Finite Group Databasebeta

← #14769694

Subgroups — #14769694

Order 2816.

1294 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×#10623369C211yesmaximal, characteristic
2#13077482C212yesmaximal, complemented
3#13077078C211yesmaximal, characteristic, complemented
4#13069511C212yesmaximal, complemented
5#13069113C212yesmaximal, complemented
6#13069110C212yesmaximal, complemented
7#13068660C211yesmaximal, characteristic, complemented
8#13068591C211yesmaximal, characteristic, complemented
9#13068589C211yesmaximal, characteristic, complemented
10#13068418C211yesmaximal, characteristic, complemented
11C11×#2884C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2211yescharacteristic
13C2×#67043C2211yescharacteristic
14C11×#519C2212yes—
15#10623369—24no—
16#10623369—24no—
17C2×#67004C412yescomplemented
18C2×#67004C2211yescharacteristic
19C2×#67003C412yescomplemented
20C2×#67003C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C22×#4326C412yescomplemented
23C22×#4326C2211yescharacteristic
24C2×#66995C412yescomplemented
25C2×#66995C2211yescharacteristic
26#10623047C2212yes—
27C11×#410—24no—
28C11×#410C2211yescharacteristic
29C11×#410C2212yes—
30C11×#410C2211yescharacteristic
31#10622853C2211yescharacteristic
32#10622850C2211yescharacteristic
33#10622849C2212yes—
34#10622838C2212yes—
35#10622643—24no—
36C4×#4326—24no—
37#10622619C2212yes—
38#10622618C2212yes—
39#10622617C2212yes—
40#10622611C2212yes—
41#10622610C2212yes—
42#10622353—24no—
43#10622171C2212yes—
44#10622169C2212yes—
45C11×2−1+4—24no—
46C11×2−1+4—42no—
47C2×C11×#41—22no—
48C2×C11×#41—21no—
49C2×C11×#41C2×C412yes—
50C2×C11×#41C2311yescharacteristic
51C2×C11×#41C2311yescharacteristic
52C22×Q8×C11—21no—
53C22×Q8×C11C2×C412yes—
54C22×Q8×C11C2311yescharacteristic
55#67043—24no—
56#67043—42no—
57C2×Q8×D11—21no—
58C2×#4341—22no—
59C2×#4341—21no—
60C2×#4339C2×C412yes—
61C2×#4339C2311yescharacteristic
62C22×Dic22C2×C412yes—
63C22×Dic22C2311yescharacteristic
64C4×Q8×C11—24no—
65C4×Q8×C11—42no—
66C11×#117—24no—
67C11×#117C2312yes—
68C11×#117C2312yes—
69#67004—24no—
70#67004—28no—
71#67003—24no—
72#67003—24no—
73#67003—22no—
74#67003—22no—
75#67001—22no—
76#67001—22no—
77C2×#4326—24no—
78C2×#4326—24no—
79C2×#4326C2×C412yes—
80C2×#4326C2×C412yes—
81C2×#4326C2×C411yescharacteristic
82C2×#4326C2×C412yes—
83C2×#4326C2×C412yes—
84C2×#4326D414yes—
85C2×#4326D414yes—
86#66995—24no—
87#66995—28no—
88C2×#4325C2×C411yescharacteristic
89C2×#4325C2×C412yes—
90C2×#4324C2×C412yes—
91C2×#4324C2×C411yescharacteristic
92C2×#4323C2×C411yescharacteristic
93#66979C2312yes—
94C2×#4318C2×C412yes—
95C2×#4318C2312yes—
96C2×#4318C2311yescharacteristic
97C22×C11⋊C8C2×C412yes—
98C22×C11⋊C8C2311yescharacteristic
99#66940—42no—
100#66930—24no—
101C4×Dic22—24no—
102C11×#99—22no—
103C11×#99—24no—
104C11×#99D414yes—
105#66901—42no—
106#66900—21no—
107#66899—24no—
108#66898—22no—
109#66897—21no—
110#66874—24no—
111#66872—22no—
112#66871—22no—
113#66870—24no—
114#66869—42no—
115#66867—22no—
116C4×C11⋊C8—22no—
117#22457—111nomaximal, Sylow
118C11×#41—22no—
119C11×#41—22no—
120C11×#41—24no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—42no—
124C11×#41—48no—
125C11×#41—44no—
126C2×Q8×C11—22no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—24no—
130C2×Q8×C11—42no—
131C2×Q8×C11—44no—
132C2×Q8×C11C22×C411yescharacteristic
133C2×Q8×C11C22×C412yes—
134C2×Q8×C11C2×D414yes—
135C2×Q8×C11#4111yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11C22×C411yescharacteristic
139C2×D4×C11C2×D412yes—
140C2×D4×C11#4111yescharacteristic
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—22no—
148C2×C22⋊D11—21no—
149C22×Dic11—22no—
150C22×Dic11—21no—
151Q8×D11—44no—
152#4341—44no—
153#4341—48no—
154#4339—24no—
155#4339—22no—
156#4339—22no—
157#4339—42no—
158C2×D44C22×C411yescharacteristic
159C2×C4×D11—22no—
160C2×C4×D11—21no—
161C2×Dic22—24no—
162C2×Dic22—22no—
163C2×Dic22—21no—
164C2×Dic22—22no—
165C2×Dic22—42no—
166C2×Dic22C22×C411yescharacteristic
167C2×Dic22C22×C412yes—
168C2×Dic22C2×D414yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—44no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4C2×D414yes—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11—44no—
177C22⋊Dic11—22no—
178#4326—24no—
179#4326—21no—
180#4326—21no—
181#4326—24no—
182#4326C22⋊C418yes—
183#4326C22⋊C414yes—
184#4326C22⋊C414yes—
185#4325—22no—
186#4325—24no—
187#4324—24no—
188#4324—22no—
189#4323—21no—
190#4323—21no—
191C4⋊Dic11—22no—
192Dic11⋊C4—44no—
193C4×Dic11—22no—
194C4×Dic11—44no—
195#4318—24no—
196#4318—22no—
197#4318—22no—
198#4318—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D412yes—
206C2×C11⋊C8C2×D412yes—
207C2×#578—111no—
208#2950—112no—
209#2884—111no—
210#2884D1111yescharacteristic, complemented
211#1976—112no—
212#1905—112no—
213#1905—112no—
214#1812—111no—
215#1796—111no—
216#1796—111no—
217#1757—111no—
218C23×C11—21no—
219C23×C11C4×D412yes—
220C23×C11C22×D411yescharacteristic
221C22×D11—21no—
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11—24no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—44no—
228Q8×C11C2×C22⋊C414yes—
229D4×C11—24no—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—22no—
233D4×C11—44no—
234D4×C11—42no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—24no—
241C2×C4×C11—44no—
242C2×C4×C11—44no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D412yes—
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)12yes—
250C22⋊D11—44no—
251C22⋊D11—42no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—21no—
255C2×Dic11—44no—
256C2×Dic11—42no—
257D44—21no—
258D44—21no—
259C4×D11—44no—
260C4×D11—42no—
261Dic22—22no—
262Dic22—24no—
263Dic22—21no—
264Dic22—21no—
265Dic22—44no—
266Dic22C2×C22⋊C414yes—
267C11⋊C8—22no—
268C11⋊C8—42no—
269C11⋊C8C2×C22⋊C411yescharacteristic
270C11⋊C8C2×C22⋊C411yescharacteristic
271C11⋊C8C2×C22⋊C412yes—
272C2×2−1+4—111no—
273C2×2−1+4C2×D1111yescharacteristic
274#578—224no—
275#578—224no—
276C2×#137—111no—
277C2×#137—112no—
278C2×#137—111no—
279C2×#137—112no—
280C2×#135—111no—
281C2×#135—112no—
282C22×Q16—111no—
283C22×Q16—112no—
284C2×#131—111no—
285#519—112no—
286#519C2×D1112yes—
287#441—224no—
288C4×Q16—224no—
289#427—112no—
290#421—112no—
291#421—112no—
292#419—112no—
293#419—112no—
294#413—111no—
295#410—24no—
296#410—111no—
297#410—112no—
298#410—224no—
299#410C2×D1111yescharacteristic
300#410C2×D1112yes—
301#410C2×D1111yescharacteristic
302#405—112no—
303#344—112no—
304H(3,ℤ/4)—112no—
305C22×C11—22no—
306C22×C11—41no—
307C22×C11—42no—
308C22×C11—41no—
309C22×C11—81no—
310C22×C11C2×C4×D411yescharacteristic
311C22×C11D4212yes—
312C2×D11—41no—
313C2×D11—81no—
314C4×C11—24no—
315C4×C11—22no—
316C4×C11—44no—
317C4×C11—41no—
318C4×C11—82no—
319C4×C11C22×C22⋊C411yescharacteristic
320C4×C11#51811yescharacteristic
321C4×C11#54612yes—
322Dic11—24no—
323Dic11—41no—
324Dic11—82no—
3252−1+4—24no—
3262−1+4—42no—
3272−1+4—224no—
3282−1+4—442no—
329C2×#41—21no—
330C2×#41—22no—
331C2×#41—112no—
332C2×#41—111no—
333C2×#41—221no—
334C2×#41—222no—
335C2×#41C4×D1112yes—
336C2×#41C22×D1111yescharacteristic
337C2×#41C22×D1111yescharacteristic
338C22×Q8—21no—
339C22×Q8—112no—
340C22×Q8—111no—
341C22×Q8—221no—
342C22×Q8C4×D1112yes—
343C22×Q8C22×D1111yescharacteristic
344#137—228no—
345#137—228no—
346#137—224no—
347#137—224no—
348#135—222no—
349#135—222no—
350#135—224no—
351#135—224no—
352C2×Q16—112no—
353C2×Q16—112no—
354C2×Q16—114no—
355C2×Q16—114no—
356C2×Q16—111no—
357C2×Q16—112no—
358C2×Q16—112no—
359C2×Q16—224no—
360C2×Q16—224no—
361C2×SD16—111no—
362C2×SD16—112no—
363C2×SD16—111no—
364C2×SD16—112no—
365C2×D8—111no—
366#131—222no—
367#131—222no—
368C2×M16—112no—
369C2×M16—111no—
370C2×M16—112no—
371C22×C8—111no—
372C22×C8—112no—
373C4×Q8—24no—
374C4×Q8—42no—
375C4×Q8—224no—
376C4×Q8—442no—
377#117—24no—
378#117—112no—
379#117—224no—
380#117C22×D1112yes—
381#117C22×D1112yes—
382#107—222no—
383#106—222no—
384#104—442no—
385#104—442no—
386#103—224no—
387#103—224no—
388#101—221no—
389#100—221no—
390#99—22no—
391#99—24no—
392#99—222no—
393#99—224no—
394#99C22⋊D1114yes—
395#97—222no—
396C4×C8—222no—
397C2×C11—22no—
398C2×C11—21no—
399C2×C11—42no—
400C2×C11—81no—
401C2×C11D4×C22⋊C411yescharacteristic
402D11—81no—
403#41—22no—
404#41—22no—
405#41—24no—
406#41—22no—
407#41—22no—
408#41—42no—
409#41—48no—
410#41—44no—
411#41—224no—
412#41—222no—
413#41—222no—
414#41—442no—
415#41—448no—
416#41—444no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—24no—
421C2×Q8—42no—
422C2×Q8—44no—
423C2×Q8—112no—
424C2×Q8—111no—
425C2×Q8—114no—
426C2×Q8—224no—
427C2×Q8—222no—
428C2×Q8—221no—
429C2×Q8—222no—
430C2×Q8—442no—
431C2×Q8—444no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×Q8C2×C4×D1112yes—
434C2×Q8#433911yescharacteristic
435C2×Q8D4×D1114yes—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—111no—
439C2×D4—222no—
440C2×D4—221no—
441C2×D4C2×C4×D1111yescharacteristic
442C2×D4#433911yescharacteristic
443C2×D4C2×C22⋊D1112yes—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—221no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—221no—
452C22×C4C2×C4×D1112yes—
453C22×C4C23×D1111yescharacteristic
454Q16—114no—
455Q16—114no—
456Q16—118no—
457Q16—221no—
458Q16—221no—
459Q16—224no—
460Q16—224no—
461SD16—222no—
462SD16—222no—
463SD16—224no—
464SD16—224no—
465D8—221no—
466D8—221no—
467M16—224no—
468M16—222no—
469M16—222no—
470M16—222no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—112no—
474C2×C8—112no—
475C2×C8—112no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—44no—
482C4⋊C4—222no—
483C4⋊C4—444no—
484C22⋊C4—22no—
485C22⋊C4—222no—
486C22⋊C4C2×C22⋊D1114yes—
487C42—22no—
488C42—22no—
489C42—44no—
490C42—222no—
491C42—444no—
492C11#2245711yescharacteristic, complemented, Sylow
493C23—21no—
494C23—221no—
495C23C4×C22⋊D1112yes—
496C23C22×C22⋊D1111yescharacteristic
497Q8—22no—
498Q8—24no—
499Q8—22no—
500Q8—21no—
501Q8—21no—
502Q8—44no—
503Q8—114no—
504Q8—222no—
505Q8—224no—
506Q8—221no—
507Q8—221no—
508Q8—444no—
509Q8C22⋊C4×D1114yes—
510D4—24no—
511D4—21no—
512D4—21no—
513D4—22no—
514D4—44no—
515D4—42no—
516D4—221no—
517D4—221no—
518D4—444no—
519D4—442no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—222no—
531C2×C4—224no—
532C2×C4—221no—
533C2×C4—444no—
534C2×C4—444no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4C4×C22⋊D1112yes—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4C2×#433911yescharacteristic
540C2×C4C2×D4×D1112yes—
541C2×C4#6703712yes—
542C8—111no—
543C8—111no—
544C8—112no—
545C8—222no—
546C8—442no—
547C22—22no—
548C22—41no—
549C22—42no—
550C22—41no—
551C22—81no—
552C22—441no—
553C22—881no—
554C22C2×C4×C22⋊D1111yescharacteristic
555C22D4×C22⋊D1112yes—
556C4—24no—
557C4—22no—
558C4—44no—
559C4—41no—
560C4—82no—
561C4—224no—
562C4—441no—
563C4—882no—
564C4C2×C22⋊C4×D1111yescharacteristic
565C4#1062301711yescharacteristic
566C4#1062302112yes—
567C2—22no—
568C2—21no—
569C2—42no—
570C2—81no—
571C2—881no—
572C2C22⋊C4×C22⋊D1111yescharacteristic
subgroupG/H
centerC2C22⋊C4×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2884C2
socleC2×C11D4×C22⋊C4
prime radicalC2×#10623369C2
cosocleC22×C4×C11C24
hypercenter#2884D11
hypocenterC11#22457
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2884

Complements

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

NH ≅ G/Ntype
2. #13077482C2semidirect
3. #13077078C2semidirect
4. #13069511C2semidirect
5. #13069113C2semidirect
6. #13069110C2semidirect
7. #13068660C2semidirect
8. #13068591C2semidirect
9. #13068589C2semidirect
10. #13068418C2semidirect
11. C11×#2884C2semidirect
17. C2×#67004C4semidirect
19. C2×#67003C4semidirect
22. C22×#4326C4semidirect
24. C2×#66995C4semidirect
210. #2884D11semidirect
492. C11#22457semidirect

Maximal subgroups

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

subgroupindex
C2×#106233692
#130774822
#130770782
#130695112
#130691132
#130691102
#130686602
#130685912
#130685892
#130684182
C11×#28842
#2245711