Finite Group Databasebeta

← #14645458

Subgroups — #14645458

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic
2#13068707C211yesmaximal, characteristic, complemented
3#13068704C211yesmaximal, characteristic, complemented
4#13068601C211yesmaximal, characteristic
5#13067188C211yesmaximal, characteristic, complemented
6#13066932C211yesmaximal, characteristic
7C11×#1520C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66999C411yescharacteristic, complemented
10C2×Q8×Dic11C411yescharacteristic, complemented
11C2×C4×C22⋊D11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13#10623166—22no—
14#10623166—22no—
15#10623166—22no—
16#10623166—22no—
17C2×#66950—21no—
18C2×C4⋊C4×D11C411yescharacteristic, complemented
19C2×#66942—21no—
20C2×#66941C411yescharacteristic, complemented
21C2×(C22⋊D11)⋊C4—21no—
22C2×#66931—21no—
23C2×C11×C22⋊C8C2211yescharacteristic
24C11×#380C2211yescharacteristic
25#10622825C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×#66870—21no—
28C11×#328—22no—
29#10622189—22no—
30#10622176—22no—
31#10622167—22no—
32#10622165—21no—
33#10622107—21no—
34#10622106—21no—
35C22×Q8×C11C2×C411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11D411yescharacteristic
38C23×Dic11—21no—
39C22×C4×D11—21no—
40C22×C4×D11C2×C411yescharacteristic
41C22×Dic22—21no—
42C22×C8×C11—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8D412yes—
46C11×C22⋊Q8D412yes—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11D411yescharacteristic
54#66999—22no—
55#66999—22no—
56Q8×Dic11—22no—
57Q8×Dic11—22no—
58C4×C22⋊D11—21no—
59C4×C22⋊D11—21no—
60C4×C22⋊D11—21no—
61C4×C22⋊D11—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4D411yescharacteristic
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2×C411yescharacteristic
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×C4⋊Dic11D412yes—
72C2×C4⋊Dic11D412yes—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4D411yescharacteristic
77C2×C4×Dic11—21no—
78C2×C4×Dic11C2×C411yescharacteristic
79C22×C11⋊C8—21no—
80#66950—24no—
81#66950—24no—
82C4⋊C4×D11—22no—
83C4⋊C4×D11—22no—
84#66942—24no—
85#66942—24no—
86#66941—22no—
87#66941—22no—
88(C22⋊D11)⋊C4—24no—
89(C22⋊D11)⋊C4—24no—
90#66931—24no—
91#66931—24no—
92C11×C22⋊C8—21no—
93C11×C22⋊C8—21no—
94C11×#95—21no—
95C11⋊#95—21no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98#66870—42no—
99#8380—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C23×D11C22⋊C411yescharacteristic
102C2×Q8×C11—21no—
103C2×Q8×C11—42no—
104C2×Q8×C11C22⋊C412yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—42no—
108C22×C4×C11—41no—
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C2×C22⋊D11—21no—
116C2×C22⋊D11—21no—
117C2×C22⋊D11—21no—
118C2×C22⋊D11—21no—
119C2×C22⋊D11SD1612yes—
120C2×C22⋊D11Q1612yes—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—41no—
126C22×Dic11—82no—
127C22×Dic11C22⋊C411yescharacteristic
128C22×Dic11C22⋊C411yescharacteristic
129C22×Dic11C22⋊C411yescharacteristic
130C2×C4×D11—24no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—42no—
134C2×C4×D11—82no—
135C2×Dic22—24no—
136C2×Dic22—82no—
137C2×C8×C11—42no—
138C2×C8×C11—41no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4C22⋊C412yes—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C22⋊Dic11—21no—
149C22⋊Dic11—21no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—21no—
154(C2×D11)⋊C4—21no—
155C4⋊Dic11—24no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11—42no—
161C4⋊Dic11C22⋊C412yes—
162C4⋊Dic11C22⋊C412yes—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165Dic11⋊C4—24no—
166Dic11⋊C4—21no—
167Dic11⋊C4—21no—
168C4×Dic11—24no—
169C4×Dic11—21no—
170C4×Dic11—21no—
171C2×C11⋊C8—42no—
172C2×C11⋊C8—41no—
173C2×#554—111no—
174#1824—111no—
175#1824—111no—
176#1799—111no—
177#1520—111no—
178#1520D1111yescharacteristic, complemented
179#1459—111no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11C2×C22⋊C411yescharacteristic
183C23×C11#12011yescharacteristic
184C23×C11#12011yescharacteristic
185C23×C11C2×SD1611yescharacteristic
186C23×C11C2×Q1611yescharacteristic
187C23×C11#13711yescharacteristic
188C23×C11#13711yescharacteristic
189C22×D11—21no—
190C22×D11—21no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11#10312yes—
194Q8×C11—42no—
195Q8×C11—42no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—81no—
207C2×C4×C11—81no—
208C2×C4×C11—81no—
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×C22⋊C411yescharacteristic
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C22⋊D11—22no—
214C22⋊D11—22no—
215C22⋊D11—22no—
216C22⋊D11—22no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—22no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—22no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—82no—
228C2×Dic11—82no—
229C2×Dic11—81no—
230C2×Dic11—81no—
231C2×Dic11—81no—
232C2×Dic11#10312yes—
233C4×D11—42no—
234C4×D11—42no—
235C4×D11—84no—
236Dic22—84no—
237C8×C11—81no—
238C11⋊C8—81no—
239#554—222no—
240#554—222no—
241#554—222no—
242#554—222no—
243C2×C4⋊Q8—111no—
244C2×#125—221no—
245C2×C22⋊Q8—111no—
246C2×C22⋊Q8—221no—
247C2×C22⋊Q8—221no—
248C2×C22⋊Q8C2×D1111yescharacteristic
249C2×C4×Q8—111no—
250C2×C4×D4—111no—
251C2×C4×D4—221no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4—111no—
254C2×#99—221no—
255C2×C22⋊C8—111no—
256C2×C22⋊C8C2×D1111yescharacteristic
257#380—111no—
258#380C2×D1111yescharacteristic
259#342—221no—
260#340—222no—
261#340—222no—
262#328—22no—
263#328—222no—
264#324—221no—
265#323—221no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—41no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11#37911yescharacteristic
277C22×C11C2×#10311yescharacteristic
278C22×C11#41911yescharacteristic
279C22×C11#44811yescharacteristic
280C22×C11#44811yescharacteristic
281C22×C11#45111yescharacteristic
282C22×C11#45111yescharacteristic
283C2×D11—22no—
284C2×D11—42no—
285C2×D11—41no—
286C2×D11—41no—
287C2×D11—42no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—161no—
294C4×C11#41012yes—
295Dic11—22no—
296Dic11—41no—
297Dic11—42no—
298Dic11—42no—
299Dic11—41no—
300Dic11—161no—
301C22×Q8—221no—
302C22×Q8C4×D1111yescharacteristic
303C22×D4—111no—
304C23×C4—111no—
305C23×C4—221no—
306C23×C4—221no—
307C23×C4C22×D1111yescharacteristic
308C22×C8—21no—
309C22×C8—221no—
310C4⋊Q8—222no—
311C4⋊Q8—222no—
312#125—224no—
313#125—224no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—224no—
317C22⋊Q8—224no—
318C22⋊Q8—224no—
319C22⋊Q8—224no—
320C22⋊Q8—222no—
321C22⋊Q8—222no—
322C22⋊Q8D4412yes—
323C22⋊Q8C22⋊D1112yes—
324C4×Q8—222no—
325C4×Q8—222no—
326C4×D4—224no—
327C4×D4—224no—
328C4×D4—221no—
329C4×D4—221no—
330C4×D4—221no—
331C4×D4—221no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—112no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4C4×D1111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—111no—
353C2×C22⋊C4—111no—
354C2×C22⋊C4—221no—
355C2×C22⋊C4—221no—
356C2×C42—111no—
357C2×C42—221no—
358#99—442no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—221no—
362C22⋊C8—221no—
363#95—21no—
364#95—221no—
365C2×C11—21no—
366C2×C11—21no—
367C2×C11—21no—
368C2×C11—21no—
369C2×C11—21no—
370C2×C11—21no—
371C2×C11#178211yescharacteristic
372C2×C11#178711yescharacteristic
373C2×C11#179511yescharacteristic
374D11—42no—
375C24—111no—
376C24D4×D1111yescharacteristic
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8—224no—
380C2×Q8—882no—
381C2×Q8(C2×D11)⋊C412yes—
382C2×D4—112no—
383C2×D4—112no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—221no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—42no—
391C22×C4—41no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—224no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—442no—
403C22×C4—441no—
404C22×C4—882no—
405C22×C4—882no—
406C22×C4C2×C4×D1111yescharacteristic
407C22×C4C2×D4411yescharacteristic
408C22×C4D4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410C22×C4D4×D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C2×C8—42no—
413C2×C8—41no—
414C2×C8—442no—
415C2×C8—441no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—42no—
420C4⋊C4—112no—
421C4⋊C4—112no—
422C4⋊C4—224no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4—222no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—222no—
431C4⋊C4—221no—
432C4⋊C4—442no—
433C4⋊C4(C2×D11)⋊C412yes—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—224no—
439C22⋊C4—221no—
440C22⋊C4—221no—
441C22⋊C4—221no—
442C22⋊C4—221no—
443C22⋊C4—441no—
444C22⋊C4—441no—
445C42—224no—
446C42—221no—
447C42—221no—
448C11#838011yescharacteristic, complemented, Sylow
449C23—41no—
450C23—41no—
451C23—112no—
452C23—221no—
453C23—221no—
454C23—441no—
455C23—441no—
456C23C22⋊C4×D1111yescharacteristic
457C23#6693511yescharacteristic
458C23SD16×D1111yescharacteristic
459C23#6696811yescharacteristic
460C23Q16×D1111yescharacteristic
461C23#6697111yescharacteristic
462C23#6699011yescharacteristic
463Q8—42no—
464Q8—42no—
465Q8—884no—
466D4—222no—
467D4—222no—
468D4—222no—
469D4—222no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—81no—
483C2×C4—112no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—221no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—884no—
497C2×C4—882no—
498C2×C4—882no—
499C2×C4—881no—
500C2×C4—881no—
501C2×C4—881no—
502C2×C4C22⋊C4×D1111yescharacteristic
503C2×C4#6693511yescharacteristic
504C2×C4C2×(C2×D11)⋊C411yescharacteristic
505C2×C4#6699011yescharacteristic
506C8—81no—
507C8—881no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—222no—
519C22—442no—
520C22—442no—
521C22—441no—
522C22—441no—
523C22D11×#10311yescharacteristic
524C22#1062241511yescharacteristic
525C22#1062241911yescharacteristic
526C22#1062242111yescharacteristic
527C22#1062256811yescharacteristic
528C22#1062278311yescharacteristic
529C22#1062279911yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—42no—
534C4—42no—
535C4—161no—
536C4—222no—
537C4—442no—
538C4—442no—
539C4—441no—
540C4—441no—
541C4—1761no—
542C4#1062235312yes—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—21no—
549C2—442no—
550C2#1306853211yescharacteristic
551C2#1306854911yescharacteristic
552C2#1306858511yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#379
prime radicalC22×C22⋊D11D4
cosocleC23×C4×C11C23
hypercenter#1520D11
hypocenterC11#8380
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
2. #13068707C2semidirect
3. #13068704C2semidirect
5. #13067188C2semidirect
7. C11×#1520C2semidirect
9. C2×#66999C4semidirect
10. C2×Q8×Dic11C4semidirect
18. C2×C4⋊C4×D11C4semidirect
20. C2×#66941C4semidirect
178. #1520D11semidirect
448. C11#8380semidirect

Maximal subgroups

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

subgroupindex
C2×#106231662
#130687072
#130687042
#130686012
#130671882
#130669322
C11×#15202
#838011