Finite Group Databasebeta

← #14756997

Subgroups — #14756997

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#13077258C211yesmaximal, characteristic, complemented
3#13069264C212yesmaximal, complemented
4#13069215C212yesmaximal, complemented
5#13068943C212yesmaximal
6#13068891C212yesmaximal, complemented
7C4×#66886C211yesmaximal, characteristic, complemented
8C4×#66889C211yesmaximal, characteristic, complemented
9C4×#66901C211yesmaximal, characteristic, complemented
10#13068361C211yesmaximal, characteristic, complemented
11C4×C11×#131C211yesmaximal, characteristic, complemented
12C2×C11×#131C2212yes—
13C4×C11×#41C2211yescharacteristic
14C2×#67003C2211yescharacteristic
15C4×#4339C2211yescharacteristic
16C11×#405—22no—
17C11×#405C2212yes—
18C4×C11×M16—21no—
19C4×C11×M16C2211yescharacteristic
20C2×C4×C8×C11—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66901C2212yes—
23#10622846C2211yescharacteristic
24C2×#66889C2212yes—
25C2×#66886C2212yes—
26#10622723C2212yes—
27#10622715C2212yes—
28C4×#4326C411yescharacteristic, complemented
29C4×#4326C411yescharacteristic, complemented
30C4×#4325C411yescharacteristic, complemented
31C4×#4325C411yescharacteristic, complemented
32C4×#4324C411yescharacteristic, complemented
33C4×#4324C411yescharacteristic, complemented
34C4×#4323C411yescharacteristic, complemented
35C4×#4323C411yescharacteristic, complemented
36#10622615C2211yescharacteristic
37#10622611C2211yescharacteristic
38C42×Dic11C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622303—22no—
42#10622298—21no—
43#10622298—21no—
44#10622196C2212yes—
45#10622193C2212yes—
46#10622188C2212yes—
47#10622188C2212yes—
48#10622170C2212yes—
49C2×C11×#41C2311yescharacteristic
50C2×#4339C2311yescharacteristic
51C11×#131—24no—
52C11×#131—24no—
53C2×C11×M16—22no—
54C2×C11×M16C2312yes—
55C22×C8×C11—22no—
56C22×C8×C11C2312yes—
57C4×Q8×C11C2×C411yescharacteristic
58C4×Q8×C11C2×C411yescharacteristic
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11C2×C411yescharacteristic
62C4×D4×C11C2×C411yescharacteristic
63C11×#117—21no—
64C11×#117C2311yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67#67003—24no—
68C2×#4326C2×C411yescharacteristic
69C2×#4325C2×C411yescharacteristic
70C2×#4324C2×C411yescharacteristic
71C2×#4323C2×C411yescharacteristic
72C4×C22⋊D11—21no—
73C4×C22⋊D11—21no—
74#66979C2311yescharacteristic
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11C2312yes—
78C2×#4318C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C4×D44C2×C411yescharacteristic
82C4×D44C2×C411yescharacteristic
83#66925—21no—
84C42×D11—21no—
85C4×Dic22C2×C411yescharacteristic
86C4×Dic22C2×C411yescharacteristic
87C11×#97—22no—
88C11×#97—21no—
89C4×C8×C11—22no—
90C4×C8×C11—21no—
91C4×C8×C11D411yescharacteristic
92C4×C8×C11D411yescharacteristic
93C4×C8×C11D412yes—
94#66901—24no—
95#66899C2×C411yescharacteristic
96#66899C2×C411yescharacteristic
97#66896C2×C411yescharacteristic
98#66896C2×C411yescharacteristic
99#66889—24no—
100#66886—24no—
101(C2×D11)⋊C8—22no—
102(C2×D11)⋊C8—22no—
103Dic11⋊C8—22no—
104Dic11⋊C8—22no—
105#66874C2×C411yescharacteristic
106#66874C2×C411yescharacteristic
107#66873C2×C411yescharacteristic
108#66873C2×C411yescharacteristic
109#66872C2×C411yescharacteristic
110#66872C2×C411yescharacteristic
111#66871C2×C411yescharacteristic
112#66871C2×C411yescharacteristic
113#66867—21no—
114C4×C11⋊C8—21no—
115C4×C11⋊C8C2×C411yescharacteristic
116C4×C11⋊C8C2×C411yescharacteristic
117C4×C11⋊C8C2×C411yescharacteristic
118C4×C11⋊C8C2×C411yescharacteristic
119#21137—111nomaximal, Sylow
120C11×#41—22no—
121C11×#41#4114yes—
122C2×Q8×C11C22×C411yescharacteristic
123C2×D4×C11—21no—
124C2×D4×C11C22×C411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11#4111yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—21no—
132C22×Dic11—22no—
133#4339—22no—
134#4339—22no—
135C2×D44C22×C411yescharacteristic
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×Dic22C22×C411yescharacteristic
140C11×M16—28no—
141C11×M16—22no—
142C11×M16#4114yes—
143C2×C8×C11—28no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11C2×D412yes—
148C2×C8×C11C2×D412yes—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C22×C411yescharacteristic
152C11×C4⋊C4C22×C411yescharacteristic
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11C22×C411yescharacteristic
160C42×C11C22×C411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C22⋊Dic11—21no—
164#4326—22no—
165#4325—22no—
166#4324—22no—
167#4323—22no—
168(C2×D11)⋊C4—21no—
169(C2×D11)⋊C4—21no—
170C4⋊Dic11C22×C411yescharacteristic
171C4⋊Dic11C22×C411yescharacteristic
172Dic11⋊C4—21no—
173Dic11⋊C4—21no—
174C4×Dic11—24no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C4×Dic11—42no—
181#4318—22no—
182#4318—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8C22×C411yescharacteristic
187C2×C11⋊C8C22×C411yescharacteristic
188C2×C11⋊C8C22×C411yescharacteristic
189C2×C11⋊C8C22×C411yescharacteristic
190C4×#135—111no—
191#2922—111no—
192C4×#131D1111yescharacteristic, complemented
193#1929—112no—
194#1922—112no—
195#1876—112no—
196#1866—112no—
197C4×#108—111no—
198C4×#104—111no—
199C4×#104—111no—
200#1744—111no—
201C23×C11—21no—
202C23×C11C2×#4111yescharacteristic
203C22×D11—21no—
204Q8×C11—21no—
205Q8×C11#11712yes—
206D4×C11—24no—
207D4×C11—21no—
208D4×C11#11712yes—
209C2×C4×C11—21no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11C4×D411yescharacteristic
218C2×C4×C11C4×D411yescharacteristic
219C2×C4×C11C4×D411yescharacteristic
220C2×C4×C11C4×D411yescharacteristic
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4112yes—
224C2×C4×C11C2×#4112yes—
225C22⋊D11—42no—
226C2×Dic11—24no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232D44—21no—
233D44—21no—
234C4×D11—42no—
235C4×D11—42no—
236C4×D11—42no—
237Dic22—21no—
238Dic22—21no—
239C8×C11—22no—
240C8×C11—24no—
241C8×C11—22no—
242C11⋊C8—21no—
243C11⋊C8—21no—
244C11⋊C8—21no—
245C11⋊C8—21no—
246C11⋊C8—42no—
247C2×#135—111no—
248C2×#131C2×D1112yes—
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×#104—112no—
267#416—111no—
268#416—111no—
269#408—112no—
270#405—22no—
271#405C2×D1112yes—
272C4×M16—21no—
273C4×M16—111no—
274C4×M16C2×D1111yescharacteristic
275C2×C4×C8—21no—
276C2×C4×C8—111no—
277C2×C4×C8C2×D1111yescharacteristic
278C43—111no—
279#341—112no—
280#339—112no—
281#339—112no—
282#336—112no—
283#336—112no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—22no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11C2×C4×D411yescharacteristic
290C22×C11#52912yes—
291C2×D11—41no—
292C2×D11—41no—
293C2×D11—41no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—22no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11#44312yes—
300C4×C11#44412yes—
301C4×C11C2×#11711yescharacteristic
302C4×C11C4×#4111yescharacteristic
303C4×C11#52512yes—
304Dic11—44no—
305Dic11—41no—
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—24no—
316#131—24no—
317C2×M16—22no—
318C2×M16—112no—
319C2×M16C22×D1112yes—
320C22×C8—22no—
321C22×C8—111no—
322C22×C8—111no—
323C22×C8C22×D1112yes—
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—112no—
342C2×C42—221no—
343C2×C42—221no—
344C2×C42—221no—
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—22no—
366#97—21no—
367#97—221no—
368C4×C8—22no—
369C4×C8—21no—
370C4×C8—111no—
371C4×C8—111no—
372C4×C8—111no—
373C4×C8—111no—
374C4×C8—221no—
375C4×C8C22⋊D1112yes—
376C4×C8C22⋊D1111yescharacteristic
377C4×C8C22⋊D1111yescharacteristic
378C2×C11—22no—
379C2×C11—42no—
380C2×C11#229011yescharacteristic
381C2×C11C2×#44311yescharacteristic
382C2×C11C2×#44411yescharacteristic
383D11—81no—
384#41—22no—
385#41—222no—
386#41—222no—
387#41#433914yes—
388C2×Q8—111no—
389C2×Q8C2×C4×D1111yescharacteristic
390C2×D4—21no—
391C2×D4—111no—
392C2×D4—221no—
393C2×D4C2×C4×D1111yescharacteristic
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—222no—
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—28no—
409M16—22no—
410M16—222no—
411M16—222no—
412M16#433914yes—
413C2×C8—28no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—111no—
418C2×C8—111no—
419C2×C8—111no—
420C2×C8—111no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8C2×C22⋊D1112yes—
425C2×C8C2×C22⋊D1112yes—
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—21no—
441C42—21no—
442C42—21no—
443C42—224no—
444C42—221no—
445C42—221no—
446C42—221no—
447C42—222no—
448C42—222no—
449C42—442no—
450C42C2×C4×D1111yescharacteristic
451C42C2×C4×D1111yescharacteristic
452C42C2×C22⋊D1111yescharacteristic
453C42C2×C22⋊D1111yescharacteristic
454C11#2113711yescharacteristic, complemented, Sylow
455C23—21no—
456C23—221no—
457C23C2×#433911yescharacteristic
458Q8—21no—
459Q8—221no—
460Q8—221no—
461Q8#6692512yes—
462D4—24no—
463D4—21no—
464D4—221no—
465D4—221no—
466D4—442no—
467D4#6692512yes—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—224no—
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×C22⋊D1111yescharacteristic
486C2×C4C4×C22⋊D1111yescharacteristic
487C2×C4C4×C22⋊D1111yescharacteristic
488C2×C4C4×C22⋊D1111yescharacteristic
489C2×C4C22×C4×D1111yescharacteristic
490C2×C4C2×#433912yes—
491C2×C4C2×#433912yes—
492C2×C4C22×C22⋊D1111yescharacteristic
493C8—22no—
494C8—24no—
495C8—22no—
496C8—221no—
497C8—221no—
498C8—221no—
499C8—221no—
500C8—442no—
501C22—21no—
502C22—21no—
503C22—22no—
504C22—41no—
505C22—41no—
506C22—441no—
507C22—441no—
508C22—441no—
509C22#1062301012yes—
510C22C2×C4×C22⋊D1111yescharacteristic
511C4—21no—
512C4—21no—
513C4—22no—
514C4—41no—
515C4—41no—
516C4—444no—
517C4—441no—
518C4—441no—
519C4—441no—
520C4#1062275712yes—
521C4#1062275812yes—
522C4C2×#6692511yescharacteristic
523C4C4×#433911yescharacteristic
524C4#1062332212yes—
525C2—22no—
526C2—42no—
527C2—881no—
528C2#1307105911yescharacteristic
529C2C2×#1062275711yescharacteristic
530C2C2×#1062275811yescharacteristic
subgroupG/H
centerC42C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#131C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C22
cosocleC22×C4×C11C24
hypercenterC4×#131D11
hypocenterC11#21137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #13077258C2semidirect
3. #13069264C2semidirect
4. #13069215C2semidirect
6. #13068891C2semidirect
7. C4×#66886C2semidirect
8. C4×#66889C2semidirect
9. C4×#66901C2semidirect
10. #13068361C2semidirect
11. C4×C11×#131C2semidirect
28. C4×#4326C4semidirect
29. C4×#4326C4semidirect
30. C4×#4325C4semidirect
31. C4×#4325C4semidirect
32. C4×#4324C4semidirect
33. C4×#4324C4semidirect
34. C4×#4323C4semidirect
35. C4×#4323C4semidirect
192. C4×#131D11semidirect
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
#130772582
#130692642
#130692152
#130689432
#130688912
C4×#668862
C4×#668892
C4×#669012
#130683612
C4×C11×#1312
#2113711