Finite Group Databasebeta

← #25138090

Subgroups — #25138090

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144404C211yesmaximal, characteristic
2C2×#14583181C211yesmaximal, characteristic, complemented
3C4×#13063358C211yesmaximal, characteristic
4#19143263C211yesmaximal, characteristic
5#19136044C212yesmaximal
6#19135897C212yesmaximal
7#19135374C212yesmaximal, complemented
8#19135370C211yesmaximal, characteristic, complemented
9#19135248C212yesmaximal, complemented
10#19134588C211yesmaximal, characteristic, complemented
11C43×#1997C211yesmaximal, characteristic, complemented
12C2×#13063358C2211yescharacteristic
13C4×#10621898C2211yescharacteristic
14C2×C4×Dic86C2211yescharacteristic
15#14583191—21no—
16#14583186—21no—
17#14583181—21no—
18#14583181—21no—
19#14583181—21no—
20#14583181—22no—
21#14583176—21no—
22#14583007—21no—
23#14583001—21no—
24C4×Dic172—21no—
25C4×#10621873—21no—
26#14582959—22no—
27#14582955—21no—
28#14582951—21no—
29C2×#13063260C2212yes—
30#14582941C2211yescharacteristic
31#14582939C2212yes—
32C2×#13063256C2212yes—
33#14582923C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35#14582909C2211yescharacteristic
36#14582901C2211yescharacteristic
37#14582898C2212yes—
38C2×#13063248C2212yes—
39C2×#13063243C2212yes—
40#14582867C2212yes—
41#14582857C2212yes—
42#14582667C2212yes—
43#14582663C2212yes—
44C2×C4⋊Q8×C43C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C43×#343C2212yes—
48C43×#343C2212yes—
49C2×#10621898C2311yescharacteristic
50C22×Dic86C2311yescharacteristic
51#13063358—22no—
52#13063358—22no—
53C2×Dic172—21no—
54C2×#10621873—21no—
55C2×#10621877C2312yes—
56C22×C43⋊C8C2312yes—
57C4×Dic86—21no—
58C4×Dic86—21no—
59C4×Dic86—21no—
60C4×Dic86—21no—
61C4×Dic86D411yescharacteristic
62C4×Dic86D411yescharacteristic
63C4×D172D411yescharacteristic
64C4×D172D411yescharacteristic
65C4×C22⋊D43—21no—
66C4×C22⋊D43—21no—
67#13063284C2311yescharacteristic
68#13063282—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×C4×Dic43—21no—
72C42×D43—21no—
73#13063260—24no—
74#13063259—21no—
75#13063258—22no—
76#13063257—21no—
77#13063256—22no—
78#13063256—22no—
79#13063256—22no—
80C4⋊(C43⋊C8)—21no—
81C4⋊(C43⋊C8)—21no—
82C4⋊(C43⋊C8)D411yescharacteristic
83C4⋊(C43⋊C8)D411yescharacteristic
84C4⋊(C43⋊C8)D412yes—
85#13063250—21no—
86#13063250—21no—
87#13063250—21no—
88#13063248—22no—
89#13063248—22no—
90#13063248—22no—
91#13063247—21no—
92#13063245—22no—
93#13063243—24no—
94(C2×D43)⋊C8—22no—
95(C2×D43)⋊C8—22no—
96#13063235—22no—
97C8×Dic43—22no—
98C22×Q8×C43—21no—
99C2×M16×C43C2312yes—
100C2×M16×C43C2311yescharacteristic
101C2×M16×C43C2311yescharacteristic
102C4⋊Q8×C43—21no—
103C4⋊Q8×C43—21no—
104C4⋊Q8×C43—21no—
105C4⋊Q8×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2312yes—
108C2×C42×C43C2311yescharacteristic
109C4⋊C8×C43—21no—
110C4⋊C8×C43—21no—
111#97×C43—21no—
112C4×C8×C43—21no—
113C2×Q8×C43—41no—
114C2×Q8×C43—41no—
115C2×Q8×C43—82no—
116C22×C4×C43—22no—
117C22×C4×C43#4111yescharacteristic
118C22×C4×C43#4111yescharacteristic
119C22×C4×C43C2411yescharacteristic
120C2×C22⋊D43—21no—
121C22×Dic43—21no—
122C22×Dic43—21no—
123#10621898—21no—
124#10621898—21no—
125#10621898—21no—
126#10621898—21no—
127C2×D172C2×D411yescharacteristic
128C2×C4×D43—21no—
129C2×C4×D43—21no—
130C2×C4×D43—21no—
131C2×Dic86—21no—
132C2×Dic86—21no—
133C2×Dic86—21no—
134C2×Dic86—21no—
135C2×Dic86—21no—
136C2×Dic86C2×D411yescharacteristic
137C2×Dic86#4112yes—
138M16×C43—21no—
139M16×C43—22no—
140M16×C43—21no—
141M16×C43—22no—
142M16×C43—21no—
143M16×C43#4112yes—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—41no—
150C4⋊C4×C43—41no—
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C22⋊Dic43—21no—
156(C2×D43)⋊C4—21no—
157(C2×D43)⋊C4—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43C2×D411yescharacteristic
161C4⋊Dic43C2×D411yescharacteristic
162Dic43⋊C4—21no—
163Dic43⋊C4—21no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166C4×Dic43—21no—
167C4×Dic43—21no—
168C4×Dic43—21no—
169C4×Dic43—41no—
170C4×Dic43—41no—
171#10621877—22no—
172#10621877—22no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8C2×D412yes—
177C2×C43⋊C8C2×D412yes—
178Dic172—24no—
179#10621873—24no—
180C23×C43C2×#4111yescharacteristic
181C22×D43—21no—
182Q8×C43—82no—
183Q8×C43—82no—
184C2×C4×C43—22no—
185C2×C4×C43—41no—
186C2×C4×C43—42no—
187C2×C4×C43—82no—
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C2×#4111yescharacteristic
195C2×C4×C43C2×#4111yescharacteristic
196C2×C4×C432−1+411yescharacteristic
197C2×C4×C432−1+411yescharacteristic
198C22⋊D43—41no—
199C22⋊D43—41no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—22no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—81no—
208D172—21no—
209D172—21no—
210C4×D43—41no—
211C4×D43—41no—
212C4×D43—42no—
213C4×D43—81no—
214Dic86—22no—
215Dic86—21no—
216Dic86—21no—
217Dic86—22no—
218Dic86—41no—
219Dic86—41no—
220C8×C43—22no—
221C8×C43—41no—
222C8×C43—42no—
223C43⋊C8—22no—
224C43⋊C8—22no—
225C43⋊C8—42no—
226#24723—431nomaximal, Sylow
227C22×C43—21no—
228C22×C43—21no—
229C22×C43C2×#12111yescharacteristic
230C22×C43#55211yescharacteristic
231C22×C43#55611yescharacteristic
232C2×D43—41no—
233C2×D43—41no—
234C2×D43—41no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—82no—
239C4×C43#47112yes—
240C4×C43#52511yescharacteristic
241C4×C43#53611yescharacteristic
242C4×C43#54711yescharacteristic
243C4×C43#54811yescharacteristic
244Dic43—42no—
245Dic43—41no—
246Dic43—41no—
247Dic43—41no—
248Dic43—81no—
249#3079—431no—
250C2×#475—431no—
251C4×#137—431no—
252#2925—431no—
253#2079—432no—
254#2052—432no—
255#1997D4311yescharacteristic, complemented
256#1951—432no—
257#1950—431no—
258#1930—432no—
259#1801—431no—
260C2×C43—21no—
261C2×C43—21no—
262C2×C43#241511yescharacteristic
263C2×C43C2×#47111yescharacteristic
264C2×C43#306911yescharacteristic
265D43—81no—
266C2×#137—431no—
267C2×C4⋊Q8C2×D4311yescharacteristic
268C4×#41—431no—
269C2×C4×Q8—431no—
270#477—861no—
271#476—861no—
272#475—861no—
273#475—861no—
274#475—862no—
275#475—861no—
276#474—861no—
277#441—861no—
278#440—861no—
279C4×Q16—861no—
280C4×SD16—861no—
281#433—862no—
282#432—861no—
283#431—861no—
284C2×#108—432no—
285#428—431no—
286#428—432no—
287C2×#106—432no—
288#423—431no—
289#423C2×D4311yescharacteristic
290C2×C4⋊C8—431no—
291#419—431no—
292#417—431no—
293#417—432no—
294C2×#103—432no—
295C2×#101—432no—
296#408—432no—
297#405—432no—
298C4×M16C2×D4311yescharacteristic
299#343—432no—
300#343C2×D4312yes—
301#343C2×D4312yes—
302#341—432no—
303C43#2472311yescharacteristic, complemented, Sylow
304C2×#41—431no—
305C22×Q8—21no—
306C22×Q8—431no—
307#137—862no—
308#137—862no—
309C2×Q16—861no—
310C2×SD16—861no—
311C2×M16—432no—
312C2×M16C22×D4311yescharacteristic
313C2×M16C22×D4312yes—
314C2×M16C22×D4311yescharacteristic
315C22×C8—432no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4×Q8—431no—
321C4×Q8—431no—
322C4×Q8—861no—
323C4×Q8—861no—
324C4×Q8—861no—
325C4×Q8—861no—
326C4×D4—431no—
327C4×D4—431no—
328C4×D4—861no—
329C4×D4—861no—
330#117—431no—
331#117—861no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—431no—
334C2×C4⋊C4—861no—
335C2×C4⋊C4C22×D4312yes—
336C2×C42—861no—
337C2×C42—861no—
338C2×C42C22×D4311yescharacteristic
339#108—864no—
340#107—862no—
341#107—861no—
342#106—862no—
343#106—862no—
344#106—862no—
345#106—861no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—431no—
349C4⋊C8—431no—
350C4⋊C8—432no—
351C4⋊C8—861no—
352C4⋊C8—861no—
353#103—862no—
354#103—862no—
355#103—862no—
356#103—861no—
357#103—861no—
358#103—861no—
359#102—862no—
360#102—861no—
361#101—864no—
362C22⋊C8—862no—
363C22⋊C8—862no—
364#97—21no—
365#97—862no—
366C4×C8—21no—
367C4×C8—862no—
368#41—861no—
369#41—861no—
370#41—861no—
371#41—861no—
372C2×Q8—41no—
373C2×Q8—41no—
374C2×Q8—82no—
375C2×Q8—431no—
376C2×Q8—432no—
377C2×Q8—861no—
378C2×Q8—861no—
379C2×Q8—861no—
380C2×Q8—861no—
381C2×Q8—861no—
382C2×D4—431no—
383C2×D4—861no—
384C22×C4—22no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—861no—
390C22×C4#1062189811yescharacteristic
391C22×C4#1062189811yescharacteristic
392C22×C4C23×D4311yescharacteristic
393Q16—864no—
394SD16—864no—
395M16—21no—
396M16—22no—
397M16—22no—
398M16—21no—
399M16—21no—
400M16—862no—
401M16—862no—
402M16#1062190212yes—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—22no—
406C2×C8—432no—
407C2×C8—432no—
408C2×C8—862no—
409C2×C8—862no—
410C2×C8—862no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—431no—
416C4⋊C4—431no—
417C4⋊C4—861no—
418C4⋊C4—861no—
419C4⋊C4—861no—
420C4⋊C4—861no—
421C4⋊C4—1721no—
422C4⋊C4—1721no—
423C22⋊C4—861no—
424C22⋊C4—861no—
425C22⋊C4—861no—
426C42—861no—
427C42—861no—
428C42—861no—
429C42—1721no—
430C42—1721no—
431C42D4×D4311yescharacteristic
432C42D4×D4311yescharacteristic
433C42D4×D4311yescharacteristic
434C42D4×D4311yescharacteristic
435C23—861no—
436C23C2×#1062189811yescharacteristic
437Q8—82no—
438Q8—82no—
439Q8—862no—
440Q8—862no—
441Q8—861no—
442Q8—861no—
443Q8—1721no—
444Q8—1721no—
445D4—861no—
446D4—861no—
447D4—1721no—
448D4—1721no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—82no—
453C2×C4—862no—
454C2×C4—861no—
455C2×C4—861no—
456C2×C4—861no—
457C2×C4—3441no—
458C2×C4—3441no—
459C2×C4—1721no—
460C2×C4—1721no—
461C2×C4—1721no—
462C2×C4—1721no—
463C2×C4—1721no—
464C2×C4—1722no—
465C2×C4#1306329811yescharacteristic
466C2×C4#1306329811yescharacteristic
467C2×C4#1306329811yescharacteristic
468C2×C4#1306329811yescharacteristic
469C2×C4C2×D4×D4311yescharacteristic
470C2×C4C2×D4×D4311yescharacteristic
471C2×C4#41×D4311yescharacteristic
472C2×C4C2×#1062190211yescharacteristic
473C2×C4#1306337211yescharacteristic
474C2×C4#1306337311yescharacteristic
475C8—22no—
476C8—42no—
477C8—41no—
478C8—862no—
479C8—862no—
480C8—1722no—
481C22—21no—
482C22—21no—
483C22—1721no—
484C22—1721no—
485C22—1721no—
486C22C2×#1306329811yescharacteristic
487C22#1458359011yescharacteristic
488C22#1458362211yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—82no—
493C4—3441no—
494C4—1721no—
495C4—1721no—
496C4—1721no—
497C4—1722no—
498C4#1458316112yes—
499C4#1458341211yescharacteristic
500C4#1458347211yescharacteristic
501C4#1458355211yescharacteristic
502C4#1458355711yescharacteristic
503C2—21no—
504C2—21no—
505C2—3441no—
506C2#1913802711yescharacteristic
507C2C2×#1458316111yescharacteristic
508C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1997C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
hypercenter#1997D43
hypocenterC43#24723
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
2. C2×#14583181C2semidirect
7. #19135374C2semidirect
8. #19135370C2semidirect
9. #19135248C2semidirect
10. #19134588C2semidirect
11. C43×#1997C2semidirect
255. #1997D43semidirect
303. C43#24723semidirect

Maximal subgroups

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

subgroupindex
#191444042
C2×#145831812
C4×#130633582
#191432632
#191360442
#191358972
#191353742
#191353702
#191352482
#191345882
C43×#19972
#2472343