Finite Group Databasebeta

← #14725382

Subgroups — #14725382

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077741C211yesmaximal, characteristic
2#13077705C211yesmaximal, characteristic, complemented
3#13067525C211yesmaximal, characteristic, complemented
4#13067513C211yesmaximal, characteristic, complemented
5#13067488C211yesmaximal, characteristic, complemented
6#13067474C211yesmaximal, characteristic, complemented
7#13067467C211yesmaximal, characteristic, complemented
8#13067453C211yesmaximal, characteristic, complemented
9SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10SD16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067383C211yesmaximal, characteristic, complemented
12#13067050C211yesmaximal, characteristic
13#13067045C211yesmaximal, characteristic, complemented
14#13066913C211yesmaximal, characteristic, complemented
15C4×C11×#137C211yesmaximal, characteristic
16C2×C11×#137C411yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C11×#441C411yescharacteristic
20C11×#441C411yescharacteristic
21C11×#440C411yescharacteristic
22C11×#440C411yescharacteristic
23C4×C11×Q16C2211yescharacteristic
24C4×C11×Q16C2211yescharacteristic
25C4×C11×SD16C2211yescharacteristic
26C4×C11×SD16C2211yescharacteristic
27C11×#428C411yescharacteristic
28C11×#419C411yescharacteristic
29C11×#417C411yescharacteristic
30C4×C11×M16C2211yescharacteristic
31#10622637—21no—
32#10622637—21no—
33#10622637C2211yescharacteristic
34#10622637C2211yescharacteristic
35#10622637C2211yescharacteristic
36#10622637C2211yescharacteristic
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622624—21no—
40#10622624—21no—
41D4×C11⋊C8C2211yescharacteristic
42D4×C11⋊C8C2211yescharacteristic
43#10622539—21no—
44#10622539—21no—
45#10622539C2211yescharacteristic
46#10622538—21no—
47#10622538C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622537C2211yescharacteristic
50C2×C4⋊(C11⋊C8)—21no—
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#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C22×Q8×C11C2×C411yescharacteristic
69C11×#137—24no—
70C2×C11×Q16C2×C411yescharacteristic
71C2×C11×Q16C2×C411yescharacteristic
72C2×C11×SD16C2×C411yescharacteristic
73C2×C11×SD16C2×C411yescharacteristic
74C2×C11×M16C2×C411yescharacteristic
75C2×C11×M16C2×C411yescharacteristic
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11C2×C411yescharacteristic
79C4×Q8×C11C2×C411yescharacteristic
80C4×Q8×C11C2×C411yescharacteristic
81C4×Q8×C11C2311yescharacteristic
82C4×Q8×C11C2311yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11C2×C411yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C11×#117C2×C411yescharacteristic
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×#4318—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98C11×#107C2×C411yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×#106C2×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×#97C2×C411yescharacteristic
111C11×#97C2×C411yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)D411yescharacteristic
119C22⋊(C11⋊C8)D411yescharacteristic
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)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)D411yescharacteristic
129C4⋊(C11⋊C8)D411yescharacteristic
130C4⋊(C11⋊C8)C2311yescharacteristic
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134#66867—21no—
135#66867—21no—
136#66867—21no—
137#66867—21no—
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18051—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C2×Q8×C11—21no—
149C2×Q8×C11—22no—
150C2×Q8×C11—41no—
151C2×Q8×C11C22×C411yescharacteristic
152C2×Q8×C11C22×C411yescharacteristic
153C2×Q8×C11C22×C411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11C22×C411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C11×Q16—22no—
165C11×Q16—22no—
166C11×SD16—22no—
167C11×SD16M1614yescomplemented
168C11×M16—22no—
169C11×M16—41no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C4⋊C4C22×C411yescharacteristic
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11C22×C411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11#4111yescharacteristic
198C42×C11C2411yescharacteristic
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#2990—111no—
213#2984—111no—
214C4×#137D1111yescharacteristic
215#1593—111no—
216#1591—111no—
217#1587—111no—
218#1585—111no—
219#1584—111no—
220#1582—111no—
221SD16⋊C8—111no—
222C8×SD16—111no—
223#1569—111no—
224#1488—111no—
225#1487—111no—
226#1453—111no—
227C23×C11—21no—
228C23×C11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—42no—
235Q8×C11C2×M1612yes—
236D4×C11—21no—
237D4×C11—42no—
238D4×C11C2×M1612yes—
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—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11C2×M1612yes—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C2×#137Dic1111yescharacteristic
278C4×#41C2×D1111yescharacteristic
279C2×C4×Q8C2×D1111yescharacteristic
280#446—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288#441Dic1111yescharacteristic
289#441Dic1111yescharacteristic
290#440Dic1111yescharacteristic
291#440Dic1111yescharacteristic
292C4×Q16C2×D1111yescharacteristic
293C4×Q16C2×D1111yescharacteristic
294C4×SD16C2×D1111yescharacteristic
295C4×SD16C2×D1111yescharacteristic
296#435—221no—
297#435—221no—
298C8×D4—111no—
299C8×D4—111no—
300#432—111no—
301#432—221no—
302#432—221no—
303#431—111no—
304#431—111no—
305#431—221no—
306#428Dic1111yescharacteristic
307#423—111no—
308C2×C4⋊C8—221no—
309#419Dic1111yescharacteristic
310#417Dic1111yescharacteristic
311C4×M16C2×D1111yescharacteristic
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8—111no—
324#322—111no—
325#322—111no—
326#322—111no—
327C82—111no—
328C22×C11—21no—
329C22×C11—22no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11C2×C4×D411yescharacteristic
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11C22×M1611yescharacteristic
347C4×C11#56811yescharacteristic
348C4×C11#57711yescharacteristic
349C4×C11#57811yescharacteristic
350C2×#41C2×Dic1111yescharacteristic
351C22×Q8C2×Dic1111yescharacteristic
352#137—24no—
353C2×Q16C2×Dic1111yescharacteristic
354C2×Q16C2×Dic1111yescharacteristic
355C2×SD16C2×Dic1111yescharacteristic
356C2×SD16C2×Dic1111yescharacteristic
357C2×M16—221no—
358C2×M16C2×Dic1111yescharacteristic
359C2×M16C2×Dic1111yescharacteristic
360C22×C8—221no—
361C22×C8—221no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8C2×Dic1111yescharacteristic
365C4×Q8C2×Dic1111yescharacteristic
366C4×Q8C2×Dic1111yescharacteristic
367C4×Q8C22×D1111yescharacteristic
368C4×Q8C22×D1111yescharacteristic
369C4×Q8C22×D1111yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4C2×Dic1111yescharacteristic
373C4×D4C22×D1111yescharacteristic
374#117—21no—
375#117C2×Dic1111yescharacteristic
376C2×C4⋊C4—21no—
377C2×C4⋊C4C2×Dic1111yescharacteristic
378C2×C42—21no—
379C2×C42—21no—
380C2×C42C22×D1111yescharacteristic
381#107C2×Dic1111yescharacteristic
382#107C2×Dic1111yescharacteristic
383#106C2×Dic1111yescharacteristic
384#106C2×Dic1111yescharacteristic
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399#103C2×Dic1111yescharacteristic
400#103C2×Dic1111yescharacteristic
401#103C2×Dic1111yescharacteristic
402#103C2×Dic1111yescharacteristic
403#103C2×Dic1111yescharacteristic
404#103C2×Dic1111yescharacteristic
405#102C2×Dic1111yescharacteristic
406#102C2×Dic1111yescharacteristic
407C22⋊C8—111no—
408C22⋊C8—111no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—221no—
414#97—221no—
415#97—221no—
416#97—221no—
417#97—221no—
418#97C2×Dic1111yescharacteristic
419#97C2×Dic1111yescharacteristic
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11—42no—
430C2×C11D4×M1611yescharacteristic
431C2×C11#294711yescharacteristic
432C2×C11#295511yescharacteristic
433#41—22no—
434#41—41no—
435C2×Q8—21no—
436C2×Q8—22no—
437C2×Q8—41no—
438C2×Q8C22×Dic1111yescharacteristic
439C2×Q8C22×Dic1111yescharacteristic
440C2×Q8C22×Dic1111yescharacteristic
441C2×D4—21no—
442C2×D4C22×Dic1111yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4D4×D1111yescharacteristic
449C22×C4#434111yescharacteristic
450C22×C4C22×Dic1111yescharacteristic
451Q16—22no—
452Q16—22no—
453SD16—22no—
454SD16#431814yescomplemented
455M16—22no—
456M16—41no—
457M16—881no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—881no—
469C2×C8—881no—
470C2×C8C22×Dic1111yescharacteristic
471C2×C8C22×Dic1111yescharacteristic
472C2×C8C22×Dic1111yescharacteristic
473C2×C8C22×Dic1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4C22×Dic1111yescharacteristic
482C4⋊C4C22×Dic1111yescharacteristic
483C4⋊C4C22×Dic1111yescharacteristic
484C4⋊C4C22×Dic1111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42D4×D1111yescharacteristic
496C42#434111yescharacteristic
497C42C22×Dic1111yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1805111yescharacteristic, complemented, Sylow
500C23—21no—
501C23D4×Dic1111yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—42no—
508Q8C2×#431812yes—
509D4—21no—
510D4—42no—
511D4C2×#431812yes—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4D4×Dic1111yescharacteristic
531C2×C4D4×Dic1111yescharacteristic
532C2×C4D4×Dic1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4C2×#434111yescharacteristic
535C2×C4C23×Dic1111yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—221no—
540C8—221no—
541C8—221no—
542C8—221no—
543C8—441no—
544C8—441no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8C2×#431812yes—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22C2×D4×Dic1111yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—22no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4#1062330911yescharacteristic
569C4#1062331011yescharacteristic
570C4C22×#431811yescharacteristic
571C4#1062335011yescharacteristic
572C2—41no—
573C2—42no—
574C2D4×#431811yescharacteristic
575C2#1307746011yescharacteristic
576C2#1307751911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC4×C11×#137C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenterC4×#137D11
hypocenterC11#18051
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. #13077705C2semidirect
3. #13067525C2semidirect
4. #13067513C2semidirect
5. #13067488C2semidirect
6. #13067474C2semidirect
7. #13067467C2semidirect
8. #13067453C2semidirect
9. SD16⋊(C11⋊C8)C2semidirect
10. SD16×C11⋊C8C2semidirect
11. #13067383C2semidirect
13. #13067045C2semidirect
14. #13066913C2semidirect
167. C11×SD16M16semidirect
454. SD16#4318semidirect
499. C11#18051semidirect

Maximal subgroups

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

subgroupindex
#130777412
#130777052
#130675252
#130675132
#130674882
#130674742
#130674672
#130674532
SD16⋊(C11⋊C8)2
SD16×C11⋊C82
#130673832
#130670502
#130670452
#130669132
C4×C11×#1372
#1805111