Finite Group Databasebeta

← #25073846

Subgroups — #25073846

Order 11008.

918 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#19148411C211yesmaximal, characteristic
2#19145543C211yesmaximal, characteristic, complemented
3#19144404C211yesmaximal, characteristic
4#19133813C214yesmaximal, complemented
5#19133806C214yesmaximal, complemented
6#19133276C211yesmaximal, characteristic, complemented
7#19133051C211yesmaximal, characteristic, complemented
8#19132978C211yesmaximal, characteristic
9C2×C43×#487C211yesmaximal, characteristic, complemented
10#14583629C2212yes—
11#14583624—21no—
12#14583610C2212yes—
13#14583604—22no—
14#14583564—21no—
15Q8×C22⋊D43—22no—
16#14583530—21no—
17#14583526—22no—
18#14583456C2211yescharacteristic
19#14583454—21no—
20C4⋊Q8×D43—21no—
21#14583380—21no—
22C4×#10621898C2211yescharacteristic
23#14583278—21no—
24#14583249—21no—
25#14583191—21no—
26#14583186—21no—
27#14583181C2212yes—
28#14583176C2212yes—
29#14583106C2214yes—
30#14583055—22no—
31#14582952C2211yescharacteristic
32#14582939—21no—
33#14582923C2211yescharacteristic
34#14582898—21no—
35#14582648C2214yes—
36#14582631C2212yes—
37#14582631C2214yes—
38#14582628C2212yes—
39C2×C4⋊Q8×C43C2211yescharacteristic
40C2×C4⋊Q8×C43C2211yescharacteristic
41C43×#487—22no—
42C43×#487C2214yes—
43C2×#103×C43—22no—
44C2×C4×C8×C43C2211yescharacteristic
45C2×#10621898D411yescharacteristic
46C2×Q8×D43—22no—
47C2×#10621885—24no—
48C2×#10621877—21no—
49#13063325D411yescharacteristic
50#13063325D411yescharacteristic
51#13063324—22no—
52#13063324—22no—
53#13063324—22no—
54#13063323—22no—
55#13063323—24no—
56#13063317—21no—
57#13063316—22no—
58#13063316—22no—
59#13063315—24no—
60#13063305—22no—
61#13063304—24no—
62#13063304—21no—
63#13063304D412yes—
64#13063303—24no—
65#13063301—22no—
66#13063301—24no—
67Q8×Dic43—22no—
68C4×Dic86—21no—
69C4×Dic86D411yescharacteristic
70C4×Dic86C2312yes—
71C4×Dic86C2311yescharacteristic
72#13063290—22no—
73#13063290—22no—
74C4×D172D411yescharacteristic
75C4×D172C2311yescharacteristic
76#13063287—22no—
77C4×C22⋊D43—24no—
78C4×C22⋊D43—21no—
79C4×C22⋊D43—21no—
80#13063284—21no—
81#13063284D411yescharacteristic
82#13063283—22no—
83#13063282—21no—
84C4⋊C4×D43—22no—
85C4⋊C4×D43—22no—
86C42×D43—21no—
87#13063258—22no—
88#13063256—22no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2312yes—
91C4⋊(C43⋊C8)C2312yes—
92#13063249—24no—
93#13063248—22no—
94#13063245—22no—
95C22⋊(C43⋊C8)—21no—
96C4×C43⋊C8—21no—
97C22×Q8×C43—21no—
98C22×Q8×C43D412yes—
99C22×C8×C43—21no—
100C4⋊Q8×C43—21no—
101C4⋊Q8×C43—21no—
102C4⋊Q8×C43—21no—
103C4⋊Q8×C43—21no—
104C4⋊Q8×C43—21no—
105C4⋊Q8×C43D412yes—
106C4⋊Q8×C43C2312yes—
107C4⋊Q8×C43C2312yes—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C42×C43C2311yescharacteristic
113#103×C43—28no—
114C4×C8×C43—21no—
115C4×C8×C43C2312yes—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—44no—
119C2×Q8×C43—41no—
120C2×Q8×C43—82no—
121C2×Q8×C43C2×D414yes—
122C22×C4×C43—22no—
123C22×C4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C2×C22⋊D43—21no—
128Q8×D43—84no—
129#10621898—22no—
130#10621898Q1614yescomplemented
131C2×D172C2×D411yescharacteristic
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×C4×D43—21no—
135C2×C4×D43—24no—
136C2×Dic86—21no—
137C2×Dic86—24no—
138C2×Dic86C2×D412yes—
139C2×Dic86C2×D411yescharacteristic
140C2×C8×C43—22no—
141C2×C8×C43—42no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43—41no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43C2411yescharacteristic
154C22⋊Dic43—22no—
155C22⋊Dic43—21no—
156#10621885—84no—
157(C2×D43)⋊C4—24no—
158(C2×D43)⋊C4—21no—
159(C2×D43)⋊C4—21no—
160C4⋊Dic43—24no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43C2×D412yes—
165C4⋊Dic43C2×D411yescharacteristic
166C4⋊Dic43C2×D411yescharacteristic
167Dic43⋊C4—24no—
168Dic43⋊C4—24no—
169Dic43⋊C4—24no—
170Dic43⋊C4—21no—
171Dic43⋊C4—22no—
172Dic43⋊C4—21no—
173Dic43⋊C4—22no—
174C4×Dic43—24no—
175C4×Dic43—21no—
176C4×Dic43—21no—
177C4×Dic43—21no—
178C4×Dic43—22no—
179#10621877—42no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C23×C43#12011yescharacteristic
183C22×D43—21no—
184Q8×C43—44no—
185Q8×C43—44no—
186Q8×C43—44no—
187Q8×C43—82no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—24no—
191C2×C4×C43—42no—
192C2×C4×C43—82no—
193C2×C4×C43—82no—
194C2×C4×C43#12011yescharacteristic
195C2×C4×C43#12011yescharacteristic
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43C2×Q1612yes—
198C2×C4×C43#13712yes—
199C2×C4×C43C22×D411yescharacteristic
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C22⋊D43—24no—
203C2×Dic43—21no—
204C2×Dic43—22no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—22no—
208D172—21no—
209D172C2×Q1612yes—
210C4×D43—24no—
211C4×D43—42no—
212C4×D43—42no—
213C4×D43—84no—
214Dic86—21no—
215Dic86—24no—
216Dic86—42no—
217Dic86—84no—
218Dic86C2×Q1612yes—
219C8×C43—42no—
220C43⋊C8—42no—
221C43⋊C8—42no—
222#18633—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43#45112yes—
226C22×C43C2×#12011yescharacteristic
227C2×D43—22no—
228C2×D43—41no—
229C2×D43—41no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—44no—
233C4×C43—82no—
234C4×C43#45112yes—
235C4×C43#45512yes—
236C4×C43C22×Q1611yescharacteristic
237C4×C43C2×#13711yescharacteristic
238C4×C43#57712yes—
239Dic43—22no—
240Dic43—42no—
241Dic43—41no—
242Dic43—42no—
243Dic43—41no—
244#3503—431no—
245#3209—431no—
246C2×#487D4311yescharacteristic, complemented
247#3079—431no—
248#1645—434no—
249#1644—434no—
250#1548—431no—
251#1493—431no—
252#1476—431no—
253C2×C43—22no—
254C2×C43C2×#45111yescharacteristic
255C2×C43#301011yescharacteristic
256C2×C43C2×#45511yescharacteristic
257D43—42no—
258Q82—432no—
259#557—861no—
260#554—432no—
261#554—862no—
262D4×Q8—861no—
263D4×Q8—862no—
264#544—861no—
265#544—862no—
266#533—431no—
267#533—861no—
268C2×C4⋊Q8—861no—
269C2×C4⋊Q8C2×D4311yescharacteristic
270C2×C4⋊Q8C2×D4311yescharacteristic
271#520—861no—
272C4×#41—431no—
273#494—861no—
274#487—22no—
275#487—861no—
276#487C2×D4314yes—
277#477—861no—
278#476—861no—
279#475—432no—
280#474—432no—
281#462—434no—
282#451—862no—
283#431—431no—
284#428—861no—
285#423—431no—
286#417—861no—
287C2×#103—22no—
288C2×C4×C8C2×D4311yescharacteristic
289#333—434no—
290Q8⋊C8—434no—
291Q8⋊C8—432no—
292D4⋊C8—432no—
293C43#1863311yescharacteristic, complemented, Sylow
294C2×#41—431no—
295C22×Q8—21no—
296C22×Q8—862no—
297C22×Q8C22⋊D4312yes—
298C2×Q16—864no—
299C2×M16—861no—
300C22×C8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—431no—
307C4⋊Q8—431no—
308C4⋊Q8—862no—
309C4⋊Q8—862no—
310C4⋊Q8—862no—
311C4⋊Q8—862no—
312C4⋊Q8—864no—
313C4⋊Q8C22⋊D4312yes—
314C4⋊Q8C22×D4312yes—
315C4⋊Q8C22×D4312yes—
316#125—862no—
317#125—862no—
318#125—864no—
319#125—861no—
320C22⋊Q8—432no—
321C22⋊Q8—862no—
322C22⋊Q8—864no—
323C22⋊Q8—864no—
324C22⋊Q8—862no—
325C22⋊Q8—864no—
326C22⋊Q8—861no—
327C4×Q8—431no—
328C4×Q8—431no—
329C4×Q8—432no—
330C4×Q8—862no—
331C4×Q8—862no—
332C4×Q8—862no—
333C4×Q8—861no—
334C4×D4—431no—
335C4×D4—431no—
336C4×D4—862no—
337C4×D4—864no—
338C4×D4—861no—
339C4×D4—861no—
340#117—431no—
341#117—862no—
342#117—861no—
343#117—861no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—862no—
349C2×C4⋊C4—862no—
350C2×C42—861no—
351C2×C42C22×D4311yescharacteristic
352#107—862no—
353#106—862no—
354C4⋊C8—432no—
355C4⋊C8—432no—
356C4⋊C8—861no—
357#103—28no—
358#103—862no—
359#103—864no—
360#102—862no—
361C22⋊C8—861no—
362C4×C8—21no—
363C4×C8—861no—
364C4×C8C22×D4312yes—
365#41—434no—
366#41—862no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—44no—
370C2×Q8—41no—
371C2×Q8—82no—
372C2×Q8—431no—
373C2×Q8—432no—
374C2×Q8—864no—
375C2×Q8—861no—
376C2×Q8—3444no—
377C2×Q8C2×C22⋊D4314yes—
378C2×D4—431no—
379C2×D4—861no—
380C22×C4—22no—
381C22×C4—41no—
382C22×C4—864no—
383C22×C4—861no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4D4×D4311yescharacteristic
387C22×C4D4×D4311yescharacteristic
388C22×C4C2×C22⋊D4311yescharacteristic
389Q16—3444no—
390M16—1722no—
391C2×C8—22no—
392C2×C8—42no—
393C2×C8—862no—
394C2×C8—862no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—432no—
404C4⋊C4—431no—
405C4⋊C4—431no—
406C4⋊C4—864no—
407C4⋊C4—864no—
408C4⋊C4—864no—
409C4⋊C4—864no—
410C4⋊C4—861no—
411C4⋊C4—861no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C4⋊C4—862no—
415C4⋊C4—861no—
416C4⋊C4—862no—
417C22⋊C4—864no—
418C22⋊C4—861no—
419C22⋊C4—862no—
420C22⋊C4—861no—
421C22⋊C4—861no—
422C42—864no—
423C42—861no—
424C42—861no—
425C42—861no—
426C42—862no—
427C42D4×D4311yescharacteristic
428C42D4×D4311yescharacteristic
429C42C2×C22⋊D4311yescharacteristic
430C42C23×D4311yescharacteristic
431C23—861no—
432C23#1306329311yescharacteristic
433Q8—44no—
434Q8—44no—
435Q8—44no—
436Q8—82no—
437Q8—432no—
438Q8—861no—
439Q8—864no—
440Q8—3444no—
441Q8—1722no—
442D4—432no—
443D4—864no—
444D4—861no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—42no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—861no—
452C2×C4—864no—
453C2×C4—862no—
454C2×C4—861no—
455C2×C4—861no—
456C2×C4—862no—
457C2×C4—3444no—
458C2×C4—1722no—
459C2×C4—1722no—
460C2×C4#1306329311yescharacteristic
461C2×C4#1306329311yescharacteristic
462C2×C4#1306329311yescharacteristic
463C2×C4Q16×D4312yes—
464C2×C4#1306335712yes—
465C2×C4C2×D4×D4311yescharacteristic
466C2×C4C2×D4×D4311yescharacteristic
467C2×C4C22×C22⋊D4311yescharacteristic
468C8—42no—
469C8—1722no—
470C8—1722no—
471C22—21no—
472C22—21no—
473C22—862no—
474C22—1721no—
475C22—1721no—
476C22#1458305312yes—
477C22C2×#1306329311yescharacteristic
478C4—21no—
479C4—21no—
480C4—44no—
481C4—82no—
482C4—862no—
483C4—1721no—
484C4—1722no—
485C4—1722no—
486C4—1721no—
487C4#1458305312yes—
488C4#1458307612yes—
489C4C2×Q16×D4311yescharacteristic
490C4C2×#1306335711yescharacteristic
491C4#1458370512yes—
492C2—22no—
493C2—1722no—
494C2C2×#1458305311yescharacteristic
495C2#1914387711yescharacteristic
496C2C2×#1458307611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#487C2
socleC22×C43C2×#120
prime radicalC2×#10621898D4
hypercenterC2×#487D43
hypocenterC43#18633
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
2. #19145543C2semidirect
4. #19133813C2semidirect
5. #19133806C2semidirect
6. #19133276C2semidirect
7. #19133051C2semidirect
9. C2×C43×#487C2semidirect
130. #10621898Q16semidirect
246. C2×#487D43semidirect
293. C43#18633semidirect

Maximal subgroups

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

subgroupindex
#191484112
#191455432
#191444042
#191338132
#191338062
#191332762
#191330512
#191329782
C2×C43×#4872
#1863343