Finite Group Databasebeta

← #25068865

Subgroups — #25068865

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#19147928C211yesmaximal, characteristic, complemented
2#19144595C212yesmaximal, complemented
3#19133597C212yesmaximal, complemented
4#19133580C212yesmaximal, complemented
5#19133529C212yesmaximal, complemented
6#19133512C212yesmaximal, complemented
7#19133089C212yesmaximal, complemented
8#19132909C211yesmaximal, characteristic, complemented
9C43×#2392C211yesmaximal, characteristic, complemented
10C22×#10621898—21no—
11#14583480—21no—
12#14583480C2212yes—
13#14583475—22no—
14#14583468—22no—
15#14583461—21no—
16#14583461C2212yes—
17#14583449—21no—
18#14583449C2212yes—
19#14583411—24no—
20#14583212C2214yescomplemented
21#14583179—22no—
22#14583094—22no—
23#14583033C2214yescomplemented
24C4×#10621882—24no—
25#14582952C2212yescomplemented
26#14582632C2214yescomplemented
27#14582632C2214yescomplemented
28#14582625C2212yescomplemented
29#14582623C2212yes—
30C2×C4×D4×C43—21no—
31C2×C4×D4×C43C2211yescharacteristic, complemented
32C2×#117×C43C2211yescharacteristic
33C43×#398C2211yescharacteristic, complemented
34C43×#397C2211yescharacteristic
35C43×#396—21no—
36C43×#394—21no—
37C43×#394C2211yescharacteristic, complemented
38C43×#392C2211yescharacteristic
39C4×C4⋊C4×C43C2211yescharacteristic, complemented
40C4×C22⋊C4×C43—21no—
41C2×#10621898—22no—
42C2×#10621898—22no—
43C2×#10621898—22no—
44C2×#10621898—22no—
45C2×#10621898—44no—
46C2×#10621898—44no—
47C22×Dic86—21no—
48C22×D172—21no—
49C22×C22⋊D43—22no—
50C22×C4×D43—22no—
51C2×#10621882—24no—
52#13063325—21no—
53#13063325D412yescomplemented
54#13063322—21no—
55#13063322D412yescomplemented
56#13063313—22no—
57#13063313—22no—
58#13063309—24no—
59#13063309—24no—
60#13063305—24no—
61#13063305—24no—
62#13063300—24no—
63#13063300—24no—
64#13063299—22no—
65#13063299—22no—
66#13063299—22no—
67#13063299C2314yes—
68#13063295—24no—
69#13063295—24no—
70C4×D172—22no—
71C4×D172—22no—
72C4×D172—22no—
73C4×D172D414yescomplemented
74#13063258—24no—
75C4⋊(C43⋊C8)—22no—
76#13063246—24no—
77#13063245—24no—
78C22⋊(C43⋊C8)C2314yes—
79C4×C43⋊C8—22no—
80C22×D4×C43—21no—
81C22×D4×C43C2311yescharacteristic
82C23×C4×C43—21no—
83C23×C4×C43D411yescharacteristic
84C4×D4×C43—22no—
85C4×D4×C43—22no—
86C4×D4×C43—44no—
87#117×C43—22no—
88#117×C43—22no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C4⋊C4×C43D411yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43D411yescharacteristic
100C2×C22⋊C4×C43C2311yescharacteristic
101C2×C42×C43—21no—
102C2×C42×C43D411yescharacteristic
103C2×C42×C43C2311yescharacteristic
104#95×C43—21no—
105#95×C43—21no—
106#95×C43C2311yescharacteristic
107#95×C43C2311yescharacteristic
108C24×C43—21no—
109C24×C43C2×D411yescharacteristic
110C23×D43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—42no—
113C2×D4×C43—42no—
114C2×D4×C43—42no—
115C2×D4×C43—42no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43D814yescomplemented
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C2×C22⋊D43—24no—
134C2×C22⋊D43—24no—
135C2×C22⋊D43—44no—
136C2×C22⋊D43—44no—
137C22×Dic43—22no—
138#10621898—44no—
139#10621898—48no—
140#10621898—48no—
141#10621898—44no—
142#10621898—44no—
143#10621898—44no—
144C2×D172—22no—
145C2×D172—22no—
146C2×D172—22no—
147C2×D172—22no—
148C2×D172—22no—
149C2×D172—44no—
150C2×D172C2×D414yes—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—48no—
154C2×Dic86—22no—
155C2×Dic86—22no—
156C2×Dic86—44no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—42no—
161C4⋊C4×C43—42no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—42no—
165C22⋊C4×C43—42no—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—42no—
168C22⋊C4×C43—42no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—42no—
172C42×C43C2×D412yes—
173C42×C43C2×D412yes—
174#10621882—48no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—24no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43—22no—
182C4⋊Dic43C2×D414yes—
183C2×C43⋊C8—24no—
184C23×C43—21no—
185C23×C43—21no—
186C23×C43—22no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43C2×D812yes—
196C23×C43C22×D411yescharacteristic
197C22×D43—24no—
198C22×D43—44no—
199C22×D43—82no—
200C22×D43—82no—
201D4×C43—24no—
202D4×C43—42no—
203D4×C43—48no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—24no—
207C2×C4×C43—24no—
208C2×C4×C43—22no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—82no—
224C2×C4×C43—82no—
225C2×C4×C43#12012yes—
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43C2×D812yes—
229C2×C4×C43C2×D812yes—
230C2×C4×C43AGL(1,ℤ/8)12yes—
231C2×C4×C43C22×D412yes—
232C22⋊D43—48no—
233C22⋊D43—44no—
234C22⋊D43—44no—
235C2×Dic43—24no—
236C2×Dic43—44no—
237D172—44no—
238D172—44no—
239D172—44no—
240D172—82no—
241D172—82no—
242D172—82no—
243C4×D43—48no—
244C4×D43—48no—
245Dic86—44no—
246Dic86—44no—
247C43⋊C8—44no—
248#18122—431nomaximal, Sylow
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—22no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—42no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—42no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43C2×#12011yescharacteristic
264C22×C43C22×D811yescharacteristic
265C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
266C2×D43—44no—
267C2×D43—44no—
268C2×D43—44no—
269C2×D43—88no—
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—22no—
273C4×C43—42no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#44712yes—
279C4×C43#44712yes—
280Dic43—44no—
281#3449—431no—
282#3100—432no—
283#2392D4311yescharacteristic, complemented
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—82no—
294C2×C43C2×#44711yescharacteristic
295C2×C43#301811yescharacteristic
296C2×C43#302511yescharacteristic
297D43—84no—
298C22×#41—861no—
299#537—432no—
300#537—861no—
301#536—862no—
302#535—862no—
303#534—432no—
304#534—861no—
305#532—432no—
306#532—861no—
307#525—864no—
308C2×C4×D4—21no—
309C2×C4×D4C2×D4311yescharacteristic, complemented
310C2×#117C2×D4311yescharacteristic
311#480—434no—
312#474—862no—
313#459—862no—
314#447—434no—
315C4×D8—864no—
316#431—432no—
317#398C2×D4311yescharacteristic, complemented
318#397C2×D4311yescharacteristic
319#396—21no—
320#394—21no—
321#394C2×D4311yescharacteristic, complemented
322#392C2×D4311yescharacteristic
323C4×C4⋊C4C2×D4311yescharacteristic, complemented
324C4×C22⋊C4—21no—
325#327—434no—
326#327—434no—
327#324—432no—
328#323—432no—
329C43#1812211yescharacteristic, complemented, Sylow
330C2×#41—862no—
331C2×#41—862no—
332C2×#41—862no—
333C2×#41—862no—
334C2×#41—1724no—
335C2×#41—1724no—
336C22×Q8—861no—
337C22×D4—21no—
338C22×D4—861no—
339C22×D4—862no—
340C22×D4C22×D4311yescharacteristic
341C23×C4—21no—
342C23×C4—862no—
343C23×C4C22⋊D4311yescharacteristic
344C2×D8—864no—
345C4⋊Q8—432no—
346C4⋊Q8—861no—
347#127—432no—
348#127—861no—
349#124—862no—
350#124—862no—
351#123—864no—
352#123—864no—
353C22⋊Q8—864no—
354C22⋊Q8—864no—
355#121—434no—
356#121—864no—
357#121—864no—
358#121—862no—
359#121—862no—
360#121—862no—
361#120—864no—
362#120—864no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—44no—
366C4×D4—434no—
367C4×D4—862no—
368C4×D4—862no—
369C4×D4—862no—
370#117—22no—
371#117—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4C22⋊D4311yescharacteristic
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4C22⋊D4311yescharacteristic
383C2×C22⋊C4C22×D4311yescharacteristic
384C2×C42—21no—
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—21no—
394#95—21no—
395#95C22×D4311yescharacteristic
396#95C22×D4311yescharacteristic
397C24—21no—
398C24—862no—
399C24C2×C22⋊D4311yescharacteristic
400#41—1724no—
401#41—1728no—
402#41—1728no—
403#41—1724no—
404#41—1724no—
405#41—1724no—
406C2×Q8—862no—
407C2×Q8—862no—
408C2×Q8—1724no—
409C2×D4—22no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—434no—
415C2×D4—862no—
416C2×D4—862no—
417C2×D4—862no—
418C2×D4—864no—
419C2×D4—864no—
420C2×D4—862no—
421C2×D4—862no—
422C2×D4—1724no—
423C2×D4—1724no—
424C2×D4—1724no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—864no—
436C22×C4—862no—
437C22×C4—864no—
438C22×C4—1728no—
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—42no—
452C4⋊C4—42no—
453C4⋊C4—434no—
454C4⋊C4—862no—
455C4⋊C4—862no—
456C4⋊C4—862no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—42no—
460C22⋊C4—42no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—42no—
464C22⋊C4—864no—
465C22⋊C4—864no—
466C22⋊C4—864no—
467C22⋊C4—864no—
468C42—21no—
469C42—21no—
470C42—42no—
471C42D4×D4312yes—
472C42D4×D4312yes—
473C23—21no—
474C23—21no—
475C23—22no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—864no—
485C23—3442no—
486C23—3442no—
487C23—1724no—
488C23C2×#1062188212yes—
489C23C22×C22⋊D4311yescharacteristic
490Q8—1724no—
491Q8—1724no—
492D4—24no—
493D4—42no—
494D4—48no—
495D4—3442no—
496D4—3442no—
497D4—3442no—
498D4—1724no—
499D4—1724no—
500D4—1728no—
501D4—1724no—
502D4—1724no—
503D4—1724no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—864no—
526C2×C4—1728no—
527C2×C4—1724no—
528C2×C4—1728no—
529C2×C4#1306329312yes—
530C2×C4#1306329311yescharacteristic
531C2×C4#1306329311yescharacteristic
532C2×C4C2×#1062188212yes—
533C2×C4C2×#1062188212yes—
534C2×C4#1306335012yes—
535C2×C4C2×D4×D4312yes—
536C8—1724no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—41no—
544C22—41no—
545C22—42no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—3448no—
552C22—1724no—
553C22—1724no—
554C22—1724no—
555C22C2×#1306329311yescharacteristic
556C22C22×#1062188211yescharacteristic
557C22C2×#1306335011yescharacteristic
558C4—22no—
559C4—22no—
560C4—22no—
561C4—42no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—1724no—
567C4#1458303212yes—
568C4#1458303212yes—
569C2—21no—
570C2—21no—
571C2—42no—
572C2—82no—
573C2—3444no—
574C2C2×#1458303211yescharacteristic
575C2#1914394311yescharacteristic
576C2#1914398611yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2392C2
socleC22×C43C2×#120
hypercenter#2392D43
hypocenterC43#18122
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2392

Complements

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

NH ≅ G/Ntype
1. #19147928C2semidirect
2. #19144595C2semidirect
3. #19133597C2semidirect
4. #19133580C2semidirect
5. #19133529C2semidirect
6. #19133512C2semidirect
7. #19133089C2semidirect
8. #19132909C2semidirect
9. C43×#2392C2semidirect
20. #14583212C22semidirect
23. #14583033C22semidirect
25. #14582952C22semidirect
26. #14582632C22semidirect
27. #14582632C22semidirect
28. #14582625C22semidirect
31. C2×C4×D4×C43C22semidirect
33. C43×#398C22semidirect
37. C43×#394C22semidirect
39. C4×C4⋊C4×C43C22semidirect
53. #13063325D4semidirect
55. #13063322D4semidirect
73. C4×D172D4semidirect
126. C22×C4×C43D8semidirect
283. #2392D43semidirect
309. C2×C4×D4C2×D43semidirect
317. #398C2×D43semidirect
321. #394C2×D43semidirect
323. C4×C4⋊C4C2×D43semidirect
329. C43#18122semidirect
439. C22×C4#10621882semidirect

Maximal subgroups

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

subgroupindex
#191479282
#191445952
#191335972
#191335802
#191335292
#191335122
#191330892
#191329092
C43×#23922
#1812243