Finite Group Databasebeta

← #14910759

Subgroups — #14910759

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic, complemented
2#13070861C211yesmaximal, characteristic, complemented
3#13070821C211yesmaximal, characteristic, complemented
4#13070811C211yesmaximal, characteristic, complemented
5#13070773C211yesmaximal, characteristic, complemented
6#13070731C211yesmaximal, characteristic, complemented
7#13070714C211yesmaximal, characteristic, complemented
8#13070658C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070539C211yesmaximal, characteristic, complemented
11#13070490C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070328C211yesmaximal, characteristic, complemented
14#13070323C211yesmaximal, characteristic, complemented
15C11×#3283C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18C11×#547—21no—
19#10623096—21no—
20C11×#494C2211yescharacteristic
21C11×#467C2211yescharacteristic
22C11×#467C2211yescharacteristic
23C11×#461—21no—
24C11×#452—21no—
25C11×#452—21no—
26C4×C11×D8C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31#10622728C2211yescharacteristic
32#10622728C2211yescharacteristic
33#10622719C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622460—21no—
38#10622350—21no—
39#10622348—21no—
40C4×D88C2211yescharacteristic
41#10622296C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622200C2211yescharacteristic
51C22⋊(C11⋊C16)C2211yescharacteristic
52C22⋊(C11⋊C16)C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×#41—21no—
60C2×C11×#41—21no—
61C11×#135—22no—
62C11×#135—22no—
63C11×#135—41no—
64C11×#135—41no—
65C2×C11×Q16—21no—
66C2×C11×Q16C2311yescharacteristic
67C2×C11×Q16C2311yescharacteristic
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×D8C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×C4⋊Q8—21no—
74C11×#123—41no—
75C11×#123—41no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×#121—41no—
79C4×D4×C11—21no—
80C4×D4×C11D411yescharacteristic
81C2×C11×C4⋊C4—41no—
82#66992—41no—
83#66983—21no—
84#66983—21no—
85#66979—21no—
86C2×C4⋊Dic11—21no—
87C2×D88C2311yescharacteristic
88#66951—41no—
89#66936—41no—
90(C22⋊D11)⋊C4—41no—
91C4×D44—21no—
92#66923—21no—
93C11×#107C2311yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×#103—21no—
96C11×#103—21no—
97C11×#102—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66892—41no—
102#66892—41no—
103#66890—22no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66881—21no—
112#66881—21no—
113#66876—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33874—111nomaximal, Sylow
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—81no—
123C11×#41—81no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11D811yescharacteristic
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C22×Dic11—41no—
138C2×D44—21no—
139C2×C4×D11—41no—
140C11×Q16—21no—
141C11×Q16—21no—
142C11×Q16—21no—
143C11×Q16—21no—
144C11×Q16—81no—
145C11×SD16—42no—
146C11×SD16—42no—
147C11×D8—21no—
148C11×D8#4112yes—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2411yescharacteristic
157C11×C4⋊C4—21no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4D811yescharacteristic
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4D811yescharacteristic
167C11×C22⋊C4D811yescharacteristic
168C42×C11C2×D411yescharacteristic
169C22⋊Dic11—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C4×Dic11—41no—
180D88—21no—
181D88—21no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339—111no—
187#3283D1111yescharacteristic, complemented
188#2245—111no—
189#2237—111no—
190#2235—111no—
191#2228—111no—
192#2220—111no—
193#2217—111no—
194#2208—111no—
195#2186—111no—
196#2186—111no—
197#2177—111no—
198#2168—111no—
199#2139—111no—
200#2138—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C23×C11C2×D811yescharacteristic
204C22×D11—41no—
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—41no—
209D4×C11—22no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—82no—
213D4×C11—82no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—82no—
222C2×C4×C11—82no—
223C2×C4×C11—82no—
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C2×D811yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C22⋊D11—82no—
230C22⋊D11—161no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—161no—
235D44—41no—
236D44—41no—
237C4×D11—161no—
238C8×C11—21no—
239C8×C11—21no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C2×#135C2×D1111yescharacteristic
244C2×#135C2×D1111yescharacteristic
245#553—221no—
246#547—21no—
247C2×SD32—111no—
248C2×SD32—111no—
249C2×D16—111no—
250C2×M32—111no—
251C22×C16—111no—
252#499—111no—
253#494C2×D1111yescharacteristic
254#482—221no—
255#481—221no—
256#478—221no—
257#467C2×D1111yescharacteristic
258#467C2×D1111yescharacteristic
259#466—111no—
260#466—111no—
261#461—21no—
262#452—21no—
263#452—21no—
264C4×D8—111no—
265C4×D8C2×D1111yescharacteristic
266C8×D4C2×D1111yescharacteristic
267#427—111no—
268C2×#107—111no—
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283C22⋊C16—111no—
284C22⋊C16—111no—
285#346—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—42no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11C22×D811yescharacteristic
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11#54611yescharacteristic
307C4×C11#57711yescharacteristic
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—21no—
312C2×#41—21no—
313#135—22no—
314#135—22no—
315#135—41no—
316#135—41no—
317C2×Q16—21no—
318C2×Q16C22×D1111yescharacteristic
319C2×Q16C22×D1111yescharacteristic
320C2×SD16—21no—
321C2×SD16—21no—
322C2×D8—111no—
323C2×D8C22×D1111yescharacteristic
324C22×C8C22×D1111yescharacteristic
325C22×C8C22×D1111yescharacteristic
326C4⋊Q8—21no—
327#126—441no—
328#125—221no—
329#123—41no—
330#123—41no—
331#123—441no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334#121—41no—
335#121—221no—
336#121—221no—
337#121—441no—
338C4×D4—21no—
339C4×D4—221no—
340C4×D4—441no—
341C4×D4C22⋊D1111yescharacteristic
342#117—221no—
343C2×C4⋊C4—41no—
344C2×C4⋊C4—221no—
345SD32—441no—
346SD32—441no—
347D16—222no—
348M32—441no—
349C2×C16—111no—
350C2×C16—111no—
351C2×C16—111no—
352C2×C16—111no—
353C2×C16—441no—
354#107—111no—
355#107—111no—
356#107—111no—
357#107—221no—
358#107C22×D1111yescharacteristic
359#106—221no—
360#106—221no—
361C4⋊C8C22⋊D1111yescharacteristic
362#103—21no—
363#103—21no—
364#102—21no—
365#102—221no—
366#102—221no—
367#102—221no—
368C22⋊C8C22⋊D1111yescharacteristic
369C22⋊C8C22⋊D1111yescharacteristic
370C4×C8C22×D1111yescharacteristic
371C2×C11—41no—
372C2×C11—41no—
373C2×C11—82no—
374C2×C11#329411yescharacteristic
375C2×C11#341411yescharacteristic
376C2×C11#341611yescharacteristic
377D11—161no—
378#41—42no—
379#41—42no—
380#41—81no—
381#41—81no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—221no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4#432311yescharacteristic
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398Q16—21no—
399Q16—21no—
400Q16—21no—
401Q16—21no—
402Q16—81no—
403SD16—42no—
404SD16—42no—
405D8—21no—
406D8—221no—
407D8—221no—
408D8#434112yes—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×C22⋊D1111yescharacteristic
414C2×C8C2×C22⋊D1111yescharacteristic
415C2×C8C2×C22⋊D1111yescharacteristic
416C2×C8C23×D1111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4#432311yescharacteristic
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4#432311yescharacteristic
437C22⋊C4#432311yescharacteristic
438C42—441no—
439C42C2×C22⋊D1111yescharacteristic
440C16—221no—
441C16—221no—
442C16—221no—
443C16—221no—
444C11#3387411yescharacteristic, complemented, Sylow
445C23—41no—
446C23—441no—
447C23C2×#432311yescharacteristic
448C23C2×#432311yescharacteristic
449Q8—41no—
450Q8—41no—
451Q8—41no—
452Q8—41no—
453D4—22no—
454D4—41no—
455D4—41no—
456D4—82no—
457D4—82no—
458D4—441no—
459D4—441no—
460D4—882no—
461D4—1761no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—1761no—
476C2×C4—1761no—
477C2×C4C2×#432311yescharacteristic
478C2×C4C2×#432311yescharacteristic
479C2×C4C2×#432311yescharacteristic
480C2×C4C2×#432311yescharacteristic
481C2×C4C22×C22⋊D1111yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8C2×#434111yescharacteristic
486C8#6703711yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22C22×#432311yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—881no—
508C4—881no—
509C4—881no—
510C4#1062333711yescharacteristic
511C4#1062336711yescharacteristic
512C2—41no—
513C2—41no—
514C2—82no—
515C2—1761no—
516C2#1308042911yescharacteristic
517C2#1308175011yescharacteristic
518C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3283C2
socleC22×C11C22×D8
hypercenter#3283D11
hypocenterC11#33874
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13070861C2semidirect
3. #13070821C2semidirect
4. #13070811C2semidirect
5. #13070773C2semidirect
6. #13070731C2semidirect
7. #13070714C2semidirect
8. #13070658C2semidirect
9. #13070539C2semidirect
10. #13070539C2semidirect
11. #13070490C2semidirect
12. #13070442C2semidirect
13. #13070328C2semidirect
14. #13070323C2semidirect
15. C11×#3283C2semidirect
187. #3283D11semidirect
444. C11#33874semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130708612
#130708212
#130708112
#130707732
#130707312
#130707142
#130706582
#130705392
#130704902
#130704422
#130703282
#130703232
C11×#32832
#3387411