Finite Group Databasebeta

← #25082059

Subgroups — #25082059

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#19144404C211yesmaximal, characteristic, complemented
2#19144044C211yesmaximal, characteristic
3#19143703C211yesmaximal, characteristic, complemented
4#19134008C212yesmaximal, complemented
5#19134001C212yesmaximal, complemented
6#19133974C212yesmaximal, complemented
7#19133967C212yesmaximal, complemented
8#19133366C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10C2×#14582648C211yesmaximal, characteristic, complemented
11C43×#3227C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13C4×#10621898C2211yescharacteristic
14#14583191C2212yes—
15#14583186C2212yes—
16#14583181—21no—
17#14583176—21no—
18#14583118—21no—
19#14583111—21no—
20#14583106C2211yescharacteristic
21#14583101C2211yescharacteristic
22#14583096C2211yescharacteristic
23#14583091C2211yescharacteristic
24C8×Dic86C2212yes—
25C8×D172C2212yes—
26(C22⋊D43)⋊C8—22no—
27#14582951—21no—
28#14582939—21no—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C4⋊C8×D43—21no—
33#14582898—21no—
34#14582895—21no—
35#14582650C2212yes—
36#14582650C2212yes—
37#14582648C2212yes—
38#14582648C2212yes—
39#14582645C2212yes—
40#14582643C2212yes—
41C43×#532C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#498C2212yes—
44C43×#486C2212yes—
45C43×#481—22no—
46C43×#476—21no—
47C43×#476—21no—
48C43×#431C2211yescharacteristic
49C2×#10621898D411yescharacteristic
50#13063345—44no—
51C2×#10621885—21no—
52C2×#10621883—21no—
53C2×#10621884—21no—
54C2×#10621882—21no—
55C2×#10621877—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8—21no—
58C2×C8×D43—22no—
59C4×Dic86D411yescharacteristic
60C4×Dic86C2311yescharacteristic
61C4×D172D411yescharacteristic
62C4×D172C2311yescharacteristic
63C4×C22⋊D43—21no—
64C4×C22⋊D43—21no—
65#13063284D411yescharacteristic
66#13063282—21no—
67C42×D43—21no—
68#13063258—22no—
69#13063256—22no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2311yescharacteristic
75C4⋊(C43⋊C8)C2312yes—
76C4⋊(C43⋊C8)C2312yes—
77Dic43⋊C8—22no—
78#13063249—21no—
79#13063249—21no—
80#13063248—22no—
81#13063246—21no—
82#13063246—21no—
83#13063245—22no—
84(C2×D43)⋊C8—22no—
85C8×Dic43—22no—
86C2×#41×C43—21no—
87C22×Q8×C43—21no—
88C4⋊Q8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43C2311yescharacteristic
92C4⋊Q8×C43C2312yes—
93#127×C43C2311yescharacteristic
94#124×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#106×C43—22no—
103#106×C43—22no—
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D411yescharacteristic
106#102×C43—22no—
107#102×C43—22no—
108C22⋊C8×C43D412yes—
109C4×C8×C43C2312yes—
110#41×C43—42no—
111#41×C43—42no—
112C2×Q8×C43—21no—
113C2×Q8×C43—22no—
114C2×Q8×C43—41no—
115C2×Q8×C43—82no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43#4111yescharacteristic
125C2×C22⋊D43—21no—
126#10621898—22no—
127#10621898SD1614yes—
128C2×D172C2×D411yescharacteristic
129C2×C4×D43—21no—
130C2×C4×D43—21no—
131C2×C4×D43—21no—
132C2×Dic86C2×D411yescharacteristic
133C2×C8×C43C2×D412yes—
134C2×C8×C43C2×D412yes—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43—41no—
141C22⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C42×C43#4111yescharacteristic
146C42×C43C2411yescharacteristic
147C22⋊Dic43—21no—
148#10621885—42no—
149#10621884—42no—
150#10621883—42no—
151#10621882—42no—
152(C2×D43)⋊C4—21no—
153(C2×D43)⋊C4—21no—
154C4⋊Dic43C2×D411yescharacteristic
155C4⋊Dic43C2×D411yescharacteristic
156Dic43⋊C4—21no—
157Dic43⋊C4—21no—
158C4×Dic43—21no—
159C4×Dic43—21no—
160C4×Dic43—21no—
161#10621877—42no—
162C2×C43⋊C8—22no—
163C2×C43⋊C8—22no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—42no—
167C2×C43⋊C8—81no—
168C8×D43—82no—
169C23×C43—41no—
170C23×C43#12111yescharacteristic
171C22×D43—21no—
172Q8×C43—41no—
173Q8×C43—41no—
174Q8×C43—82no—
175Q8×C43—82no—
176D4×C43—41no—
177D4×C43—41no—
178D4×C43—41no—
179D4×C43—41no—
180D4×C43—81no—
181D4×C43—82no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—42no—
187C2×C4×C43—82no—
188C2×C4×C43—82no—
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43C2×SD1612yes—
193C2×C4×C43#13512yes—
194C2×C4×C43C22×D411yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C2×C4×C43C2×#4111yescharacteristic
197C22⋊D43—24no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201D172—21no—
202D172C2×SD1612yes—
203C4×D43—24no—
204C4×D43—41no—
205C4×D43—41no—
206C4×D43—81no—
207Dic86—21no—
208Dic86C2×SD1612yes—
209C8×C43—22no—
210C8×C43—22no—
211C43⋊C8—41no—
212C43⋊C8—41no—
213C43⋊C8—42no—
214C43⋊C8—42no—
215#19414—431nomaximal, Sylow
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—81no—
219C22×C43—81no—
220C22×C43—81no—
221C22×C43#46512yes—
222C22×C43C2×#12111yescharacteristic
223C2×D43—22no—
224C2×D43—41no—
225C2×D43—41no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—81no—
230C4×C43—82no—
231C4×C43#46512yes—
232C4×C43C22×SD1611yescharacteristic
233C4×C43C2×#13511yescharacteristic
234C4×C43#57711yescharacteristic
235C4×C43#57811yescharacteristic
236Dic43—22no—
237Dic43—41no—
238Dic43—41no—
239#3227D4311yescharacteristic, complemented
240#3079—431no—
241#3035—431no—
242#2988—431no—
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—161no—
252C2×C43#304611yescharacteristic
253C2×C43C2×#46511yescharacteristic
254C2×C43#306811yescharacteristic
255D43—42no—
256C2×#135—861no—
257#532C2×D4311yescharacteristic
258C2×C4⋊Q8C2×D4311yescharacteristic
259C4×#41—431no—
260#498C2×D4312yes—
261#486C2×D4312yes—
262#481—22no—
263#477—432no—
264#476—21no—
265#476—21no—
266#476—432no—
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×Q8—432no—
276C8×D4—432no—
277C8×D4—862no—
278#431—861no—
279#431C2×D4311yescharacteristic
280#428—861no—
281#423—431no—
282C2×C4⋊C8—431no—
283C2×C4⋊C8—431no—
284C2×C4⋊C8—861no—
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—21no—
295C2×#41—431no—
296C22×Q8—21no—
297#135—1724no—
298C2×Q16—861no—
299C2×SD16—861no—
300C2×SD16—861no—
301C2×D8—861no—
302C2×M16—861no—
303C22×C8—861no—
304C22×C8—861no—
305C22×C8—862no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8C22×D4312yes—
310C4⋊Q8C22×D4311yescharacteristic
311#127C22×D4311yescharacteristic
312#124—21no—
313#121—21no—
314#121—21no—
315C4×Q8—431no—
316C4×Q8—431no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—431no—
320C4×D4—431no—
321C4×D4—861no—
322C4×D4—861no—
323#117—431no—
324#117—861no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C42—861no—
328C2×C42C22×D4311yescharacteristic
329#107—862no—
330#106—22no—
331#106—22no—
332#106—862no—
333C4⋊C8—432no—
334C4⋊C8—432no—
335C4⋊C8—431no—
336C4⋊C8—431no—
337C4⋊C8—862no—
338C4⋊C8—861no—
339C4⋊C8—861no—
340C4⋊C8—861no—
341C4⋊C8C22⋊D4311yescharacteristic
342C4⋊C8C22⋊D4311yescharacteristic
343#103—862no—
344#103—861no—
345#103—861no—
346#102—22no—
347#102—22no—
348#102—862no—
349#102—861no—
350#102—861no—
351C22⋊C8—862no—
352C22⋊C8C22⋊D4312yes—
353C4×C8—862no—
354C4×C8C22×D4312yes—
355#41—42no—
356#41—42no—
357#41—434no—
358#41—862no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—41no—
362C2×Q8—82no—
363C2×Q8—431no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—431no—
369C2×D4—861no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—861no—
373C22×C4—861no—
374C22×C4—861no—
375C22×C4D4×D4311yescharacteristic
376C22×C4#1062190011yescharacteristic
377C22×C4C2×C22⋊D4311yescharacteristic
378Q16—1722no—
379SD16—1722no—
380SD16—1722no—
381D8—1722no—
382M16—1722no—
383C2×C8—862no—
384C2×C8—861no—
385C2×C8—861no—
386C2×C8—862no—
387C2×C8—3442no—
388C2×C8—3441no—
389C2×C8—1722no—
390C2×C8C2×C22⋊D4312yes—
391C2×C8C2×C22⋊D4312yes—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—431no—
399C4⋊C4—431no—
400C4⋊C4—861no—
401C4⋊C4—861no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—861no—
405C22⋊C4—861no—
406C22⋊C4—861no—
407C42—861no—
408C42—861no—
409C42—861no—
410C42D4×D4311yescharacteristic
411C42#1062190011yescharacteristic
412C42C2×C22⋊D4311yescharacteristic
413C42C23×D4311yescharacteristic
414C23—41no—
415C23—861no—
416C23#1306329611yescharacteristic
417Q8—41no—
418Q8—41no—
419Q8—82no—
420Q8—82no—
421Q8—432no—
422Q8—861no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—82no—
429D4—432no—
430D4—864no—
431D4—861no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—861no—
440C2×C4—864no—
441C2×C4—861no—
442C2×C4—861no—
443C2×C4—3441no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4#1306329611yescharacteristic
447C2×C4#1306329611yescharacteristic
448C2×C4#1306329611yescharacteristic
449C2×C4SD16×D4312yes—
450C2×C4#1306334612yes—
451C2×C4C2×D4×D4311yescharacteristic
452C2×C4C22×C22⋊D4311yescharacteristic
453C2×C4C2×#1062190011yescharacteristic
454C8—22no—
455C8—22no—
456C8—1721no—
457C8—1721no—
458C8—1722no—
459C8—1722no—
460C22—21no—
461C22—21no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—862no—
466C22—1721no—
467C22—1721no—
468C22#1458312512yes—
469C22C2×#1306329611yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—82no—
474C4—81no—
475C4—862no—
476C4—1721no—
477C4—1721no—
478C4#1458312512yes—
479C4C2×SD16×D4311yescharacteristic
480C4C2×#1306334611yescharacteristic
481C4#1458370711yescharacteristic
482C4#1458371411yescharacteristic
483C2—22no—
484C2—161no—
485C2—1722no—
486C2#1914414111yescharacteristic
487C2C2×#1458312511yescharacteristic
488C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3227C2
socleC22×C43C2×#121
prime radical#19144044C2
hypercenter#3227D43
hypocenterC43#19414
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
1. #19144404C2semidirect
3. #19143703C2semidirect
4. #19134008C2semidirect
5. #19134001C2semidirect
6. #19133974C2semidirect
7. #19133967C2semidirect
8. #19133366C2semidirect
9. #19133272C2semidirect
10. C2×#14582648C2semidirect
11. C43×#3227C2semidirect
239. #3227D43semidirect
293. C43#19414semidirect

Maximal subgroups

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

subgroupindex
#191444042
#191440442
#191437032
#191340082
#191340012
#191339742
#191339672
#191333662
#191332722
C2×#145826482
C43×#32272
#1941443