Finite Group Databasebeta

← #14756995

Subgroups — #14756995

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#13077261C211yesmaximal, characteristic, complemented
3C4×#66960C211yesmaximal, characteristic, complemented
4#13069263C212yesmaximal, complemented
5#13069214C212yesmaximal, complemented
6#13068944C212yesmaximal
7#13068888C212yesmaximal, complemented
8C4×#66889C211yesmaximal, characteristic, complemented
9C4×#66889C211yesmaximal, characteristic, complemented
10#13068361C211yesmaximal, characteristic, complemented
11C4×C11×#108C211yesmaximal, characteristic, complemented
12C2×#66960C2212yes—
13C2×#66957C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C4×#4339C2211yescharacteristic
16C2×C11×#108C2212yes—
17C4×C11×M16C2211yescharacteristic
18C4×C11×M16C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20C2×#66889C2212yes—
21C2×#66889C2212yes—
22#10622742C2212yes—
23#10622735C2212yes—
24#10622732C2212yes—
25#10622726C2211yescharacteristic
26#10622726C2211yescharacteristic
27#10622719C2211yescharacteristic
28C42×Dic11C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30#10622322—22no—
31#10622321—22no—
32C4×Dic44C411yescharacteristic, complemented
33C4×Dic44C411yescharacteristic, complemented
34C4×D88C411yescharacteristic, complemented
35C4×D88C411yescharacteristic, complemented
36C4×#4314C411yescharacteristic, complemented
37C4×#4314C411yescharacteristic, complemented
38C4×#4314C411yescharacteristic, complemented
39C4×#4314C411yescharacteristic, complemented
40C4×#4313—21no—
41#10622298—21no—
42#10622298—21no—
43C4×C8×D11—21no—
44C11×#341C2212yes—
45#10622193C2212yes—
46#10622193C2212yes—
47#10622188C2212yes—
48#10622188C2212yes—
49C2×#4339C2311yescharacteristic
50C2×#4339C2311yescharacteristic
51C2×C11×M16C2312yes—
52C2×C11×M16C2312yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C4×C22⋊D11—21no—
57C4×C22⋊D11—21no—
58C4×C22⋊D11—21no—
59C4×C22⋊D11—21no—
60#66979C2311yescharacteristic
61#66979C2311yescharacteristic
62C2×C4×Dic11—21no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11C2312yes—
65C22×C11⋊C8C2312yes—
66#66960—24no—
67#66960—24no—
68C2×Dic44C2×C411yescharacteristic
69#66957—24no—
70C2×D88C2×C411yescharacteristic
71C2×#4314C2×C411yescharacteristic
72C2×#4314C2×C411yescharacteristic
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
87C11×#108—24no—
88C11×#97—21no—
89C11×#97—21no—
90C4×C8×C11—21no—
91C4×C8×C11—21no—
92C4×C8×C11C2×C411yescharacteristic
93C4×C8×C11C2×C411yescharacteristic
94C4×C8×C11C2×C411yescharacteristic
95C4×C8×C11C2×C411yescharacteristic
96#66889—24no—
97#66889—24no—
98#66885C2×C411yescharacteristic
99#66885C2×C411yescharacteristic
100#66885C2×C411yescharacteristic
101#66885C2×C411yescharacteristic
102(C2×D11)⋊C8—22no—
103(C2×D11)⋊C8—22no—
104#66882C2×C411yescharacteristic
105#66882C2×C411yescharacteristic
106#66881C2×C411yescharacteristic
107#66881C2×C411yescharacteristic
108#66880C2×C411yescharacteristic
109#66880C2×C411yescharacteristic
110#66880C2×C411yescharacteristic
111#66880C2×C411yescharacteristic
112#66879—22no—
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115C8×Dic11—22no—
116C4×C11⋊C8D411yescharacteristic
117C4×C11⋊C8D411yescharacteristic
118C4×C11⋊C8D412yes—
119#21137—111nomaximal, Sylow
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—21no—
124C2×C22⋊D11—21no—
125C22×Dic11—22no—
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
140C11×M16—22no—
141C11×M16—22no—
142C11×M16—22no—
143C11×M16#4114yes—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11C22×C411yescharacteristic
149C2×C8×C11C22×C411yescharacteristic
150C2×C8×C11C22×C411yescharacteristic
151C2×C8×C11C22×C411yescharacteristic
152C42×C11C22×C411yescharacteristic
153C42×C11C22×C411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C22⋊Dic11—21no—
157C22⋊Dic11—21no—
158(C2×D11)⋊C4—21no—
159(C2×D11)⋊C4—21no—
160(C2×D11)⋊C4—21no—
161(C2×D11)⋊C4—21no—
162C4⋊Dic11C22×C411yescharacteristic
163C4⋊Dic11C22×C411yescharacteristic
164C4⋊Dic11C22×C411yescharacteristic
165C4⋊Dic11C22×C411yescharacteristic
166Dic11⋊C4—21no—
167Dic11⋊C4—21no—
168Dic11⋊C4—21no—
169Dic11⋊C4—21no—
170C4×Dic11—24no—
171C4×Dic11—21no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—22no—
178C4×Dic11—22no—
179C4×Dic11—42no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8C2×D412yes—
183C2×C11⋊C8C2×D412yes—
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×#108D1111yescharacteristic, complemented
198C4×#104—111no—
199C4×#104—111no—
200#1744—111no—
201C23×C11C2×#4111yescharacteristic
202C22×D11—21no—
203C22×D11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C4×D411yescharacteristic
208C2×C4×C11C4×D411yescharacteristic
209C2×C4×C11C4×D411yescharacteristic
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4112yes—
213C2×C4×C11C2×#4112yes—
214C22⋊D11—24no—
215C22⋊D11—42no—
216C2×Dic11—21no—
217C2×Dic11—24no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—42no—
224C2×Dic11—42no—
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—24no—
244C8×C11—42no—
245C11⋊C8—22no—
246C11⋊C8—22no—
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×#108C2×D1112yes—
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—221no—
273C4×M16C2×D1111yescharacteristic
274C4×M16C2×D1111yescharacteristic
275C2×C4×C8—111no—
276C2×C4×C8—221no—
277C2×C4×C8C2×D1111yescharacteristic
278C43—111no—
279#341C2×D1112yes—
280#339—112no—
281#339—112no—
282#336—112no—
283#336—112no—
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#44312yes—
297C4×C11#44412yes—
298C4×C11C2×#11711yescharacteristic
299C4×C11C4×#4111yescharacteristic
300C4×C11#52512yes—
301Dic11—22no—
302Dic11—44no—
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—222no—
318C2×M16C22×D1112yes—
319C2×M16C22×D1112yes—
320C22×C8—112no—
321C22×C8—222no—
322C22×C8C22×D1111yescharacteristic
323C22×C8C22×D1111yescharacteristic
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—112no—
341C2×C42—221no—
342C2×C42—221no—
343C2×C42—221no—
344C2×C42—221no—
345C2×C42C22×D1111yescharacteristic
346#108—24no—
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—21no—
366#97—21no—
367#97—222no—
368C4×C8—21no—
369C4×C8—21no—
370C4×C8—112no—
371C4×C8—111no—
372C4×C8—111no—
373C4×C8—222no—
374C4×C8C4×D1111yescharacteristic
375C4×C8C4×D1111yescharacteristic
376C4×C8C4×D1111yescharacteristic
377C4×C8C4×D1111yescharacteristic
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—221no—
395C22×C4—222no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4#434311yescharacteristic
402C22×C4#434311yescharacteristic
403C22×C4C23×D1111yescharacteristic
404Q16—222no—
405SD16—222no—
406SD16—222no—
407D8—222no—
408M16—22no—
409M16—22no—
410M16—22no—
411M16—228no—
412M16#433914yes—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—112no—
418C2×C8—112no—
419C2×C8—228no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8C2×C4×D1111yescharacteristic
423C2×C8C2×C4×D1111yescharacteristic
424C2×C8C2×C4×D1111yescharacteristic
425C2×C8C2×C4×D1111yescharacteristic
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—224no—
441C42—221no—
442C42—221no—
443C42—221no—
444C42—221no—
445C42—221no—
446C42—221no—
447C42—222no—
448C42—222no—
449C42—442no—
450C42C2×C4×D1111yescharacteristic
451C42C2×C4×D1111yescharacteristic
452C42D4×D1111yescharacteristic
453C42D4×D1111yescharacteristic
454C11#2113711yescharacteristic, complemented, Sylow
455C23—221no—
456C23—221no—
457C23C2×#434311yescharacteristic
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—221no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4#6694611yescharacteristic
486C2×C4#6694611yescharacteristic
487C2×C4#6694611yescharacteristic
488C2×C4#6694611yescharacteristic
489C2×C4C22×C4×D1111yescharacteristic
490C2×C4C2×#433912yes—
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4#41×D1112yes—
493C8—21no—
494C8—21no—
495C8—21no—
496C8—21no—
497C8—24no—
498C8—42no—
499C8—222no—
500C8—222no—
501C22—21no—
502C22—21no—
503C22—222no—
504C22—441no—
505C22—441no—
506C22—441no—
507C22—441no—
508C22—441no—
509C22C2×#6694611yescharacteristic
510C22#1062311112yes—
511C4—21no—
512C4—21no—
513C4—222no—
514C4—444no—
515C4—441no—
516C4—441no—
517C4—441no—
518C4—441no—
519C4—441no—
520C4#1062250712yes—
521C4#1062250812yes—
522C4C4×#433911yescharacteristic
523C4D11×#11711yescharacteristic
524C4#1062307812yes—
525C2—22no—
526C2—442no—
527C2—881no—
528C2#1307105711yescharacteristic
529C2C2×#1062250811yescharacteristic
530C2C2×#1062250711yescharacteristic
subgroupG/H
centerC42D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#108C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C22
cosocleC22×C4×C11C24
hypercenterC4×#108D11
hypocenterC11#21137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#108

Complements

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

NH ≅ G/Ntype
2. #13077261C2semidirect
3. C4×#66960C2semidirect
4. #13069263C2semidirect
5. #13069214C2semidirect
7. #13068888C2semidirect
8. C4×#66889C2semidirect
9. C4×#66889C2semidirect
10. #13068361C2semidirect
11. C4×C11×#108C2semidirect
32. C4×Dic44C4semidirect
33. C4×Dic44C4semidirect
34. C4×D88C4semidirect
35. C4×D88C4semidirect
36. C4×#4314C4semidirect
37. C4×#4314C4semidirect
38. C4×#4314C4semidirect
39. C4×#4314C4semidirect
197. C4×#108D11semidirect
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
#130772612
C4×#669602
#130692632
#130692142
#130689442
#130688882
C4×#668892
#130683612
C4×C11×#1082
#2113711