Finite Group Databasebeta

← #25254184

Subgroups — #25254184

Order 11008.

502 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147022C211yesmaximal, characteristic, complemented
2#19146940C211yesmaximal, characteristic
3#19136869C211yesmaximal, characteristic, complemented
4#19136796C211yesmaximal, characteristic, complemented
5#19136789C211yesmaximal, characteristic, complemented
6#19136787C211yesmaximal, characteristic, complemented
7#19136735C211yesmaximal, characteristic, complemented
8#19136731C211yesmaximal, characteristic, complemented
9#19136711C211yesmaximal, characteristic, complemented
10#19136710C211yesmaximal, characteristic, complemented
11#19136444C211yesmaximal, characteristic, complemented
12#19136424C211yesmaximal, characteristic, complemented
13#19136381C211yesmaximal, characteristic, complemented
14#19136380C211yesmaximal, characteristic, complemented
15C43×#2236C211yesmaximal, characteristic, complemented
16#14583620—21no—
17#14583550—21no—
18C2×#13063268C2211yescharacteristic
19C2×#13063265C2211yescharacteristic
20C2×#13063264C2211yescharacteristic
21#14583303C2211yescharacteristic
22#14583303C2211yescharacteristic
23#14583238—21no—
24#14583237—21no—
25#14583214—21no—
26#14583212—21no—
27#14583182—21no—
28#14583178—21no—
29#14583137C2211yescharacteristic
30#14583136C2211yescharacteristic
31#14583135C2211yescharacteristic
32Q16×Dic43C2211yescharacteristic
33#14582981C2211yescharacteristic
34C8×C22⋊D43C2211yescharacteristic
35#14582937C2211yescharacteristic
36#14582936C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582727C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582725C2211yescharacteristic
42#14582724C2211yescharacteristic
43#14582724C2211yescharacteristic
44#14582724C2211yescharacteristic
45Dic43⋊C16C2211yescharacteristic
46#14582703C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582701C2211yescharacteristic
49#14582699C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C43×#467C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C43×#366C2211yescharacteristic
55C43×#366C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×#10621898—41no—
60C2×D344C2311yescharacteristic
61C2×C8×D43C2311yescharacteristic
62#13063324—21no—
63#13063324—21no—
64#13063320—41no—
65#13063318—41no—
66#13063311—41no—
67#13063310—41no—
68#13063308—41no—
69#13063303—41no—
70#13063301—21no—
71#13063300—21no—
72#13063299—21no—
73Q8×Dic43—21no—
74#13063290—41no—
75#13063287—21no—
76C4×C22⋊D43D411yescharacteristic
77#13063284—21no—
78#13063283—21no—
79C4⋊C4×D43—21no—
80#13063268—22no—
81#13063265—22no—
82#13063264—22no—
83C2×C43⋊C16C2311yescharacteristic
84C2×C43⋊C16C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063257—21no—
92#13063256—21no—
93Dic43⋊C8D411yescharacteristic
94#13063249—21no—
95#13063249—21no—
96#13063247—21no—
97#13063245—21no—
98#13063245—21no—
99C22⋊(C43⋊C8)D411yescharacteristic
100(C2×D43)⋊C8D411yescharacteristic
101C8×Dic43C2311yescharacteristic
102C2×Q16×C43C2311yescharacteristic
103C22×C8×C43C2311yescharacteristic
104C22⋊Q8×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C16×C43C2311yescharacteristic
107C2×C16×C43C2311yescharacteristic
108#107×C43—21no—
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#103×C43—21no—
113C2×Q8×C43—21no—
114C22×C4×C43—41no—
115C22×C4×C43C2×D411yescharacteristic
116C2×C22⋊D43—41no—
117C2×C22⋊D43D811yescharacteristic
118#10621898—84no—
119C2×D172—21no—
120C2×D172—41no—
121C2×C4×D43—41no—
122C2×C4×D43—41no—
123C2×C4×D43C2×D411yescharacteristic
124C2×Dic86—41no—
125C2×Dic86—41no—
126Q16×C43—21no—
127Q16×C43—21no—
128C2×C8×C43—21no—
129C2×C8×C43—21no—
130C2×C8×C43C2×D411yescharacteristic
131C2×C8×C43C2411yescharacteristic
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C22⋊C4×C43—41no—
138C22⋊Dic43—41no—
139C22⋊Dic43D811yescharacteristic
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4D811yescharacteristic
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4D811yescharacteristic
155C4×Dic43—41no—
156C4×Dic43—41no—
157C4×Dic43—41no—
158C4×Dic43C2×D411yescharacteristic
159C2×C43⋊C8C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161D344—21no—
162D344—21no—
163C8×D43—21no—
164C8×D43—21no—
165C16×C43—21no—
166C16×C43—21no—
167C43⋊C16—21no—
168C43⋊C16#4112yescomplemented
169C23×C43C2×D811yescharacteristic
170C22×D43—41no—
171C22×D43C2×D811yescharacteristic
172Q8×C43—41no—
173Q8×C43—41no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—82no—
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C22⋊D43—22no—
184C22⋊D43—82no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43C2×D811yescharacteristic
189C2×Dic43C2×D811yescharacteristic
190C2×Dic43C2×D811yescharacteristic
191D172—41no—
192D172—41no—
193D172—82no—
194C4×D43—21no—
195C4×D43—21no—
196C4×D43—82no—
197C4×D43—82no—
198Dic86—82no—
199Dic86—82no—
200C8×C43—21no—
201C8×C43C2×#4111yescharacteristic
202C8×C432−1+411yescharacteristic
203C43⋊C8—21no—
204C43⋊C8—21no—
205#33920—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43C22×D811yescharacteristic
210C2×D43—21no—
211C2×D43—21no—
212C2×D43—21no—
213C2×D43—81no—
214C2×D43—81no—
215C2×D43—81no—
216C4×C43—21no—
217C4×C43—81no—
218C4×C43—81no—
219C4×C43—81no—
220C4×C43—81no—
221C4×C43#54711yescharacteristic
222C4×C43#57811yescharacteristic
223Dic43—21no—
224Dic43—21no—
225Dic43—81no—
226Dic43—81no—
227Dic43—81no—
228Dic43#50912yes—
229#3342—431no—
230#3334—431no—
231#2252—431no—
232#2236—431no—
233#2236D4311yescharacteristic, complemented
234#2234—431no—
235#2234—431no—
236#2225—431no—
237#2224—431no—
238#2220—431no—
239#2220—431no—
240C4×SD32—431no—
241#2169—431no—
242#2159—431no—
243#2159—431no—
244C2×C43—41no—
245C2×C43#333411yescharacteristic
246C2×C43C2×#50911yescharacteristic
247C2×C43#341711yescharacteristic
248D43—41no—
249D43—161no—
250#556—861no—
251#547—861no—
252C2×SD32—431no—
253C2×M32—431no—
254C2×M32—431no—
255#500—431no—
256#500—431no—
257#485—861no—
258#485—861no—
259#480—861no—
260#480—861no—
261#475—861no—
262#474—861no—
263#467—431no—
264#467C2×D4311yescharacteristic
265#466—431no—
266#466—431no—
267C4×Q16—431no—
268C4×D8—431no—
269C8×D4—431no—
270#427—431no—
271#427—431no—
272C2×#107—431no—
273C2×#107C2×D4311yescharacteristic
274#367—431no—
275#367—431no—
276#367—431no—
277#366—431no—
278#366—431no—
279#366—431no—
280#366—431no—
281#366C2×D4311yescharacteristic
282#366C2×D4311yescharacteristic
283C4⋊C16—431no—
284#358—431no—
285#358C2×D4311yescharacteristic
286#358C2×D4311yescharacteristic
287#357—431no—
288#357—431no—
289#357—431no—
290C22⋊C16—431no—
291C22⋊C16C2×D4311yescharacteristic
292C4×C16—431no—
293C43#3392011yescharacteristic, complemented, Sylow
294C2×#41—1721no—
295C2×Q16C22×D4311yescharacteristic
296C2×D8—431no—
297C22×C8—431no—
298C22×C8C22×D4311yescharacteristic
299C4⋊Q8—861no—
300C4⋊Q8—861no—
301#126—1721no—
302#126—1721no—
303#124—1721no—
304#123—1721no—
305#123—1721no—
306C22⋊Q8—21no—
307C22⋊Q8—861no—
308C22⋊Q8—1721no—
309#121—861no—
310#121—861no—
311C4×Q8—861no—
312C4×Q8—1721no—
313C4×D4—431no—
314C4×D4—861no—
315#117—861no—
316#117—861no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—861no—
319SD32—862no—
320M32—862no—
321M32—862no—
322C2×C16—431no—
323C2×C16—431no—
324C2×C16C22×D4311yescharacteristic
325C2×C16C22×D4311yescharacteristic
326#107—21no—
327#107—431no—
328#107—431no—
329#107—431no—
330#107—861no—
331#107—861no—
332#107—861no—
333#107C22×D4311yescharacteristic
334#107C22×D4311yescharacteristic
335#107C22×D4311yescharacteristic
336#106—861no—
337#106—861no—
338C4⋊C8—431no—
339#103—21no—
340#103—861no—
341#103—861no—
342#102—861no—
343#102—861no—
344#102—861no—
345C22⋊C8—431no—
346C22⋊C8—431no—
347C4×C8—431no—
348#41—3444no—
349C2×Q8—21no—
350C2×Q8—1721no—
351C2×Q8—1721no—
352C2×D4—431no—
353C2×D4—861no—
354C2×D4—1721no—
355C2×D4—1721no—
356C22×C4—41no—
357C22×C4—431no—
358C22×C4—1721no—
359C22×C4—1721no—
360C22×C4D4×D4311yescharacteristic
361Q16—21no—
362Q16—21no—
363D8—861no—
364D8—861no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—431no—
368C2×C8—431no—
369C2×C8—861no—
370C2×C8—861no—
371C2×C8D4×D4311yescharacteristic
372C2×C8C23×D4311yescharacteristic
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—431no—
379C4⋊C4—861no—
380C4⋊C4—861no—
381C4⋊C4—861no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C4⋊C4—1721no—
387C22⋊C4—41no—
388C22⋊C4—431no—
389C22⋊C4—431no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C22⋊C4—1721no—
396C42—431no—
397C42—1721no—
398C42—1721no—
399C42—1721no—
400C16—21no—
401C16—21no—
402C16—432no—
403C16—861no—
404C23—431no—
405C23—1721no—
406C23D8×D4311yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—3442no—
410Q8—3442no—
411D4—862no—
412D4—3442no—
413D4—3442no—
414D4—1721no—
415D4—1721no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—82no—
423C2×C4—431no—
424C2×C4—431no—
425C2×C4—431no—
426C2×C4—861no—
427C2×C4—861no—
428C2×C4—3442no—
429C2×C4—3442no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—1721no—
433C2×C4D8×D4311yescharacteristic
434C2×C4C2×D4×D4311yescharacteristic
435C8—21no—
436C8—861no—
437C8—861no—
438C8#41×D4311yescharacteristic
439C8#1306337211yescharacteristic
440C22—21no—
441C22—21no—
442C22—21no—
443C22—861no—
444C22—861no—
445C22—861no—
446C22—3441no—
447C22—3441no—
448C22—3441no—
449C22C2×D8×D4311yescharacteristic
450C4—21no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—432no—
456C4—861no—
457C4—861no—
458C4—3441no—
459C4—3441no—
460C4—3441no—
461C4#1458354711yescharacteristic
462C4#1458371511yescharacteristic
463C2—41no—
464C2—1721no—
465C2—6881no—
466C2#1914693711yescharacteristic
467C2#509×D4311yescharacteristic
468C2#1914774411yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2236C2
socleC22×C43C22×D8
prime radical#19146940C2
hypercenter#2236D43
hypocenterC43#33920
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
1. #19147022C2semidirect
3. #19136869C2semidirect
4. #19136796C2semidirect
5. #19136789C2semidirect
6. #19136787C2semidirect
7. #19136735C2semidirect
8. #19136731C2semidirect
9. #19136711C2semidirect
10. #19136710C2semidirect
11. #19136444C2semidirect
12. #19136424C2semidirect
13. #19136381C2semidirect
14. #19136380C2semidirect
15. C43×#2236C2semidirect
168. C43⋊C16#41semidirect
233. #2236D43semidirect
293. C43#33920semidirect

Maximal subgroups

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

subgroupindex
#191470222
#191469402
#191368692
#191367962
#191367892
#191367872
#191367352
#191367312
#191367112
#191367102
#191364442
#191364242
#191363812
#191363802
C43×#22362
#3392043