Finite Group Databasebeta

← #14649352

Subgroups — #14649352

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622332C211yesmaximal, characteristic
2#13076956C211yesmaximal, characteristic
3C2×#10622105C211yesmaximal, characteristic
4C2×#10622090C211yesmaximal, characteristic
5#13066840C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C2×#66977C2211yescharacteristic
9C22×C4×Dic11C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C2×C11×#95C2211yescharacteristic
13C2×C11⋊#95—21no—
14C2×C11⋊#95—21no—
15C2×C11⋊#95C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66879—21no—
18C2×Dic11⋊C8—21no—
19#10622598C411yescharacteristic, complemented
20#10622598C411yescharacteristic, complemented
21#10622587C411yescharacteristic, complemented
22#10622587C411yescharacteristic, complemented
23#10622563—21no—
24#10622556—21no—
25#10622332—22no—
26#10622332—22no—
27#10622266—21no—
28#10622266—21no—
29#10622105—22no—
30#10622090—22no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C23×Dic11D411yescharacteristic
35C23×Dic11D411yescharacteristic
36C22×Dic22C2×C411yescharacteristic
37C22×C8×C11—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45#66977—21no—
46#66977—21no—
47#66977—21no—
48#66977—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—21no—
53C2×C4×Dic11—21no—
54C2×C4×Dic11C2×C411yescharacteristic
55C2×C4×Dic11C2×C411yescharacteristic
56C2×C4×Dic11D411yescharacteristic
57C2×C4×Dic11D411yescharacteristic
58C22×C11⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8D412yes—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64C11⋊#95—24no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—42no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)D412yes—
76#66879—24no—
77Dic11⋊C8—24no—
78#9116—111nomaximal, Sylow
79C24×C11C2×D411yescharacteristic
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11C22⋊C411yescharacteristic
117C22×Dic11C22⋊C411yescharacteristic
118C22×Dic11C22⋊C411yescharacteristic
119C22×Dic11C22⋊C411yescharacteristic
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×Dic22—41no—
123C2×Dic22—41no—
124C2×C8×C11—22no—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C22⋊Dic11—41no—
132C22⋊Dic11—41no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—42no—
136C4⋊Dic11—42no—
137Dic11⋊C4—41no—
138Dic11⋊C4—41no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C4×Dic11—21no—
144C4×Dic11—21no—
145C4×Dic11—21no—
146C4×Dic11—21no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—41no—
149C2×C11⋊C8—41no—
150C2×#432—111no—
151#2855—111no—
152C2×#328—111no—
153C2×#328—111no—
154#1434—111no—
155#1294—111no—
156#1294D1111yescharacteristic
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11C2×C22⋊C411yescharacteristic
162C23×C11#12111yescharacteristic
163C23×C11#12111yescharacteristic
164C23×C11AGL(1,ℤ/8)11yescharacteristic
165C23×C11#13711yescharacteristic
166C23×C11#13711yescharacteristic
167C23×C11#13711yescharacteristic
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11C4×D411yescharacteristic
190C2×C4×C11C4×D411yescharacteristic
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12311yescharacteristic
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
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—81no—
220C2×Dic11—81no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223C2×Dic11#10412yes—
224Dic22—81no—
225Dic22—81no—
226C8×C11—42no—
227C11⋊C8—42no—
228C2×C22⋊Q8—111no—
229C22×C42—111no—
230#432—222no—
231#432—222no—
232C2×C4⋊C8—221no—
233C2×C22⋊C8—111no—
234C2×C22⋊C8C2×D1111yescharacteristic
235C2×#97—221no—
236#391—111no—
237#391—111no—
238#389—111no—
239#389—111no—
240#387—221no—
241#387—221no—
242#385—221no—
243#381—221no—
244#380C2×D1111yescharacteristic
245C2×#95—111no—
246C2×#95—221no—
247C2×#95—221no—
248C2×#95C2×D1111yescharacteristic
249#328—222no—
250#328—222no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
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#38611yescharacteristic
264C22×C11#41011yescharacteristic
265C22×C11#41011yescharacteristic
266C22×C11#41711yescharacteristic
267C22×C11#41911yescharacteristic
268C22×C11C2×#10411yescharacteristic
269C22×C11#42111yescharacteristic
270C22×C11#46811yescharacteristic
271C22×C11#46811yescharacteristic
272C22×C11#47011yescharacteristic
273C22×C11#47011yescharacteristic
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—82no—
279C4×C11—81no—
280C4×C11—81no—
281Dic11—22no—
282Dic11—41no—
283Dic11—41no—
284Dic11—41no—
285Dic11—82no—
286Dic11—81no—
287Dic11—81no—
288C22×Q8—111no—
289C23×C4—21no—
290C23×C4—111no—
291C23×C4—111no—
292C23×C4—221no—
293C23×C4C22×D1111yescharacteristic
294C22×C8—21no—
295C22×C8—221no—
296C22⋊Q8—221no—
297C22⋊Q8—221no—
298C22⋊Q8—221no—
299C22⋊Q8—221no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4C4×D1111yescharacteristic
305C2×C4⋊C4C4×D1111yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—221no—
308C2×C42—111no—
309C2×C42—111no—
310C2×C42—111no—
311C2×C42—111no—
312C2×C42—221no—
313C2×C42—221no—
314C2×C42—221no—
315C2×C42—221no—
316C4⋊C8—224no—
317C22⋊C8—21no—
318C22⋊C8—112no—
319C22⋊C8—221no—
320C22⋊C8D4412yes—
321#97—224no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95—221no—
326#95—221no—
327#95—221no—
328#95—221no—
329#95—221no—
330#95—221no—
331#95—224no—
332#95—221no—
333#95—221no—
334#95—442no—
335C2×C11—21no—
336C2×C11—21no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11#150611yescharacteristic
340C2×C11#150911yescharacteristic
341C2×C11#151211yescharacteristic
342C2×C11#151511yescharacteristic
343C2×C11#187111yescharacteristic
344C2×C11#189411yescharacteristic
345C2×C11#189911yescharacteristic
346C24D4×D1111yescharacteristic
347C2×Q8—221no—
348C2×Q8—221no—
349C2×Q8—441no—
350C2×Q8—441no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—222no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—222no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4C2×C4×D1111yescharacteristic
386C22×C4C2×D4411yescharacteristic
387C22×C4#433911yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4#434311yescharacteristic
391C2×C8—22no—
392C2×C8—41no—
393C2×C8—41no—
394C2×C8—222no—
395C2×C8—441no—
396C2×C8—441no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—221no—
400C4⋊C4—221no—
401C4⋊C4—442no—
402C4⋊C4—442no—
403C4⋊C4—441no—
404C4⋊C4—441no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C42—221no—
410C42—221no—
411C42—221no—
412C42—221no—
413C42—221no—
414C42—221no—
415C42—221no—
416C42—221no—
417C11#911611yescharacteristic, complemented, Sylow
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23C22⋊C4×D1111yescharacteristic
423C23#6693711yescharacteristic
424C23#6694811yescharacteristic
425C23#6696411yescharacteristic
426C23#6696811yescharacteristic
427C23#6696811yescharacteristic
428C23#6697111yescharacteristic
429Q8—881no—
430Q8—881no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—112no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—881no—
480C2×C4—881no—
481C2×C4—881no—
482C2×C4—881no—
483C2×C4C4×D4411yescharacteristic
484C2×C4#6693511yescharacteristic
485C2×C4#6694611yescharacteristic
486C2×C4#6694711yescharacteristic
487C8—42no—
488C8—442no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22#1062227811yescharacteristic
502C22#1062235311yescharacteristic
503C22#1062235311yescharacteristic
504C22#1062238411yescharacteristic
505C22#1062239311yescharacteristic
506C22#1062241511yescharacteristic
507C22#1062242911yescharacteristic
508C22D11×#10411yescharacteristic
509C22#1062243411yescharacteristic
510C22#1062248111yescharacteristic
511C22#1062249911yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—82no—
517C4—81no—
518C4—81no—
519C4—222no—
520C4—441no—
521C4—441no—
522C4—441no—
523C4—882no—
524C4—881no—
525C4—881no—
526C2—21no—
527C2—21no—
528C2—21no—
529C2—21no—
530C2#1306712611yescharacteristic
531C2#1306713811yescharacteristic
532C2#1306715111yescharacteristic
533C2#1306716511yescharacteristic
534C2#1306891711yescharacteristic
535C2#1306904811yescharacteristic
536C2#1306907311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9116
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
19. #10622598C4semidirect
20. #10622598C4semidirect
21. #10622587C4semidirect
22. #10622587C4semidirect
417. C11#9116semidirect

Maximal subgroups

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

subgroupindex
C2×#106223322
#130769562
C2×#106221052
C2×#106220902
#130668402
#130664942
C11×#12942
#911611