋊Q8C22⋊D4312yes—
369C4×Q8—862no—
370C4×Q8—864no—
371C4×Q8—864no—
372C4×Q8—862no—
373C4×Q8—862no—
374C4×Q8—862no—
375#117—864no—
376#117—864no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4C4×D4311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—861no—
388C2×C42—431no—
389C2×C42—431no—
390C2×C42—431no—
391C2×C42—431no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42—861no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—861no—
401C22⋊C8—861no—
402#95—21no—
403#95—21no—
404#95—864no—
405#95—861no—
406#95—861no—
407#95—1722no—
408C24D4×D4311yescharacteristic
409C2×Q8—21no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—432no—
413C2×Q8—864no—
414C2×Q8—861no—
415C2×Q8—1721no—
416C2×Q8—1721no—
417C2×Q8—1722no—
418C2×Q8—1722no—
419C2×Q8(C2×D43)⋊C412yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—431no—
437C22×C4—862no—
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—862no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4—1721no—
454C22×C4C2×C4×D4311yescharacteristic
455C22×C4C2×D17211yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—1721no—
464C2×C8—1721no—
465C2×C8—1721no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—432no—
470C4⋊C4—864no—
471C4⋊C4—864no—
472C4⋊C4—864no—
473C4⋊C4—864no—
474C4⋊C4—864no—
475C4⋊C4—861no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4(C2×D43)⋊C412yes—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—862no—
482C22⋊C4—862no—
483C42—864no—
484C42—864no—
485C42—861no—
486C42—861no—
487C42—861no—
488C42—861no—
489C42—861no—
490C42—861no—
491C42—861no—
492C42—861no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23C22⋊C4×D4311yescharacteristic
498C23#1306329311yescharacteristic
499C23#1306329511yescharacteristic
500C23SD16×D4311yescharacteristic
501C23Q16×D4311yescharacteristic
502C23#1306335411yescharacteristic
503C23#1306335711yescharacteristic
504Q8—42no—
505Q8—42no—
506Q8—1722no—
507Q8—1722no—
508Q8—1728no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—81no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—432no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—862no—
534C2×C4—862no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—3441no—
549C2×C4—3441no—
550C2×C4—3441no—
551C2×C4—3441no—
552C2×C4—1722no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4C22⋊C4×D4311yescharacteristic
562C2×C4C2×(C2×D43)⋊C411yescharacteristic
563C2×C4#1306329311yescharacteristic
564C2×C4#1306329511yescharacteristic
565C8—81no—
566C8—3441no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22#1458275411yescharacteristic
580C22#1458287111yescharacteristic
581C22#1458287111yescharacteristic
582C22#103×D4311yescharacteristic
583C22#1458290611yescharacteristic
584C22#104×D4311yescharacteristic
585C22#1458291411yescharacteristic
586C22#1458303611yescharacteristic
587C22#1458303911yescharacteristic
588C22#1458305311yescharacteristic
589C22#1458305611yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—42no—
595C4—42no—
596C4—82no—
597C4—862no—
598C4—862no—
599C4—862no—
600C4—3442no—
601C4—1722no—
602C4—1721no—
603C4—1722no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2#1913309211yescharacteristic
609C2#1913310511yescharacteristic
610C2#1913314411yescharacteristic
611C2#1913315711yescharacteristic
612C2#1913451111yescharacteristic
613C2#1913452811yescharacteristic
614C2#1913453711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#328C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#328D43
hypocenterC43#8333
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
12. C2×#13063324C4semidirect
13. C2×#13063323C4semidirect
17. C2×Q8×Dic43C4semidirect
19. C2×#13063290C4semidirect
342. C43#8333semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
#191346612
C2×#145826372
C2×#145826362
C2×#145826352
#191328192
C2×C43×#3282
#833343