Finite Group Databasebeta

← #14757000

Subgroups — #14757000

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×#67003C211yesmaximal, characteristic
2#13077260C211yesmaximal, characteristic, complemented
3C4×#66960C211yesmaximal, characteristic, complemented
4#13069267C212yesmaximal, complemented
5#13069218C212yesmaximal, complemented
6#13068940C212yesmaximal
7#13068892C212yesmaximal, complemented
8C4×#66886C211yesmaximal, characteristic, complemented
9C4×#66869C211yesmaximal, characteristic, complemented
10#13068362C211yesmaximal, characteristic, complemented
11C4×C11×#104C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003C2211yescharacteristic
14C2×#66960C2212yes—
15C4×#4339C2211yescharacteristic
16C2×C11×#104C2212yes—
17C4×C11×M16C2211yescharacteristic
18C43×C11C2211yescharacteristic
19#10622847C2212yes—
20#10622846C2211yescharacteristic
21C2×#66886C2212yes—
22#10622735C2212yes—
23C4×#4326C411yescharacteristic, complemented
24C4×#4326C411yescharacteristic, complemented
25C4×#4325C411yescharacteristic, complemented
26C4×#4325C411yescharacteristic, complemented
27C4×#4324C411yescharacteristic, complemented
28C4×#4324C411yescharacteristic, complemented
29C4×#4323C411yescharacteristic, complemented
30C4×#4323C411yescharacteristic, complemented
31#10622615C2211yescharacteristic
32#10622613—22no—
33#10622612C2212yes—
34#10622611C2211yescharacteristic
35C2×#66869C2212yes—
36#10622538—21no—
37#10622538—21no—
38C4×#4318C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622321—22no—
42C4×#4313—21no—
43C4×C8×D11—21no—
44C11×#339C2212yes—
45#10622196C2212yes—
46#10622162C2212yes—
47#10622162C2212yes—
48#10622161C2212yes—
49C2×C11×#41C2311yescharacteristic
50C2×#4339C2311yescharacteristic
51C2×C11×M16C2312yes—
52C4×Q8×C11C2×C411yescharacteristic
53C4×Q8×C11C2×C411yescharacteristic
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11C2×C411yescharacteristic
57C4×D4×C11C2×C411yescharacteristic
58C11×#117—21no—
59C11×#117C2311yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11—21no—
62C2×C42×C11—21no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65#67003—24no—
66C2×#4326C2×C411yescharacteristic
67C2×#4325C2×C411yescharacteristic
68C2×#4324C2×C411yescharacteristic
69C2×#4323C2×C411yescharacteristic
70C4×C22⋊D11—21no—
71C4×C22⋊D11—21no—
72#66979C2311yescharacteristic
73C2×#4318C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77#66960—24no—
78#66960—24no—
79C2×#4313—22no—
80C2×C8×D11—22no—
81C4×D44C2×C411yescharacteristic
82C4×D44C2×C411yescharacteristic
83#66925—21no—
84C42×D11—21no—
85C4×Dic22C2×C411yescharacteristic
86C4×Dic22C2×C411yescharacteristic
87C11×#104—24no—
88C11×#97—21no—
89C4×C8×C11—21no—
90#66899C2×C411yescharacteristic
91#66899C2×C411yescharacteristic
92#66896C2×C411yescharacteristic
93#66896C2×C411yescharacteristic
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)—22no—
96#66886—24no—
97#66879—22no—
98C8×Dic11—22no—
99#66874C2×C411yescharacteristic
100#66874C2×C411yescharacteristic
101#66873C2×C411yescharacteristic
102#66873C2×C411yescharacteristic
103#66872C2×C411yescharacteristic
104#66872C2×C411yescharacteristic
105#66871C2×C411yescharacteristic
106#66871C2×C411yescharacteristic
107#66869—24no—
108C4⋊(C11⋊C8)—22no—
109C4⋊(C11⋊C8)—22no—
110#66867—21no—
111C4×C11⋊C8—21no—
112C4×C11⋊C8C2×C411yescharacteristic
113C4×C11⋊C8C2×C411yescharacteristic
114C4×C11⋊C8C2×C411yescharacteristic
115C4×C11⋊C8C2×C411yescharacteristic
116C4×C11⋊C8D411yescharacteristic
117C4×C11⋊C8D411yescharacteristic
118C4×C11⋊C8D412yes—
119#21137—111nomaximal, Sylow
120C11×#41—22no—
121C11×#41—22no—
122C2×Q8×C11C22×C411yescharacteristic
123C2×D4×C11—21no—
124C2×D4×C11C22×C411yescharacteristic
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—21no—
133#4339—22no—
134#4339#4114yes—
135C2×D44C22×C411yescharacteristic
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×Dic22C22×C411yescharacteristic
140C11×M16—22no—
141C11×M16#4114yes—
142C2×C8×C11—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4C22×C411yescharacteristic
146C11×C4⋊C4C22×C411yescharacteristic
147C11×C22⋊C4—21no—
148C11×C22⋊C4—21no—
149C11×C22⋊C4—21no—
150C42×C11—24no—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11—21no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—42no—
157C42×C11C22×C411yescharacteristic
158C42×C11C22×C411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C22⋊Dic11—21no—
162#4326—22no—
163#4325—22no—
164#4324—22no—
165#4323—22no—
166(C2×D11)⋊C4—21no—
167(C2×D11)⋊C4—21no—
168C4⋊Dic11C22×C411yescharacteristic
169C4⋊Dic11C22×C411yescharacteristic
170Dic11⋊C4—21no—
171Dic11⋊C4—21no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174C4×Dic11—21no—
175#4318—22no—
176#4318—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8C22×C411yescharacteristic
183C2×C11⋊C8C22×C411yescharacteristic
184C2×C11⋊C8C22×C411yescharacteristic
185C2×C11⋊C8C22×C411yescharacteristic
186C2×C11⋊C8C2×D412yes—
187C2×C11⋊C8C2×D412yes—
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×#104D1111yescharacteristic, complemented
200#1744—111no—
201C23×C11—21no—
202C23×C11C2×#4111yescharacteristic
203C22×D11—21no—
204Q8×C11—21no—
205Q8×C11—21no—
206D4×C11—21no—
207D4×C11—21no—
208D4×C11—42no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11C4×D411yescharacteristic
221C2×C4×C11C4×D411yescharacteristic
222C2×C4×C11C4×D411yescharacteristic
223C2×C4×C11C4×D411yescharacteristic
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4112yes—
227C2×C4×C11C2×#4112yes—
228C22⋊D11—24no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232D44—21no—
233D44#11712yes—
234C4×D11—24no—
235C4×D11—42no—
236C4×D11—42no—
237Dic22—21no—
238Dic22#11712yes—
239C8×C11—24no—
240C11⋊C8—21no—
241C11⋊C8—21no—
242C11⋊C8—21no—
243C11⋊C8—21no—
244C11⋊C8—22no—
245C11⋊C8—22no—
246C11⋊C8—42no—
247C2×#135—111no—
248C2×#131—112no—
249C4×#41—111no—
250C4×#41C2×D1111yescharacteristic
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×#104C2×D1112yes—
267#416—111no—
268#416—111no—
269#408—112no—
270#405—112no—
271#405—222no—
272C4×M16—111no—
273C4×M16—221no—
274C4×M16C2×D1111yescharacteristic
275C2×C4×C8—111no—
276C2×C4×C8—111no—
277C2×C4×C8—221no—
278C43C2×D1111yescharacteristic
279#341—112no—
280#339—112no—
281#339C2×D1112yes—
282#336—112no—
283#336—112no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11C2×C4×D411yescharacteristic
290C22×C11#52912yes—
291C2×D11—22no—
292C2×D11—41no—
293C2×D11—41no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—44no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—41no—
300C4×C11#44312yes—
301C4×C11#44412yes—
302C4×C11C2×#11711yescharacteristic
303C4×C11C4×#4111yescharacteristic
304C4×C11#52512yes—
305Dic11—22no—
306Dic11—41no—
307Dic11—41no—
308C2×#41—111no—
309C2×#41C22×D1111yescharacteristic
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—222no—
319C2×M16C22×D1112yes—
320C22×C8—112no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8—222no—
324C4×Q8—111no—
325C4×Q8—111no—
326C4×Q8C4×D1111yescharacteristic
327C4×Q8C4×D1111yescharacteristic
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—111no—
331C4×D4—111no—
332C4×D4—221no—
333C4×D4—221no—
334C4×D4C4×D1111yescharacteristic
335C4×D4C4×D1111yescharacteristic
336#117—21no—
337#117—111no—
338#117—221no—
339#117C22×D1111yescharacteristic
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
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—24no—
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—21no—
366#97—222no—
367#97—221no—
368C4×C8—21no—
369C4×C8—111no—
370C4×C8—111no—
371C4×C8—111no—
372C4×C8—111no—
373C4×C8—112no—
374C4×C8—111no—
375C4×C8—111no—
376C4×C8—222no—
377C4×C8—221no—
378C2×C11—22no—
379C2×C11—81no—
380C2×C11#229011yescharacteristic
381C2×C11C2×#44311yescharacteristic
382C2×C11C2×#44411yescharacteristic
383D11—42no—
384#41—22no—
385#41—22no—
386#41—114no—
387#41—222no—
388C2×Q8—111no—
389C2×Q8C2×C4×D1111yescharacteristic
390C2×D4—21no—
391C2×D4—111no—
392C2×D4—221no—
393C2×D4C2×C4×D1111yescharacteristic
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4#434111yescharacteristic
402C22×C4#434111yescharacteristic
403C22×C4C23×D1111yescharacteristic
404Q16—222no—
405SD16—222no—
406SD16—222no—
407D8—222no—
408M16—22no—
409M16—228no—
410M16—222no—
411M16—222no—
412M16#433914yes—
413C2×C8—22no—
414C2×C8—111no—
415C2×C8—111no—
416C2×C8—111no—
417C2×C8—111no—
418C2×C8—112no—
419C2×C8—112no—
420C2×C8—228no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—222no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—111no—
429C4⋊C4—111no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C4⋊C4C2×C4×D1111yescharacteristic
433C4⋊C4C2×C4×D1111yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—221no—
438C22⋊C4—221no—
439C22⋊C4—221no—
440C42—24no—
441C42—21no—
442C42—21no—
443C42—21no—
444C42—22no—
445C42—22no—
446C42—42no—
447C42—221no—
448C42—221no—
449C42—221no—
450C42C2×C4×D1111yescharacteristic
451C42C2×C4×D1111yescharacteristic
452C42D4×D1111yescharacteristic
453C42D4×D1111yescharacteristic
454C11#2113711yescharacteristic, complemented, Sylow
455C23—21no—
456C23—221no—
457C23C2×#434111yescharacteristic
458Q8—21no—
459Q8—21no—
460Q8—112no—
461Q8—221no—
462D4—21no—
463D4—21no—
464D4—42no—
465D4—112no—
466D4—224no—
467D4—221no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—221no—
480C2×C4—224no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4(C22⋊D11)⋊C411yescharacteristic
486C2×C4(C22⋊D11)⋊C411yescharacteristic
487C2×C4(C22⋊D11)⋊C411yescharacteristic
488C2×C4(C22⋊D11)⋊C411yescharacteristic
489C2×C4C22×C4×D1111yescharacteristic
490C2×C4C2×#433912yes—
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4#41×D1112yes—
493C8—24no—
494C8—221no—
495C8—221no—
496C8—221no—
497C8—221no—
498C8—222no—
499C8—222no—
500C8—442no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—222no—
507C22—441no—
508C22—441no—
509C22C2×(C22⋊D11)⋊C411yescharacteristic
510C22#1062308812yes—
511C4—21no—
512C4—21no—
513C4—44no—
514C4—41no—
515C4—41no—
516C4—41no—
517C4—222no—
518C4—441no—
519C4—441no—
520C4#1062243612yes—
521C4#1062243712yes—
522C4C4×#433911yescharacteristic
523C4D11×#11711yescharacteristic
524C4#1062307812yes—
525C2—22no—
526C2—81no—
527C2—442no—
528C2#1307106211yescharacteristic
529C2C2×#1062243711yescharacteristic
530C2C2×#1062243611yescharacteristic
subgroupG/H
centerC42D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#104C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C22
cosocleC22×C4×C11C24
hypercenterC4×#104D11
hypocenterC11#21137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#104

Complements

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

NH ≅ G/Ntype
2. #13077260C2semidirect
3. C4×#66960C2semidirect
4. #13069267C2semidirect
5. #13069218C2semidirect
7. #13068892C2semidirect
8. C4×#66886C2semidirect
9. C4×#66869C2semidirect
10. #13068362C2semidirect
11. C4×C11×#104C2semidirect
23. C4×#4326C4semidirect
24. C4×#4326C4semidirect
25. C4×#4325C4semidirect
26. C4×#4325C4semidirect
27. C4×#4324C4semidirect
28. C4×#4324C4semidirect
29. C4×#4323C4semidirect
30. C4×#4323C4semidirect
199. C4×#104D11semidirect
454. C11#21137semidirect

Maximal subgroups

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

subgroupindex
C4×#670032
#130772602
C4×#669602
#130692672
#130692182
#130689402
#130688922
C4×#668862
C4×#668692
#130683622
C4×C11×#1042
#2113711