Finite Group Databasebeta

← #14908896

Subgroups — #14908896

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079266C211yesmaximal, characteristic, complemented
2#13070801C211yesmaximal, characteristic, complemented
3#13070796C211yesmaximal, characteristic, complemented
4#13070780C211yesmaximal, characteristic, complemented
5#13070773C211yesmaximal, characteristic, complemented
6#13070656C211yesmaximal, characteristic, complemented
7#13070651C211yesmaximal, characteristic, complemented
8#13070539C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070490C211yesmaximal, characteristic, complemented
11#13070478C211yesmaximal, characteristic, complemented
12C4×#66892C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14#13070423C211yesmaximal, characteristic, complemented
15C11×#2951C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C11×#520—21no—
18#10623066—21no—
19C11×#440—21no—
20C11×#440—21no—
21C4×C11×Q16C2211yescharacteristic
22C4×C11×Q16C2211yescharacteristic
23C4×C11×D8C2211yescharacteristic
24C4×C11×D8C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C11×#417—21no—
27C11×#405C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32#10622748—21no—
33#10622728C2211yescharacteristic
34#10622728C2211yescharacteristic
35#10622326—21no—
36#10622324—21no—
37#10622308C2211yescharacteristic
38C4×D88C2211yescharacteristic
39C4×D88C2211yescharacteristic
40#10622296C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45C22⋊(C11⋊C16)C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622129C2211yescharacteristic
48#10622129C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622129C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56C4⋊(C11⋊C16)C2211yescharacteristic
57#10622099C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×#41—21no—
60C11×#135—22no—
61C11×#135—22no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×SD16—21no—
64C2×C11×D8C2311yescharacteristic
65C2×C11×M16D411yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11—41no—
72C4×D4×C11—41no—
73C11×#117—41no—
74C11×#117D411yescharacteristic
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—41no—
77#66983—21no—
78#66983—21no—
79C2×D88—21no—
80C2×D88C2311yescharacteristic
81C2×D88C2311yescharacteristic
82#66947—41no—
83#66947—41no—
84#66937—41no—
85#66937—41no—
86#66927—21no—
87C4×D44—21no—
88C4×D44—21no—
89#66923—21no—
90C11×#107—21no—
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#103—21no—
94C11×#103—21no—
95C11×#102—21no—
96C11×#102—21no—
97C11×#97D411yescharacteristic
98C11×#97D411yescharacteristic
99C4×C8×C11C2311yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66892—22no—
102#66892—22no—
103#66890—22no—
104#66890—22no—
105#66885—21no—
106#66885—21no—
107#66885—21no—
108#66885—21no—
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66881—21no—
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#33679—111nomaximal, Sylow
117C11×#41—24no—
118C11×#41—42no—
119C2×Q8×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—41no—
132C2×D44—41no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C11×Q16—21no—
136C11×Q16#4112yes—
137C11×SD16—24no—
138C11×D8—21no—
139C11×D8#4112yes—
140C11×M16—41no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4D811yescharacteristic
153C11×C4⋊C4D811yescharacteristic
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C11×C22⋊C4D811yescharacteristic
157C11×C22⋊C4D811yescharacteristic
158C42×C11—41no—
159C42×C11—41no—
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170D88—21no—
171D88—21no—
172D88—21no—
173D88—21no—
174D88—42no—
175C11⋊C16—21no—
176C11⋊C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3176—111no—
180#2951D1111yescharacteristic, complemented
181#2233—111no—
182#2232—111no—
183#2229—111no—
184#2228—111no—
185#2207—111no—
186#2206—111no—
187#2186—111no—
188#2186—111no—
189#2177—111no—
190#2175—111no—
191C4×SD32—111no—
192C4×D16—111no—
193#2164—111no—
194C23×C11—41no—
195C23×C11C2×D811yescharacteristic
196C22×D11—41no—
197C22×D11—41no—
198Q8×C11—22no—
199Q8×C11—41no—
200D4×C11—22no—
201D4×C11—44no—
202D4×C11—41no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—44no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—161no—
210C2×C4×C11—161no—
211C2×C4×C11—161no—
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C22⋊D11—161no—
219C22⋊D11—161no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222D44—41no—
223D44—41no—
224D44—41no—
225D44—41no—
226D44—161no—
227D44—161no—
228C4×D11—161no—
229C4×D11—161no—
230C8×C11—21no—
231C8×C11—21no—
232C8×C11—21no—
233C8×C11C2×#4111yescharacteristic
234C8×C11C2×#4111yescharacteristic
235C2×#135C2×D1111yescharacteristic
236#540—221no—
237#520—21no—
238C2×SD32—111no—
239C2×SD32—111no—
240C2×D16—111no—
241C2×D16—111no—
242#499—111no—
243#493—111no—
244#490—221no—
245#469—221no—
246#466—111no—
247#466—111no—
248#442—221no—
249#440—21no—
250#440—21no—
251C4×Q16C2×D1111yescharacteristic
252C4×Q16C2×D1111yescharacteristic
253C4×D8—111no—
254C4×D8—111no—
255C4×D8C2×D1111yescharacteristic
256C4×D8C2×D1111yescharacteristic
257C2×#107C2×D1111yescharacteristic
258#417—21no—
259#405C2×D1111yescharacteristic
260#367—111no—
261#367—111no—
262#366—111no—
263#366—111no—
264C4⋊C16—111no—
265C4⋊C16—111no—
266#358—111no—
267#358—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271#357—111no—
272#357—111no—
273#357—111no—
274C22⋊C16—111no—
275C22⋊C16—111no—
276#346—111no—
277C4×C16—111no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—42no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11C22×D811yescharacteristic
285C2×D11—81no—
286C2×D11—81no—
287C2×D11—81no—
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—42no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11#52511yescharacteristic
300C4×C11#57511yescharacteristic
301Dic11—81no—
302Dic11—81no—
303C2×#41—21no—
304#135—22no—
305#135—22no—
306C2×Q16C22×D1111yescharacteristic
307C2×SD16—21no—
308C2×D8—111no—
309C2×D8—111no—
310C2×D8—221no—
311C2×D8C22×D1111yescharacteristic
312C2×M16C22⋊D1111yescharacteristic
313C22×C8C22×D1111yescharacteristic
314#127—221no—
315#125—221no—
316#123—441no—
317#123—441no—
318#121—221no—
319#121—221no—
320#121—441no—
321#121—441no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—41no—
327C4×D4—41no—
328C4×D4—221no—
329C4×D4—221no—
330#117—41no—
331#117C22⋊D1111yescharacteristic
332C2×C4⋊C4—21no—
333C2×C4⋊C4—41no—
334SD32—222no—
335SD32—222no—
336D16—222no—
337D16—222no—
338C2×C16—111no—
339C2×C16—111no—
340C2×C16—111no—
341C2×C16—111no—
342#107—21no—
343#107—111no—
344#107—111no—
345#107C22×D1111yescharacteristic
346#107C22×D1111yescharacteristic
347#106—221no—
348#103—21no—
349#103—21no—
350#102—21no—
351#102—21no—
352#102—221no—
353#102—221no—
354#102—221no—
355#102—221no—
356#97C22⋊D1111yescharacteristic
357#97C22⋊D1111yescharacteristic
358C4×C8C22×D1111yescharacteristic
359C4×C8C22×D1111yescharacteristic
360C2×C11—41no—
361C2×C11—82no—
362C2×C11#310011yescharacteristic
363C2×C11#341511yescharacteristic
364C2×C11#341611yescharacteristic
365D11—161no—
366D11—161no—
367#41—24no—
368#41—42no—
369C2×Q8—21no—
370C2×D4—21no—
371C2×D4—41no—
372C2×D4—221no—
373C2×D4—221no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—441no—
377C2×D4—441no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4C2×C22⋊D1111yescharacteristic
385Q16—21no—
386Q16#433912yes—
387SD16—24no—
388D8—21no—
389D8—221no—
390D8—221no—
391D8—221no—
392D8—221no—
393D8—442no—
394D8#433912yes—
395M16—41no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8C2×C22⋊D1111yescharacteristic
399C2×C8C2×C22⋊D1111yescharacteristic
400C2×C8C2×C22⋊D1111yescharacteristic
401C2×C8C23×D1111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4#432311yescharacteristic
412C4⋊C4#432311yescharacteristic
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4#432311yescharacteristic
420C22⋊C4#432311yescharacteristic
421C42—41no—
422C42—41no—
423C42C2×C22⋊D1111yescharacteristic
424C42C2×C22⋊D1111yescharacteristic
425C16—221no—
426C16—221no—
427C16—221no—
428C16—221no—
429C11#3367911yescharacteristic, complemented, Sylow
430C23—41no—
431C23—441no—
432C23—441no—
433C23C2×#432311yescharacteristic
434Q8—22no—
435Q8—41no—
436D4—22no—
437D4—44no—
438D4—41no—
439D4—441no—
440D4—441no—
441D4—441no—
442D4—441no—
443D4—1761no—
444D4—1761no—
445D4—1761no—
446D4—1761no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—161no—
454C2×C4—161no—
455C2×C4—161no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—1761no—
459C2×C4—1761no—
460C2×C4C2×#432311yescharacteristic
461C2×C4C2×#432311yescharacteristic
462C2×C4C2×#432311yescharacteristic
463C2×C4C2×#432311yescharacteristic
464C2×C4C2×#432311yescharacteristic
465C2×C4C22×C22⋊D1111yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8C2×#433911yescharacteristic
470C8C2×#433911yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—881no—
478C22—881no—
479C22—881no—
480C22—881no—
481C22—881no—
482C22—881no—
483C22C22×#432311yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—81no—
491C4—81no—
492C4—881no—
493C4—881no—
494C4#1062332211yescharacteristic
495C4#1062335311yescharacteristic
496C2—41no—
497C2—82no—
498C2—1761no—
499C2—1761no—
500C2#1307861611yescharacteristic
501C2#1308175511yescharacteristic
502C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2951C2
socleC22×C11C22×D8
hypercenter#2951D11
hypocenterC11#33679
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #13079266C2semidirect
2. #13070801C2semidirect
3. #13070796C2semidirect
4. #13070780C2semidirect
5. #13070773C2semidirect
6. #13070656C2semidirect
7. #13070651C2semidirect
8. #13070539C2semidirect
9. #13070539C2semidirect
10. #13070490C2semidirect
11. #13070478C2semidirect
12. C4×#66892C2semidirect
13. C4×#66890C2semidirect
14. #13070423C2semidirect
15. C11×#2951C2semidirect
180. #2951D11semidirect
429. C11#33679semidirect

Maximal subgroups

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

subgroupindex
#130792662
#130708012
#130707962
#130707802
#130707732
#130706562
#130706512
#130705392
#130704902
#130704782
C4×#668922
C4×#668902
#130704232
C11×#29512
#3367911