Finite Group Databasebeta

← #14908645

Subgroups — #14908645

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078287C211yesmaximal, characteristic
2#13077213C211yesmaximal, characteristic, complemented
3#13070822C211yesmaximal, characteristic, complemented
4#13070812C211yesmaximal, characteristic, complemented
5#13070811C211yesmaximal, characteristic, complemented
6#13070810C211yesmaximal, characteristic, complemented
7#13070807C211yesmaximal, characteristic, complemented
8#13070803C211yesmaximal, characteristic, complemented
9#13070802C211yesmaximal, characteristic, complemented
10#13070401C211yesmaximal, characteristic, complemented
11D11×#367C211yesmaximal, characteristic, complemented
12#13070327C211yesmaximal, characteristic, complemented
13#13070322C211yesmaximal, characteristic, complemented
14#13070228C211yesmaximal, characteristic, complemented
15C11×#2237C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18#10623160—21no—
19#10623054—21no—
20C11×#467C2211yescharacteristic
21C11×#427C2211yescharacteristic
22#10622801C2211yescharacteristic
23#10622728C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25#10622662—21no—
26#10622608—21no—
27C2×#66862C2211yescharacteristic
28C2×C16×D11C2211yescharacteristic
29#10622496C2211yescharacteristic
30#10622493C2211yescharacteristic
31#10622493C2211yescharacteristic
32D11×#107C2211yescharacteristic
33D11×#107C2211yescharacteristic
34D11×#107C2211yescharacteristic
35#10622474—21no—
36#10622474—21no—
37#10622425—21no—
38#10622416—21no—
39C11×#367C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622143C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4343—21no—
60C2×#4339D411yescharacteristic
61C2×C11×Q16C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—21no—
64C11×#117—21no—
65#66999—21no—
66C2×#4325—21no—
67#66983—21no—
68C2×C4⋊Dic11—21no—
69C2×#4318D411yescharacteristic
70#66972—22no—
71#66972—22no—
72C2×D88C2311yescharacteristic
73#66954—22no—
74#66954—22no—
75C2×#4313D411yescharacteristic
76C2×#4313D411yescharacteristic
77C2×C8×D11C2311yescharacteristic
78C2×C8×D11C2311yescharacteristic
79#66949—41no—
80#66948—21no—
81#66948—41no—
82#66945—21no—
83#66945—21no—
84C4⋊C4×D11—21no—
85C4⋊C4×D11—21no—
86C4⋊C4×D11—21no—
87#66937—41no—
88#66937—41no—
89(C22⋊D11)⋊C4—41no—
90(C22⋊D11)⋊C4—41no—
91C4×D44—41no—
92C4×Dic22—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#106—21no—
99C11×#103—21no—
100#66899—21no—
101#66885—21no—
102#66882—21no—
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66873—21no—
109#66872—21no—
110#66872—21no—
111#66871—21no—
112#66871—21no—
113#66871—21no—
114#66862—22no—
115C16×D11—22no—
116#33653—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C2×C22⋊D11—41no—
120C2×C22⋊D11D811yescharacteristic
121C2×C22⋊D11D811yescharacteristic
122C22×Dic11—41no—
123#4343—42no—
124#4343—42no—
125#4339—22no—
126#4339—22no—
127C2×D44—21no—
128C2×D44—41no—
129C2×D44—41no—
130C2×D44D811yescharacteristic
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11C2×D411yescharacteristic
136C2×C4×D11C2×D411yescharacteristic
137C2×Dic22D811yescharacteristic
138C11×Q16—21no—
139C11×Q16—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2411yescharacteristic
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C42×C11—41no—
151#4325—42no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167#4318—22no—
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170D88—21no—
171D88—21no—
172#4313—22no—
173#4313—22no—
174C8×D11—21no—
175C8×D11—21no—
176C8×D11#4112yes—
177C8×D11#4112yes—
178C11×C16—21no—
179C11×C16—21no—
180C11⋊C16—21no—
181C11⋊C16—21no—
182#3061—111no—
183#2913—111no—
184#2237—111no—
185#2237D1111yescharacteristic, complemented
186#2235—111no—
187#2235—111no—
188#2234—111no—
189#2234—111no—
190#2233—111no—
191#2233—111no—
192#2159—111no—
193C2×#367—111no—
194#2139—111no—
195#2138—111no—
196#2113—111no—
197C23×C11C2×D811yescharacteristic
198C22×D11—41no—
199C22×D11C2×D811yescharacteristic
200C22×D11C2×D811yescharacteristic
201Q8×C11—41no—
202Q8×C11—41no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C22⋊D11—22no—
212C22⋊D11—22no—
213C22⋊D11—161no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—161no—
218C2×Dic11C2×D811yescharacteristic
219C2×Dic11C2×D811yescharacteristic
220D44—22no—
221D44—41no—
222D44—41no—
223D44—82no—
224D44—161no—
225C4×D11—21no—
226C4×D11—21no—
227C4×D11—82no—
228C4×D11—161no—
229C4×D11—161no—
230C4×D11—161no—
231C4×D11#12312yes—
232C4×D11#13712yes—
233Dic22—22no—
234C8×C11—21no—
235C8×C11C2×#4111yescharacteristic
236C8×C11C2×#4111yescharacteristic
237C11⋊C8—21no—
238C11⋊C8#12312yes—
239C2×#135—111no—
240C2×#131—111no—
241#537—221no—
242#520—221no—
243C2×M32—111no—
244C22×C16—111no—
245#468—221no—
246#468—221no—
247#467—111no—
248#467C2×D1111yescharacteristic
249#466—111no—
250#466—111no—
251#428—221no—
252#428—221no—
253#428—221no—
254#427—111no—
255#427—111no—
256#427C2×D1111yescharacteristic
257C2×#107—111no—
258C2×#107—111no—
259C2×#107—111no—
260C2×#107—111no—
261#417—221no—
262#367—111no—
263#367—111no—
264#367—111no—
265#367—111no—
266#367—111no—
267#367C2×D1111yescharacteristic
268#366—111no—
269#366C2×D1111yescharacteristic
270#358—111no—
271#358—111no—
272#358C2×D1111yescharacteristic
273#358C2×D1111yescharacteristic
274#357—111no—
275#357—111no—
276#357—111no—
277#357—111no—
278C22⋊C16—111no—
279C22⋊C16—111no—
280C22⋊C16—111no—
281C22⋊C16C2×D1111yescharacteristic
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11C22×D811yescharacteristic
286C2×D11—21no—
287C2×D11—21no—
288C2×D11—21no—
289C2×D11—21no—
290C2×D11—21no—
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11#48012yes—
295C4×C11—21no—
296C4×C11—81no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11—81no—
300C4×C11C2×#12311yescharacteristic
301C4×C11C2×#13711yescharacteristic
302Dic11—21no—
303Dic11—81no—
304Dic11—81no—
305Dic11—81no—
306Dic11#48012yes—
307C2×#41—111no—
308C2×#41—221no—
309#135—222no—
310#135—222no—
311C2×Q16C22×D1111yescharacteristic
312C2×SD16—221no—
313C2×D8—111no—
314#131—222no—
315#131—222no—
316C2×M16—111no—
317C2×M16—111no—
318C2×M16—111no—
319C22×C8—111no—
320C22×C8—111no—
321C22×C8C22×D1111yescharacteristic
322C22⋊Q8—21no—
323C22⋊Q8—221no—
324C22⋊Q8—441no—
325#121—221no—
326#121—221no—
327#121—441no—
328#121—441no—
329#121—441no—
330C4×Q8—441no—
331C4×D4—441no—
332C4×D4—441no—
333C4×D4—441no—
334#117—21no—
335#117—221no—
336#117—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341M32—222no—
342C2×C16—111no—
343C2×C16—111no—
344C2×C16—222no—
345C2×C16C22×D1111yescharacteristic
346C2×C16C22×D1111yescharacteristic
347#107—111no—
348#107—111no—
349#107—111no—
350#107—221no—
351#107—221no—
352#107—221no—
353#107—221no—
354#107C22×D1111yescharacteristic
355#107C22×D1111yescharacteristic
356#107C22×D1111yescharacteristic
357#106—21no—
358#106—221no—
359#106—221no—
360#103—21no—
361#103—221no—
362#102—221no—
363#102—221no—
364C2×C11—41no—
365C2×C11C2×#48011yescharacteristic
366C2×C11#341611yescharacteristic
367C2×C11#341611yescharacteristic
368D11—22no—
369D11—41no—
370D11—161no—
371#41—222no—
372#41—222no—
373#41—442no—
374#41—442no—
375C2×Q8—21no—
376C2×Q8—111no—
377C2×D4—111no—
378C2×D4—111no—
379C2×D4—111no—
380C2×D4—221no—
381C2×D4—441no—
382C2×D4—441no—
383C2×D4—441no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4D4×D1111yescharacteristic
392Q16—21no—
393Q16—21no—
394SD16—442no—
395D8—221no—
396D8—221no—
397M16—222no—
398M16—222no—
399M16—222no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—111no—
403C2×C8—112no—
404C2×C8—112no—
405C2×C8—111no—
406C2×C8—221no—
407C2×C8—221no—
408C2×C8D4×D1111yescharacteristic
409C2×C8C23×D1111yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—441no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C4⋊C4—441no—
421C4⋊C4—441no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4—441no—
429C42—41no—
430C42—441no—
431C42—441no—
432C16—21no—
433C16—21no—
434C16—221no—
435C16—221no—
436C11#3365311yescharacteristic, complemented, Sylow
437C23—111no—
438C23—111no—
439C23—441no—
440C23D8×D1111yescharacteristic
441Q8—41no—
442Q8—41no—
443Q8—222no—
444D4—222no—
445D4—222no—
446D4—222no—
447D4—441no—
448D4—441no—
449D4—882no—
450D4—1761no—
451D4—1761no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—111no—
459C2×C4—112no—
460C2×C4—112no—
461C2×C4—111no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—882no—
468C2×C4—1761no—
469C2×C4—1761no—
470C2×C4—1761no—
471C2×C4—1761no—
472C2×C4D8×D1111yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C8—21no—
475C8—112no—
476C8—221no—
477C8#41×D1111yescharacteristic
478C8#41×D1111yescharacteristic
479C22—21no—
480C22—21no—
481C22—21no—
482C22—112no—
483C22—221no—
484C22—221no—
485C22—221no—
486C22—221no—
487C22—221no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22C2×D8×D1111yescharacteristic
492C4—21no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—112no—
498C4—221no—
499C4—881no—
500C4—881no—
501C4—881no—
502C4D11×#12311yescharacteristic
503C4D11×#13711yescharacteristic
504C2—41no—
505C2—222no—
506C2—441no—
507C2—1761no—
508C2D11×#48011yescharacteristic
509C2#1308175911yescharacteristic
510C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2237C2
socleC22×C11C22×D8
prime radical#13078287C2
hypercenter#2237D11
hypocenterC11#33653
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
2. #13077213C2semidirect
3. #13070822C2semidirect
4. #13070812C2semidirect
5. #13070811C2semidirect
6. #13070810C2semidirect
7. #13070807C2semidirect
8. #13070803C2semidirect
9. #13070802C2semidirect
10. #13070401C2semidirect
11. D11×#367C2semidirect
12. #13070327C2semidirect
13. #13070322C2semidirect
14. #13070228C2semidirect
15. C11×#2237C2semidirect
185. #2237D11semidirect
436. C11#33653semidirect

Maximal subgroups

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

subgroupindex
#130782872
#130772132
#130708222
#130708122
#130708112
#130708102
#130708072
#130708032
#130708022
#130704012
D11×#3672
#130703272
#130703222
#130702282
C11×#22372
#3365311