Finite Group Databasebeta

← #14908313

Subgroups — #14908313

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic, complemented
2C2×#10622753C211yesmaximal, characteristic, complemented
3#13078264C211yesmaximal, characteristic, complemented
4#13070731C212yesmaximal, complemented
5#13070717C212yesmaximal, complemented
6#13070714C212yesmaximal, complemented
7#13070700C212yesmaximal, complemented
8#13070402C211yesmaximal, characteristic, complemented
9#13070323C211yesmaximal, characteristic, complemented
10C2×#10622129C211yesmaximal, characteristic, complemented
11C11×#3061C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C2×C11×#131C2211yescharacteristic
14C11×#537—21no—
15#10623361—21no—
16C22×D88C2211yescharacteristic
17C11×#468—22no—
18C11×#467C2212yescomplemented
19C11×#466C2212yescomplemented
20C2×C11×#107C2211yescharacteristic
21C11×#417—21no—
22#10622806—24no—
23C2×#66892C2212yes—
24C2×#66890C2212yes—
25#10622753—24no—
26#10622748—22no—
27#10622744—21no—
28#10622728C2212yes—
29#10622728C2212yes—
30#10622719C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32C2×#66876C2212yescomplemented
33C22×C11⋊C16C2211yescharacteristic
34C22×C11⋊C16C2212yescomplemented
35#10622202C2211yescharacteristic, complemented
36#10622202C2211yescharacteristic, complemented
37#10622200C2211yescharacteristic, complemented
38#10622200C2211yescharacteristic, complemented
39#10622129C2212yes—
40#10622129C2212yes—
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×C11×#41—21no—
44C2×C11×#41D411yescharacteristic
45C22×D44—21no—
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C11×#131—22no—
52C11×#131—22no—
53C2×C11×M16D411yescharacteristic
54C2×C11×M16D412yes—
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—41no—
59C11×#121—22no—
60C11×#121—41no—
61C11×#121—42no—
62C2×C11×C4⋊C4—21no—
63#67000—41no—
64#66993—41no—
65#66990—42no—
66#66983—22no—
67#66983—22no—
68#66979—21no—
69C2×D88—22no—
70C2×D88—22no—
71C2×D88—21no—
72C2×D88C2312yes—
73C11×#107—21no—
74C11×#107C2312yes—
75C11×#103—22no—
76C11×#102—22no—
77#66892—24no—
78#66890—24no—
79#66885—22no—
80#66885—22no—
81#66882C2311yescharacteristic
82#66882C2311yescharacteristic
83#66881—21no—
84#66876—24no—
85#66876D414yescomplemented
86C2×C11⋊C16—22no—
87C2×C11⋊C16—24no—
88C2×C11⋊C16C2311yescharacteristic
89C2×C11⋊C16C2311yescharacteristic
90C2×C11⋊C16C2312yes—
91#33612—111nomaximal, Sylow
92C23×D11—41no—
93C11×#41—22no—
94C11×#41—22no—
95C11×#41—42no—
96C11×#41—42no—
97C2×Q8×C11—21no—
98C2×Q8×C11D811yescharacteristic
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C2×D4×C11—42no—
102C2×D4×C11D812yes—
103C2×D4×C11D811yescharacteristic
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C2×C22⋊D11—42no—
109C2×C22⋊D11—42no—
110C2×D44—22no—
111C2×D44—42no—
112C2×D44—41no—
113C2×D44—42no—
114C11×Q16—21no—
115C11×Q16—21no—
116C11×SD16—42no—
117C11×D8—21no—
118C11×D8—21no—
119C11×M16—24no—
120C11×M16—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11C2×D412yes—
124C2×C8×C11C2×D412yes—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11#4112yes—
127C2×C8×C11C2411yescharacteristic
128C11×C4⋊C4—22no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—42no—
131C11×C22⋊C4—42no—
132C11×C22⋊C4—42no—
133C22⋊Dic11—41no—
134(C2×D11)⋊C4—42no—
135(C2×D11)⋊C4—42no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4×Dic11—41no—
139D88—22no—
140D88—22no—
141D88—42no—
142C11⋊C16—21no—
143C11⋊C16—21no—
144C11⋊C16C2×D414yes—
145C2×#509—111no—
146C2×#504—111no—
147#3061D1111yescharacteristic, complemented
148#3058—111no—
149#2220—112no—
150#2218—112no—
151#2217—112no—
152#2215—112no—
153#2159—111no—
154#2138—111no—
155C2×#357—111no—
156C23×C11—41no—
157C23×C11C2×D812yes—
158C23×C11C2×D811yescharacteristic
159C22×D11—42no—
160C22×D11—82no—
161C22×D11—161no—
162C22×D11—161no—
163Q8×C11—22no—
164Q8×C11—41no—
165Q8×C11—41no—
166D4×C11—24no—
167D4×C11—22no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—82no—
171D4×C11—162no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—82no—
177C2×C4×C11—161no—
178C2×C4×C11#12112yes—
179C2×C4×C11C2×D812yes—
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11#13512yes—
182C2×C4×C11C22×D411yescharacteristic
183C22⋊D11—162no—
184C22⋊D11—162no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187D44—42no—
188D44—42no—
189D44—82no—
190C8×C11—22no—
191C8×C11#12112yes—
192C8×C11C22×D411yescharacteristic
193C8×C11C2×#4111yescharacteristic
194C2×#135C2×D1111yescharacteristic
195C22×D8—111no—
196C2×#131C2×D1111yescharacteristic
197#537—21no—
198#535—221no—
199#509—224no—
200C2×SD32—112no—
201C2×D16—112no—
202#504—224no—
203C2×M32—111no—
204C2×M32—112no—
205C22×C16—111no—
206C22×C16—112no—
207#469—222no—
208#468—22no—
209#467C2×D1112yescomplemented
210#466—112no—
211#466—112no—
212#466C2×D1112yescomplemented
213#427—111no—
214C2×#107C2×D1111yescharacteristic
215#418—221no—
216#417—21no—
217#367—112no—
218#366—112no—
219#358—111no—
220#358—111no—
221#357—111no—
222#357—111no—
223#357—112no—
224#357—112no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11#46612yes—
234C22×C11C22×D811yescharacteristic
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—82no—
238C2×D11—164no—
239C4×C11—22no—
240C4×C11—82no—
241C4×C11—81no—
242C4×C11#46612yes—
243C4×C11C2×#12111yescharacteristic
244C4×C11C2×#13511yescharacteristic
245Dic11—81no—
246Dic11—81no—
247C2×#41—21no—
248C2×#41C22⋊D1111yescharacteristic
249C22×D4—221no—
250#135—22no—
251#135—22no—
252C2×Q16C22×D1111yescharacteristic
253C2×SD16—21no—
254C2×D8—112no—
255C2×D8—222no—
256C2×D8—222no—
257C2×D8—221no—
258C2×D8C22×D1111yescharacteristic
259#131—22no—
260#131—22no—
261C2×M16C22⋊D1111yescharacteristic
262C2×M16C22⋊D1112yes—
263C22×C8C22×D1112yes—
264C22×C8C22×D1111yescharacteristic
265#127—441no—
266#124—441no—
267C22⋊Q8—22no—
268C22⋊Q8—41no—
269#121—22no—
270#121—41no—
271#121—42no—
272#121—222no—
273#121—222no—
274#120—442no—
275#117—221no—
276C2×C4⋊C4—21no—
277SD32—224no—
278D16—224no—
279M32—114no—
280M32—224no—
281C2×C16—112no—
282C2×C16—111no—
283C2×C16—111no—
284C2×C16—224no—
285C2×C16—222no—
286#107—21no—
287#107—111no—
288#107—111no—
289#107C22×D1112yes—
290#106—221no—
291#103—22no—
292#102—22no—
293#102—222no—
294#102—222no—
295C2×C11—22no—
296C2×C11—42no—
297C2×C11—161no—
298C2×C11C2×#46611yescharacteristic
299C2×C11#341511yescharacteristic
300C2×C11#341611yescharacteristic
301D11—162no—
302C24—441no—
303#41—22no—
304#41—22no—
305#41—42no—
306#41—42no—
307C2×Q8—21no—
308C2×Q8#432311yescharacteristic
309C2×D4—21no—
310C2×D4—41no—
311C2×D4—42no—
312C2×D4—222no—
313C2×D4—442no—
314C2×D4—442no—
315C2×D4—441no—
316C2×D4—442no—
317C2×D4—442no—
318C2×D4#432312yes—
319C2×D4#432311yescharacteristic
320C22×C4—41no—
321C22×C4—41no—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1111yescharacteristic
324Q16—21no—
325Q16—21no—
326SD16—42no—
327D8—21no—
328D8—21no—
329D8—222no—
330D8—222no—
331D8—442no—
332M16—22no—
333M16—24no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8D4×D1112yes—
337C2×C8#434112yes—
338C2×C8C2×C22⋊D1112yes—
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C23×D1111yescharacteristic
341C4⋊C4—22no—
342C4⋊C4—41no—
343C4⋊C4—42no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4—441no—
349C22⋊C4—442no—
350C22⋊C4—442no—
351C42—441no—
352C16—114no—
353C16—221no—
354C16—221no—
355C11#3361211yescharacteristic, complemented, Sylow
356C23—41no—
357C23—442no—
358C23—882no—
359C23—1761no—
360C23—1761no—
361C23C2×#432312yes—
362C23C2×#432311yescharacteristic
363Q8—22no—
364Q8—41no—
365Q8—41no—
366D4—24no—
367D4—22no—
368D4—41no—
369D4—41no—
370D4—82no—
371D4—162no—
372D4—442no—
373D4—442no—
374D4—882no—
375D4—1762no—
376D4—1762no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—82no—
382C2×C4—161no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4C2×#432312yes—
386C2×C4C2×#432311yescharacteristic
387C2×C4#6699212yes—
388C2×C4#6700312yes—
389C2×C4C22×C22⋊D1111yescharacteristic
390C8—22no—
391C8#6699212yes—
392C8C2×D4×D1111yescharacteristic
393C8C2×#434111yescharacteristic
394C22—21no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—882no—
403C22—882no—
404C22—882no—
405C22—1764no—
406C22#1062265112yes—
407C22C22×#432311yescharacteristic
408C4—22no—
409C4—82no—
410C4—81no—
411C4—881no—
412C4—881no—
413C4#1062265112yes—
414C4C2×#6699211yescharacteristic
415C4C2×#6700311yescharacteristic
416C2—22no—
417C2—42no—
418C2—161no—
419C2—1762no—
420C2C2×#1062265111yescharacteristic
421C2#1308175511yescharacteristic
422C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3061C2
socleC22×C11C22×D8
hypercenter#3061D11
hypocenterC11#33612
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3061

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. C2×#10622753C2semidirect
3. #13078264C2semidirect
4. #13070731C2semidirect
5. #13070717C2semidirect
6. #13070714C2semidirect
7. #13070700C2semidirect
8. #13070402C2semidirect
9. #13070323C2semidirect
10. C2×#10622129C2semidirect
11. C11×#3061C2semidirect
18. C11×#467C22semidirect
19. C11×#466C22semidirect
32. C2×#66876C22semidirect
34. C22×C11⋊C16C22semidirect
35. #10622202C22semidirect
36. #10622202C22semidirect
37. #10622200C22semidirect
38. #10622200C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
85. #66876D4semidirect
147. #3061D11semidirect
209. #467C2×D11semidirect
212. #466C2×D11semidirect
355. C11#33612semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
C2×#106227532
#130782642
#130707312
#130707172
#130707142
#130707002
#130704022
#130703232
C2×#106221292
C11×#30612
#3361211