Finite Group Databasebeta

← #14908209

Subgroups — #14908209

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622807C211yesmaximal, characteristic, complemented
2C23×C11⋊C16C211yesmaximal, characteristic, complemented
3#13078197C211yesmaximal, characteristic, complemented
4#13070714C212yesmaximal, complemented
5#13070710C212yesmaximal, complemented
6#13070705C212yesmaximal, complemented
7#13070700C212yesmaximal, complemented
8#13070398C211yesmaximal, characteristic, complemented
9#13070323C211yesmaximal, characteristic, complemented
10#13070321C211yesmaximal, characteristic, complemented
11C11×#3050C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#525—21no—
15#10623322—21no—
16C2×#66957C2211yescharacteristic
17C11×#467C2212yes—
18C11×#466C2212yes—
19C11×#465—22no—
20C11×#427C2211yescharacteristic
21C11×#416—21no—
22#10622807—24no—
23C2×#66893C2211yescharacteristic, complemented
24C2×#66892C2211yescharacteristic, complemented
25C2×#66891C2211yescharacteristic, complemented
26C2×#66890C2211yescharacteristic, complemented
27#10622729C2212yes—
28#10622728C2212yes—
29#10622727—22no—
30#10622726—21no—
31#10622719C2211yescharacteristic
32C22×C11⋊C16—24no—
33C22×C11⋊C16C2212yes—
34C22×C11⋊C16C2212yes—
35C22×C11⋊C16C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622202C2212yescomplemented
38#10622200C2212yescomplemented
39#10622130C2212yescomplemented
40#10622129C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×C11×#41—21no—
44C23×C4×C11D411yescharacteristic
45C2×#4339—21no—
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C22×C8×C11—22no—
52C22×C8×C11—22no—
53C22×C8×C11D411yescharacteristic
54C22×C8×C11D412yes—
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×#123—41no—
58C11×C22⋊Q8—22no—
59C11×#121—22no—
60C11×#120—41no—
61C4×D4×C11—42no—
62C11×#117—21no—
63#67006—41no—
64#66983—22no—
65#66982—41no—
66C4×C22⋊D11—42no—
67#66979—21no—
68#66977—22no—
69C2×Dic44C2311yescharacteristic
70#66957—22no—
71#66957—22no—
72C2×D88C2311yescharacteristic
73C2×#4314—21no—
74C11×#107C2312yes—
75C11×#106—21no—
76C11×#103—22no—
77C11×#102—22no—
78#66893—22no—
79#66892—22no—
80#66891—22no—
81#66890—22no—
82#66885—22no—
83#66882C2312yes—
84#66881—21no—
85#66880—22no—
86C2×C11⋊C16—22no—
87C2×C11⋊C16—24no—
88C2×C11⋊C16—24no—
89C2×C11⋊C16D414yescomplemented
90C2×C11⋊C16C2312yes—
91C2×C11⋊C16C2311yescharacteristic
92C2×C11⋊C16C2311yescharacteristic
93#33600—111nomaximal, Sylow
94C24×C11D811yescharacteristic
95C11×#41—42no—
96C11×#41—42no—
97C2×Q8×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—41no—
104C22×C4×C11D812yes—
105C22×C4×C11D811yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C2×C22⋊D11—42no—
109C2×C22⋊D11—41no—
110#4339—42no—
111#4339—42no—
112C2×D44—21no—
113C2×C4×D11—41no—
114C2×Dic22—21no—
115C11×Q16—21no—
116C11×Q16—21no—
117C11×SD16—42no—
118C11×D8—21no—
119C11×D8—21no—
120C2×C8×C11—24no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D412yes—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11#4112yes—
128C2×C8×C11C2411yescharacteristic
129C11×C4⋊C4—22no—
130C11×C4⋊C4—42no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—42no—
134C42×C11—41no—
135C22⋊Dic11—42no—
136C22⋊Dic11—41no—
137(C2×D11)⋊C4—42no—
138C4⋊Dic11—22no—
139Dic11⋊C4—42no—
140C4×Dic11—41no—
141Dic44—21no—
142Dic44—21no—
143D88—21no—
144D88—21no—
145#4314—42no—
146C11⋊C16—22no—
147C11⋊C16C2×D412yes—
148C11⋊C16C2×D412yes—
149C2×#508—111no—
150C23×C16—111no—
151#3050—111no—
152#3050D1111yescharacteristic, complemented
153#2217—112no—
154#2217—112no—
155#2216—112no—
156#2215—112no—
157#2158—111no—
158#2138—111no—
159#2138—111no—
160C23×C11—22no—
161C23×C11—24no—
162C23×C11—41no—
163C23×C11C2×D811yescharacteristic
164C23×C11C2×D812yes—
165C22×D11—41no—
166Q8×C11—41no—
167Q8×C11—41no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—82no—
171D4×C11—84no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—82no—
179C2×C4×C11#12112yes—
180C2×C4×C11C2×D812yes—
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11#13512yes—
183C2×C4×C11C22×D411yescharacteristic
184C22⋊D11—82no—
185C22⋊D11—84no—
186C2×Dic11—42no—
187C2×Dic11—41no—
188D44—41no—
189D44—41no—
190C4×D11—82no—
191Dic22—41no—
192Dic22—41no—
193C8×C11—22no—
194C8×C11#12112yes—
195C8×C11C22×D411yescharacteristic
196C8×C11C2×#4111yescharacteristic
197C2×#135—111no—
198C2×#135C2×D1111yescharacteristic
199C23×C8C2×D1111yescharacteristic
200#525—21no—
201#525—221no—
202#508—224no—
203C2×Q32—111no—
204C2×SD32—111no—
205C2×SD32—111no—
206C2×D16—111no—
207C22×C16—111no—
208C22×C16—111no—
209C22×C16—112no—
210C22×C16—112no—
211C22×C16—224no—
212#467—112no—
213#467C2×D1112yes—
214#466—112no—
215#466C2×D1112yes—
216#465—22no—
217#465—222no—
218#427—111no—
219#427C2×D1111yescharacteristic
220#416—21no—
221#416—221no—
222#367—112no—
223#366—112no—
224#358—112no—
225#358—112no—
226#357—112no—
227#357—112no—
228C22×C11—28no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—82no—
233C22×C11—81no—
234C22×C11#46612yes—
235C22×C11#50814yescomplemented
236C22×C11C22×D811yescharacteristic
237C2×D11—82no—
238C2×D11—81no—
239C4×C11—22no—
240C4×C11—82no—
241C4×C11—81no—
242C4×C11#46612yes—
243C4×C11C2×#12111yescharacteristic
244C4×C11C2×#13511yescharacteristic
245Dic11—82no—
246Dic11—81no—
247C2×#41—21no—
248C2×#41—221no—
249C23×C4C22⋊D1111yescharacteristic
250#135—22no—
251#135—22no—
252#135—222no—
253#135—222no—
254C2×Q16—111no—
255C2×Q16C22×D1111yescharacteristic
256C2×SD16—21no—
257C2×SD16—221no—
258C2×D8—111no—
259C2×D8C22×D1111yescharacteristic
260C22×C8—22no—
261C22×C8—22no—
262C22×C8C22⋊D1111yescharacteristic
263C22×C8C22⋊D1112yes—
264C22×C8C22×D1112yes—
265C22×C8C22×D1111yescharacteristic
266#123—41no—
267#123—441no—
268C22⋊Q8—22no—
269C22⋊Q8—222no—
270#121—22no—
271#121—222no—
272#120—41no—
273#120—441no—
274C4×D4—42no—
275C4×D4—442no—
276#117—21no—
277#117—221no—
278Q32—222no—
279SD32—222no—
280SD32—222no—
281D16—222no—
282C2×C16—114no—
283C2×C16—111no—
284C2×C16—111no—
285C2×C16—112no—
286C2×C16—224no—
287C2×C16—224no—
288C2×C16—222no—
289#107—112no—
290#107C22×D1112yes—
291#106—21no—
292#106—221no—
293#103—22no—
294#103—222no—
295#102—22no—
296#102—222no—
297C2×C11—22no—
298C2×C11—24no—
299C2×C11—161no—
300C2×C11C2×#46611yescharacteristic
301C2×C11C2×#50812yes—
302D11—161no—
303C24#432311yescharacteristic
304#41—42no—
305#41—42no—
306#41—442no—
307#41—442no—
308C2×Q8—21no—
309C2×Q8—221no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—41no—
313C2×D4—221no—
314C2×D4—442no—
315C2×D4—441no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—41no—
319C22×C4—441no—
320C22×C4#432311yescharacteristic
321C22×C4#432312yes—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1111yescharacteristic
324Q16—21no—
325Q16—21no—
326Q16—221no—
327Q16—221no—
328SD16—42no—
329SD16—442no—
330D8—21no—
331D8—21no—
332D8—221no—
333D8—221no—
334C2×C8—22no—
335C2×C8—24no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8D4×D1112yes—
339C2×C8#434112yes—
340C2×C8C2×C22⋊D1112yes—
341C2×C8C2×C22⋊D1111yescharacteristic
342C2×C8C23×D1111yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—42no—
345C4⋊C4—222no—
346C4⋊C4—442no—
347C22⋊C4—41no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C22⋊C4—441no—
351C22⋊C4—442no—
352C22⋊C4—442no—
353C42—41no—
354C42—441no—
355C16—112no—
356C16—112no—
357C16—222no—
358C11#3360011yescharacteristic, complemented, Sylow
359C23—24no—
360C23—22no—
361C23—41no—
362C23—441no—
363C23C2×#432312yes—
364C23C2×#432311yescharacteristic
365Q8—41no—
366Q8—41no—
367Q8—441no—
368Q8—441no—
369D4—41no—
370D4—41no—
371D4—84no—
372D4—82no—
373D4—441no—
374D4—441no—
375D4—884no—
376D4—882no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—82no—
384C2×C4—442no—
385C2×C4—441no—
386C2×C4—882no—
387C2×C4C2×#432312yes—
388C2×C4C2×#432311yescharacteristic
389C2×C4#6699212yes—
390C2×C4#6700312yes—
391C2×C4C22×C22⋊D1111yescharacteristic
392C8—22no—
393C8#6699212yes—
394C8C2×D4×D1111yescharacteristic
395C8C2×#434111yescharacteristic
396C22—28no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—82no—
401C22—81no—
402C22—882no—
403C22—881no—
404C22#1062265112yes—
405C22#1062280714yescomplemented
406C22C22×#432311yescharacteristic
407C4—22no—
408C4—82no—
409C4—81no—
410C4—882no—
411C4—881no—
412C4#1062265112yes—
413C4C2×#6699211yescharacteristic
414C4C2×#6700311yescharacteristic
415C2—24no—
416C2—22no—
417C2—161no—
418C2—1761no—
419C2C2×#1062265111yescharacteristic
420C2C2×#1062280712yes—
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3050C2
socleC22×C11C22×D8
hypercenter#3050D11
hypocenterC11#33600
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#10622807C2semidirect
2. C23×C11⋊C16C2semidirect
3. #13078197C2semidirect
4. #13070714C2semidirect
5. #13070710C2semidirect
6. #13070705C2semidirect
7. #13070700C2semidirect
8. #13070398C2semidirect
9. #13070323C2semidirect
10. #13070321C2semidirect
11. C11×#3050C2semidirect
23. C2×#66893C22semidirect
24. C2×#66892C22semidirect
25. C2×#66891C22semidirect
26. C2×#66890C22semidirect
37. #10622202C22semidirect
38. #10622200C22semidirect
39. #10622130C22semidirect
40. #10622129C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
89. C2×C11⋊C16D4semidirect
152. #3050D11semidirect
235. C22×C11#508semidirect
358. C11#33600semidirect
405. C22#10622807semidirect

Maximal subgroups

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

subgroupindex
C2×#106228072
C23×C11⋊C162
#130781972
#130707142
#130707102
#130707052
#130707002
#130703982
#130703232
#130703212
C11×#30502
#3360011