Finite Group Databasebeta

← #25124574

Subgroups — #25124574

Order 11008.

1458 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063345C211yesmaximal, characteristic
2C2×#14582926C211yesmaximal, characteristic, complemented
3C2×#14582900C211yesmaximal, characteristic, complemented
4C2×#14582898C211yesmaximal, characteristic, complemented
5#19137183C211yesmaximal, characteristic, complemented
6#19135917C212yesmaximal, complemented
7#19135912C212yesmaximal, complemented
8#19135910C212yesmaximal, complemented
9#19135905C212yesmaximal, complemented
10C2×#14582661C211yesmaximal, characteristic, complemented
11C43×#2311C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C2×#13063345—24no—
14C2×#13063345—24no—
15C2×#13063345—24no—
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C22×#10621877C2211yescharacteristic
21C23×C43⋊C8C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23#14582926—24no—
24C2×C4⋊(C43⋊C8)C2212yes—
25C2×C4⋊(C43⋊C8)C2212yes—
26#14582900—24no—
27#14582898—24no—
28C2×#13063249C2212yes—
29C2×#13063248C2212yes—
30C2×#13063246C2212yes—
31C2×#13063245C2212yes—
32#14582805C2212yes—
33#14582801C2212yes—
34#14582776—22no—
35#14582756—21no—
36#14582756—21no—
37#14582661C2212yes—
38#14582661C2212yes—
39C22×#41×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C22×C4⋊C4×C43C2211yescharacteristic
42C43×#391C2212yes—
43C43×#390C2212yes—
44C43×#386—22no—
45C43×#380—21no—
46C43×#380—21no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898D414yes—
53C22×Dic86C2311yescharacteristic
54C22×D172C2311yescharacteristic
55C22×C22⋊D43—21no—
56C23×Dic43—21no—
57C22×C4×D43—21no—
58#13063345—232no—
59C2×#10621885—22no—
60C2×#10621885—22no—
61C2×#10621885—22no—
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621877—22no—
72C2×#10621877—22no—
73C2×#10621877—22no—
74C22×C43⋊C8—22no—
75C22×C43⋊C8—22no—
76C22×C43⋊C8D414yes—
77C22×C43⋊C8C2312yes—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2312yes—
84C2×(C2×D43)⋊C4—22no—
85C2×(C2×D43)⋊C4—22no—
86C4⋊(C43⋊C8)—24no—
87C4⋊(C43⋊C8)—24no—
88#13063249—24no—
89#13063248—24no—
90#13063246—24no—
91#13063245—24no—
92C43⋊#95—22no—
93C43⋊#95—22no—
94C2×#41×C43—22no—
95C2×#41×C43—22no—
96C2×#41×C43—22no—
97C2×#41×C43—22no—
98C2×#41×C43—22no—
99C2×#41×C43D414yes—
100C22×Q8×C43C2311yescharacteristic
101C22×D4×C43—21no—
102C22×D4×C43C2311yescharacteristic
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C23×C4×C43C2311yescharacteristic
106#117×C43—22no—
107#117×C43—22no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43—22no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43C2312yes—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43D412yes—
117C2×C42×C43C2312yes—
118#95×C43—22no—
119#95×C43—22no—
120C24×C43—21no—
121C24×C43C2×D411yescharacteristic
122C23×D43—21no—
123#41×C43—28no—
124#41×C43—28no—
125#41×C43—44no—
126#41×C43—44no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43C2×D412yes—
133C2×D4×C43—21no—
134C2×D4×C43—24no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—42no—
140C2×D4×C43—42no—
141C2×D4×C43C2×D412yes—
142C22×C4×C43—24no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43—81no—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4112yes—
157C22×C4×C43#4112yes—
158C22×C4×C43#4112yes—
159C22×C4×C43C2411yescharacteristic
160C2×C22⋊D43—24no—
161C2×C22⋊D43—42no—
162C2×C22⋊D43—42no—
163C22×Dic43—21no—
164C22×Dic43—22no—
165C22×Dic43—42no—
166C22×Dic43—81no—
167C22×Dic43—81no—
168#10621898—28no—
169#10621898—28no—
170#10621898—44no—
171#10621898—44no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172C2×D412yes—
178C2×C4×D43—24no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86C2×D412yes—
187C4⋊C4×C43—22no—
188C4⋊C4×C43—22no—
189C4⋊C4×C43—22no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—42no—
192C22⋊C4×C43—24no—
193C22⋊C4×C43—82no—
194C22⋊C4×C43—82no—
195C42×C43—22no—
196C42×C43—22no—
197#10621885—28no—
198#10621884—28no—
199#10621883—28no—
200#10621882—28no—
201(C2×D43)⋊C4—82no—
202(C2×D43)⋊C4—82no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43—42no—
206#10621877—44no—
207C2×C43⋊C8—28no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—22no—
214C2×C43⋊C8—22no—
215C2×C43⋊C8C2×D412yes—
216C2×C43⋊C8C2×D412yes—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—22no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43#12112yes—
229C23×C43#12112yes—
230C23×C43#12112yes—
231C23×C43C22×D411yescharacteristic
232C22×D43—22no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239Q8×C43—22no—
240Q8×C43—22no—
241Q8×C43—41no—
242Q8×C43—41no—
243D4×C43—22no—
244D4×C43—22no—
245D4×C43—48no—
246D4×C43—41no—
247D4×C43—41no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—48no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—84no—
262C2×C4×C43#12014yes—
263C2×C4×C43#12112yes—
264C2×C4×C43#12112yes—
265C2×C4×C43#12112yes—
266C2×C4×C43#12314yes—
267C2×C4×C43#12314yes—
268C2×C4×C43#12414yes—
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C22⋊D43—48no—
276C2×Dic43—22no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—84no—
283D172—22no—
284D172—22no—
285D172—41no—
286D172—41no—
287C4×D43—48no—
288Dic86—22no—
289Dic86—22no—
290Dic86—41no—
291Dic86—41no—
292C43⋊C8—22no—
293C43⋊C8—22no—
294C43⋊C8—42no—
295#23543—431nomaximal, Sylow
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—22no—
301C22×C43—22no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43#39414yes—
310C22×C43C2×#12111yescharacteristic
311C22×C43C2×#12111yescharacteristic
312C22×C43C2×#12111yescharacteristic
313C22×C43#57611yescharacteristic
314C22×C43#57711yescharacteristic
315C22×C43#57711yescharacteristic
316C22×C43#57811yescharacteristic
317C2×D43—42no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—81no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C4×C43—42no—
325C4×C43—42no—
326C4×C43—42no—
327C4×C43—82no—
328C4×C43#39414yes—
329C4×C43C2×#12011yescharacteristic
330C4×C43C2×#12311yescharacteristic
331C4×C43C2×#12311yescharacteristic
332C4×C43C2×#12411yescharacteristic
333Dic43—42no—
334Dic43—82no—
335C22×#135—431no—
336C2×#424—431no—
337C2×#417—431no—
338C2×#417—431no—
339#2311—431no—
340#2311D4311yescharacteristic, complemented
341#2056—432no—
342#2055—432no—
343#2055—432no—
344#2054—432no—
345C2×#340—431no—
346C2×C43—24no—
347C2×C43—82no—
348C2×C43C2×#39411yescharacteristic
349C2×C43#304511yescharacteristic
350C2×C43#304511yescharacteristic
351C2×C43#304611yescharacteristic
352C2×C43#304611yescharacteristic
353C2×C43#306011yescharacteristic
354C2×C43#306111yescharacteristic
355D43—82no—
356C22×#41—431no—
357C22×#41C2×D4311yescharacteristic
358C2×#135—864no—
359C2×#135—864no—
360C2×#135—864no—
361C22×Q16—431no—
362C22×SD16—431no—
363C22×SD16—431no—
364C22×D8—431no—
365C22×M16—431no—
366C23×C8—431no—
367C2×#117C2×D4311yescharacteristic
368C22×C4⋊C4—431no—
369C22×C4⋊C4C2×D4311yescharacteristic
370#424—864no—
371C2×C4⋊C8—432no—
372C2×C4⋊C8—432no—
373#417—864no—
374#417—864no—
375C2×#103—432no—
376C2×#103—432no—
377C2×#102—432no—
378C2×#102—432no—
379#391—432no—
380#391C2×D4312yes—
381#390—432no—
382#390C2×D4312yes—
383#386—22no—
384#386—862no—
385#380—21no—
386#380—21no—
387#380—861no—
388#380—861no—
389#340—432no—
390#340—432no—
391C43#2354311yescharacteristic, complemented, Sylow
392C2×#41—22no—
393C2×#41—22no—
394C2×#41—22no—
395C2×#41—22no—
396C2×#41—22no—
397C2×#41—434no—
398C2×#41—862no—
399C2×#41—862no—
400C2×#41—862no—
401C2×#41—862no—
402C2×#41—862no—
403C2×#41D17214yes—
404C22×Q8—431no—
405C22×Q8C22×D4311yescharacteristic
406C22×D4—21no—
407C22×D4—431no—
408C22×D4—861no—
409C22×D4C22×D4311yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4—861no—
413C23×C4—861no—
414C23×C4C22×D4311yescharacteristic
415#135—8632no—
416C2×Q16—862no—
417C2×Q16—862no—
418C2×Q16—862no—
419C2×SD16—862no—
420C2×SD16—862no—
421C2×SD16—862no—
422C2×SD16—862no—
423C2×SD16—862no—
424C2×SD16—862no—
425C2×D8—862no—
426C2×D8—862no—
427C2×D8—862no—
428C2×M16—862no—
429C2×M16—862no—
430C2×M16—862no—
431C22×C8—434no—
432C22×C8—431no—
433C22×C8—431no—
434C22×C8—432no—
435C22×C8—862no—
436C22×C8—862no—
437#117—22no—
438#117—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—432no—
443C2×C4⋊C4—862no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4C22⋊D4311yescharacteristic
447C2×C4⋊C4C22⋊D4311yescharacteristic
448C2×C4⋊C4C22×D4312yes—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—862no—
452C2×C22⋊C4—862no—
453C2×C22⋊C4C22⋊D4312yes—
454C2×C42C22×D4312yes—
455C4⋊C8—864no—
456C4⋊C8—864no—
457#103—864no—
458#103—864no—
459#102—864no—
460#102—864no—
461#95—22no—
462#95—22no—
463#95—862no—
464#95—862no—
465C24—21no—
466C24—861no—
467C24C2×C22⋊D4311yescharacteristic
468#41—28no—
469#41—28no—
470#41—44no—
471#41—44no—
472#41—868no—
473#41—868no—
474#41—1724no—
475#41—1724no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—432no—
482C2×Q8—861no—
483C2×Q8—861no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8C2×D17212yes—
488C2×D4—24no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—432no—
497C2×D4—864no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4—861no—
503C2×D4—1722no—
504C2×D4—1722no—
505C2×D4C2×D17212yes—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4—861no—
515C22×C4—864no—
516C22×C4—862no—
517C22×C4—3441no—
518C22×C4—3441no—
519C22×C4—1722no—
520C22×C4—1722no—
521C22×C4—1722no—
522C22×C4C2×D17212yes—
523C22×C4#1062189812yes—
524C22×C4D4×D4312yes—
525C22×C4D4×D4312yes—
526C22×C4#1062190012yes—
527C22×C4#1062190012yes—
528C22×C4C2×C22⋊D4312yes—
529C22×C4C2×C22⋊D4312yes—
530C22×C4C2×C22⋊D4311yescharacteristic
531C22×C4C23×D4311yescharacteristic
532Q16—868no—
533SD16—868no—
534SD16—868no—
535D8—868no—
536M16—1724no—
537C2×C8—432no—
538C2×C8—432no—
539C2×C8—868no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—862no—
545C2×C8—862no—
546C2×C8—862no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—42no—
552C4⋊C4—862no—
553C4⋊C4—862no—
554C4⋊C4—1722no—
555C22⋊C4—24no—
556C22⋊C4—82no—
557C22⋊C4—82no—
558C22⋊C4—3442no—
559C22⋊C4—3442no—
560C42—22no—
561C42—22no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—22no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—862no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23—1721no—
580C23#1306329612yes—
581C23#1306329712yes—
582C23#1306329912yes—
583C23C22×C22⋊D4311yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—41no—
587Q8—41no—
588Q8—862no—
589Q8—862no—
590Q8—1721no—
591Q8—1721no—
592D4—22no—
593D4—22no—
594D4—48no—
595D4—41no—
596D4—41no—
597D4—862no—
598D4—862no—
599D4—1728no—
600D4—1721no—
601D4—1721no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—48no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—84no—
616C2×C4—862no—
617C2×C4—3444no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1728no—
624C2×C4#1306329514yes—
625C2×C4#1306329612yes—
626C2×C4#1306329712yes—
627C2×C4#1306329912yes—
628C2×C4#1306330714yes—
629C2×C4#1306330914yes—
630C2×C4#1306331114yes—
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4C2×D4×D4311yescharacteristic
633C2×C4C22×D17211yescharacteristic
634C2×C4C2×#1062190011yescharacteristic
635C2×C4C2×#1062190011yescharacteristic
636C2×C4C2×#1062189811yescharacteristic
637C8—862no—
638C8—862no—
639C8—1722no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—3441no—
654C22—3441no—
655C22—3441no—
656C22—3441no—
657C22—1722no—
658C22—1722no—
659C22—1722no—
660C22#1458281514yes—
661C22C2×#1306329611yescharacteristic
662C22C2×#1306329711yescharacteristic
663C22C2×#1306329911yescharacteristic
664C22#1458370211yescharacteristic
665C22#1458370711yescharacteristic
666C22#1458371011yescharacteristic
667C22#1458371411yescharacteristic
668C4—42no—
669C4—42no—
670C4—42no—
671C4—82no—
672C4—3442no—
673C4—1722no—
674C4#1458281514yes—
675C4C2×#1306329511yescharacteristic
676C4C2×#1306330711yescharacteristic
677C4C2×#1306330911yescharacteristic
678C4C2×#1306331111yescharacteristic
679C2—24no—
680C2—82no—
681C2—3442no—
682C2C2×#1458281511yescharacteristic
683C2#1914413011yescharacteristic
684C2#1914413411yescharacteristic
685C2#1914414111yescharacteristic
686C2#1914414511yescharacteristic
687C2#1914425411yescharacteristic
688C2#1914426211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2311C2
socleC23×C43C22×D4
prime radicalC22×#13063345C2
hypercenter#2311D43
hypocenterC43#23543
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#14582926C2semidirect
3. C2×#14582900C2semidirect
4. C2×#14582898C2semidirect
5. #19137183C2semidirect
6. #19135917C2semidirect
7. #19135912C2semidirect
8. #19135910C2semidirect
9. #19135905C2semidirect
10. C2×#14582661C2semidirect
11. C43×#2311C2semidirect
340. #2311D43semidirect
391. C43#23543semidirect

Maximal subgroups

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

subgroupindex
C22×#130633452
C2×#145829262
C2×#145829002
C2×#145828982
#191371832
#191359172
#191359122
#191359102
#191359052
C2×#145826612
C43×#23112
#2354343