Finite Group Databasebeta

← #14788546

Subgroups — #14788546

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623101C211yesmaximal, characteristic, complemented
2C2×#10622454C211yesmaximal, characteristic
3C2×C4×#4314C211yesmaximal, characteristic
4#13073534C211yesmaximal, characteristic
5#13069863C212yesmaximal, complemented
6#13069701C212yesmaximal
7#13069418C211yesmaximal, characteristic, complemented
8#13068970C212yesmaximal
9#13068887C212yesmaximal, complemented
10#13068622C211yesmaximal, characteristic, complemented
11C11×#1984C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999—21no—
14C2×Q8×Dic11—21no—
15C22×#4314C2211yescharacteristic
16C22×#4314C2212yes—
17#10623101—24no—
18#10623101—24no—
19C2×#66943—21no—
20C2×#66943—22no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2212yes—
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2212yes—
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66880C2212yes—
31C2×#66880C2211yescharacteristic
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34C2×#66880C2212yes—
35#10622607—22no—
36#10622600—21no—
37#10622552C2212yes—
38#10622548C2211yescharacteristic
39#10622541C2212yes—
40#10622454—24no—
41C4×#4314—24no—
42C11×#336C2212yes—
43C11×#336C2212yes—
44#10622189C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×Dic22C2312yes—
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D412yes—
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59#66999—44no—
60Q8×Dic11—28no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—21no—
78C2×#4314—22no—
79C2×#4314—22no—
80C2×#4314—22no—
81C2×#4314—24no—
82C2×#4314—24no—
83C2×#4314—42no—
84#66943—216no—
85#66943—28no—
86C4×D44—22no—
87C4×D44—22no—
88#66922—24no—
89#66922—24no—
90#66922—22no—
91#66922D414yes—
92C4×Dic22—24no—
93C4×Dic22—22no—
94C4×Dic22—24no—
95C4×Dic22D414yes—
96C11×C4⋊C8—22no—
97C4×C8×C11—22no—
98C11⋊#95—22no—
99#66885—22no—
100#66881—22no—
101#66880—22no—
102#66880—24no—
103#66880—24no—
104#66880—42no—
105#66880—42no—
106#24187—111nomaximal, Sylow
107C23×D11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11SD1614yescomplemented
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—21no—
117C22×Dic11—22no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44#4112yes—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×Dic22—22no—
131C2×Dic22—21no—
132C2×Dic22—22no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C2×Dic22—22no—
136C2×Dic22—21no—
137C2×Dic22—22no—
138C2×Dic22—21no—
139C2×Dic22—22no—
140C2×Dic22C2×D414yes—
141C2×Dic22C2×D412yes—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—22no—
149C2×C8×C11—21no—
150C2×C8×C11#4112yes—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11C2×D412yes—
156C42×C11C2×D412yes—
157(C2×D11)⋊C4—42no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—82no—
160C4⋊Dic11—28no—
161C4⋊Dic11—28no—
162C4⋊Dic11—24no—
163C4⋊Dic11—24no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—42no—
170C4⋊Dic11—81no—
171C4⋊Dic11C2×D412yes—
172Dic11⋊C4—28no—
173Dic11⋊C4—24no—
174Dic11⋊C4—44no—
175C4×Dic11—28no—
176C4×Dic11—24no—
177#4314—28no—
178#4314—48no—
179C2×#557—111no—
180C2×#461—111no—
181C2×C4×SD16—111no—
182#2538—111no—
183#2043—112no—
184#2013—112no—
185#1984D1111yescharacteristic, complemented
186#1956—111no—
187#1880—112no—
188#1865—112no—
189#1803—111no—
190C23×C11C22×D411yescharacteristic
191C22×D11—22no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198Q8×C11—28no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11#12012yes—
207C2×C4×C11#12012yes—
208C2×C4×C11C2×SD1614yes—
209C2×C4×C11C2×SD1612yes—
210C2×C4×C11#13712yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11H(5,𝔽2)11yescharacteristic
216C2×C4×C112−1+411yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—24no—
219C2×Dic11—22no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232D44—22no—
233D44—22no—
234D44—41no—
235D44—41no—
236C4×D11—84no—
237Dic22—22no—
238Dic22—22no—
239Dic22—24no—
240Dic22—24no—
241Dic22—42no—
242Dic22—42no—
243Dic22—41no—
244Dic22—41no—
245C8×C11—22no—
246C8×C11—41no—
247C8×C11—42no—
248C22×SD16—111no—
249C22×SD16—112no—
250#557—224no—
251#557—224no—
252C2×C4⋊Q8—111no—
253C2×C4⋊Q8—112no—
254C2×#125—221no—
255C2×#125—222no—
256C2×C22⋊Q8—221no—
257C2×C4×Q8—111no—
258C2×C4×Q8—112no—
259C2×C4×Q8—221no—
260C2×C4×Q8C2×D1111yescharacteristic
261C2×C4×D4—111no—
262#461—224no—
263C4×SD16—224no—
264C2×#106—111no—
265C2×C4⋊C8C2×D1111yescharacteristic
266C2×#103—112no—
267C2×#103—112no—
268C2×#103—111no—
269C2×#103—112no—
270C2×#103—112no—
271C2×#102—111no—
272C2×C4×C8C2×D1111yescharacteristic
273#396—222no—
274#390—112no—
275#389—112no—
276#384—111no—
277#380—221no—
278#340—112no—
279#336C2×D1112yes—
280#336C2×D1112yes—
281C22×C11C2×#12011yescharacteristic
282C22×C11#54811yescharacteristic
283C22×C11#55011yescharacteristic
284C22×C11C22×SD1611yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C22×C11#57711yescharacteristic
287C22×C11#57811yescharacteristic
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11—81no—
295C4×C11—24no—
296C4×C11—22no—
297C4×C11—42no—
298C4×C11#44814yes—
299C4×C11#52511yescharacteristic
300C4×C11#53711yescharacteristic
301C4×C11#54611yescharacteristic
302C4×C11#54711yescharacteristic
303Dic11—42no—
304Dic11—44no—
305Dic11—42no—
306Dic11—82no—
307Dic11—81no—
308C22×Q8—111no—
309C22×Q8—112no—
310C22×Q8D4411yescharacteristic
311C22×D4—111no—
312C23×C4—221no—
313C2×SD16—222no—
314C2×SD16—222no—
315C2×SD16—224no—
316C2×SD16—224no—
317C2×SD16—222no—
318C2×SD16—442no—
319C22×C8C22×D1112yes—
320C22×C8C22×D1111yescharacteristic
321C22×C8C22×D1111yescharacteristic
322C4⋊Q8—114no—
323C4⋊Q8—224no—
324C4⋊Q8—224no—
325C4⋊Q8—222no—
326#125—2216no—
327#125—228no—
328C22⋊Q8—444no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—114no—
332C4×Q8—224no—
333C4×Q8—224no—
334C4×Q8—228no—
335C4×Q8—222no—
336C4×D4—222no—
337C4×D4—222no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4D4411yescharacteristic
351C2×C4⋊C4D4412yes—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C42—222no—
356C2×C42—221no—
357C2×C42C22×D1112yes—
358C2×C42C22×D1111yescharacteristic
359#106—222no—
360C4⋊C8—22no—
361#103—222no—
362#103—224no—
363#103—224no—
364#103—442no—
365#103—442no—
366#102—222no—
367C4×C8—22no—
368#95—222no—
369C2×C11#240711yescharacteristic
370C2×C11C2×#44811yescharacteristic
371C2×C11#301311yescharacteristic
372C2×C11#335911yescharacteristic
373C2×C11#337211yescharacteristic
374C2×C11#339211yescharacteristic
375C2×C11#339811yescharacteristic
376D11—82no—
377C24—221no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—112no—
381C2×Q8—114no—
382C2×Q8—221no—
383C2×Q8—222no—
384C2×Q8—222no—
385C2×Q8—221no—
386C2×Q8—222no—
387C2×Q8—221no—
388C2×Q8—221no—
389C2×Q8—222no—
390C2×Q8—221no—
391C2×Q8—222no—
392C2×Q8#431414yescomplemented
393C2×D4—112no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—221no—
399C22×C4—221no—
400C22×C4—222no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4—442no—
405C22×C4—442no—
406C22×C4—442no—
407C22×C4C2×D4412yes—
408C22×C4C2×D4411yescharacteristic
409C22×C4C2×D4412yes—
410C22×C4C2×D4411yescharacteristic
411C22×C4C23×D1111yescharacteristic
412SD16—228no—
413SD16—448no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—22no—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8#434312yes—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—112no—
426C4⋊C4—228no—
427C4⋊C4—228no—
428C4⋊C4—228no—
429C4⋊C4—224no—
430C4⋊C4—224no—
431C4⋊C4—224no—
432C4⋊C4—221no—
433C4⋊C4—221no—
434C4⋊C4—221no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—444no—
438C4⋊C4—442no—
439C4⋊C4—881no—
440C22⋊C4—442no—
441C22⋊C4—444no—
442C22⋊C4—882no—
443C42—22no—
444C42—22no—
445C42—228no—
446C42—224no—
447C42D4×D1112yes—
448C42D4×D1112yes—
449C11#2418711yescharacteristic, complemented, Sylow
450C23—222no—
451C23—441no—
452C23—441no—
453C23—441no—
454C23—441no—
455C23—441no—
456C23—441no—
457C23C22×D4411yescharacteristic
458Q8—28no—
459Q8—224no—
460Q8—222no—
461Q8—222no—
462Q8—224no—
463Q8—441no—
464Q8—442no—
465Q8—442no—
466Q8—441no—
467D4—222no—
468D4—222no—
469D4—441no—
470D4—441no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—222no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—442no—
484C2×C4—441no—
485C2×C4—442no—
486C2×C4—441no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—884no—
494C2×C4#6693512yes—
495C2×C4#6693512yes—
496C2×C4C2×#431414yes—
497C2×C4C2×#431412yes—
498C2×C4#6696212yes—
499C2×C4C2×D4×D1111yescharacteristic
500C2×C4C2×D4×D1111yescharacteristic
501C2×C4C2×#434311yescharacteristic
502C2×C4#6704011yescharacteristic
503C2×C4#41×D1111yescharacteristic
504C2×C4#6704211yescharacteristic
505C8—22no—
506C8—41no—
507C8—42no—
508C22—442no—
509C22—442no—
510C22—442no—
511C22—881no—
512C22—881no—
513C22—881no—
514C22—881no—
515C22C2×#6693511yescharacteristic
516C22#1062310711yescharacteristic
517C22#1062310811yescharacteristic
518C22C22×#431411yescharacteristic
519C22C2×#6696211yescharacteristic
520C22#1062328211yescharacteristic
521C22#1062328411yescharacteristic
522C4—24no—
523C4—22no—
524C4—42no—
525C4—444no—
526C4—442no—
527C4—442no—
528C4—881no—
529C4—882no—
530C4#1062235114yes—
531C4#1062315811yescharacteristic
532C4#1062316011yescharacteristic
533C4#1062320711yescharacteristic
534C4#1062325711yescharacteristic
535C2—882no—
536C2#1307196411yescharacteristic
537C2C2×#1062235111yescharacteristic
538C2#1307793411yescharacteristic
539C2#1308125911yescharacteristic
540C2#1308139911yescharacteristic
541C2#1308159811yescharacteristic
542C2#1308164911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1984C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1984D11
hypocenterC11#24187
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #1984

Complements

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

NH ≅ G/Ntype
1. C2×#10623101C2semidirect
5. #13069863C2semidirect
7. #13069418C2semidirect
9. #13068887C2semidirect
10. #13068622C2semidirect
11. C11×#1984C2semidirect
110. C2×Q8×C11SD16semidirect
185. #1984D11semidirect
392. C2×Q8#4314semidirect
449. C11#24187semidirect

Maximal subgroups

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

subgroupindex
C2×#106231012
C2×#106224542
C2×C4×#43142
#130735342
#130698632
#130697012
#130694182
#130689702
#130688872
#130686222
C11×#19842
#2418711