Finite Group Databasebeta

← #14908252

Subgroups — #14908252

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
2C22×#66876C211yesmaximal, characteristic, complemented
3C2×#10622728C211yesmaximal, characteristic, complemented
4#13070731C212yesmaximal, complemented
5#13070717C212yesmaximal, complemented
6#13070714C212yesmaximal, complemented
7#13070700C212yesmaximal, complemented
8#13070405C211yesmaximal, characteristic, complemented
9#13070331C211yesmaximal, characteristic, complemented
10#13070328C211yesmaximal, characteristic, complemented
11C11×#3050C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#525—21no—
15C2×#66983—21no—
16C22×D88C2211yescharacteristic
17C11×#467C2211yescharacteristic, complemented
18C11×#467C2211yescharacteristic, complemented
19C11×#466C2211yescharacteristic, complemented
20C11×#466C2211yescharacteristic, complemented
21C11×#465—21no—
22C11×#465—21no—
23C11×#427C2211yescharacteristic
24C11×#416—21no—
25#10622806—24no—
26C2×#66892C2212yescomplemented
27C2×#66890C2212yescomplemented
28#10622728—21no—
29#10622728—21no—
30#10622728C2212yes—
31#10622728C2212yes—
32C2×#66885—21no—
33C2×#66882C2211yescharacteristic
34C2×#66876—24no—
35C2×#66876C2211yescharacteristic
36C2×#66876C2211yescharacteristic
37C2×#66876C2212yescomplemented
38C22×C11⋊C16C2212yescomplemented
39#10622202C2212yescomplemented
40#10622200C2212yescomplemented
41#10622129C2212yescomplemented
42#10622129C2212yescomplemented
43#10622128C2212yescomplemented
44#10622127C2212yescomplemented
45C2×C11×#41—21no—
46C23×C4×C11D411yescharacteristic
47C22×C22⋊D11—41no—
48C22×D44—21no—
49C11×#135—22no—
50C11×#135—22no—
51C2×C11×Q16C2311yescharacteristic
52C2×C11×SD16—21no—
53C2×C11×D8C2311yescharacteristic
54C22×C8×C11—22no—
55C22×C8×C11—22no—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C22×C8×C11D411yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#123—41no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—21no—
65C11×#121—21no—
66C11×#121—21no—
67C11×#120—41no—
68C4×D4×C11—41no—
69C4×D4×C11—41no—
70C11×#117—21no—
71#66983—22no—
72#66983—22no—
73#66983—41no—
74#66983—41no—
75C2×(C2×D11)⋊C4—41no—
76C2×C4⋊Dic11—21no—
77C2×D88—22no—
78C2×D88—22no—
79C2×D88—21no—
80C2×D88C2312yes—
81C11×#107C2311yescharacteristic
82C11×#107C2311yescharacteristic
83C11×#106—21no—
84C11×#103—21no—
85C11×#103—21no—
86C11×#102—21no—
87C11×#102—21no—
88#66892—24no—
89#66890—24no—
90#66885—22no—
91#66885—22no—
92#66882—21no—
93#66882C2312yes—
94#66876—22no—
95#66876—24no—
96#66876D414yescomplemented
97C2×C11⋊C16—24no—
98C2×C11⋊C16C2312yes—
99C2×C11⋊C16C2312yes—
100#33605—111nomaximal, Sylow
101C24×C11D811yescharacteristic
102C23×D11—41no—
103C11×#41—42no—
104C11×#41—42no—
105C2×Q8×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—41no—
113C22×C4×C11D811yescharacteristic
114C22×C4×C11D811yescharacteristic
115C22×C4×C11D811yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C2×C22⋊D11—42no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—84no—
122C22×Dic11—41no—
123C2×D44—22no—
124C2×D44—42no—
125C2×D44—41no—
126C2×D44—42no—
127C11×Q16—21no—
128C11×Q16—21no—
129C11×SD16—42no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11C2×D412yes—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11#4112yes—
144C2×C8×C11C2411yescharacteristic
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C42×C11—41no—
155(C2×D11)⋊C4—42no—
156(C2×D11)⋊C4—42no—
157C4⋊Dic11—22no—
158C4⋊Dic11—41no—
159D88—22no—
160D88—22no—
161D88—42no—
162C11⋊C16—22no—
163C11⋊C16C2×D414yescomplemented
164C2×#509—111no—
165C22×M32—111no—
166#3050D1111yescharacteristic, complemented
167C2×#466—111no—
168#2220—112no—
169#2218—112no—
170#2217—112no—
171#2215—112no—
172#2159—111no—
173#2140—111no—
174#2139—111no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11C2×D811yescharacteristic
180C23×C11C2×D811yescharacteristic
181C23×C11C2×D811yescharacteristic
182C22×D11—42no—
183C22×D11—82no—
184C22×D11—82no—
185C22×D11—82no—
186Q8×C11—41no—
187Q8×C11—41no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—82no—
191D4×C11—82no—
192D4×C11—82no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—82no—
204C2×C4×C11#12112yes—
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11#13512yes—
209C2×C4×C11C22×D411yescharacteristic
210C22⋊D11—84no—
211C22⋊D11—84no—
212C2×Dic11—42no—
213C2×Dic11—82no—
214D44—42no—
215D44—42no—
216D44—82no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11#12112yes—
220C8×C11C22×D411yescharacteristic
221C8×C11C2×#4111yescharacteristic
222C2×#135C2×D1111yescharacteristic
223C22×D8—111no—
224C23×C8C2×D1111yescharacteristic
225#525—21no—
226C2×#121—221no—
227#509—224no—
228C2×SD32—112no—
229C2×D16—112no—
230C2×M32—111no—
231C2×M32—111no—
232C2×M32—112no—
233C2×M32—224no—
234C22×C16—112no—
235#467C2×D1111yescharacteristic, complemented
236#467C2×D1111yescharacteristic, complemented
237#466—112no—
238#466—112no—
239#466—221no—
240#466—221no—
241#466C2×D1111yescharacteristic, complemented
242#466C2×D1111yescharacteristic, complemented
243#465—21no—
244#465—21no—
245#427C2×D1111yescharacteristic
246C2×#107—111no—
247#416—21no—
248C2×#102—221no—
249#367—112no—
250#366—112no—
251#358—112no—
252#357—112no—
253#357—112no—
254#357—112no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—44no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11#46612yes—
267C22×C11#50912yescomplemented
268C22×C11C22×D811yescharacteristic
269C2×D11—82no—
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—164no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11#46612yes—
279C4×C11C2×#12111yescharacteristic
280C4×C11C2×#13511yescharacteristic
281Dic11—82no—
282C2×#41—21no—
283C22×D4—221no—
284C22×D4—441no—
285C23×C4C22⋊D1111yescharacteristic
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—22no—
296C22×C8—22no—
297C22×C8C22⋊D1111yescharacteristic
298C22×C8C22⋊D1111yescharacteristic
299C22×C8C22⋊D1111yescharacteristic
300C22×C8C22×D1111yescharacteristic
301C22×C8C22×D1111yescharacteristic
302C22×C8C22×D1111yescharacteristic
303#123—41no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306#121—21no—
307#121—21no—
308#121—222no—
309#121—222no—
310#121—441no—
311#121—441no—
312#120—41no—
313C4×D4—41no—
314C4×D4—41no—
315#117—21no—
316C2×C4⋊C4—221no—
317C2×C22⋊C4—441no—
318SD32—224no—
319D16—224no—
320M32—114no—
321M32—224no—
322M32—222no—
323C2×C16—112no—
324C2×C16—112no—
325C2×C16—224no—
326#107—112no—
327#107—221no—
328#107C22×D1111yescharacteristic
329#107C22×D1111yescharacteristic
330#106—21no—
331#103—21no—
332#103—21no—
333#102—21no—
334#102—21no—
335#102—222no—
336#102—222no—
337C2×C11—22no—
338C2×C11—22no—
339C2×C11—41no—
340C2×C11—161no—
341C2×C11C2×#46611yescharacteristic
342C2×C11C2×#50911yescharacteristic
343C2×C11#341411yescharacteristic
344D11—162no—
345C24—441no—
346C24#432311yescharacteristic
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—222no—
355C2×D4—442no—
356C2×D4—442no—
357C2×D4—441no—
358C2×D4—442no—
359C2×D4—442no—
360C2×D4—884no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—41no—
364C22×C4—441no—
365C22×C4#432311yescharacteristic
366C22×C4#432311yescharacteristic
367C22×C4#432311yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371Q16—21no—
372Q16—21no—
373SD16—42no—
374D8—21no—
375D8—21no—
376D8—222no—
377D8—222no—
378D8—442no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8D4×D1112yes—
387C2×C8#434112yes—
388C2×C8C2×C22⋊D1111yescharacteristic
389C2×C8C2×C22⋊D1111yescharacteristic
390C2×C8C2×C22⋊D1111yescharacteristic
391C2×C8C23×D1111yescharacteristic
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—222no—
397C4⋊C4—441no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—442no—
404C22⋊C4—442no—
405C42—41no—
406C16—114no—
407C16—222no—
408C11#3360511yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—41no—
412C23—41no—
413C23—442no—
414C23—882no—
415C23—882no—
416C23—882no—
417C23C2×#432311yescharacteristic
418C23C2×#432311yescharacteristic
419C23C2×#432311yescharacteristic
420Q8—41no—
421Q8—41no—
422D4—41no—
423D4—41no—
424D4—82no—
425D4—82no—
426D4—82no—
427D4—442no—
428D4—442no—
429D4—884no—
430D4—884no—
431D4—882no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—82no—
443C2×C4—442no—
444C2×C4—882no—
445C2×C4C2×#432311yescharacteristic
446C2×C4C2×#432311yescharacteristic
447C2×C4C2×#432311yescharacteristic
448C2×C4#6699212yes—
449C2×C4#6700312yes—
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—21no—
452C8—21no—
453C8#6699212yes—
454C8C2×D4×D1111yescharacteristic
455C8C2×#434111yescharacteristic
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—882no—
468C22—882no—
469C22—882no—
470C22—1764no—
471C22#1062265112yes—
472C22#1062280612yescomplemented
473C22C22×#432311yescharacteristic
474C4—21no—
475C4—21no—
476C4—81no—
477C4—81no—
478C4—81no—
479C4—882no—
480C4#1062265112yes—
481C4C2×#6699211yescharacteristic
482C4C2×#6700311yescharacteristic
483C2—22no—
484C2—22no—
485C2—41no—
486C2—161no—
487C2—1762no—
488C2C2×#1062265111yescharacteristic
489C2C2×#1062280611yescharacteristic
490C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3050C2
socleC22×C11C22×D8
hypercenter#3050D11
hypocenterC11#33605
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. C22×#66876C2semidirect
3. C2×#10622728C2semidirect
4. #13070731C2semidirect
5. #13070717C2semidirect
6. #13070714C2semidirect
7. #13070700C2semidirect
8. #13070405C2semidirect
9. #13070331C2semidirect
10. #13070328C2semidirect
11. C11×#3050C2semidirect
17. C11×#467C22semidirect
18. C11×#467C22semidirect
19. C11×#466C22semidirect
20. C11×#466C22semidirect
26. C2×#66892C22semidirect
27. C2×#66890C22semidirect
37. C2×#66876C22semidirect
38. C22×C11⋊C16C22semidirect
39. #10622202C22semidirect
40. #10622200C22semidirect
41. #10622129C22semidirect
42. #10622129C22semidirect
43. #10622128C22semidirect
44. #10622127C22semidirect
96. #66876D4semidirect
163. C11⋊C16C2×D4semidirect
166. #3050D11semidirect
235. #467C2×D11semidirect
236. #467C2×D11semidirect
241. #466C2×D11semidirect
242. #466C2×D11semidirect
267. C22×C11#509semidirect
408. C11#33605semidirect
472. C22#10622806semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
C22×#668762
C2×#106227282
#130707312
#130707172
#130707142
#130707002
#130704052
#130703312
#130703282
C11×#30502
#3360511