Finite Group Databasebeta

← #14720703

Subgroups — #14720703

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4339C211yesmaximal, characteristic
2#13077582C211yesmaximal, characteristic
3#13077281C211yesmaximal, characteristic
4#13067087C212yesmaximal, complemented
5#13067072C211yesmaximal, characteristic, complemented
6#13067061C212yesmaximal, complemented
7#13067045C211yesmaximal, characteristic, complemented
8#13067035C212yesmaximal, complemented
9#13067018C211yesmaximal, characteristic, complemented
10#13067009C212yesmaximal, complemented
11C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13Q8×C22⋊D11C412yes—
14#10623110—21no—
15#10623110C411yescharacteristic
16#10623109—22no—
17#10623109C2212yes—
18Q8×D44C411yescharacteristic
19C4×Q8×D11C2212yes—
20#10623098—21no—
21#10623098C411yescharacteristic
22Q8×Dic22C411yescharacteristic
23#10623042—22no—
24#10623042C412yes—
25C4×#4339—21no—
26C4×#4339C2211yescharacteristic
27#10623001—21no—
28#10623001C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31#10622724—22no—
32#10622723—21no—
33#10622714—21no—
34#10622538C2211yescharacteristic
35#10622537C2211yescharacteristic
36#10622453—22no—
37#10622448C2212yes—
38#10622446C2212yes—
39#10622301—21no—
40C4×#4313C2212yes—
41#10622298C2212yes—
42#10622292—21no—
43C11×Q8⋊C8C2211yescharacteristic
44C11×Q8⋊C8C2211yescharacteristic
45C11×Q8⋊C8C2211yescharacteristic
46C11×Q8⋊C8C2211yescharacteristic
47Q8⋊(C11⋊C8)C2212yes—
48Q8⋊(C11⋊C8)C2212yes—
49#10622122C2212yes—
50#10622122C2212yes—
51#10622094C2212yes—
52#10622094C2212yes—
53C22×Q8×C11C2×C411yescharacteristic
54C2×Q8×D11C2×C412yes—
55C2×#4339D411yescharacteristic
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11C2×C411yescharacteristic
61C4×Q8×C11C2×C411yescharacteristic
62C4×Q8×C11C2311yescharacteristic
63C4×Q8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68#66999—22no—
69#66999C2×C412yes—
70Q8×Dic11C2×C412yes—
71#66997—22no—
72#66997C2×C412yes—
73C4×C22⋊D11—22no—
74C4×C22⋊D11—22no—
75C4×C22⋊D11C2×C412yes—
76C4×C22⋊D11D412yes—
77#66979—21no—
78#66979D411yescharacteristic
79#66977—21no—
80#66977—22no—
81#66977—22no—
82#66977C2×C412yes—
83C2×#4318—21no—
84C2×#4313—22no—
85#66950—22no—
86#66950C2×C412yes—
87#66949—22no—
88#66949—22no—
89#66949—22no—
90C4⋊C4×D11—22no—
91C4⋊C4×D11C2×C412yes—
92#66942—22no—
93#66942—22no—
94#66942—22no—
95#66941—22no—
96#66941C2×C412yes—
97#66940—22no—
98#66940C2×C412yes—
99C4×D44—21no—
100C4×D44—21no—
101C4×D44C2×C411yescharacteristic
102C4×D44D411yescharacteristic
103#66925—22no—
104#66925D412yes—
105C42×D11—22no—
106C42×D11C2312yes—
107#66923—21no—
108#66923—21no—
109#66923—21no—
110#66922—21no—
111#66922—21no—
112#66922C2×C411yescharacteristic
113#66922C2×C411yescharacteristic
114C4×Dic22—21no—
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—22no—
118C4×Dic22—22no—
119C4×Dic22C2×C411yescharacteristic
120C4×Dic22D411yescharacteristic
121C4×Dic22C2312yes—
122C11×C4⋊C8—21no—
123C11×C4⋊C8C2311yescharacteristic
124C11×C4⋊C8C2311yescharacteristic
125C4×C8×C11—21no—
126C4×C8×C11C2311yescharacteristic
127C4×C8×C11C2311yescharacteristic
128C22⋊(C11⋊C8)—21no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132#66879—22no—
133#66879—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2312yes—
139C4×C11⋊C8C2312yes—
140#17514—111nomaximal, Sylow
141C2×Q8×C11—21no—
142C2×Q8×C11—22no—
143C2×Q8×C11—41no—
144C2×Q8×C11C22×C411yescharacteristic
145C2×Q8×C11C22×C411yescharacteristic
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C2×C22⋊D11C22⋊C412yes—
152Q8×D11—24no—
153Q8×D11—42no—
154#4339—22no—
155#4339—22no—
156C2×D44C22⋊C411yescharacteristic
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11C22×C412yes—
160C2×C4×D11C2×D412yes—
161C2×C4×D11C2×D412yes—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22—21no—
165C2×Dic22C22⋊C411yescharacteristic
166C2×Dic22C22×C412yes—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—42no—
172C2×C8×C11—42no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C22×C411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—22no—
189C22⋊Dic11C22⋊C412yes—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4C22⋊C412yes—
193(C2×D11)⋊C4C22⋊C412yes—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11C22⋊C411yescharacteristic
200C4⋊Dic11C22⋊C411yescharacteristic
201C4⋊Dic11C22×C412yes—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4C22⋊C412yes—
211Dic11⋊C4C22⋊C412yes—
212C4×Dic11—22no—
213C4×Dic11—22no—
214C4×Dic11—22no—
215C4×Dic11C22×C412yes—
216C4×Dic11C2×D412yes—
217C4×Dic11C2×D412yes—
218#4318—42no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—22no—
221#4313—44no—
222Q8×#41—111no—
223#2965—111no—
224#2925—111no—
225#1497—112no—
226#1493—111no—
227#1491—112no—
228#1487—111no—
229#1485—112no—
230#1481—111no—
231#1479—112no—
232C2×Q8⋊C8D1111yescharacteristic, complemented
233C23×C11C2×C22⋊C411yescharacteristic
234C22×D11C2×C22⋊C412yes—
235Q8×C11—21no—
236Q8×C11—21no—
237Q8×C11—21no—
238Q8×C11—42no—
239Q8×C11#13112yes—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—81no—
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11#13712yes—
253C2×C4×C11#13712yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C22⋊D11—24no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11C2×C22⋊C412yes—
261C2×Dic11C2×C22⋊C412yes—
262C2×Dic11C2×C22⋊C412yes—
263D44—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—42no—
269C4×D11—44no—
270C4×D11—82no—
271Dic22—22no—
272Dic22—22no—
273Dic22—22no—
274Dic22—44no—
275Dic22—82no—
276Dic22—81no—
277C8×C11—22no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281C11⋊C8—42no—
282C11⋊C8—42no—
283Q82—111no—
284#557—111no—
285#557—221no—
286#554—111no—
287#554—112no—
288#554—222no—
289#554—221no—
290D4×Q8—112no—
291D4×Q8—111no—
292#533—112no—
293#533—111no—
294#533—221no—
295#533—222no—
296C4×#41—111no—
297C4×#41—221no—
298C2×C4×Q8—112no—
299C2×C4×Q8C2×D1111yescharacteristic
300#446—221no—
301#436—221no—
302#435—222no—
303#433—222no—
304#432—112no—
305#431—111no—
306#431—112no—
307#431—112no—
308#423—111no—
309C2×C4⋊C8C2×D1111yescharacteristic
310#408—221no—
311#405—221no—
312C4×M16—112no—
313C2×C4×C8C2×D1111yescharacteristic
314Q8⋊C8—112no—
315Q8⋊C8—112no—
316Q8⋊C8—112no—
317Q8⋊C8—112no—
318Q8⋊C8—112no—
319Q8⋊C8—112no—
320Q8⋊C8C2×D1111yescharacteristic
321Q8⋊C8C2×D1111yescharacteristic
322Q8⋊C8C2×D1111yescharacteristic
323Q8⋊C8C2×D1111yescharacteristic
324C22×C11—21no—
325C22×C11—21no—
326C22×C11#41912yes—
327C22×C11C22×C22⋊C411yescharacteristic
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C4×C11—21no—
332C4×C11—22no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11#41912yes—
339C4×C11C2×#13111yescharacteristic
340C4×C11#56811yescharacteristic
341C4×C11C2×#13711yescharacteristic
342C4×C11C2×#13711yescharacteristic
343Dic11—22no—
344Dic11—22no—
345Dic11—22no—
346Dic11—42no—
347Dic11—42no—
348C2×#41—111no—
349C22×Q8—112no—
350C22×Q8C4×D1111yescharacteristic
351C2×M16—222no—
352C2×M16—221no—
353C22×C8—21no—
354C22×C8—21no—
355C4⋊Q8—112no—
356C4⋊Q8—112no—
357C4⋊Q8—111no—
358C4⋊Q8—111no—
359C4⋊Q8—221no—
360C4⋊Q8—221no—
361C4⋊Q8—222no—
362C4⋊Q8—222no—
363#125—221no—
364#125—221no—
365#125—222no—
366#125—222no—
367#125—222no—
368#125—221no—
369C22⋊Q8—112no—
370C22⋊Q8—112no—
371C22⋊Q8—112no—
372C22⋊Q8—222no—
373C22⋊Q8—222no—
374C22⋊Q8—222no—
375C22⋊Q8—222no—
376C22⋊Q8—222no—
377C22⋊Q8—222no—
378C22⋊Q8—222no—
379C22⋊Q8—221no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—111no—
383C4×Q8—111no—
384C4×Q8—112no—
385C4×Q8—112no—
386C4×Q8—112no—
387C4×Q8—222no—
388C4×Q8—222no—
389C4×Q8—221no—
390C4×Q8—221no—
391C4×Q8—222no—
392C4×Q8—221no—
393C4×Q8C4×D1111yescharacteristic
394C4×Q8C4×D1111yescharacteristic
395C4×Q8C22×D1111yescharacteristic
396C4×Q8C22×D1111yescharacteristic
397C4×D4—112no—
398C4×D4—112no—
399C4×D4—111no—
400C4×D4—111no—
401C4×D4—221no—
402C4×D4—221no—
403C4×D4—222no—
404C4×D4—222no—
405#117—111no—
406#117—112no—
407#117—222no—
408#117—221no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4C4×D1111yescharacteristic
413C2×C42—21no—
414C2×C42—112no—
415C2×C42—222no—
416C2×C42C22×D1111yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—112no—
419C4⋊C8—222no—
420C4⋊C8—221no—
421C4⋊C8—221no—
422C4⋊C8C22×D1111yescharacteristic
423C4⋊C8C22×D1111yescharacteristic
424C22⋊C8—222no—
425C22⋊C8—222no—
426C22⋊C8—222no—
427C22⋊C8—221no—
428#97—222no—
429#97—222no—
430C4×C8—21no—
431C4×C8—112no—
432C4×C8—222no—
433C4×C8C22×D1111yescharacteristic
434C4×C8C22×D1111yescharacteristic
435C2×C11—22no—
436C2×C11#288011yescharacteristic
437C2×C11C2×#41911yescharacteristic
438C2×C11#290111yescharacteristic
439D11—42no—
440#41—222no—
441#41—222no—
442C2×Q8—21no—
443C2×Q8—22no—
444C2×Q8—41no—
445C2×Q8—111no—
446C2×Q8—112no—
447C2×Q8—222no—
448C2×Q8—222no—
449C2×Q8—221no—
450C2×Q8—224no—
451C2×Q8—442no—
452C2×Q8C2×C4×D1111yescharacteristic
453C2×Q8C2×C4×D1111yescharacteristic
454C2×D4—112no—
455C2×D4—111no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4D4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466M16—444no—
467M16—442no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—42no—
474C2×C8—222no—
475C2×C8—222no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—112no—
482C4⋊C4—112no—
483C4⋊C4—111no—
484C4⋊C4—111no—
485C4⋊C4—112no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—222no—
497C4⋊C4—221no—
498C4⋊C4—222no—
499C4⋊C4C2×C4×D1111yescharacteristic
500C4⋊C4C2×C4×D1111yescharacteristic
501C22⋊C4—112no—
502C22⋊C4—112no—
503C22⋊C4—112no—
504C22⋊C4—222no—
505C22⋊C4—222no—
506C22⋊C4—222no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—112no—
512C42—112no—
513C42—112no—
514C42—222no—
515C42—222no—
516C42—222no—
517C42C2×C4×D1111yescharacteristic
518C42D4×D1111yescharacteristic
519C42D4×D1111yescharacteristic
520C42C23×D1111yescharacteristic
521C11#1751411yescharacteristic, complemented, Sylow
522C23—112no—
523C23C22⋊C4×D1111yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—21no—
527Q8—42no—
528Q8—222no—
529Q8—222no—
530Q8—222no—
531Q8—444no—
532Q8—881no—
533Q8—882no—
534Q8#6695412yes—
535D4—224no—
536D4—222no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—81no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—442no—
556C2×C4—444no—
557C2×C4—882no—
558C2×C4C22⋊C4×D1111yescharacteristic
559C2×C4C22⋊C4×D1111yescharacteristic
560C2×C4C22⋊C4×D1111yescharacteristic
561C2×C4#6696812yes—
562C2×C4#6697112yes—
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C8—22no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—442no—
571C8—442no—
572C22—21no—
573C22—21no—
574C22—222no—
575C22—222no—
576C22—222no—
577C22#1062241512yes—
578C22C2×C22⋊C4×D1111yescharacteristic
579C4—21no—
580C4—22no—
581C4—21no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—222no—
587C4—222no—
588C4—222no—
589C4—442no—
590C4—442no—
591C4#1062241512yes—
592C4C2×#6695411yescharacteristic
593C4#1062327611yescharacteristic
594C4C2×#6696811yescharacteristic
595C4C2×#6697111yescharacteristic
596C2—22no—
597C2—442no—
598C2#1307706211yescharacteristic
599C2C2×#1062241511yescharacteristic
600C2#1307716011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#4339D4
cosocleC42×C11C24
hypercenterC2×Q8⋊C8D11
hypocenterC11#17514
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #13067087C2semidirect
5. #13067072C2semidirect
6. #13067061C2semidirect
7. #13067045C2semidirect
8. #13067035C2semidirect
9. #13067018C2semidirect
10. #13067009C2semidirect
11. C2×C11×Q8⋊C8C2semidirect
232. C2×Q8⋊C8D11semidirect
521. C11#17514semidirect

Maximal subgroups

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

subgroupindex
Q8×#43392
#130775822
#130772812
#130670872
#130670722
#130670612
#130670452
#130670352
#130670182
#130670092
C2×C11×Q8⋊C82
#1751411