Finite Group Databasebeta

← #14804244

Subgroups — #14804244

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622689C211yesmaximal, characteristic, complemented
2C2×#10622688C212yesmaximal, complemented
3C2×#10622632C211yesmaximal, characteristic, complemented
4#13071672C211yesmaximal, characteristic, complemented
5#13069933C212yesmaximal, complemented
6#13069704C212yesmaximal, complemented
7#13069544C211yesmaximal, characteristic, complemented
8#13069335C211yesmaximal, characteristic, complemented
9#13068974C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C11×#2541C211yesmaximal, characteristic
12C2×C11×#127C2211yescharacteristic
13C2×C11×#127C2212yes—
14C2×C11×#121—21no—
15C2×C11×#121—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4324C2212yes—
18C22×#4324C2212yes—
19C22×#4324C2212yes—
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2212yes—
22C11×#392—22no—
23C11×#390C2212yes—
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66896C2212yes—
26C2×#66896C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66896C2211yescharacteristic
29#10622689—24no—
30#10622688—28no—
31#10622632—24no—
32C4⋊C4×Dic11—21no—
33#10622586—21no—
34C2×#66874C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36#10622542C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622267—22no—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43#10622162C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11C2312yes—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C22×Dic22C2312yes—
52C11×#127—24no—
53C11×#127—22no—
54C11×#127—22no—
55C11×#127—42no—
56C11×#121—44no—
57C11×#121—44no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C42×C11C2312yes—
67C2×C42×C11C2311yescharacteristic
68C2×#4324—24no—
69C2×#4324—24no—
70C2×#4324—24no—
71C2×#4324—24no—
72C2×#4324—24no—
73C2×#4324—24no—
74C2×#4324—42no—
75C2×#4324—42no—
76C2×#4324—42no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—21no—
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87#66922—22no—
88#66922D414yescomplemented
89C4×Dic22—24no—
90C4×Dic22—42no—
91C11×#95D412yes—
92#66896—24no—
93#66896—22no—
94#66896—42no—
95#66896D414yescomplemented
96C11⋊#95—21no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99#66874—24no—
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)—24no—
102C4×C11⋊C8—22no—
103#25366—111nomaximal, Sylow
104C24×C11—21no—
105C24×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—82no—
126C2×D4×C11—81no—
127C2×D4×C11—81no—
128C2×D4×C11—82no—
129C2×D4×C11C2×D412yes—
130C22×C4×C11—21no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22C2×D414yes—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4SD1614yescomplemented
152C11×C22⋊C4—44no—
153C11×C22⋊C4—42no—
154C11×C22⋊C4—44no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11C2×D412yes—
158C42×C11#4112yes—
159#4324—48no—
160#4324—48no—
161#4324—48no—
162C4⋊Dic11—24no—
163C4⋊Dic11—24no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11C2×D412yes—
168Dic11⋊C4—44no—
169C4×Dic11—44no—
170C4×Dic11—42no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8C2×D412yes—
179C2×C11⋊C8#4112yes—
180C2×#492—111no—
181C2×#460—112no—
182C2×#461—111no—
183#2541D1111yescharacteristic
184#2365—111no—
185#2055—112no—
186#2014—112no—
187#1982—111no—
188#1939—111no—
189#1880—112no—
190C4×#102—111no—
191C23×C11—22no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11C22×D411yescharacteristic
206D4×C11—22no—
207D4×C11—22no—
208D4×C11—42no—
209D4×C11—41no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—41no—
213D4×C11—42no—
214D4×C11—88no—
215D4×C11—84no—
216D4×C11—88no—
217D4×C11—84no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—84no—
229C2×C4×C11#12112yes—
230C2×C4×C11#12112yes—
231C2×C4×C11C2×SD1614yes—
232C2×C4×C11C2×SD1612yes—
233C2×C4×C11AGL(1,ℤ/8)12yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249Dic22—24no—
250Dic22—24no—
251Dic22—42no—
252Dic22—42no—
253C11⋊C8—22no—
254C11⋊C8—22no—
255C11⋊C8—42no—
256C22×SD16—112no—
257C22×SD16—112no—
258C22×SD16—112no—
259C2×C4⋊Q8—111no—
260C2×#127C2×D1111yescharacteristic
261C2×#127C2×D1112yes—
262C2×#121—21no—
263C2×#121—21no—
264C2×C4×Q8—112no—
265C2×C4×D4C2×D1111yescharacteristic
266#492—224no—
267#461—224no—
268#460—228no—
269C2×C4⋊C8—112no—
270C2×C4⋊C8—111no—
271C2×#103—112no—
272C2×#102—111no—
273C2×#102—112no—
274C2×#102—111no—
275C2×#102—112no—
276C2×C4×C8—111no—
277#392—22no—
278#391—112no—
279#390C2×D1112yes—
280#389—221no—
281#387—222no—
282C4×C4⋊C4—111no—
283C4×C4⋊C4—221no—
284C4×C4⋊C4C2×D1111yescharacteristic
285#340—111no—
286#340—111no—
287#336—112no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11C2×#12111yescharacteristic
303C22×C11D4211yescharacteristic
304C22×C11#55011yescharacteristic
305C22×C11C22×SD1611yescharacteristic
306C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C11#57711yescharacteristic
308C22×C11#57711yescharacteristic
309C4×C11—24no—
310C4×C11—22no—
311C4×C11—42no—
312C4×C11—81no—
313C4×C11#46014yescomplemented
314C4×C11#53211yescharacteristic
315C4×C11#54011yescharacteristic
316C4×C11D4211yescharacteristic
317C4×C11#54611yescharacteristic
318Dic11—44no—
319Dic11—42no—
320Dic11—81no—
321C22×Q8—112no—
322C22×D4—21no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4C22×D1112yes—
327C22×D4C22×D1111yescharacteristic
328C23×C4—21no—
329C2×SD16—224no—
330C2×SD16—224no—
331C2×SD16—224no—
332C2×SD16—224no—
333C2×SD16—224no—
334C2×SD16—224no—
335C2×SD16—442no—
336C2×SD16—442no—
337C2×SD16—442no—
338C22×C8—111no—
339C22×C8—111no—
340C22×C8—112no—
341C4⋊Q8—114no—
342C4⋊Q8—222no—
343#127—24no—
344#127—22no—
345#127—22no—
346#127—42no—
347#121—44no—
348#121—44no—
349C4×Q8—224no—
350C4×Q8—442no—
351C4×D4—22no—
352C4×D4—22no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4C22⋊D1111yescharacteristic
359C2×C4⋊C4C22⋊D1111yescharacteristic
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C42—222no—
365C2×C42—221no—
366C2×C42C22×D1112yes—
367C2×C42C22×D1111yescharacteristic
368C4⋊C8—224no—
369C4⋊C8—222no—
370#103—224no—
371#102—114no—
372#102—224no—
373#102—222no—
374#102—442no—
375C4×C8—222no—
376#95—221no—
377#95—222no—
378#95—222no—
379#95C22⋊D1112yes—
380C2×C11—82no—
381C2×C11—162no—
382C2×C11#242811yescharacteristic
383C2×C11C2×#46011yescharacteristic
384C2×C11#304311yescharacteristic
385C2×C11#327211yescharacteristic
386C2×C11D4×SD1611yescharacteristic
387C2×C11#339211yescharacteristic
388C2×C11#339711yescharacteristic
389C24—21no—
390C24—22no—
391C2×Q8—114no—
392C2×Q8—222no—
393C2×Q8—222no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—22no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—42no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—82no—
417C2×D4—81no—
418C2×D4—81no—
419C2×D4—82no—
420C2×D4D4×D1112yes—
421C22×C4—21no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1112yes—
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C23×D1111yescharacteristic
433SD16—448no—
434SD16—448no—
435SD16—448no—
436C2×C8—112no—
437C2×C8—112no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—112no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—444no—
455C4⋊C4#432414yescomplemented
456C22⋊C4—44no—
457C22⋊C4—44no—
458C22⋊C4—42no—
459C42—22no—
460C42—22no—
461C42—444no—
462C42—442no—
463C42D4×D1112yes—
464C42#434112yes—
465C11#2536611yescharacteristic, complemented, Sylow
466C23—22no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23C22×C22⋊D1111yescharacteristic
481Q8—224no—
482Q8—224no—
483Q8—442no—
484Q8—442no—
485D4—22no—
486D4—22no—
487D4—42no—
488D4—42no—
489D4—41no—
490D4—42no—
491D4—41no—
492D4—42no—
493D4—88no—
494D4—84no—
495D4—88no—
496D4—84no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—84no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—441no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4#6698512yes—
518C2×C4C2×#432414yes—
519C2×C4C2×#432412yes—
520C2×C4#6699112yes—
521C2×C4#6699112yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4#6703711yescharacteristic
526C2×C4#41×D1111yescharacteristic
527C2×C4#6704211yescharacteristic
528C8—222no—
529C8—222no—
530C8—442no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—82no—
539C22—82no—
540C22—82no—
541C22—82no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22C2×#6698511yescharacteristic
546C22C22×#432411yescharacteristic
547C22C2×#6699111yescharacteristic
548C22D4×C22⋊D1111yescharacteristic
549C22#1062336511yescharacteristic
550C22#1062336711yescharacteristic
551C22#1062336711yescharacteristic
552C4—22no—
553C4—24no—
554C4—42no—
555C4—81no—
556C4—444no—
557C4—442no—
558C4—881no—
559C4#1062268814yescomplemented
560C4#1062312711yescharacteristic
561C4#1062314011yescharacteristic
562C4#1062314311yescharacteristic
563C4#1062315011yescharacteristic
564C2—82no—
565C2—162no—
566C2#1307220011yescharacteristic
567C2C2×#1062268811yescharacteristic
568C2#1307813311yescharacteristic
569C2#1308021211yescharacteristic
570C2D4×#432411yescharacteristic
571C2#1308159711yescharacteristic
572C2#1308163211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2541C2
socleC23×C11C22×D4
hypercenter#2541D11
hypocenterC11#25366
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#10622689C2semidirect
2. C2×#10622688C2semidirect
3. C2×#10622632C2semidirect
4. #13071672C2semidirect
5. #13069933C2semidirect
6. #13069704C2semidirect
7. #13069544C2semidirect
8. #13069335C2semidirect
9. #13068974C2semidirect
10. C4×#66896C2semidirect
88. #66922D4semidirect
95. #66896D4semidirect
151. C11×C4⋊C4SD16semidirect
313. C4×C11#460semidirect
455. C4⋊C4#4324semidirect
465. C11#25366semidirect
559. C4#10622688semidirect

Maximal subgroups

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

subgroupindex
C2×#106226892
C2×#106226882
C2×#106226322
#130716722
#130699332
#130697042
#130695442
#130693352
#130689742
C4×#668962
C11×#25412
#2536611