Finite Group Databasebeta

← #25068866

Subgroups — #25068866

Order 11008.

1292 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144591C212yesmaximal, complemented
2#19137831C211yesmaximal, characteristic, complemented
3#19133598C212yesmaximal, complemented
4#19133581C212yesmaximal, complemented
5#19133530C212yesmaximal, complemented
6#19133513C212yesmaximal, complemented
7#19133090C212yesmaximal, complemented
8#19132909C211yesmaximal, characteristic, complemented
9C43×#3449C211yesmaximal, characteristic, complemented
10C2×C4×D172C2211yescharacteristic, complemented
11C2×C4×C22⋊D43—21no—
12#14583210C2214yescomplemented
13#14583176—22no—
14#14583091—22no—
15#14583032C2214yescomplemented
16C4×#10621882—24no—
17#14582952C2212yescomplemented
18#14582829C2211yescharacteristic, complemented
19#14582824C2211yescharacteristic
20#14582821—21no—
21#14582816C2211yescharacteristic, complemented
22#14582815—21no—
23#14582808C2211yescharacteristic
24C4×C4⋊Dic43C2211yescharacteristic, complemented
25C4×(C2×D43)⋊C4—21no—
26#14582633C2214yescomplemented
27#14582633C2214yescomplemented
28#14582625C2212yescomplemented
29#14582623C2212yes—
30C22×#41×C43—21no—
31C43×#537—21no—
32C43×#537C2212yes—
33C43×#536—22no—
34C43×#535—22no—
35C43×#534—21no—
36C43×#534C2212yes—
37C43×#532—21no—
38C43×#532C2212yes—
39C43×#525—24no—
40C2×#117×C43C2211yescharacteristic
41C22×D172C2311yescharacteristic
42C22×C22⋊D43—21no—
43C22×C4×D43—21no—
44C2×#10621882—24no—
45C4×D172—22no—
46C4×D172—22no—
47C4×C22⋊D43—44no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43C2311yescharacteristic
50C2×Dic43⋊C4—21no—
51C2×C22⋊Dic43—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—21no—
56C2×C4×Dic43—21no—
57#13063258—24no—
58C4⋊(C43⋊C8)—22no—
59#13063246—24no—
60#13063245—24no—
61C22⋊(C43⋊C8)C2314yes—
62C4×C43⋊C8—22no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95C2311yescharacteristic
66C43⋊#95C2311yescharacteristic
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—22no—
71C2×#41×C43—44no—
72C2×#41×C43—44no—
73C22×Q8×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43—22no—
76C23×C4×C43—22no—
77C23×C4×C43D411yescharacteristic
78C4⋊Q8×C43—21no—
79C4⋊Q8×C43D412yescomplemented
80#127×C43—21no—
81#127×C43D412yescomplemented
82#124×C43—22no—
83#124×C43—22no—
84#123×C43—24no—
85#123×C43—24no—
86C22⋊Q8×C43—24no—
87C22⋊Q8×C43—24no—
88#121×C43—24no—
89#121×C43—24no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—22no—
93#121×C43C2314yes—
94#120×C43—24no—
95#120×C43—24no—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43—22no—
99C4×D4×C43D414yescomplemented
100#117×C43—22no—
101#117×C43—22no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C22⋊C4×C43D411yescharacteristic
105C2×C22⋊C4×C43C2311yescharacteristic
106C2×C42×C43D411yescharacteristic
107C2×C42×C43C2311yescharacteristic
108C24×C43—22no—
109C24×C43C2×D411yescharacteristic
110C23×D43—21no—
111#41×C43—44no—
112#41×C43—48no—
113#41×C43—48no—
114#41×C43—44no—
115#41×C43—44no—
116#41×C43—44no—
117C2×Q8×C43—22no—
118C2×Q8×C43—22no—
119C2×Q8×C43—44no—
120C2×D4×C43—24no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—24no—
127C2×D4×C43—44no—
128C2×D4×C43—44no—
129C2×D4×C43—44no—
130C2×D4×C43C2×D414yes—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—24no—
135C22×C4×C43—22no—
136C22×C4×C43—24no—
137C22×C4×C43—48no—
138C22×C4×C43D814yescomplemented
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—42no—
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C2×D172—22no—
152C2×D172—42no—
153C2×C4×D43—41no—
154C2×C4×D43—41no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43C2×D414yes—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—24no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43C2×D412yes—
172C42×C43C2×D412yes—
173C22⋊Dic43—42no—
174#10621882—48no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179C4⋊Dic43—22no—
180C4⋊Dic43—42no—
181Dic43⋊C4—42no—
182C4×Dic43—42no—
183C2×C43⋊C8—24no—
184C23×C43—21no—
185C23×C43—21no—
186C23×C43—24no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—44no—
190C23×C43—82no—
191C23×C43—82no—
192C23×C43C2×D812yes—
193C23×C43C22×D411yescharacteristic
194C22×D43—22no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201Q8×C43—44no—
202Q8×C43—44no—
203D4×C43—44no—
204D4×C43—44no—
205D4×C43—48no—
206D4×C43—44no—
207D4×C43—44no—
208D4×C43—44no—
209D4×C43—82no—
210D4×C43—82no—
211D4×C43—82no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—24no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—48no—
222C2×C4×C43—44no—
223C2×C4×C43—48no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43#12012yes—
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C2×C4×C43C2×D812yes—
230C2×C4×C43C2×D812yes—
231C2×C4×C43AGL(1,ℤ/8)12yes—
232C2×C4×C43C22×D412yes—
233C22⋊D43—48no—
234C2×Dic43—22no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243D172—24no—
244D172—42no—
245C4×D43—82no—
246C4×D43—82no—
247C43⋊C8—44no—
248#18122—431nomaximal, Sylow
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—22no—
252C22×C43—42no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—44no—
256C22×C43—44no—
257C22×C43—44no—
258C22×C43—81no—
259C22×C43—88no—
260C22×C43C2×#12011yescharacteristic
261C22×C43C22×D811yescharacteristic
262C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—22no—
273C4×C43—44no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43#44712yes—
277C4×C43#44712yes—
278Dic43—42no—
279Dic43—81no—
280Dic43—81no—
281#3449D4311yescharacteristic, complemented
282#3100—432no—
283#2392—431no—
284#1610—432no—
285#1607—432no—
286#1598—432no—
287#1595—432no—
288#1502—432no—
289#1458—431no—
290C2×C43—21no—
291C2×C43—21no—
292C2×C43—42no—
293C2×C43—84no—
294C2×C43C2×#44711yescharacteristic
295C2×C43#301811yescharacteristic
296C2×C43#302511yescharacteristic
297D43—82no—
298C22×#41—21no—
299#537—21no—
300#537C2×D4312yes—
301#536—22no—
302#535—22no—
303#534—21no—
304#534C2×D4312yes—
305#532—21no—
306#532C2×D4312yes—
307#525—24no—
308C2×C4×D4—431no—
309C2×C4×D4—861no—
310C2×#117C2×D4311yescharacteristic
311#480—434no—
312#474—862no—
313#459—862no—
314#447—434no—
315C4×D8—864no—
316#431—432no—
317#398—431no—
318#397—431no—
319#396—861no—
320#394—431no—
321#394—861no—
322#392—431no—
323C4×C4⋊C4—431no—
324C4×C22⋊C4—861no—
325#327—434no—
326#327—434no—
327#324—432no—
328#323—432no—
329C43#1812211yescharacteristic, complemented, Sylow
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—44no—
335C2×#41—44no—
336C22×Q8—21no—
337C22×D4—21no—
338C22×D4—22no—
339C22×D4—431no—
340C22×D4—861no—
341C23×C4—22no—
342C23×C4—861no—
343C23×C4C22⋊D4311yescharacteristic
344C2×D8—864no—
345C4⋊Q8—21no—
346C4⋊Q8C22⋊D4312yescomplemented
347#127—21no—
348#127C22⋊D4312yescomplemented
349#124—22no—
350#124—22no—
351#123—24no—
352#123—24no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355#121—24no—
356#121—24no—
357#121—22no—
358#121—22no—
359#121—22no—
360#121C22×D4314yes—
361#120—24no—
362#120—24no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—862no—
367C4×D4—862no—
368C4×D4—1724no—
369C4×D4C22⋊D4314yescomplemented
370#117—22no—
371#117—22no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4C22⋊D4311yescharacteristic
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C22⋊C4—861no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4C22⋊D4311yescharacteristic
383C2×C22⋊C4C22×D4311yescharacteristic
384C2×C42—861no—
385C2×C42C22⋊D4311yescharacteristic
386C2×C42C22×D4311yescharacteristic
387#107—864no—
388C4⋊C8—862no—
389#102—864no—
390#102—864no—
391C22⋊C8—434no—
392C4×C8—862no—
393#95—431no—
394#95—431no—
395#95—861no—
396#95—861no—
397C24—22no—
398C24—861no—
399C24C2×C22⋊D4311yescharacteristic
400#41—44no—
401#41—48no—
402#41—48no—
403#41—44no—
404#41—44no—
405#41—44no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—44no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—24no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—862no—
420C2×D4—1722no—
421C2×D4—1722no—
422C2×D4—1722no—
423C2×D4—1722no—
424C2×D4C2×C22⋊D4314yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—48no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—1721no—
436C22×C4—1721no—
437C22×C4—1722no—
438C22×C4—1722no—
439C22×C4#1062188214yescomplemented
440C22×C4C2×C22⋊D4311yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C23×D4311yescharacteristic
446D8—1728no—
447C2×C8—864no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—862no—
454C4⋊C4—1722no—
455C4⋊C4—1722no—
456C4⋊C4C2×C22⋊D4314yes—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—24no—
461C22⋊C4—22no—
462C22⋊C4—24no—
463C22⋊C4—1722no—
464C22⋊C4—1722no—
465C22⋊C4—1722no—
466C22⋊C4—1722no—
467C22⋊C4—1722no—
468C42—21no—
469C42—21no—
470C42—1722no—
471C42C2×C22⋊D4312yes—
472C42C2×C22⋊D4312yes—
473C23—21no—
474C23—21no—
475C23—24no—
476C23—41no—
477C23—41no—
478C23—44no—
479C23—82no—
480C23—82no—
481C23—862no—
482C23—1721no—
483C23—1721no—
484C23—1721no—
485C23—1721no—
486C23—1721no—
487C23—1721no—
488C23C2×#1062188212yes—
489C23C22×C22⋊D4311yescharacteristic
490Q8—44no—
491Q8—44no—
492D4—44no—
493D4—44no—
494D4—48no—
495D4—44no—
496D4—44no—
497D4—44no—
498D4—82no—
499D4—82no—
500D4—82no—
501D4—864no—
502D4—1722no—
503D4—1728no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—24no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—48no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—862no—
519C2×C4—3442no—
520C2×C4—3442no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306329412yes—
530C2×C4#1306329411yescharacteristic
531C2×C4#1306329411yescharacteristic
532C2×C4C2×#1062188212yes—
533C2×C4C2×#1062188212yes—
534C2×C4#1306335112yes—
535C2×C4C22×C22⋊D4312yes—
536C8—1724no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—42no—
541C22—41no—
542C22—41no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—81no—
547C22—88no—
548C22—3441no—
549C22—3441no—
550C22—3441no—
551C22—3441no—
552C22—1722no—
553C22—1722no—
554C22—1722no—
555C22C2×#1306329411yescharacteristic
556C22C22×#1062188211yescharacteristic
557C22C2×#1306335111yescharacteristic
558C4—22no—
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—44no—
564C4—3441no—
565C4—3441no—
566C4—1722no—
567C4#1458303312yes—
568C4#1458303312yes—
569C2—21no—
570C2—21no—
571C2—42no—
572C2—84no—
573C2—3442no—
574C2C2×#1458303311yescharacteristic
575C2#1914394411yescharacteristic
576C2#1914398711yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3449C2
socleC22×C43C2×#120
hypercenter#3449D43
hypocenterC43#18122
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #19144591C2semidirect
2. #19137831C2semidirect
3. #19133598C2semidirect
4. #19133581C2semidirect
5. #19133530C2semidirect
6. #19133513C2semidirect
7. #19133090C2semidirect
8. #19132909C2semidirect
9. C43×#3449C2semidirect
10. C2×C4×D172C22semidirect
12. #14583210C22semidirect
15. #14583032C22semidirect
17. #14582952C22semidirect
18. #14582829C22semidirect
21. #14582816C22semidirect
24. C4×C4⋊Dic43C22semidirect
26. #14582633C22semidirect
27. #14582633C22semidirect
28. #14582625C22semidirect
79. C4⋊Q8×C43D4semidirect
81. #127×C43D4semidirect
99. C4×D4×C43D4semidirect
138. C22×C4×C43D8semidirect
281. #3449D43semidirect
329. C43#18122semidirect
346. C4⋊Q8C22⋊D43semidirect
348. #127C22⋊D43semidirect
369. C4×D4C22⋊D43semidirect
439. C22×C4#10621882semidirect

Maximal subgroups

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

subgroupindex
#191445912
#191378312
#191335982
#191335812
#191335302
#191335132
#191330902
#191329092
C43×#34492
#1812243