Finite Group Databasebeta

← #14652906

Subgroups — #14652906

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076964C211yesmaximal, characteristic
2#13068594C211yesmaximal, characteristic
3C2×#10622105C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic
5C2×#10622090C211yesmaximal, characteristic
6#13066841C211yesmaximal, characteristic
7C2×C11×#328C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66997C411yescharacteristic, complemented
10C2×#66977C2211yescharacteristic
11C22×C4×Dic11C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622843C411yescharacteristic, complemented
15C2×C11⋊#95—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×Dic11⋊C8—21no—
20#10622589C411yescharacteristic, complemented
21#10622587C411yescharacteristic, complemented
22#10622585—21no—
23#10622585—21no—
24#10622555—21no—
25#10622555—21no—
26C11×#328—22no—
27#10622188—21no—
28#10622176—22no—
29#10622105—22no—
30#10622090—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11D411yescharacteristic
36C23×Dic11D411yescharacteristic
37C22×Dic22C2×C411yescharacteristic
38C22×C8×C11—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C22⋊Dic11—21no—
47#66997—42no—
48C2×C4⋊Dic11C2×C411yescharacteristic
49#66977—21no—
50#66977—21no—
51#66977—21no—
52#66977—21no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×C4×Dic11—42no—
59C2×C4×Dic11C2×C411yescharacteristic
60C2×C4×Dic11C2×C411yescharacteristic
61C2×C4×Dic11D411yescharacteristic
62C2×C4×Dic11D411yescharacteristic
63C22×C11⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8—21no—
66C11×#95—21no—
67C11×#95D412yes—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95D412yes—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78Dic11⋊C8—42no—
79#9714—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×Dic11—22no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—22no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11C22⋊C411yescharacteristic
118C22×Dic11C22⋊C411yescharacteristic
119C22×Dic11C22⋊C411yescharacteristic
120C22×Dic11C22⋊C411yescharacteristic
121C22×Dic11SD1612yes—
122C22×Dic11Q1612yes—
123C2×Dic22—21no—
124C2×Dic22—21no—
125C2×Dic22—41no—
126C2×Dic22—41no—
127C2×C8×C11—41no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140Dic11⋊C4—42no—
141Dic11⋊C4—42no—
142Dic11⋊C4—42no—
143Dic11⋊C4—42no—
144Dic11⋊C4—41no—
145Dic11⋊C4—41no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—41no—
149C4×Dic11—41no—
150C2×C11⋊C8—41no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—41no—
153#2857—111no—
154#1797—111no—
155C2×#328—111no—
156C2×#328—111no—
157C2×#328—111no—
158C2×#328D1111yescharacteristic
159#1434—111no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11C2×C22⋊C411yescharacteristic
165C23×C11#12111yescharacteristic
166C23×C11#12111yescharacteristic
167C23×C11C2×SD1611yescharacteristic
168C23×C11C2×Q1611yescharacteristic
169C23×C11#13711yescharacteristic
170C23×C11#13711yescharacteristic
171Q8×C11—81no—
172Q8×C11—81no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—81no—
191C2×C4×C11—81no—
192C2×C4×C11—81no—
193C2×C4×C11—81no—
194C2×C4×C11C4×D411yescharacteristic
195C2×C4×C11C4×D411yescharacteristic
196C2×C4×C11#12411yescharacteristic
197C2×C4×C11#12711yescharacteristic
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—81no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223C2×Dic11—81no—
224C2×Dic11#9912yes—
225C2×Dic11#10312yes—
226C2×Dic11#10312yes—
227Dic22—81no—
228Dic22—81no—
229C8×C11—81no—
230C11⋊C8—81no—
231C2×C4⋊Q8—111no—
232C2×C22⋊Q8—111no—
233C2×C22⋊Q8C2×D1111yescharacteristic
234C22×C42—111no—
235C2×C4⋊C8—221no—
236C2×C22⋊C8—111no—
237C2×C22⋊C8C2×D1111yescharacteristic
238#391—111no—
239#391—111no—
240#389—221no—
241#389—221no—
242#384—111no—
243#380—221no—
244#380—221no—
245C2×#95—111no—
246C2×#95—221no—
247C2×#95—221no—
248C2×#95C2×D1111yescharacteristic
249#336—221no—
250#328—22no—
251#328—222no—
252#328—222no—
253#328—222no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11#39011yescharacteristic
267C22×C11C2×#9911yescharacteristic
268C22×C11#41011yescharacteristic
269C22×C11C2×#10311yescharacteristic
270C22×C11#41911yescharacteristic
271C22×C11#42111yescharacteristic
272C22×C11#42111yescharacteristic
273C22×C11#46111yescharacteristic
274C22×C11#46111yescharacteristic
275C22×C11#46211yescharacteristic
276C22×C11#46211yescharacteristic
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—82no—
282C4×C11—81no—
283C4×C11—81no—
284Dic11—22no—
285Dic11—22no—
286Dic11—22no—
287Dic11—41no—
288Dic11—82no—
289Dic11—81no—
290Dic11—81no—
291C22×Q8—111no—
292C22×Q8C4×D1111yescharacteristic
293C23×C4—21no—
294C23×C4—111no—
295C23×C4—111no—
296C23×C4—221no—
297C23×C4C22×D1111yescharacteristic
298C22×C8—21no—
299C22×C8—221no—
300C4⋊Q8—442no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—221no—
306C22⋊Q8—221no—
307C22⋊Q8—221no—
308C22⋊Q8—221no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4C4×D1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—221no—
319C2×C42—111no—
320C2×C42—111no—
321C2×C42—111no—
322C2×C42—111no—
323C2×C42—442no—
324C4⋊C8—442no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C22⋊C8—221no—
328C22⋊C8—221no—
329#95—21no—
330#95—112no—
331#95—221no—
332#95—221no—
333#95—221no—
334#95—221no—
335#95—221no—
336#95—442no—
337#95—442no—
338#95C22⋊D1112yes—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—21no—
342C2×C11—21no—
343C2×C11#151111yescharacteristic
344C2×C11#151511yescharacteristic
345C2×C11#151811yescharacteristic
346C2×C11#152011yescharacteristic
347C2×C11#196311yescharacteristic
348C2×C11#196411yescharacteristic
349C2×C11#198111yescharacteristic
350C24D4×D1111yescharacteristic
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—221no—
356C2×Q8—221no—
357C2×Q8—441no—
358C2×Q8—441no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—111no—
376C22×C4—222no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—222no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4C2×C4×D1111yescharacteristic
392C22×C4#433911yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4D4×D1111yescharacteristic
395C22×C4#434111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C2×C8—41no—
398C2×C8—41no—
399C2×C8—41no—
400C2×C8—441no—
401C2×C8—441no—
402C2×C8—441no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—442no—
410C4⋊C4—442no—
411C4⋊C4—442no—
412C4⋊C4—442no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C42—222no—
420C42—222no—
421C42—441no—
422C42—441no—
423C11#971411yescharacteristic, complemented, Sylow
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23C22⋊C4×D1111yescharacteristic
429C23#6693711yescharacteristic
430C23SD16×D1111yescharacteristic
431C23#6696811yescharacteristic
432C23Q16×D1111yescharacteristic
433C23#6697111yescharacteristic
434C23#6699211yescharacteristic
435Q8—81no—
436Q8—81no—
437Q8—881no—
438Q8—881no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—112no—
461C2×C4—112no—
462C2×C4—112no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—442no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—881no—
486C2×C4—881no—
487C2×C4—881no—
488C2×C4—881no—
489C2×C4(C22⋊D11)⋊C411yescharacteristic
490C2×C4#6693811yescharacteristic
491C2×C4C4×C22⋊D1111yescharacteristic
492C2×C4#6699311yescharacteristic
493C8—81no—
494C8—881no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22#1062235311yescharacteristic
508C22D11×#9911yescharacteristic
509C22#1062240611yescharacteristic
510C22D11×#10311yescharacteristic
511C22#1062241511yescharacteristic
512C22#1062243111yescharacteristic
513C22#1062243411yescharacteristic
514C22#1062243411yescharacteristic
515C22#1062257011yescharacteristic
516C22#1062277511yescharacteristic
517C22#1062279511yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—82no—
523C4—81no—
524C4—81no—
525C4—222no—
526C4—222no—
527C4—222no—
528C4—441no—
529C4—882no—
530C4—881no—
531C4—881no—
532C2—21no—
533C2—21no—
534C2—21no—
535C2—21no—
536C2#1306714711yescharacteristic
537C2#1306716511yescharacteristic
538C2#1306717811yescharacteristic
539C2#1306718611yescharacteristic
540C2#1306944611yescharacteristic
541C2#1306945011yescharacteristic
542C2#1306953711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#328D11
hypocenterC11#9714
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
9. C2×#66997C4semidirect
14. #10622843C4semidirect
20. #10622589C4semidirect
21. #10622587C4semidirect
423. C11#9714semidirect

Maximal subgroups

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

subgroupindex
#130769642
#130685942
C2×#106221052
C2×#106221762
C2×#106220902
#130668412
C2×C11×#3282
#971411