Finite Group Databasebeta

← #14650348

Subgroups — #14650348

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071668C211yesmaximal, characteristic, complemented
2#13069453C211yesmaximal, characteristic, complemented
3#13067184C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic, complemented
5#13066496C211yesmaximal, characteristic, complemented
6#13066462C211yesmaximal, characteristic, complemented
7C11×#3186C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C2×D4×Dic11—21no—
11C11×#480—21no—
12C11×#480C412yescomplemented
13C11×#466—22no—
14C11×#447—21no—
15C11×#447C412yescomplemented
16C2×C11×C22⋊C8C2211yescharacteristic
17#10622833—21no—
18#10622833—21no—
19C2×#66898—21no—
20C2×#66898—21no—
21#10622825C2211yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×C11⋊#95C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622594—21no—
26#10622564—21no—
27C22⋊C4×Dic11—21no—
28#10622175—22no—
29#10622175—21no—
30#10622175—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11C2×C411yescharacteristic, complemented
34C22×D4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11—21no—
37C23×Dic11—21no—
38C2×C11×D8—22no—
39C22×C8×C11—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C11×#121C2×C412yes—
47C11×#121D412yes—
48C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—21no—
56C2×C22⋊Dic11D411yescharacteristic
57C2×C22⋊Dic11D411yescharacteristic
58D4×Dic11—42no—
59D4×Dic11—42no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4×Dic11—21no—
63C2×C4×Dic11—21no—
64C22×C11⋊C8—21no—
65C11×#107—22no—
66C11×#102—22no—
67C11×#102—22no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8C2×C412yescomplemented
70#66898—42no—
71#66898—42no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—21no—
77C11⋊#95D411yescharacteristic
78C11⋊#95D411yescharacteristic
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—21no—
81#9277—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C24×C11C2×D411yescharacteristic
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—81no—
101C2×D4×C11—81no—
102C2×D4×C11C22⋊C412yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—81no—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—42no—
117C22×Dic11—42no—
118C22×Dic11—42no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—81no—
123C22×Dic11—81no—
124C11×D8—82no—
125C2×C8×C11—22no—
126C2×C8×C11—81no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4C22⋊C412yes—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C22⋊Dic11—21no—
136C22⋊Dic11—21no—
137C22⋊Dic11—21no—
138C22⋊Dic11—42no—
139C22⋊Dic11—42no—
140C22⋊Dic11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—81no—
143C22⋊Dic11D812yescomplemented
144C4⋊Dic11—42no—
145C4⋊Dic11—81no—
146C4×Dic11—42no—
147C4×Dic11—81no—
148C2×C11⋊C8—41no—
149C2×C11⋊C8—81no—
150#3186D1111yescharacteristic
151#2364—111no—
152#1964—111no—
153#1519—111no—
154C2×#327—111no—
155#1294—111no—
156#1282—111no—
157C23×C11—22no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—81no—
170C23×C11—81no—
171C23×C11C4×D411yescharacteristic
172C23×C11#12011yescharacteristic
173C23×C11#12111yescharacteristic
174C23×C11C2×D811yescharacteristic
175C23×C11#13511yescharacteristic
176C23×C11AGL(1,ℤ/8)11yescharacteristic
177C23×C11AGL(1,ℤ/8)11yescharacteristic
178D4×C11—42no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—42no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—81no—
185D4×C11—81no—
186D4×C11—81no—
187D4×C11—81no—
188D4×C11—81no—
189D4×C11—81no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11C2×C22⋊C411yescharacteristic
203C2×C4×C11C4×D411yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12311yescharacteristic
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—84no—
219C2×Dic11—82no—
220C2×Dic11—82no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223C2×Dic11—81no—
224C8×C11—42no—
225C11⋊C8—81no—
226C2×#121C2×D1111yescharacteristic
227C2×#121C2×D1111yescharacteristic
228C2×C4×D4—221no—
229#480—21no—
230#480Dic1112yescomplemented
231#466—22no—
232#447—21no—
233#447Dic1112yescomplemented
234C2×#99—221no—
235C2×#99—221no—
236C2×C22⋊C8—111no—
237C2×C22⋊C8C2×D1111yescharacteristic
238#388—221no—
239#387—221no—
240#386—221no—
241#386—221no—
242#380—111no—
243C4×C22⋊C4—111no—
244C4×C22⋊C4—221no—
245C2×#95—111no—
246#327—221no—
247#327—221no—
248#327—222no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—161no—
270C22×C11—161no—
271C22×C11#38611yescharacteristic
272C22×C11C4×D811yescharacteristic
273C22×C11#44211yescharacteristic
274C22×C11#44711yescharacteristic
275C22×C11#44911yescharacteristic
276C22×C11#45911yescharacteristic
277C22×C11#46311yescharacteristic
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—81no—
284Dic11—42no—
285Dic11—42no—
286Dic11—81no—
287Dic11—81no—
288Dic11—161no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2×Dic1111yescharacteristic, complemented
292C22×D4C22⋊D1111yescharacteristic
293C23×C4—221no—
294C23×C4—221no—
295C23×C4C22×D1111yescharacteristic
296C2×D8—22no—
297C22×C8—21no—
298C22×C8—221no—
299#121—21no—
300#121—21no—
301#121—21no—
302#121—21no—
303#121—21no—
304#121—21no—
305#121C2×Dic1112yes—
306#121C22⋊D1112yes—
307C4×D4—442no—
308C4×D4—442no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
312C2×C4⋊C4C22⋊D1111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—111no—
316C2×C22⋊C4—111no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—221no—
321C2×C42—221no—
322C2×C42—221no—
323#107—22no—
324#102—22no—
325#102—22no—
326#99—442no—
327#99—442no—
328C22⋊C8—21no—
329C22⋊C8—221no—
330C22⋊C8—221no—
331C22⋊C8C2×Dic1112yescomplemented
332#95—111no—
333#95—111no—
334#95—221no—
335#95—221no—
336#95—221no—
337#95—221no—
338#95—221no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—21no—
342C2×C11—21no—
343C2×C11—21no—
344C2×C11—21no—
345C2×C11—82no—
346C2×C11—161no—
347C2×C11#187911yescharacteristic
348C2×C11#190611yescharacteristic
349C2×C11#191311yescharacteristic
350C24—21no—
351C24—21no—
352C24D4×D1111yescharacteristic
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—81no—
369C2×D4—81no—
370C2×D4C22⋊Dic1112yes—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—81no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—442no—
379C22×C4—442no—
380C22×C4—442no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—881no—
385C22×C4—881no—
386C22×C4D4×D1111yescharacteristic
387C22×C4#434111yescharacteristic
388C22×C4#434111yescharacteristic
389C22×C4C22×Dic1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392D8—82no—
393C2×C8—22no—
394C2×C8—81no—
395C2×C8—441no—
396C2×C8—881no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—442no—
401C4⋊C4—881no—
402C4⋊C4C22⋊Dic1112yes—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—112no—
408C22⋊C4—221no—
409C22⋊C4—221no—
410C22⋊C4—221no—
411C22⋊C4—442no—
412C22⋊C4—442no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C22⋊C4—881no—
416C42—442no—
417C42—881no—
418C11#927711yescharacteristic, complemented, Sylow
419C23—22no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—81no—
432C23—81no—
433C23D8×D1111yescharacteristic
434C23#6696411yescharacteristic
435C23#6696411yescharacteristic
436C23#6696511yescharacteristic
437C23D4×Dic1111yescharacteristic
438C23#6699011yescharacteristic
439C23#6699211yescharacteristic
440D4—42no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—42no—
446D4—81no—
447D4—81no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—884no—
477C2×C4—882no—
478C2×C4—882no—
479C2×C4—881no—
480C2×C4—881no—
481C2×C4—881no—
482C2×C4D4×Dic1111yescharacteristic
483C2×C4#6698811yescharacteristic
484C2×C4#6699211yescharacteristic
485C2×C4C2×C22⋊Dic1111yescharacteristic
486C8—42no—
487C8—881no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—161no—
509C22—161no—
510C22D8×Dic1111yescharacteristic
511C22#1062276311yescharacteristic
512C22#1062276511yescharacteristic
513C22#1062276611yescharacteristic
514C22#1062276911yescharacteristic
515C22#1062277111yescharacteristic
516C22#1062283311yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—81no—
523C4—442no—
524C4—442no—
525C4—881no—
526C4—881no—
527C4—1761no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—82no—
535C2—161no—
536C2#1306896611yescharacteristic
537C2#1306911911yescharacteristic
538C2#1306915911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3186C2
socleC22×C11#386
cosocleC23×C4×C11C23
hypercenter#3186D11
hypocenterC11#9277
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #13071668C2semidirect
2. #13069453C2semidirect
3. #13067184C2semidirect
4. C2×#10622175C2semidirect
5. #13066496C2semidirect
6. #13066462C2semidirect
12. C11×#480C4semidirect
15. C11×#447C4semidirect
33. C22×D4×C11C2×C4semidirect
48. C2×C11×C4⋊C4C2×C4semidirect
69. C11×C22⋊C8C2×C4semidirect
143. C22⋊Dic11D8semidirect
230. #480Dic11semidirect
233. #447Dic11semidirect
291. C22×D4C2×Dic11semidirect
311. C2×C4⋊C4C2×Dic11semidirect
331. C22⋊C8C2×Dic11semidirect
418. C11#9277semidirect

Maximal subgroups

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

subgroupindex
#130716682
#130694532
#130671842
C2×#106221752
#130664962
#130664622
C11×#31862
#927711