Finite Group Databasebeta

← #14760978

Subgroups — #14760978

Order 2816.

1048 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
2C4×#66983C211yesmaximal, characteristic
3C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13069237C212yesmaximal, complemented
5#13069202C212yesmaximal, complemented
6#13068931C211yesmaximal, characteristic
7#13068806C211yesmaximal, characteristic, complemented
8#13068707C211yesmaximal, characteristic, complemented
9#13068513C212yesmaximal, complemented
10#13068442C212yesmaximal, complemented
11C11×#1749C211yesmaximal, characteristic, complemented
12C22×C42×C11C2211yescharacteristic
13C2×#66983C2211yescharacteristic
14C2×C4×C22⋊D11—21no—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4×Dic11—21no—
18C2×C4×D44C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×#97C2212yes—
22#10622826—21no—
23#10622825C2211yescharacteristic
24C2×C11⋊#95—21no—
25C2×#66885C2212yes—
26C2×#66885C2212yes—
27C2×#66882C2212yes—
28C2×#66881C2212yes—
29#10622553—21no—
30#10622552C2211yescharacteristic
31C4×(C2×D11)⋊C4—21no—
32C4×C4⋊Dic11—21no—
33C4×C4⋊Dic11—21no—
34C4×C4⋊Dic11C2211yescharacteristic
35C4×C4⋊Dic11C2212yes—
36C4×C4⋊Dic11C2212yes—
37#10622541C2211yescharacteristic
38#10622348C418yescomplemented
39C11×#336C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2212yes—
43#10622189C2212yes—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—21no—
48C23×Dic11—21no—
49C23×Dic11—21no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C2×C42×C11—24no—
55C2×C42×C11D411yescharacteristic
56C2×C42×C11D411yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—21no—
60#66983—22no—
61#66983C2×C414yes—
62C4×C22⋊D11—44no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—24no—
71C2×C4⋊Dic11C2×C414yescomplemented
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—44no—
82C4×D44—24no—
83C11×C22⋊C8—22no—
84C11×C22⋊C8C2×C414yescomplemented
85C11×#97—24no—
86C11⋊#95—21no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91#66885—24no—
92#66885C2×C418yescomplemented
93#66882—24no—
94#66881C2×C418yescomplemented
95#21580—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C23×D11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—41no—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4112yes—
113C22×C4×C11C2411yescharacteristic
114C2×C22⋊D11—24no—
115C2×C22⋊D11—42no—
116C2×C22⋊D11—42no—
117C22×Dic11—24no—
118C22×Dic11—24no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11—42no—
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×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11C22×C414yes—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11#4114yes—
145C22⋊Dic11—42no—
146(C2×D11)⋊C4—24no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—42no—
149(C2×D11)⋊C4—42no—
150C4⋊Dic11—24no—
151C4⋊Dic11—24no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C22×C412yes—
158C4⋊Dic11C22×C414yes—
159C4⋊Dic11#4114yes—
160Dic11⋊C4—42no—
161C4×Dic11—44no—
162C4×Dic11—42no—
163C4×Dic11—44no—
164C2×#481—111no—
165C4×#121—111no—
166C2×C4×C4⋊C4—111no—
167#1925—112no—
168#1920—112no—
169#1874—111no—
170#1852—111no—
171#1824—111no—
172#1776—112no—
173#1762—112no—
174#1749D1111yescharacteristic, complemented
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11C4×D412yes—
180C23×C11AGL(1,ℤ/8)12yes—
181C23×C11#13712yes—
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—28no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—44no—
205C2×C4×C11C4×D412yes—
206C2×C4×C11#12312yes—
207C2×C4×C11#12312yes—
208C2×C4×C11AGL(1,ℤ/8)12yes—
209C2×C4×C11C23×C411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4112yes—
212C2×C4×C11C2×#4112yes—
213C22⋊D11—48no—
214C2×Dic11—24no—
215C2×Dic11—22no—
216C2×Dic11—24no—
217C2×Dic11—48no—
218C2×Dic11—48no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—42no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231D44—24no—
232D44—42no—
233C4×D11—84no—
234C8×C11—24no—
235C8×C11—42no—
236C2×#121—111no—
237C2×C4×D4—111no—
238C2×C4×D4—221no—
239C22×C4⋊C4—111no—
240C22×C4⋊C4—111no—
241C22×C42—221no—
242C22×C42C2×D1111yescharacteristic
243#481—118no—
244C2×#107—112no—
245C2×#106—112no—
246C2×#102—112no—
247C2×#102—112no—
248C2×C22⋊C8C2×D1111yescharacteristic
249C2×C22⋊C8C2×D1111yescharacteristic
250C2×#97C2×D1112yes—
251#390—111no—
252#389—111no—
253#388—221no—
254#386—221no—
255#380—111no—
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#340—112no—
267#336C2×D1112yes—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11#44014yes—
275C22×C11C2×C4×D411yescharacteristic
276C22×C11C2×#12311yescharacteristic
277C22×C11#52511yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C11C2×#13711yescharacteristic
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—22no—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—41no—
294C4×C11C4×#4112yes—
295C4×C11#52912yes—
296Dic11—44no—
297Dic11—42no—
298Dic11—44no—
299Dic11—81no—
300Dic11—81no—
301C22×D4—111no—
302C22×D4—221no—
303C23×C4—221no—
304C23×C4—221no—
305C23×C4—221no—
306C23×C4D4411yescharacteristic
307C23×C4D4411yescharacteristic
308C23×C4C22×D1111yescharacteristic
309C22×C8C22×D1112yes—
310C22×C8C22×D1112yes—
311#121—114no—
312#121—222no—
313C4×D4—224no—
314C4×D4—444no—
315C2×C4⋊C4—114no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—224no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—221no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—221no—
331C2×C42—24no—
332C2×C42—221no—
333C2×C42—222no—
334C2×C42—222no—
335C2×C42—444no—
336C2×C42D4411yescharacteristic
337C2×C42D4411yescharacteristic
338C2×C42C22×D1111yescharacteristic
339C2×C42C22×D1111yescharacteristic
340#107—224no—
341#106—118no—
342#102—118no—
343#102—224no—
344C22⋊C8—22no—
345C22⋊C8C4×D1114yescomplemented
346#97—24no—
347#95—222no—
348#95—222no—
349#95—221no—
350#95—221no—
351#95—221no—
352C2×C11—24no—
353C2×C11C4×#12311yescharacteristic
354C2×C11C2×#44011yescharacteristic
355C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
356C2×C11#309211yescharacteristic
357C2×C11#309411yescharacteristic
358C2×C11#310911yescharacteristic
359C2×C11#311711yescharacteristic
360D11—82no—
361C24—221no—
362C24C2×D4411yescharacteristic
363C2×D4—112no—
364C2×D4—224no—
365C2×D4—221no—
366C2×D4—222no—
367C2×D4—222no—
368C2×D4—442no—
369C2×D4—442no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—41no—
378C22×C4—224no—
379C22×C4—224no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4C2×C4×D1112yes—
393C22×C4C2×D4411yescharacteristic
394C22×C4C2×D4411yescharacteristic
395C22×C4C2×D4411yescharacteristic
396C22×C4C2×D4411yescharacteristic
397C22×C4C2×D4411yescharacteristic
398C22×C4#433912yes—
399C22×C4C23×D1111yescharacteristic
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8C2×C4×D1114yes—
406C4⋊C4—114no—
407C4⋊C4—112no—
408C4⋊C4—114no—
409C4⋊C4—224no—
410C4⋊C4—224no—
411C4⋊C4—222no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4—442no—
417C22⋊C4—224no—
418C22⋊C4—442no—
419C22⋊C4—442no—
420C22⋊C4—442no—
421C22⋊C4—442no—
422C42—22no—
423C42—22no—
424C42—22no—
425C42—444no—
426C42—442no—
427C42—444no—
428C42#434114yes—
429C11#2158011yescharacteristic, complemented, Sylow
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23C4×D4412yes—
442C23#6696112yes—
443C23#6696212yes—
444C23C22×D4411yescharacteristic
445D4—224no—
446D4—448no—
447D4—442no—
448C2×C4—28no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—44no—
463C2×C4—222no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—448no—
467C2×C4—448no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—442no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—884no—
481C2×C4C4×D4412yes—
482C2×C4#6693912yes—
483C2×C4#6693912yes—
484C2×C4#6696112yes—
485C2×C4C22×C4×D1111yescharacteristic
486C2×C4C2×#433911yescharacteristic
487C2×C4C2×#434112yes—
488C2×C4#41×D1112yes—
489C8—24no—
490C8—42no—
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#1062232314yes—
505C22C2×C4×D4411yescharacteristic
506C22C2×#6693911yescharacteristic
507C22#1062305511yescharacteristic
508C22C2×#6696111yescharacteristic
509C22C2×#6696111yescharacteristic
510C22C2×#6696211yescharacteristic
511C22#1062327911yescharacteristic
512C4—22no—
513C4—22no—
514C4—22no—
515C4—22no—
516C4—41no—
517C4—442no—
518C4—444no—
519C4—444no—
520C4—881no—
521C4—881no—
522C4C4×#434112yes—
523C4#1062306912yes—
524C2—24no—
525C2—882no—
526C2C4×#6693911yescharacteristic
527C2C2×#1062232311yescharacteristic
528C2C4×#6696111yescharacteristic
529C2#1307854111yescharacteristic
530C2#1307855711yescharacteristic
531C2#1307870811yescharacteristic
532C2#1307878911yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1749C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1749D11
hypocenterC11#21580
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. C2×C4×C4⋊Dic11C2semidirect
4. #13069237C2semidirect
5. #13069202C2semidirect
7. #13068806C2semidirect
8. #13068707C2semidirect
9. #13068513C2semidirect
10. #13068442C2semidirect
11. C11×#1749C2semidirect
38. #10622348C4semidirect
71. C2×C4⋊Dic11C2×C4semidirect
84. C11×C22⋊C8C2×C4semidirect
92. #66885C2×C4semidirect
94. #66881C2×C4semidirect
174. #1749D11semidirect
345. C22⋊C8C4×D11semidirect
429. C11#21580semidirect

Maximal subgroups

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

subgroupindex
C2×#106223482
C4×#669832
C2×C4×C4⋊Dic112
#130692372
#130692022
#130689312
#130688062
#130687072
#130685132
#130684422
C11×#17492
#2158011