Finite Group Databasebeta

← #14780941

Subgroups — #14780941

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic
2C22×#66997C211yesmaximal, characteristic, complemented
3C2×#10622733C211yesmaximal, characteristic, complemented
4C2×#10622838C211yesmaximal, characteristic, complemented
5#13071107C211yesmaximal, characteristic
6#13069714C214yesmaximal, complemented
7#13069697C214yesmaximal, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C22×C11×#137C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C2×C11×#137—24no—
14C2×C11×#137—24no—
15C2×C11×#137—24no—
16C22×C11×Q16C2212yes—
17C22×C11×SD16C2212yes—
18C22×C11×M16C2211yescharacteristic
19C2×#67004—24no—
20C2×#67004—24no—
21C2×#67004—24no—
22C2×#66997—24no—
23C2×#66997—24no—
24C2×#66997—22no—
25C2×#66997C2214yes—
26C22×#4326C2212yes—
27C22×#4324C2212yes—
28C2×#66979C2211yescharacteristic
29C22×Dic11⋊C4—22no—
30C22×C4×Dic11C2211yescharacteristic
31C22×#4318C2211yescharacteristic
32#10622843C2212yes—
33#10622838—24no—
34C2×#66899C2214yes—
35#10622834C2212yes—
36#10622833—22no—
37C4×C22⋊Dic11—22no—
38#10622733—24no—
39C2×#66880C2214yes—
40#10622188C2214yes—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41D414yes—
47C22×Q8×C11—22no—
48C22×Q8×C11—21no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11D414yes—
54C22×Q8×C11C2311yescharacteristic
55C22×Q8×C11C2312yes—
56C22×D4×C11—21no—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C23×Dic11D412yes—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22—22no—
67C22×Dic22—21no—
68C22×Dic22—22no—
69C22×Dic22D414yes—
70C22×Dic22C2312yes—
71C11×#137—232no—
72C2×C11×Q16—24no—
73C2×C11×Q16—24no—
74C2×C11×Q16—24no—
75C2×C11×SD16—24no—
76C2×C11×SD16—24no—
77C2×C11×SD16—24no—
78C2×C11×M16—22no—
79C2×C11×M16—22no—
80C2×C11×M16D414yes—
81C22×C8×C11C2312yes—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—24no—
84#67004—232no—
85#66997—216no—
86#66997—28no—
87#66997—28no—
88C2×#4326—24no—
89C2×#4326—24no—
90C2×#4326—24no—
91C2×#4324—24no—
92C2×#4324—24no—
93C2×#4324—24no—
94#66979—22no—
95#66979—22no—
96C2×C4⋊Dic11C2312yes—
97C2×Dic11⋊C4—216no—
98C2×Dic11⋊C4—28no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11D412yes—
103C2×C4×Dic11C2312yes—
104C2×#4318—22no—
105C2×#4318—22no—
106C2×#4318D414yes—
107C22×C11⋊C8C2312yes—
108#66899—28no—
109C11⋊#95—24no—
110#66880—28no—
111#23432—111nomaximal, Sylow
112C24×C11—21no—
113C24×C11C2×D411yescharacteristic
114C11×#41—28no—
115C11×#41—28no—
116C11×#41—44no—
117C11×#41—44no—
118C2×Q8×C11—24no—
119C2×Q8×C11—22no—
120C2×Q8×C11—21no—
121C2×Q8×C11—28no—
122C2×Q8×C11—28no—
123C2×Q8×C11—22no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C2×Q8×C11—42no—
133C2×Q8×C11—44no—
134C2×Q8×C11—42no—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×D414yes—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11C2×D412yes—
146C22×C4×C11—24no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—28no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11C2×D414yes—
170C2×Dic22—28no—
171C2×Dic22—24no—
172C2×Dic22—28no—
173C2×Dic22—22no—
174C2×Dic22—22no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—44no—
179C2×Dic22—44no—
180C2×Dic22—42no—
181C2×Dic22—42no—
182C2×Dic22C2×D414yes—
183C11×Q16—216no—
184C11×SD16—216no—
185C11×M16—28no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C2×C8×C11C2×D414yes—
189C22⋊Dic11—48no—
190C22⋊Dic11—42no—
191#4326—216no—
192#4324—216no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195Dic11⋊C4—232no—
196C4×Dic11—24no—
197C4×Dic11—22no—
198C4×Dic11—22no—
199C4×Dic11—42no—
200#4318—28no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8C2×D414yes—
204C22×#137—111no—
205C22×#137D1111yescharacteristic
206C22×C4⋊Q8—111no—
207C2×#419—111no—
208C2×#419—111no—
209#2297—111no—
210#2016—114no—
211#2013—114no—
212#1728—111no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—44no—
218C23×C11#12012yes—
219C23×C11#12112yes—
220C23×C11#12712yes—
221C23×C11C22×D411yescharacteristic
222Q8×C11—22no—
223Q8×C11—24no—
224Q8×C11—22no—
225Q8×C11—24no—
226Q8×C11—42no—
227Q8×C11—42no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—48no—
231D4×C11—22no—
232D4×C11—22no—
233D4×C11—48no—
234D4×C11—41no—
235D4×C11—41no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—48no—
243C2×C4×C11—48no—
244C2×C4×C11#12014yes—
245C2×C4×C11#12012yes—
246C2×C4×C11#12014yes—
247C2×C4×C11#12114yes—
248C2×C4×C11#12114yes—
249C2×C4×C11#12112yes—
250C2×C4×C11#12712yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×Dic11—216no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—48no—
264C2×Dic11—42no—
265C2×Dic11—44no—
266C2×Dic11#13718yescomplemented
267Dic22—24no—
268Dic22—24no—
269Dic22—42no—
270Dic22—42no—
271Dic22—48no—
272C8×C11—24no—
273C11⋊C8—24no—
274C22×#41C2×D1111yescharacteristic
275C23×Q8—111no—
276C23×Q8C2×D1111yescharacteristic
277C2×#137—24no—
278C2×#137—24no—
279C2×#137—24no—
280C2×#137—224no—
281C2×#137—224no—
282C2×#137—224no—
283C22×Q16—112no—
284C22×Q16C2×D1112yes—
285C22×SD16—112no—
286C22×SD16C2×D1112yes—
287C22×M16—111no—
288C22×M16C2×D1111yescharacteristic
289C2×C4⋊Q8—114no—
290C2×C4⋊Q8—222no—
291C2×C4⋊Q8—224no—
292C2×C4⋊Q8—224no—
293C2×#117—111no—
294C22×C4⋊C4—222no—
295C22×C42—111no—
296#419—224no—
297#419—224no—
298C2×#103—114no—
299C2×#103—114no—
300#391—112no—
301#390—112no—
302#386—222no—
303C4×C22⋊C4—222no—
304#336—114no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11#39214yes—
313C22×C11C2×#12011yescharacteristic
314C22×C11C2×#12111yescharacteristic
315C22×C11C2×#12711yescharacteristic
316C22×C11C2×#13714yes—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11#39214yes—
320C4×C11C2×#12011yescharacteristic
321C4×C11C2×#12011yescharacteristic
322C4×C11C2×#12111yescharacteristic
323C4×C11C2×#12111yescharacteristic
324Dic11—28no—
325Dic11—44no—
326Dic11—82no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41C22⋊D1114yes—
333C22×Q8—22no—
334C22×Q8—21no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—114no—
340C22×Q8—112no—
341C22×Q8—221no—
342C22×Q8—222no—
343C22×Q8—222no—
344C22×Q8—222no—
345C22×Q8—222no—
346C22×Q8—222no—
347C22×Q8C22⋊D1114yes—
348C22×Q8C22×D1112yes—
349C22×Q8C22×D1111yescharacteristic
350C22×D4—21no—
351C22×D4C22×D1111yescharacteristic
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—112no—
355C23×C4—221no—
356C23×C4C22×D1111yescharacteristic
357#137—232no—
358#137—2232no—
359C2×Q16—24no—
360C2×Q16—24no—
361C2×Q16—24no—
362C2×Q16—224no—
363C2×Q16—224no—
364C2×Q16—224no—
365C2×SD16—24no—
366C2×SD16—24no—
367C2×SD16—24no—
368C2×SD16—224no—
369C2×SD16—224no—
370C2×SD16—224no—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—114no—
374C2×M16—222no—
375C2×M16—222no—
376C2×M16C22⋊D1114yes—
377C22×C8—112no—
378C22×C8C22×D1112yes—
379C4⋊Q8—228no—
380C4⋊Q8—2216no—
381C4⋊Q8—228no—
382#117—222no—
383#117—222no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—228no—
386C2×C4⋊C4—2216no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—221no—
389C2×C42—112no—
390C2×C42—112no—
391C2×C42—222no—
392C2×C42—222no—
393C2×C42—221no—
394#103—228no—
395#103—228no—
396#95—224no—
397C2×C11—24no—
398C2×C11—82no—
399C2×C11C2×#39211yescharacteristic
400C2×C11#300412yes—
401C2×C11#303912yes—
402C2×C11#315212yes—
403C24—21no—
404C24D4×D1111yescharacteristic
405#41—28no—
406#41—28no—
407#41—44no—
408#41—44no—
409C2×Q8—24no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—28no—
413C2×Q8—28no—
414C2×Q8—22no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8—42no—
425C2×Q8—42no—
426C2×Q8—114no—
427C2×Q8—224no—
428C2×Q8—222no—
429C2×Q8—228no—
430C2×Q8—228no—
431C2×Q8—222no—
432C2×Q8—222no—
433C2×Q8—222no—
434C2×Q8—222no—
435C2×Q8—442no—
436C2×Q8—444no—
437C2×Q8—442no—
438C2×Q8—444no—
439C2×Q8C2×C22⋊D1114yes—
440C2×Q8C2×C22⋊D1112yes—
441C2×D4—24no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4C2×C22⋊D1112yes—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—114no—
459C22×C4—228no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4D4×D1112yes—
467C22×C4D4×D1111yescharacteristic
468C22×C4D4×D1112yes—
469C22×C4#434112yes—
470C22×C4C2×C22⋊D1112yes—
471C22×C4C2×C22⋊D1112yes—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C23×D1111yescharacteristic
474Q16—216no—
475Q16—2216no—
476SD16—216no—
477SD16—2216no—
478M16—28no—
479M16—228no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—114no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8C2×C22⋊D1114yes—
486C4⋊C4—2232no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C22⋊C4—448no—
490C22⋊C4—442no—
491C42—224no—
492C42—222no—
493C42—222no—
494C42—442no—
495C11#2343211yescharacteristic, complemented, Sylow
496C23—24no—
497C23—22no—
498C23—44no—
499C23—41no—
500C23—41no—
501C23#6699012yes—
502C23#6699212yes—
503C23#6699312yes—
504C23C2×D4×D1111yescharacteristic
505Q8—22no—
506Q8—24no—
507Q8—24no—
508Q8—22no—
509Q8—42no—
510Q8—42no—
511Q8—41no—
512Q8—41no—
513Q8—48no—
514Q8—224no—
515Q8—224no—
516Q8—442no—
517Q8—448no—
518Q8—442no—
519D4—22no—
520D4—22no—
521D4—48no—
522D4—41no—
523D4—41no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—48no—
531C2×C4—48no—
532C2×C4—118no—
533C2×C4—2216no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—448no—
540C2×C4—444no—
541C2×C4—442no—
542C2×C4#6699014yes—
543C2×C4#6699012yes—
544C2×C4#6699114yes—
545C2×C4#6699214yes—
546C2×C4#6699212yes—
547C2×C4#6699312yes—
548C2×C4#6700614yes—
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4C2×#434111yescharacteristic
552C2×C4C22×C22⋊D1111yescharacteristic
553C2×C4C22×C22⋊D1111yescharacteristic
554C2×C4C22×C22⋊D1111yescharacteristic
555C8—24no—
556C8—224no—
557C22—24no—
558C22—24no—
559C22—24no—
560C22—44no—
561C22—42no—
562C22—82no—
563C22—82no—
564C22#1062283614yes—
565C22D11×#13714yes—
566C22C2×#6699011yescharacteristic
567C22C2×#6699211yescharacteristic
568C22C2×#6699311yescharacteristic
569C4—42no—
570C4—44no—
571C4—228no—
572C4—444no—
573C4—882no—
574C4#1062283614yes—
575C4C2×#6699011yescharacteristic
576C4C2×#6699111yescharacteristic
577C4C2×#6699211yescharacteristic
578C4C2×#6700611yescharacteristic
579C2—24no—
580C2—82no—
581C2C2×#1062283611yescharacteristic
582C2#1307784812yes—
583C2#1307810112yes—
584C2#1307907112yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC22×#137D11
hypocenterC11#23432
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C22×#66997C2semidirect
3. C2×#10622733C2semidirect
4. C2×#10622838C2semidirect
6. #13069714C2semidirect
7. #13069697C2semidirect
8. #13068309C2semidirect
266. C2×Dic11#137semidirect
495. C11#23432semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C22×#669972
C2×#106227332
C2×#106228382
#130711072
#130697142
#130696972
#130683092
C22×C11×#1372
#2343211