Finite Group Databasebeta

← #14722710

Subgroups — #14722710

Order 2816.

1112 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082399C211yesmaximal, characteristic
2#13077743C212yesmaximal, complemented
3#13067350C211yesmaximal, characteristic, complemented
4#13067340C211yesmaximal, characteristic, complemented
5#13067312C212yesmaximal, complemented
6#13067310C212yesmaximal, complemented
7#13067295C212yesmaximal, complemented
8#13067277C211yesmaximal, characteristic, complemented
9C2×#10622184C211yesmaximal, characteristic, complemented
10D11×#333C211yesmaximal, characteristic, complemented
11C11×#1558C211yesmaximal, characteristic, complemented
12C2×#67040C412yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14#10623347C412yes—
15#10623258—22no—
16#10623257—22no—
17#10623256C2211yescharacteristic
18#10623256C2211yescharacteristic
19#10623255C412yes—
20#10623255C412yes—
21D11×C4⋊Q8C2211yescharacteristic
22D11×C4⋊Q8C2211yescharacteristic
23#10623038—22no—
24#10623038—22no—
25#10623008C2211yescharacteristic
26C4×#4339C2211yescharacteristic
27C11×#432C2212yes—
28C2×C4⋊(C11⋊C8)C2212yes—
29#10622450C2212yes—
30#10622448C2212yes—
31#10622446C2212yes—
32D11×C4⋊C8C2212yes—
33#10622343—22no—
34(C22⋊D11)⋊C8—22no—
35#10622319—22no—
36#10622314—22no—
37C11×#333C2211yescharacteristic
38C11×#333C2211yescharacteristic
39C11×#333C2212yes—
40#10622184C2211yescharacteristic
41#10622184C2212yes—
42#10622184C2211yescharacteristic
43#10622123C2212yes—
44#10622123C2212yes—
45#10622119C2212yes—
46#10622119C2212yes—
47C22×Q8×C11C2×C412yes—
48#67040—48no—
49C2×#4343—22no—
50C2×#4343C2×C412yes—
51C2×#4343C2×C412yes—
52C2×Q8×D11—22no—
53C2×Q8×D11C2×C412yes—
54C2×Q8×D11C2×C412yes—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339C2×C411yescharacteristic
58C2×#4339C2×C412yes—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8C2×C412yes—
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C2×C11×C4⋊C4—22no—
64C2×C42×C11C2311yescharacteristic
65#67000C2×C412yes—
66#67000C2×C412yes—
67#66999—24no—
68#66997C2×C412yes—
69#66997C2×C412yes—
70#66983—22no—
71#66982—24no—
72C4×C22⋊D11D412yes—
73C4×C22⋊D11D412yes—
74#66979C2×C411yescharacteristic
75C22×C11⋊C8—22no—
76C2×#4313—22no—
77C2×C8×D11—22no—
78#66949—24no—
79#66949—24no—
80#66948—22no—
81#66948—22no—
82#66947—24no—
83#66947—24no—
84#66946—22no—
85#66946—22no—
86C4⋊C4×D11—22no—
87C4⋊C4×D11—22no—
88#66941—22no—
89#66941—22no—
90#66928C2×C412yes—
91#66927C2311yescharacteristic
92C4×D44—22no—
93C4×D44D412yes—
94#66925C2×C411yescharacteristic
95#66925C2×C411yescharacteristic
96C42×D11C2311yescharacteristic
97C42×D11C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22D412yes—
100C11×C4⋊C8C2312yes—
101C11×C4⋊C8C2312yes—
102C11×C22⋊C8—22no—
103C11×#97—22no—
104(C2×D11)⋊C8—22no—
105(C2×D11)⋊C8—22no—
106#66879—22no—
107Dic11⋊C8—22no—
108Dic11⋊C8—22no—
109C8×Dic11—22no—
110C4⋊(C11⋊C8)—22no—
111C4⋊(C11⋊C8)C2312yes—
112C4⋊(C11⋊C8)C2312yes—
113#17779—111nomaximal, Sylow
114C2×Q8×C11—22no—
115C2×Q8×C11—44no—
116C2×Q8×C11C22×C412yes—
117C2×Q8×C11C22×C412yes—
118C22×C4×C11—22no—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D412yes—
121C2×C22⋊D11—22no—
122C2×C22⋊D11C22⋊C411yescharacteristic
123C2×C22⋊D11C22⋊C411yescharacteristic
124#4343—44no—
125#4343—44no—
126#4343—48no—
127Q8×D11—48no—
128Q8×D11—44no—
129Q8×D11—44no—
130#4339—24no—
131#4339—44no—
132#4339—48no—
133#4339—48no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44C22⋊C411yescharacteristic
138C2×D44C22×C412yes—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11C22×C411yescharacteristic
145C2×C4×D11C22×C411yescharacteristic
146C2×C4×D11C2×D412yes—
147C2×C4×D11C2×D412yes—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22C22⋊C411yescharacteristic
151C2×Dic22C22×C412yes—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C42×C11C22×C411yescharacteristic
158C42×C11C2×D412yes—
159C42×C11C2411yescharacteristic
160C22⋊Dic11C22⋊C412yes—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4C22⋊C412yes—
165(C2×D11)⋊C4C22⋊C412yes—
166C4⋊Dic11—22no—
167C4⋊Dic11C22⋊C412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4C22⋊C412yes—
171Dic11⋊C4C22⋊C412yes—
172C4×Dic11C22×C411yescharacteristic
173C4×Dic11C22×C411yescharacteristic
174C4×Dic11C2×D412yes—
175C4×Dic11C2×D412yes—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—82no—
179#4313—82no—
180C8×D11—82no—
181#3499—111no—
182#2990—112no—
183#1560—111no—
184#1558—111no—
185#1558D1111yescharacteristic, complemented
186#1551—112no—
187#1551—112no—
188#1548—112no—
189#1543—111no—
190C2×#333—111no—
191C2×#333—111no—
192C23×C11C2×C22⋊C411yescharacteristic
193C22×D11—22no—
194C22×D11C2×C22⋊C411yescharacteristic
195C22×D11C2×C22⋊C411yescharacteristic
196Q8×C11—42no—
197Q8×C11—42no—
198Q8×C11—44no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—44no—
205C2×C4×C11C2×C22⋊C412yes—
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C23×C411yescharacteristic
208C2×C4×C11C22×D412yes—
209C22⋊D11—22no—
210C22⋊D11—44no—
211C22⋊D11#10014yes—
212C2×Dic11—22no—
213C2×Dic11C2×C22⋊C412yes—
214C2×Dic11C2×C22⋊C412yes—
215C2×Dic11C2×C22⋊C411yescharacteristic
216C2×Dic11C2×C22⋊C411yescharacteristic
217D44—22no—
218D44—42no—
219D44—44no—
220D44—44no—
221D44—42no—
222D44—42no—
223C4×D11—22no—
224C4×D11—22no—
225C4×D11—22no—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—44no—
230C4×D11—44no—
231C4×D11—44no—
232C4×D11—44no—
233C4×D11—44no—
234Dic22—22no—
235Dic22—44no—
236Dic22—44no—
237Dic22—42no—
238C8×C11—42no—
239C8×C11—42no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242C2×2−1+4—112no—
243D4×Q8—222no—
244#547—222no—
245#547—222no—
246#547—222no—
247#536—112no—
248#536—112no—
249#536—112no—
250#532—111no—
251#532—111no—
252#532—111no—
253C2×C4⋊Q8—111no—
254C2×C4⋊Q8—111no—
255C2×C4⋊Q8C2×D1111yescharacteristic
256C4×#41—111no—
257#446—222no—
258#435—222no—
259#435—222no—
260C8×D4—222no—
261#432—112no—
262#432C2×D1112yes—
263#431—112no—
264#423—112no—
265C2×C4⋊C8—112no—
266C2×C4⋊C8—112no—
267#333—111no—
268#333—112no—
269#333—111no—
270#333—112no—
271#333—112no—
272#333C2×D1111yescharacteristic
273#333C2×D1111yescharacteristic
274#333C2×D1112yes—
275#331—112no—
276#331—112no—
277C22×C11—22no—
278C22×C11C2×#10012yes—
279C22×C11C22×C22⋊C411yescharacteristic
280C2×D11—22no—
281C2×D11—21no—
282C2×D11—22no—
283C2×D11—42no—
284C2×D11—44no—
285C2×D11C2×#10012yes—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11#57712yes—
292C4×C11#57812yes—
293Dic11—21no—
294Dic11—22no—
295Dic11—22no—
296Dic11—42no—
297Dic11C2×#10012yes—
2982−1+4—448no—
299C2×#41—111no—
300C2×#41—112no—
301C2×#41—112no—
302C2×#41—112no—
303C2×#41—222no—
304C2×#41—222no—
305C2×#41—222no—
306C22×Q8—112no—
307C22×Q8—112no—
308C22×Q8—222no—
309C22×Q8C4×D1112yes—
310C2×M16—222no—
311C22×C8—222no—
312C22×C8—222no—
313C4⋊Q8—22no—
314C4⋊Q8—112no—
315C4⋊Q8—112no—
316C4⋊Q8—111no—
317C4⋊Q8—222no—
318C4⋊Q8—222no—
319C4⋊Q8C4×D1112yes—
320C4⋊Q8C22×D1111yescharacteristic
321C4⋊Q8C22×D1111yescharacteristic
322#127—111no—
323#124—112no—
324#124—112no—
325#124—112no—
326#123—224no—
327#123—224no—
328#123—224no—
329C22⋊Q8—224no—
330C22⋊Q8—224no—
331C22⋊Q8—224no—
332#121—222no—
333#121—222no—
334#121—222no—
335C4×Q8—112no—
336C4×D4—112no—
337C4×D4—112no—
338C4×D4—112no—
339C4×D4—222no—
340C4×D4—222no—
341C4×D4—222no—
342#117—111no—
343#117—111no—
344#117—111no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42C22×D1111yescharacteristic
351C4⋊C8—112no—
352C4⋊C8—112no—
353C4⋊C8—222no—
354C4⋊C8—222no—
355C4⋊C8—222no—
356C4⋊C8C22×D1112yes—
357C4⋊C8C22×D1112yes—
358C22⋊C8—22no—
359C22⋊C8—222no—
360C22⋊C8—222no—
361#97—22no—
362#97—222no—
363C4×C8—222no—
364C2×C11—22no—
365C2×C11C22×#10011yescharacteristic
366C2×C11#289812yes—
367D11—22no—
368D11—41no—
369D11—82no—
370#41—224no—
371#41—444no—
372#41—448no—
373#41—448no—
374#41—444no—
375#41—444no—
376#41—448no—
377C2×Q8—22no—
378C2×Q8—44no—
379C2×Q8—111no—
380C2×Q8—112no—
381C2×Q8—222no—
382C2×Q8—222no—
383C2×Q8—444no—
384C2×Q8—444no—
385C2×Q8—448no—
386C2×Q8C2×C4×D1112yes—
387C2×Q8C2×C4×D1112yes—
388C2×D4—111no—
389C2×D4—111no—
390C2×D4—111no—
391C2×D4—112no—
392C2×D4—222no—
393C2×D4—222no—
394C2×D4—222no—
395C2×D4—222no—
396C22×C4—22no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4C2×C4×D1111yescharacteristic
407C22×C4D4×D1112yes—
408M16—882no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—222no—
412C2×C8—222no—
413C2×C8—882no—
414C2×C8—882no—
415C4⋊C4—24no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—112no—
419C4⋊C4—112no—
420C4⋊C4—112no—
421C4⋊C4—224no—
422C4⋊C4—224no—
423C4⋊C4—222no—
424C22⋊C4—112no—
425C22⋊C4—112no—
426C22⋊C4—112no—
427C22⋊C4—224no—
428C22⋊C4—224no—
429C22⋊C4—224no—
430C42—111no—
431C42—111no—
432C42—112no—
433C42—112no—
434C42C2×C4×D1111yescharacteristic
435C42D4×D1112yes—
436C42C23×D1111yescharacteristic
437C11#1777911yescharacteristic, complemented, Sylow
438C23—111no—
439C23—111no—
440C23—222no—
441C23C22⋊C4×D1111yescharacteristic
442Q8—42no—
443Q8—42no—
444Q8—44no—
445Q8—222no—
446Q8—442no—
447Q8—444no—
448Q8—444no—
449D4—114no—
450D4—222no—
451D4—222no—
452D4—442no—
453D4—444no—
454D4—444no—
455D4—444no—
456D4—442no—
457D4—442no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—44no—
464C2×C4—111no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—111no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—444no—
476C2×C4—444no—
477C2×C4—444no—
478C2×C4—444no—
479C2×C4—444no—
480C2×C4C22⋊C4×D1112yes—
481C2×C4C22⋊C4×D1111yescharacteristic
482C2×C4C22×C4×D1111yescharacteristic
483C2×C4C2×D4×D1112yes—
484C8—42no—
485C8—42no—
486C8—442no—
487C8—442no—
488C22—22no—
489C22—112no—
490C22—222no—
491C22—221no—
492C22—222no—
493C22—442no—
494C22—444no—
495C22D11×#10012yes—
496C22C2×C22⋊C4×D1111yescharacteristic
497C4—21no—
498C4—21no—
499C4—22no—
500C4—42no—
501C4—42no—
502C4—112no—
503C4—221no—
504C4—222no—
505C4—222no—
506C4—442no—
507C4#1062330912yes—
508C4#1062331012yes—
509C2—22no—
510C2—222no—
511C2—441no—
512C2—882no—
513C2C2×D11×#10011yescharacteristic
514C2#1307714812yes—
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1558C2
socleC22×C11C22×C22⋊C4
prime radical#13082399C2
cosocleC42×C11C24
hypercenter#1558D11
hypocenterC11#17779
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

Complements

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

NH ≅ G/Ntype
2. #13077743C2semidirect
3. #13067350C2semidirect
4. #13067340C2semidirect
5. #13067312C2semidirect
6. #13067310C2semidirect
7. #13067295C2semidirect
8. #13067277C2semidirect
9. C2×#10622184C2semidirect
10. D11×#333C2semidirect
11. C11×#1558C2semidirect
185. #1558D11semidirect
437. C11#17779semidirect

Maximal subgroups

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

subgroupindex
#130823992
#130777432
#130673502
#130673402
#130673122
#130673102
#130672952
#130672772
C2×#106221842
D11×#3332
C11×#15582
#1777911