Finite Group Databasebeta

← #25254375

Subgroups — #25254375

Order 11008.

480 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#19147608C211yesmaximal, characteristic
2#19136838C211yesmaximal, characteristic
3#19136834C211yesmaximal, characteristic, complemented
4#19136829C211yesmaximal, characteristic, complemented
5#19136756C211yesmaximal, characteristic, complemented
6#19136749C211yesmaximal, characteristic, complemented
7#19136739C211yesmaximal, characteristic, complemented
8#19136657C211yesmaximal, characteristic, complemented
9#19136657C211yesmaximal, characteristic, complemented
10#19136635C211yesmaximal, characteristic
11#19136504C211yesmaximal, characteristic, complemented
12#19136464C211yesmaximal, characteristic, complemented
13#19136457C211yesmaximal, characteristic, complemented
14C4×#13063268C211yesmaximal, characteristic, complemented
15C43×#3383C211yesmaximal, characteristic, complemented
16#14583634—21no—
17C2×#13063271C2211yescharacteristic
18C2×#13063268C2211yescharacteristic
19C2×#13063268C2211yescharacteristic
20#14583283C2211yescharacteristic
21#14583283C2211yescharacteristic
22#14583276C2211yescharacteristic
23#14583115—21no—
24#14583115—21no—
25#14583100—21no—
26C4×Dic172C2211yescharacteristic
27C4×D344C2211yescharacteristic
28C4×D344C2211yescharacteristic
29#14582726C2211yescharacteristic
30#14582726C2211yescharacteristic
31#14582724C2211yescharacteristic
32C4⋊(C43⋊C16)C2211yescharacteristic
33C4⋊(C43⋊C16)C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35#14582703C2211yescharacteristic
36#14582702C2211yescharacteristic
37#14582702C2211yescharacteristic
38#14582702C2211yescharacteristic
39#14582699C2211yescharacteristic
40#14582699C2211yescharacteristic
41#14582699C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44#14582699C2211yescharacteristic
45#14582675C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C43×#557—21no—
49C43×#500C2211yescharacteristic
50C43×#499C2211yescharacteristic
51C43×#499C2211yescharacteristic
52C43×#479—21no—
53C43×#479—21no—
54C43×#475—21no—
55C8×Q8×C43C2211yescharacteristic
56C4×Q16×C43C2211yescharacteristic
57C4×Q16×C43C2211yescharacteristic
58C4×Q16×C43C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621873—21no—
61C2×#10621873—21no—
62C2×D344—21no—
63C2×D344C2311yescharacteristic
64C2×D344C2311yescharacteristic
65#13063322—21no—
66#13063314—41no—
67#13063313—21no—
68#13063313—21no—
69#13063310—41no—
70#13063310—41no—
71C4×Dic86—21no—
72C4×D172—21no—
73C4×D172—21no—
74#13063287—41no—
75#13063271—22no—
76#13063268—22no—
77#13063268—22no—
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259C2311yescharacteristic
83#13063250—21no—
84#13063247—21no—
85#13063247—21no—
86C2×Q16×C43C2311yescharacteristic
87C4⋊Q8×C43—21no—
88C4⋊Q8×C43—41no—
89#125×C43—21no—
90#125×C43—21no—
91#125×C43—41no—
92#125×C43—41no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—41no—
97C4×Q8×C43D411yescharacteristic
98#107×C43—21no—
99#107×C43C2311yescharacteristic
100#107×C43C2311yescharacteristic
101#107×C43C2311yescharacteristic
102#106×C43—21no—
103#106×C43—21no—
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D411yescharacteristic
106C4⋊C8×C43D411yescharacteristic
107#103×C43—21no—
108#103×C43—21no—
109#103×C43—21no—
110C4×C8×C43C2311yescharacteristic
111C4×C8×C43C2311yescharacteristic
112C4×C8×C43C2311yescharacteristic
113C2×Q8×C43—21no—
114C2×Q8×C43—41no—
115C2×Q8×C43D811yescharacteristic
116C2×D172—21no—
117C2×D172—21no—
118C2×D172—41no—
119C2×D172—41no—
120C2×C4×D43—41no—
121C2×C4×D43—41no—
122C2×Dic86—21no—
123Q16×C43—21no—
124Q16×C43#4112yes—
125C2×C8×C43C2×D411yescharacteristic
126C2×C8×C43C2×D411yescharacteristic
127C2×C8×C43C2×D411yescharacteristic
128C2×C8×C43C2411yescharacteristic
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43—41no—
138C4⋊C4×C43—41no—
139C4⋊C4×C43—41no—
140C4⋊C4×C43D811yescharacteristic
141C4⋊C4×C43D811yescharacteristic
142C4⋊C4×C43D811yescharacteristic
143C42×C43—41no—
144C42×C43—41no—
145C42×C43—41no—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149(C2×D43)⋊C4—41no—
150(C2×D43)⋊C4—41no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154(C2×D43)⋊C4—41no—
155C4⋊Dic43—21no—
156Dic43⋊C4—41no—
157C4×Dic43—41no—
158Dic172—21no—
159Dic172—21no—
160D344—21no—
161D344—21no—
162D344—21no—
163D344—21no—
164D344—81no—
165#10621873—81no—
166#10621873—81no—
167C43⋊C16—21no—
168C43⋊C16—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C22×D43—41no—
172C22×D43—41no—
173Q8×C43—22no—
174Q8×C43—41no—
175Q8×C43—41no—
176Q8×C43—82no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C2×D811yescharacteristic
183C2×C4×C43C2×D811yescharacteristic
184C2×C4×C43C2×D811yescharacteristic
185C2×C4×C43C2×D811yescharacteristic
186C2×C4×C43C2×D811yescharacteristic
187C2×C4×C43C22×D411yescharacteristic
188C2×Dic43—41no—
189C2×Dic43—41no—
190D172—41no—
191D172—41no—
192D172—41no—
193D172—41no—
194D172—82no—
195D172—161no—
196C4×D43—161no—
197C4×D43—161no—
198Dic86—41no—
199Dic86—41no—
200C8×C43—21no—
201C8×C43—21no—
202C8×C43—21no—
203C8×C43C2×#4111yescharacteristic
204C8×C432−1+411yescharacteristic
205#33938—431nomaximal, Sylow
206C22×C43C22×D811yescharacteristic
207C2×D43—81no—
208C2×D43—81no—
209C2×D43—81no—
210C2×D43—81no—
211C2×D43—81no—
212C2×D43—81no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—42no—
220C4×C43—81no—
221C4×C43—81no—
222C4×C43—81no—
223C4×C43#54811yescharacteristic
224C4×C43#57711yescharacteristic
225Dic43—81no—
226Dic43—81no—
227#3396—431no—
228#3383D4311yescharacteristic, complemented
229#2244—431no—
230#2243—431no—
231#2242—431no—
232#2229—431no—
233#2228—431no—
234#2226—431no—
235#2211—431no—
236#2211—431no—
237#2207—431no—
238#2183—431no—
239#2176—431no—
240#2175—431no—
241C4×SD32—431no—
242C2×C43#335811yescharacteristic
243C2×C43#341411yescharacteristic
244C2×C43#341611yescharacteristic
245D43—161no—
246D43—161no—
247#559—861no—
248#557—21no—
249C2×Q32—431no—
250C2×SD32—431no—
251C2×SD32—431no—
252#500C2×D4311yescharacteristic
253#499C2×D4311yescharacteristic
254#499C2×D4311yescharacteristic
255#495—431no—
256#495—431no—
257#493—431no—
258#479—21no—
259#479—21no—
260#475—21no—
261#463—861no—
262#463—861no—
263#460—861no—
264C8×Q8C2×D4311yescharacteristic
265C4×Q16—431no—
266C4×Q16C2×D4311yescharacteristic
267C4×Q16C2×D4311yescharacteristic
268C4×Q16C2×D4311yescharacteristic
269C4×D8—431no—
270C4×D8—431no—
271#367—431no—
272#367—431no—
273#366—431no—
274C4⋊C16—431no—
275C4⋊C16—431no—
276C4⋊C16—431no—
277#358—431no—
278#358—431no—
279#358—431no—
280#358—431no—
281#357—431no—
282#357—431no—
283#357—431no—
284#357—431no—
285#357—431no—
286#357—431no—
287#346—431no—
288#346—431no—
289C4×C16—431no—
290C43#3393811yescharacteristic, complemented, Sylow
291C2×Q16—431no—
292C2×Q16C22×D4311yescharacteristic
293C2×SD16—861no—
294C2×SD16—861no—
295C2×D8—431no—
296C2×D8—431no—
297C2×D8—861no—
298C4⋊Q8—21no—
299C4⋊Q8—41no—
300#127—861no—
301#125—21no—
302#125—21no—
303#125—41no—
304#125—41no—
305#124—861no—
306#124—861no—
307#124—1721no—
308#123—1721no—
309#123—1721no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—41no—
314C4×Q8—861no—
315C4×Q8C22⋊D4311yescharacteristic
316C4×D4—861no—
317C4×D4—861no—
318C4×D4—1721no—
319Q32—862no—
320SD32—862no—
321SD32—862no—
322C2×C16—431no—
323C2×C16—431no—
324C2×C16—431no—
325C2×C16—431no—
326#107—21no—
327#107—431no—
328#107C22×D4311yescharacteristic
329#107C22×D4311yescharacteristic
330#107C22×D4311yescharacteristic
331#106—21no—
332#106—21no—
333C4⋊C8C22⋊D4311yescharacteristic
334C4⋊C8C22⋊D4311yescharacteristic
335C4⋊C8C22⋊D4311yescharacteristic
336#103—21no—
337#103—21no—
338#103—21no—
339#103—861no—
340#102—861no—
341#102—861no—
342C4×C8C22×D4311yescharacteristic
343C4×C8C22×D4311yescharacteristic
344C4×C8C22×D4311yescharacteristic
345C2×Q8—21no—
346C2×Q8—41no—
347C2×Q8—861no—
348C2×Q8#1062188211yescharacteristic
349C2×D4—861no—
350C2×D4—861no—
351C2×D4—1721no—
352C2×D4—1721no—
353C22×C4—1721no—
354C22×C4—1721no—
355Q16—21no—
356Q16—861no—
357Q16—861no—
358Q16#1062190212yes—
359SD16—3441no—
360SD16—3441no—
361D8—861no—
362D8—861no—
363D8—861no—
364D8—861no—
365D8—3441no—
366C2×C8C2×C22⋊D4311yescharacteristic
367C2×C8C2×C22⋊D4311yescharacteristic
368C2×C8C2×C22⋊D4311yescharacteristic
369C2×C8C23×D4311yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—861no—
382C4⋊C4—1721no—
383C4⋊C4#1062188211yescharacteristic
384C4⋊C4#1062188211yescharacteristic
385C4⋊C4#1062188211yescharacteristic
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—41no—
393C42—41no—
394C42—41no—
395C42—1721no—
396C42C2×C22⋊D4311yescharacteristic
397C42C2×C22⋊D4311yescharacteristic
398C42C2×C22⋊D4311yescharacteristic
399C16—861no—
400C16—861no—
401C16—861no—
402C16—861no—
403C23—1721no—
404C23—1721no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—82no—
409Q8—1721no—
410Q8—1721no—
411D4—3442no—
412D4—1721no—
413D4—1721no—
414D4—1721no—
415D4—1721no—
416D4—6881no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—6881no—
424C2×C4—6881no—
425C2×C4C2×#1062188211yescharacteristic
426C2×C4C2×#1062188211yescharacteristic
427C2×C4C2×#1062188211yescharacteristic
428C2×C4C2×#1062188211yescharacteristic
429C2×C4C2×#1062188211yescharacteristic
430C2×C4C2×#1062188211yescharacteristic
431C2×C4C22×C22⋊D4311yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8C2×#1062190211yescharacteristic
436C8#1306337311yescharacteristic
437C22—3441no—
438C22—3441no—
439C22—3441no—
440C22—3441no—
441C22—3441no—
442C22—3441no—
443C22C22×#1062188211yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—42no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—3441no—
455C4—3441no—
456C4#1458356011yescharacteristic
457C4#1458370711yescharacteristic
458C2—6881no—
459C2—6881no—
460C2#1914723011yescharacteristic
461C2#1914772911yescharacteristic
462C2#1914773911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3383C2
socleC22×C43C22×D8
prime radical#14583276C22
hypercenter#3383D43
hypocenterC43#33938
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
3. #19136834C2semidirect
4. #19136829C2semidirect
5. #19136756C2semidirect
6. #19136749C2semidirect
7. #19136739C2semidirect
8. #19136657C2semidirect
9. #19136657C2semidirect
11. #19136504C2semidirect
12. #19136464C2semidirect
13. #19136457C2semidirect
14. C4×#13063268C2semidirect
15. C43×#3383C2semidirect
228. #3383D43semidirect
290. C43#33938semidirect

Maximal subgroups

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

subgroupindex
#191476082
#191368382
#191368342
#191368292
#191367562
#191367492
#191367392
#191366572
#191366352
#191365042
#191364642
#191364572
C4×#130632682
C43×#33832
#3393843