Finite Group Databasebeta

← #25081989

Subgroups — #25081989

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145522C211yesmaximal, characteristic, complemented
2#19144410C211yesmaximal, characteristic, complemented
3#19144050C211yesmaximal, characteristic
4#19134025C212yesmaximal, complemented
5#19134018C212yesmaximal, complemented
6#19133943C212yesmaximal, complemented
7#19133936C212yesmaximal, complemented
8#19133366C211yesmaximal, characteristic, complemented
9#19133270C211yesmaximal, characteristic, complemented
10C2×#14582646C211yesmaximal, characteristic, complemented
11C43×#2988C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13#14583449C2211yescharacteristic
14C2×#13063325C2211yescharacteristic
15#14583272C2212yes—
16#14583250C2212yes—
17#14583194—21no—
18#14583189—21no—
19#14583184C2212yes—
20#14583179C2212yes—
21#14583121—21no—
22#14583114—21no—
23#14583109C2211yescharacteristic
24#14583105—21no—
25#14583105—21no—
26#14583104C2211yescharacteristic
27#14583099C2211yescharacteristic
28#14583094C2211yescharacteristic
29#14583040—22no—
30#14582942—21no—
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582900—21no—
34#14582893—21no—
35#14582650C2212yes—
36#14582650C2212yes—
37#14582646C2212yes—
38#14582646C2212yes—
39#14582644C2212yes—
40#14582642C2212yes—
41C4×#41×C43C2211yescharacteristic
42C8×Q8×C43C2212yes—
43C8×D4×C43—22no—
44C8×D4×C43C2212yes—
45C43×#431—21no—
46C43×#431C2211yescharacteristic
47C2×C4⋊C8×C43—21no—
48C2×C4⋊C8×C43C2211yescharacteristic
49C2×#10621898—21no—
50C22×Dic86—21no—
51#13063345—44no—
52C2×#10621885—21no—
53C2×#10621873—22no—
54C2×#10621873—22no—
55C2×#10621883—21no—
56C2×#10621884—21no—
57C2×#10621882—21no—
58C2×#10621877—21no—
59C22×C43⋊C8—21no—
60#13063325—21no—
61#13063325—21no—
62#13063325—21no—
63#13063325C2311yescharacteristic
64#13063325C2312yes—
65#13063322C2311yescharacteristic
66#13063313—21no—
67#13063299—21no—
68#13063299—21no—
69C4×D172—21no—
70C4×D172—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73#13063258—22no—
74#13063256—22no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)C2311yescharacteristic
78C4⋊(C43⋊C8)C2311yescharacteristic
79C4⋊(C43⋊C8)C2312yes—
80#13063250—22no—
81#13063250—22no—
82#13063249—22no—
83#13063248—21no—
84#13063248—21no—
85#13063246—22no—
86#13063245—21no—
87#13063245—21no—
88C2×#41×C43D411yescharacteristic
89C22×C8×C43—21no—
90C22×C8×C43—22no—
91C4×Q8×C43D411yescharacteristic
92C4×Q8×C43C2311yescharacteristic
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43D411yescharacteristic
96C4×D4×C43C2311yescharacteristic
97#117×C43—21no—
98#117×C43D411yescharacteristic
99C2×C42×C43—21no—
100C2×C42×C43C2311yescharacteristic
101C4⋊C8×C43—22no—
102C4⋊C8×C43—21no—
103C4⋊C8×C43D411yescharacteristic
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43C2312yes—
106C22⋊C8×C43—22no—
107C22⋊C8×C43D412yes—
108C4×C8×C43—22no—
109C4×C8×C43C2312yes—
110#41×C43—22no—
111#41×C43SD1614yescomplemented
112C2×Q8×C43C2×D411yescharacteristic
113C2×D4×C43—21no—
114C2×D4×C43C2×D411yescharacteristic
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C2×C22⋊D43—41no—
122C22×Dic43—41no—
123#10621898—42no—
124#10621898—42no—
125C2×D172—21no—
126C2×D172—21no—
127C2×D172—21no—
128C2×C4×D43—41no—
129C2×Dic86—21no—
130C2×Dic86—22no—
131C2×Dic86—41no—
132C2×Dic86—81no—
133C2×Dic86—81no—
134C2×C8×C43—22no—
135C2×C8×C43—82no—
136C2×C8×C43—81no—
137C2×C8×C43C2×D412yes—
138C2×C8×C43C2×D412yes—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43C2×D411yescharacteristic
142C4⋊C4×C43C2×D411yescharacteristic
143C22⋊C4×C43—21no—
144C22⋊C4×C43—21no—
145C22⋊C4×C43—21no—
146C42×C43—21no—
147C42×C43—21no—
148C42×C43—21no—
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43#4111yescharacteristic
152C42×C43C2411yescharacteristic
153#10621885—42no—
154#10621884—42no—
155#10621883—42no—
156#10621882—42no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159C4⋊Dic43—22no—
160C4⋊Dic43—21no—
161C4⋊Dic43—22no—
162C4⋊Dic43—21no—
163C4⋊Dic43—41no—
164C4⋊Dic43—41no—
165#10621877—42no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—21no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—42no—
170#10621873—82no—
171#10621873—82no—
172C23×C43—21no—
173C23×C43#12111yescharacteristic
174C22×D43—41no—
175Q8×C43—21no—
176Q8×C43C2×SD1612yes—
177D4×C43—24no—
178D4×C43—21no—
179D4×C43C2×SD1612yes—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—24no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—81no—
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43C2×SD1612yes—
194C2×C4×C43#13512yes—
195C2×C4×C43C22×D411yescharacteristic
196C2×C4×C43C22×D411yescharacteristic
197C2×C4×C43C2×#4111yescharacteristic
198C22⋊D43—82no—
199C2×Dic43—42no—
200C2×Dic43—41no—
201C2×Dic43—82no—
202D172—41no—
203D172—41no—
204D172—41no—
205D172—41no—
206D172—81no—
207C4×D43—82no—
208Dic86—41no—
209Dic86—41no—
210Dic86—42no—
211Dic86—42no—
212Dic86—82no—
213C8×C43—22no—
214C8×C43—22no—
215C8×C43—42no—
216C43⋊C8—41no—
217C43⋊C8—41no—
218C43⋊C8—42no—
219#19408—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—22no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43#46512yes—
226C22×C43C2×#12111yescharacteristic
227C2×D43—81no—
228C2×D43—81no—
229C2×D43—81no—
230C4×C43—21no—
231C4×C43—22no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—41no—
235C4×C43—41no—
236C4×C43#46512yes—
237C4×C43C22×SD1611yescharacteristic
238C4×C43C2×#13511yescharacteristic
239C4×C43#57611yescharacteristic
240C4×C43#57711yescharacteristic
241Dic43—82no—
242Dic43—81no—
243#3206—431no—
244#3079—431no—
245#3035—431no—
246#2988D4311yescharacteristic, complemented
247#1680—432no—
248#1679—432no—
249#1666—432no—
250#1665—432no—
251#1570—431no—
252#1547—431no—
253C2×#332—431no—
254C2×C43—22no—
255C2×C43—42no—
256C2×C43#304511yescharacteristic
257C2×C43C2×#46511yescharacteristic
258C2×C43#306911yescharacteristic
259D43—161no—
260C2×#135—861no—
261#532—431no—
262C2×C4⋊Q8—431no—
263C4×#41C2×D4311yescharacteristic
264#492—432no—
265#487—432no—
266#477—861no—
267#476—861no—
268#475—432no—
269#474—432no—
270#464—861no—
271#463—861no—
272#462—431no—
273#461—431no—
274#461—861no—
275#461—861no—
276#460—431no—
277#459—431no—
278#448—862no—
279C8×Q8C2×D4312yes—
280C8×D4—22no—
281C8×D4C2×D4312yes—
282#431—21no—
283#431C2×D4311yescharacteristic
284#428—861no—
285#423—431no—
286C2×C4⋊C8—21no—
287C2×C4⋊C8—431no—
288C2×C4⋊C8C2×D4311yescharacteristic
289#417—861no—
290#416—861no—
291#334—432no—
292#334—432no—
293#332—432no—
294#332—432no—
295#332—432no—
296#331—432no—
297C43#1940811yescharacteristic, complemented, Sylow
298C2×#41—861no—
299C2×#41D17211yescharacteristic
300C22×Q8—861no—
301#135—1724no—
302C2×Q16—861no—
303C2×SD16—861no—
304C2×SD16—861no—
305C2×SD16—862no—
306C2×SD16—862no—
307C2×D8—861no—
308C2×M16—861no—
309C22×C8—21no—
310C22×C8—22no—
311C22×C8—861no—
312C4⋊Q8—432no—
313C4⋊Q8—431no—
314C4⋊Q8—861no—
315C4⋊Q8—861no—
316C4⋊Q8—861no—
317#127—431no—
318#124—861no—
319#121—861no—
320#121—861no—
321C4×Q8D17211yescharacteristic
322C4×Q8C22×D4311yescharacteristic
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—861no—
326C4×D4—861no—
327C4×D4D17211yescharacteristic
328C4×D4C22×D4311yescharacteristic
329#117—21no—
330#117D17211yescharacteristic
331C2×C4⋊C4—861no—
332C2×C4⋊C4—861no—
333C2×C42—21no—
334C2×C42C22×D4311yescharacteristic
335#107—862no—
336#106—862no—
337C4⋊C8—22no—
338C4⋊C8—21no—
339C4⋊C8—432no—
340C4⋊C8—431no—
341C4⋊C8—431no—
342C4⋊C8—861no—
343C4⋊C8—861no—
344C4⋊C8C22⋊D4311yescharacteristic
345C4⋊C8C22⋊D4311yescharacteristic
346C4⋊C8C22×D4312yes—
347#103—862no—
348#103—862no—
349#103—862no—
350#103—861no—
351#103—861no—
352#102—862no—
353#102—861no—
354#102—861no—
355C22⋊C8—22no—
356C22⋊C8C22⋊D4312yes—
357C4×C8—22no—
358C4×C8C22×D4312yes—
359#41—22no—
360#41—1722no—
361#41—1722no—
362#41#1062187314yescomplemented
363C2×Q8—862no—
364C2×Q8—861no—
365C2×Q8—3441no—
366C2×Q8—3441no—
367C2×Q8—1721no—
368C2×Q8C2×D17211yescharacteristic
369C2×D4—21no—
370C2×D4—861no—
371C2×D4—861no—
372C2×D4—861no—
373C2×D4—1721no—
374C2×D4C2×D17211yescharacteristic
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—1721no—
379C22×C4—1721no—
380C22×C4C2×D17211yescharacteristic
381C22×C4#1062189811yescharacteristic
382C22×C4C2×C22⋊D4311yescharacteristic
383Q16—1722no—
384SD16—3442no—
385SD16—3442no—
386SD16—1722no—
387SD16—1722no—
388D8—1722no—
389M16—1722no—
390C2×C8—22no—
391C2×C8—82no—
392C2×C8—81no—
393C2×C8—862no—
394C2×C8—861no—
395C2×C8—861no—
396C2×C8—1722no—
397C2×C8C2×C22⋊D4312yes—
398C2×C8C2×C22⋊D4312yes—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—861no—
402C4⋊C4—862no—
403C4⋊C4—862no—
404C4⋊C4—861no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C4⋊C4C2×D17211yescharacteristic
408C4⋊C4C2×D17211yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42C2×D17211yescharacteristic
418C42#1062189811yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—21no—
422C23—1721no—
423C23#1306329911yescharacteristic
424Q8—21no—
425Q8—3442no—
426Q8—1721no—
427Q8—1721no—
428Q8—1722no—
429Q8—1722no—
430Q8C2×#1062187312yes—
431D4—24no—
432D4—21no—
433D4—3441no—
434D4—3442no—
435D4—1721no—
436D4—1721no—
437D4—1721no—
438D4—1721no—
439D4C2×#1062187312yes—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—81no—
450C2×C4—3442no—
451C2×C4—3442no—
452C2×C4—1721no—
453C2×C4—1722no—
454C2×C4#1306329911yescharacteristic
455C2×C4#1306329911yescharacteristic
456C2×C4#1306329911yescharacteristic
457C2×C4C2×#1062187312yes—
458C2×C4#1306334712yes—
459C2×C4C22×C22⋊D4311yescharacteristic
460C2×C4C22×D17211yescharacteristic
461C2×C4C2×#1062189811yescharacteristic
462C8—22no—
463C8—22no—
464C8—42no—
465C8—1721no—
466C8—1721no—
467C8—1722no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—3441no—
474C22—3441no—
475C22—3441no—
476C22#1458312812yes—
477C22C2×#1306329911yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—3442no—
485C4—3441no—
486C4#1458312812yes—
487C4C22×#1062187311yescharacteristic
488C4C2×#1306334711yescharacteristic
489C4#1458370211yescharacteristic
490C4#1458370711yescharacteristic
491C2—22no—
492C2—42no—
493C2—6881no—
494C2#1914413411yescharacteristic
495C2C2×#1458312811yescharacteristic
496C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×#121
prime radical#19144050C2
hypercenter#2988D43
hypocenterC43#19408
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #19145522C2semidirect
2. #19144410C2semidirect
4. #19134025C2semidirect
5. #19134018C2semidirect
6. #19133943C2semidirect
7. #19133936C2semidirect
8. #19133366C2semidirect
9. #19133270C2semidirect
10. C2×#14582646C2semidirect
11. C43×#2988C2semidirect
111. #41×C43SD16semidirect
246. #2988D43semidirect
297. C43#19408semidirect
362. #41#10621873semidirect

Maximal subgroups

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

subgroupindex
#191455222
#191444102
#191440502
#191340252
#191340182
#191339432
#191339362
#191333662
#191332702
C2×#145826462
C43×#29882
#1940843