Finite Group Databasebeta

← #25254174

Subgroups — #25254174

Order 11008.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146999C211yesmaximal, characteristic
2#19146962C211yesmaximal, characteristic, complemented
3#19136871C211yesmaximal, characteristic, complemented
4#19136805C211yesmaximal, characteristic, complemented
5#19136794C211yesmaximal, characteristic, complemented
6#19136784C211yesmaximal, characteristic, complemented
7#19136779C211yesmaximal, characteristic, complemented
8#19136760C211yesmaximal, characteristic, complemented
9#19136707C211yesmaximal, characteristic, complemented
10#19136707C211yesmaximal, characteristic, complemented
11C4×#13063269C211yesmaximal, characteristic, complemented
12#19136426C211yesmaximal, characteristic, complemented
13#19136382C211yesmaximal, characteristic, complemented
14#19136380C211yesmaximal, characteristic, complemented
15C43×#2228C211yesmaximal, characteristic, complemented
16#14583599—21no—
17#14583587—21no—
18C2×#13063269C2211yescharacteristic
19C2×#13063264C2211yescharacteristic
20C2×#13063264C2211yescharacteristic
21#14583301C2211yescharacteristic
22#14583243—21no—
23#14583231—21no—
24#14583222—21no—
25#14583216—21no—
26#14583203—21no—
27#14583199—21no—
28#14583141C2211yescharacteristic
29#14583141C2211yescharacteristic
30#14583132C2211yescharacteristic
31#14583132C2211yescharacteristic
32C4×Dic172C2211yescharacteristic
33C8×D172C2211yescharacteristic
34#14582936C2211yescharacteristic
35#14582936C2211yescharacteristic
36#107×D43C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582727C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582726C2211yescharacteristic
42#14582725C2211yescharacteristic
43#14582724C2211yescharacteristic
44#14582724C2211yescharacteristic
45#14582704C2211yescharacteristic
46#14582704C2211yescharacteristic
47#14582702C2211yescharacteristic
48#14582700C2211yescharacteristic
49(C2×D43)⋊C16C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C4×C43⋊C16C2211yescharacteristic
52C43×#499C2211yescharacteristic
53C4×D8×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic
55C43×#366C2211yescharacteristic
56C43×C4⋊C16C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×C8×D43C2311yescharacteristic
61C2×C8×D43C2311yescharacteristic
62#13063320—41no—
63#13063318—41no—
64#13063317—21no—
65#13063316—41no—
66#13063310—41no—
67#13063308—41no—
68#13063305—21no—
69#13063305—21no—
70#13063298—41no—
71#13063296—21no—
72#13063296—21no—
73C4×Dic86—21no—
74C4×D172D411yescharacteristic
75C4×C22⋊D43—41no—
76#13063283—21no—
77#13063283—21no—
78#13063283—41no—
79C4⋊C4×D43—21no—
80C4⋊C4×D43—21no—
81#13063269—22no—
82#13063264—22no—
83#13063264—22no—
84C2×C43⋊C16C2311yescharacteristic
85C2×C43⋊C16C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063258—21no—
90#13063258—21no—
91#13063257—21no—
92#13063256—21no—
93#13063256—21no—
94C4⋊(C43⋊C8)D411yescharacteristic
95#13063250—21no—
96#13063248—21no—
97#13063248—21no—
98#13063246—21no—
99#13063246—21no—
100(C2×D43)⋊C8D411yescharacteristic
101(C2×D43)⋊C8D411yescharacteristic
102C2×D8×C43C2311yescharacteristic
103#125×C43—21no—
104C4×D4×C43—21no—
105C2×C16×C43C2311yescharacteristic
106C2×C16×C43C2311yescharacteristic
107#107×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#106×C43—21no—
111#102×C43—21no—
112C4×C8×C43C2311yescharacteristic
113C2×D4×C43—21no—
114C22×C4×C43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C2×D172D811yescharacteristic
118C2×C4×D43—41no—
119C2×C4×D43—41no—
120C2×C4×D43C2×D411yescharacteristic
121C2×C4×D43C2×D411yescharacteristic
122C2×Dic86—21no—
123D8×C43—21no—
124D8×C43—21no—
125C2×C8×C43C2×D411yescharacteristic
126C2×C8×C43C2411yescharacteristic
127C4⋊C4×C43—21no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C42×C43C2×D411yescharacteristic
134C22⋊Dic43—41no—
135C22⋊Dic43—41no—
136(C2×D43)⋊C4—41no—
137(C2×D43)⋊C4—41no—
138(C2×D43)⋊C4—41no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4D811yescharacteristic
141(C2×D43)⋊C4D811yescharacteristic
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43—21no—
145C4⋊Dic43—41no—
146C4⋊Dic43—41no—
147C4⋊Dic43D811yescharacteristic
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153C4×Dic43—41no—
154C4×Dic43—41no—
155C4×Dic43—41no—
156C2×C43⋊C8C2×D411yescharacteristic
157C2×C43⋊C8C2×D411yescharacteristic
158Dic172—21no—
159Dic172—21no—
160C8×D43—21no—
161C8×D43—21no—
162C8×D43—21no—
163C8×D43—21no—
164C16×C43—21no—
165C16×C43—21no—
166C43⋊C16—21no—
167C43⋊C16#4112yes—
168C23×C43—41no—
169C22×D43C2×D811yescharacteristic
170C22×D43C2×D811yescharacteristic
171D4×C43—41no—
172D4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—161no—
177C2×C4×C43C2×D811yescharacteristic
178C2×C4×C43C2×D811yescharacteristic
179C2×C4×C43C22×D411yescharacteristic
180C22⋊D43—82no—
181C22⋊D43—161no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43C2×D811yescharacteristic
187C2×Dic43C2×D811yescharacteristic
188D172—41no—
189C4×D43—21no—
190C4×D43—21no—
191C4×D43—21no—
192C4×D43—21no—
193C4×D43—82no—
194C4×D43—161no—
195Dic86—41no—
196Dic86—41no—
197C8×C43—21no—
198C8×C43C2×#4111yescharacteristic
199C8×C432−1+411yescharacteristic
200C43⋊C8—21no—
201C43⋊C8—21no—
202#33918—431nomaximal, Sylow
203C22×C43—81no—
204C22×C43—81no—
205C22×C43—81no—
206C22×C43C22×D811yescharacteristic
207C2×D43—21no—
208C2×D43—21no—
209C2×D43—21no—
210C2×D43—21no—
211C2×D43—21no—
212C2×D43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43—81no—
218C4×C43#54711yescharacteristic
219C4×C43#57811yescharacteristic
220Dic43—21no—
221Dic43—21no—
222Dic43—81no—
223Dic43—81no—
224Dic43—81no—
225Dic43—81no—
226#3339—431no—
227#3336—431no—
228#2253—431no—
229#2237—431no—
230#2235—431no—
231#2234—431no—
232#2233—431no—
233#2229—431no—
234#2228D4311yescharacteristic, complemented
235#2220—431no—
236#2220—431no—
237C4×SD32—431no—
238#2169—431no—
239#2159—431no—
240#2159—431no—
241C2×C43—161no—
242C2×C43#333411yescharacteristic
243C2×C43#341411yescharacteristic
244C2×C43#341611yescharacteristic
245D43—41no—
246D43—41no—
247#553—861no—
248#552—861no—
249C2×SD32—431no—
250C2×M32—431no—
251C2×M32—431no—
252#499—431no—
253#499C2×D4311yescharacteristic
254#485—861no—
255#483—861no—
256#482—861no—
257#481—861no—
258#479—861no—
259#478—861no—
260#467—431no—
261#467—431no—
262#466—431no—
263#466—431no—
264C4×Q16—431no—
265C4×D8C2×D4311yescharacteristic
266C8×D4—431no—
267#427—431no—
268#427—431no—
269C2×#107—431no—
270C2×#107—431no—
271#367—431no—
272#367—431no—
273#367—431no—
274#367—431no—
275#367C2×D4311yescharacteristic
276#366—431no—
277#366—431no—
278#366—431no—
279#366C2×D4311yescharacteristic
280C4⋊C16C2×D4311yescharacteristic
281#358—431no—
282#358—431no—
283#358—431no—
284#357—431no—
285#357C2×D4311yescharacteristic
286#357C2×D4311yescharacteristic
287C22⋊C16—431no—
288C22⋊C16—431no—
289C4×C16—431no—
290C43#3391811yescharacteristic, complemented, Sylow
291C2×Q16—431no—
292C2×D8C22×D4311yescharacteristic
293C22×C8—431no—
294C22×C8—431no—
295#126—1721no—
296#126—1721no—
297#125—21no—
298#125—861no—
299#125—1721no—
300#123—1721no—
301#123—1721no—
302C22⋊Q8—861no—
303C22⋊Q8—861no—
304#121—861no—
305#121—861no—
306#121—1721no—
307C4×Q8—861no—
308C4×D4—21no—
309C4×D4—431no—
310C4×D4—1721no—
311#117—861no—
312#117—861no—
313#117—1721no—
314C2×C4⋊C4—861no—
315C2×C4⋊C4—861no—
316SD32—862no—
317M32—862no—
318M32—862no—
319C2×C16—431no—
320C2×C16—431no—
321C2×C16C22×D4311yescharacteristic
322C2×C16C22×D4311yescharacteristic
323#107—431no—
324#107—431no—
325#107—431no—
326#107—861no—
327#107—861no—
328#107C22×D4311yescharacteristic
329#107C22×D4311yescharacteristic
330#107C22×D4311yescharacteristic
331#106—21no—
332#106—861no—
333#106—861no—
334#106—861no—
335C4⋊C8—431no—
336#103—861no—
337#103—861no—
338#103—861no—
339#102—21no—
340#102—861no—
341#102—861no—
342C22⋊C8—431no—
343C22⋊C8—431no—
344C4×C8C22×D4311yescharacteristic
345C2×Q8—861no—
346C2×D4—21no—
347C2×D4—431no—
348C2×D4—1721no—
349C2×D4—1721no—
350C22×C4—41no—
351C22×C4—431no—
352C22×C4—431no—
353C22×C4—1721no—
354C22×C4—1721no—
355Q16—861no—
356Q16—861no—
357D8—21no—
358D8—21no—
359C2×C8—431no—
360C2×C8—431no—
361C2×C8—861no—
362C2×C8—861no—
363C2×C8—861no—
364C2×C8—861no—
365C2×C8D4×D4311yescharacteristic
366C2×C8C23×D4311yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—431no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—861no—
376C4⋊C4—1721no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C22⋊C4—41no—
384C22⋊C4—431no—
385C22⋊C4—431no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—1721no—
393C42—1721no—
394C42—1721no—
395C42D4×D4311yescharacteristic
396C16—21no—
397C16—21no—
398C16—432no—
399C16—861no—
400C23—41no—
401C23—431no—
402C23—431no—
403Q8—1721no—
404Q8—1721no—
405D4—41no—
406D4—41no—
407D4—3442no—
408D4—1721no—
409D4—6881no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—161no—
414C2×C4—431no—
415C2×C4—431no—
416C2×C4—861no—
417C2×C4—861no—
418C2×C4—861no—
419C2×C4—861no—
420C2×C4—3442no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4—1721no—
425C2×C4—6881no—
426C2×C4D8×D4311yescharacteristic
427C2×C4D8×D4311yescharacteristic
428C2×C4C2×D4×D4311yescharacteristic
429C8—21no—
430C8—861no—
431C8—861no—
432C8#41×D4311yescharacteristic
433C8#1306337311yescharacteristic
434C22—81no—
435C22—81no—
436C22—81no—
437C22—861no—
438C22—861no—
439C22—861no—
440C22—861no—
441C22—861no—
442C22—861no—
443C22C2×D8×D4311yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—861no—
450C4—861no—
451C4—3441no—
452C4—3441no—
453C4—3441no—
454C4—3441no—
455C4#1458355111yescharacteristic
456C4#1458371511yescharacteristic
457C2—161no—
458C2—1721no—
459C2—1721no—
460C2#1914694111yescharacteristic
461C2#1914772811yescharacteristic
462C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2228C2
socleC22×C43C22×D8
prime radical#19146999C2
hypercenter#2228D43
hypocenterC43#33918
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
2. #19146962C2semidirect
3. #19136871C2semidirect
4. #19136805C2semidirect
5. #19136794C2semidirect
6. #19136784C2semidirect
7. #19136779C2semidirect
8. #19136760C2semidirect
9. #19136707C2semidirect
10. #19136707C2semidirect
11. C4×#13063269C2semidirect
12. #19136426C2semidirect
13. #19136382C2semidirect
14. #19136380C2semidirect
15. C43×#2228C2semidirect
234. #2228D43semidirect
290. C43#33918semidirect

Maximal subgroups

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

subgroupindex
#191469992
#191469622
#191368712
#191368052
#191367942
#191367842
#191367792
#191367602
#191367072
C4×#130632692
#191364262
#191363822
#191363802
C43×#22282
#3391843