Finite Group Databasebeta

← #14724968

Subgroups — #14724968

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077776C211yesmaximal, characteristic
2#13077705C211yesmaximal, characteristic, complemented
3#13067513C211yesmaximal, characteristic, complemented
4#13067507C211yesmaximal, characteristic, complemented
5#13067495C211yesmaximal, characteristic, complemented
6#13067488C211yesmaximal, characteristic, complemented
7#13067488C211yesmaximal, characteristic, complemented
8#13067474C211yesmaximal, characteristic, complemented
9Q16×C11⋊C8C211yesmaximal, characteristic, complemented
10SD16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067401C211yesmaximal, characteristic, complemented
12#13067076C211yesmaximal, characteristic
13C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
14#13066900C211yesmaximal, characteristic, complemented
15C11×#3108C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#483C411yescharacteristic
19C11×#480C411yescharacteristic
20C11×#479C411yescharacteristic
21C11×#479C411yescharacteristic
22C11×#464C411yescharacteristic
23C11×#464C411yescharacteristic
24C11×#451C411yescharacteristic
25C11×#448C411yescharacteristic
26C4×C11×Q16C2211yescharacteristic
27C4×C11×Q16C2211yescharacteristic
28C4×C11×SD16C2211yescharacteristic
29C4×C11×SD16C2211yescharacteristic
30C11×#431C2211yescharacteristic
31#10622637—21no—
32#10622637—21no—
33#10622637C2211yescharacteristic
34#10622637C2211yescharacteristic
35#10622637C2211yescharacteristic
36Q8×C11⋊C8C2211yescharacteristic
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622625C2211yescharacteristic
40#10622624—21no—
41D4×C11⋊C8—21no—
42D4×C11⋊C8C2211yescharacteristic
43#10622613—21no—
44#10622612—21no—
45#10622539—21no—
46#10622539C2211yescharacteristic
47#10622538—21no—
48#10622538C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57D4⋊(C11⋊C8)C2211yescharacteristic
58D4⋊(C11⋊C8)C2211yescharacteristic
59#10622096C2211yescharacteristic
60#10622096C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622092C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×SD16C2×C411yescharacteristic
72C11×#126—21no—
73C11×#125C2×C411yescharacteristic
74C11×#124C2×C411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8C2×C411yescharacteristic
77C11×#121C2×C411yescharacteristic
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11C2×C411yescharacteristic
81C4×Q8×C11C2×C411yescharacteristic
82C4×Q8×C11C2311yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×Q8×C11C2311yescharacteristic
85C4×D4×C11—21no—
86C4×D4×C11C2311yescharacteristic
87C11×#117—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×#4318—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95C22×C11⋊C8—21no—
96C11×#107C2×C411yescharacteristic
97C11×#107C2×C411yescharacteristic
98C11×#106C2×C411yescharacteristic
99C11×#106C2×C411yescharacteristic
100C11×C4⋊C8C2×C411yescharacteristic
101C11×C4⋊C8C2×C411yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×C22⋊C8C2×C411yescharacteristic
111C11×C22⋊C8C2×C411yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)D411yescharacteristic
118C22⋊(C11⋊C8)D411yescharacteristic
119C4⋊(C11⋊C8)—21no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)—21no—
123C4⋊(C11⋊C8)—21no—
124C4⋊(C11⋊C8)—21no—
125C4⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)D411yescharacteristic
127C4⋊(C11⋊C8)D411yescharacteristic
128C4⋊(C11⋊C8)C2311yescharacteristic
129C4⋊(C11⋊C8)C2311yescharacteristic
130C4⋊(C11⋊C8)C2311yescharacteristic
131C4⋊(C11⋊C8)C2311yescharacteristic
132#66867—21no—
133#66867—21no—
134#66867—21no—
135#66867—21no—
136C4×C11⋊C8—21no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18017—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—41no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×Q8×C11C22×C411yescharacteristic
150C2×Q8×C11C22×C411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11C22×C411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C11×Q16—22no—
160C11×Q16—41no—
161C11×SD16—22no—
162C11×SD16—41no—
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C22×C411yescharacteristic
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11C22×C411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11#4111yescharacteristic
193C42×C11C2411yescharacteristic
194#4318—81no—
195C2×C11⋊C8—24no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3108D1111yescharacteristic
209#2994—111no—
210#2984—111no—
211#1591—111no—
212#1590—111no—
213#1588—111no—
214#1587—111no—
215#1587—111no—
216#1585—111no—
217C8×Q16—111no—
218C8×SD16—111no—
219#1573—111no—
220#1494—111no—
221C2×Q8⋊C8—111no—
222#1450—111no—
223C23×C11—21no—
224C23×C11C4×D411yescharacteristic
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—42no—
231Q8×C11#13112yes—
232D4×C11—21no—
233D4×C11—21no—
234D4×C11—42no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
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—21no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C11⋊C8—22no—
262C11⋊C8—22no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271#529C2×D1111yescharacteristic
272C2×C4×Q8C2×D1111yescharacteristic
273#483Dic1111yescharacteristic
274#480Dic1111yescharacteristic
275#479Dic1111yescharacteristic
276#479Dic1111yescharacteristic
277#464Dic1111yescharacteristic
278#464Dic1111yescharacteristic
279#451Dic1111yescharacteristic
280#448Dic1111yescharacteristic
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C4×Q16C2×D1111yescharacteristic
290C4×Q16C2×D1111yescharacteristic
291C4×SD16C2×D1111yescharacteristic
292C4×SD16C2×D1111yescharacteristic
293#436—111no—
294#435—221no—
295C8×D4—111no—
296C8×D4—221no—
297#433—221no—
298#432—111no—
299#432—221no—
300#431—111no—
301#431—221no—
302#431C2×D1111yescharacteristic
303#424—221no—
304C2×C4⋊C8—111no—
305C2×C4×C8—111no—
306#335—111no—
307#335—111no—
308#334—111no—
309#334—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—111no—
318#322—111no—
319#322—111no—
320C82—111no—
321C82—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11#44312yes—
328C22×C11C2×C4×D411yescharacteristic
329C4×C11—21no—
330C4×C11—22no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11C2×#13111yescharacteristic
341C4×C11#56811yescharacteristic
342C4×C11#57711yescharacteristic
343C4×C11#57811yescharacteristic
344C22×Q8C2×Dic1111yescharacteristic
345C2×Q16C2×Dic1111yescharacteristic
346C2×Q16C2×Dic1111yescharacteristic
347C2×SD16C2×Dic1111yescharacteristic
348C2×SD16C2×Dic1111yescharacteristic
349C2×M16—221no—
350C22×C8—221no—
351C22×C8—221no—
352C22×C8—221no—
353#126—21no—
354#125C2×Dic1111yescharacteristic
355#124C2×Dic1111yescharacteristic
356#123—21no—
357C22⋊Q8C2×Dic1111yescharacteristic
358#121C2×Dic1111yescharacteristic
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8C2×Dic1111yescharacteristic
362C4×Q8C2×Dic1111yescharacteristic
363C4×Q8C22×D1111yescharacteristic
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—21no—
367C4×D4C22×D1111yescharacteristic
368#117—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C2×Dic1111yescharacteristic
371C2×C42—21no—
372C2×C42C22×D1111yescharacteristic
373#107C2×Dic1111yescharacteristic
374#107C2×Dic1111yescharacteristic
375#106C2×Dic1111yescharacteristic
376#106C2×Dic1111yescharacteristic
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C2×Dic1111yescharacteristic
391C4⋊C8C2×Dic1111yescharacteristic
392#103C2×Dic1111yescharacteristic
393#103C2×Dic1111yescharacteristic
394#103C2×Dic1111yescharacteristic
395#103C2×Dic1111yescharacteristic
396#103C2×Dic1111yescharacteristic
397#103C2×Dic1111yescharacteristic
398#102C2×Dic1111yescharacteristic
399#102C2×Dic1111yescharacteristic
400C22⋊C8—111no—
401C22⋊C8—111no—
402C22⋊C8—221no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8C2×Dic1111yescharacteristic
406C22⋊C8C2×Dic1111yescharacteristic
407#97—221no—
408#97—221no—
409#97—221no—
410#97—221no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—22no—
422C2×C11—81no—
423C2×C11#293311yescharacteristic
424C2×C11#294711yescharacteristic
425C2×C11C2×#44311yescharacteristic
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—41no—
429C2×Q8C22×Dic1111yescharacteristic
430C2×Q8C22×Dic1111yescharacteristic
431C2×Q8C22×Dic1111yescharacteristic
432C2×D4—21no—
433C2×D4C22×Dic1111yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4D4×D1111yescharacteristic
438C22×C4#434111yescharacteristic
439C22×C4C22×Dic1111yescharacteristic
440Q16—22no—
441Q16—41no—
442SD16—22no—
443SD16—41no—
444M16—881no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—224no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—881no—
457C2×C8—881no—
458C2×C8C22×Dic1111yescharacteristic
459C2×C8C22×Dic1111yescharacteristic
460C2×C8C22×Dic1111yescharacteristic
461C2×C8C22×Dic1111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4C22×Dic1111yescharacteristic
472C4⋊C4C22×Dic1111yescharacteristic
473C4⋊C4C22×Dic1111yescharacteristic
474C4⋊C4C22×Dic1111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42D4×D1111yescharacteristic
486C42#434111yescharacteristic
487C42C22×Dic1111yescharacteristic
488C42C23×D1111yescharacteristic
489C11#1801711yescharacteristic, complemented, Sylow
490C23—21no—
491C23D4×Dic1111yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8#6700112yes—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4D4×Dic1111yescharacteristic
519C2×C4D4×Dic1111yescharacteristic
520C2×C4D4×Dic1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×#434111yescharacteristic
523C2×C4C23×Dic1111yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—222no—
529C8—222no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—441no—
535C8—441no—
536C8—441no—
537C8—441no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1062280912yes—
544C22C2×D4×Dic1111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—22no—
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4#1062330911yescharacteristic
557C4#1062331011yescharacteristic
558C4C2×#6700111yescharacteristic
559C4#1062335011yescharacteristic
560C2—22no—
561C2—81no—
562C2#1307734311yescharacteristic
563C2#1307746011yescharacteristic
564C2C2×#1062280911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3108C2
socleC22×C11C2×C4×D4
prime radicalC11×#121C2×C4
cosocleC42×C11C24
hypercenter#3108D11
hypocenterC11#18017
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3108

Complements

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

NH ≅ G/Ntype
2. #13077705C2semidirect
3. #13067513C2semidirect
4. #13067507C2semidirect
5. #13067495C2semidirect
6. #13067488C2semidirect
7. #13067488C2semidirect
8. #13067474C2semidirect
9. Q16×C11⋊C8C2semidirect
10. SD16×C11⋊C8C2semidirect
11. #13067401C2semidirect
13. C2×Q8⋊(C11⋊C8)C2semidirect
14. #13066900C2semidirect
489. C11#18017semidirect

Maximal subgroups

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

subgroupindex
#130777762
#130777052
#130675132
#130675072
#130674952
#130674882
#130674742
Q16×C11⋊C82
SD16×C11⋊C82
#130674012
#130670762
C2×Q8⋊(C11⋊C8)2
#130669002
C11×#31082
#1801711