Finite Group Databasebeta

← #25097606

Subgroups — #25097606

Order 11008.

1458 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583379C211yesmaximal, characteristic
2C2×#14582941C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic
4C2×#14582896C211yesmaximal, characteristic
5#19137211C211yesmaximal, characteristic, complemented
6#19134866C212yesmaximal, complemented
7#19134859C212yesmaximal, complemented
8#19134852C212yesmaximal, complemented
9#19134845C212yesmaximal, complemented
10C2×#14582662C211yesmaximal, characteristic, complemented
11C43×#1729C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13#14583379—24no—
14#14583379—24no—
15C2×C4×Dic86C2212yes—
16C2×C4×D172C2212yes—
17C2×(C22⋊D43)⋊C4—22no—
18C2×#13063284C2211yescharacteristic
19C2×#13063283—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C2×C4⋊C4×D43—21no—
23#14582941—24no—
24C2×#13063259C2212yes—
25C2×#13063257C2212yes—
26#14582901C418yescomplemented
27#14582896—24no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2212yes—
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2212yes—
34#14582797C2212yes—
35#14582797C2212yes—
36#14582795—21no—
37#14582795—21no—
38#14582757—22no—
39#14582662C2212yes—
40#14582662C2212yes—
41C22×M16×C43C2211yescharacteristic
42C23×C8×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C43×#336C2212yes—
45C43×#336C2212yes—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898C2×C414yes—
50C2×#10621898D414yes—
51C2×#10621898Q814yes—
52C22×Dic86C2311yescharacteristic
53C22×D172C2311yescharacteristic
54C22×C22⋊D43—21no—
55C23×Dic43—21no—
56C23×Dic43—21no—
57C22×C4×D43—21no—
58C22×C4×D43—22no—
59C4×Dic86—24no—
60C4×Dic86—24no—
61C4×D172—24no—
62C4×D172—24no—
63(C22⋊D43)⋊C4—216no—
64#13063284—22no—
65#13063284—22no—
66#13063283—28no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—22no—
70C2×C4⋊Dic43—22no—
71C2×C4⋊Dic43C2×C414yescomplemented
72C2×C4⋊Dic43D414yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2312yes—
76C2×C4⋊Dic43C2312yes—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—22no—
80C4⋊C4×D43—28no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×C4×Dic43—22no—
84C2×C4×Dic43—21no—
85#13063259—24no—
86#13063257—24no—
87#13063250—22no—
88#13063250—22no—
89#13063250C2×C418yescomplemented
90#13063247—22no—
91#13063247—22no—
92#13063247C2×C418yescomplemented
93C43⋊#95—22no—
94C43⋊#95—22no—
95C23×C4×C43C2311yescharacteristic
96C2×M16×C43—22no—
97C2×M16×C43—22no—
98C2×M16×C43C2×C414yescomplemented
99C22×C8×C43—22no—
100C22×C8×C43—22no—
101C22×C8×C43—22no—
102C22×C8×C43C2311yescharacteristic
103C22×C8×C43C2311yescharacteristic
104C22×C8×C43C2312yes—
105#117×C43—22no—
106#117×C43—22no—
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C22⋊C4×C43D412yes—
110C2×C42×C43C2312yes—
111C24×C43C2×D411yescharacteristic
112C23×D43—21no—
113C22×C4×C43C22×C412yes—
114C22×C4×C43C2×D412yes—
115C22×C4×C43C2×D412yes—
116C22×C4×C43C2×D412yes—
117C22×C4×C43C2×D412yes—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×Q812yes—
120C22×C4×C43#4112yes—
121C22×C4×C43#4112yes—
122C22×C4×C43C2411yescharacteristic
123C2×C22⋊D43—24no—
124C2×C22⋊D43—24no—
125C2×C22⋊D43—24no—
126C22×Dic43—24no—
127C22×Dic43—24no—
128C22×Dic43—21no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—81no—
134C22×Dic43—81no—
135C22×Dic43—81no—
136C22×Dic43—81no—
137#10621898—28no—
138#10621898—28no—
139#10621898—28no—
140#10621898C4⋊C4116yescomplemented
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172C22×C412yes—
145C2×D172C2×D412yes—
146C2×D172C2×Q812yes—
147C2×C4×D43—24no—
148C2×C4×D43—24no—
149C2×C4×D43—24no—
150C2×C4×D43—28no—
151C2×C4×D43—82no—
152C2×C4×D43—82no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86C22×C412yes—
157C2×Dic86C2×D412yes—
158C2×Dic86C2×Q812yes—
159M16×C43—28no—
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—44no—
169C2×C8×C43C22×C414yes—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C22⋊C4×C43—24no—
173C42×C43—22no—
174C42×C43—22no—
175C22⋊Dic43—42no—
176(C2×D43)⋊C4—28no—
177C4⋊Dic43—24no—
178C4⋊Dic43—24no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C22×C414yes—
186C4⋊Dic43C2×D414yes—
187Dic43⋊C4—28no—
188Dic43⋊C4—82no—
189Dic43⋊C4—82no—
190C4×Dic43—28no—
191C4×Dic43—42no—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43C4×D412yes—
197C23×C43#12012yes—
198C23×C43C22⋊Q812yes—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43C2×C4⋊C414yes—
214C2×C4×C43C4×D414yes—
215C2×C4×C43C4×D412yes—
216C2×C4×C43#12012yes—
217C2×C4×C43C22⋊Q814yes—
218C2×C4×C43C22⋊Q812yes—
219C2×C4×C43#12314yes—
220C2×C4×C43C23×C411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×Q811yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—216no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—24no—
231C2×Dic43—24no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—84no—
243C2×Dic43—84no—
244D172—22no—
245D172—22no—
246D172—22no—
247D172C2×C4⋊C414yes—
248C4×D43—216no—
249C4×D43—88no—
250Dic86—22no—
251Dic86—22no—
252Dic86—22no—
253Dic86C2×C4⋊C414yes—
254C8×C43—24no—
255C8×C43—41no—
256C8×C43—41no—
257#20878—431nomaximal, Sylow
258C22×C43—22no—
259C22×C43—22no—
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—22no—
264C22×C43#38514yes—
265C22×C43C2×C4×D411yescharacteristic
266C22×C43C2×#12011yescharacteristic
267C22×C43C2×C22⋊Q811yescharacteristic
268C22×C43#57611yescharacteristic
269C22×C43#57711yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57811yescharacteristic
272C2×D43—24no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—42no—
279C4×C43—42no—
280C4×C43—42no—
281C4×C43#38514yes—
282C4×C43C22×C4⋊C411yescharacteristic
283C4×C43C2×C4×D411yescharacteristic
284C4×C43C2×C22⋊Q811yescharacteristic
285C4×C43C2×#12311yescharacteristic
286Dic43—24no—
287Dic43—44no—
288Dic43—44no—
289Dic43—81no—
290Dic43—81no—
291C2×#520—431no—
292C2×#428—431no—
293C2×#417—431no—
294C2×#416—431no—
295#2316—431no—
296#1865—432no—
297#1864—432no—
298#1863—432no—
299#1862—432no—
300C2×#340—431no—
301#1729D4311yescharacteristic, complemented
302C2×C43—24no—
303C2×C43C2×#38511yescharacteristic
304C2×C43#294611yescharacteristic
305C2×C43#294711yescharacteristic
306C2×C43#301211yescharacteristic
307C2×C43#301311yescharacteristic
308C2×C43#308311yescharacteristic
309C2×C43#308411yescharacteristic
310D43—44no—
311C22×#41—431no—
312C22×M16C2×D4311yescharacteristic
313C23×C8C2×D4311yescharacteristic
314#520—864no—
315#520—864no—
316C2×C4×Q8—432no—
317C2×C4×D4—432no—
318C2×C4×D4—862no—
319C2×#117—431no—
320C2×#117—861no—
321C2×#117C2×D4311yescharacteristic
322C22×C4⋊C4—431no—
323C22×C4⋊C4—431no—
324C22×C4⋊C4—861no—
325#428—864no—
326C2×#107—432no—
327C2×#106—432no—
328#417—438no—
329#416—864no—
330C2×#103—432no—
331C2×#103—431no—
332C2×#103—431no—
333C2×#102—432no—
334C2×#102—431no—
335C2×#102—431no—
336#389—432no—
337#389—432no—
338#389—861no—
339#389—861no—
340#380—862no—
341#340—432no—
342#340—432no—
343#336C2×D4312yes—
344#336C2×D4312yes—
345C43#2087811yescharacteristic, complemented, Sylow
346C2×#41—434no—
347C2×#41—434no—
348C2×#41—434no—
349C2×#41—862no—
350C2×#41—862no—
351C2×#41—862no—
352C22×Q8—431no—
353C22×D4—431no—
354C22×D4—861no—
355C23×C4—861no—
356C23×C4—861no—
357C23×C4—861no—
358C23×C4—862no—
359C23×C4C22×D4311yescharacteristic
360C2×M16—22no—
361C2×M16—22no—
362C2×M16C4×D4314yescomplemented
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—22no—
366C22×C8C22×D4311yescharacteristic
367C22×C8C22×D4311yescharacteristic
368C22×C8C22×D4312yes—
369C4×Q8—864no—
370C4×Q8—864no—
371C4×D4—864no—
372C4×D4—864no—
373C4×D4—8616no—
374#117—22no—
375#117—22no—
376#117—868no—
377#117—862no—
378#117—862no—
379C2×C4⋊C4—434no—
380C2×C4⋊C4—434no—
381C2×C4⋊C4—432no—
382C2×C4⋊C4—432no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—868no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—862no—
389C2×C4⋊C4—862no—
390C2×C4⋊C4—862no—
391C2×C4⋊C4—862no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4D17211yescharacteristic
394C2×C4⋊C4D17211yescharacteristic
395C2×C22⋊C4—862no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4D17212yes—
398C2×C42—862no—
399C2×C42—861no—
400C2×C42C22×D4312yes—
401#107—864no—
402#106—864no—
403#103—438no—
404#103—862no—
405#103—862no—
406#102—438no—
407#102—862no—
408#102—862no—
409#95—862no—
410#95—862no—
411C24—861no—
412C24C2×D17211yescharacteristic
413#41—4316no—
414#41—868no—
415#41—868no—
416#41—868no—
417C2×Q8—432no—
418C2×Q8—432no—
419C2×Q8—432no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×D4—432no—
424C2×D4—432no—
425C2×D4—432no—
426C2×D4—864no—
427C2×D4—864no—
428C2×D4—864no—
429C2×D4—861no—
430C2×D4—861no—
431C2×D4—861no—
432C22×C4—868no—
433C22×C4—861no—
434C22×C4—864no—
435C22×C4—864no—
436C22×C4—864no—
437C22×C4—864no—
438C22×C4—864no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—3442no—
444C22×C4—3442no—
445C22×C4—3441no—
446C22×C4—3441no—
447C22×C4—3441no—
448C22×C4—3441no—
449C22×C4C2×C4×D4312yes—
450C22×C4C2×D17212yes—
451C22×C4C2×D17212yes—
452C22×C4C2×D17211yescharacteristic
453C22×C4#1062189812yes—
454C22×C4D4×D4312yes—
455C22×C4D4×D4312yes—
456C22×C4#1062190012yes—
457C22×C4Q8×D4312yes—
458C22×C4C23×D4311yescharacteristic
459M16—28no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—44no—
469C2×C8C2×C4×D4314yes—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—434no—
473C4⋊C4—434no—
474C4⋊C4—868no—
475C4⋊C4—864no—
476C4⋊C4—864no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—3442no—
484C4⋊C4—3442no—
485C22⋊C4—24no—
486C22⋊C4—868no—
487C22⋊C4—1722no—
488C42—22no—
489C42—22no—
490C42—868no—
491C42—1722no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—862no—
497C23—862no—
498C23—862no—
499C23—1721no—
500C23—1721no—
501C23—1721no—
502C23—1721no—
503C23C4×D17212yes—
504C23#1306329512yes—
505C23#1306330512yes—
506C23C22×D17211yescharacteristic
507Q8—434no—
508Q8—862no—
509Q8—862no—
510Q8—862no—
511D4—434no—
512D4—8616no—
513D4—862no—
514D4—862no—
515D4—862no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—8616no—
526C2×C4—864no—
527C2×C4—864no—
528C2×C4—3448no—
529C2×C4—3444no—
530C2×C4—3444no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4C4⋊C4×D4314yes—
542C2×C4(C22⋊D43)⋊C414yes—
543C2×C4C4×D17212yes—
544C2×C4#1306329512yes—
545C2×C4#1306330314yes—
546C2×C4#1306330512yes—
547C2×C4#1306330714yes—
548C2×C4C22×C4×D4311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C2×D4×D4311yescharacteristic
551C2×C4C2×Q8×D4311yescharacteristic
552C2×C4C2×#1062190011yescharacteristic
553C2×C4C2×#1062189811yescharacteristic
554C8—24no—
555C8—41no—
556C8—41no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—864no—
564C22—1722no—
565C22—1722no—
566C22—1722no—
567C22—1722no—
568C22—1722no—
569C22—1722no—
570C22#1458277314yes—
571C22C2×C4×D17211yescharacteristic
572C22C2×#1306329511yescharacteristic
573C22C2×#1306330511yescharacteristic
574C22#1458370411yescharacteristic
575C22#1458371111yescharacteristic
576C22#1458371111yescharacteristic
577C22#1458371611yescharacteristic
578C4—42no—
579C4—42no—
580C4—864no—
581C4—3441no—
582C4—3441no—
583C4—1724no—
584C4—1724no—
585C4#1458277314yes—
586C4C2×C4⋊C4×D4311yescharacteristic
587C4C2×(C22⋊D43)⋊C411yescharacteristic
588C4C2×#1306330311yescharacteristic
589C4C2×#1306330711yescharacteristic
590C2—24no—
591C2—1724no—
592C2C2×#1458277311yescharacteristic
593C2#1914342911yescharacteristic
594C2#1914344011yescharacteristic
595C2#1914390211yescharacteristic
596C2#1914391311yescharacteristic
597C2#1914444811yescharacteristic
598C2#1914445911yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1729C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1729D43
hypocenterC43#20878
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1729

Complements

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

NH ≅ G/Ntype
2. C2×#14582941C2semidirect
5. #19137211C2semidirect
6. #19134866C2semidirect
7. #19134859C2semidirect
8. #19134852C2semidirect
9. #19134845C2semidirect
10. C2×#14582662C2semidirect
11. C43×#1729C2semidirect
26. #14582901C4semidirect
71. C2×C4⋊Dic43C2×C4semidirect
89. #13063250C2×C4semidirect
92. #13063247C2×C4semidirect
98. C2×M16×C43C2×C4semidirect
140. #10621898C4⋊C4semidirect
301. #1729D43semidirect
345. C43#20878semidirect
362. C2×M16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833792
C2×#145829412
C2×#145829012
C2×#145828962
#191372112
#191348662
#191348592
#191348522
#191348452
C2×#145826622
C43×#17292
#2087843