Finite Group Databasebeta

← #14760899

Subgroups — #14760899

Order 2816.

1060 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622348C211yesmaximal, characteristic
2#13071122C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4#13069242C212yesmaximal, complemented
5#13069193C212yesmaximal, complemented
6#13068933C211yesmaximal, characteristic
7#13068704C211yesmaximal, characteristic, complemented
8#106×Dic11C212yesmaximal, complemented
9#13068430C212yesmaximal, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C11×#1853C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66983C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4×Dic11—21no—
16C22×C4×Dic11C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×(C22⋊D11)⋊C4—21no—
19C2×C11×#106C2212yes—
20C2×C11×C22⋊C8C2211yescharacteristic
21C11×#380C2211yescharacteristic
22C2×C11⋊#95—21no—
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×#66885C2212yes—
25C2×#66881C2212yes—
26C2×C8×Dic11C2212yes—
27#10622601C2211yescharacteristic
28C4⋊C4×Dic11—21no—
29C4⋊C4×Dic11—21no—
30C4⋊C4×Dic11C2211yescharacteristic
31C4⋊C4×Dic11C2212yes—
32C4⋊C4×Dic11C2212yes—
33#10622586C2211yescharacteristic
34C2×#66873C2212yes—
35#10622571—21no—
36#10622348C418yescomplemented
37#10622282—21no—
38#10622279—21no—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—21no—
47C23×Dic11—21no—
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C22×C8×C11C2312yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—21no—
59#66983—22no—
60#66983C2×C414yes—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2×C414yescomplemented
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—21no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—44no—
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C22×C11⋊C8C2312yes—
81#66946—24no—
82(C22⋊D11)⋊C4—44no—
83C11×#106—24no—
84C11×C22⋊C8C2×C414yescomplemented
85C11×#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C22⋊(C11⋊C8)—22no—
91#66885C2×C418yescomplemented
92#66881C2×C418yescomplemented
93C8×Dic11—24no—
94#66873—24no—
95C4×#481—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C23×D11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4112yes—
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—24no—
111C2×C22⋊D11—42no—
112C2×C22⋊D11—42no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—24no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—21no—
120C22×Dic11—41no—
121C22×Dic11—42no—
122C22×Dic11—42no—
123C22×Dic11SD1614yes—
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44C22×C412yes—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11C22×C414yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4#4114yes—
143C11×C22⋊C4—42no—
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—42no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—42no—
148C4⋊Dic11—24no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11C22×C412yes—
152C4⋊Dic11C22×C414yes—
153Dic11⋊C4—42no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C4×Dic11—44no—
158C4×Dic11—42no—
159C4×Dic11—44no—
160C4×Dic11#4114yes—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×#481—111no—
165C4×#121—111no—
166C2×C4×C4⋊C4—111no—
167#1926—112no—
168#1919—112no—
169#1874—111no—
170#1853D1111yescharacteristic, complemented
171#1824—111no—
172C4×#106—112no—
173C4×#102—112no—
174C4×C22⋊C8—111no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11C4×D412yes—
180C23×C11C2×SD1612yes—
181C23×C11#13512yes—
182C23×C11C22×D411yescharacteristic
183C22×D11—22no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—48no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11C4×D412yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C2×#4112yes—
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4112yes—
209C22⋊D11—48no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—28no—
215C2×Dic11—24no—
216C2×Dic11—22no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—44no—
221C2×Dic11—48no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11#12312yes—
227C2×Dic11#12312yes—
228C2×Dic11C2×SD1612yes—
229C2×Dic11C2×SD1612yes—
230C2×Dic11AGL(1,ℤ/8)12yes—
231D44—24no—
232D44—42no—
233C4×D11—84no—
234C8×C11—24no—
235C11⋊C8—42no—
236C2×#121—111no—
237C2×C4×D4—111no—
238C2×C4×D4—221no—
239C22×C4⋊C4—111no—
240C22×C4⋊C4C2×D1111yescharacteristic
241C22×C42—111no—
242C22×C42—221no—
243#481—118no—
244C2×#106—112no—
245C2×#106C2×D1112yes—
246C2×#102—112no—
247C2×#102—112no—
248C2×C22⋊C8—111no—
249C2×C22⋊C8C2×D1111yescharacteristic
250C2×C4×C8—112no—
251#390—111no—
252#389—111no—
253#388—221no—
254#386—221no—
255#380C2×D1111yescharacteristic
256C4×C4⋊C4—112no—
257C4×C4⋊C4—112no—
258C4×C4⋊C4—111no—
259C4×C4⋊C4—221no—
260C4×C4⋊C4—221no—
261C4×C22⋊C4—221no—
262C2×#95—221no—
263#340—112no—
264#340—112no—
265#340—112no—
266#340C2×D1112yes—
267#336—112no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11C4×SD1614yes—
275C22×C11C2×C4×D411yescharacteristic
276C22×C11C2×#12311yescharacteristic
277C22×C11#52511yescharacteristic
278C22×C11C22×SD1611yescharacteristic
279C22×C11C2×#13511yescharacteristic
280C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C11#57511yescharacteristic
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—81no—
286C2×D11—81no—
287C2×D11—81no—
288C2×D11—81no—
289C4×C11—22no—
290C4×C11—44no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11C4×#4112yes—
294C4×C11#52912yes—
295Dic11—22no—
296Dic11—22no—
297Dic11—41no—
298Dic11—42no—
299Dic11—44no—
300Dic11#48114yescomplemented
301C22×D4—111no—
302C22×D4—221no—
303C23×C4—21no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—221no—
307C23×C4—221no—
308C23×C4C22×D1111yescharacteristic
309C22×C8—112no—
310C22×C8C22×D1112yes—
311#121—114no—
312#121—222no—
313C4×D4—224no—
314C4×D4—444no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—114no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C4⋊C4C22×D1111yescharacteristic
325C2×C4⋊C4C22×D1112yes—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—221no—
331C2×C42—111no—
332C2×C42—111no—
333C2×C42—111no—
334C2×C42—111no—
335C2×C42—224no—
336C2×C42—221no—
337C2×C42—222no—
338C2×C42—222no—
339C2×C42—444no—
340#106—24no—
341#106—118no—
342#102—118no—
343#102—224no—
344C22⋊C8—222no—
345C22⋊C8C4×D1114yescomplemented
346C4×C8—224no—
347#95—21no—
348#95—222no—
349#95—222no—
350#95—221no—
351#95—221no—
352C2×C11—24no—
353C2×C11C4×#12311yescharacteristic
354C2×C11C2×C4×SD1611yescharacteristic
355C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
356C2×C11C2×#48111yescharacteristic
357C2×C11#309111yescharacteristic
358C2×C11#310311yescharacteristic
359C2×C11#310511yescharacteristic
360D11—82no—
361C24—221no—
362C24D4×D1111yescharacteristic
363C2×D4—112no—
364C2×D4—224no—
365C2×D4—222no—
366C2×D4—221no—
367C2×D4—222no—
368C2×D4—442no—
369C2×D4—442no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—111no—
379C22×C4—114no—
380C22×C4—111no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—224no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—221no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—441no—
394C22×C4—442no—
395C22×C4—442no—
396C22×C4C2×C4×D1112yes—
397C22×C4D4×D1111yescharacteristic
398C22×C4#434312yes—
399C22×C4C23×D1111yescharacteristic
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8C2×C4×D1114yes—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—114no—
411C4⋊C4—112no—
412C4⋊C4—224no—
413C4⋊C4—222no—
414C4⋊C4—221no—
415C4⋊C4—442no—
416C4⋊C4#434114yes—
417C22⋊C4—42no—
418C22⋊C4—224no—
419C22⋊C4—442no—
420C22⋊C4—442no—
421C22⋊C4—442no—
422C42—114no—
423C42—222no—
424C42—222no—
425C42—222no—
426C42—444no—
427C42—442no—
428C42—444no—
429C11C4×#48111yescharacteristic, complemented, Sylow
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23#6694612yes—
442C23SD16×D1112yes—
443C23#6696912yes—
444C23C2×D4×D1111yescharacteristic
445D4—224no—
446D4—448no—
447D4—442no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—48no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—112no—
463C2×C4—112no—
464C2×C4—112no—
465C2×C4—112no—
466C2×C4—112no—
467C2×C4—228no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—222no—
473C2×C4—224no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—444no—
478C2×C4—448no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—884no—
484C2×C4#6694612yes—
485C2×C4C22×C4×D1111yescharacteristic
486C2×C4C2×#434112yes—
487C2×C4C2×#434311yescharacteristic
488C2×C4#41×D1112yes—
489C8—24no—
490C8—442no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—442no—
498C22—442no—
499C22—442no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22#1062246514yes—
505C22C2×#6694611yescharacteristic
506C22#1062311711yescharacteristic
507C22D11×#12311yescharacteristic
508C22C2×SD16×D1111yescharacteristic
509C22C2×#6696911yescharacteristic
510C22D11×AGL(1,ℤ/8)11yescharacteristic
511C22#1062330811yescharacteristic
512C4—22no—
513C4—44no—
514C4—81no—
515C4—81no—
516C4—114no—
517C4—222no—
518C4—222no—
519C4—441no—
520C4—442no—
521C4—444no—
522C4C4×#434112yes—
523C4#1062315512yes—
524C2—24no—
525C2—882no—
526C2#1307113511yescharacteristic
527C2C2×#1062246511yescharacteristic
528C2#1307742311yescharacteristic
529C2D11×#48111yescharacteristic
530C2#1307853011yescharacteristic
531C2#1307864211yescharacteristic
532C2#1307866411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1853C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1853D11
hypocenterC11C4×#481
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic11C2semidirect
4. #13069242C2semidirect
5. #13069193C2semidirect
7. #13068704C2semidirect
8. #106×Dic11C2semidirect
9. #13068430C2semidirect
10. C22⋊C8×Dic11C2semidirect
11. C11×#1853C2semidirect
36. #10622348C4semidirect
67. C2×C4⋊Dic11C2×C4semidirect
84. C11×C22⋊C8C2×C4semidirect
91. #66885C2×C4semidirect
92. #66881C2×C4semidirect
170. #1853D11semidirect
300. Dic11#481semidirect
345. C22⋊C8C4×D11semidirect
429. C11C4×#481semidirect

Maximal subgroups

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

subgroupindex
C2×#106223482
#130711222
C2×C4⋊C4×Dic112
#130692422
#130691932
#130689332
#130687042
#106×Dic112
#130684302
C22⋊C8×Dic112
C11×#18532
C4×#48111