Finite Group Databasebeta

← #25150276

Subgroups — #25150276

Order 11008.

1216 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic, complemented
2C2×#14583286C211yesmaximal, characteristic, complemented
3C2×#14583245C211yesmaximal, characteristic, complemented
4#19135598C212yesmaximal, complemented
5#19135591C212yesmaximal, complemented
6#19135567C211yesmaximal, characteristic, complemented
7#19135404C211yesmaximal, characteristic, complemented
8#19134953C212yesmaximal, complemented
9#19134946C212yesmaximal, complemented
10#19134361C211yesmaximal, characteristic, complemented
11C43×#2619C211yesmaximal, characteristic, complemented
12C22×#10621883C2212yes—
13C22×#10621882C2212yes—
14#14583520—24no—
15#14583520—24no—
16C2×#13063325C2211yescharacteristic
17C2×#13063320—21no—
18C2×#13063313C2211yescharacteristic
19C2×#13063311—21no—
20C2×#13063307—21no—
21C2×#13063304C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063299C2211yescharacteristic
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26#14583286—24no—
27#14583245—24no—
28C2×#13063248C2212yes—
29C2×#13063246C2212yes—
30C2×#13063246C2212yes—
31C2×#13063245C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×#13063236C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582661C2212yes—
36#14582661C2212yes—
37#14582654C2212yes—
38C2×#127×C43C2211yescharacteristic
39C2×#121×C43C2212yes—
40C2×#117×C43C2211yescharacteristic
41C43×#394—21no—
42C43×#394—21no—
43C43×#392—21no—
44C43×#392—21no—
45C43×#390C2212yes—
46C43×#382C2211yescharacteristic
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C22×D172C2311yescharacteristic
50C22×C22⋊D43—21no—
51C22×C4×D43—21no—
52C2×#10621883—24no—
53C2×#10621883—24no—
54C2×#10621883—42no—
55C2×#10621882—24no—
56C2×#10621882—24no—
57C2×#10621882—42no—
58C22×C43⋊C8C2312yes—
59C22×C43⋊C8C2312yes—
60#13063325—22no—
61#13063325D414yescomplemented
62#13063320—28no—
63#13063313—22no—
64#13063313D414yescomplemented
65#13063311—28no—
66#13063307—28no—
67#13063304—22no—
68#13063304—22no—
69#13063303—28no—
70#13063299—22no—
71#13063299—22no—
72C4×Dic86—22no—
73C4×Dic86—22no—
74C4×D172—22no—
75C4×D172—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87#13063248—42no—
88#13063246—24no—
89#13063246—24no—
90#13063245—42no—
91C22⋊(C43⋊C8)—24no—
92#13063236—22no—
93C4×C43⋊C8—22no—
94C22×D4×C43—22no—
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43C2312yes—
98C23×C4×C43C2311yescharacteristic
99#127×C43—22no—
100#127×C43—22no—
101#121×C43—42no—
102#121×C43—42no—
103#117×C43—22no—
104#117×C43—22no—
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C4⋊C4×C43C2312yes—
108C2×C22⋊C4×C43—22no—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43D411yescharacteristic
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C42×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#95×C43—21no—
116#95×C43—21no—
117C24×C43—22no—
118C24×C43C2×D411yescharacteristic
119C23×D43—21no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—44no—
127C2×D4×C43—42no—
128C2×D4×C43—42no—
129C2×D4×C43—82no—
130C2×D4×C43—82no—
131C2×D4×C43—82no—
132C2×D4×C43—82no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C2×C22⋊D43—24no—
145C2×C22⋊D43—82no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C2×D172—21no—
150C2×D172—22no—
151C2×D172—22no—
152C2×D172C2×D412yes—
153C2×C4×D43—24no—
154C2×C4×D43—82no—
155C2×Dic86—22no—
156C2×Dic86—22no—
157C2×Dic86—21no—
158C2×Dic86—24no—
159C2×Dic86—82no—
160C2×Dic86C2×D412yes—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—44no—
168C22⋊C4×C43—82no—
169C22⋊C4×C43—82no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43C2×D412yes—
173C42×C43C2×D412yes—
174C22⋊Dic43—24no—
175#10621883—48no—
176#10621882—48no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—24no—
181C4⋊Dic43—24no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C2×D412yes—
185C4⋊Dic43C2×D412yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—24no—
188C4×Dic43—24no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8#4114yes—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43C22×D411yescharacteristic
208C22×D43—22no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—42no—
212C22×D43—42no—
213D4×C43—42no—
214D4×C43—42no—
215D4×C43—42no—
216D4×C43—42no—
217D4×C43—84no—
218D4×C43—84no—
219D4×C43—88no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43#12012yes—
235C2×C4×C43#12012yes—
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C2×#4112yes—
239C2×C4×C43H(5,𝔽2)12yes—
240C22⋊D43—84no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248D172—24no—
249D172—42no—
250C4×D43—84no—
251Dic86—24no—
252Dic86—42no—
253Dic86—84no—
254C43⋊C8—24no—
255C43⋊C8—42no—
256#25614—431nomaximal, Sylow
257C22×C43—42no—
258C22×C43—41no—
259C22×C43—42no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—82no—
263C22×C43—82no—
264C22×C43—82no—
265C22×C43—82no—
266C22×C43—82no—
267C22×C43—82no—
268C22×C43—82no—
269C22×C43C2×#12011yescharacteristic
270C22×C43#53211yescharacteristic
271C22×C43#53511yescharacteristic
272C22×C43#57612yes—
273C22×C43#57712yes—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—82no—
278C2×D43—82no—
279C4×C43—22no—
280C4×C43—22no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—82no—
285C4×C43#54612yes—
286C4×C43#55012yes—
287Dic43—42no—
288Dic43—42no—
289Dic43—42no—
290C2×#542—431no—
291C2×#496—431no—
292C2×#486—431no—
293#2619D4311yescharacteristic, complemented
294#2000—432no—
295#1999—432no—
296#1993—431no—
297#1958—431no—
298#1880—432no—
299#1879—432no—
300#1750—431no—
301C2×C43—81no—
302C2×C43—162no—
303C2×C43#243111yescharacteristic
304C2×C43#300811yescharacteristic
305C2×C43#301011yescharacteristic
306C2×C43#317912yes—
307C2×C43#322412yes—
308D43—82no—
309C22×SD16—432no—
310C22×D8—432no—
311#542—864no—
312#542—864no—
313C2×C4⋊Q8—431no—
314C2×#127C2×D4311yescharacteristic
315C2×#126—861no—
316C2×#124—431no—
317C2×#124—861no—
318C2×#123—861no—
319C2×C22⋊Q8—431no—
320C2×C22⋊Q8—861no—
321C2×#121—431no—
322C2×#121C2×D4312yes—
323C2×C4×Q8—431no—
324C2×C4×D4—431no—
325C2×#117C2×D4311yescharacteristic
326#496—864no—
327#486—864no—
328C2×#103—432no—
329C2×#102—432no—
330C2×#102—432no—
331C2×#102—432no—
332C2×C22⋊C8—432no—
333C2×#97—431no—
334C2×C4×C8—431no—
335#394—21no—
336#394—21no—
337#392—21no—
338#392—21no—
339#390C2×D4312yes—
340#382C2×D4311yescharacteristic
341#340—432no—
342#340—432no—
343#336—432no—
344C43#2561411yescharacteristic, complemented, Sylow
345C22×Q8—431no—
346C22×Q8—861no—
347C22×D4—22no—
348C22×D4—21no—
349C22×D4—21no—
350C22×D4—431no—
351C22×D4—861no—
352C22×D4C22×D4312yes—
353C23×C4—861no—
354C23×C4C22×D4311yescharacteristic
355C2×SD16—864no—
356C2×SD16—864no—
357C2×SD16—1722no—
358C2×D8—864no—
359C2×D8—864no—
360C2×D8—1722no—
361C22×C8—432no—
362C22×C8—432no—
363C4⋊Q8—434no—
364C4⋊Q8—862no—
365#127—22no—
366#127—22no—
367#126—868no—
368#124—434no—
369#124—868no—
370#124—862no—
371#123—868no—
372C22⋊Q8—868no—
373C22⋊Q8—862no—
374C22⋊Q8—862no—
375#121—42no—
376#121—42no—
377#121—862no—
378#121—862no—
379C4×Q8—862no—
380C4×Q8—862no—
381C4×D4—862no—
382C4×D4—862no—
383#117—22no—
384#117—22no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4C22⋊D4311yescharacteristic
391C2×C4⋊C4C22⋊D4311yescharacteristic
392C2×C4⋊C4C22×D4312yes—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C22⋊C4C22⋊D4311yescharacteristic
402C2×C22⋊C4C22⋊D4311yescharacteristic
403C2×C42—861no—
404C2×C42C22×D4311yescharacteristic
405C2×C42C22×D4311yescharacteristic
406#103—1722no—
407#102—864no—
408#102—864no—
409#102—1722no—
410C22⋊C8—864no—
411#97—862no—
412C4×C8—862no—
413#95—21no—
414#95—21no—
415C24—22no—
416C24—861no—
417C24C2×C22⋊D4311yescharacteristic
418C2×Q8—432no—
419C2×Q8—864no—
420C2×Q8—861no—
421C2×Q8—862no—
422C2×Q8—862no—
423C2×Q8—3442no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—44no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—82no—
434C2×D4—82no—
435C2×D4—82no—
436C2×D4—82no—
437C2×D4—432no—
438C2×D4—864no—
439C2×D4—861no—
440C2×D4—862no—
441C2×D4—862no—
442C2×D4—3442no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—864no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—3442no—
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C23×D4311yescharacteristic
459SD16—1728no—
460D8—1728no—
461C2×C8—434no—
462C2×C8—862no—
463C2×C8—862no—
464C2×C8—862no—
465C2×C8—862no—
466C2×C8—862no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—432no—
472C4⋊C4—432no—
473C4⋊C4—864no—
474C4⋊C4—864no—
475C4⋊C4—864no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—44no—
481C22⋊C4—82no—
482C22⋊C4—82no—
483C22⋊C4—864no—
484C22⋊C4—864no—
485C22⋊C4—864no—
486C22⋊C4—864no—
487C22⋊C4—864no—
488C42—21no—
489C42—21no—
490C42—864no—
491C42D4×D4312yes—
492C42D4×D4312yes—
493C23—21no—
494C23—21no—
495C23—22no—
496C23—22no—
497C23—21no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—862no—
506C23—1721no—
507C23—1722no—
508C23—1722no—
509C23—1721no—
510C23C22×C22⋊D4311yescharacteristic
511Q8—864no—
512Q8—3444no—
513Q8—1722no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—84no—
519D4—84no—
520D4—88no—
521D4—864no—
522D4—3444no—
523D4—1722no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—862no—
541C2×C4—3444no—
542C2×C4—1721no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4—1721no—
546C2×C4#1306329312yes—
547C2×C4#1306329312yes—
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4#41×D4312yes—
551C2×C4#1306337012yes—
552C8—864no—
553C8—1722no—
554C22—42no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—82no—
560C22—82no—
561C22—82no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22—82no—
566C22—3442no—
567C22—3442no—
568C22—1722no—
569C22—1722no—
570C22—1722no—
571C22C2×#1306329311yescharacteristic
572C22#1458344511yescharacteristic
573C22#1458346611yescharacteristic
574C22#1458370212yes—
575C22#1458371012yes—
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—82no—
582C4—1722no—
583C4—1722no—
584C4—1722no—
585C4#1458354612yes—
586C4#1458356712yes—
587C2—81no—
588C2—162no—
589C2—3442no—
590C2#1913821511yescharacteristic
591C2#1914386111yescharacteristic
592C2#1914387911yescharacteristic
593C2#1914528012yes—
594C2#1914568912yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2619C2
socleC23×C43C22×D4
hypercenter#2619D43
hypocenterC43#25614
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. C2×#14583520C2semidirect
2. C2×#14583286C2semidirect
3. C2×#14583245C2semidirect
4. #19135598C2semidirect
5. #19135591C2semidirect
6. #19135567C2semidirect
7. #19135404C2semidirect
8. #19134953C2semidirect
9. #19134946C2semidirect
10. #19134361C2semidirect
11. C43×#2619C2semidirect
61. #13063325D4semidirect
64. #13063313D4semidirect
293. #2619D43semidirect
344. C43#25614semidirect

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145832862
C2×#145832452
#191355982
#191355912
#191355672
#191354042
#191349532
#191349462
#191343612
C43×#26192
#2561443