Finite Group Databasebeta

← #14911262

Subgroups — #14911262

Order 2816.

484 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#13081019C211yesmaximal, characteristic
2#13070899C211yesmaximal, characteristic, complemented
3#13070821C211yesmaximal, characteristic, complemented
4#13070816C211yesmaximal, characteristic, complemented
5#13070801C211yesmaximal, characteristic, complemented
6#13070796C211yesmaximal, characteristic, complemented
7#13070780C211yesmaximal, characteristic, complemented
8#13070750C211yesmaximal, characteristic, complemented
9#13070731C211yesmaximal, characteristic, complemented
10#13070714C211yesmaximal, characteristic, complemented
11#13070478C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070402C211yesmaximal, characteristic, complemented
14C2×#10622127C211yesmaximal, characteristic, complemented
15C11×#3338C211yesmaximal, characteristic, complemented
16C11×#554—21no—
17#10623096—21no—
18C11×#500C2211yescharacteristic
19C11×#484—21no—
20C11×#484—21no—
21C11×#477—21no—
22C11×#467C2211yescharacteristic
23C11×#467C2211yescharacteristic
24C4×C11×Q16C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29#10622728C2211yescharacteristic
30#10622728C2211yescharacteristic
31#10622719C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66876C2211yescharacteristic
34C22×C11⋊C16C2211yescharacteristic
35#10622460—21no—
36#10622350—21no—
37#10622348—21no—
38C4×D88C2211yescharacteristic
39#10622296C2211yescharacteristic
40#10622202C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622129C2211yescharacteristic
46#10622129C2211yescharacteristic
47#10622129C2211yescharacteristic
48#10622128C2211yescharacteristic
49#10622128C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622127C2211yescharacteristic
52#10622127C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C4⋊Q8—21no—
63C11×#125—41no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—41no—
67C11×C22⋊Q8—41no—
68C4×Q8×C11—21no—
69C4×D4×C11—41no—
70C4×D4×C11D411yescharacteristic
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73#66992—41no—
74#66983—21no—
75#66983—21no—
76#66979—21no—
77C2×C4⋊Dic11—21no—
78C2×D88C2311yescharacteristic
79#66951—41no—
80#66936—41no—
81(C22⋊D11)⋊C4—41no—
82C4×D44—21no—
83#66923—21no—
84C11×#107—21no—
85C11×#107—21no—
86C11×#107—21no—
87C11×#107C2311yescharacteristic
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×#103—21no—
92C11×#103—21no—
93C11×#103—21no—
94C11×C22⋊C8D411yescharacteristic
95C11×C22⋊C8D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66892—22no—
98#66885—21no—
99#66885—21no—
100#66885—21no—
101#66882—21no—
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106#66881—21no—
107#66876—22no—
108C2×C11⋊C16—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33913—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—41no—
116C2×D4×C11D811yescharacteristic
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C22×Dic11—41no—
124C2×D44—21no—
125C2×C4×D11—41no—
126C11×Q16—21no—
127C11×Q16—21no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2411yescharacteristic
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4D811yescharacteristic
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4D811yescharacteristic
149C11×C22⋊C4D811yescharacteristic
150C42×C11—41no—
151C42×C11C2×D411yescharacteristic
152C22⋊Dic11—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163D88—21no—
164D88—21no—
165C11⋊C16—21no—
166C11⋊C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3339—111no—
170#3338D1111yescharacteristic, complemented
171#2255—111no—
172#2237—111no—
173#2236—111no—
174#2233—111no—
175#2232—111no—
176#2229—111no—
177#2224—111no—
178#2220—111no—
179#2217—111no—
180#2175—111no—
181#2168—111no—
182#2159—111no—
183C2×#366—111no—
184C23×C11C2×D811yescharacteristic
185C23×C11C2×D811yescharacteristic
186C22×D11—41no—
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—161no—
190D4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—161no—
200C2×C4×C11—161no—
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C22⋊D11—82no—
207C22⋊D11—161no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—161no—
212D44—41no—
213D44—41no—
214C4×D11—161no—
215C8×C11—21no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11C2×#4111yescharacteristic
219C8×C112−1+411yescharacteristic
220#554—21no—
221#553—221no—
222C2×SD32—111no—
223C2×M32—111no—
224C22×C16—111no—
225#500C2×D1111yescharacteristic
226#499—111no—
227#484—21no—
228#484—21no—
229#482—221no—
230#481—221no—
231#478—221no—
232#477—21no—
233#467C2×D1111yescharacteristic
234#467C2×D1111yescharacteristic
235#466—111no—
236#466—111no—
237C4×Q16C2×D1111yescharacteristic
238C4×D8—111no—
239C8×D4C2×D1111yescharacteristic
240#427—111no—
241C2×#107—111no—
242C2×#107C2×D1111yescharacteristic
243C2×#107C2×D1111yescharacteristic
244#367—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252#366—111no—
253C4⋊C16—111no—
254#358—111no—
255#358—111no—
256#358—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260C22⋊C16—111no—
261C22⋊C16—111no—
262#346—111no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11#51012yes—
269C22×C11C22×D811yescharacteristic
270C2×D11—81no—
271C2×D11—81no—
272C2×D11—81no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11#54711yescharacteristic
282C4×C11#57811yescharacteristic
283Dic11—81no—
284Dic11—81no—
285Dic11—81no—
286C2×Q16C22×D1111yescharacteristic
287C2×D8—111no—
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1111yescharacteristic
290C4⋊Q8—21no—
291#126—441no—
292#125—41no—
293#125—221no—
294#123—441no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—41no—
298C22⋊Q8—41no—
299#121—221no—
300#121—221no—
301#121—441no—
302C4×Q8—21no—
303C4×D4—41no—
304C4×D4—221no—
305C4×D4—441no—
306C4×D4C22⋊D1111yescharacteristic
307#117—221no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—221no—
311SD32—222no—
312M32—222no—
313C2×C16—111no—
314C2×C16—111no—
315C2×C16—111no—
316C2×C16—111no—
317C2×C16—222no—
318#107—21no—
319#107—21no—
320#107—21no—
321#107—111no—
322#107—111no—
323#107—111no—
324#107—221no—
325#107C22×D1111yescharacteristic
326#107C22×D1111yescharacteristic
327#107C22×D1111yescharacteristic
328#106—221no—
329#106—221no—
330C4⋊C8C22⋊D1111yescharacteristic
331#103—21no—
332#103—21no—
333#103—21no—
334#102—221no—
335#102—221no—
336#102—221no—
337C22⋊C8C22⋊D1111yescharacteristic
338C22⋊C8C22⋊D1111yescharacteristic
339C4×C8C22×D1111yescharacteristic
340C2×C11—22no—
341C2×C11—41no—
342C2×C11#333411yescharacteristic
343C2×C11C2×#51011yescharacteristic
344C2×C11#341511yescharacteristic
345D11—161no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×D4—221no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4#432311yescharacteristic
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358Q16—21no—
359Q16—21no—
360D8—221no—
361D8—221no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8C2×C22⋊D1111yescharacteristic
367C2×C8C2×C22⋊D1111yescharacteristic
368C2×C8C2×C22⋊D1111yescharacteristic
369C2×C8C23×D1111yescharacteristic
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—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4#432311yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4#432311yescharacteristic
393C22⋊C4#432311yescharacteristic
394C42—41no—
395C42—441no—
396C42C2×C22⋊D1111yescharacteristic
397C16—112no—
398C16—221no—
399C16—221no—
400C16—221no—
401C11#3391311yescharacteristic, complemented, Sylow
402C23—441no—
403C23C2×#432311yescharacteristic
404C23C2×#432311yescharacteristic
405Q8—41no—
406Q8—41no—
407Q8—161no—
408D4—22no—
409D4—441no—
410D4—441no—
411D4—882no—
412D4—1761no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—161no—
422C2×C4—161no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—1761no—
427C2×C4—1761no—
428C2×C4C2×#432311yescharacteristic
429C2×C4C2×#432311yescharacteristic
430C2×C4C2×#432311yescharacteristic
431C2×C4C2×#432311yescharacteristic
432C2×C4C22×C22⋊D1111yescharacteristic
433C8—21no—
434C8—21no—
435C8—21no—
436C8#41×D1111yescharacteristic
437C8#6704311yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—881no—
444C22—881no—
445C22—881no—
446C22#1062279212yes—
447C22C22×#432311yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4—881no—
457C4—881no—
458C4—881no—
459C4#1062335511yescharacteristic
460C4#1062336911yescharacteristic
461C2—22no—
462C2—41no—
463C2—1761no—
464C2#1308095911yescharacteristic
465C2C2×#1062279211yescharacteristic
466C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3338C2
socleC22×C11C22×D8
prime radical#13081019C2
hypercenter#3338D11
hypocenterC11#33913
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3338

Complements

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

NH ≅ G/Ntype
2. #13070899C2semidirect
3. #13070821C2semidirect
4. #13070816C2semidirect
5. #13070801C2semidirect
6. #13070796C2semidirect
7. #13070780C2semidirect
8. #13070750C2semidirect
9. #13070731C2semidirect
10. #13070714C2semidirect
11. #13070478C2semidirect
12. #13070442C2semidirect
13. #13070402C2semidirect
14. C2×#10622127C2semidirect
15. C11×#3338C2semidirect
170. #3338D11semidirect
401. C11#33913semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130708992
#130708212
#130708162
#130708012
#130707962
#130707802
#130707502
#130707312
#130707142
#130704782
#130704422
#130704022
C2×#106221272
C11×#33382
#3391311