Finite Group Databasebeta

← #14908263

Subgroups — #14908263

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×#10622808C211yesmaximal, characteristic, complemented
2C22×#66876C211yesmaximal, characteristic, complemented
3C2×#10622729C211yesmaximal, characteristic, complemented
4#13070727C212yesmaximal, complemented
5#13070722C212yesmaximal, complemented
6#13070710C212yesmaximal, complemented
7#13070705C212yesmaximal, complemented
8#13070405C211yesmaximal, characteristic, complemented
9#13070335C211yesmaximal, characteristic, complemented
10#13070328C211yesmaximal, characteristic, complemented
11C11×#3050C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#525—21no—
15C2×#66977—21no—
16C22×Dic44C2211yescharacteristic
17C11×#467C2211yescharacteristic
18C11×#467C2211yescharacteristic
19C11×#466C2211yescharacteristic
20C11×#466C2211yescharacteristic
21C11×#465—21no—
22C11×#465—21no—
23C11×#427C2211yescharacteristic
24C11×#416—21no—
25#10622808—24no—
26C2×#66893C2212yescomplemented
27C2×#66891C2212yescomplemented
28#10622729—21no—
29#10622729—21no—
30#10622729C2212yes—
31#10622729C2212yes—
32C2×#66882C2211yescharacteristic
33C2×#66880—21no—
34C2×#66876—24no—
35C2×#66876C2212yes—
36C2×#66876C2211yescharacteristic
37C2×#66876C2211yescharacteristic
38C22×C11⋊C16C2212yes—
39#10622202C2212yescomplemented
40#10622200C2212yescomplemented
41#10622130C2212yescomplemented
42#10622130C2212yescomplemented
43#10622128C2212yescomplemented
44#10622127C2212yescomplemented
45C2×C11×#41—21no—
46C23×C4×C11D411yescharacteristic
47C22×Dic22—21no—
48C11×#135—22no—
49C11×#135—22no—
50C2×C11×Q16C2311yescharacteristic
51C2×C11×SD16—21no—
52C2×C11×D8C2311yescharacteristic
53C22×C8×C11—22no—
54C22×C8×C11—22no—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#123—41no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×#121—21no—
65C11×#121—21no—
66C11×#120—41no—
67C4×D4×C11—41no—
68C4×D4×C11—41no—
69C11×#117—21no—
70C2×C22⋊Dic11—41no—
71C2×C4⋊Dic11—21no—
72#66977—22no—
73#66977—22no—
74#66977—41no—
75#66977—41no—
76C2×Dic11⋊C4—41no—
77C2×Dic44—22no—
78C2×Dic44—22no—
79C2×Dic44—21no—
80C2×Dic44C2312yes—
81C11×#107C2311yescharacteristic
82C11×#107C2311yescharacteristic
83C11×#106—21no—
84C11×#103—21no—
85C11×#103—21no—
86C11×#102—21no—
87C11×#102—21no—
88#66893—24no—
89#66891—24no—
90#66882—21no—
91#66882C2312yes—
92#66880—22no—
93#66880—22no—
94#66876—22no—
95#66876—24no—
96#66876D414yescomplemented
97C2×C11⋊C16—24no—
98C2×C11⋊C16C2312yes—
99C2×C11⋊C16C2312yes—
100#33606—111nomaximal, Sylow
101C24×C11D811yescharacteristic
102C11×#41—42no—
103C11×#41—42no—
104C2×Q8×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—41no—
112C22×C4×C11D811yescharacteristic
113C22×C4×C11D811yescharacteristic
114C22×C4×C11D811yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×Dic11—41no—
119C22×Dic11—41no—
120C2×Dic22—22no—
121C2×Dic22—42no—
122C2×Dic22—41no—
123C2×Dic22—42no—
124C11×Q16—21no—
125C11×Q16—21no—
126C11×SD16—42no—
127C11×D8—21no—
128C11×D8—21no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—22no—
136C2×C8×C11C2×D412yes—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11#4112yes—
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11—41no—
152C22⋊Dic11—42no—
153C22⋊Dic11—42no—
154C4⋊Dic11—22no—
155C4⋊Dic11—41no—
156Dic11⋊C4—42no—
157Dic11⋊C4—42no—
158Dic44—22no—
159Dic44—22no—
160Dic44—42no—
161C11⋊C16—22no—
162C11⋊C16C2×D414yes—
163C2×#510—111no—
164C22×M32—111no—
165#3050D1111yescharacteristic
166C2×#467—111no—
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×C11—41no—
178C23×C11C2×D811yescharacteristic
179C23×C11C2×D811yescharacteristic
180C23×C11C2×D811yescharacteristic
181Q8×C11—41no—
182Q8×C11—41no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—82no—
186D4×C11—82no—
187D4×C11—82no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—82no—
199C2×C4×C11#12112yes—
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11#13512yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—82no—
208C2×Dic11—82no—
209Dic22—42no—
210Dic22—42no—
211Dic22—82no—
212C8×C11—21no—
213C8×C11—21no—
214C8×C11#12112yes—
215C8×C11C22×D411yescharacteristic
216C8×C11C2×#4111yescharacteristic
217C2×#135C2×D1111yescharacteristic
218C22×Q16—111no—
219C23×C8C2×D1111yescharacteristic
220#525—21no—
221C2×C22⋊Q8—221no—
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—112no—
231#467—112no—
232#467—221no—
233#467—221no—
234#467C2×D1111yescharacteristic
235#467C2×D1111yescharacteristic
236#466C2×D1111yescharacteristic
237#466C2×D1111yescharacteristic
238#465—21no—
239#465—21no—
240#427C2×D1111yescharacteristic
241C2×#107—111no—
242#416—21no—
243C2×#103—221no—
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—81no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11#46612yes—
262C22×C11#51012yescomplemented
263C22×C11C22×D811yescharacteristic
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—81no—
267C4×C11—81no—
268C4×C11—81no—
269C4×C11#46612yes—
270C4×C11C2×#12111yescharacteristic
271C4×C11C2×#13511yescharacteristic
272Dic11—82no—
273Dic11—82no—
274C2×#41—21no—
275C22×Q8—221no—
276C23×C4C22⋊D1111yescharacteristic
277#135—22no—
278#135—22no—
279C2×Q16—112no—
280C2×Q16—222no—
281C2×Q16—222no—
282C2×Q16—221no—
283C2×Q16C22×D1111yescharacteristic
284C2×SD16—21no—
285C2×D8C22×D1111yescharacteristic
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—41no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—222no—
298C22⋊Q8—222no—
299C22⋊Q8—441no—
300C22⋊Q8—441no—
301#121—21no—
302#121—21no—
303#120—41no—
304C4×D4—41no—
305C4×D4—41no—
306#117—21no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—441no—
309C2×C22⋊C4—441no—
310Q32—224no—
311SD32—224no—
312M32—114no—
313M32—224no—
314M32—222no—
315C2×C16—112no—
316C2×C16—112no—
317C2×C16—224no—
318#107—112no—
319#107—221no—
320#107C22×D1111yescharacteristic
321#107C22×D1111yescharacteristic
322#106—21no—
323#103—21no—
324#103—21no—
325#103—222no—
326#103—222no—
327#102—21no—
328#102—21no—
329C2×C11—22no—
330C2×C11—22no—
331C2×C11—41no—
332C2×C11—161no—
333C2×C11C2×#46611yescharacteristic
334C2×C11C2×#51011yescharacteristic
335C2×C11#341411yescharacteristic
336C24#432311yescharacteristic
337#41—42no—
338#41—42no—
339C2×Q8—21no—
340C2×Q8—222no—
341C2×Q8—441no—
342C2×Q8—442no—
343C2×Q8—442no—
344C2×D4—21no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—41no—
351C22×C4—441no—
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—21no—
360Q16—21no—
361Q16—222no—
362Q16—222no—
363Q16—442no—
364SD16—42no—
365D8—21no—
366D8—21no—
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—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—222no—
385C4⋊C4—441no—
386C4⋊C4—442no—
387C4⋊C4—442no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—442no—
394C22⋊C4—442no—
395C42—41no—
396C16—114no—
397C16—222no—
398C11#3360611yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—41no—
402C23—41no—
403C23C2×#432311yescharacteristic
404C23C2×#432311yescharacteristic
405C23C2×#432311yescharacteristic
406Q8—41no—
407Q8—41no—
408Q8—442no—
409Q8—442no—
410Q8—882no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—82no—
415D4—82no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—882no—
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—81no—
451C22—81no—
452C22—81no—
453C22#1062265112yes—
454C22#1062280812yescomplemented
455C22C22×#432311yescharacteristic
456C4—21no—
457C4—21no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—882no—
462C4—882no—
463C4#1062265112yes—
464C4C2×#6699211yescharacteristic
465C4C2×#6700311yescharacteristic
466C2—22no—
467C2—22no—
468C2—41no—
469C2—161no—
470C2C2×#1062265111yescharacteristic
471C2C2×#1062280811yescharacteristic
472C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3050C2
socleC22×C11C22×D8
hypercenter#3050D11
hypocenterC11#33606
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×#10622808C2semidirect
2. C22×#66876C2semidirect
3. C2×#10622729C2semidirect
4. #13070727C2semidirect
5. #13070722C2semidirect
6. #13070710C2semidirect
7. #13070705C2semidirect
8. #13070405C2semidirect
9. #13070335C2semidirect
10. #13070328C2semidirect
26. C2×#66893C22semidirect
27. C2×#66891C22semidirect
39. #10622202C22semidirect
40. #10622200C22semidirect
41. #10622130C22semidirect
42. #10622130C22semidirect
43. #10622128C22semidirect
44. #10622127C22semidirect
96. #66876D4semidirect
262. C22×C11#510semidirect
398. C11#33606semidirect
454. C22#10622808semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
C22×#668762
C2×#106227292
#130707272
#130707222
#130707102
#130707052
#130704052
#130703352
#130703282
C11×#30502
#3360611