Finite Group Databasebeta

← #14719839

Subgroups — #14719839

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic
2D11×#407C212yesmaximal, complemented
3#13066961C218yesmaximal, complemented
4#13066945C212yesmaximal, complemented
5#13066943C211yesmaximal, characteristic, complemented
6C11×#1462C211yesmaximal, characteristic, complemented
7C23×C22⋊D11C411yescharacteristic
8C23×C4×D11C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11C411yescharacteristic
11C22×(C2×D11)⋊C4C411yescharacteristic
12C22×C4⋊Dic11C411yescharacteristic
13C22×Dic11⋊C4C2211yescharacteristic
14C2×M16×D11—22no—
15C2×#66936—22no—
16C2×#66936—22no—
17C2×#66936—22no—
18C2×#66936—22no—
19C2×#66936C414yes—
20C2×#66936C2214yes—
21C11×#407C2212yes—
22#10622820C2212yes—
23#10622739—22no—
24#10622339—22no—
25#10622339C2214yescomplemented
26D11×C22⋊C8—22no—
27D11×C22⋊C8C2214yescomplemented
28C11×#323C2214yescomplemented
29#10622163C2214yescomplemented
30#10622107C2218yescomplemented
31C25×C11C2×C411yescharacteristic
32C24×D11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—22no—
36C22×C22⋊D11—21no—
37C22×C22⋊D11—21no—
38C22×C22⋊D11—44no—
39C22×C22⋊D11C2×C414yes—
40C23×Dic11C2×C411yescharacteristic
41C23×Dic11C2×C411yescharacteristic
42C23×Dic11C2×C411yescharacteristic
43C22×C4×D11—44no—
44C22×C4×D11C2×C412yes—
45C22×C4×D11D412yes—
46C22×C4×D11D412yes—
47C22×C4×D11D412yes—
48C22×C4×D11D412yes—
49C22×C4×D11C2312yes—
50C2×C11×M16—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2312yes—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—21no—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11C2×C414yes—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4C2×C414yes—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2×C414yes—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4C2×C412yes—
70C2×Dic11⋊C4C2312yes—
71C2×#4318—22no—
72M16×D11—48no—
73C2×#4313—24no—
74C2×C8×D11—24no—
75#66936—24no—
76#66936—24no—
77#66936—24no—
78#66936—24no—
79#66936—24no—
80#66936—24no—
81#66936—24no—
82#66936—24no—
83C11×C22⋊C8—22no—
84C11×C22⋊C8C2314yes—
85C22⋊(C11⋊C8)—22no—
86C22⋊(C11⋊C8)C2314yes—
87(C2×D11)⋊C8—24no—
88(C2×D11)⋊C8—24no—
89#17392—111nomaximal, Sylow
90C24×C11—21no—
91C24×C11—21no—
92C24×C11—42no—
93C24×C11—42no—
94C24×C11—42no—
95C24×C11C22×C411yescharacteristic
96C24×C11C22×C412yes—
97C23×D11—24no—
98C23×D11—42no—
99C23×D11—42no—
100C23×D11C22⋊C412yes—
101C23×D11C22⋊C411yescharacteristic
102C23×D11C22⋊C411yescharacteristic
103C23×D11C22×C412yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—24no—
114C2×C22⋊D11—24no—
115C2×C22⋊D11—48no—
116C2×C22⋊D11—44no—
117C2×C22⋊D11—48no—
118C2×C22⋊D11—44no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—42no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11C22⋊C412yes—
127C22×Dic11C22⋊C411yescharacteristic
128C22×Dic11C22⋊C411yescharacteristic
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C412yes—
131C22×Dic11C22×C412yes—
132C2×C4×D11—28no—
133C2×C4×D11—44no—
134C2×C4×D11—44no—
135C2×C4×D11—44no—
136C2×C4×D11—44no—
137C2×C4×D11—44no—
138C2×C4×D11C22⋊C412yes—
139C2×C4×D11C22⋊C412yes—
140C2×C4×D11C22⋊C412yes—
141C2×C4×D11C22⋊C412yes—
142C2×C4×D11C2×D412yes—
143C2×C4×D11C2×D412yes—
144C2×C4×D11C2×D412yes—
145C2×C4×D11C2×D412yes—
146C11×M16—44no—
147C2×C8×C11—24no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—24no—
150C22⋊Dic11—24no—
151C22⋊Dic11—24no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—24no—
154C4⋊Dic11—24no—
155C4⋊Dic11—24no—
156Dic11⋊C4—24no—
157Dic11⋊C4—24no—
158#4318—44no—
159C2×C11⋊C8—24no—
160#4313—48no—
161C8×D11—48no—
162C22×#123—111no—
163C2×#407—112no—
164#1468—118no—
165#1463—112no—
166#1462—111no—
167#1462D1111yescharacteristic, complemented
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—24no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—88no—
182C23×C11C2×C22⋊C411yescharacteristic
183C23×C11C2×C22⋊C411yescharacteristic
184C23×C11C23×C411yescharacteristic
185C22×D11—24no—
186C22×D11—22no—
187C22×D11—24no—
188C22×D11—24no—
189C22×D11—24no—
190C22×D11—41no—
191C22×D11—42no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—42no—
196C22×D11—416no—
197C22×D11#9914yes—
198C22×D11C2×C22⋊C412yes—
199C22×D11C2×C22⋊C412yes—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C22×D412yes—
210C22⋊D11—48no—
211C22⋊D11—48no—
212C2×Dic11—24no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—24no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11C2×C22⋊C412yes—
225C2×Dic11C2×C22⋊C412yes—
226C4×D11—24no—
227C4×D11—24no—
228C4×D11—24no—
229C4×D11—24no—
230C4×D11—42no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—42no—
234C8×C11—44no—
235C11⋊C8—44no—
236C23×D4—111no—
237C24×C4—111no—
238C22×M16—222no—
239C2×#123—114no—
240C2×#123—114no—
241C2×#123—222no—
242C2×#123—222no—
243C2×#123—222no—
244C2×#123—222no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4—111no—
247C22×C22⋊C4—111no—
248C22×C22⋊C4—111no—
249C22×C22⋊C4C2×D1111yescharacteristic
250#407—112no—
251#407—114no—
252#407—222no—
253#407—222no—
254#407C2×D1112yes—
255C2×C22⋊C8—114no—
256C2×C22⋊C8—222no—
257#324—118no—
258#323—114no—
259#323C2×D1114yescomplemented
260C22×C11—28no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—84no—
271C22×C11—84no—
272C22×C11—84no—
273C22×C11C2×#9912yes—
274C22×C11#41312yes—
275C22×C11C22×C22⋊C411yescharacteristic
276C22×C11#56812yes—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—44no—
283C2×D11—48no—
284C2×D11—48no—
285C2×D11—44no—
286C2×D11C2×#9914yes—
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—42no—
290Dic11—22no—
291Dic11—22no—
292Dic11—42no—
293Dic11—42no—
294C25—111no—
295C25C4×D1111yescharacteristic
296C22×D4—114no—
297C22×D4—221no—
298C22×D4—222no—
299C22×D4—221no—
300C22×D4—444no—
301C23×C4—111no—
302C23×C4—112no—
303C23×C4—112no—
304C23×C4—112no—
305C23×C4—112no—
306C23×C4—112no—
307C23×C4—112no—
308C23×C4—111no—
309C23×C4—111no—
310C23×C4—444no—
311C23×C4C4×D1111yescharacteristic
312C23×C4C22×D1111yescharacteristic
313C2×M16—22no—
314C2×M16—224no—
315C2×M16—222no—
316C2×M16—448no—
317C22×C8—224no—
318#123—224no—
319#123—224no—
320#123—224no—
321#123—224no—
322#123—224no—
323#123—224no—
324#123—224no—
325#123—224no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—114no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—114no—
337C2×C22⋊C4—114no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4—221no—
344C2×C22⋊C4C4×D1112yes—
345C2×C22⋊C4C22×D1112yes—
346C22⋊C8—22no—
347C22⋊C8—114no—
348C22⋊C8—224no—
349C22⋊C8—224no—
350C22⋊C8—222no—
351C22⋊C8C22×D1114yes—
352C2×C11—22no—
353C2×C11—22no—
354C2×C11—22no—
355C2×C11—82no—
356C2×C11#287911yescharacteristic
357C2×C11C22×#9911yescharacteristic
358C2×C11C2×#41311yescharacteristic
359D11—24no—
360D11—42no—
361C24—21no—
362C24—21no—
363C24—42no—
364C24—42no—
365C24—42no—
366C24—111no—
367C24—112no—
368C24—112no—
369C24—111no—
370C24—224no—
371C24—442no—
372C24—442no—
373C24C2×C4×D1111yescharacteristic
374C24C2×C4×D1112yes—
375C2×D4—224no—
376C2×D4—224no—
377C2×D4—444no—
378C2×D4—448no—
379C2×D4—444no—
380C2×D4—448no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—112no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—112no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—112no—
399C22×C4—228no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—444no—
405C22×C4—444no—
406C22×C4—444no—
407C22×C4—444no—
408C22×C4—444no—
409C22×C4—442no—
410C22×C4—442no—
411C22×C4—442no—
412C22×C4C2×C4×D1112yes—
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4D4×D1112yes—
415C22×C4D4×D1112yes—
416C22×C4C23×D1111yescharacteristic
417M16—44no—
418M16—448no—
419M16—444no—
420C2×C8—24no—
421C2×C8—224no—
422C2×C8—448no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—224no—
430C22⋊C4—224no—
431C22⋊C4—224no—
432C22⋊C4—224no—
433C11#1739211yescharacteristic, complemented, Sylow
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—24no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—88no—
448C23—112no—
449C23—114no—
450C23—112no—
451C23—224no—
452C23—224no—
453C23—224no—
454C23—222no—
455C23—224no—
456C23—441no—
457C23—442no—
458C23—441no—
459C23—441no—
460C23—441no—
461C23—442no—
462C23—4416no—
463C23C22⋊C4×D1111yescharacteristic
464C23C22⋊C4×D1111yescharacteristic
465C23C22×C4×D1111yescharacteristic
466D4—448no—
467D4—448no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—112no—
477C2×C4—112no—
478C2×C4—224no—
479C2×C4—224no—
480C2×C4—224no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—224no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4C22⋊C4×D1112yes—
499C2×C4C2×D4×D1112yes—
500C8—44no—
501C8—444no—
502C22—28no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—84no—
513C22—84no—
514C22—84no—
515C22—114no—
516C22—222no—
517C22—222no—
518C22—222no—
519C22—222no—
520C22—222no—
521C22—444no—
522C22—448no—
523C22—448no—
524C22—444no—
525C22D11×#9912yes—
526C22#1062235812yes—
527C22C2×C22⋊C4×D1111yescharacteristic
528C22#1062327612yes—
529C4—22no—
530C4—22no—
531C4—42no—
532C4—222no—
533C4—222no—
534C4—442no—
535C4—442no—
536C2—22no—
537C2—22no—
538C2—22no—
539C2—82no—
540C2—224no—
541C2—442no—
542C2#1307705911yescharacteristic
543C2C2×D11×#9911yescharacteristic
544C2C2×#1062235811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1462C2
socleC22×C11C22×C22⋊C4
prime radicalC23×C22⋊D11C4
cosocleC22×C4×C11C24
hypercenter#1462D11
hypocenterC11#17392
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. D11×#407C2semidirect
3. #13066961C2semidirect
4. #13066945C2semidirect
5. #13066943C2semidirect
6. C11×#1462C2semidirect
25. #10622339C22semidirect
27. D11×C22⋊C8C22semidirect
28. C11×#323C22semidirect
29. #10622163C22semidirect
30. #10622107C22semidirect
167. #1462D11semidirect
259. #323C2×D11semidirect
433. C11#17392semidirect

Maximal subgroups

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

subgroupindex
C22×#669362
D11×#4072
#130669612
#130669452
#130669432
C11×#14622
#1739211