Finite Group Databasebeta

← #25003728

Subgroups — #25003728

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063253C211yesmaximal, characteristic
2C2×#14582901C211yesmaximal, characteristic
3#19137183C211yesmaximal, characteristic
4C2×#14582765C211yesmaximal, characteristic, complemented
5C2×#14582667C211yesmaximal, characteristic, complemented
6#19134316C211yesmaximal, characteristic, complemented
7C2×C43×#339C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C2×#13063253—22no—
13C2×#13063253—22no—
14C2×#13063253C414yescomplemented
15#14582901—22no—
16#14582901—22no—
17C2×#13063250—21no—
18C2×#13063247—21no—
19#14582805—21no—
20#14582801—21no—
21#14582776—22no—
22#14582765—22no—
23#14582765—22no—
24#14582756—22no—
25C2×C43⋊#95—22no—
26#14582667—22no—
27#14582661—22no—
28C22×M16×C43C2211yescharacteristic
29C2×#117×C43C2211yescharacteristic
30C22×C42×C43C2211yescharacteristic
31C43×#339—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×#10621877C2×C412yes—
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×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43D412yes—
69C2×(C2×D43)⋊C4—24no—
70#13063253—28no—
71#13063250—24no—
72#13063247—24no—
73C43⋊#95—24no—
74C43⋊#95—28no—
75C23×C4×C43—21no—
76C23×C4×C43C2311yescharacteristic
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43D412yes—
83C22×C8×C43—21no—
84#117×C43—21no—
85#117×C43—21no—
86#117×C43—21no—
87#117×C43—21no—
88C2×C4⋊C4×C43D412yes—
89C2×C22⋊C4×C43—21no—
90C2×C42×C43—21no—
91C2×C42×C43—21no—
92C2×C42×C43—21no—
93C2×C42×C43—21no—
94C2×C42×C43C2×C412yes—
95C2×C42×C43D412yes—
96C2×C42×C43D412yes—
97C24×C43C2×D411yescharacteristic
98C23×D43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—42no—
104C22×C4×C43—42no—
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—21no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—44no—
131C22×Dic43—44no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134#10621898—22no—
135#10621898—22no—
136#10621898—22no—
137#10621898—22no—
138#10621898—22no—
139#10621898—22no—
140#10621898—22no—
141#10621898—22no—
142#10621898—41no—
143#10621898—41no—
144#10621898—41no—
145#10621898—41no—
146#10621898—41no—
147#10621898—41no—
148#10621898—41no—
149#10621898—41no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C4⋊C412yes—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—41no—
159C2×C4×D43—41no—
160C2×C4×D43—41no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86C4⋊C412yes—
168M16×C43—22no—
169M16×C43—22no—
170M16×C43—41no—
171M16×C43—41no—
172C2×C8×C43—22no—
173C2×C8×C43—41no—
174C2×C8×C43—41no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—22no—
180C42×C43—22no—
181C42×C43—22no—
182C42×C43—41no—
183C42×C43—41no—
184C42×C43C22⋊C414yescomplemented
185(C2×D43)⋊C4—84no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43—41no—
191C4⋊Dic43—41no—
192C4⋊Dic43—41no—
193C4⋊Dic43—41no—
194#10621877—22no—
195#10621877—22no—
196#10621877—41no—
197#10621877—41no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—41no—
200C2×C43⋊C8—41no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43C4×D411yescharacteristic
204C23×C43#12011yescharacteristic
205C23×C43#12011yescharacteristic
206C23×C43#12111yescharacteristic
207C23×C43#12111yescharacteristic
208C23×C43C22⋊Q811yescharacteristic
209C23×C43#12411yescharacteristic
210C22×D43—22no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—42no—
214C22×D43—42no—
215C2×C4×C43—24no—
216C2×C4×C43—44no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—44no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43C2×C22⋊C411yescharacteristic
224C2×C4×C43C2×C4⋊C411yescharacteristic
225C2×C4×C43#11711yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43#12011yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43C22⋊Q811yescharacteristic
237C2×C4×C43C22⋊Q811yescharacteristic
238C2×C4×C43C22⋊Q811yescharacteristic
239C2×C4×C43C22⋊Q811yescharacteristic
240C2×C4×C43C22⋊Q811yescharacteristic
241C2×C4×C43#12311yescharacteristic
242C2×C4×C43#12311yescharacteristic
243C2×C4×C43#12311yescharacteristic
244C2×C4×C43#12311yescharacteristic
245C2×C4×C43#12311yescharacteristic
246C2×C4×C43#12411yescharacteristic
247C2×C4×C43#12411yescharacteristic
248C2×C4×C43#12611yescharacteristic
249C2×C4×C43#12611yescharacteristic
250C2×C4×C43#12711yescharacteristic
251C22⋊D43—42no—
252C22⋊D43—42no—
253C22⋊D43—42no—
254C22⋊D43—42no—
255C2×Dic43—22no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—44no—
259C2×Dic43—44no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—44no—
263C2×Dic43—82no—
264C2×Dic43—82no—
265C2×Dic43—82no—
266D172—22no—
267D172—22no—
268D172—41no—
269D172—41no—
270C4×D43—42no—
271C4×D43—42no—
272C4×D43—42no—
273C4×D43—42no—
274Dic86—22no—
275Dic86—22no—
276Dic86—41no—
277Dic86—41no—
278C8×C43—42no—
279C43⋊C8—42no—
280#11079—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43#38511yescharacteristic
290C22×C43#38611yescharacteristic
291C22×C43#38811yescharacteristic
292C22×C43#39211yescharacteristic
293C22×C43#39311yescharacteristic
294C22×C43#39411yescharacteristic
295C22×C43#39611yescharacteristic
296C22×C43#45412yes—
297C22×C43#45512yes—
298C2×D43—44no—
299C2×D43—42no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—82no—
303C4×C43—44no—
304C4×C43—82no—
305C4×C43#38011yescharacteristic
306C4×C43#38511yescharacteristic
307C4×C43#38811yescharacteristic
308C4×C43#39011yescharacteristic
309C4×C43#39411yescharacteristic
310C4×C43#39611yescharacteristic
311C4×C43#39711yescharacteristic
312C4×C43#39911yescharacteristic
313Dic43—42no—
314Dic43—82no—
315Dic43—82no—
316C22×#104—431no—
317C2×#417—431no—
318#2311—431no—
319C2×#382—431no—
320C2×#343—431no—
321#1736—431no—
322C2×#339D4311yescharacteristic, complemented
323C2×C43—21no—
324C2×C43—21no—
325C2×C43—21no—
326C2×C43—21no—
327C2×C43#143911yescharacteristic
328C2×C43#186012yes—
329C2×C43#200311yescharacteristic
330C2×C43#200411yescharacteristic
331C2×C43#204012yes—
332D43—82no—
333C22×#41—431no—
334C22×M16—431no—
335C22×M16C2×D4311yescharacteristic
336C2×#117C2×D4311yescharacteristic
337C22×C4⋊C4—431no—
338C22×C4⋊C4—431no—
339C22×C42C2×D4311yescharacteristic
340C2×#104—434no—
341C2×#104—862no—
342C2×#104—862no—
343#417—862no—
344#417—862no—
345C2×#103—861no—
346C2×#102—861no—
347#391—861no—
348#390—861no—
349#386—862no—
350#382—862no—
351#382—862no—
352#380—862no—
353C2×#95—862no—
354#343—862no—
355#340—862no—
356#339—22no—
357C43#1107911yescharacteristic, complemented, Sylow
358C2×#41—432no—
359C2×#41—432no—
360C2×#41—861no—
361C2×#41—861no—
362C2×#41—861no—
363C2×#41—861no—
364C2×#41—861no—
365C2×#41—861no—
366C2×#41—861no—
367C2×#41—861no—
368C2×#41—861no—
369C2×#41—861no—
370C22×Q8—431no—
371C22×D4—431no—
372C22×D4—861no—
373C23×C4—21no—
374C23×C4—432no—
375C23×C4—861no—
376C23×C4—861no—
377C23×C4C22×D4311yescharacteristic
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—432no—
384C2×M16—861no—
385C2×M16—861no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16D17212yes—
390C22×C8—21no—
391C22×C8—861no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4D17212yes—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—864no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42C4×D4312yes—
416C2×C42D17212yes—
417C2×C42C22⋊D4312yes—
418#104—868no—
419#103—864no—
420#102—864no—
421#95—868no—
422#95—864no—
423C24—861no—
424C24D4×D4311yescharacteristic
425#41—862no—
426#41—862no—
427#41—862no—
428#41—862no—
429#41—862no—
430#41—862no—
431#41—862no—
432#41—862no—
433#41—1721no—
434#41—1721no—
435#41—1721no—
436#41—1721no—
437#41—1721no—
438#41—1721no—
439#41—1721no—
440#41—1721no—
441C2×Q8—432no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×D4—432no—
448C2×D4—862no—
449C2×D4—862no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—1721no—
456C2×D4—1721no—
457C2×D4—1721no—
458C2×D4—1721no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—861no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—1724no—
473C22×C4—1721no—
474C22×C4—1721no—
475C22×C4—1724no—
476C22×C4—1721no—
477C22×C4—1721no—
478C22×C4—1721no—
479C22×C4—1721no—
480C22×C4C2×C4×D4311yescharacteristic
481C22×C4C2×D17211yescharacteristic
482C22×C4C2×D17211yescharacteristic
483C22×C4C2×D17211yescharacteristic
484C22×C4#1062189811yescharacteristic
485C22×C4#1062189811yescharacteristic
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4#1062190011yescharacteristic
489C22×C4#1062190011yescharacteristic
490C22×C4#1062190011yescharacteristic
491C22×C4Q8×D4311yescharacteristic
492C22×C4#1062190211yescharacteristic
493C22×C4C2×C22⋊D4311yescharacteristic
494M16—22no—
495M16—22no—
496M16—41no—
497M16—41no—
498M16—862no—
499M16—862no—
500M16—1721no—
501M16—1721no—
502C2×C8—22no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—862no—
506C2×C8—1721no—
507C2×C8—1721no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—1721no—
513C4⋊C4—1721no—
514C4⋊C4—1721no—
515C4⋊C4—1721no—
516C4⋊C4—1721no—
517C4⋊C4—1721no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—3444no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—41no—
525C42—41no—
526C42(C2×D43)⋊C414yescomplemented
527C23—22no—
528C23—22no—
529C23—862no—
530C23—1721no—
531C23—1721no—
532C23—1722no—
533C23—1722no—
534C23(C22⋊D43)⋊C411yescharacteristic
535C23#1306329511yescharacteristic
536C23#1306329511yescharacteristic
537C23#1306329711yescharacteristic
538C23#1306330011yescharacteristic
539C23#1306330311yescharacteristic
540C23#1306331111yescharacteristic
541Q8—862no—
542Q8—862no—
543Q8—1721no—
544Q8—1721no—
545D4—862no—
546D4—862no—
547D4—1722no—
548D4—1722no—
549D4—1722no—
550D4—1722no—
551D4—1721no—
552D4—1721no—
553C2×C4—24no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—862no—
562C2×C4—3442no—
563C2×C4—3442no—
564C2×C4—3442no—
565C2×C4—1724no—
566C2×C4—1724no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1724no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4C2×(C2×D43)⋊C411yescharacteristic
577C2×C4C4⋊C4×D4311yescharacteristic
578C2×C4#1306328311yescharacteristic
579C2×C4(C22⋊D43)⋊C411yescharacteristic
580C2×C4C4×D17211yescharacteristic
581C2×C4C4×D17211yescharacteristic
582C2×C4#1306329511yescharacteristic
583C2×C4#1306329611yescharacteristic
584C2×C4#1306329711yescharacteristic
585C2×C4#1306329911yescharacteristic
586C2×C4#1306329911yescharacteristic
587C2×C4#1306330011yescharacteristic
588C2×C4#1306330011yescharacteristic
589C2×C4#1306330111yescharacteristic
590C2×C4#1306330311yescharacteristic
591C2×C4#1306330511yescharacteristic
592C2×C4#1306330511yescharacteristic
593C2×C4#1306330511yescharacteristic
594C2×C4#1306330711yescharacteristic
595C2×C4#1306330711yescharacteristic
596C2×C4#1306330911yescharacteristic
597C2×C4#1306330911yescharacteristic
598C2×C4#1306330911yescharacteristic
599C2×C4#1306331111yescharacteristic
600C2×C4#1306331311yescharacteristic
601C2×C4#1306332011yescharacteristic
602C2×C4#1306332011yescharacteristic
603C2×C4#1306332211yescharacteristic
604C8—42no—
605C8—1722no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—3442no—
615C22—3441no—
616C22—3441no—
617C22—1724no—
618C22—1722no—
619C22#1458277311yescharacteristic
620C22#1458277611yescharacteristic
621C22#1458279111yescharacteristic
622C22#1458280911yescharacteristic
623C22#1458281211yescharacteristic
624C22#1458281511yescharacteristic
625C22#1458282111yescharacteristic
626C22#1458307312yes—
627C22#1458307812yes—
628C4—44no—
629C4—82no—
630C4—3442no—
631C4—3442no—
632C4—1722no—
633C4#1458275611yescharacteristic
634C4#1458277311yescharacteristic
635C4#1458279111yescharacteristic
636C4#1458280111yescharacteristic
637C4#1458281511yescharacteristic
638C4#1458282111yescharacteristic
639C4#1458282611yescharacteristic
640C4#1458283611yescharacteristic
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—3442no—
646C2#1913284111yescharacteristic
647C2#1913482912yes—
648C2#1913562011yescharacteristic
649C2#1913562711yescharacteristic
650C2#1913582312yes—
subgroupG/H
centerC23#13063295
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#339C2
socleC23×C43#120
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#339D43
hypocenterC43#11079
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#14582765C2semidirect
5. C2×#14582667C2semidirect
6. #19134316C2semidirect
7. C2×C43×#339C2semidirect
14. C2×#13063253C4semidirect
184. C42×C43C22⋊C4semidirect
322. C2×#339D43semidirect
357. C43#11079semidirect
526. 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×#145829012
#191371832
C2×#145827652
C2×#145826672
#191343162
C2×C43×#3392
#1107943