Finite Group Databasebeta

← #14909199

Subgroups — #14909199

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2C2×#10622760C211yesmaximal, characteristic, complemented
3C2×#10622806C211yesmaximal, characteristic, complemented
4#13079040C211yesmaximal, characteristic, complemented
5C2×#10622764C211yesmaximal, characteristic, complemented
6#13070881C212yesmaximal, complemented
7#13070879C212yesmaximal, complemented
8#13070870C212yesmaximal, complemented
9#13070864C212yesmaximal, complemented
10M32×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#509C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14#10623363—21no—
15C2×#67003—21no—
16C2×#66993—21no—
17C22×#4323—21no—
18C2×#66957C2211yescharacteristic
19C22×D88C2211yescharacteristic
20C11×#509—24no—
21C2×C11×SD32C2212yescomplemented
22C2×C11×D16C2212yescomplemented
23C2×C11×M32C2211yescharacteristic
24#10622806—24no—
25#10622804C2211yescharacteristic, complemented
26#10622794C2211yescharacteristic, complemented
27C2×#66892C2212yescomplemented
28#10622788—21no—
29#10622781—21no—
30#10622768C2211yescharacteristic, complemented
31#10622764—21no—
32#10622764—21no—
33#10622764C2212yes—
34#10622764C2212yes—
35#10622764C2211yescharacteristic, complemented
36C2×#66891C2212yescomplemented
37#10622760—24no—
38C2×#66890C2212yescomplemented
39C2×#66890C2212yescomplemented
40C2×C8×Dic11C2211yescharacteristic
41C2×#66876C2211yescharacteristic
42#10622521—24no—
43C2×#66864C2212yescomplemented
44C2×D176C2212yescomplemented
45#10622140C2212yescomplemented
46C16×Dic11C2212yescomplemented
47C2×C11×#41—21no—
48C22×D4×C11—21no—
49C22×C22⋊D11—42no—
50C2×#4339—21no—
51C22×D44—21no—
52C11×#135—22no—
53C11×#135—22no—
54C2×C11×Q16C2311yescharacteristic
55C2×C11×SD16—21no—
56C2×C11×D8—22no—
57C2×C11×D8—22no—
58C2×C11×D8—21no—
59C2×C11×D8C2311yescharacteristic
60C2×C11×D8C2312yes—
61C22×C8×C11C2311yescharacteristic
62#67003—44no—
63#67000—21no—
64#66997—21no—
65C2×#4326—21no—
66C2×#4325—21no—
67#66993—22no—
68#66993—22no—
69#66993—21no—
70#66993—42no—
71#66992—42no—
72#66989—21no—
73C2×#4324—21no—
74C2×#4323—22no—
75C2×#4323—22no—
76C2×#4323—21no—
77C2×#4323—44no—
78C4×C22⋊D11—42no—
79C2×C4×Dic11D411yescharacteristic
80C22×C11⋊C8D411yescharacteristic
81C2×Dic44C2311yescharacteristic
82#66957—22no—
83#66957—22no—
84C2×D88—22no—
85C2×D88—22no—
86C2×D88—21no—
87C2×D88C2311yescharacteristic
88C2×D88C2312yes—
89C2×#4314—21no—
90C11×SD32—24no—
91C11×D16—24no—
92C11×M32D414yescomplemented
93C2×C11×C16C2312yes—
94#66892—24no—
95#66891—24no—
96#66890—24no—
97#66890—24no—
98C8×Dic11D411yescharacteristic
99C8×Dic11D411yescharacteristic
100C8×Dic11C2311yescharacteristic
101C8×Dic11C2311yescharacteristic
102#66876D414yescomplemented
103C2×C11⋊C16C2312yes—
104#66864—24no—
105D176—24no—
106#33717—111nomaximal, Sylow
107C24×C11—41no—
108C23×D11—41no—
109C11×#41—42no—
110C11×#41—42no—
111C2×Q8×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—41no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C2×C22⋊D11—42no—
121C2×C22⋊D11—44no—
122C2×C22⋊D11—44no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—88no—
125C22×Dic11D812yes—
126#4339—42no—
127#4339—42no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—42no—
131C2×D44—41no—
132C2×D44—42no—
133C2×C4×D11—41no—
134C2×Dic22—21no—
135C11×Q16—21no—
136C11×Q16—21no—
137C11×SD16—42no—
138C11×D8—21no—
139C11×D8—22no—
140C11×D8—21no—
141C11×D8—22no—
142C11×D8—42no—
143C2×C8×C11C2×D412yes—
144C2×C8×C11C2×D412yes—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C22⋊Dic11—42no—
148#4326—42no—
149#4325—42no—
150#4324—42no—
151#4323—44no—
152#4323—44no—
153#4323—42no—
154(C2×D11)⋊C4—42no—
155Dic11⋊C4—42no—
156C4×Dic11D812yes—
157C4×Dic11C2×D411yescharacteristic
158C4×Dic11C2×D411yescharacteristic
159C2×C11⋊C8D814yes—
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162Dic44—21no—
163Dic44—21no—
164D88—21no—
165D88—22no—
166D88—21no—
167D88—22no—
168D88—42no—
169#4314—42no—
170C11×C16C2×D414yescomplemented
171C11⋊C16C2×D414yescomplemented
172C2×#509—111no—
173C2×#509—111no—
174C2×#509—111no—
175C2×#509D1111yescharacteristic, complemented
176#3147—111no—
177C2×#493—111no—
178#2250—112no—
179#2250—112no—
180#2248—112no—
181#2246—112no—
182C4×M32—111no—
183C23×C11—41no—
184C23×C11—42no—
185C23×C11—84no—
186C23×C11—82no—
187C23×C11C2×D811yescharacteristic
188C22×D11—41no—
189C22×D11—42no—
190C22×D11—84no—
191C22×D11—82no—
192Q8×C11—41no—
193Q8×C11—41no—
194D4×C11—42no—
195D4×C11—41no—
196D4×C11—42no—
197D4×C11—41no—
198D4×C11—82no—
199D4×C11—82no—
200C2×C4×C11—41no—
201C2×C4×C11—82no—
202C2×C4×C11#12712yes—
203C2×C4×C11C2×D812yes—
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C22⋊D11—88no—
207C22⋊D11—82no—
208C22⋊D11—84no—
209C22⋊D11—88no—
210C2×Dic11—24no—
211C2×Dic11—41no—
212C2×Dic11C2×D812yes—
213C2×Dic11C2×D812yes—
214D44—41no—
215D44—42no—
216D44—42no—
217D44—41no—
218D44—82no—
219C4×D11—82no—
220Dic22—41no—
221Dic22—41no—
222C8×C11#12712yes—
223C8×C11C22×D411yescharacteristic
224C8×C11C22×D411yescharacteristic
225C11⋊C8C2×D812yes—
226C11⋊C8C2×D812yes—
227C2×#135—111no—
228C2×#135—221no—
229C2×#135C2×D1111yescharacteristic
230C22×D8—111no—
231C22×D8—221no—
232C22×D8C2×D1111yescharacteristic
233#532—221no—
234C2×#127—221no—
235#509—24no—
236#509—224no—
237#509—224no—
238#509—224no—
239C2×SD32—112no—
240C2×SD32—112no—
241C2×SD32—112no—
242C2×SD32C2×D1112yescomplemented
243C2×D16—112no—
244C2×D16—112no—
245C2×D16—112no—
246C2×D16C2×D1112yescomplemented
247C2×M32—111no—
248C2×M32C2×D1111yescharacteristic
249#495—111no—
250#495—111no—
251#495—221no—
252#494—111no—
253#493—112no—
254#493—112no—
255#493—111no—
256#493—221no—
257#493—221no—
258#492—221no—
259C2×C4×C8—111no—
260#346—112no—
261C4×C16—112no—
262C22×C11—22no—
263C22×C11—81no—
264C22×C11—82no—
265C22×C11—84no—
266C22×C11—82no—
267C22×C11—164no—
268C22×C11#49312yes—
269C22×C11C22×D811yescharacteristic
270C2×D11—82no—
271C2×D11—81no—
272C2×D11—84no—
273C2×D11—82no—
274C2×D11—164no—
275C4×C11—81no—
276C4×C11#49312yes—
277C4×C11C2×#12711yescharacteristic
278C4×C11C22×D811yescharacteristic
279Dic11—22no—
280Dic11—81no—
281Dic11#50914yescomplemented
282C2×#41—21no—
283C2×#41—221no—
284C22×D4—21no—
285C22×D4—221no—
286C22×D4—442no—
287#135—22no—
288#135—22no—
289#135—222no—
290#135—222no—
291#135—444no—
292C2×Q16—111no—
293C2×Q16—221no—
294C2×Q16C22×D1111yescharacteristic
295C2×SD16—21no—
296C2×SD16—221no—
297C2×SD16—221no—
298C2×SD16—221no—
299C2×D8—22no—
300C2×D8—21no—
301C2×D8—22no—
302C2×D8—112no—
303C2×D8—111no—
304C2×D8—222no—
305C2×D8—222no—
306C2×D8—221no—
307C2×D8—222no—
308C2×D8—221no—
309C2×D8—222no—
310C2×D8—444no—
311C2×D8C22×D1112yes—
312C2×D8C22×D1111yescharacteristic
313C22×C8—111no—
314C22×C8C22×D1111yescharacteristic
315C4⋊Q8—221no—
316#127—222no—
317#127—222no—
318#127—221no—
319#127—442no—
320#124—221no—
321#124—221no—
322#121—442no—
323C4×D4—442no—
324C2×C42—111no—
325SD32—24no—
326SD32—224no—
327SD32—224no—
328SD32—224no—
329D16—24no—
330D16—224no—
331D16—224no—
332D16—224no—
333M32—114no—
334M32C22⋊D1114yescomplemented
335C2×C16—112no—
336C2×C16C22×D1112yes—
337C4×C8—111no—
338C4×C8—111no—
339C4×C8—111no—
340C4×C8—111no—
341C2×C11—22no—
342C2×C11—161no—
343C2×C11—162no—
344C2×C11C2×#49311yescharacteristic
345C2×C11C2×#50912yes—
346D11—161no—
347D11—162no—
348C24—41no—
349C24—441no—
350#41—42no—
351#41—42no—
352#41—442no—
353#41—442no—
354C2×Q8—21no—
355C2×Q8—221no—
356C2×D4—21no—
357C2×D4—22no—
358C2×D4—41no—
359C2×D4—42no—
360C2×D4—41no—
361C2×D4—42no—
362C2×D4—221no—
363C2×D4—222no—
364C2×D4—442no—
365C2×D4—444no—
366C2×D4—444no—
367C2×D4—441no—
368C2×D4—442no—
369C2×D4—441no—
370C2×D4—442no—
371C2×D4—888no—
372C22×C4—41no—
373C22×C4—112no—
374C22×C4—441no—
375C22×C4D4×D1111yescharacteristic
376Q16—21no—
377Q16—21no—
378Q16—221no—
379Q16—221no—
380Q16—442no—
381SD16—42no—
382SD16—442no—
383SD16—442no—
384SD16—442no—
385D8—21no—
386D8—22no—
387D8—21no—
388D8—22no—
389D8—42no—
390D8—221no—
391D8—222no—
392D8—221no—
393D8—222no—
394D8—444no—
395D8—444no—
396D8—442no—
397D8—442no—
398C2×C8—114no—
399C2×C8—111no—
400C2×C8—111no—
401C2×C8D4×D1111yescharacteristic
402C2×C8D4×D1112yes—
403C2×C8C2×C22⋊D1112yes—
404C2×C8C23×D1111yescharacteristic
405C4⋊C4—442no—
406C22⋊C4—442no—
407C22⋊C4—442no—
408C42—112no—
409C42—111no—
410C42—111no—
411C16—114no—
412C16C2×C22⋊D1114yescomplemented
413C11#3371711yescharacteristic, complemented, Sylow
414C23—41no—
415C23—42no—
416C23—84no—
417C23—82no—
418C23—441no—
419C23—442no—
420C23—884no—
421C23—882no—
422C23D8×D1111yescharacteristic
423Q8—41no—
424Q8—41no—
425Q8—441no—
426Q8—441no—
427D4—42no—
428D4—41no—
429D4—42no—
430D4—41no—
431D4—82no—
432D4—82no—
433D4—442no—
434D4—441no—
435D4—442no—
436D4—441no—
437D4—888no—
438D4—884no—
439D4—888no—
440D4—882no—
441D4—882no—
442C2×C4—41no—
443C2×C4—82no—
444C2×C4—112no—
445C2×C4—112no—
446C2×C4—224no—
447C2×C4—441no—
448C2×C4—882no—
449C2×C4D8×D1111yescharacteristic
450C2×C4D8×D1112yes—
451C2×C4#6699312yes—
452C2×C4C2×D4×D1111yescharacteristic
453C8—112no—
454C8—112no—
455C8#6699312yes—
456C8C2×D4×D1111yescharacteristic
457C8C22×C22⋊D1111yescharacteristic
458C22—22no—
459C22—84no—
460C22—82no—
461C22—81no—
462C22—82no—
463C22—164no—
464C22—884no—
465C22—882no—
466C22—881no—
467C22—882no—
468C22—1764no—
469C22#1062276412yes—
470C22C2×D8×D1111yescharacteristic
471C4—81no—
472C4—114no—
473C4—222no—
474C4—881no—
475C4#1062276412yes—
476C4C2×D8×D1111yescharacteristic
477C4C2×#6699311yescharacteristic
478C2—22no—
479C2—162no—
480C2—161no—
481C2—1762no—
482C2—1761no—
483C2C2×#1062276411yescharacteristic
484C2D11×#50912yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#509C2
socleC22×C11C22×D8
hypercenterC2×#509D11
hypocenterC11#33717
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. C2×#10622760C2semidirect
3. C2×#10622806C2semidirect
4. #13079040C2semidirect
5. C2×#10622764C2semidirect
6. #13070881C2semidirect
7. #13070879C2semidirect
8. #13070870C2semidirect
9. #13070864C2semidirect
10. M32×Dic11C2semidirect
11. C2×C11×#509C2semidirect
21. C2×C11×SD32C22semidirect
22. C2×C11×D16C22semidirect
25. #10622804C22semidirect
26. #10622794C22semidirect
27. C2×#66892C22semidirect
30. #10622768C22semidirect
35. #10622764C22semidirect
36. C2×#66891C22semidirect
38. C2×#66890C22semidirect
39. C2×#66890C22semidirect
43. C2×#66864C22semidirect
44. C2×D176C22semidirect
45. #10622140C22semidirect
46. C16×Dic11C22semidirect
92. C11×M32D4semidirect
102. #66876D4semidirect
170. C11×C16C2×D4semidirect
171. C11⋊C16C2×D4semidirect
175. C2×#509D11semidirect
242. C2×SD32C2×D11semidirect
246. C2×D16C2×D11semidirect
281. Dic11#509semidirect
334. M32C22⋊D11semidirect
412. C16C2×C22⋊D11semidirect
413. C11#33717semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
C2×#106227602
C2×#106228062
#130790402
C2×#106227642
#130708812
#130708792
#130708702
#130708642
M32×Dic112
C2×C11×#5092
#3371711