Finite Group Databasebeta

← #25003717

Subgroups — #25003717

Order 11008.

1078 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063253C211yesmaximal, characteristic
2C2×#14582898C211yesmaximal, characteristic
3#19137188C211yesmaximal, characteristic
4C2×#14582668C211yesmaximal, characteristic, complemented
5#19134314C211yesmaximal, characteristic, complemented
6C2×#14582659C211yesmaximal, characteristic, complemented
7C2×C43×#384C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12C2×#13063253—22no—
13C2×#13063253—22no—
14C2×#13063253C414yescomplemented
15#14582898—22no—
16#14582898—22no—
17C2×#13063248—21no—
18C2×#13063245—21no—
19#14582804—21no—
20#14582800—21no—
21#14582778—22no—
22#14582756—22no—
23#14582668—22no—
24#14582661—22no—
25#14582659—22no—
26C22×C4⋊C4×C43—22no—
27C22×C4⋊C4×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C22×C42×C43C2211yescharacteristic
30C43×#384—22no—
31C43×#384—22no—
32C2×#10621898—21no—
33C2×#10621898—21no—
34C2×#10621898—21no—
35C2×#10621898—21no—
36C2×#10621898—21no—
37C2×#10621898—21no—
38C2×#10621898—21no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898C2×C412yes—
43C2×#10621898Q812yes—
44C22×Dic86D411yescharacteristic
45C22×D172D411yescharacteristic
46C22×C22⋊D43—21no—
47C22×C4×D43—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877C2×C412yes—
59C2×#10621877D412yes—
60C22×C43⋊C8—21no—
61C22×C43⋊C8—21no—
62#13063284—21no—
63#13063284—21no—
64#13063284—21no—
65#13063284—21no—
66C2×C4⋊Dic43D412yes—
67C2×C22⋊Dic43—21no—
68C2×(C2×D43)⋊C4—24no—
69C2×C4×Dic43—21no—
70#13063253—28no—
71#13063248—24no—
72#13063245—24no—
73C43⋊#95—24no—
74C23×C4×C43—21no—
75C23×C4×C43—21no—
76C23×C4×C43D412yes—
77C23×C4×C43C2311yescharacteristic
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—28no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—48no—
91C2×C4⋊C4×C43D412yes—
92C2×C42×C43—21no—
93C2×C42×C43—21no—
94C2×C42×C43—21no—
95C2×C42×C43C2×C412yes—
96C2×C42×C43D412yes—
97C2×C42×C43D412yes—
98C24×C43C2×D411yescharacteristic
99C23×D43—21no—
100C22×C4×C43—24no—
101C22×C4×C43—24no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—44no—
110C22×C4×C43—44no—
111C22×C4×C43—41no—
112C22×C4×C43—41no—
113C22×C4×C43C22×C411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×Q811yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C22×C4×C43#4111yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C2×C22⋊D43—22no—
128C2×C22⋊D43—22no—
129C2×C22⋊D43—41no—
130C2×C22⋊D43—41no—
131C2×C22⋊D43—41no—
132C2×C22⋊D43—41no—
133C22×Dic43—21no—
134C22×Dic43—22no—
135#10621898—22no—
136#10621898—22no—
137#10621898—22no—
138#10621898—22no—
139#10621898—22no—
140#10621898—22no—
141#10621898—22no—
142#10621898—22no—
143#10621898—41no—
144#10621898—41no—
145#10621898—41no—
146#10621898—41no—
147#10621898—41no—
148#10621898—41no—
149#10621898—41no—
150#10621898—41no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172C4⋊C412yescomplemented
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—41no—
160C2×C4×D43—41no—
161C2×C4×D43—41no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86C4⋊C412yescomplemented
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—416no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43—22no—
181C42×C43C22⋊C414yescomplemented
182C22⋊Dic43—41no—
183C22⋊Dic43—41no—
184(C2×D43)⋊C4—84no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4×Dic43—41no—
188C4×Dic43—41no—
189#10621877—22no—
190#10621877—22no—
191#10621877—22no—
192#10621877—22no—
193#10621877—41no—
194#10621877—41no—
195#10621877—41no—
196#10621877—41no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—41no—
200C2×C43⋊C8—41no—
201C2×C43⋊C8—41no—
202C2×C43⋊C8—41no—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43C4×D411yescharacteristic
206C23×C43#12011yescharacteristic
207C23×C43#12011yescharacteristic
208C23×C43#12111yescharacteristic
209C23×C43#12111yescharacteristic
210C23×C43C22⋊Q811yescharacteristic
211C23×C43#12411yescharacteristic
212C22×D43—22no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—42no—
216C22×D43—42no—
217C2×C4×C43—24no—
218C2×C4×C43—28no—
219C2×C4×C43—24no—
220C2×C4×C43—28no—
221C2×C4×C43—24no—
222C2×C4×C43—44no—
223C2×C4×C43—44no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—44no—
227C2×C4×C43—82no—
228C2×C4×C43—82no—
229C2×C4×C43—82no—
230C2×C4×C43C2×C22⋊C411yescharacteristic
231C2×C4×C43C2×C4⋊C411yescharacteristic
232C2×C4×C43#11711yescharacteristic
233C2×C4×C43C4×D411yescharacteristic
234C2×C4×C43C4×D411yescharacteristic
235C2×C4×C43C4×D411yescharacteristic
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43C22⋊Q811yescharacteristic
244C2×C4×C43C22⋊Q811yescharacteristic
245C2×C4×C43C22⋊Q811yescharacteristic
246C2×C4×C43C22⋊Q811yescharacteristic
247C2×C4×C43C22⋊Q811yescharacteristic
248C2×C4×C43#12311yescharacteristic
249C2×C4×C43#12311yescharacteristic
250C2×C4×C43#12311yescharacteristic
251C2×C4×C43#12311yescharacteristic
252C2×C4×C43#12311yescharacteristic
253C2×C4×C43#12411yescharacteristic
254C2×C4×C43#12411yescharacteristic
255C2×C4×C43#12611yescharacteristic
256C2×C4×C43#12611yescharacteristic
257C2×C4×C43#12711yescharacteristic
258C22⋊D43—42no—
259C22⋊D43—42no—
260C22⋊D43—42no—
261C22⋊D43—42no—
262C2×Dic43—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268D172—22no—
269D172—22no—
270D172—41no—
271D172—41no—
272C4×D43—42no—
273C4×D43—42no—
274C4×D43—42no—
275C4×D43—42no—
276Dic86—22no—
277Dic86—22no—
278Dic86—41no—
279Dic86—41no—
280C43⋊C8—42no—
281C43⋊C8—42no—
282#11078—431nomaximal, Sylow
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43#38511yescharacteristic
292C22×C43#38611yescharacteristic
293C22×C43#38811yescharacteristic
294C22×C43#39211yescharacteristic
295C22×C43#39311yescharacteristic
296C22×C43#39411yescharacteristic
297C22×C43#39611yescharacteristic
298C22×C43#45312yes—
299C22×C43#45612yes—
300C2×D43—44no—
301C2×D43—42no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—82no—
305C4×C43—28no—
306C4×C43—82no—
307C4×C43—82no—
308C4×C43#38011yescharacteristic
309C4×C43#38511yescharacteristic
310C4×C43#38811yescharacteristic
311C4×C43#39011yescharacteristic
312C4×C43#39411yescharacteristic
313C4×C43#39611yescharacteristic
314C4×C43#39711yescharacteristic
315C4×C43#39911yescharacteristic
316Dic43—42no—
317Dic43—82no—
318C22×#104—431no—
319C2×#417—431no—
320#2311—431no—
321C2×#384D4311yescharacteristic, complemented
322C2×#343—431no—
323#1736—431no—
324C2×#339—431no—
325C2×C43—21no—
326C2×C43—21no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43#143911yescharacteristic
330C2×C43#185912yes—
331C2×C43#200211yescharacteristic
332C2×C43#200511yescharacteristic
333C2×C43#203912yes—
334D43—82no—
335C22×#41—431no—
336C22×M16—431no—
337C22×M16—431no—
338C2×#117—431no—
339C22×C4⋊C4—22no—
340C22×C4⋊C4C2×D4311yescharacteristic
341C22×C4⋊C4C2×D4311yescharacteristic
342C22×C42C2×D4311yescharacteristic
343C2×#104—434no—
344C2×#104—862no—
345C2×#104—862no—
346#417—862no—
347#417—862no—
348C2×#103—861no—
349C2×#102—861no—
350#391—861no—
351#390—861no—
352#386—862no—
353#384—22no—
354#384—22no—
355#380—862no—
356#343—862no—
357#340—862no—
358#339—862no—
359C43#1107811yescharacteristic, complemented, Sylow
360C2×#41—432no—
361C2×#41—432no—
362C2×#41—861no—
363C2×#41—861no—
364C2×#41—861no—
365C2×#41—861no—
366C2×#41—861no—
367C2×#41—861no—
368C2×#41—861no—
369C2×#41—861no—
370C2×#41—861no—
371C2×#41—861no—
372C22×Q8—431no—
373C22×D4—431no—
374C22×D4—861no—
375C23×C4—21no—
376C23×C4—21no—
377C23×C4—861no—
378C23×C4C22⋊D4312yes—
379C23×C4C22×D4311yescharacteristic
380C2×M16—432no—
381C2×M16—432no—
382C2×M16—861no—
383C2×M16—861no—
384C2×M16—861no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16—861no—
390C2×M16—861no—
391C2×M16—861no—
392C22×C8—861no—
393C22×C8—861no—
394#117—861no—
395#117—861no—
396#117—861no—
397#117—861no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—28no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—48no—
411C2×C4⋊C4—432no—
412C2×C4⋊C4C22⋊D4312yes—
413C2×C22⋊C4—864no—
414C2×C22⋊C4—861no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—861no—
419C2×C42C4×D4312yes—
420C2×C42D17212yes—
421C2×C42C22⋊D4312yes—
422#104—868no—
423#103—864no—
424#102—864no—
425#95—864no—
426C24—861no—
427C24C2×C22⋊D4311yescharacteristic
428#41—862no—
429#41—862no—
430#41—862no—
431#41—862no—
432#41—862no—
433#41—862no—
434#41—862no—
435#41—862no—
436#41—1721no—
437#41—1721no—
438#41—1721no—
439#41—1721no—
440#41—1721no—
441#41—1721no—
442#41—1721no—
443#41—1721no—
444C2×Q8—432no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×D4—432no—
451C2×D4—862no—
452C2×D4—862no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—1721no—
459C2×D4—1721no—
460C2×D4—1721no—
461C2×D4—1721no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—861no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—1721no—
480C22×C4—1721no—
481C22×C4—1721no—
482C22×C4—1721no—
483C22×C4C2×C4×D4311yescharacteristic
484C22×C4C2×D17211yescharacteristic
485C22×C4#1062189811yescharacteristic
486C22×C4#1062189811yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4D4×D4311yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4#1062190011yescharacteristic
491C22×C4Q8×D4311yescharacteristic
492C22×C4#1062190211yescharacteristic
493C22×C4#1062190211yescharacteristic
494C22×C4#1062190211yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497M16—862no—
498M16—862no—
499M16—862no—
500M16—862no—
501M16—1721no—
502M16—1721no—
503M16—1721no—
504M16—1721no—
505C2×C8—862no—
506C2×C8—862no—
507C2×C8—1721no—
508C2×C8—1721no—
509C2×C8—1721no—
510C2×C8—1721no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—416no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C22⋊C4—3444no—
523C22⋊C4—1721no—
524C22⋊C4—1721no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—1721no—
529C42—1721no—
530C42(C2×D43)⋊C414yescomplemented
531C23—22no—
532C23—22no—
533C23—862no—
534C23—1721no—
535C23—1722no—
536C23—1721no—
537C23—1722no—
538C23C4×C22⋊D4311yescharacteristic
539C23#1306329311yescharacteristic
540C23#1306329411yescharacteristic
541C23#1306329711yescharacteristic
542C23#1306329911yescharacteristic
543C23#1306330111yescharacteristic
544C23#1306331411yescharacteristic
545Q8—862no—
546Q8—862no—
547Q8—1721no—
548Q8—1721no—
549D4—862no—
550D4—862no—
551D4—1722no—
552D4—1722no—
553D4—1722no—
554D4—1722no—
555D4—1721no—
556D4—1721no—
557C2×C4—24no—
558C2×C4—28no—
559C2×C4—28no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—44no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—862no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4C2×(C2×D43)⋊C411yescharacteristic
581C2×C4C4⋊C4×D4311yescharacteristic
582C2×C4#1306328311yescharacteristic
583C2×C4C4×C22⋊D4311yescharacteristic
584C2×C4#1306328711yescharacteristic
585C2×C4#1306328711yescharacteristic
586C2×C4#1306329311yescharacteristic
587C2×C4#1306329611yescharacteristic
588C2×C4#1306329711yescharacteristic
589C2×C4#1306329911yescharacteristic
590C2×C4#1306330011yescharacteristic
591C2×C4#1306330011yescharacteristic
592C2×C4#1306330011yescharacteristic
593C2×C4#1306330111yescharacteristic
594C2×C4#1306330111yescharacteristic
595C2×C4#1306330311yescharacteristic
596C2×C4#1306330311yescharacteristic
597C2×C4#1306330511yescharacteristic
598C2×C4#1306330811yescharacteristic
599C2×C4#1306331011yescharacteristic
600C2×C4#1306331011yescharacteristic
601C2×C4#1306331011yescharacteristic
602C2×C4#1306331011yescharacteristic
603C2×C4#1306331411yescharacteristic
604C2×C4#1306331411yescharacteristic
605C2×C4#1306332011yescharacteristic
606C2×C4#1306332011yescharacteristic
607C2×C4#1306332111yescharacteristic
608C8—1722no—
609C8—1722no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—3442no—
619C22—3441no—
620C22—3441no—
621C22—1724no—
622C22—1722no—
623C22#1458277011yescharacteristic
624C22#1458277811yescharacteristic
625C22#1458278911yescharacteristic
626C22#1458280711yescharacteristic
627C22#1458281011yescharacteristic
628C22#1458281611yescharacteristic
629C22#1458282111yescharacteristic
630C22#1458306612yes—
631C22#1458308112yes—
632C4—28no—
633C4—82no—
634C4—82no—
635C4—3442no—
636C4—1722no—
637C4#1458275611yescharacteristic
638C4#1458277011yescharacteristic
639C4#1458278911yescharacteristic
640C4#1458280011yescharacteristic
641C4#1458281611yescharacteristic
642C4#1458282111yescharacteristic
643C4#1458282511yescharacteristic
644C4#1458283411yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—3442no—
650C2#1913283711yescharacteristic
651C2#1913482012yes—
652C2#1913561011yescharacteristic
653C2#1913563111yescharacteristic
654C2#1913581912yes—
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#384C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#384D43
hypocenterC43#11078
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
4. C2×#14582668C2semidirect
5. #19134314C2semidirect
6. C2×#14582659C2semidirect
7. C2×C43×#384C2semidirect
14. C2×#13063253C4semidirect
156. C2×D172C4⋊C4semidirect
168. C2×Dic86C4⋊C4semidirect
181. C42×C43C22⋊C4semidirect
321. C2×#384D43semidirect
359. C43#11078semidirect
530. C42(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130632532
C2×#145828982
#191371882
C2×#145826682
#191343142
C2×#145826592
C2×C43×#3842
#1107843