Finite Group Databasebeta

← #14804271

Subgroups — #14804271

Order 2816.

1086 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
1C2×#10622698C211yesmaximal, characteristic
2C2×#10622461C211yesmaximal, characteristic
3C2×#10622431C212yesmaximal, complemented
4#13073605C211yesmaximal, characteristic, complemented
5#13071680C211yesmaximal, characteristic
6#13069930C212yesmaximal, complemented
7#13069700C212yesmaximal, complemented
8#13069332C211yesmaximal, characteristic, complemented
9#13068947C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#1981C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66997C2212yes—
14C22×#4325C2212yes—
15C22×#4325C2212yes—
16C22×#4314C2212yes—
17C2×#66946C2212yes—
18C2×#66927C2211yescharacteristic
19C2×C4×D44—21no—
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2212yes—
23C2×C11×#103C2212yes—
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622843C2212yes—
26C2×#66885C2212yes—
27C2×Dic11⋊C8C2212yes—
28#10622698—24no—
29#10622601C2212yes—
30#10622593—22no—
31#10622586—21no—
32#10622586—21no—
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35#10622552—21no—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622461—24no—
39#10622431—28no—
40#10622278—22no—
41#10622188C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44C2312yes—
48C22×C4×D11—22no—
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59#66997—24no—
60#66997—42no—
61C2×#4325—24no—
62C2×#4325—24no—
63C2×#4325—24no—
64C2×#4325—24no—
65C2×#4325—42no—
66C2×#4325—42no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C2×#4314—24no—
81C2×#4314—24no—
82C2×#4314—42no—
83#66946—24no—
84#66946—42no—
85#66927—22no—
86#66927D414yes—
87C4×D44—44no—
88C4×Dic22—22no—
89C4×Dic22—22no—
90C11×C4⋊C8—22no—
91C11×#103—24no—
92C11×#103—42no—
93C11×#95—21no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95D412yes—
97#66885—24no—
98Dic11⋊C8—24no—
99#66874—22no—
100#66874D414yescomplemented
101C4×C11⋊C8—22no—
102#25368—111nomaximal, Sylow
103C23×D11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11C2×D412yes—
119C22×Dic11C2×D412yes—
120C2×D44—24no—
121C2×D44—24no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—42no—
128C2×D44—42no—
129C2×D44—81no—
130C2×D44—81no—
131C2×D44C2×D414yes—
132C2×C4×D11—44no—
133C2×C4×D11—44no—
134C2×C4×D11—82no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22C2×D412yes—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4C2×D412yes—
150C42×C11—42no—
151C42×C11C2×D412yes—
152C42×C11#4112yes—
153#4325—48no—
154#4325—48no—
155(C2×D11)⋊C4—44no—
156(C2×D11)⋊C4—44no—
157(C2×D11)⋊C4—82no—
158C4⋊Dic11—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11SD1614yescomplemented
162Dic11⋊C4—44no—
163Dic11⋊C4—44no—
164Dic11⋊C4—42no—
165C4×Dic11—22no—
166C4×Dic11—22no—
167C4×Dic11—42no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8C2×D412yes—
173C2×C11⋊C8#4112yes—
174#4314—48no—
175C2×#492—111no—
176C2×#460—111no—
177C2×#461—112no—
178#2546—111no—
179#2366—111no—
180#2055—112no—
181#2013—112no—
182#1981D1111yescharacteristic, complemented
183#1939—111no—
184#1877—112no—
185C4×#103—111no—
186C23×C11C22×D411yescharacteristic
187C22×D11—24no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—42no—
197Q8×C11—42no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11#12112yes—
210C2×C4×C11#12112yes—
211C2×C4×C11C2×SD1612yes—
212C2×C4×C11#13712yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11C2×SD1614yes—
231D44—24no—
232D44—24no—
233D44—42no—
234D44—42no—
235D44—48no—
236D44—84no—
237C4×D11—88no—
238Dic22—22no—
239Dic22—22no—
240Dic22—41no—
241Dic22—41no—
242C8×C11—42no—
243C11⋊C8—22no—
244C11⋊C8—22no—
245C22×SD16—112no—
246C22×SD16—112no—
247C22×SD16—112no—
248C2×C4⋊Q8—112no—
249C2×C4⋊Q8C2×D1111yescharacteristic
250C2×#127—111no—
251C2×C4×Q8—111no—
252C2×C4×D4—112no—
253C2×C4×D4—221no—
254#492—224no—
255#461—228no—
256#460—224no—
257C2×C4⋊C8—112no—
258C2×C4⋊C8C2×D1111yescharacteristic
259C2×#103—111no—
260C2×#103—111no—
261C2×#103C2×D1112yes—
262C2×#103C2×D1112yes—
263C2×#102—112no—
264C2×C4×C8—111no—
265#398—222no—
266#391—112no—
267#390—112no—
268#390—221no—
269#389—221no—
270#389—221no—
271#386—222no—
272C4×C4⋊C4—111no—
273C4×C4⋊C4C2×D1111yescharacteristic
274#340—111no—
275#340—111no—
276#336—112no—
277C22×C11C2×#12111yescharacteristic
278C22×C11D4211yescharacteristic
279C22×C11#55011yescharacteristic
280C22×C11C22×SD1611yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C22×C11#57711yescharacteristic
283C22×C11#57711yescharacteristic
284C2×D11—44no—
285C2×D11—44no—
286C2×D11—44no—
287C2×D11—82no—
288C2×D11—82no—
289C2×D11—82no—
290C2×D11—82no—
291C4×C11—22no—
292C4×C11—42no—
293C4×C11—81no—
294C4×C11—82no—
295C4×C11#46114yescomplemented
296C4×C11#53211yescharacteristic
297C4×C11#54011yescharacteristic
298C4×C11D4211yescharacteristic
299C4×C11#54611yescharacteristic
300Dic11—24no—
301Dic11—42no—
302Dic11—42no—
303Dic11—81no—
304C22×Q8—111no—
305C22×Q8C22×D1112yes—
306C22×D4—112no—
307C22×D4—221no—
308C22×D4—221no—
309C23×C4—222no—
310C2×SD16—224no—
311C2×SD16—224no—
312C2×SD16—224no—
313C2×SD16—224no—
314C2×SD16—224no—
315C2×SD16—224no—
316C2×SD16—442no—
317C2×SD16—442no—
318C2×SD16—442no—
319C22×C8—111no—
320C22×C8—111no—
321C22×C8C22×D1112yes—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—224no—
325C4⋊Q8—442no—
326#127—114no—
327#127—222no—
328C4×Q8—222no—
329C4×Q8—222no—
330C4×D4—224no—
331C4×D4—444no—
332C4×D4—442no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4C22×D1111yescharacteristic
342C2×C4⋊C4C22×D1111yescharacteristic
343C2×C22⋊C4—222no—
344C2×C22⋊C4—222no—
345C2×C22⋊C4—222no—
346C2×C42—21no—
347C2×C42—112no—
348C2×C42—221no—
349C2×C42C22×D1111yescharacteristic
350C4⋊C8—22no—
351C4⋊C8—224no—
352#103—24no—
353#103—42no—
354#103—114no—
355#103—222no—
356#102—224no—
357C4×C8—222no—
358#95—21no—
359#95—112no—
360#95—222no—
361#95—222no—
362C2×C11#242811yescharacteristic
363C2×C11C2×#46111yescharacteristic
364C2×C11#304211yescharacteristic
365C2×C11#327811yescharacteristic
366C2×C11D4×SD1611yescharacteristic
367C2×C11#339211yescharacteristic
368C2×C11#340011yescharacteristic
369D11—84no—
370C24—222no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—112no—
378C2×Q8—221no—
379C2×Q8—221no—
380C2×Q8—221no—
381C2×Q8—221no—
382C2×Q8—221no—
383C2×D4—114no—
384C2×D4—224no—
385C2×D4—224no—
386C2×D4—222no—
387C2×D4—222no—
388C2×D4—222no—
389C2×D4—222no—
390C2×D4—222no—
391C2×D4—442no—
392C2×D4—442no—
393C2×D4—881no—
394C2×D4—881no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—112no—
399C22×C4—112no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—444no—
403C22×C4—444no—
404C22×C4—882no—
405C22×C4D4×D1111yescharacteristic
406C22×C4D4×D1111yescharacteristic
407C22×C4C23×D1111yescharacteristic
408SD16—448no—
409SD16—448no—
410SD16—448no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—112no—
415C2×C8—112no—
416C2×C8—221no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—221no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—42no—
424C4⋊C4—42no—
425C4⋊C4—114no—
426C4⋊C4—222no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—444no—
430C4⋊C4—444no—
431C4⋊C4—442no—
432C4⋊C4D4×D1112yes—
433C22⋊C4—444no—
434C22⋊C4—444no—
435C22⋊C4—882no—
436C42—42no—
437C42—222no—
438C42—222no—
439C42—442no—
440C42#433912yes—
441C42D4×D1112yes—
442C11#2536811yescharacteristic, complemented, Sylow
443C23—224no—
444C23—442no—
445C23—442no—
446C23—442no—
447C23—442no—
448C23—442no—
449C23—442no—
450C23C2×D4×D1111yescharacteristic
451Q8—42no—
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—222no—
456Q8—222no—
457Q8—441no—
458Q8—441no—
459D4—224no—
460D4—224no—
461D4—442no—
462D4—442no—
463D4—448no—
464D4—884no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—114no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4—888no—
489C2×C4#6693712yes—
490C2×C4#6693712yes—
491C2×C4SD16×D1112yes—
492C2×C4#6697112yes—
493C2×C4C2×#433911yescharacteristic
494C2×C4C2×D4×D1111yescharacteristic
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4#6703711yescharacteristic
497C2×C4#41×D1111yescharacteristic
498C2×C4#6704211yescharacteristic
499C8—42no—
500C8—222no—
501C8—222no—
502C22—444no—
503C22—444no—
504C22—444no—
505C22—882no—
506C22—882no—
507C22—882no—
508C22—882no—
509C22C2×#6693711yescharacteristic
510C22#1062313011yescharacteristic
511C22#1062314011yescharacteristic
512C22C2×SD16×D1111yescharacteristic
513C22C2×#6697111yescharacteristic
514C22#1062330911yescharacteristic
515C22#1062330911yescharacteristic
516C4—22no—
517C4—42no—
518C4—82no—
519C4—81no—
520C4—224no—
521C4—442no—
522C4—442no—
523C4—881no—
524C4#1062243114yescomplemented
525C4#1062307911yescharacteristic
526C4#1062309311yescharacteristic
527C4#1062320711yescharacteristic
528C4#1062324811yescharacteristic
529C2—884no—
530C2#1307220511yescharacteristic
531C2C2×#1062243111yescharacteristic
532C2#1307812711yescharacteristic
533C2#1308027711yescharacteristic
534C2#1308031511yescharacteristic
535C2#1308159211yescharacteristic
536C2#1308167311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1981C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1981D11
hypocenterC11#25368
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
3. C2×#10622431C2semidirect
4. #13073605C2semidirect
6. #13069930C2semidirect
7. #13069700C2semidirect
8. #13069332C2semidirect
9. #13068947C2semidirect
10. C4×#66874C2semidirect
11. C11×#1981C2semidirect
100. #66874D4semidirect
161. C4⋊Dic11SD16semidirect
182. #1981D11semidirect
295. C4×C11#461semidirect
442. C11#25368semidirect
524. C4#10622431semidirect

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106224612
C2×#106224312
#130736052
#130716802
#130699302
#130697002
#130693322
#130689472
C4×#668742
C11×#19812
#2536811