Finite Group Databasebeta

← #14908257

Subgroups — #14908257

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic, complemented
2C22×#66876C211yesmaximal, characteristic, complemented
3#13078197C211yesmaximal, characteristic
4#13070731C212yesmaximal, complemented
5#13070722C212yesmaximal, complemented
6#13070714C212yesmaximal, complemented
7#13070705C212yesmaximal, complemented
8#13070402C211yesmaximal, characteristic, complemented
9#13070336C211yesmaximal, characteristic, complemented
10#13070326C211yesmaximal, characteristic, complemented
11C2×C11×#467C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×C22⋊Q8—21no—
15#10623322—21no—
16C2×#66957C2211yescharacteristic
17C11×#467—21no—
18C11×#467—21no—
19C11×#467C2212yes—
20C11×#467C2212yes—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#103—21no—
23C2×#66893C2212yescomplemented
24#10622792—24no—
25C2×#66892C2212yescomplemented
26#10622729C2211yescharacteristic
27#10622729C2211yescharacteristic
28#10622728C2211yescharacteristic
29#10622728C2211yescharacteristic
30#10622727—21no—
31#10622727—21no—
32#10622726—21no—
33#10622719C2211yescharacteristic
34C2×#66876—24no—
35C2×#66876C2211yescharacteristic
36C2×#66876C2212yes—
37C2×#66876C2211yescharacteristic
38C22×C11⋊C16C2212yes—
39#10622202C2212yescomplemented
40#10622202C2212yescomplemented
41#10622130C2212yescomplemented
42#10622129C2212yescomplemented
43#10622128C2212yescomplemented
44#10622127C2212yescomplemented
45C22×Q8×C11—21no—
46C23×C4×C11D411yescharacteristic
47C2×#4339—21no—
48C2×C11×Q16—22no—
49C2×C11×Q16—21no—
50C2×C11×Q16—22no—
51C2×C11×Q16C2312yes—
52C22×C8×C11—22no—
53C22×C8×C11—22no—
54C22×C8×C11D411yescharacteristic
55C22×C8×C11D411yescharacteristic
56C22×C8×C11D411yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—41no—
63C11×C22⋊Q8—41no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—41no—
66C2×C11×C22⋊C4—41no—
67#67006—41no—
68#66983—21no—
69#66983—21no—
70#66982—41no—
71C4×C22⋊D11—41no—
72C4×C22⋊D11—41no—
73#66979—21no—
74#66977—21no—
75#66977—21no—
76C2×Dic44C2311yescharacteristic
77#66957—22no—
78#66957—22no—
79C2×D88C2311yescharacteristic
80C2×#4314—21no—
81C11×#107—21no—
82C11×#107C2312yes—
83C11×#103—22no—
84C11×#103—22no—
85#66893—24no—
86#66892—24no—
87#66885—21no—
88#66885—21no—
89#66882C2311yescharacteristic
90#66882C2311yescharacteristic
91#66881—21no—
92#66880—21no—
93#66880—21no—
94#66876—22no—
95#66876—24no—
96#66876D414yescomplemented
97C2×C11⋊C16—24no—
98C2×C11⋊C16C2312yes—
99C2×C11⋊C16C2312yes—
100#33606—111nomaximal, Sylow
101C24×C11D811yescharacteristic
102C2×Q8×C11—22no—
103C2×Q8×C11—41no—
104C2×Q8×C11—42no—
105C2×Q8×C11—42no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11D811yescharacteristic
111C22×C4×C11D811yescharacteristic
112C22×C4×C11D811yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119#4339—42no—
120#4339—42no—
121C2×D44—21no—
122C2×C4×D11—41no—
123C2×Dic22—21no—
124C11×Q16—22no—
125C11×Q16—22no—
126C11×Q16—42no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11C2×D412yes—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11#4112yes—
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—22no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—42no—
146C22⋊Dic11—41no—
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155C4×Dic11—41no—
156Dic44—21no—
157Dic44—21no—
158D88—21no—
159D88—21no—
160#4314—42no—
161C11⋊C16—22no—
162C11⋊C16C2×D414yes—
163C2×#510—111no—
164C22×M32—111no—
165#3050—111no—
166C2×#467D1111yescharacteristic, complemented
167#2220—112no—
168#2219—112no—
169#2217—112no—
170#2216—112no—
171#2159—111no—
172#2141—111no—
173#2139—111no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—41no—
177C23×C11C2×D811yescharacteristic
178C23×C11C2×D811yescharacteristic
179C23×C11C2×D811yescharacteristic
180C22×D11—41no—
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—82no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—82no—
194C2×C4×C11—82no—
195C2×C4×C11#12112yes—
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C2×D811yescharacteristic
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11#13512yes—
200C2×C4×C11C22×D411yescharacteristic
201C22⋊D11—82no—
202C22⋊D11—82no—
203C22⋊D11—82no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207D44—41no—
208D44—41no—
209C4×D11—82no—
210Dic22—41no—
211Dic22—41no—
212C8×C11—21no—
213C8×C11—21no—
214C8×C11#12112yes—
215C8×C11C22×D411yescharacteristic
216C8×C11C2×#4111yescharacteristic
217C2×#135—111no—
218C22×Q16C2×D1111yescharacteristic
219C23×C8C2×D1111yescharacteristic
220#525—221no—
221C2×C22⋊Q8—21no—
222#510—224no—
223C2×Q32—112no—
224C2×SD32—112no—
225C2×M32—111no—
226C2×M32—111no—
227C2×M32—112no—
228C2×M32—224no—
229C22×C16—112no—
230#467—21no—
231#467—21no—
232#467—111no—
233#467—111no—
234#467C2×D1112yes—
235#467C2×D1112yes—
236#466—111no—
237#466—111no—
238#465—221no—
239#465—221no—
240#427—111no—
241C2×#107C2×D1111yescharacteristic
242#416—221no—
243C2×#103—21no—
244#367—112no—
245#366—112no—
246#358—112no—
247#358—112no—
248#358—112no—
249#357—112no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—44no—
258C22×C11#46612yes—
259C22×C11#51012yescomplemented
260C22×C11C22×D811yescharacteristic
261C2×D11—81no—
262C2×D11—81no—
263C2×D11—81no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—82no—
267C4×C11—82no—
268C4×C11#46612yes—
269C4×C11C2×#12111yescharacteristic
270C4×C11C2×#13511yescharacteristic
271Dic11—81no—
272Dic11—81no—
273Dic11—81no—
274C2×#41—221no—
275C22×Q8—21no—
276C23×C4C22⋊D1111yescharacteristic
277#135—222no—
278#135—222no—
279C2×Q16—22no—
280C2×Q16—22no—
281C2×Q16—21no—
282C2×Q16—111no—
283C2×Q16C22×D1112yes—
284C2×SD16—221no—
285C2×D8—111no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8C22⋊D1111yescharacteristic
289C22×C8C22⋊D1111yescharacteristic
290C22×C8C22⋊D1111yescharacteristic
291C22×C8C22×D1111yescharacteristic
292C22×C8C22×D1111yescharacteristic
293C22×C8C22×D1111yescharacteristic
294#123—441no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—41no—
298C22⋊Q8—41no—
299C22⋊Q8—221no—
300C22⋊Q8—221no—
301#121—221no—
302#121—221no—
303#120—441no—
304C4×D4—441no—
305C4×D4—441no—
306#117—221no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—41no—
309C2×C22⋊C4—41no—
310Q32—224no—
311SD32—224no—
312M32—114no—
313M32—224no—
314M32—222no—
315C2×C16—112no—
316C2×C16—112no—
317C2×C16—224no—
318#107—21no—
319#107—111no—
320#107—111no—
321#107C22×D1112yes—
322#106—221no—
323#103—22no—
324#103—22no—
325#103—221no—
326#103—221no—
327#102—221no—
328#102—221no—
329C2×C11—22no—
330C2×C11—22no—
331C2×C11—41no—
332C2×C11C2×#46611yescharacteristic
333C2×C11C2×#51011yescharacteristic
334C2×C11#341411yescharacteristic
335D11—161no—
336C24#432311yescharacteristic
337#41—442no—
338#41—442no—
339C2×Q8—22no—
340C2×Q8—41no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8—221no—
344C2×D4—221no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—441no—
353C22×C4#432311yescharacteristic
354C22×C4#432311yescharacteristic
355C22×C4#432311yescharacteristic
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359Q16—22no—
360Q16—22no—
361Q16—42no—
362Q16—221no—
363Q16—221no—
364SD16—442no—
365D8—221no—
366D8—221no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8D4×D1112yes—
375C2×C8#434112yes—
376C2×C8C2×C22⋊D1111yescharacteristic
377C2×C8C2×C22⋊D1111yescharacteristic
378C2×C8C2×C22⋊D1111yescharacteristic
379C2×C8C23×D1111yescharacteristic
380C4⋊C4—22no—
381C4⋊C4—41no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C22⋊C4—42no—
389C22⋊C4—42no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C42—441no—
396C16—114no—
397C16—222no—
398C11#3360611yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—41no—
402C23—441no—
403C23C2×#432311yescharacteristic
404C23C2×#432311yescharacteristic
405C23C2×#432311yescharacteristic
406Q8—42no—
407Q8—42no—
408Q8—82no—
409Q8—441no—
410Q8—441no—
411D4—441no—
412D4—441no—
413D4—882no—
414D4—882no—
415D4—882no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—882no—
431C2×C4C2×#432311yescharacteristic
432C2×C4C2×#432311yescharacteristic
433C2×C4C2×#432311yescharacteristic
434C2×C4#6699212yes—
435C2×C4#6700312yes—
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—21no—
438C8—21no—
439C8#6699212yes—
440C8C2×D4×D1111yescharacteristic
441C8C2×#434111yescharacteristic
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—44no—
450C22—881no—
451C22—881no—
452C22—881no—
453C22#1062265112yes—
454C22#1062279212yescomplemented
455C22C22×#432311yescharacteristic
456C4—21no—
457C4—21no—
458C4—82no—
459C4—82no—
460C4—881no—
461C4—881no—
462C4—881no—
463C4#1062265112yes—
464C4C2×#6699211yescharacteristic
465C4C2×#6700311yescharacteristic
466C2—22no—
467C2—22no—
468C2—41no—
469C2—1761no—
470C2C2×#1062265111yescharacteristic
471C2C2×#1062279211yescharacteristic
472C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#467C2
socleC22×C11C22×D8
prime radical#13078197C2
hypercenterC2×#467D11
hypocenterC11#33606
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
2. C22×#66876C2semidirect
4. #13070731C2semidirect
5. #13070722C2semidirect
6. #13070714C2semidirect
7. #13070705C2semidirect
8. #13070402C2semidirect
9. #13070336C2semidirect
10. #13070326C2semidirect
11. C2×C11×#467C2semidirect
23. C2×#66893C22semidirect
25. C2×#66892C22semidirect
39. #10622202C22semidirect
40. #10622202C22semidirect
41. #10622130C22semidirect
42. #10622129C22semidirect
43. #10622128C22semidirect
44. #10622127C22semidirect
96. #66876D4semidirect
166. C2×#467D11semidirect
259. C22×C11#510semidirect
398. C11#33606semidirect
454. C22#10622792semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
C22×#668762
#130781972
#130707312
#130707222
#130707142
#130707052
#130704022
#130703362
#130703262
C2×C11×#4672
#3360611