Finite Group Databasebeta

← #14911551

Subgroups — #14911551

Order 2816.

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#13081629C211yesmaximal, characteristic
2#13070859C211yesmaximal, characteristic
3#13070855C211yesmaximal, characteristic, complemented
4#13070850C211yesmaximal, characteristic, complemented
5#13070777C211yesmaximal, characteristic, complemented
6#13070770C211yesmaximal, characteristic, complemented
7#13070760C211yesmaximal, characteristic, complemented
8#13070678C211yesmaximal, characteristic, complemented
9#13070678C211yesmaximal, characteristic, complemented
10#13070656C211yesmaximal, characteristic
11#13070525C211yesmaximal, characteristic, complemented
12#13070485C211yesmaximal, characteristic, complemented
13#13070478C211yesmaximal, characteristic, complemented
14C4×#66892C211yesmaximal, characteristic, complemented
15C11×#3383C211yesmaximal, characteristic, complemented
16C11×#557—21no—
17#10623116—21no—
18C11×#500C2211yescharacteristic
19C11×#499C2211yescharacteristic
20C11×#499C2211yescharacteristic
21C11×#479—21no—
22C11×#479—21no—
23C11×#475—21no—
24C8×Q8×C11C2211yescharacteristic
25C4×C11×Q16C2211yescharacteristic
26C4×C11×Q16C2211yescharacteristic
27C4×C11×Q16C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66892C2211yescharacteristic
31#10622461—21no—
32#10622457—21no—
33#10622457—21no—
34C4×Dic44C2211yescharacteristic
35#10622309C2211yescharacteristic
36#10622309C2211yescharacteristic
37#10622308C2211yescharacteristic
38C4×D88C2211yescharacteristic
39C4×D88C2211yescharacteristic
40#10622202C2211yescharacteristic
41#10622130C2211yescharacteristic
42#10622130C2211yescharacteristic
43#10622130C2211yescharacteristic
44#10622129C2211yescharacteristic
45#10622129C2211yescharacteristic
46#10622129C2211yescharacteristic
47#10622129C2211yescharacteristic
48#10622129C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622127C2211yescharacteristic
53C4⋊(C11⋊C16)C2211yescharacteristic
54C4⋊(C11⋊C16)C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56#10622099C2211yescharacteristic
57#10622099C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—41no—
62C11×#125—21no—
63C11×#125—21no—
64C11×#125—41no—
65C11×#125—41no—
66C4×Q8×C11—21no—
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11—41no—
70C4×Q8×C11D411yescharacteristic
71#67000—41no—
72C2×Dic44C2311yescharacteristic
73C2×D88—21no—
74C2×D88C2311yescharacteristic
75C2×D88C2311yescharacteristic
76C2×#4314—21no—
77C2×#4314—21no—
78#66947—41no—
79#66947—41no—
80#66946—41no—
81#66928—21no—
82#66928—21no—
83#66927—21no—
84C4×D44—21no—
85C4×D44—21no—
86C4×Dic22—21no—
87C11×#107—21no—
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#106—21no—
92C11×#106—21no—
93C11×C4⋊C8D411yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×C4⋊C8D411yescharacteristic
96C11×#103—21no—
97C11×#103—21no—
98C11×#103—21no—
99C4×C8×C11C2311yescharacteristic
100C4×C8×C11C2311yescharacteristic
101C4×C8×C11C2311yescharacteristic
102#66893—22no—
103#66892—22no—
104#66892—22no—
105#66885—21no—
106#66885—21no—
107#66882C2311yescharacteristic
108#66880—21no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33938—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×Q8×C11—41no—
116C2×Q8×C11D811yescharacteristic
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—41no—
120C2×D44—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×Dic22—21no—
124C11×Q16—21no—
125C11×Q16#4112yes—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4D811yescharacteristic
142C11×C4⋊C4D811yescharacteristic
143C11×C4⋊C4D811yescharacteristic
144C42×C11—41no—
145C42×C11—41no—
146C42×C11—41no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157Dic11⋊C4—41no—
158C4×Dic11—41no—
159Dic44—21no—
160Dic44—21no—
161D88—21no—
162D88—21no—
163D88—21no—
164D88—21no—
165D88—81no—
166#4314—81no—
167#4314—81no—
168C11⋊C16—21no—
169C11⋊C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3396—111no—
173#3383D1111yescharacteristic, complemented
174#2244—111no—
175#2243—111no—
176#2242—111no—
177#2229—111no—
178#2228—111no—
179#2226—111no—
180#2211—111no—
181#2211—111no—
182#2207—111no—
183#2183—111no—
184#2176—111no—
185#2175—111no—
186C4×SD32—111no—
187C22×D11—41no—
188C22×D11—41no—
189Q8×C11—22no—
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—82no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×Dic11—41no—
205C2×Dic11—41no—
206D44—41no—
207D44—41no—
208D44—41no—
209D44—41no—
210D44—82no—
211D44—161no—
212C4×D11—161no—
213C4×D11—161no—
214Dic22—41no—
215Dic22—41no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11C2×#4111yescharacteristic
220C8×C112−1+411yescharacteristic
221#559—221no—
222#557—21no—
223C2×Q32—111no—
224C2×SD32—111no—
225C2×SD32—111no—
226#500C2×D1111yescharacteristic
227#499C2×D1111yescharacteristic
228#499C2×D1111yescharacteristic
229#495—111no—
230#495—111no—
231#493—111no—
232#479—21no—
233#479—21no—
234#475—21no—
235#463—221no—
236#463—221no—
237#460—221no—
238C8×Q8C2×D1111yescharacteristic
239C4×Q16—111no—
240C4×Q16C2×D1111yescharacteristic
241C4×Q16C2×D1111yescharacteristic
242C4×Q16C2×D1111yescharacteristic
243C4×D8—111no—
244C4×D8—111no—
245#367—111no—
246#367—111no—
247#366—111no—
248C4⋊C16—111no—
249C4⋊C16—111no—
250C4⋊C16—111no—
251#358—111no—
252#358—111no—
253#358—111no—
254#358—111no—
255#357—111no—
256#357—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261#346—111no—
262#346—111no—
263C4×C16—111no—
264C22×C11C22×D811yescharacteristic
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—42no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11#54811yescharacteristic
282C4×C11#57711yescharacteristic
283Dic11—81no—
284Dic11—81no—
285C2×Q16—111no—
286C2×Q16C22×D1111yescharacteristic
287C2×SD16—221no—
288C2×SD16—221no—
289C2×D8—111no—
290C2×D8—111no—
291C2×D8—221no—
292C4⋊Q8—21no—
293C4⋊Q8—41no—
294#127—221no—
295#125—21no—
296#125—21no—
297#125—41no—
298#125—41no—
299#124—221no—
300#124—221no—
301#124—441no—
302#123—441no—
303#123—441no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—41no—
308C4×Q8—221no—
309C4×Q8C22⋊D1111yescharacteristic
310C4×D4—221no—
311C4×D4—221no—
312C4×D4—441no—
313Q32—222no—
314SD32—222no—
315SD32—222no—
316C2×C16—111no—
317C2×C16—111no—
318C2×C16—111no—
319C2×C16—111no—
320#107—21no—
321#107—111no—
322#107C22×D1111yescharacteristic
323#107C22×D1111yescharacteristic
324#107C22×D1111yescharacteristic
325#106—21no—
326#106—21no—
327C4⋊C8C22⋊D1111yescharacteristic
328C4⋊C8C22⋊D1111yescharacteristic
329C4⋊C8C22⋊D1111yescharacteristic
330#103—21no—
331#103—21no—
332#103—21no—
333#103—221no—
334#102—221no—
335#102—221no—
336C4×C8C22×D1111yescharacteristic
337C4×C8C22×D1111yescharacteristic
338C4×C8C22×D1111yescharacteristic
339C2×C11#335811yescharacteristic
340C2×C11#341411yescharacteristic
341C2×C11#341611yescharacteristic
342D11—161no—
343D11—161no—
344C2×Q8—21no—
345C2×Q8—41no—
346C2×Q8—221no—
347C2×Q8#432311yescharacteristic
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—441no—
351C2×D4—441no—
352C22×C4—441no—
353C22×C4—441no—
354Q16—21no—
355Q16—221no—
356Q16—221no—
357Q16#434312yes—
358SD16—881no—
359SD16—881no—
360D8—221no—
361D8—221no—
362D8—221no—
363D8—221no—
364D8—881no—
365C2×C8C2×C22⋊D1111yescharacteristic
366C2×C8C2×C22⋊D1111yescharacteristic
367C2×C8C2×C22⋊D1111yescharacteristic
368C2×C8C23×D1111yescharacteristic
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—221no—
381C4⋊C4—441no—
382C4⋊C4#432311yescharacteristic
383C4⋊C4#432311yescharacteristic
384C4⋊C4#432311yescharacteristic
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C42—41no—
392C42—41no—
393C42—41no—
394C42—441no—
395C42C2×C22⋊D1111yescharacteristic
396C42C2×C22⋊D1111yescharacteristic
397C42C2×C22⋊D1111yescharacteristic
398C16—221no—
399C16—221no—
400C16—221no—
401C16—221no—
402C11#3393811yescharacteristic, complemented, Sylow
403C23—441no—
404C23—441no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—82no—
409Q8—441no—
410Q8—441no—
411D4—441no—
412D4—441no—
413D4—441no—
414D4—441no—
415D4—882no—
416D4—1761no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—1761no—
424C2×C4—1761no—
425C2×C4C2×#432311yescharacteristic
426C2×C4C2×#432311yescharacteristic
427C2×C4C2×#432311yescharacteristic
428C2×C4C2×#432311yescharacteristic
429C2×C4C2×#432311yescharacteristic
430C2×C4C2×#432311yescharacteristic
431C2×C4C22×C22⋊D1111yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8C2×#434311yescharacteristic
436C8#6704011yescharacteristic
437C22—881no—
438C22—881no—
439C22—881no—
440C22—881no—
441C22—881no—
442C22—881no—
443C22C22×#432311yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—42no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—881no—
455C4—881no—
456C4#1062334811yescharacteristic
457C4#1062336811yescharacteristic
458C2—1761no—
459C2—1761no—
460C2#1308125111yescharacteristic
461C2#1308175011yescharacteristic
462C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3383C2
socleC22×C11C22×D8
prime radical#10622308C22
hypercenter#3383D11
hypocenterC11#33938
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
3. #13070855C2semidirect
4. #13070850C2semidirect
5. #13070777C2semidirect
6. #13070770C2semidirect
7. #13070760C2semidirect
8. #13070678C2semidirect
9. #13070678C2semidirect
11. #13070525C2semidirect
12. #13070485C2semidirect
13. #13070478C2semidirect
14. C4×#66892C2semidirect
15. C11×#3383C2semidirect
173. #3383D11semidirect
402. C11#33938semidirect

Maximal subgroups

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

subgroupindex
#130816292
#130708592
#130708552
#130708502
#130707772
#130707702
#130707602
#130706782
#130706562
#130705252
#130704852
#130704782
C4×#668922
C11×#33832
#3393811