Finite Group Databasebeta

← #24988523

Subgroups — #24988523

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#19148506C211yesmaximal, characteristic
2#19135543C211yesmaximal, characteristic, complemented
3#19133281C211yesmaximal, characteristic, complemented
4#19133273C211yesmaximal, characteristic, complemented
5#19133089C211yesmaximal, characteristic, complemented
6#19132982C211yesmaximal, characteristic, complemented
7C43×#1806C211yesmaximal, characteristic, complemented
8#14583622C412yescomplemented
9#14583614—21no—
10#14583609—21no—
11#14583595—22no—
12#14583558—22no—
13#14583554C412yescomplemented
14#14583520—22no—
15#14583477—21no—
16#14583456—21no—
17#14583449—21no—
18#14583449C2211yescharacteristic
19C2×#13063325C2211yescharacteristic
20#14583379—21no—
21#14582952C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23#14582661—22no—
24#14582646—21no—
25#14582644—22no—
26#14582642—21no—
27#14582632—22no—
28Q8⋊(C43⋊C8)—21no—
29D4⋊(C43⋊C8)—21no—
30C4×#41×C43C2211yescharacteristic
31C43×#423C2211yescharacteristic
32C2×#104×C43—21no—
33C4×C4⋊C4×C43C2211yescharacteristic
34C43×#339—21no—
35C2×#10621898—21no—
36C2×#10621898—22no—
37C22×Dic86—21no—
38C22×C43⋊C8—21no—
39#13063325—21no—
40#13063325—21no—
41#13063325C2×C412yes—
42#13063325D412yes—
43#13063325D411yescharacteristic
44#13063322D411yescharacteristic
45#13063320—24no—
46#13063317—22no—
47#13063313—22no—
48#13063313—21no—
49#13063311—24no—
50#13063307—24no—
51#13063304—22no—
52#13063304—22no—
53#13063303—24no—
54#13063301—22no—
55#13063299—22no—
56#13063299—22no—
57#13063299—21no—
58#13063299D412yes—
59#13063297—24no—
60#13063296—22no—
61C4×Dic86—22no—
62C4×Dic86—22no—
63C4×D172—22no—
64C4×D172—22no—
65C4×D172—21no—
66C4×D172C2×C412yes—
67(C22⋊D43)⋊C4—24no—
68#13063284—22no—
69#13063283—22no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43D412yes—
72C4⋊C4×D43—22no—
73C4⋊(C43⋊C8)—21no—
74C4⋊(C43⋊C8)—21no—
75C4⋊(C43⋊C8)—21no—
76C22⋊(C43⋊C8)—21no—
77C4×C43⋊C8—21no—
78C2×#41×C43D411yescharacteristic
79C2×M16×C43—21no—
80C4×Q8×C43C2×C411yescharacteristic
81C4×Q8×C43D411yescharacteristic
82C4×D4×C43—21no—
83C4×D4×C43—21no—
84C4×D4×C43C2×C411yescharacteristic
85C4×D4×C43D411yescharacteristic
86#117×C43—21no—
87#117×C43D411yescharacteristic
88C2×C4⋊C4×C43—21no—
89C2×C42×C43—21no—
90C2×C42×C43—21no—
91C2×C42×C43C2311yescharacteristic
92C4⋊C8×C43—21no—
93C4⋊C8×C43—21no—
94#104×C43—42no—
95#95×C43—21no—
96#41×C43—21no—
97#41×C43—21no—
98#41×C43—21no—
99#41×C43—21no—
100C2×Q8×C43C22⋊C411yescharacteristic
101C2×D4×C43—21no—
102C2×D4×C43C22⋊C411yescharacteristic
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—41no—
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C2×C22⋊D43—24no—
111C2×C22⋊D43—22no—
112C22×Dic43—22no—
113#10621898—41no—
114#10621898—41no—
115#10621898—41no—
116#10621898—41no—
117#10621898—84no—
118C2×D172—21no—
119C2×D172—21no—
120C2×D172C22⋊C412yes—
121C2×C4×D43—22no—
122C2×C4×D43—24no—
123C2×Dic86—22no—
124C2×Dic86—21no—
125C2×Dic86—22no—
126C2×Dic86—82no—
127M16×C43—41no—
128M16×C43—41no—
129C2×C8×C43—41no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43C22⋊C411yescharacteristic
135C4⋊C4×C43C22⋊C411yescharacteristic
136C22⋊C4×C43—21no—
137C22⋊C4×C43—21no—
138C22⋊C4×C43—21no—
139C42×C43—21no—
140C42×C43—21no—
141C42×C43—21no—
142C42×C43—41no—
143C42×C43—41no—
144C42×C43C22×C411yescharacteristic
145C42×C43C2×D411yescharacteristic
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C22⋊Dic43—24no—
149(C2×D43)⋊C4—24no—
150(C2×D43)⋊C4—24no—
151(C2×D43)⋊C4—22no—
152(C2×D43)⋊C4—22no—
153C4⋊Dic43—22no—
154C4⋊Dic43—22no—
155C4⋊Dic43—22no—
156C4⋊Dic43—21no—
157C4⋊Dic43C22⋊C414yes—
158C4⋊Dic43C22⋊C412yes—
159Dic43⋊C4—24no—
160Dic43⋊C4—24no—
161C4×Dic43—24no—
162C2×C43⋊C8—42no—
163C2×C43⋊C8—41no—
164C2×C43⋊C8—41no—
165C23×C43—21no—
166C23×C43#12011yescharacteristic
167C22×D43—22no—
168Q8×C43—21no—
169Q8×C43—21no—
170D4×C43—21no—
171D4×C43—21no—
172D4×C43—41no—
173D4×C43—41no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—21no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—41no—
180C2×C4×C43—42no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—42no—
186C2×C4×C43—81no—
187C2×C4×C43—81no—
188C2×C4×C43C2×C22⋊C411yescharacteristic
189C2×C4×C43C2×C22⋊C411yescharacteristic
190C2×C4×C43C2×C22⋊C411yescharacteristic
191C2×C4×C43#12011yescharacteristic
192C2×C4×C43#12011yescharacteristic
193C2×C4×C43#12011yescharacteristic
194C2×C4×C43#13511yescharacteristic
195C2×C4×C43#13511yescharacteristic
196C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C43#13711yescharacteristic
198C22⋊D43—42no—
199C22⋊D43—42no—
200C22⋊D43—84no—
201C2×Dic43—22no—
202C2×Dic43—24no—
203C2×Dic43—82no—
204D172—42no—
205D172—41no—
206D172—41no—
207D172—41no—
208D172—41no—
209C4×D43—42no—
210C4×D43—42no—
211C4×D43—84no—
212Dic86—44no—
213Dic86—41no—
214Dic86—41no—
215Dic86—82no—
216C8×C43—81no—
217C43⋊C8—81no—
218C43⋊C8—81no—
219#8422—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—41no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43#37911yescharacteristic
226C22×C43#44911yescharacteristic
227C22×C43#45211yescharacteristic
228C2×D43—42no—
229C2×D43—42no—
230C2×D43—42no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—41no—
235C4×C43—41no—
236C4×C43—41no—
237C4×C43—82no—
238C4×C43#41611yescharacteristic
239C4×C43#41711yescharacteristic
240C4×C43#44911yescharacteristic
241C4×C43#45211yescharacteristic
242C4×C43#45411yescharacteristic
243C4×C43#45611yescharacteristic
244Dic43—44no—
245Dic43—42no—
246#3511—431no—
247#1987—431no—
248#1806D4311yescharacteristic, complemented
249#1549—431no—
250#1547—431no—
251#1502—431no—
252#1477—431no—
253C2×C43—21no—
254C2×C43—21no—
255C2×C43—81no—
256C2×C43#178811yescharacteristic
257C2×C43#179311yescharacteristic
258C2×C43#179511yescharacteristic
259D43—82no—
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—431no—
270#532—861no—
271C2×C4⋊Q8—431no—
272#520—861no—
273C4×#41C2×D4311yescharacteristic
274#431—431no—
275#423C2×D4311yescharacteristic
276C2×C4⋊C8—431no—
277C2×#104—21no—
278C4×C4⋊C4C2×D4311yescharacteristic
279#340—862no—
280#339—21no—
281#332—861no—
282#332—862no—
283#331—861no—
284#327—862no—
285Q8⋊C8—861no—
286D4⋊C8—861no—
287C43#842211yescharacteristic, complemented, Sylow
288C2×#41—862no—
289C2×#41—861no—
290C2×#41C22⋊D4311yescharacteristic
291C22×Q8—861no—
292C2×M16—21no—
293C22×C8—861no—
294C4⋊Q8—432no—
295C4⋊Q8—432no—
296C4⋊Q8—431no—
297C4⋊Q8—861no—
298C4⋊Q8—861no—
299#127—431no—
300#126—864no—
301#125—862no—
302#124—862no—
303#124—864no—
304#124—861no—
305#123—864no—
306C22⋊Q8—864no—
307C22⋊Q8—862no—
308C22⋊Q8—862no—
309C22⋊Q8—862no—
310#121—432no—
311#121—862no—
312#121—862no—
313#121—864no—
314#121—862no—
315#121—861no—
316C4×Q8—862no—
317C4×Q8—862no—
318C4×Q8C4×D4311yescharacteristic
319C4×Q8D17211yescharacteristic
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—432no—
323C4×D4—862no—
324C4×D4—862no—
325C4×D4—864no—
326C4×D4—861no—
327C4×D4C4×D4311yescharacteristic
328C4×D4D17211yescharacteristic
329#117—21no—
330#117—862no—
331#117—862no—
332#117C22⋊D4311yescharacteristic
333C2×C4⋊C4—21no—
334C2×C4⋊C4—432no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4—862no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42C22×D4311yescharacteristic
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8—861no—
343C4⋊C8—861no—
344C4⋊C8—861no—
345#104—42no—
346C22⋊C8—861no—
347C4×C8—861no—
348#95—21no—
349#41—21no—
350#41—21no—
351#41—21no—
352#41—21no—
353#41—3444no—
354#41—1721no—
355#41—1721no—
356#41—1721no—
357#41—1721no—
358C2×Q8—862no—
359C2×Q8—861no—
360C2×Q8—862no—
361C2×Q8—3442no—
362C2×Q8(C2×D43)⋊C411yescharacteristic
363C2×D4—21no—
364C2×D4—432no—
365C2×D4—864no—
366C2×D4—862no—
367C2×D4—861no—
368C2×D4—861no—
369C2×D4(C2×D43)⋊C411yescharacteristic
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—864no—
375C22×C4—862no—
376C22×C4—862no—
377C22×C4D4×D4311yescharacteristic
378C22×C4D4×D4311yescharacteristic
379C22×C4C2×C22⋊D4311yescharacteristic
380M16—41no—
381M16—41no—
382C2×C8—41no—
383C2×C8—1722no—
384C2×C8—1721no—
385C2×C8—1721no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—41no—
390C4⋊C4—434no—
391C4⋊C4—432no—
392C4⋊C4—864no—
393C4⋊C4—864no—
394C4⋊C4—862no—
395C4⋊C4—862no—
396C4⋊C4—862no—
397C4⋊C4—861no—
398C4⋊C4(C2×D43)⋊C411yescharacteristic
399C4⋊C4(C2×D43)⋊C411yescharacteristic
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—864no—
404C22⋊C4—864no—
405C22⋊C4—864no—
406C22⋊C4—862no—
407C22⋊C4—862no—
408C42—21no—
409C42—21no—
410C42—21no—
411C42—41no—
412C42—41no—
413C42—864no—
414C42C2×C4×D4311yescharacteristic
415C42C2×D17211yescharacteristic
416C42D4×D4311yescharacteristic
417C42D4×D4311yescharacteristic
418C23—21no—
419C23—862no—
420C23#1306329311yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—3442no—
424Q8—1724no—
425Q8—1721no—
426Q8—1721no—
427D4—21no—
428D4—21no—
429D4—41no—
430D4—41no—
431D4—3444no—
432D4—1722no—
433D4—1722no—
434D4—1722no—
435D4—1721no—
436D4—1721no—
437D4—1721no—
438D4—1721no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—862no—
454C2×C4—864no—
455C2×C4—3444no—
456C2×C4—3442no—
457C2×C4—1722no—
458C2×C4—1722no—
459C2×C4C22⋊C4×D4311yescharacteristic
460C2×C4C22⋊C4×D4311yescharacteristic
461C2×C4C2×(C2×D43)⋊C411yescharacteristic
462C2×C4#1306329311yescharacteristic
463C2×C4#1306329511yescharacteristic
464C2×C4#1306329511yescharacteristic
465C2×C4#1306334511yescharacteristic
466C2×C4#1306334511yescharacteristic
467C2×C4#1306335111yescharacteristic
468C2×C4#1306335611yescharacteristic
469C8—81no—
470C8—3441no—
471C8—3441no—
472C22—21no—
473C22—21no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—1722no—
478C22—1722no—
479C22—1722no—
480C22#1458275411yescharacteristic
481C22#1458304211yescharacteristic
482C22#1458305911yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—82no—
490C4—1722no—
491C4—1724no—
492C4#1458289311yescharacteristic
493C4#1458289811yescharacteristic
494C4#1458304211yescharacteristic
495C4#1458305911yescharacteristic
496C4#1458307311yescharacteristic
497C4#1458308311yescharacteristic
498C2—21no—
499C2—21no—
500C2—81no—
501C2—3442no—
502C2#1913453311yescharacteristic
503C2#1913455511yescharacteristic
504C2#1913456411yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1806C2
socleC22×C43#379
prime radical#19148506C2
cosocleC2×C42×C43C23
hypercenter#1806D43
hypocenterC43#8422
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19135543C2semidirect
3. #19133281C2semidirect
4. #19133273C2semidirect
5. #19133089C2semidirect
6. #19132982C2semidirect
7. C43×#1806C2semidirect
8. #14583622C4semidirect
13. #14583554C4semidirect
248. #1806D43semidirect
287. C43#8422semidirect

Maximal subgroups

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

subgroupindex
#191485062
#191355432
#191332812
#191332732
#191330892
#191329822
C43×#18062
#842243