Finite Group Databasebeta

← #14908253

Subgroups — #14908253

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic, complemented
2C2×D11×M32C211yesmaximal, characteristic, complemented
3#13078193C211yesmaximal, characteristic, complemented
4C2×#10622496C211yesmaximal, characteristic, complemented
5#13070732C212yesmaximal, complemented
6#13070718C212yesmaximal, complemented
7#13070715C212yesmaximal, complemented
8#13070701C212yesmaximal, complemented
9#13070402C211yesmaximal, characteristic, complemented
10#13070333C211yesmaximal, characteristic, complemented
11C11×#2139C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623359—21no—
14C22×D88C2211yescharacteristic
15C22×C8×D11C2211yescharacteristic
16C2×#66948—21no—
17C2×C11×M32C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622846—21no—
20#10622806—24no—
21#10622801C2211yescharacteristic, complemented
22#10622801C2211yescharacteristic, complemented
23C2×#66892C2212yescomplemented
24#10622784—21no—
25#10622784—21no—
26#10622770C2211yescharacteristic, complemented
27#10622770C2211yescharacteristic, complemented
28C2×#66890C2212yescomplemented
29#10622719C2211yescharacteristic
30C2×#66876C2211yescharacteristic
31C2×#66873—21no—
32D11×M32—24no—
33C2×#66862C2212yescomplemented
34C2×C16×D11C2212yescomplemented
35#10622496—21no—
36#10622496—21no—
37#10622496C2212yes—
38#10622496C2212yes—
39C11×#358C2212yescomplemented
40C11×#357C2212yescomplemented
41#10622147C2212yescomplemented
42#10622147C2212yescomplemented
43#10622128C2212yescomplemented
44#10622127C2212yescomplemented
45C2×C11×#41—21no—
46C22×D44—21no—
47C22×D44—41no—
48C22×C4×D11D411yescharacteristic
49C11×#135—22no—
50C11×#135—22no—
51C2×C11×Q16C2311yescharacteristic
52C2×C11×SD16—21no—
53C2×C11×D8C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C2×C11×C4⋊C4—21no—
56#66999—21no—
57#66999—21no—
58#66991—21no—
59#66991—21no—
60#66990—41no—
61#66988—41no—
62C4×C22⋊D11—41no—
63C4×C22⋊D11—41no—
64C2×(C2×D11)⋊C4—41no—
65#66979—21no—
66C22×C11⋊C8D411yescharacteristic
67C2×D88—22no—
68C2×D88—22no—
69C2×D88—21no—
70C2×D88C2312yes—
71C2×C8×D11—22no—
72C2×C8×D11—22no—
73C2×C8×D11D411yescharacteristic
74C2×C8×D11D411yescharacteristic
75C2×C8×D11C2311yescharacteristic
76C2×C8×D11C2311yescharacteristic
77#66948—22no—
78#66948—22no—
79#66948—41no—
80#66948—41no—
81C11×M32—22no—
82C2×C11×C16C2312yes—
83C11×#107—21no—
84C11×#107C2312yes—
85#66899—21no—
86#66899—21no—
87#66896—21no—
88#66896—21no—
89#66892—24no—
90#66890—24no—
91#66882C2311yescharacteristic
92#66882C2311yescharacteristic
93#66881—21no—
94#66876D414yescomplemented
95C2×C11⋊C16C2312yes—
96#66873—22no—
97#66873—22no—
98#66862—24no—
99C16×D11—24no—
100#33605—111nomaximal, Sylow
101C23×D11—41no—
102C23×D11D811yescharacteristic
103C11×#41—42no—
104C11×#41—42no—
105C2×Q8×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C2×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113C22×Dic11D811yescharacteristic
114C2×D44—22no—
115C2×D44—42no—
116C2×D44—42no—
117C2×D44—42no—
118C2×D44—41no—
119C2×D44—42no—
120C2×D44—84no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11D811yescharacteristic
124C2×C4×D11D811yescharacteristic
125C2×C4×D11C2×D411yescharacteristic
126C2×C4×D11C2×D411yescharacteristic
127C11×Q16—21no—
128C11×Q16—21no—
129C11×SD16—42no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11C2×D412yes—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11#4112yes—
135C2×C8×C11C2411yescharacteristic
136C11×C4⋊C4—22no—
137C11×C4⋊C4—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—41no—
140C22⋊Dic11—41no—
141(C2×D11)⋊C4—42no—
142(C2×D11)⋊C4—42no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147Dic11⋊C4—41no—
148Dic11⋊C4—41no—
149C4×Dic11—41no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8C2×D411yescharacteristic
152C2×C11⋊C8C2×D411yescharacteristic
153D88—22no—
154D88—22no—
155D88—42no—
156C8×D11—22no—
157C8×D11—22no—
158C8×D11—21no—
159C8×D11—21no—
160C8×D11—21no—
161C8×D11—21no—
162C11×C16—22no—
163C11⋊C16C2×D414yescomplemented
164C2×#509—111no—
165C22×M32—111no—
166#3050—111no—
167C2×#466—111no—
168#2220—112no—
169#2218—112no—
170#2217—112no—
171#2215—112no—
172#2159—111no—
173#2140—111no—
174#2139D1111yescharacteristic, complemented
175C23×C11—41no—
176C23×C11C2×D811yescharacteristic
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—41no—
180C22×D11—42no—
181C22×D11—82no—
182C22×D11—82no—
183C22×D11—82no—
184C22×D11C2×D811yescharacteristic
185C22×D11C2×D811yescharacteristic
186Q8×C11—41no—
187Q8×C11—41no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—82no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—82no—
194C2×C4×C11—82no—
195C2×C4×C11#12112yes—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11#13512yes—
198C2×C4×C11C22×D411yescharacteristic
199C22⋊D11—82no—
200C22⋊D11—82no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11C2×D811yescharacteristic
205C2×Dic11C2×D811yescharacteristic
206D44—42no—
207D44—42no—
208D44—84no—
209D44—84no—
210D44—82no—
211C4×D11—21no—
212C4×D11—21no—
213C4×D11—21no—
214C4×D11—21no—
215C4×D11—22no—
216C4×D11—22no—
217C8×C11#12112yes—
218C8×C11C22×D411yescharacteristic
219C8×C11C2×#4111yescharacteristic
220C11⋊C8—21no—
221C11⋊C8—21no—
222C2×#135C2×D1111yescharacteristic
223C22×D8—111no—
224C23×C8—111no—
225#525—221no—
226C2×#121—221no—
227#509—224no—
228C2×SD32—112no—
229C2×D16—112no—
230C2×M32—111no—
231C2×M32—112no—
232C2×M32—224no—
233C2×M32C2×D1111yescharacteristic
234C22×C16—112no—
235#467—111no—
236#467—111no—
237#466—111no—
238#466—111no—
239#466—112no—
240#466—112no—
241#466—221no—
242#466—221no—
243#465—221no—
244#465—221no—
245#427—111no—
246C2×#107C2×D1111yescharacteristic
247#416—221no—
248C2×#102—221no—
249#367—112no—
250#366—112no—
251#358C2×D1112yescomplemented
252#357—112no—
253#357—112no—
254#357C2×D1112yescomplemented
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11—81no—
260C22×C11#46612yes—
261C22×C11C22×D811yescharacteristic
262C2×D11—21no—
263C2×D11—21no—
264C2×D11—21no—
265C2×D11—21no—
266C2×D11—21no—
267C2×D11—44no—
268C2×D11—82no—
269C2×D11—82no—
270C2×D11—82no—
271C2×D11—164no—
272C2×D11#50912yescomplemented
273C4×C11—82no—
274C4×C11—81no—
275C4×C11#46612yes—
276C4×C11C2×#12111yescharacteristic
277C4×C11C2×#13511yescharacteristic
278Dic11—21no—
279Dic11—21no—
280Dic11—81no—
281Dic11—81no—
282C2×#41—21no—
283C22×D4—221no—
284C22×D4—441no—
285C23×C4—111no—
286#135—22no—
287#135—22no—
288C2×Q16C22×D1111yescharacteristic
289C2×SD16—21no—
290C2×D8—112no—
291C2×D8—222no—
292C2×D8—222no—
293C2×D8—221no—
294C2×D8C22×D1111yescharacteristic
295C22×C8—111no—
296C22×C8—111no—
297C22×C8—111no—
298C22×C8—111no—
299C22×C8—111no—
300C22×C8—222no—
301C22×C8—222no—
302C22×C8C22×D1111yescharacteristic
303#123—441no—
304C22⋊Q8—221no—
305C22⋊Q8—221no—
306#121—222no—
307#121—222no—
308#121—221no—
309#121—221no—
310#121—441no—
311#121—441no—
312#120—441no—
313C4×D4—441no—
314C4×D4—441no—
315#117—221no—
316C2×C4⋊C4—21no—
317C2×C22⋊C4—441no—
318SD32—224no—
319D16—224no—
320M32—22no—
321M32—114no—
322M32—224no—
323C2×C16—112no—
324C2×C16—224no—
325C2×C16C22×D1112yes—
326#107—21no—
327#107—111no—
328#107—111no—
329#107C22×D1112yes—
330#106—221no—
331#103—221no—
332#103—221no—
333#102—222no—
334#102—222no—
335#102—221no—
336#102—221no—
337C2×C11—22no—
338C2×C11—161no—
339C2×C11C2×#46611yescharacteristic
340C2×C11C2×#50911yescharacteristic
341C2×C11#341411yescharacteristic
342D11—22no—
343D11—41no—
344D11—162no—
345C24—111no—
346C24—441no—
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—222no—
353C2×D4—442no—
354C2×D4—442no—
355C2×D4—441no—
356C2×D4—441no—
357C2×D4—442no—
358C2×D4—441no—
359C2×D4—442no—
360C2×D4—884no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—111no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4D4×D1111yescharacteristic
371Q16—21no—
372Q16—21no—
373SD16—42no—
374D8—21no—
375D8—21no—
376D8—222no—
377D8—222no—
378D8—442no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—221no—
385C2×C8—221no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8#433912yes—
389C2×C8D4×D1111yescharacteristic
390C2×C8D4×D1112yes—
391C2×C8C23×D1111yescharacteristic
392C4⋊C4—22no—
393C4⋊C4—41no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C22⋊C4—442no—
399C22⋊C4—442no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C42—441no—
406C16—22no—
407C16—114no—
408C11#3360511yescharacteristic, complemented, Sylow
409C23—41no—
410C23—111no—
411C23—111no—
412C23—222no—
413C23—222no—
414C23—441no—
415C23—442no—
416C23—882no—
417C23—882no—
418C23—882no—
419C23D8×D1111yescharacteristic
420Q8—41no—
421Q8—41no—
422D4—41no—
423D4—41no—
424D4—82no—
425D4—442no—
426D4—442no—
427D4—884no—
428D4—884no—
429D4—882no—
430D4—882no—
431D4—882no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—222no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4#6693712yes—
448C2×C4D8×D1111yescharacteristic
449C2×C4#6696912yes—
450C2×C4C2×D4×D1111yescharacteristic
451C8—221no—
452C8—221no—
453C8#6693712yes—
454C8C2×#433911yescharacteristic
455C8C2×D4×D1111yescharacteristic
456C22—21no—
457C22—21no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—112no—
462C22—221no—
463C22—221no—
464C22—221no—
465C22—221no—
466C22—221no—
467C22—444no—
468C22—882no—
469C22—882no—
470C22—882no—
471C22—1764no—
472C22#1062238812yes—
473C22C2×D8×D1111yescharacteristic
474C4—82no—
475C4—81no—
476C4—221no—
477C4—221no—
478C4—881no—
479C4—881no—
480C4#1062238812yes—
481C4C2×#6693711yescharacteristic
482C4C2×#6696911yescharacteristic
483C2—22no—
484C2—161no—
485C2—222no—
486C2—441no—
487C2—1762no—
488C2C2×#1062238811yescharacteristic
489C2D11×#50911yescharacteristic
490C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2139C2
socleC22×C11C22×D8
hypercenter#2139D11
hypocenterC11#33605
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. C2×D11×M32C2semidirect
3. #13078193C2semidirect
4. C2×#10622496C2semidirect
5. #13070732C2semidirect
6. #13070718C2semidirect
7. #13070715C2semidirect
8. #13070701C2semidirect
9. #13070402C2semidirect
10. #13070333C2semidirect
11. C11×#2139C2semidirect
21. #10622801C22semidirect
22. #10622801C22semidirect
23. C2×#66892C22semidirect
26. #10622770C22semidirect
27. #10622770C22semidirect
28. C2×#66890C22semidirect
33. C2×#66862C22semidirect
34. C2×C16×D11C22semidirect
39. C11×#358C22semidirect
40. C11×#357C22semidirect
41. #10622147C22semidirect
42. #10622147C22semidirect
43. #10622128C22semidirect
44. #10622127C22semidirect
94. #66876D4semidirect
163. C11⋊C16C2×D4semidirect
174. #2139D11semidirect
251. #358C2×D11semidirect
254. #357C2×D11semidirect
272. C2×D11#509semidirect
408. C11#33605semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×D11×M322
#130781932
C2×#106224962
#130707322
#130707182
#130707152
#130707012
#130704022
#130703332
C11×#21392
#3360511