Finite Group Databasebeta

← #25063485

Subgroups — #25063485

Order 11008.

970 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148190C211yesmaximal, characteristic
2#19143551C211yesmaximal, characteristic, complemented
3#19143263C211yesmaximal, characteristic, complemented
4#19133054C212yesmaximal, complemented
5#19133045C211yesmaximal, characteristic, complemented
6#19133028C212yesmaximal, complemented
7#19133002C212yesmaximal, complemented
8#19132995C211yesmaximal, characteristic, complemented
9#19132976C212yesmaximal, complemented
10C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
11C43×#1487C211yesmaximal, characteristic, complemented
12#14583634—21no—
13#14583634C411yescharacteristic
14#14583628C411yescharacteristic
15#14583622—21no—
16#14583622C411yescharacteristic
17#14583597—22no—
18#14583597C412yes—
19#14583571C411yescharacteristic
20#14583560C412yes—
21#14583449—21no—
22#14583449C2211yescharacteristic
23#14583436—22no—
24#14583436C2212yes—
25C4×#10621902C2212yes—
26C4×#10621898—21no—
27C4×#10621898C2211yescharacteristic
28#14583023—21no—
29#14582964—21no—
30(C22⋊D43)⋊C8—22no—
31#14582959—22no—
32#14582955C2212yes—
33#14582951C2212yes—
34#14582950C2212yes—
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36#14582867—21no—
37#14582857—21no—
38C2×C4×C43⋊C8C2211yescharacteristic
39C4×C8×D43C2212yes—
40Q8⋊(C43⋊C8)C2211yescharacteristic
41Q8⋊(C43⋊C8)C2211yescharacteristic
42Q8⋊(C43⋊C8)C2211yescharacteristic
43Q8⋊(C43⋊C8)C2211yescharacteristic
44#14582628C2212yes—
45#14582628C2212yes—
46#14582626C2212yes—
47#14582626C2212yes—
48C2×C4×Q8×C43C2211yescharacteristic
49C43×#431C2211yescharacteristic
50C43×#423C2211yescharacteristic
51C43×Q8⋊C8C2212yes—
52C43×Q8⋊C8C2212yes—
53C2×#10621902C2×C412yes—
54C2×#10621898—21no—
55C2×#10621898D411yescharacteristic
56C22×C43⋊C8—21no—
57C22×C43⋊C8—21no—
58C2×C8×D43—22no—
59#13063325—21no—
60#13063325C2×C411yescharacteristic
61#13063322—21no—
62#13063322C2×C411yescharacteristic
63#13063320—22no—
64#13063320—22no—
65#13063320—22no—
66#13063316—22no—
67#13063316C2×C412yes—
68#13063314—22no—
69#13063314C2×C412yes—
70#13063313—21no—
71#13063313—21no—
72#13063313—21no—
73#13063310—22no—
74#13063310—22no—
75#13063310—22no—
76#13063301—22no—
77#13063301C2×C412yes—
78#13063300—22no—
79#13063300C2×C412yes—
80#13063299—21no—
81#13063299—22no—
82#13063299—22no—
83#13063299C2×C412yes—
84Q8×Dic43C2×C412yes—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86C2×C411yescharacteristic
88C4×Dic86D411yescharacteristic
89C4×D172—22no—
90C4×D172—22no—
91C4×D172—21no—
92C4×D172—21no—
93C4×D172—21no—
94C4×D172C2×C411yescharacteristic
95C4×D172D411yescharacteristic
96C4×D172C2312yes—
97#13063287—22no—
98#13063287C2×C412yes—
99C4×C22⋊D43—22no—
100C4×C22⋊D43—22no—
101C4×C22⋊D43C2×C412yes—
102C4×C22⋊D43D412yes—
103#13063284D411yescharacteristic
104#13063283—22no—
105#13063283C2×C412yes—
106#13063282—22no—
107#13063282D412yes—
108C42×D43—22no—
109C42×D43C2312yes—
110C4⋊(C43⋊C8)—21no—
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113Dic43⋊C8—22no—
114(C2×D43)⋊C8—22no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117#13063235—22no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8C2311yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C8×Dic43—22no—
122C8×Dic43—22no—
123C22×Q8×C43C2×C411yescharacteristic
124C2×M16×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2×C411yescharacteristic
128C4×Q8×C43C2×C411yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2312yes—
138C22⋊C8×C43—21no—
139C4×C8×C43C2312yes—
140C2×Q8×C43—21no—
141C2×Q8×C43—22no—
142C2×Q8×C43—41no—
143C2×Q8×C43C22×C411yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C2×C22⋊D43—22no—
151C2×C22⋊D43C22⋊C412yes—
152#10621902—24no—
153#10621902—42no—
154#10621898—22no—
155#10621898—22no—
156#10621898—42no—
157#10621898—42no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—22no—
161C2×D172—22no—
162C2×D172C22⋊C411yescharacteristic
163C2×D172C22×C412yes—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43C22×C412yes—
168C2×C4×D43C2×D412yes—
169C2×C4×D43C2×D412yes—
170C2×Dic86—21no—
171C2×Dic86C22⋊C411yescharacteristic
172M16×C43—42no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C22×C411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2411yescharacteristic
190C22⋊Dic43C22⋊C412yes—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4C22⋊C412yes—
200(C2×D43)⋊C4C22⋊C412yes—
201C4⋊Dic43—21no—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43C22⋊C411yescharacteristic
205C4⋊Dic43C22⋊C411yescharacteristic
206C4⋊Dic43C22×C412yes—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4C22⋊C412yes—
210Dic43⋊C4C22⋊C412yes—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43C22×C412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43C2×D412yes—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—42no—
221C2×C43⋊C8—42no—
222C8×D43—44no—
223C23×C43C2×C22⋊C411yescharacteristic
224C22×D43—22no—
225C22×D43C2×C22⋊C412yes—
226Q8×C43—21no—
227Q8×C43—21no—
228Q8×C43—21no—
229Q8×C43—42no—
230Q8×C43#13112yes—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—81no—
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43#13512yes—
244C2×C4×C43#13512yes—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C22⋊D43—24no—
249C22⋊D43—44no—
250C2×Dic43—22no—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43C2×C22⋊C412yes—
253C2×Dic43C2×C22⋊C412yes—
254D172—22no—
255D172—22no—
256D172—22no—
257D172—44no—
258D172—42no—
259D172—81no—
260D172—82no—
261C4×D43—22no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—42no—
266C4×D43—44no—
267C4×D43—42no—
268C4×D43—42no—
269C4×D43—82no—
270Dic86—22no—
271Dic86—42no—
272C8×C43—42no—
273C8×C43—42no—
274C43⋊C8—22no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#17510—431nomaximal, Sylow
279C22×C43—21no—
280C22×C43—21no—
281C22×C43#41612yes—
282C22×C43C22×C22⋊C411yescharacteristic
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—22no—
286C2×D43—42no—
287C2×D43—42no—
288C2×D43—42no—
289C4×C43—22no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43#41612yes—
297C4×C43C2×#13111yescharacteristic
298C4×C43#56811yescharacteristic
299C4×C43C2×#13511yescharacteristic
300C4×C43C2×#13511yescharacteristic
301Dic43—22no—
302Dic43—22no—
303Dic43—22no—
304Dic43—42no—
305#3480—431no—
306C8×#41—431no—
307#2925—431no—
308#1494—432no—
309#1492—431no—
310#1488—432no—
311#1487D4311yescharacteristic, complemented
312#1482—432no—
313#1480—431no—
314#1476—432no—
315C2×Q8⋊C8—431no—
316C2×C43—22no—
317C2×C43#288011yescharacteristic
318C2×C43C2×#41611yescharacteristic
319C2×C43#290111yescharacteristic
320D43—42no—
321D43—82no—
322#559—431no—
323#559—861no—
324#557—431no—
325#556—431no—
326#556—861no—
327#553—432no—
328#553—862no—
329#550—431no—
330#548—432no—
331#532—431no—
332#532—861no—
333#529—432no—
334#529—862no—
335C4×#41—431no—
336C4×#41—432no—
337C4×#41—861no—
338C2×C4×Q8C2×D4311yescharacteristic
339C8×Q8—861no—
340C8×D4—862no—
341C8×D4—861no—
342#433—862no—
343#432—432no—
344#431—432no—
345#431—432no—
346#431C2×D4311yescharacteristic
347#423C2×D4311yescharacteristic
348C2×C4⋊C8—431no—
349#408—861no—
350#405—861no—
351C2×C4×C8—431no—
352C2×C4×C8—432no—
353Q8⋊C8—431no—
354Q8⋊C8—431no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357Q8⋊C8C2×D4312yes—
358Q8⋊C8C2×D4312yes—
359D4⋊C8—432no—
360D4⋊C8—432no—
361D4⋊C8—432no—
362D4⋊C8—432no—
363C43#1751011yescharacteristic, complemented, Sylow
364C2×#41—431no—
365C2×#41—432no—
366C2×#41—861no—
367C22×Q8C4×D4311yescharacteristic
368C2×M16—21no—
369C22×C8—862no—
370C22×C8—861no—
371C22×C8—861no—
372C4⋊Q8—431no—
373C4⋊Q8—861no—
374#127—431no—
375#127—861no—
376#126—862no—
377#126—862no—
378#126—862no—
379#125—432no—
380#125—862no—
381#124—432no—
382#124—861no—
383#124—861no—
384#124—862no—
385#124—861no—
386#123—862no—
387#123—862no—
388#123—862no—
389C22⋊Q8—432no—
390C22⋊Q8—862no—
391#121—432no—
392#121—432no—
393#121—862no—
394#121—862no—
395#121—862no—
396#121—861no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—431no—
400C4×Q8—431no—
401C4×Q8—432no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×Q8C4×D4311yescharacteristic
405C4×Q8C4×D4311yescharacteristic
406C4×Q8C22×D4311yescharacteristic
407C4×Q8C22×D4311yescharacteristic
408C4×D4—432no—
409C4×D4—432no—
410C4×D4—432no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—432no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—861no—
422#117—431no—
423#117—432no—
424#117—432no—
425#117—862no—
426#117—862no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4C4×D4311yescharacteristic
429C2×C42—21no—
430C2×C42—432no—
431C2×C42—862no—
432C2×C42C22×D4311yescharacteristic
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8—431no—
436C4⋊C8—431no—
437C4⋊C8—862no—
438C4⋊C8—861no—
439C4⋊C8C22×D4312yes—
440C22⋊C8—21no—
441C22⋊C8—862no—
442C22⋊C8—862no—
443C22⋊C8—862no—
444#97—862no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—862no—
448C4×C8—862no—
449C4×C8—861no—
450C4×C8C22×D4312yes—
451#41—862no—
452#41—862no—
453#41—864no—
454#41—1722no—
455#41—1722no—
456#41—1722no—
457C2×Q8—21no—
458C2×Q8—22no—
459C2×Q8—41no—
460C2×Q8—431no—
461C2×Q8—861no—
462C2×Q8C2×C4×D4311yescharacteristic
463C2×Q8C2×C4×D4311yescharacteristic
464C2×D4—432no—
465C2×D4—431no—
466C2×D4—432no—
467C2×D4—862no—
468C2×D4—862no—
469C2×D4—862no—
470C2×D4—861no—
471C2×D4—861no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—432no—
475C22×C4—432no—
476C22×C4—432no—
477C22×C4—862no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4C2×C4×D4311yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483M16—42no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—1724no—
491C2×C8—1722no—
492C2×C8—1722no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—432no—
501C4⋊C4—432no—
502C4⋊C4—432no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—862no—
506C4⋊C4—862no—
507C4⋊C4—861no—
508C4⋊C4C2×C4×D4311yescharacteristic
509C4⋊C4C2×C4×D4311yescharacteristic
510C22⋊C4—432no—
511C22⋊C4—432no—
512C22⋊C4—432no—
513C22⋊C4—862no—
514C22⋊C4—862no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—432no—
526C42—432no—
527C42—432no—
528C42—862no—
529C42—862no—
530C42C2×C4×D4311yescharacteristic
531C42D4×D4311yescharacteristic
532C42D4×D4311yescharacteristic
533C42C23×D4311yescharacteristic
534C23—432no—
535C23—862no—
536C23C22⋊C4×D4311yescharacteristic
537Q8—21no—
538Q8—21no—
539Q8—21no—
540Q8—42no—
541Q8—862no—
542Q8—1722no—
543Q8#1306333312yes—
544D4—864no—
545D4—862no—
546D4—862no—
547D4—862no—
548D4—3441no—
549D4—3442no—
550D4—1724no—
551D4—1724no—
552D4—1722no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—81no—
562C2×C4—432no—
563C2×C4—432no—
564C2×C4—432no—
565C2×C4—862no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—862no—
570C2×C4—3442no—
571C2×C4—1722no—
572C2×C4—1724no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4C22⋊C4×D4311yescharacteristic
576C2×C4C22⋊C4×D4311yescharacteristic
577C2×C4C22⋊C4×D4311yescharacteristic
578C2×C4#1306334612yes—
579C2×C4#1306334812yes—
580C2×C4C22×C4×D4311yescharacteristic
581C2×C4C2×D4×D4311yescharacteristic
582C2×C4C2×D4×D4311yescharacteristic
583C8—42no—
584C8—42no—
585C8—862no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C22—21no—
590C22—21no—
591C22—862no—
592C22—862no—
593C22—862no—
594C22—1722no—
595C22—1722no—
596C22—1722no—
597C22#1458289412yes—
598C22C2×C22⋊C4×D4311yescharacteristic
599C4—21no—
600C4—22no—
601C4—21no—
602C4—21no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—862no—
607C4—862no—
608C4—862no—
609C4—1722no—
610C4#1458289412yes—
611C4C2×#1306333311yescharacteristic
612C4#1458366511yescharacteristic
613C4C2×#1306334611yescharacteristic
614C4C2×#1306334811yescharacteristic
615C2—22no—
616C2—3442no—
617C2—1722no—
618C2#1914304511yescharacteristic
619C2C2×#1458289411yescharacteristic
620C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1487C2
socleC22×C43C22×C22⋊C4
prime radical#19148190C2
cosocleC42×C43C24
hypercenter#1487D43
hypocenterC43#17510
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. #19143551C2semidirect
3. #19143263C2semidirect
4. #19133054C2semidirect
5. #19133045C2semidirect
6. #19133028C2semidirect
7. #19133002C2semidirect
8. #19132995C2semidirect
9. #19132976C2semidirect
10. C2×Q8⋊(C43⋊C8)C2semidirect
11. C43×#1487C2semidirect
311. #1487D43semidirect
363. C43#17510semidirect

Maximal subgroups

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

subgroupindex
#191481902
#191435512
#191432632
#191330542
#191330452
#191330282
#191330022
#191329952
#191329762
C2×Q8⋊(C43⋊C8)2
C43×#14872
#1751043