Finite Group Databasebeta

← #25082070

Subgroups — #25082070

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144377C211yesmaximal, characteristic
2#19144078C211yesmaximal, characteristic
3#19143703C211yesmaximal, characteristic
4#19134022C212yesmaximal, complemented
5#19134015C212yesmaximal, complemented
6#19133974C212yesmaximal, complemented
7#19133967C212yesmaximal, complemented
8#19133366C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10C2×#14582645C211yesmaximal, characteristic, complemented
11C43×#3229C211yesmaximal, characteristic, complemented
12C2×#13063356—21no—
13C4×#10621898C2211yescharacteristic
14#14583203—21no—
15#14583196—21no—
16#14583191C2211yescharacteristic
17#14583186C2211yescharacteristic
18#14583181C2211yescharacteristic
19#14583176C2211yescharacteristic
20#14583106—21no—
21#14583106C2212yes—
22#14583101—21no—
23#14583101C2212yes—
24C8×Dic86C2212yes—
25C8×D172C2212yes—
26(C22⋊D43)⋊C8—22no—
27#14582951—21no—
28#14582935—21no—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C4⋊C8×D43—21no—
33#14582908—21no—
34#14582893—21no—
35#14582650C2212yes—
36#14582650C2212yes—
37#14582648C2212yes—
38#14582645C2212yes—
39#14582645C2212yes—
40#14582645C2212yes—
41C43×#533C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#498C2212yes—
44C43×#487C2212yes—
45C43×#483—22no—
46C43×#475—21no—
47C43×#475—21no—
48C43×#431C2211yescharacteristic
49C2×#10621898D411yescharacteristic
50#13063356—44no—
51C2×#10621885—22no—
52C2×#10621884—22no—
53C2×#10621877—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56C2×C8×D43—22no—
57C4×Dic86D411yescharacteristic
58C4×Dic86C2311yescharacteristic
59C4×D172D411yescharacteristic
60C4×D172C2311yescharacteristic
61C4×C22⋊D43—21no—
62C4×C22⋊D43—21no—
63#13063284D411yescharacteristic
64#13063282—21no—
65C42×D43—21no—
66#13063258—21no—
67#13063258—21no—
68#13063256—21no—
69#13063256—21no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)C2312yes—
74C4⋊(C43⋊C8)C2312yes—
75C4⋊(C43⋊C8)C2311yescharacteristic
76C4⋊(C43⋊C8)C2311yescharacteristic
77Dic43⋊C8—22no—
78#13063249—22no—
79#13063249—22no—
80#13063248—21no—
81#13063248—21no—
82#13063245—21no—
83#13063245—21no—
84(C2×D43)⋊C8—22no—
85C8×Dic43—22no—
86C22×Q8×C43—21no—
87C4⋊Q8×C43—21no—
88C4⋊Q8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43C2311yescharacteristic
91C4⋊Q8×C43C2312yes—
92C4⋊Q8×C43C2311yescharacteristic
93#125×C43—21no—
94C22⋊Q8×C43—21no—
95C22⋊Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98#117×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#103×C43—22no—
107#103×C43—22no—
108C22⋊C8×C43D412yes—
109C4×C8×C43C2312yes—
110C2×Q8×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—21no—
113C2×Q8×C43—41no—
114C2×Q8×C43—42no—
115C2×Q8×C43—42no—
116C22×C4×C43—41no—
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43#4111yescharacteristic
120C2×C22⋊D43—21no—
121#10621898—22no—
122#10621898SD1614yes—
123C2×D172C2×D411yescharacteristic
124C2×C4×D43—21no—
125C2×C4×D43—21no—
126C2×C4×D43—21no—
127C2×Dic86C2×D411yescharacteristic
128C2×C8×C43C2×D412yes—
129C2×C8×C43C2×D412yes—
130C4⋊C4×C43—22no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43—41no—
138C4⋊C4×C43—41no—
139C4⋊C4×C43—41no—
140C22⋊C4×C43—41no—
141C42×C43—41no—
142C42×C43C2×D411yescharacteristic
143C42×C43C2×D411yescharacteristic
144C42×C43#4111yescharacteristic
145C42×C43C2411yescharacteristic
146C22⋊Dic43—21no—
147#10621885—44no—
148#10621884—44no—
149(C2×D43)⋊C4—21no—
150(C2×D43)⋊C4—21no—
151C4⋊Dic43C2×D411yescharacteristic
152C4⋊Dic43C2×D411yescharacteristic
153Dic43⋊C4—21no—
154Dic43⋊C4—21no—
155C4×Dic43—21no—
156C4×Dic43—21no—
157C4×Dic43—21no—
158#10621877—42no—
159C2×C43⋊C8—22no—
160C2×C43⋊C8—21no—
161C2×C43⋊C8—21no—
162C2×C43⋊C8—22no—
163C2×C43⋊C8—42no—
164C2×C43⋊C8—81no—
165C8×D43—82no—
166C23×C43#12111yescharacteristic
167C22×D43—21no—
168Q8×C43—42no—
169Q8×C43—42no—
170Q8×C43—41no—
171Q8×C43—41no—
172Q8×C43—81no—
173Q8×C43—82no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—42no—
180C2×C4×C43—82no—
181C2×C4×C43#12111yescharacteristic
182C2×C4×C43#12111yescharacteristic
183C2×C4×C43#12111yescharacteristic
184C2×C4×C43C2×SD1612yes—
185C2×C4×C43#13512yes—
186C2×C4×C43C22×D411yescharacteristic
187C2×C4×C43C22×D411yescharacteristic
188C2×C4×C43C2×#4111yescharacteristic
189C22⋊D43—24no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193D172—21no—
194D172C2×SD1612yes—
195C4×D43—24no—
196C4×D43—41no—
197C4×D43—41no—
198C4×D43—81no—
199Dic86—21no—
200Dic86C2×SD1612yes—
201C8×C43—22no—
202C8×C43—22no—
203C43⋊C8—42no—
204C43⋊C8—41no—
205C43⋊C8—41no—
206C43⋊C8—42no—
207#19415—431nomaximal, Sylow
208C22×C43—21no—
209C22×C43—21no—
210C22×C43#46512yes—
211C22×C43C2×#12111yescharacteristic
212C2×D43—22no—
213C2×D43—41no—
214C2×D43—41no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—81no—
219C4×C43—82no—
220C4×C43—81no—
221C4×C43#46512yes—
222C4×C43C22×SD1611yescharacteristic
223C4×C43C2×#13511yescharacteristic
224C4×C43#57711yescharacteristic
225C4×C43#57811yescharacteristic
226Dic43—22no—
227Dic43—41no—
228Dic43—41no—
229#3229D4311yescharacteristic, complemented
230#3076—431no—
231#3039—431no—
232#2988—431no—
233#1680—432no—
234#1679—432no—
235#1672—432no—
236#1671—432no—
237#1570—431no—
238#1550—431no—
239C2×#332—431no—
240C2×C43—22no—
241C2×C43#304611yescharacteristic
242C2×C43C2×#46511yescharacteristic
243C2×C43#306911yescharacteristic
244D43—42no—
245C2×#137—861no—
246#533C2×D4311yescharacteristic
247C2×C4⋊Q8C2×D4311yescharacteristic
248C4×#41—431no—
249#498C2×D4312yes—
250#487C2×D4312yes—
251#483—22no—
252#479—861no—
253#478—861no—
254#477—431no—
255#476—431no—
256#475—21no—
257#475—21no—
258#475—431no—
259#474—431no—
260#462—432no—
261#462—861no—
262#461—432no—
263#461—861no—
264C8×Q8—432no—
265C8×D4—432no—
266C8×D4—862no—
267#431—861no—
268#431C2×D4311yescharacteristic
269#427—861no—
270#423—431no—
271C2×C4⋊C8—431no—
272C2×C4⋊C8—431no—
273C2×C4⋊C8—861no—
274#419—861no—
275#416—861no—
276#334—432no—
277#334—432no—
278#333—432no—
279#332—432no—
280#332—432no—
281#332—432no—
282C43#1941511yescharacteristic, complemented, Sylow
283C2×#41—431no—
284C22×Q8—21no—
285#137—1724no—
286C2×Q16—862no—
287C2×SD16—862no—
288C2×M16—861no—
289C22×C8—861no—
290C22×C8—861no—
291C22×C8—862no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8C22×D4312yes—
296C4⋊Q8C22×D4311yescharacteristic
297C4⋊Q8C22×D4311yescharacteristic
298#125—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—431no—
304C4×Q8—431no—
305C4×D4—431no—
306C4×D4—431no—
307C4×D4—861no—
308C4×D4—861no—
309#117—21no—
310#117—431no—
311#117—861no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C42—861no—
315C2×C42C22×D4311yescharacteristic
316#107—861no—
317#107—861no—
318#106—22no—
319#106—22no—
320#106—861no—
321#106—861no—
322C4⋊C8—432no—
323C4⋊C8—431no—
324C4⋊C8—431no—
325C4⋊C8—432no—
326C4⋊C8—862no—
327C4⋊C8—861no—
328C4⋊C8—861no—
329C4⋊C8—861no—
330C4⋊C8C22⋊D4311yescharacteristic
331C4⋊C8C22⋊D4311yescharacteristic
332#103—22no—
333#103—22no—
334#103—861no—
335#103—861no—
336#103—862no—
337#103—862no—
338#102—861no—
339#102—861no—
340C22⋊C8—862no—
341C22⋊C8C22⋊D4312yes—
342C4×C8—862no—
343C4×C8C22×D4312yes—
344#41—434no—
345#41—862no—
346C2×Q8—22no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—41no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8—431no—
353C2×D4—431no—
354C2×D4—861no—
355C22×C4—41no—
356C22×C4—861no—
357C22×C4—861no—
358C22×C4—861no—
359C22×C4D4×D4311yescharacteristic
360C22×C4#1062190011yescharacteristic
361C22×C4C2×C22⋊D4311yescharacteristic
362Q16—1724no—
363SD16—1724no—
364M16—1722no—
365C2×C8—861no—
366C2×C8—861no—
367C2×C8—862no—
368C2×C8—862no—
369C2×C8—3442no—
370C2×C8—3441no—
371C2×C8—1722no—
372C2×C8C2×C22⋊D4312yes—
373C2×C8C2×C22⋊D4312yes—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—431no—
385C4⋊C4—431no—
386C4⋊C4—861no—
387C4⋊C4—861no—
388C22⋊C4—41no—
389C22⋊C4—861no—
390C22⋊C4—861no—
391C22⋊C4—861no—
392C42—41no—
393C42—861no—
394C42—861no—
395C42—861no—
396C42D4×D4311yescharacteristic
397C42#1062190011yescharacteristic
398C42C2×C22⋊D4311yescharacteristic
399C42C23×D4311yescharacteristic
400C23—861no—
401C23#1306329611yescharacteristic
402Q8—42no—
403Q8—42no—
404Q8—41no—
405Q8—41no—
406Q8—81no—
407Q8—82no—
408Q8—432no—
409Q8—861no—
410D4—432no—
411D4—864no—
412D4—861no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—82no—
420C2×C4—861no—
421C2×C4—864no—
422C2×C4—861no—
423C2×C4—861no—
424C2×C4—3441no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4#1306329611yescharacteristic
428C2×C4#1306329611yescharacteristic
429C2×C4#1306329611yescharacteristic
430C2×C4SD16×D4312yes—
431C2×C4#1306334612yes—
432C2×C4C2×D4×D4311yescharacteristic
433C2×C4C22×C22⋊D4311yescharacteristic
434C2×C4C2×#1062190011yescharacteristic
435C8—22no—
436C8—22no—
437C8—1722no—
438C8—1721no—
439C8—1721no—
440C8—1722no—
441C22—21no—
442C22—21no—
443C22—862no—
444C22—1721no—
445C22—1721no—
446C22#1458312512yes—
447C22C2×#1306329611yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—81no—
452C4—81no—
453C4—82no—
454C4—862no—
455C4—1721no—
456C4—1721no—
457C4#1458312512yes—
458C4C2×SD16×D4311yescharacteristic
459C4C2×#1306334611yescharacteristic
460C4#1458370711yescharacteristic
461C4#1458371411yescharacteristic
462C2—22no—
463C2—1722no—
464C2#1914414111yescharacteristic
465C2C2×#1458312511yescharacteristic
466C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3229C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#3229D43
hypocenterC43#19415
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
4. #19134022C2semidirect
5. #19134015C2semidirect
6. #19133974C2semidirect
7. #19133967C2semidirect
8. #19133366C2semidirect
9. #19133285C2semidirect
10. C2×#14582645C2semidirect
11. C43×#3229C2semidirect
229. #3229D43semidirect
282. C43#19415semidirect

Maximal subgroups

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

subgroupindex
#191443772
#191440782
#191437032
#191340222
#191340152
#191339742
#191339672
#191333662
#191332852
C2×#145826452
C43×#32292
#1941543