Finite Group Databasebeta

← #25082063

Subgroups — #25082063

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145725C211yesmaximal, characteristic, complemented
2#19144410C211yesmaximal, characteristic, complemented
3#19144050C211yesmaximal, characteristic
4#19134011C212yesmaximal, complemented
5#19134004C212yesmaximal, complemented
6#19133977C212yesmaximal, complemented
7#19133970C212yesmaximal, complemented
8#19133366C211yesmaximal, characteristic, complemented
9#19133270C211yesmaximal, characteristic, complemented
10C2×#14582647C211yesmaximal, characteristic, complemented
11C43×#2988C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13#14583449C2211yescharacteristic
14C2×#13063325C2211yescharacteristic
15#14583297C2212yes—
16#14583246C2212yes—
17#14583218—22no—
18#14583194C2212yes—
19#14583190—21no—
20#14583190—21no—
21#14583189C2212yes—
22#14583184—21no—
23#14583179—21no—
24#14583121—21no—
25#14583114—21no—
26#14583109C2211yescharacteristic
27#14583104C2211yescharacteristic
28#14583099C2211yescharacteristic
29#14583094C2211yescharacteristic
30#14582942—21no—
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582900—21no—
34#14582893—21no—
35#14582650C2212yes—
36#14582650C2212yes—
37#14582647C2212yes—
38#14582647C2212yes—
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×#10621883—21no—
54C2×#10621884—21no—
55C2×#10621882—21no—
56C2×#10621877—21no—
57C22×C43⋊C8—21no—
58#13063325—21no—
59#13063325—21no—
60#13063325—21no—
61#13063325C2311yescharacteristic
62#13063325C2312yes—
63#13063322C2311yescharacteristic
64#13063313—21no—
65#13063299—21no—
66#13063299—21no—
67C4×D172—21no—
68C4×D172—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71#13063258—22no—
72#13063257—22no—
73#13063257—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#13063249—22no—
81#13063248—21no—
82#13063248—21no—
83#13063247—22no—
84#13063247—22no—
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×C43SD1614yes—
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—82no—
133C2×C8×C43—22no—
134C2×C8×C43—82no—
135C2×C8×C43—81no—
136C2×C8×C43C2×D412yes—
137C2×C8×C43C2×D412yes—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43C2×D411yescharacteristic
141C4⋊C4×C43C2×D411yescharacteristic
142C22⋊C4×C43—21no—
143C22⋊C4×C43—21no—
144C22⋊C4×C43—21no—
145C42×C43—21no—
146C42×C43—21no—
147C42×C43—21no—
148C42×C43C2×D411yescharacteristic
149C42×C43C2×D411yescharacteristic
150C42×C43#4111yescharacteristic
151C42×C43C2411yescharacteristic
152#10621885—42no—
153#10621884—42no—
154#10621883—42no—
155#10621882—42no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158C4⋊Dic43—22no—
159C4⋊Dic43—22no—
160C4⋊Dic43—21no—
161C4⋊Dic43—21no—
162C4⋊Dic43—41no—
163C4⋊Dic43—41no—
164#10621877—42no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—42no—
169C23×C43—21no—
170C23×C43#12111yescharacteristic
171C22×D43—41no—
172Q8×C43—21no—
173Q8×C43C2×SD1612yes—
174D4×C43—24no—
175D4×C43—21no—
176D4×C43C2×SD1612yes—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—24no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—81no—
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43C2×SD1612yes—
191C2×C4×C43#13512yes—
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C2×#4111yescharacteristic
195C22⋊D43—82no—
196C2×Dic43—42no—
197C2×Dic43—41no—
198C2×Dic43—82no—
199D172—41no—
200D172—41no—
201D172—41no—
202D172—41no—
203D172—81no—
204C4×D43—82no—
205Dic86—41no—
206Dic86—41no—
207Dic86—82no—
208Dic86—82no—
209C8×C43—22no—
210C8×C43—22no—
211C8×C43—42no—
212C43⋊C8—41no—
213C43⋊C8—41no—
214C43⋊C8—42no—
215#19414—431nomaximal, Sylow
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—22no—
219C22×C43—41no—
220C22×C43—41no—
221C22×C43#46512yes—
222C22×C43C2×#12111yescharacteristic
223C2×D43—81no—
224C2×D43—81no—
225C2×D43—81no—
226C4×C43—21no—
227C4×C43—22no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—41no—
231C4×C43—41no—
232C4×C43#46512yes—
233C4×C43C22×SD1611yescharacteristic
234C4×C43C2×#13511yescharacteristic
235C4×C43#57711yescharacteristic
236C4×C43#57811yescharacteristic
237Dic43—81no—
238Dic43—82no—
239#3227—431no—
240#3079—431no—
241#3035—431no—
242#2988D4311yescharacteristic, complemented
243#1678—432no—
244#1677—432no—
245#1672—432no—
246#1671—432no—
247#1570—431no—
248#1547—431no—
249C2×#333—431no—
250C2×C43—22no—
251C2×C43—42no—
252C2×C43#304611yescharacteristic
253C2×C43C2×#46511yescharacteristic
254C2×C43#306811yescharacteristic
255D43—161no—
256C2×#135—861no—
257#532—431no—
258C2×C4⋊Q8—431no—
259C4×#41C2×D4311yescharacteristic
260#498—432no—
261#486—432no—
262#481—862no—
263#477—432no—
264#476—432no—
265#476—861no—
266#476—861no—
267#475—861no—
268#474—861no—
269#464—861no—
270#463—861no—
271#462—431no—
272#461—431no—
273#460—431no—
274#459—431no—
275C8×Q8C2×D4312yes—
276C8×D4—22no—
277C8×D4C2×D4312yes—
278#431—21no—
279#431C2×D4311yescharacteristic
280#428—861no—
281#423—431no—
282C2×C4⋊C8—21no—
283C2×C4⋊C8—431no—
284C2×C4⋊C8C2×D4311yescharacteristic
285#417—861no—
286#416—861no—
287#334—432no—
288#334—432no—
289#333—432no—
290#333—432no—
291#332—432no—
292#331—432no—
293C43#1941411yescharacteristic, complemented, Sylow
294C2×#41—861no—
295C2×#41D17211yescharacteristic
296C22×Q8—861no—
297#135—1724no—
298C2×Q16—861no—
299C2×SD16—861no—
300C2×SD16—861no—
301C2×D8—861no—
302C2×M16—861no—
303C22×C8—21no—
304C22×C8—22no—
305C22×C8—861no—
306C4⋊Q8—432no—
307C4⋊Q8—431no—
308C4⋊Q8—861no—
309C4⋊Q8—861no—
310C4⋊Q8—861no—
311#127—431no—
312#124—861no—
313#121—861no—
314#121—861no—
315C4×Q8D17211yescharacteristic
316C4×Q8C22×D4311yescharacteristic
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—861no—
320C4×D4—861no—
321C4×D4D17211yescharacteristic
322C4×D4C22×D4311yescharacteristic
323#117—21no—
324#117D17211yescharacteristic
325C2×C4⋊C4—861no—
326C2×C4⋊C4—861no—
327C2×C42—21no—
328C2×C42C22×D4311yescharacteristic
329#107—862no—
330#106—862no—
331#106—862no—
332#106—862no—
333C4⋊C8—22no—
334C4⋊C8—21no—
335C4⋊C8—432no—
336C4⋊C8—431no—
337C4⋊C8—431no—
338C4⋊C8—861no—
339C4⋊C8—861no—
340C4⋊C8C22⋊D4311yescharacteristic
341C4⋊C8C22⋊D4311yescharacteristic
342C4⋊C8C22×D4312yes—
343#103—862no—
344#103—861no—
345#103—861no—
346#102—862no—
347#102—862no—
348#102—862no—
349#102—861no—
350#102—861no—
351C22⋊C8—22no—
352C22⋊C8C22⋊D4312yes—
353C4×C8—22no—
354C4×C8C22×D4312yes—
355#41—22no—
356#41—1722no—
357#41—1722no—
358#41#1062187314yes—
359C2×Q8—861no—
360C2×Q8—862no—
361C2×Q8—3442no—
362C2×Q8—1721no—
363C2×Q8C2×D17211yescharacteristic
364C2×D4—21no—
365C2×D4—861no—
366C2×D4—861no—
367C2×D4—861no—
368C2×D4—1721no—
369C2×D4C2×D17211yescharacteristic
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—1721no—
374C22×C4—1721no—
375C22×C4C2×D17211yescharacteristic
376C22×C4#1062189811yescharacteristic
377C22×C4C2×C22⋊D4311yescharacteristic
378Q16—1722no—
379SD16—1722no—
380SD16—1722no—
381D8—1722no—
382M16—1722no—
383C2×C8—22no—
384C2×C8—82no—
385C2×C8—81no—
386C2×C8—862no—
387C2×C8—861no—
388C2×C8—861no—
389C2×C8—1722no—
390C2×C8C2×C22⋊D4312yes—
391C2×C8C2×C22⋊D4312yes—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—862no—
395C4⋊C4—861no—
396C4⋊C4—862no—
397C4⋊C4—861no—
398C4⋊C4—1721no—
399C4⋊C4—1721no—
400C4⋊C4C2×D17211yescharacteristic
401C4⋊C4C2×D17211yescharacteristic
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—1721no—
406C22⋊C4—1721no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42C2×D17211yescharacteristic
411C42#1062189811yescharacteristic
412C42C2×C22⋊D4311yescharacteristic
413C42C23×D4311yescharacteristic
414C23—21no—
415C23—1721no—
416C23#1306329911yescharacteristic
417Q8—21no—
418Q8—3442no—
419Q8—3442no—
420Q8—1721no—
421Q8—1721no—
422Q8C2×#1062187312yes—
423D4—24no—
424D4—21no—
425D4—3441no—
426D4—3442no—
427D4—1721no—
428D4—1721no—
429D4—1721no—
430D4—1721no—
431D4C2×#1062187312yes—
432C2×C4—21no—
433C2×C4—24no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—81no—
442C2×C4—3442no—
443C2×C4—3442no—
444C2×C4—1721no—
445C2×C4—1722no—
446C2×C4#1306329911yescharacteristic
447C2×C4#1306329911yescharacteristic
448C2×C4#1306329911yescharacteristic
449C2×C4C2×#1062187312yes—
450C2×C4#1306334712yes—
451C2×C4C22×C22⋊D4311yescharacteristic
452C2×C4C22×D17211yescharacteristic
453C2×C4C2×#1062189811yescharacteristic
454C8—22no—
455C8—22no—
456C8—42no—
457C8—1721no—
458C8—1721no—
459C8—1722no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—3441no—
466C22—3441no—
467C22—3441no—
468C22#1458312812yes—
469C22C2×#1306329911yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—22no—
474C4—41no—
475C4—41no—
476C4—3442no—
477C4—3441no—
478C4#1458312812yes—
479C4C22×#1062187311yescharacteristic
480C4C2×#1306334711yescharacteristic
481C4#1458371011yescharacteristic
482C4#1458371411yescharacteristic
483C2—22no—
484C2—42no—
485C2—6881no—
486C2#1914414511yescharacteristic
487C2C2×#1458312811yescharacteristic
488C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×#121
prime radical#19144050C2
hypercenter#2988D43
hypocenterC43#19414
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. #19145725C2semidirect
2. #19144410C2semidirect
4. #19134011C2semidirect
5. #19134004C2semidirect
6. #19133977C2semidirect
7. #19133970C2semidirect
8. #19133366C2semidirect
9. #19133270C2semidirect
10. C2×#14582647C2semidirect
11. C43×#2988C2semidirect
242. #2988D43semidirect
293. C43#19414semidirect

Maximal subgroups

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

subgroupindex
#191457252
#191444102
#191440502
#191340112
#191340042
#191339772
#191339702
#191333662
#191332702
C2×#145826472
C43×#29882
#1941443