Finite Group Databasebeta

← #25075118

Subgroups — #25075118

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583609C211yesmaximal, characteristic, complemented
2#19145517C211yesmaximal, characteristic, complemented
3#19144591C211yesmaximal, characteristic
4#19133807C214yesmaximal, complemented
5#19133666C214yesmaximal, complemented
6#19133277C211yesmaximal, characteristic, complemented
7#19133019C211yesmaximal, characteristic, complemented
8#19132990C211yesmaximal, characteristic, complemented
9C43×#3037C211yesmaximal, characteristic, complemented
10#14583609—22no—
11#14583609—22no—
12#14583609—22no—
13#14583609C2214yes—
14C2×#13063325C2211yescharacteristic
15C2×#13063317—21no—
16C2×#13063303—22no—
17C2×#13063301—21no—
18C2×C4×D172—21no—
19C2×C4×D172C2211yescharacteristic
20C2×C4⋊C4×D43—21no—
21#14583271C2212yescomplemented
22#14583251C2212yescomplemented
23#14583210—21no—
24#14583176C2212yes—
25#14583104—22no—
26#14583091C2212yes—
27#14583037—22no—
28#14583032—21no—
29C4×#10621882—22no—
30#14582952C2211yescharacteristic
31#14582952C2211yescharacteristic
32#14582647C2214yescomplemented
33Q8⋊(C43⋊C8)C2214yescomplemented
34#14582626C2214yes—
35C2×#137×C43—21no—
36C43×#532C2211yescharacteristic
37C2×C4×Q8×C43C2211yescharacteristic
38C43×#464—22no—
39C43×#462C2212yescomplemented
40C43×#460C2212yescomplemented
41C43×#423C2211yescharacteristic
42C43×#417—21no—
43C22×Dic86D412yes—
44C22×D172D411yescharacteristic
45C22×C4×D43—21no—
46C22×C4×D43—22no—
47C2×#10621883—24no—
48C2×#10621882—22no—
49#13063325—21no—
50#13063325—21no—
51#13063325D412yes—
52#13063325C2312yes—
53#13063317—24no—
54#13063317—24no—
55#13063303—28no—
56#13063303—28no—
57#13063301—24no—
58#13063301—24no—
59C4×D172—24no—
60C4×D172—24no—
61C4×D172—21no—
62C4×D172—21no—
63C4×D172D412yes—
64C4×D172C2312yes—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43D411yescharacteristic
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—22no—
70C4⋊C4×D43—24no—
71C4⋊C4×D43—24no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—21no—
74#13063258—22no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)C2312yes—
77#13063248—24no—
78#13063246—22no—
79#13063245—22no—
80C22⋊(C43⋊C8)—21no—
81C22⋊(C43⋊C8)—21no—
82C4×C43⋊C8—21no—
83C4×C43⋊C8C2312yes—
84C2×#41×C43—21no—
85C22×Q8×C43D411yescharacteristic
86#137×C43—44no—
87C2×Q16×C43—22no—
88C2×SD16×C43—22no—
89C2×M16×C43—21no—
90C4⋊Q8×C43C2311yescharacteristic
91#127×C43C2311yescharacteristic
92#124×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43D412yes—
98C4×Q8×C43C2312yes—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C42×C43—21no—
104C2×C42×C43C2311yescharacteristic
105C4⋊C8×C43—21no—
106C4⋊C8×C43C2312yes—
107#103×C43—22no—
108#102×C43—22no—
109C23×D43—21no—
110#41×C43—42no—
111#41×C43—42no—
112C2×Q8×C43—21no—
113C2×Q8×C43—22no—
114C2×Q8×C43—22no—
115C2×Q8×C43—21no—
116C2×Q8×C43C2×D412yes—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—41no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—22no—
129C2×D172—21no—
130C2×D172—24no—
131C2×D172C2×D412yes—
132C2×C4×D43—22no—
133C2×C4×D43—22no—
134C2×C4×D43—28no—
135C2×C4×D43—42no—
136C2×C4×D43—42no—
137C2×C4×D43—84no—
138C2×Dic86—22no—
139C2×Dic86—82no—
140C2×Dic86C2×D414yes—
141Q16×C43—44no—
142SD16×C43—44no—
143M16×C43—42no—
144C2×C8×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43C2×D412yes—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C42×C43—22no—
154C42×C43—22no—
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C42×C43C2411yescharacteristic
159#10621883—84no—
160#10621882—44no—
161(C2×D43)⋊C4—28no—
162(C2×D43)⋊C4—22no—
163(C2×D43)⋊C4—22no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43—21no—
167C4⋊Dic43—22no—
168C4⋊Dic43—22no—
169C4⋊Dic43C2×D412yes—
170Dic43⋊C4—28no—
171Dic43⋊C4—28no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—22no—
174C23×C43—41no—
175C23×C43#12011yescharacteristic
176C22×D43—24no—
177C22×D43—22no—
178C22×D43—42no—
179C22×D43—42no—
180Q8×C43—22no—
181Q8×C43—22no—
182Q8×C43—42no—
183Q8×C43—41no—
184Q8×C43—41no—
185D4×C43—42no—
186D4×C43—41no—
187D4×C43—41no—
188D4×C43—42no—
189D4×C43—82no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—41no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—41no—
197C2×C4×C43—82no—
198C2×C4×C43#12011yescharacteristic
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#12011yescharacteristic
201C2×C4×C43#13512yes—
202C2×C4×C43AGL(1,ℤ/8)12yes—
203C2×C4×C43C22×D411yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×Dic43—22no—
207C2×Dic43—24no—
208C2×Dic43—44no—
209C2×Dic43—42no—
210D172—24no—
211D172—22no—
212D172#13714yescomplemented
213C4×D43—42no—
214C4×D43—42no—
215C4×D43—44no—
216C4×D43—88no—
217Dic86—44no—
218Dic86—82no—
219C8×C43—42no—
220C43⋊C8—42no—
221C43⋊C8—42no—
222#18752—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—81no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43#44912yes—
229C22×C43C2×#12011yescharacteristic
230C2×D43—24no—
231C2×D43—48no—
232C2×D43—42no—
233C2×D43—42no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—42no—
238C4×C43—42no—
239C4×C43—81no—
240C4×C43#44912yes—
241C4×C43C2×#13511yescharacteristic
242C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
243C4×C43C2×#13712yes—
244Dic43—42no—
245Dic43—44no—
246C2×#554—431no—
247#3206—431no—
248#3100—431no—
249#3037D4311yescharacteristic, complemented
250#1644—434no—
251#1622—434no—
252#1548—431no—
253#1486—431no—
254#1479—431no—
255C2×C43—22no—
256C2×C43—161no—
257C2×C43C2×#44911yescharacteristic
258C2×C43#300411yescharacteristic
259C2×C43#301911yescharacteristic
260D43—44no—
261C2×#137—21no—
262#554—434no—
263#554—862no—
264#554—862no—
265#554—862no—
266#532C2×D4311yescharacteristic
267C2×C4⋊Q8—431no—
268C2×#125—861no—
269C2×C22⋊Q8—862no—
270C2×C22⋊Q8—861no—
271C2×C4×Q8C2×D4311yescharacteristic
272C2×C4×D4—431no—
273C2×C4×D4—861no—
274C22×C4⋊C4—861no—
275#492—432no—
276#487—432no—
277#480—861no—
278#474—432no—
279#464—22no—
280#462C2×D4312yescomplemented
281#461—862no—
282#460C2×D4312yescomplemented
283#459—432no—
284#448—862no—
285#447—861no—
286C4×D8—862no—
287#431—431no—
288#431—431no—
289#423C2×D4311yescharacteristic
290#417—21no—
291#333—434no—
292Q8⋊C8—434no—
293D4⋊C8—434no—
294C43#1875211yescharacteristic, complemented, Sylow
295C2×#41—21no—
296C22×Q8—432no—
297C22×Q8C22⋊D4311yescharacteristic
298C22×D4—431no—
299C23×C4—862no—
300C23×C4—861no—
301#137—44no—
302C2×Q16—22no—
303C2×SD16—22no—
304C2×SD16—864no—
305C2×D8—862no—
306C2×M16—21no—
307C4⋊Q8—432no—
308C4⋊Q8—432no—
309C4⋊Q8—861no—
310C4⋊Q8—861no—
311C4⋊Q8C22×D4311yescharacteristic
312#127C22×D4311yescharacteristic
313#125—864no—
314#125—864no—
315#124—21no—
316C22⋊Q8—868no—
317C22⋊Q8—868no—
318C22⋊Q8—864no—
319C22⋊Q8—864no—
320#121—21no—
321#121—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8C22⋊D4312yes—
325C4×Q8C22×D4312yes—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—432no—
329C4×D4—432no—
330C4×D4—864no—
331C4×D4—864no—
332C4×D4—861no—
333C4×D4—861no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—431no—
336C2×C4⋊C4—864no—
337C2×C4⋊C4—862no—
338C2×C4⋊C4—862no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4—864no—
342C2×C4⋊C4C22⋊D4311yescharacteristic
343C2×C22⋊C4—862no—
344C2×C22⋊C4—861no—
345C2×C42—21no—
346C2×C42C22×D4311yescharacteristic
347#107—862no—
348C4⋊C8—21no—
349C4⋊C8—432no—
350C4⋊C8—861no—
351C4⋊C8C22×D4312yes—
352#103—22no—
353#103—864no—
354#102—22no—
355#102—862no—
356#102—862no—
357C22⋊C8—861no—
358C22⋊C8—861no—
359C4×C8—432no—
360C4×C8—861no—
361C24—861no—
362#41—42no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—21no—
368C2×Q8—434no—
369C2×Q8—862no—
370C2×Q8—3442no—
371C2×Q8C2×C22⋊D4312yes—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—41no—
376C2×D4—432no—
377C2×D4—864no—
378C2×D4—861no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—41no—
382C22×C4—868no—
383C22×C4—861no—
384C22×C4—862no—
385C22×C4—862no—
386C22×C4—862no—
387C22×C4—3444no—
388C22×C4—1722no—
389C22×C4—1722no—
390C22×C4D4×D4311yescharacteristic
391C22×C4D4×D4311yescharacteristic
392C22×C4C2×C22⋊D4311yescharacteristic
393Q16—44no—
394SD16—44no—
395SD16—3444no—
396D8—1724no—
397M16—42no—
398C2×C8—22no—
399C2×C8—862no—
400C2×C8—862no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—432no—
407C4⋊C4—868no—
408C4⋊C4—868no—
409C4⋊C4—861no—
410C4⋊C4—862no—
411C4⋊C4—862no—
412C4⋊C4—862no—
413C4⋊C4—862no—
414C4⋊C4C2×C22⋊D4312yes—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—868no—
418C22⋊C4—862no—
419C22⋊C4—862no—
420C42—22no—
421C42—22no—
422C42D4×D4311yescharacteristic
423C42D4×D4311yescharacteristic
424C42C2×C22⋊D4311yescharacteristic
425C42C23×D4311yescharacteristic
426C23—41no—
427C23—864no—
428C23—862no—
429C23—1722no—
430C23—1722no—
431C23#1306329311yescharacteristic
432Q8—22no—
433Q8—22no—
434Q8—42no—
435Q8—41no—
436Q8—41no—
437Q8—3442no—
438Q8—1724no—
439D4—42no—
440D4—41no—
441D4—41no—
442D4—42no—
443D4—82no—
444D4—434no—
445D4—864no—
446D4—862no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—82no—
455C2×C4—862no—
456C2×C4—864no—
457C2×C4—3448no—
458C2×C4—1724no—
459C2×C4—1722no—
460C2×C4—1724no—
461C2×C4—1722no—
462C2×C4—1722no—
463C2×C4#1306329311yescharacteristic
464C2×C4#1306329311yescharacteristic
465C2×C4#1306329311yescharacteristic
466C2×C4#1306334512yes—
467C2×C4#1306335112yes—
468C2×C4C2×D4×D4311yescharacteristic
469C2×C4C2×D4×D4311yescharacteristic
470C2×C4C22×C22⋊D4311yescharacteristic
471C8—42no—
472C8—1722no—
473C8—1722no—
474C22—21no—
475C22—21no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—864no—
480C22—1728no—
481C22—1722no—
482C22—1722no—
483C22#1458304212yes—
484C22C2×#1306329311yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—42no—
490C4—81no—
491C4—1724no—
492C4—1722no—
493C4#1458304212yes—
494C4C2×#1306334511yescharacteristic
495C4C2×#1306335111yescharacteristic
496C4#137×D4312yes—
497C2—22no—
498C2—161no—
499C2—1724no—
500C2C2×#1458304211yescharacteristic
501C2#1914382711yescharacteristic
502C2#1914395011yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3037C2
socleC22×C43C2×#120
prime radical#19144591C2
hypercenter#3037D43
hypocenterC43#18752
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
1. C2×#14583609C2semidirect
2. #19145517C2semidirect
4. #19133807C2semidirect
5. #19133666C2semidirect
6. #19133277C2semidirect
7. #19133019C2semidirect
8. #19132990C2semidirect
9. C43×#3037C2semidirect
21. #14583271C22semidirect
22. #14583251C22semidirect
32. #14582647C22semidirect
33. Q8⋊(C43⋊C8)C22semidirect
39. C43×#462C22semidirect
40. C43×#460C22semidirect
212. D172#137semidirect
249. #3037D43semidirect
280. #462C2×D43semidirect
282. #460C2×D43semidirect
294. C43#18752semidirect

Maximal subgroups

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

subgroupindex
C2×#145836092
#191455172
#191445912
#191338072
#191336662
#191332772
#191330192
#191329902
C43×#30372
#1875243