Finite Group Databasebeta

← #14911268

Subgroups — #14911268

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#13081009C211yesmaximal, characteristic, complemented
2#13070903C211yesmaximal, characteristic, complemented
3#13070824C211yesmaximal, characteristic, complemented
4#13070818C211yesmaximal, characteristic, complemented
5#13070799C211yesmaximal, characteristic, complemented
6#13070794C211yesmaximal, characteristic, complemented
7#13070777C211yesmaximal, characteristic, complemented
8#13070753C211yesmaximal, characteristic, complemented
9#13070727C211yesmaximal, characteristic, complemented
10#13070710C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070405C211yesmaximal, characteristic, complemented
14C2×#10622127C211yesmaximal, characteristic, complemented
15C11×#3339C211yesmaximal, characteristic
16C11×#553—21no—
17#10623074—21no—
18C11×#499C2211yescharacteristic
19C11×#482—21no—
20C11×#481—21no—
21C11×#478—21no—
22C11×#466C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C4×C11×D8C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C11×#427C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29#10622729C2211yescharacteristic
30#10622729C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66876C2211yescharacteristic
34C22×C11⋊C16C2211yescharacteristic
35#10622463—21no—
36#10622335—21no—
37#10622335—21no—
38C4×Dic44C2211yescharacteristic
39#10622295C2211yescharacteristic
40#10622200C2211yescharacteristic
41#10622200C2211yescharacteristic
42#10622200C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622130C2211yescharacteristic
46#10622130C2211yescharacteristic
47#10622130C2211yescharacteristic
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×D8C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#126—41no—
63C11×#125—21no—
64C11×#123—41no—
65C11×#121—21no—
66C11×#121—21no—
67C11×#121—41no—
68C4×D4×C11—21no—
69C4×D4×C11—41no—
70C4×D4×C11D411yescharacteristic
71C11×#117—21no—
72C2×C11×C4⋊C4—21no—
73D4×Dic11—41no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76#66977—21no—
77#66977—21no—
78C2×Dic44C2311yescharacteristic
79#66943—41no—
80#66931—41no—
81#66931—41no—
82#66922—21no—
83C4×Dic22—21no—
84C11×#107—21no—
85C11×#107C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#106—21no—
89C11×#106—21no—
90C11×C4⋊C8D411yescharacteristic
91C11×#102—21no—
92C11×#102—21no—
93C11×#102—21no—
94C11×C22⋊C8D411yescharacteristic
95C11×C22⋊C8D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66891—22no—
98#66882—21no—
99#66882—21no—
100#66882—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66880—21no—
105#66880—21no—
106#66880—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×D4×C11—21no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11D811yescharacteristic
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×Dic11—41no—
123C22×Dic11—41no—
124C2×Dic22—21no—
125C2×Dic22—41no—
126C11×D8—21no—
127C11×D8—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⋊C4D811yescharacteristic
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4D811yescharacteristic
148C11×C22⋊C4D811yescharacteristic
149C42×C11—41no—
150C42×C11C2×D411yescharacteristic
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158C4⋊Dic11—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163Dic44—21no—
164Dic44—21no—
165C11⋊C16—21no—
166C11⋊C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3339D1111yescharacteristic
170#3338—111no—
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×C11—41no—
185C23×C11C2×D811yescharacteristic
186C23×C11C2×D811yescharacteristic
187D4×C11—22no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—82no—
191D4×C11—161no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
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
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—161no—
211C2×Dic11—161no—
212Dic22—41no—
213Dic22—41no—
214Dic22—161no—
215C8×C11—21no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11C2×#4111yescharacteristic
219C8×C112−1+411yescharacteristic
220#554—221no—
221#553—21no—
222C2×SD32—111no—
223C2×M32—111no—
224C22×C16—111no—
225#500—111no—
226#499C2×D1111yescharacteristic
227#484—221no—
228#484—221no—
229#482—21no—
230#481—21no—
231#478—21no—
232#477—221no—
233#467—111no—
234#467—111no—
235#466C2×D1111yescharacteristic
236#466C2×D1111yescharacteristic
237C4×Q16—111no—
238C4×D8C2×D1111yescharacteristic
239C8×D4C2×D1111yescharacteristic
240#427C2×D1111yescharacteristic
241C2×#107—111no—
242C2×#107—111no—
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—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11#51012yes—
272C22×C11C22×D811yescharacteristic
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11#54711yescharacteristic
281C4×C11#57811yescharacteristic
282Dic11—81no—
283Dic11—81no—
284Dic11—81no—
285Dic11—81no—
286C2×Q16—111no—
287C2×D8C22×D1111yescharacteristic
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1111yescharacteristic
290C4⋊Q8—221no—
291#126—41no—
292#125—21no—
293#125—441no—
294#123—41no—
295C22⋊Q8—221no—
296C22⋊Q8—221no—
297C22⋊Q8—441no—
298C22⋊Q8—441no—
299#121—21no—
300#121—21no—
301#121—41no—
302C4×Q8—221no—
303C4×D4—21no—
304C4×D4—41no—
305C4×D4—441no—
306C4×D4C22⋊D1111yescharacteristic
307#117—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—221no—
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—111no—
320#107—111no—
321#107—111no—
322#107—221no—
323#107—221no—
324#107—221no—
325#107C22×D1111yescharacteristic
326#107C22×D1111yescharacteristic
327#107C22×D1111yescharacteristic
328#106—21no—
329#106—21no—
330C4⋊C8C22⋊D1111yescharacteristic
331#103—221no—
332#103—221no—
333#103—221no—
334#102—21no—
335#102—21no—
336#102—21no—
337C22⋊C8C22⋊D1111yescharacteristic
338C22⋊C8C22⋊D1111yescharacteristic
339C4×C8C22×D1111yescharacteristic
340C2×C11—22no—
341C2×C11—41no—
342C2×C11—161no—
343C2×C11#333411yescharacteristic
344C2×C11C2×#51011yescharacteristic
345C2×C11#341511yescharacteristic
346C2×Q8—221no—
347C2×Q8—441no—
348C2×D4—21no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4#432311yescharacteristic
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358Q16—221no—
359Q16—221no—
360D8—21no—
361D8—21no—
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—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4#432311yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
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—41no—
403C23C2×#432311yescharacteristic
404C23C2×#432311yescharacteristic
405Q8—441no—
406Q8—441no—
407Q8—1761no—
408D4—22no—
409D4—41no—
410D4—41no—
411D4—82no—
412D4—161no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—161no—
421C2×C4—161no—
422C2×C4—441no—
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—81no—
444C22—81no—
445C22—81no—
446C22#1062280812yes—
447C22C22×#432311yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—881no—
456C4—881no—
457C4—881no—
458C4—881no—
459C4#1062335511yescharacteristic
460C4#1062336911yescharacteristic
461C2—22no—
462C2—41no—
463C2—161no—
464C2#1308095911yescharacteristic
465C2C2×#1062280811yescharacteristic
466C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3339C2
socleC22×C11C22×D8
hypercenter#3339D11
hypocenterC11#33913
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #13081009C2semidirect
2. #13070903C2semidirect
3. #13070824C2semidirect
4. #13070818C2semidirect
5. #13070799C2semidirect
6. #13070794C2semidirect
7. #13070777C2semidirect
8. #13070753C2semidirect
9. #13070727C2semidirect
10. #13070710C2semidirect
11. #13070480C2semidirect
12. #13070442C2semidirect
13. #13070405C2semidirect
14. C2×#10622127C2semidirect
401. C11#33913semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130709032
#130708242
#130708182
#130707992
#130707942
#130707772
#130707532
#130707272
#130707102
#130704802
#130704422
#130704052
C2×#106221272
C11×#33392
#3391311