Finite Group Databasebeta

← #24988522

Subgroups — #24988522

Order 11008.

756 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148502C211yesmaximal, characteristic
2#19135542C211yesmaximal, characteristic, complemented
3#19134612C211yesmaximal, characteristic, complemented
4#19133281C211yesmaximal, characteristic, complemented
5#19133090C211yesmaximal, characteristic, complemented
6#19132980C211yesmaximal, characteristic, complemented
7C43×#1547C211yesmaximal, characteristic, complemented
8#14583619C412yescomplemented
9#14583614—21no—
10#14583606—21no—
11#14583601—22no—
12#14583555—22no—
13#14583553C412yescomplemented
14#14583518—22no—
15#14583477—21no—
16#14583454—21no—
17#14583447—21no—
18C2×#13063325C2211yescharacteristic
19#14583382—21no—
20C4×#10621898C2211yescharacteristic
21#14582952C2211yescharacteristic
22C2×#13063251—21no—
23C4×C4⋊Dic43C2211yescharacteristic
24#14582662—22no—
25#14582660—21no—
26#14582644—22no—
27#14582633—22no—
28#14582629—21no—
29#14582626—21no—
30C43×#532C2211yescharacteristic
31C43×#423C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C43×#332—21no—
34C43×#331—21no—
35C2×#10621898D411yescharacteristic
36C2×#10621900—22no—
37C22×Dic86—21no—
38#13063325—21no—
39#13063325—21no—
40#13063325C2×C412yes—
41#13063325D412yes—
42#13063318—24no—
43#13063316—22no—
44#13063312—22no—
45#13063311—24no—
46#13063309—24no—
47#13063305—22no—
48#13063304—22no—
49#13063302—24no—
50#13063301—22no—
51#13063299—22no—
52#13063297—24no—
53#13063296—22no—
54#13063296—22no—
55Q8×Dic43—22no—
56C4×Dic86C2×C411yescharacteristic
57C4×Dic86D411yescharacteristic
58#13063290—22no—
59C4×D172C2×C411yescharacteristic
60C4×D172D411yescharacteristic
61D4×Dic43—24no—
62D4×Dic43—22no—
63D4×Dic43—22no—
64C4×C22⋊D43—21no—
65C4×C22⋊D43—21no—
66#13063284—22no—
67#13063284D411yescharacteristic
68#13063283—22no—
69#13063282—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43D412yes—
74C2×C4×Dic43—21no—
75C42×D43—21no—
76C4⋊(C43⋊C8)—21no—
77#13063251—42no—
78C22⋊(C43⋊C8)—21no—
79C4×C43⋊C8—21no—
80C43⋊#95—21no—
81C2×#41×C43—21no—
82C2×M16×C43—21no—
83C22×C8×C43—21no—
84C4⋊Q8×C43D411yescharacteristic
85#127×C43D411yescharacteristic
86#124×C43—21no—
87#121×C43—21no—
88#121×C43D412yes—
89C4×D4×C43—21no—
90C4×D4×C43C2×C412yes—
91C2×C42×C43C2311yescharacteristic
92C4⋊C8×C43—21no—
93C4⋊C8×C43—21no—
94C4⋊C8×C43—21no—
95C4⋊C8×C43—21no—
96#41×C43—41no—
97#41×C43—41no—
98#41×C43—41no—
99#41×C43—41no—
100C2×Q8×C43—21no—
101C2×D4×C43—21no—
102C2×D4×C43—21no—
103C2×D4×C43—22no—
104C2×D4×C43C22⋊C412yes—
105C22×C4×C43—22no—
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C2×C22⋊D43—24no—
110C2×C22⋊D43—21no—
111C22×Dic43—24no—
112C22×Dic43—22no—
113C22×Dic43—41no—
114#10621900—84no—
115#10621898—21no—
116#10621898—21no—
117#10621898—21no—
118#10621898—21no—
119C2×D172C22⋊C411yescharacteristic
120C2×C4×D43—21no—
121C2×C4×D43—21no—
122C2×C4×D43—21no—
123C2×Dic86—22no—
124C2×Dic86—22no—
125C2×Dic86—82no—
126C2×Dic86C22⋊C411yescharacteristic
127M16×C43—41no—
128M16×C43—41no—
129C2×C8×C43—42no—
130C2×C8×C43—41no—
131C2×C8×C43—41no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43C22⋊C412yes—
134C22⋊C4×C43—22no—
135C22⋊C4×C43—22no—
136C42×C43C22×C411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C42×C43C2×D411yescharacteristic
139C42×C43C2×D411yescharacteristic
140C22⋊Dic43—24no—
141C22⋊Dic43—24no—
142C22⋊Dic43—21no—
143(C2×D43)⋊C4—24no—
144(C2×D43)⋊C4—21no—
145(C2×D43)⋊C4—21no—
146C4⋊Dic43—24no—
147C4⋊Dic43—22no—
148C4⋊Dic43—22no—
149C4⋊Dic43—22no—
150C4⋊Dic43—22no—
151C4⋊Dic43—41no—
152C4⋊Dic43C22⋊C411yescharacteristic
153C4⋊Dic43C22⋊C414yes—
154C4⋊Dic43C22⋊C411yescharacteristic
155Dic43⋊C4—24no—
156Dic43⋊C4—21no—
157Dic43⋊C4—21no—
158C4×Dic43—24no—
159C4×Dic43—21no—
160C4×Dic43—21no—
161C4×Dic43—21no—
162C4×Dic43—41no—
163C4×Dic43—41no—
164C2×C43⋊C8—41no—
165C23×C43—22no—
166C23×C43#12011yescharacteristic
167C22×D43—21no—
168Q8×C43—41no—
169Q8×C43—41no—
170D4×C43—42no—
171D4×C43—42no—
172D4×C43—42no—
173D4×C43—41no—
174D4×C43—41no—
175D4×C43—41no—
176D4×C43—41no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—22no—
180C2×C4×C43—41no—
181C2×C4×C43—42no—
182C2×C4×C43—42no—
183C2×C4×C43C2×C22⋊C411yescharacteristic
184C2×C4×C43C2×C22⋊C411yescharacteristic
185C2×C4×C43C2×C22⋊C411yescharacteristic
186C2×C4×C43#12011yescharacteristic
187C2×C4×C43#12011yescharacteristic
188C2×C4×C43#12011yescharacteristic
189C2×C4×C43#13511yescharacteristic
190C2×C4×C43#13511yescharacteristic
191C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C43#13711yescharacteristic
193C22⋊D43—41no—
194C22⋊D43—41no—
195C22⋊D43—84no—
196C2×Dic43—21no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—24no—
200C2×Dic43—42no—
201C2×Dic43—82no—
202C2×Dic43—84no—
203C2×Dic43—81no—
204C2×Dic43—81no—
205D172—21no—
206D172—21no—
207C4×D43—42no—
208C4×D43—41no—
209C4×D43—41no—
210C4×D43—41no—
211C4×D43—41no—
212Dic86—21no—
213Dic86—21no—
214Dic86—44no—
215Dic86—82no—
216C8×C43—81no—
217C8×C43—81no—
218C43⋊C8—81no—
219#8422—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—42no—
223C22×C43—42no—
224C22×C43—42no—
225C22×C43#37911yescharacteristic
226C22×C43#44911yescharacteristic
227C22×C43#45211yescharacteristic
228C2×D43—41no—
229C2×D43—41no—
230C2×D43—41no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—42no—
235C4×C43#41611yescharacteristic
236C4×C43#41711yescharacteristic
237C4×C43#44911yescharacteristic
238C4×C43#45211yescharacteristic
239C4×C43#45411yescharacteristic
240C4×C43#45611yescharacteristic
241Dic43—41no—
242Dic43—44no—
243Dic43—41no—
244Dic43—41no—
245Dic43—82no—
246#3511—431no—
247#1987—431no—
248#1806—431no—
249#1549—431no—
250#1547D4311yescharacteristic, complemented
251#1502—431no—
252#1477—431no—
253C2×C43—21no—
254C2×C43—21no—
255C2×C43—82no—
256C2×C43#178811yescharacteristic
257C2×C43#179311yescharacteristic
258C2×C43#179511yescharacteristic
259D43—81no—
260#556—432no—
261#555—861no—
262#554—861no—
263#553—862no—
264#548—862no—
265#547—432no—
266#542—862no—
267#537—861no—
268#533—861no—
269#532—861no—
270#532C2×D4311yescharacteristic
271C2×C4⋊Q8—431no—
272#520—861no—
273C4×#41—431no—
274#431—431no—
275#423C2×D4311yescharacteristic
276C2×C4⋊C8C2×D4311yescharacteristic
277C2×#104—861no—
278C4×C4⋊C4—431no—
279#340—862no—
280#339—861no—
281#332—21no—
282#332—862no—
283#331—21no—
284#327—862no—
285Q8⋊C8—861no—
286D4⋊C8—861no—
287C43#842211yescharacteristic, complemented, Sylow
288C2×#41—21no—
289C2×#41—431no—
290C2×#41—862no—
291C22×Q8—861no—
292C2×M16—21no—
293C22×C8—21no—
294C4⋊Q8—432no—
295C4⋊Q8—432no—
296C4⋊Q8—861no—
297C4⋊Q8—861no—
298C4⋊Q8C22⋊D4311yescharacteristic
299#127C22⋊D4311yescharacteristic
300#126—864no—
301#125—862no—
302#124—21no—
303#124—864no—
304#124—862no—
305#123—864no—
306C22⋊Q8—864no—
307C22⋊Q8—862no—
308C22⋊Q8—862no—
309C22⋊Q8—862no—
310#121—21no—
311#121—862no—
312#121—862no—
313#121—862no—
314#121—864no—
315#121D17212yes—
316C4×Q8—431no—
317C4×Q8—431no—
318C4×Q8—862no—
319C4×Q8—862no—
320C4×D4—21no—
321C4×D4—431no—
322C4×D4—431no—
323C4×D4—862no—
324C4×D4—864no—
325C4×D4—862no—
326C4×D4—861no—
327C4×D4—861no—
328C4×D4C4×D4312yes—
329#117—431no—
330#117—862no—
331#117—862no—
332#117—861no—
333C2×C4⋊C4—432no—
334C2×C4⋊C4—862no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4—861no—
337C2×C42—861no—
338C2×C42—861no—
339C2×C42C22×D4311yescharacteristic
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8—861no—
345#104—1722no—
346C22⋊C8—861no—
347C4×C8—861no—
348#95—861no—
349#41—41no—
350#41—41no—
351#41—41no—
352#41—41no—
353#41—861no—
354#41—861no—
355#41—861no—
356#41—861no—
357#41—3444no—
358C2×Q8—21no—
359C2×Q8—431no—
360C2×Q8—862no—
361C2×Q8—862no—
362C2×Q8—3442no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—431no—
367C2×D4—864no—
368C2×D4—861no—
369C2×D4(C2×D43)⋊C412yes—
370C22×C4—22no—
371C22×C4—864no—
372C22×C4—862no—
373C22×C4—861no—
374C22×C4—861no—
375C22×C4—861no—
376C22×C4—1721no—
377C22×C4C2×D17211yescharacteristic
378C22×C4D4×D4311yescharacteristic
379C22×C4D4×D4311yescharacteristic
380M16—41no—
381M16—41no—
382C2×C8—42no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—1721no—
386C4⋊C4—21no—
387C4⋊C4—434no—
388C4⋊C4—431no—
389C4⋊C4—431no—
390C4⋊C4—864no—
391C4⋊C4—864no—
392C4⋊C4—862no—
393C4⋊C4—862no—
394C4⋊C4—861no—
395C4⋊C4—862no—
396C4⋊C4—862no—
397C4⋊C4—861no—
398C4⋊C4—1721no—
399C4⋊C4(C2×D43)⋊C412yes—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—864no—
403C22⋊C4—864no—
404C22⋊C4—864no—
405C22⋊C4—861no—
406C22⋊C4—861no—
407C22⋊C4—861no—
408C42—864no—
409C42—861no—
410C42—861no—
411C42—861no—
412C42—1721no—
413C42—1721no—
414C42C2×C4×D4311yescharacteristic
415C42D4×D4311yescharacteristic
416C42D4×D4311yescharacteristic
417C42C2×C22⋊D4311yescharacteristic
418C23—22no—
419C23—861no—
420C23#1306329511yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—861no—
424Q8—861no—
425Q8—3442no—
426Q8—1724no—
427D4—42no—
428D4—42no—
429D4—42no—
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—861no—
435D4—861no—
436D4—3444no—
437D4—1721no—
438D4—1721no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—861no—
446C2×C4—861no—
447C2×C4—861no—
448C2×C4—864no—
449C2×C4—3441no—
450C2×C4—3441no—
451C2×C4—3442no—
452C2×C4—3444no—
453C2×C4—1722no—
454C2×C4—1722no—
455C2×C4—1721no—
456C2×C4—1721no—
457C2×C4—1721no—
458C2×C4—1721no—
459C2×C4C22⋊C4×D4311yescharacteristic
460C2×C4C22⋊C4×D4311yescharacteristic
461C2×C4C2×(C2×D43)⋊C411yescharacteristic
462C2×C4#1306329311yescharacteristic
463C2×C4#1306329311yescharacteristic
464C2×C4#1306329511yescharacteristic
465C2×C4#1306334411yescharacteristic
466C2×C4#1306334611yescharacteristic
467C2×C4#1306334911yescharacteristic
468C2×C4#1306335411yescharacteristic
469C8—81no—
470C8—81no—
471C8—3441no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—1721no—
478C22—1721no—
479C22—1721no—
480C22#1458275411yescharacteristic
481C22#1458304511yescharacteristic
482C22#1458306211yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—42no—
487C4—3442no—
488C4—1721no—
489C4—1721no—
490C4—1721no—
491C4—1724no—
492C4#1458289211yescharacteristic
493C4#1458289711yescharacteristic
494C4#1458304111yescharacteristic
495C4#1458305811yescharacteristic
496C4#1458307011yescharacteristic
497C4#1458308011yescharacteristic
498C2—21no—
499C2—21no—
500C2—82no—
501C2—3441no—
502C2#1913453211yescharacteristic
503C2#1913455211yescharacteristic
504C2#1913456611yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1547C2
socleC22×C43#379
prime radical#19148502C2
cosocleC2×C42×C43C23
hypercenter#1547D43
hypocenterC43#8422
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
2. #19135542C2semidirect
3. #19134612C2semidirect
4. #19133281C2semidirect
5. #19133090C2semidirect
6. #19132980C2semidirect
7. C43×#1547C2semidirect
8. #14583619C4semidirect
13. #14583553C4semidirect
250. #1547D43semidirect
287. C43#8422semidirect

Maximal subgroups

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

subgroupindex
#191485022
#191355422
#191346122
#191332812
#191330902
#191329802
C43×#15472
#842243