Finite Group Databasebeta

← #25003723

Subgroups — #25003723

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×#13063251C211yesmaximal, characteristic
2C2×#14582898C211yesmaximal, characteristic
3#19137183C211yesmaximal, characteristic
4C2×#14582768C211yesmaximal, characteristic, complemented
5C2×#14582667C211yesmaximal, characteristic, complemented
6C2×#14582658C211yesmaximal, characteristic, complemented
7C43×#1736C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×Dic43⋊C4—22no—
12C22×C4×Dic43C2211yescharacteristic
13C2×#13063251—22no—
14C2×#13063251—22no—
15C2×#13063251C414yescomplemented
16#14582898—22no—
17#14582898—22no—
18C2×#13063248—21no—
19C2×#13063245—21no—
20#14582805—21no—
21#14582801—21no—
22#14582776—22no—
23#14582768—22no—
24#14582768—22no—
25#14582756—22no—
26#14582667—22no—
27#14582658—22no—
28C22×M16×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C22×C4⋊C4×C43C2211yescharacteristic
31C43×#340—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—
47C23×Dic43—21no—
48C23×Dic43D412yes—
49C22×C4×D43—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877D412yes—
56C22×C43⋊C8—21no—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×Dic43⋊C4—28no—
64C2×Dic43⋊C4—48no—
65C2×(C2×D43)⋊C4—24no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43—21no—
68C2×C4×Dic43—21no—
69C2×C4×Dic43C2×C412yes—
70C2×C4×Dic43D412yes—
71C2×C4×Dic43D412yes—
72#13063251—28no—
73#13063248—24no—
74#13063245—24no—
75C43⋊#95—24no—
76C23×C4×C43—21no—
77C23×C4×C43C2311yescharacteristic
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43C2×C412yes—
84C22×C8×C43—21no—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43—21no—
88#117×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43D412yes—
95C2×C4⋊C4×C43D412yes—
96C2×C22⋊C4×C43—21no—
97C2×C42×C43—21no—
98C24×C43C2×D411yescharacteristic
99C23×D43—21no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—44no—
103C22×C4×C43—41no—
104C22×C4×C43—41no—
105C22×C4×C43C22×C411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×Q811yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C2×C22⋊D43—22no—
120C2×C22⋊D43—22no—
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C2×C22⋊D43—41no—
125C22×Dic43—24no—
126C22×Dic43—24no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—21no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—44no—
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
169M16×C43—22no—
170M16×C43—22no—
171M16×C43—41no—
172M16×C43—41no—
173C2×C8×C43—22no—
174C2×C8×C43—41no—
175C2×C8×C43—41no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—41no—
185C42×C43—41no—
186(C2×D43)⋊C4—84no—
187C4⋊Dic43—41no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43—41no—
191Dic43⋊C4—416no—
192C4×Dic43—22no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43C22⋊C414yescomplemented
196#10621877—22no—
197#10621877—22no—
198#10621877—41no—
199#10621877—41no—
200C2×C43⋊C8—22no—
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—44no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—82no—
223C2×C4×C43—82no—
224C2×C4×C43C2×C22⋊C411yescharacteristic
225C2×C4×C43C2×C4⋊C411yescharacteristic
226C2×C4×C43#11711yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43C4×D411yescharacteristic
230C2×C4×C43#12011yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43C22⋊Q811yescharacteristic
238C2×C4×C43C22⋊Q811yescharacteristic
239C2×C4×C43C22⋊Q811yescharacteristic
240C2×C4×C43C22⋊Q811yescharacteristic
241C2×C4×C43C22⋊Q811yescharacteristic
242C2×C4×C43#12311yescharacteristic
243C2×C4×C43#12311yescharacteristic
244C2×C4×C43#12311yescharacteristic
245C2×C4×C43#12311yescharacteristic
246C2×C4×C43#12311yescharacteristic
247C2×C4×C43#12411yescharacteristic
248C2×C4×C43#12411yescharacteristic
249C2×C4×C43#12611yescharacteristic
250C2×C4×C43#12611yescharacteristic
251C2×C4×C43#12711yescharacteristic
252C22⋊D43—42no—
253C22⋊D43—42no—
254C22⋊D43—42no—
255C22⋊D43—42no—
256C2×Dic43—24no—
257C2×Dic43—28no—
258C2×Dic43—24no—
259C2×Dic43—28no—
260C2×Dic43—24no—
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—44no—
265C2×Dic43—42no—
266C2×Dic43—44no—
267C2×Dic43—82no—
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—
280C8×C43—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—82no—
306C4×C43—82no—
307C4×C43#38011yescharacteristic
308C4×C43#38511yescharacteristic
309C4×C43#38811yescharacteristic
310C4×C43#39011yescharacteristic
311C4×C43#39411yescharacteristic
312C4×C43#39611yescharacteristic
313C4×C43#39711yescharacteristic
314C4×C43#39911yescharacteristic
315Dic43—28no—
316Dic43—42no—
317Dic43—82no—
318C22×#104—431no—
319C2×#417—431no—
320#2311—431no—
321C2×#384—431no—
322C2×#343—431no—
323#1736D4311yescharacteristic, complemented
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×M16C2×D4311yescharacteristic
338C2×#117C2×D4311yescharacteristic
339C22×C4⋊C4—431no—
340C22×C4⋊C4—862no—
341C22×C4⋊C4C2×D4311yescharacteristic
342C22×C42—431no—
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—862no—
354#384—862no—
355#380—862no—
356#343—862no—
357#340—22no—
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—432no—
377C23×C4—861no—
378C23×C4—861no—
379C23×C4C22×D4311yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—432no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16—861no—
390C2×M16—861no—
391C2×M16C4×D4312yes—
392C22×C8—21no—
393C22×C8—861no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—868no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—1728no—
411C2×C4⋊C4D17212yes—
412C2×C4⋊C4C22⋊D4312yes—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—864no—
415C2×C42—21no—
416C2×C42—432no—
417C2×C42—432no—
418C2×C42—432no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422#104—868no—
423#103—864no—
424#102—864no—
425#95—864no—
426C24—861no—
427C24D4×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—22no—
463C22×C4—22no—
464C22×C4—44no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—864no—
468C22×C4—864no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—861no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—1724no—
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×C4#1062189811yescharacteristic
488C22×C4#1062189811yescharacteristic
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4D4×D4311yescharacteristic
493C22×C4#1062190011yescharacteristic
494C22×C4Q8×D4311yescharacteristic
495C22×C4#1062190211yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497M16—22no—
498M16—22no—
499M16—41no—
500M16—41no—
501M16—862no—
502M16—862no—
503M16—1721no—
504M16—1721no—
505C2×C8—22no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—862no—
509C2×C8—1721no—
510C2×C8—1721no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—17216no—
518C4⋊C4—1721no—
519C4⋊C4—1721no—
520C4⋊C4—1721no—
521C4⋊C4—1721no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—3444no—
525C42—41no—
526C42—41no—
527C42—434no—
528C42—862no—
529C42—862no—
530C42—862no—
531C23—22no—
532C23—22no—
533C23—862no—
534C23—1721no—
535C23—1722no—
536C23—1721no—
537C23—1722no—
538C23#1306328711yescharacteristic
539C23#1306329311yescharacteristic
540C23#1306329511yescharacteristic
541C23#1306329811yescharacteristic
542C23#1306329811yescharacteristic
543C23#1306330311yescharacteristic
544C23#1306331111yescharacteristic
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—44no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—864no—
565C2×C4—868no—
566C2×C4—868no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—862no—
570C2×C4—3442no—
571C2×C4—1724no—
572C2×C4—1722no—
573C2×C4—1724no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4C22⋊C4×D4311yescharacteristic
581C2×C4C4⋊C4×D4311yescharacteristic
582C2×C4#1306328211yescharacteristic
583C2×C4(C22⋊D43)⋊C411yescharacteristic
584C2×C4C4×C22⋊D4311yescharacteristic
585C2×C4C4×D17211yescharacteristic
586C2×C4#1306329511yescharacteristic
587C2×C4#1306329711yescharacteristic
588C2×C4#1306329811yescharacteristic
589C2×C4#1306329811yescharacteristic
590C2×C4#1306329811yescharacteristic
591C2×C4#1306329911yescharacteristic
592C2×C4#1306330011yescharacteristic
593C2×C4#1306330111yescharacteristic
594C2×C4#1306330311yescharacteristic
595C2×C4#1306330311yescharacteristic
596C2×C4#1306330311yescharacteristic
597C2×C4#1306330511yescharacteristic
598C2×C4#1306330711yescharacteristic
599C2×C4#1306330811yescharacteristic
600C2×C4#1306331011yescharacteristic
601C2×C4#1306331011yescharacteristic
602C2×C4#1306331011yescharacteristic
603C2×C4#1306331111yescharacteristic
604C2×C4#1306331311yescharacteristic
605C2×C4#1306331911yescharacteristic
606C2×C4#1306332011yescharacteristic
607C2×C4#1306332111yescharacteristic
608C8—42no—
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#1458277711yescharacteristic
625C22#1458278811yescharacteristic
626C22#1458280811yescharacteristic
627C22#1458281211yescharacteristic
628C22#1458281411yescharacteristic
629C22#1458282311yescharacteristic
630C22#1458306512yes—
631C22#1458308012yes—
632C4—82no—
633C4—82no—
634C4—868no—
635C4—3442no—
636C4—1722no—
637C4#1458275811yescharacteristic
638C4#1458277311yescharacteristic
639C4#1458279011yescharacteristic
640C4#1458279911yescharacteristic
641C4#1458281711yescharacteristic
642C4#1458282111yescharacteristic
643C4#1458282811yescharacteristic
644C4#1458283411yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—3442no—
650C2#1913283911yescharacteristic
651C2#1913481812yes—
652C2#1913561111yescharacteristic
653C2#1913563211yescharacteristic
654C2#1913581712yes—
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1736C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenter#1736D43
hypocenterC43#11078
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. C2×#14582768C2semidirect
5. C2×#14582667C2semidirect
6. C2×#14582658C2semidirect
7. C43×#1736C2semidirect
15. C2×#13063251C4semidirect
156. C2×D172C4⋊C4semidirect
168. C2×Dic86C4⋊C4semidirect
195. C4×Dic43C22⋊C4semidirect
323. #1736D43semidirect
359. C43#11078semidirect

Maximal subgroups

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

subgroupindex
C22×#130632512
C2×#145828982
#191371832
C2×#145827682
C2×#145826672
C2×#145826582
C43×#17362
#1107843