Finite Group Databasebeta

← #14907184

Subgroups — #14907184

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081750C211yesmaximal, characteristic
2C2×#10622313C211yesmaximal, characteristic, complemented
3#13070500C214yesmaximal, complemented
4#13070495C214yesmaximal, complemented
5#13070410C211yesmaximal, characteristic, complemented
6#13070344C211yesmaximal, characteristic, complemented
7#13070343C211yesmaximal, characteristic, complemented
8C4×#66876C211yesmaximal, characteristic, complemented
9C2×C11×#443C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11C2×C11×#131—21no—
12C2×#66957C2211yescharacteristic
13C2×#66954—21no—
14C11×#443—21no—
15C11×#443—21no—
16C11×#443C2212yescomplemented
17C11×#443C2212yescomplemented
18C2×C11×#108C2211yescharacteristic
19C2×C11×#104—21no—
20C2×C4×C8×C11C2211yescharacteristic
21#10622808C412yescomplemented
22#10622807C2214yes—
23#10622806C412yescomplemented
24#10622792C412yescomplemented
25#10622760C412yescomplemented
26C2×#66883C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28C2×#66876C2211yescharacteristic
29C2×#66869—21no—
30#10622313—21no—
31#10622313—21no—
32#10622313C2212yescomplemented
33#10622313C2212yescomplemented
34#10622205C2214yescomplemented
35#10622135C2214yescomplemented
36#10622131C2214yescomplemented
37#10622099C2212yescomplemented
38C4×C11⋊C16C2212yescomplemented
39C2×C11×#41—21no—
40C2×#4339—21no—
41C11×#135—21no—
42C11×#135—21no—
43C11×#135C2×C412yes—
44C11×#135C2312yes—
45C2×C11×Q16C2×C411yescharacteristic
46C2×C11×SD16—21no—
47C2×C11×D8C2×C411yescharacteristic
48C11×#131—22no—
49C11×#131—22no—
50C11×#131—41no—
51C11×#131—41no—
52C2×C11×M16—21no—
53C2×C11×M16—41no—
54C22×C8×C11—41no—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C2×C42×C11D411yescharacteristic
58C2×#4318—21no—
59C2×Dic44C2×C411yescharacteristic
60#66957—21no—
61#66957—21no—
62#66957C2×C412yes—
63#66957C2312yes—
64C2×D88C2×C411yescharacteristic
65C2×#4314—21no—
66#66954—22no—
67#66954—22no—
68#66954—41no—
69#66954—41no—
70C2×#4313—41no—
71C2×C8×D11—41no—
72C11×#108—21no—
73C11×#108C2312yes—
74C11×#104—22no—
75C11×#104—22no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80#66893C2×C414yescomplemented
81#66892C2×C414yescomplemented
82#66891C2×C414yescomplemented
83#66890C2×C414yescomplemented
84#66883—21no—
85#66883C2312yes—
86#66876—21no—
87#66876—21no—
88#66876C2×C412yes—
89#66876C2×C412yes—
90C2×C11⋊C16C2312yes—
91C2×C11⋊C16C2312yes—
92#66869—22no—
93#66869—22no—
94#33463—111nomaximal, Sylow
95C11×#41—22no—
96C11×#41—22no—
97C11×#41—41no—
98C11×#41—41no—
99C2×Q8×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—41no—
102C22×C4×C11—21no—
103C22×C4×C11—41no—
104C22×C4×C11C2×D411yescharacteristic
105C2×C22⋊D11—41no—
106#4339—22no—
107#4339—22no—
108#4339—41no—
109#4339—41no—
110C2×D44—21no—
111C2×C4×D11—41no—
112C2×Dic22—21no—
113C11×Q16—21no—
114C11×Q16C22×C412yes—
115C11×SD16—22no—
116C11×SD16—22no—
117C11×D8—21no—
118C11×D8C22×C412yes—
119C11×M16—22no—
120C11×M16—42no—
121C11×M16—42no—
122C11×M16—41no—
123C2×C8×C11—42no—
124C2×C8×C11—42no—
125C2×C8×C11—41no—
126C2×C8×C11D811yescharacteristic
127C2×C8×C11D811yescharacteristic
128C2×C8×C11D811yescharacteristic
129C2×C8×C11D811yescharacteristic
130C2×C8×C11C22×C411yescharacteristic
131C2×C8×C11C22×C411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11#4111yescharacteristic
136C2×C8×C11#4111yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C42×C11—21no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141#4318—22no—
142#4318—41no—
143C2×C11⋊C8—41no—
144Dic44—21no—
145Dic44C22×C412yes—
146D88—21no—
147D88C22×C412yes—
148#4314—22no—
149#4314—22no—
150#4313—42no—
151#4313—42no—
152C8×D11—42no—
153C8×D11—42no—
154C11⋊C16—22no—
155C11⋊C16C22×C414yes—
156#3414—111no—
157C2×#443—111no—
158C2×#443D1111yescharacteristic, complemented
159#2179—114no—
160#2178—114no—
161#2161—111no—
162#2143—111no—
163#2143—111no—
164C4×M32—111no—
165C23×C11—41no—
166C23×C11#13511yescharacteristic
167C22×D11—41no—
168Q8×C11—22no—
169Q8×C11—41no—
170D4×C11—22no—
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—41no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C4×D411yescharacteristic
181C2×C4×C11C4×D411yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11#13511yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—42no—
187C22⋊D11—42no—
188C2×Dic11—41no—
189D44—22no—
190D44—41no—
191C4×D11—42no—
192C4×D11—42no—
193Dic22—22no—
194Dic22—41no—
195C8×C11—42no—
196C8×C11C4×D411yescharacteristic
197C8×C11C4×D411yescharacteristic
198C8×C11C2×D811yescharacteristic
199C8×C11C2×D811yescharacteristic
200C8×C11C2×D811yescharacteristic
201C8×C11C2×D811yescharacteristic
202C8×C11C23×C411yescharacteristic
203C8×C11C2×#4111yescharacteristic
204C11⋊C8—42no—
205C2×#135—111no—
206C2×#135C2×D1111yescharacteristic
207C2×#131—21no—
208C2×#131—221no—
209#510—112no—
210#510—112no—
211#509—112no—
212#509—112no—
213#508—114no—
214C2×M32—111no—
215C2×M32—111no—
216#443—21no—
217#443—21no—
218#443—112no—
219#443—112no—
220#443—221no—
221#443—221no—
222#443C2×D1112yescomplemented
223#443C2×D1112yescomplemented
224C2×#108—111no—
225C2×#108C2×D1111yescharacteristic
226C2×#104—21no—
227C2×#104—221no—
228C2×C4×C8C2×D1111yescharacteristic
229#368—114no—
230#359—114no—
231#359—114no—
232#346—112no—
233C4×C16—112no—
234C22×C11—41no—
235C22×C11—42no—
236C22×C11—82no—
237C22×C11C4×D811yescharacteristic
238C22×C11C4×D811yescharacteristic
239C22×C11C2×#13511yescharacteristic
240C2×D11—42no—
241C2×D11—82no—
242C4×C11—22no—
243C4×C11—41no—
244C4×C11—42no—
245C4×C11C4×D811yescharacteristic
246C4×C11C4×D811yescharacteristic
247C4×C11C2×C4×D411yescharacteristic
248C4×C11C22×D811yescharacteristic
249Dic11—42no—
250C2×#41—21no—
251C2×#41—221no—
252#135—21no—
253#135—21no—
254#135—112no—
255#135—112no—
256#135—221no—
257#135—221no—
258#135C4×D1112yes—
259#135C22×D1112yes—
260C2×Q16—111no—
261C2×Q16C4×D1111yescharacteristic
262C2×SD16—21no—
263C2×SD16—221no—
264C2×D8—111no—
265C2×D8C4×D1111yescharacteristic
266#131—22no—
267#131—22no—
268#131—41no—
269#131—41no—
270#131—222no—
271#131—222no—
272#131—441no—
273#131—441no—
274C2×M16—21no—
275C2×M16—41no—
276C2×M16—221no—
277C2×M16—441no—
278C22×C8—41no—
279C22×C8—441no—
280C22×C8C22⋊D1111yescharacteristic
281C22×C8C22×D1111yescharacteristic
282C2×C42C22⋊D1111yescharacteristic
283Q32—114no—
284SD32—114no—
285SD32—114no—
286D16—114no—
287M32—112no—
288M32—112no—
289M32—221no—
290M32—221no—
291C2×C16—112no—
292C2×C16—112no—
293#108—21no—
294#108—112no—
295#108—221no—
296#108C22×D1112yes—
297#104—22no—
298#104—22no—
299#104—222no—
300#104—222no—
301C4×C8C22⋊D1111yescharacteristic
302C4×C8C22⋊D1111yescharacteristic
303C4×C8C22×D1111yescharacteristic
304C4×C8C22×D1111yescharacteristic
305C2×C11—21no—
306C2×C11—21no—
307C2×C11—21no—
308C2×C11—82no—
309C2×C11C2×C4×D811yescharacteristic
310D11—82no—
311#41—22no—
312#41—22no—
313#41—41no—
314#41—41no—
315#41—222no—
316#41—222no—
317#41—441no—
318#41—441no—
319C2×Q8—21no—
320C2×Q8—221no—
321C2×D4—21no—
322C2×D4—41no—
323C2×D4—221no—
324C2×D4—441no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—441no—
328C22×C4C2×C22⋊D1111yescharacteristic
329Q16—21no—
330Q16—112no—
331Q16—221no—
332Q16C2×C4×D1112yes—
333SD16—22no—
334SD16—22no—
335SD16—222no—
336SD16—222no—
337D8—21no—
338D8—112no—
339D8—221no—
340D8C2×C4×D1112yes—
341M16—22no—
342M16—41no—
343M16—42no—
344M16—42no—
345M16—222no—
346M16—441no—
347M16—442no—
348M16—442no—
349C2×C8—41no—
350C2×C8—42no—
351C2×C8—42no—
352C2×C8—441no—
353C2×C8—442no—
354C2×C8—442no—
355C2×C8#432311yescharacteristic
356C2×C8#432311yescharacteristic
357C2×C8#432311yescharacteristic
358C2×C8#432311yescharacteristic
359C2×C8C2×C4×D1111yescharacteristic
360C2×C8C2×C4×D1111yescharacteristic
361C2×C8#433911yescharacteristic
362C2×C8#433911yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C2×C8C2×C22⋊D1111yescharacteristic
366C2×C8C23×D1111yescharacteristic
367C42—21no—
368C42C2×C22⋊D1111yescharacteristic
369C42C2×C22⋊D1111yescharacteristic
370C16—114no—
371C16—222no—
372C11#3346311yescharacteristic, complemented, Sylow
373C23—41no—
374C23—441no—
375C23#6700311yescharacteristic
376Q8—22no—
377Q8—41no—
378Q8—222no—
379Q8—441no—
380D4—22no—
381D4—42no—
382D4—42no—
383D4—41no—
384D4—222no—
385D4—442no—
386D4—442no—
387D4—441no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—441no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4C4×C22⋊D1111yescharacteristic
398C2×C4C4×C22⋊D1111yescharacteristic
399C2×C4C2×#432311yescharacteristic
400C2×C4C2×#432311yescharacteristic
401C2×C4#6700311yescharacteristic
402C2×C4C22×C22⋊D1111yescharacteristic
403C8—42no—
404C8—442no—
405C8C4×C22⋊D1111yescharacteristic
406C8C4×C22⋊D1111yescharacteristic
407C8C2×#432311yescharacteristic
408C8C2×#432311yescharacteristic
409C8C2×#432311yescharacteristic
410C8C2×#432311yescharacteristic
411C8C22×C4×D1111yescharacteristic
412C8C2×#433911yescharacteristic
413C22—41no—
414C22—42no—
415C22—82no—
416C22—442no—
417C22—882no—
418C22C4×#432311yescharacteristic
419C22C4×#432311yescharacteristic
420C22C2×#6700311yescharacteristic
421C4—22no—
422C4—41no—
423C4—42no—
424C4—442no—
425C4C4×#432311yescharacteristic
426C4C4×#432311yescharacteristic
427C4C2×C4×C22⋊D1111yescharacteristic
428C4C22×#432311yescharacteristic
429C2—21no—
430C2—21no—
431C2—21no—
432C2—82no—
433C2—882no—
434C2C2×C4×#432311yescharacteristic
subgroupG/H
centerC8C2×#4323
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#443C2
socleC2×C11C2×C4×D8
prime radical#13081750C2
cosocleC2×C8×C11C24
hypercenterC2×#443D11
hypocenterC11#33463
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#10622313C2semidirect
3. #13070500C2semidirect
4. #13070495C2semidirect
5. #13070410C2semidirect
6. #13070344C2semidirect
7. #13070343C2semidirect
8. C4×#66876C2semidirect
9. C2×C11×#443C2semidirect
16. C11×#443C22semidirect
17. C11×#443C22semidirect
21. #10622808C4semidirect
23. #10622806C4semidirect
24. #10622792C4semidirect
25. #10622760C4semidirect
32. #10622313C22semidirect
33. #10622313C22semidirect
34. #10622205C22semidirect
35. #10622135C22semidirect
36. #10622131C22semidirect
37. #10622099C22semidirect
38. C4×C11⋊C16C22semidirect
80. #66893C2×C4semidirect
81. #66892C2×C4semidirect
82. #66891C2×C4semidirect
83. #66890C2×C4semidirect
158. C2×#443D11semidirect
222. #443C2×D11semidirect
223. #443C2×D11semidirect
372. C11#33463semidirect

Maximal subgroups

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

subgroupindex
#130817502
C2×#106223132
#130705002
#130704952
#130704102
#130703442
#130703432
C4×#668762
C2×C11×#4432
#3346311