Finite Group Databasebeta

← #14725734

Subgroups — #14725734

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077776C211yesmaximal, characteristic
2#13077718C211yesmaximal, characteristic, complemented
3#13067525C211yesmaximal, characteristic, complemented
4#13067507C211yesmaximal, characteristic, complemented
5#13067495C211yesmaximal, characteristic, complemented
6#13067488C211yesmaximal, characteristic, complemented
7#13067467C211yesmaximal, characteristic, complemented
8#13067453C211yesmaximal, characteristic, complemented
9SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10Q16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067368C211yesmaximal, characteristic, complemented
12#13067024C211yesmaximal, characteristic
13#13067019C211yesmaximal, characteristic, complemented
14#13066913C211yesmaximal, characteristic, complemented
15C11×#3172C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18C11×#501C411yescharacteristic
19C11×#497C411yescharacteristic
20C11×#491C411yescharacteristic
21C11×#489C411yescharacteristic
22C11×#470C411yescharacteristic
23C11×#470C411yescharacteristic
24C11×#468C411yescharacteristic
25C11×#468C411yescharacteristic
26C4×C11×Q16C2211yescharacteristic
27C4×C11×Q16C2211yescharacteristic
28C4×C11×SD16C2211yescharacteristic
29C4×C11×SD16C2211yescharacteristic
30C4×C11×M16C2211yescharacteristic
31#10622637—21no—
32#10622637C2211yescharacteristic
33#10622637C2211yescharacteristic
34#10622637C2211yescharacteristic
35Q8×C11⋊C8—21no—
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#10622613—21no—
45#10622613—21no—
46#10622612—21no—
47#10622538C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622538C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
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×Q16C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×M16C2×C411yescharacteristic
72C2×C11×M16C2×C411yescharacteristic
73C11×C4⋊Q8C2×C411yescharacteristic
74C11×C4⋊Q8C2×C411yescharacteristic
75C11×#126—21no—
76C11×#125—21no—
77C11×#125C2×C411yescharacteristic
78C11×#124C2×C411yescharacteristic
79C11×#123—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8C2×C411yescharacteristic
82C11×C22⋊Q8C2×C411yescharacteristic
83C11×C22⋊Q8C2×C411yescharacteristic
84C11×#121C2×C411yescharacteristic
85C4×Q8×C11—21no—
86C4×Q8×C11C2311yescharacteristic
87C4×Q8×C11C2311yescharacteristic
88C4×Q8×C11C2311yescharacteristic
89C4×D4×C11—21no—
90C4×D4×C11C2311yescharacteristic
91C11×#117—21no—
92C11×#117—21no—
93C2×C42×C11C2311yescharacteristic
94C2×#4318—21no—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97C11×#107C2×C411yescharacteristic
98C11×#107C2×C411yescharacteristic
99C11×#106C2×C411yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×#97C2×C411yescharacteristic
110C11×#97C2×C411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C22⋊(C11⋊C8)—21no—
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)—21no—
127C4⋊(C11⋊C8)D411yescharacteristic
128C4⋊(C11⋊C8)D411yescharacteristic
129C4⋊(C11⋊C8)C2311yescharacteristic
130C4⋊(C11⋊C8)C2311yescharacteristic
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
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#18083—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C11×Q16—22no—
156C11×Q16—41no—
157C11×SD16—22no—
158C11×SD16—41no—
159C11×M16—22no—
160C11×M16—41no—
161C2×C8×C11C22×C411yescharacteristic
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
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—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—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—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—81no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#3172D1111yescharacteristic
208#2994—111no—
209#2986—111no—
210#1593—111no—
211#1590—111no—
212#1588—111no—
213#1587—111no—
214#1584—111no—
215#1582—111no—
216SD16⋊C8—111no—
217C8×Q16—111no—
218#1565—111no—
219#1482—111no—
220#1481—111no—
221#1453—111no—
222C23×C11—21no—
223C23×C11C4×D411yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—42no—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—42no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
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—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C8×C11—21no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11#13112yes—
258C11⋊C8—21no—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533C2×D1111yescharacteristic
269#529C2×D1111yescharacteristic
270#501Dic1111yescharacteristic
271#497Dic1111yescharacteristic
272#491Dic1111yescharacteristic
273#489Dic1111yescharacteristic
274#470Dic1111yescharacteristic
275#470Dic1111yescharacteristic
276#468Dic1111yescharacteristic
277#468Dic1111yescharacteristic
278#446—111no—
279#446—111no—
280#446—111no—
281#446—221no—
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—111no—
285C8×Q8—221no—
286C4×Q16C2×D1111yescharacteristic
287C4×Q16C2×D1111yescharacteristic
288C4×SD16C2×D1111yescharacteristic
289C4×SD16C2×D1111yescharacteristic
290#436—111no—
291#435—221no—
292C8×D4—111no—
293C8×D4—221no—
294#433—221no—
295#433—221no—
296#433—221no—
297#431—111no—
298#431—111no—
299#431—111no—
300#424—221no—
301C2×C4⋊C8—111no—
302C4×M16C2×D1111yescharacteristic
303#335—111no—
304#335—111no—
305#334—111no—
306#334—111no—
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313D4⋊C8—111no—
314D4⋊C8—111no—
315#322—111no—
316#322—111no—
317#322—111no—
318C82—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11C2×C4×D411yescharacteristic
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11C2×#13111yescharacteristic
338C4×C11#56811yescharacteristic
339C4×C11#57711yescharacteristic
340C4×C11#57811yescharacteristic
341C2×Q16C2×Dic1111yescharacteristic
342C2×Q16C2×Dic1111yescharacteristic
343C2×SD16C2×Dic1111yescharacteristic
344C2×SD16C2×Dic1111yescharacteristic
345C2×M16—221no—
346C2×M16C2×Dic1111yescharacteristic
347C2×M16C2×Dic1111yescharacteristic
348C22×C8—221no—
349C22×C8—221no—
350C4⋊Q8C2×Dic1111yescharacteristic
351C4⋊Q8C2×Dic1111yescharacteristic
352#126—21no—
353#125—21no—
354#125C2×Dic1111yescharacteristic
355#124C2×Dic1111yescharacteristic
356#123—21no—
357C22⋊Q8—21no—
358C22⋊Q8C2×Dic1111yescharacteristic
359C22⋊Q8C2×Dic1111yescharacteristic
360C22⋊Q8C2×Dic1111yescharacteristic
361#121C2×Dic1111yescharacteristic
362C4×Q8—21no—
363C4×Q8C22×D1111yescharacteristic
364C4×Q8C22×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—21no—
367C4×D4C22×D1111yescharacteristic
368#117—21no—
369#117—21no—
370C2×C42C22×D1111yescharacteristic
371#107C2×Dic1111yescharacteristic
372#107C2×Dic1111yescharacteristic
373#106C2×Dic1111yescharacteristic
374#106C2×Dic1111yescharacteristic
375C4⋊C8—111no—
376C4⋊C8—111no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389#103C2×Dic1111yescharacteristic
390#103C2×Dic1111yescharacteristic
391#103C2×Dic1111yescharacteristic
392#103C2×Dic1111yescharacteristic
393#103C2×Dic1111yescharacteristic
394#103C2×Dic1111yescharacteristic
395#102C2×Dic1111yescharacteristic
396#102C2×Dic1111yescharacteristic
397C22⋊C8—111no—
398C22⋊C8—111no—
399C22⋊C8—221no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—221no—
404#97—221no—
405#97—221no—
406#97C2×Dic1111yescharacteristic
407#97C2×Dic1111yescharacteristic
408C4×C8—111no—
409C4×C8—111no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—221no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11—41no—
419C2×C11—81no—
420C2×C11#293511yescharacteristic
421C2×C11#294711yescharacteristic
422C2×C11#295511yescharacteristic
423C2×Q8—21no—
424C2×Q8C22×Dic1111yescharacteristic
425C2×Q8C22×Dic1111yescharacteristic
426C2×Q8C22×Dic1111yescharacteristic
427C2×D4—21no—
428C2×D4C22×Dic1111yescharacteristic
429C22×C4—21no—
430C22×C4D4×D1111yescharacteristic
431C22×C4#434111yescharacteristic
432C22×C4C22×Dic1111yescharacteristic
433Q16—22no—
434Q16—41no—
435SD16—22no—
436SD16—41no—
437M16—22no—
438M16—41no—
439M16—881no—
440C2×C8—111no—
441C2×C8—111no—
442C2×C8—111no—
443C2×C8—111no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—881no—
451C2×C8—881no—
452C2×C8C22×Dic1111yescharacteristic
453C2×C8C22×Dic1111yescharacteristic
454C2×C8C22×Dic1111yescharacteristic
455C2×C8C22×Dic1111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4C22×Dic1111yescharacteristic
468C4⋊C4C22×Dic1111yescharacteristic
469C4⋊C4C22×Dic1111yescharacteristic
470C4⋊C4C22×Dic1111yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42D4×D1111yescharacteristic
482C42#434111yescharacteristic
483C42C22×Dic1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1808311yescharacteristic, complemented, Sylow
486C23—21no—
487C23D4×Dic1111yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—42no—
495D4—21no—
496D4—21no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4D4×Dic1111yescharacteristic
513C2×C4D4×Dic1111yescharacteristic
514C2×C4D4×Dic1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×#434111yescharacteristic
517C2×C4C23×Dic1111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—221no—
522C8—221no—
523C8—221no—
524C8—221no—
525C8—441no—
526C8—441no—
527C8—441no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8#6700112yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×D4×Dic1111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4#1062330911yescharacteristic
551C4#1062331011yescharacteristic
552C4C2×#6700111yescharacteristic
553C4#1062335011yescharacteristic
554C2—41no—
555C2—81no—
556C2#1307736011yescharacteristic
557C2#1307746011yescharacteristic
558C2#1307751911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3172C2
socleC22×C11C2×C4×D4
prime radicalC11×#121C2×C4
cosocleC42×C11C24
hypercenter#3172D11
hypocenterC11#18083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3172

Complements

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

NH ≅ G/Ntype
2. #13077718C2semidirect
3. #13067525C2semidirect
4. #13067507C2semidirect
5. #13067495C2semidirect
6. #13067488C2semidirect
7. #13067467C2semidirect
8. #13067453C2semidirect
9. SD16⋊(C11⋊C8)C2semidirect
10. Q16×C11⋊C8C2semidirect
11. #13067368C2semidirect
13. #13067019C2semidirect
14. #13066913C2semidirect
485. C11#18083semidirect

Maximal subgroups

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

subgroupindex
#130777762
#130777182
#130675252
#130675072
#130674952
#130674882
#130674672
#130674532
SD16⋊(C11⋊C8)2
Q16×C11⋊C82
#130673682
#130670242
#130670192
#130669132
C11×#31722
#1808311