Finite Group Databasebeta

← #25004433

Subgroups — #25004433

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582901C211yesmaximal, characteristic
2C2×#14582898C211yesmaximal, characteristic
3C2×#14582867C211yesmaximal, characteristic
4C2×#14582667C211yesmaximal, characteristic, complemented
5C2×#14582663C211yesmaximal, characteristic, complemented
6C2×#14582661C211yesmaximal, characteristic, complemented
7C2×C43×#343C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C23×C43⋊C8C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12#14582901—22no—
13#14582901—22no—
14#14582898—22no—
15#14582898C414yescomplemented
16C2×#13063250—21no—
17C2×#13063248—21no—
18C2×#13063247—21no—
19C2×#13063245—21no—
20#14582867—22no—
21#14582867—22no—
22C2×(C2×D43)⋊C8—22no—
23#14582667—22no—
24#14582663—22no—
25#14582661—22no—
26C22×M16×C43C2211yescharacteristic
27C22×M16×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C43×#343—22no—
30C2×#10621898—21no—
31C2×#10621898—21no—
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×#10621898C2×C412yes—
41C2×#10621898D412yes—
42C22×Dic86D411yescharacteristic
43C22×D172D411yescharacteristic
44C22×C22⋊D43—21no—
45C23×Dic43—21no—
46C22×C4×D43—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877C2×C412yes—
53C22×C43⋊C8—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59C22×C43⋊C8—21no—
60C22×C43⋊C8D412yes—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D412yes—
67#13063250—24no—
68#13063248—24no—
69#13063247—24no—
70#13063245—24no—
71(C2×D43)⋊C8—28no—
72C23×C4×C43—21no—
73C23×C4×C43C2311yescharacteristic
74C2×M16×C43—21no—
75C2×M16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C2×M16×C43—21no—
79C2×M16×C43—21no—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43D412yes—
85C2×M16×C43D412yes—
86C22×C8×C43—21no—
87C22×C8×C43—21no—
88C2×C4⋊C4×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×C43C2×C412yes—
94C24×C43#4111yescharacteristic
95C23×D43—21no—
96C22×C4×C43—22no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—81no—
100C22×C4×C43—81no—
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C2×C22⋊D43—22no—
116C2×C22⋊D43—22no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121C22×Dic43—21no—
122C22×Dic43—22no—
123C22×Dic43—41no—
124C22×Dic43—41no—
125C22×Dic43—81no—
126C22×Dic43—81no—
127#10621898—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—22no—
131#10621898—22no—
132#10621898—22no—
133#10621898—22no—
134#10621898—22no—
135#10621898—41no—
136#10621898—41no—
137#10621898—41no—
138#10621898—41no—
139#10621898—41no—
140#10621898—41no—
141#10621898—41no—
142#10621898—41no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172C22⋊C412yes—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—41no—
152C2×C4×D43—41no—
153C2×C4×D43—41no—
154C2×C4×D43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86C22⋊C412yes—
161M16×C43—22no—
162M16×C43—22no—
163M16×C43—22no—
164M16×C43—22no—
165M16×C43—41no—
166M16×C43—41no—
167M16×C43—41no—
168M16×C43—41no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43—41no—
172C2×C8×C43—41no—
173C2×C8×C43—41no—
174C2×C8×C43—41no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43—41no—
182C4⋊Dic43—41no—
183#10621877—22no—
184#10621877—22no—
185#10621877—41no—
186#10621877—41no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—41no—
192C2×C43⋊C8—41no—
193C2×C43⋊C8—41no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—41no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43C4×D411yescharacteristic
202C23×C43#12111yescharacteristic
203C23×C43#12311yescharacteristic
204C23×C43#12311yescharacteristic
205C23×C43#12411yescharacteristic
206C23×C43#12611yescharacteristic
207C23×C43#12611yescharacteristic
208C22×D43—22no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—82no—
217C2×C4×C43—81no—
218C2×C4×C43—81no—
219C2×C4×C43—82no—
220C2×C4×C43C2×C22⋊C411yescharacteristic
221C2×C4×C43#11711yescharacteristic
222C2×C4×C43#11711yescharacteristic
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12311yescharacteristic
236C2×C4×C43#12311yescharacteristic
237C2×C4×C43#12311yescharacteristic
238C2×C4×C43#12311yescharacteristic
239C2×C4×C43#12311yescharacteristic
240C2×C4×C43#12311yescharacteristic
241C2×C4×C43#12311yescharacteristic
242C2×C4×C43#12311yescharacteristic
243C2×C4×C43#12411yescharacteristic
244C2×C4×C43#12411yescharacteristic
245C2×C4×C43#12411yescharacteristic
246C2×C4×C43#12611yescharacteristic
247C2×C4×C43#12611yescharacteristic
248C22⋊D43—42no—
249C22⋊D43—42no—
250C22⋊D43—42no—
251C22⋊D43—42no—
252C2×Dic43—22no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256C2×Dic43—82no—
257C2×Dic43—81no—
258C2×Dic43—81no—
259C2×Dic43—82no—
260D172—22no—
261D172—22no—
262D172—41no—
263D172—41no—
264C4×D43—42no—
265C4×D43—42no—
266C4×D43—42no—
267C4×D43—42no—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272C8×C43—42no—
273C8×C43—42no—
274C43⋊C8—42no—
275C43⋊C8—42no—
276#11192—431nomaximal, Sylow
277C22×C43—21no—
278C22×C43—21no—
279C22×C43—21no—
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—21no—
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43#38611yescharacteristic
290C22×C43#38811yescharacteristic
291C22×C43#38811yescharacteristic
292C22×C43#39411yescharacteristic
293C22×C43#39711yescharacteristic
294C22×C43#39711yescharacteristic
295C22×C43#39711yescharacteristic
296C22×C43#47111yescharacteristic
297C22×C43#47111yescharacteristic
298C22×C43#47211yescharacteristic
299C22×C43#47311yescharacteristic
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C4×C43—82no—
308C4×C43#38111yescharacteristic
309C4×C43#38611yescharacteristic
310C4×C43#38811yescharacteristic
311C4×C43#38811yescharacteristic
312C4×C43#39411yescharacteristic
313C4×C43#39411yescharacteristic
314C4×C43#39411yescharacteristic
315C4×C43#39711yescharacteristic
316Dic43—42no—
317Dic43—82no—
318C2×#417—431no—
319C2×#417—431no—
320C2×#408—431no—
321C2×#343—431no—
322C2×#343D4311yescharacteristic, complemented
323C2×#341—431no—
324C2×#340—431no—
325C2×C43—21no—
326C2×C43—21no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43#144011yescharacteristic
330C2×C43#190711yescharacteristic
331C2×C43#190811yescharacteristic
332C2×C43#205111yescharacteristic
333C2×C43#205211yescharacteristic
334C2×C43#207811yescharacteristic
335C2×C43#207911yescharacteristic
336D43—82no—
337C22×#41—431no—
338C22×M16—431no—
339C22×M16C2×D4311yescharacteristic
340C22×M16C2×D4311yescharacteristic
341C23×C8—431no—
342C22×C4⋊C4—431no—
343C22×C4⋊C4C2×D4311yescharacteristic
344#417—434no—
345#417—862no—
346#417—862no—
347#417—862no—
348C2×#103—861no—
349C2×#103—861no—
350C2×#102—861no—
351C2×#102—861no—
352#408—862no—
353#408—862no—
354C2×C22⋊C8—862no—
355#343—22no—
356#343—862no—
357#341—862no—
358#340—862no—
359C43#1119211yescharacteristic, 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—861no—
377C23×C4—861no—
378C23×C4C22×D4311yescharacteristic
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16—432no—
390C2×M16—861no—
391C2×M16—861no—
392C2×M16—861no—
393C2×M16—861no—
394C2×M16—861no—
395C2×M16D17212yes—
396C2×M16C22⋊D4312yes—
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—432no—
400C22×C8—861no—
401C22×C8—861no—
402C22×C8—861no—
403C22×C8—861no—
404C22×C8—861no—
405C22×C8—861no—
406C22×C8—861no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—432no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C4×D4312yes—
419#103—864no—
420#103—864no—
421#102—864no—
422#102—864no—
423C22⋊C8—868no—
424C24—861no—
425C24#1062189811yescharacteristic
426#41—862no—
427#41—862no—
428#41—862no—
429#41—862no—
430#41—862no—
431#41—862no—
432#41—862no—
433#41—862no—
434#41—1721no—
435#41—1721no—
436#41—1721no—
437#41—1721no—
438#41—1721no—
439#41—1721no—
440#41—1721no—
441#41—1721no—
442C2×Q8—432no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×D4—432no—
449C2×D4—862no—
450C2×D4—862no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—1721no—
457C2×D4—1721no—
458C2×D4—1721no—
459C2×D4—1721no—
460C22×C4—22no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—81no—
464C22×C4—81no—
465C22×C4—861no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—3441no—
470C22×C4—3441no—
471C22×C4—1721no—
472C22×C4—1721no—
473C22×C4—1721no—
474C22×C4—1721no—
475C22×C4—1721no—
476C22×C4—1721no—
477C22×C4C2×C4×D4311yescharacteristic
478C22×C4C2×D17211yescharacteristic
479C22×C4#1062189811yescharacteristic
480C22×C4#1062189811yescharacteristic
481C22×C4#1062189811yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4D4×D4311yescharacteristic
486C22×C4#1062190011yescharacteristic
487C22×C4#1062190011yescharacteristic
488C22×C4#1062190211yescharacteristic
489C22×C4#1062190211yescharacteristic
490C22×C4C2×C22⋊D4311yescharacteristic
491M16—22no—
492M16—22no—
493M16—22no—
494M16—22no—
495M16—41no—
496M16—41no—
497M16—41no—
498M16—41no—
499M16—862no—
500M16—862no—
501M16—1721no—
502M16—1721no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—862no—
510C2×C8—862no—
511C2×C8—862no—
512C2×C8—862no—
513C2×C8—1721no—
514C2×C8—1721no—
515C2×C8—1721no—
516C2×C8—1721no—
517C2×C8—1721no—
518C2×C8—1721no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—862no—
524C4⋊C4—862no—
525C4⋊C4—1721no—
526C4⋊C4—1721no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—862no—
532C23—1721no—
533C23—1721no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23C4×C22⋊D4311yescharacteristic
539C23#1306329811yescharacteristic
540C23#1306330711yescharacteristic
541C23#1306331011yescharacteristic
542C23#1306331311yescharacteristic
543C23#1306331911yescharacteristic
544C23#1306332011yescharacteristic
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—42no—
558C2×C4—82no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—82no—
562C2×C4—862no—
563C2×C4—3442no—
564C2×C4—3441no—
565C2×C4—3441no—
566C2×C4—3442no—
567C2×C4—1722no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4C22⋊C4×D4311yescharacteristic
575C2×C4#1306328211yescharacteristic
576C2×C4#1306328311yescharacteristic
577C2×C4(C22⋊D43)⋊C411yescharacteristic
578C2×C4#1306328711yescharacteristic
579C2×C4C4×D17211yescharacteristic
580C2×C4#1306329311yescharacteristic
581C2×C4#1306329511yescharacteristic
582C2×C4#1306329611yescharacteristic
583C2×C4#1306329711yescharacteristic
584C2×C4#1306329811yescharacteristic
585C2×C4#1306329811yescharacteristic
586C2×C4#1306329911yescharacteristic
587C2×C4#1306330011yescharacteristic
588C2×C4#1306330011yescharacteristic
589C2×C4#1306330711yescharacteristic
590C2×C4#1306330711yescharacteristic
591C2×C4#1306330811yescharacteristic
592C2×C4#1306330911yescharacteristic
593C2×C4#1306331011yescharacteristic
594C2×C4#1306331011yescharacteristic
595C2×C4#1306331011yescharacteristic
596C2×C4#1306331011yescharacteristic
597C2×C4#1306331111yescharacteristic
598C2×C4#1306331111yescharacteristic
599C2×C4#1306331411yescharacteristic
600C2×C4#1306332011yescharacteristic
601C2×C4#1306332011yescharacteristic
602C8—42no—
603C8—42no—
604C8—1722no—
605C8—1722no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—3441no—
619C22—3441no—
620C22—3441no—
621C22—3441no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22#1458277511yescharacteristic
626C22#1458278911yescharacteristic
627C22#1458279011yescharacteristic
628C22#1458281711yescharacteristic
629C22#1458282611yescharacteristic
630C22#1458282811yescharacteristic
631C22#1458282811yescharacteristic
632C22#1458316111yescharacteristic
633C22#1458316511yescharacteristic
634C22#1458316811yescharacteristic
635C22#1458317311yescharacteristic
636C4—82no—
637C4—3442no—
638C4—1722no—
639C4#1458276111yescharacteristic
640C4#1458277711yescharacteristic
641C4#1458278811yescharacteristic
642C4#1458279111yescharacteristic
643C4#1458281411yescharacteristic
644C4#1458281511yescharacteristic
645C4#1458281611yescharacteristic
646C4#1458282511yescharacteristic
647C2—21no—
648C2—21no—
649C2—21no—
650C2—21no—
651C2—3442no—
652C2#1913284311yescharacteristic
653C2#1913510011yescharacteristic
654C2#1913510711yescharacteristic
655C2#1913589011yescharacteristic
656C2#1913589711yescharacteristic
657C2#1913603911yescharacteristic
658C2#1913604411yescharacteristic
subgroupG/H
centerC23#13063298
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#343C2
socleC23×C43#121
prime radicalC22×#10621898C22
cosocleC23×C4×C43C23
hypercenterC2×#343D43
hypocenterC43#11192
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C2×#14582667C2semidirect
5. C2×#14582663C2semidirect
6. C2×#14582661C2semidirect
7. C2×C43×#343C2semidirect
15. #14582898C4semidirect
322. C2×#343D43semidirect
359. C43#11192semidirect

Maximal subgroups

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

subgroupindex
C2×#145829012
C2×#145828982
C2×#145828672
C2×#145826672
C2×#145826632
C2×#145826612
C2×C43×#3432
#1119243