Finite Group Databasebeta

← #14756998

Subgroups — #14756998

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66957C211yesmaximal, characteristic
2#13077258C211yesmaximal, characteristic, complemented
3C4×#66954C211yesmaximal, characteristic, complemented
4#13069265C212yesmaximal, complemented
5#13069216C212yesmaximal, complemented
6#13068942C212yesmaximal
7#13068894C212yesmaximal, complemented
8C4×#66883C211yesmaximal, characteristic, complemented
9C4×#66869C211yesmaximal, characteristic, complemented
10C4×#66869C211yesmaximal, characteristic, complemented
11C11×#1744C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C2×#66954C2212yes—
14C4×#4339C2211yescharacteristic
15C4×#4339C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18C43×C11C2211yescharacteristic
19#10622726C2211yescharacteristic
20#10622726C2211yescharacteristic
21#10622723C2212yes—
22C2×#66883C2212yes—
23#10622719C2211yescharacteristic
24#10622715C2212yes—
25#10622714C2212yes—
26C2×#66869C2212yes—
27C2×#66869C2212yes—
28C4×#4318C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30C4×Dic44C411yescharacteristic, complemented
31C4×Dic44C411yescharacteristic, complemented
32C4×D88C411yescharacteristic, complemented
33C4×D88C411yescharacteristic, complemented
34C4×#4314C411yescharacteristic, complemented
35C4×#4314C411yescharacteristic, complemented
36C4×#4314C411yescharacteristic, complemented
37C4×#4314C411yescharacteristic, complemented
38#10622303—22no—
39#10622302—22no—
40C4×#4313—21no—
41#10622298—21no—
42#10622298—21no—
43C4×C8×D11—21no—
44C11×#336C2212yes—
45C11×#336C2212yes—
46#10622190C2212yes—
47#10622161C2212yes—
48#10622161C2212yes—
49C2×#4339C2311yescharacteristic
50C2×#4339C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C2×C42×C11—21no—
55C2×C42×C11—21no—
56C2×C42×C11C2312yes—
57C2×C42×C11C2311yescharacteristic
58C4×C22⋊D11—21no—
59C4×C22⋊D11—21no—
60C4×C22⋊D11—21no—
61C4×C22⋊D11—21no—
62#66979C2311yescharacteristic
63#66979C2311yescharacteristic
64C2×#4318C2312yes—
65C2×#4318C2312yes—
66C2×Dic44C2×C411yescharacteristic
67#66957—24no—
68C2×D88C2×C411yescharacteristic
69C2×#4314C2×C411yescharacteristic
70C2×#4314C2×C411yescharacteristic
71#66954—24no—
72#66954—24no—
73C2×#4313—22no—
74C2×C8×D11—22no—
75C4×D44C2×C411yescharacteristic
76C4×D44C2×C411yescharacteristic
77C4×D44C2×C411yescharacteristic
78C4×D44C2×C411yescharacteristic
79#66925—21no—
80#66925—21no—
81C42×D11—21no—
82C42×D11—21no—
83C4×Dic22C2×C411yescharacteristic
84C4×Dic22C2×C411yescharacteristic
85C4×Dic22C2×C411yescharacteristic
86C4×Dic22C2×C411yescharacteristic
87C4×C8×C11C2×C411yescharacteristic
88C4×C8×C11C2×C411yescharacteristic
89C4×C8×C11C2×C411yescharacteristic
90C4×C8×C11C2×C411yescharacteristic
91C4×C8×C11D411yescharacteristic
92C4×C8×C11D411yescharacteristic
93C4×C8×C11D412yes—
94#66885C2×C411yescharacteristic
95#66885C2×C411yescharacteristic
96#66885C2×C411yescharacteristic
97#66885C2×C411yescharacteristic
98(C2×D11)⋊C8—22no—
99(C2×D11)⋊C8—22no—
100#66883—24no—
101#66882C2×C411yescharacteristic
102#66882C2×C411yescharacteristic
103#66881C2×C411yescharacteristic
104#66881C2×C411yescharacteristic
105#66880C2×C411yescharacteristic
106#66880C2×C411yescharacteristic
107#66880C2×C411yescharacteristic
108#66880C2×C411yescharacteristic
109#66879—22no—
110Dic11⋊C8—22no—
111Dic11⋊C8—22no—
112C8×Dic11—22no—
113#66869—24no—
114#66869—24no—
115#66867—21no—
116#66867—21no—
117C4×C11⋊C8—21no—
118C4×C11⋊C8—21no—
119#21137—111nomaximal, Sylow
120C22×C4×C11—22no—
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—21no—
125C2×C22⋊D11—21no—
126#4339—22no—
127#4339—22no—
128#4339—22no—
129#4339#4114yes—
130C2×D44C22×C411yescharacteristic
131C2×D44C22×C411yescharacteristic
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×Dic22C22×C411yescharacteristic
139C2×Dic22C22×C411yescharacteristic
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11C22×C411yescharacteristic
145C2×C8×C11C22×C411yescharacteristic
146C2×C8×C11C22×C411yescharacteristic
147C2×C8×C11C22×C411yescharacteristic
148C2×C8×C11C2×D412yes—
149C2×C8×C11C2×D412yes—
150C42×C11—24no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—42no—
154C42×C11C22×C411yescharacteristic
155C42×C11C22×C411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C22⋊Dic11—21no—
159C22⋊Dic11—21no—
160(C2×D11)⋊C4—21no—
161(C2×D11)⋊C4—21no—
162(C2×D11)⋊C4—21no—
163(C2×D11)⋊C4—21no—
164C4⋊Dic11C22×C411yescharacteristic
165C4⋊Dic11C22×C411yescharacteristic
166C4⋊Dic11C22×C411yescharacteristic
167C4⋊Dic11C22×C411yescharacteristic
168Dic11⋊C4—21no—
169Dic11⋊C4—21no—
170Dic11⋊C4—21no—
171Dic11⋊C4—21no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178#4318—22no—
179#4318—22no—
180#4318—22no—
181#4318#4114yes—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184Dic44—22no—
185D88—22no—
186#4314—22no—
187#4314—22no—
188#4313—28no—
189C8×D11—28no—
190C4×#135—111no—
191#2922—111no—
192C4×#131—111no—
193#1929—112no—
194#1922—112no—
195#1876—112no—
196#1866—112no—
197C4×#108—111no—
198C4×#104—111no—
199C4×#104—111no—
200#1744D1111yescharacteristic, complemented
201C23×C11C2×#4111yescharacteristic
202C22×D11—21no—
203C22×D11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11C4×D411yescharacteristic
210C2×C4×C11C4×D411yescharacteristic
211C2×C4×C11C4×D411yescharacteristic
212C2×C4×C11C4×D411yescharacteristic
213C2×C4×C11C23×C411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4112yes—
216C2×C4×C11C2×#4112yes—
217C22⋊D11—24no—
218C22⋊D11—42no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225D44—21no—
226D44—21no—
227D44—21no—
228D44#11712yes—
229C4×D11—24no—
230C4×D11—42no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—42no—
234C4×D11—42no—
235Dic22—21no—
236Dic22—21no—
237Dic22—21no—
238Dic22#11712yes—
239C8×C11—21no—
240C8×C11—21no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11—22no—
244C8×C11—22no—
245C11⋊C8—24no—
246C11⋊C8—42no—
247C2×#135—111no—
248C2×#131—112no—
249C4×#41—111no—
250C4×#41—111no—
251C4×Q16—111no—
252C4×Q16—111no—
253C4×SD16—111no—
254C4×SD16—111no—
255C4×SD16—111no—
256C4×SD16—111no—
257C4×D8—111no—
258C4×D8—111no—
259#433—222no—
260#431—221no—
261#431—221no—
262C2×#108—112no—
263#427—111no—
264#424—112no—
265C2×#104—112no—
266C2×#104—112no—
267#416—111no—
268#416—111no—
269#408—112no—
270#405—112no—
271#405—222no—
272C4×M16—111no—
273C4×M16—111no—
274C4×M16—221no—
275C2×C4×C8—221no—
276C2×C4×C8C2×D1111yescharacteristic
277C2×C4×C8C2×D1111yescharacteristic
278C43C2×D1111yescharacteristic
279#341—112no—
280#339—112no—
281#339—112no—
282#336C2×D1112yes—
283#336C2×D1112yes—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11C2×C4×D411yescharacteristic
287C22×C11#52912yes—
288C2×D11—22no—
289C2×D11—41no—
290C2×D11—41no—
291C2×D11—41no—
292C2×D11—41no—
293C2×D11—41no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—44no—
297C4×C11#44312yes—
298C4×C11#44412yes—
299C4×C11C2×#11711yescharacteristic
300C4×C11C4×#4111yescharacteristic
301C4×C11#52512yes—
302Dic11—22no—
303Dic11—41no—
304Dic11—41no—
305Dic11—41no—
306Dic11—41no—
307Dic11—41no—
308C2×#41—111no—
309C2×#41—111no—
310#135—224no—
311C2×Q16—111no—
312C2×SD16—111no—
313C2×SD16—111no—
314C2×D8—111no—
315#131—224no—
316#131—224no—
317C2×M16—112no—
318C2×M16—112no—
319C2×M16—222no—
320C22×C8—222no—
321C22×C8C22×D1111yescharacteristic
322C22×C8C22×D1111yescharacteristic
323C22×C8C22×D1112yes—
324C4×Q8—111no—
325C4×Q8—111no—
326C4×Q8—111no—
327C4×Q8—111no—
328C4×D4—111no—
329C4×D4—111no—
330C4×D4—111no—
331C4×D4—111no—
332C4×D4—221no—
333C4×D4—221no—
334C4×D4—221no—
335C4×D4—221no—
336#117—111no—
337#117—111no—
338#117—221no—
339#117—221no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—221no—
343C2×C42—221no—
344C2×C42C22×D1112yes—
345C2×C42C22×D1111yescharacteristic
346#108—224no—
347#107—111no—
348#107—111no—
349#106—111no—
350#106—111no—
351C4⋊C8—222no—
352C4⋊C8—222no—
353#104—224no—
354#104—224no—
355#103—111no—
356#103—111no—
357#103—111no—
358#103—111no—
359#102—111no—
360#102—111no—
361#102—111no—
362#102—111no—
363C22⋊C8—222no—
364C22⋊C8—222no—
365#97—222no—
366#97—221no—
367#97—221no—
368C4×C8—222no—
369C4×C8—221no—
370C4×C8—221no—
371C4×C8C4×D1111yescharacteristic
372C4×C8C4×D1111yescharacteristic
373C4×C8C4×D1111yescharacteristic
374C4×C8C4×D1111yescharacteristic
375C4×C8D4412yes—
376C4×C8D4411yescharacteristic
377C4×C8D4411yescharacteristic
378C2×C11—22no—
379C2×C11#229011yescharacteristic
380C2×C11C2×#44311yescharacteristic
381C2×C11C2×#44411yescharacteristic
382D11—42no—
383D11—81no—
384#41—114no—
385#41—222no—
386#41—222no—
387#41—222no—
388C2×Q8—111no—
389C2×Q8—111no—
390C2×D4—111no—
391C2×D4—111no—
392C2×D4—221no—
393C2×D4—221no—
394C22×C4—22no—
395C22×C4—221no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4#433911yescharacteristic
402C22×C4#433911yescharacteristic
403C22×C4C23×D1111yescharacteristic
404Q16—222no—
405SD16—222no—
406SD16—222no—
407D8—222no—
408M16—114no—
409M16—228no—
410M16—222no—
411M16—222no—
412M16—222no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—228no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8C2×C4×D1111yescharacteristic
421C2×C8C2×C4×D1111yescharacteristic
422C2×C8C2×C4×D1111yescharacteristic
423C2×C8C2×C4×D1111yescharacteristic
424C2×C8C2×D4412yes—
425C2×C8C2×D4412yes—
426C4⋊C4—111no—
427C4⋊C4—111no—
428C4⋊C4—111no—
429C4⋊C4—111no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C4⋊C4—221no—
433C4⋊C4—221no—
434C22⋊C4—221no—
435C22⋊C4—221no—
436C22⋊C4—221no—
437C22⋊C4—221no—
438C22⋊C4—221no—
439C22⋊C4—221no—
440C42—24no—
441C42—22no—
442C42—22no—
443C42—42no—
444C42—221no—
445C42—221no—
446C42—221no—
447C42—221no—
448C42—221no—
449C42—221no—
450C42C2×C4×D1111yescharacteristic
451C42C2×C4×D1111yescharacteristic
452C42C2×D4411yescharacteristic
453C42C2×D4411yescharacteristic
454C11#2113711yescharacteristic, complemented, Sylow
455C23—221no—
456C23—221no—
457C23C2×#433911yescharacteristic
458Q8—112no—
459Q8—221no—
460Q8—221no—
461Q8—221no—
462D4—112no—
463D4—224no—
464D4—221no—
465D4—221no—
466D4—221no—
467D4—442no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—221no—
474C2×C4—224no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4C4×D4411yescharacteristic
486C2×C4C4×D4411yescharacteristic
487C2×C4C4×D4411yescharacteristic
488C2×C4C4×D4411yescharacteristic
489C2×C4C22×C4×D1111yescharacteristic
490C2×C4C22×D4411yescharacteristic
491C2×C4#41×D1112yes—
492C2×C4#41×D1112yes—
493C8—21no—
494C8—21no—
495C8—21no—
496C8—21no—
497C8—22no—
498C8—22no—
499C8—224no—
500C8—442no—
501C22—21no—
502C22—21no—
503C22—222no—
504C22—441no—
505C22—441no—
506C22—441no—
507C22—441no—
508C22—441no—
509C22C2×C4×D4411yescharacteristic
510C22#1062305912yes—
511C4—21no—
512C4—21no—
513C4—44no—
514C4—222no—
515C4—441no—
516C4—441no—
517C4—441no—
518C4—441no—
519C4—441no—
520C4#1062231312yes—
521C4#1062233012yes—
522C4D11×#11711yescharacteristic
523C4#1062305311yescharacteristic
524C4#1062305512yes—
525C2—22no—
526C2—442no—
527C2—881no—
528C2#1307106011yescharacteristic
529C2C2×#1062231311yescharacteristic
530C2C2×#1062233011yescharacteristic
subgroupG/H
centerC42C2×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1744C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C22
cosocleC22×C4×C11C24
hypercenter#1744D11
hypocenterC11#21137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ #1744

Complements

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

NH ≅ G/Ntype
2. #13077258C2semidirect
3. C4×#66954C2semidirect
4. #13069265C2semidirect
5. #13069216C2semidirect
7. #13068894C2semidirect
8. C4×#66883C2semidirect
9. C4×#66869C2semidirect
10. C4×#66869C2semidirect
11. C11×#1744C2semidirect
30. C4×Dic44C4semidirect
31. C4×Dic44C4semidirect
32. C4×D88C4semidirect
33. C4×D88C4semidirect
34. C4×#4314C4semidirect
35. C4×#4314C4semidirect
36. C4×#4314C4semidirect
37. C4×#4314C4semidirect
200. #1744D11semidirect
454. C11#21137semidirect

Maximal subgroups

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

subgroupindex
C4×#669572
#130772582
C4×#669542
#130692652
#130692162
#130689422
#130688942
C4×#668832
C4×#668692
C11×#17442
#2113711