Finite Group Databasebeta

← #14732344

Subgroups — #14732344

Order 2816.

1224 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic, complemented
4#13067851C214yesmaximal, complemented
5#13067705C214yesmaximal, complemented
6#13067288C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067007C211yesmaximal, characteristic, complemented
9C2×C11×#547C211yesmaximal, characteristic, complemented
10C22×C11×#41—21no—
11C11×#547—22no—
12C11×#547—22no—
13C11×#547—22no—
14C11×#547C2214yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×#121—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22C2×#66985—21no—
23#10623008C2211yescharacteristic
24#10622830—21no—
25#10622701C2212yescomplemented
26#10622700—22no—
27#10622691C2212yescomplemented
28#10622632C2212yescomplemented
29#10622629—22no—
30#10622628C2212yescomplemented
31#10622628C2212yescomplemented
32C4×#4323—22no—
33#10622620C2212yescomplemented
34#10622580—21no—
35#10622580—22no—
36#10622579—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622185C2214yescomplemented
41D4⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yescomplemented
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41—44no—
46C2×C11×#41—44no—
47C22×Q8×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11D411yescharacteristic
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C2×#4339—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8D412yes—
58C11×C4⋊Q8C2312yes—
59C11×#123—28no—
60C11×#123—28no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C11×#121—24no—
64C11×#121—24no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11D412yes—
70C4×D4×C11D412yes—
71C4×D4×C11C2312yes—
72C4×D4×C11C2312yes—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D412yes—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×#4324—22no—
85#66985—44no—
86C2×#4323—22no—
87C2×#4323—22no—
88#66983—21no—
89#66983—21no—
90C2×#4318—21no—
91#66928—21no—
92#66927C2311yescharacteristic
93C4×D44—21no—
94C4×D44—21no—
95#66922C2311yescharacteristic
96#66896—22no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99#66874—22no—
100#66873—22no—
101#66873—22no—
102#66873—24no—
103#66871—22no—
104#66871—24no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109C4×C11⋊C8—21no—
110C4×C11⋊C8C2312yes—
111#18756—111nomaximal, Sylow
112C24×C11—21no—
113C24×C11—21no—
114C11×#41—48no—
115C11×#41—416no—
116C11×#41—48no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—42no—
120C2×Q8×C11—42no—
121C2×D4×C11—28no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—42no—
126C2×D4×C11—48no—
127C2×D4×C11D814yescomplemented
128C2×D4×C11C2×D412yes—
129C2×D4×C11C2×D412yes—
130C22×C4×C11—28no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—44no—
139C22×C4×C11—48no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C2×C22⋊D11—41no—
146#4339—42no—
147#4339—42no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×C4×D11—41no—
152C2×Dic22—21no—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2×D412yes—
160C11×C4⋊C4C2×D414yes—
161C11×C4⋊C4C2×D412yes—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11C2411yescharacteristic
171#4324—44no—
172#4323—44no—
173#4323—44no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—41no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178#4318—42no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×#547D1111yescharacteristic, complemented
183#3226—111no—
184#3100—111no—
185#3036—111no—
186#1647—114no—
187#1625—114no—
188#1546—111no—
189#1486—111no—
190#1478—111no—
191C23×C11—22no—
192C23×C11—24no—
193C23×C11—22no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11#12011yescharacteristic
200C22×D11—41no—
201Q8×C11—42no—
202Q8×C11—42no—
203Q8×C11—44no—
204D4×C11—22no—
205D4×C11—22no—
206D4×C11—22no—
207D4×C11—24no—
208D4×C11—42no—
209D4×C11—416no—
210D4×C11C2×D814yes—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—41no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11—416no—
219C2×C4×C11—42no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—44no—
224C2×C4×C11—44no—
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11C2×D812yes—
229C2×C4×C11AGL(1,ℤ/8)12yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C22⋊D11—82no—
234C2×Dic11—41no—
235D44—42no—
236D44—41no—
237D44—41no—
238D44—42no—
239C4×D11—82no—
240Dic22—41no—
241Dic22—41no—
242C11⋊C8—42no—
243C11⋊C8—42no—
244C11⋊C8—42no—
245C22×#41—21no—
246C2×AGL(1,ℤ/8)—221no—
247#547—22no—
248#547—22no—
249#547—22no—
250#547C2×D1114yes—
251#532—111no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×#123—22no—
254C2×C22⋊Q8—21no—
255C2×#121—21no—
256C2×C4×D4C2×D1111yescharacteristic
257C2×C4×D4C2×D1111yescharacteristic
258C22×C4⋊C4—21no—
259#500—112no—
260#486—112no—
261#480—221no—
262#480—222no—
263#474—112no—
264#474—222no—
265#463—222no—
266#461—112no—
267#459—112no—
268#459—112no—
269#447—221no—
270C4×D8—222no—
271#431—111no—
272#431—111no—
273#423—111no—
274#417—221no—
275#332—114no—
276D4⋊C8—114no—
277D4⋊C8—114no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—24no—
281C22×C11—48no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—84no—
288C22×C11#44712yes—
289C22×C11C2×#12011yescharacteristic
290C2×D11—81no—
291C2×D11—81no—
292C2×D11—81no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—42no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11#44712yes—
300C4×C11C22×D811yescharacteristic
301C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C11#57512yes—
303Dic11—81no—
304C2×#41—24no—
305C2×#41—24no—
306C2×#41—44no—
307C2×#41—44no—
308C2×#41—221no—
309C22×Q8—21no—
310C22×D4—22no—
311C22×D4C22⋊D1111yescharacteristic
312C22×D4C22⋊D1111yescharacteristic
313C23×C4—22no—
314C23×C4—21no—
315C23×C4—21no—
316AGL(1,ℤ/8)—444no—
317C2×SD16—222no—
318C2×D8—222no—
319C2×D8—222no—
320C2×M16—221no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8—111no—
324C4⋊Q8C22⋊D1112yes—
325C4⋊Q8C22×D1112yes—
326#127—111no—
327#124—221no—
328#123—28no—
329#123—28no—
330C22⋊Q8—24no—
331C22⋊Q8—24no—
332#121—24no—
333#121—24no—
334#121—221no—
335#121—221no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—221no—
341C4×D4—221no—
342C4×D4C22⋊D1112yes—
343C4×D4C22⋊D1112yes—
344C4×D4C22×D1112yes—
345C4×D4C22×D1112yes—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4C22⋊D1111yescharacteristic
351C2×C4⋊C4C22⋊D1111yescharacteristic
352C2×C4⋊C4C22⋊D1112yes—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C42C22×D1111yescharacteristic
357#107—222no—
358#107—224no—
359C4⋊C8—112no—
360C4⋊C8—112no—
361C4⋊C8—221no—
362C4⋊C8—221no—
363#103—222no—
364#102—222no—
365#102—222no—
366#102—222no—
367#102—224no—
368C22⋊C8—221no—
369C22⋊C8—221no—
370C4×C8—112no—
371C4×C8—221no—
372C2×C11—22no—
373C2×C11—44no—
374C2×C11—82no—
375C2×C11C2×#44711yescharacteristic
376C2×C11#300511yescharacteristic
377C2×C11#302011yescharacteristic
378D11—161no—
379C24—21no—
380C24—21no—
381#41—48no—
382#41—416no—
383#41—48no—
384#41—442no—
385#41—442no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—42no—
389C2×Q8—42no—
390C2×Q8—221no—
391C2×D4—28no—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—42no—
396C2×D4—48no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4—221no—
400C2×D4—441no—
401C2×D4#432314yescomplemented
402C2×D4C2×C22⋊D1112yes—
403C2×D4C2×C22⋊D1112yes—
404C22×C4—28no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—44no—
413C22×C4—48no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—441no—
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C2×C22⋊D1111yescharacteristic
420SD16—444no—
421D8—444no—
422D8—444no—
423M16—442no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C4⋊C4—28no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—221no—
434C4⋊C4—221no—
435C4⋊C4C2×C22⋊D1112yes—
436C4⋊C4C2×C22⋊D1112yes—
437C4⋊C4C2×C22⋊D1114yes—
438C22⋊C4—28no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—441no—
444C22⋊C4—441no—
445C42C2×C22⋊D1111yescharacteristic
446C42C2×C22⋊D1111yescharacteristic
447C42C2×C22⋊D1111yescharacteristic
448C42C23×D1111yescharacteristic
449C11#1875611yescharacteristic, complemented, Sylow
450C23—24no—
451C23—22no—
452C23—22no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—441no—
459C23#6700611yescharacteristic
460Q8—42no—
461Q8—42no—
462Q8—44no—
463Q8—441no—
464Q8—441no—
465D4—22no—
466D4—24no—
467D4—22no—
468D4—22no—
469D4—42no—
470D4—416no—
471D4—442no—
472D4—441no—
473D4—441no—
474D4—442no—
475D4—882no—
476D4C2×#432314yes—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—41no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—416no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—441no—
492C2×C4—882no—
493C2×C4C2×#432312yes—
494C2×C4#6698512yes—
495C2×C4#6700611yescharacteristic
496C2×C4#6700611yescharacteristic
497C2×C4#6700611yescharacteristic
498C2×C4C22×C22⋊D1111yescharacteristic
499C2×C4C22×C22⋊D1111yescharacteristic
500C2×C4C22×C22⋊D1111yescharacteristic
501C8—442no—
502C8—442no—
503C8—442no—
504C22—21no—
505C22—21no—
506C22—24no—
507C22—48no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—84no—
514C22—881no—
515C22—881no—
516C22—881no—
517C22#1062283012yes—
518C22C2×#6700611yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—44no—
524C4—42no—
525C4—881no—
526C4#1062283012yes—
527C4C22×#432311yescharacteristic
528C4C2×#6698511yescharacteristic
529C4#1062335312yes—
530C2—22no—
531C2—44no—
532C2—82no—
533C2—1761no—
534C2C2×#1062283011yescharacteristic
535C2#1307785811yescharacteristic
536C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#547C2
socleC22×C11C2×#120
hypercenterC2×#547D11
hypocenterC11#18756
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13079737C2semidirect
2. #13078616C2semidirect
3. #13078080C2semidirect
4. #13067851C2semidirect
5. #13067705C2semidirect
6. #13067288C2semidirect
7. #13067041C2semidirect
8. #13067007C2semidirect
9. C2×C11×#547C2semidirect
25. #10622701C22semidirect
27. #10622691C22semidirect
28. #10622632C22semidirect
30. #10622628C22semidirect
31. #10622628C22semidirect
33. #10622620C22semidirect
40. #10622185C22semidirect
41. D4⋊(C11⋊C8)C22semidirect
42. D4⋊(C11⋊C8)C22semidirect
127. C2×D4×C11D8semidirect
182. C2×#547D11semidirect
401. C2×D4#4323semidirect
449. C11#18756semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130786162
#130780802
#130678512
#130677052
#130672882
#130670412
#130670072
C2×C11×#5472
#1875611