Finite Group Databasebeta

← #14719657

Subgroups — #14719657

Order 2816.

1646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2#13077245C212yesmaximal, complemented
3#13066955C214yesmaximal, complemented
4#13066943C211yesmaximal, characteristic, complemented
5#13066942C212yesmaximal, complemented
6#13066935C214yesmaximal, complemented
7C11×#1462C211yesmaximal, characteristic, complemented
8C23×C22⋊D11C411yescharacteristic
9C24×Dic11C411yescharacteristic
10C23×C4×D11C411yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×(C2×D11)⋊C4C2211yescharacteristic
13C22×Dic11⋊C4C411yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C2×(C22⋊D11)⋊C4—22no—
16C2×(C22⋊D11)⋊C4—22no—
17C2×(C22⋊D11)⋊C4—22no—
18C2×(C22⋊D11)⋊C4—22no—
19C2×(C22⋊D11)⋊C4C412yes—
20C2×(C22⋊D11)⋊C4C412yes—
21C2×(C22⋊D11)⋊C4C2212yes—
22C2×(C22⋊D11)⋊C4C2212yes—
23C11×#407C2212yes—
24#10622820C2212yes—
25#10622731—22no—
26M16×Dic11—22no—
27#10622332—22no—
28#10622332C2214yescomplemented
29#10622331—22no—
30#10622331C2214yescomplemented
31C11×#323C2214yescomplemented
32#10622163C2214yescomplemented
33#10622106C2218yescomplemented
34C25×C11C2×C411yescharacteristic
35C24×D11C2×C411yescharacteristic
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11—28no—
39C22×C22⋊D11—22no—
40C22×C22⋊D11—22no—
41C22×C22⋊D11C2×C412yes—
42C22×C22⋊D11C2×C412yes—
43C23×Dic11—21no—
44C23×Dic11—21no—
45C23×Dic11—21no—
46C23×Dic11—21no—
47C23×Dic11—44no—
48C23×Dic11C2×C411yescharacteristic
49C23×Dic11C2×C411yescharacteristic
50C23×Dic11C2×C412yes—
51C23×Dic11C2×C412yes—
52C23×Dic11C2×C411yescharacteristic
53C22×C4×D11—21no—
54C22×C4×D11—21no—
55C22×C4×D11—21no—
56C22×C4×D11—21no—
57C22×C4×D11—44no—
58C22×C4×D11C2×C412yes—
59C22×C4×D11C2×C412yes—
60C2×C11×M16—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4C2×C412yes—
64C2×C11×C22⋊C4C2312yes—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2312yes—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4C2×C412yes—
72C2×Dic11⋊C4C2×C412yes—
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11D412yes—
76C2×C4×Dic11D412yes—
77C2×C4×Dic11D412yes—
78C2×C4×Dic11D412yes—
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C2×#4318—22no—
82(C22⋊D11)⋊C4—24no—
83(C22⋊D11)⋊C4—24no—
84(C22⋊D11)⋊C4—24no—
85(C22⋊D11)⋊C4—24no—
86(C22⋊D11)⋊C4—24no—
87(C22⋊D11)⋊C4—24no—
88(C22⋊D11)⋊C4—24no—
89(C22⋊D11)⋊C4—24no—
90C11×C22⋊C8—22no—
91C11×C22⋊C8C2314yes—
92C22⋊(C11⋊C8)—22no—
93C22⋊(C11⋊C8)C2314yes—
94#66879—24no—
95Dic11⋊C8—24no—
96Dic11⋊C8—24no—
97C8×Dic11—24no—
98#17364—111nomaximal, Sylow
99C24×C11—21no—
100C24×C11—21no—
101C24×C11—24no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11C22×C411yescharacteristic
105C24×C11C22×C412yes—
106C23×D11—21no—
107C23×D11—21no—
108C23×D11—24no—
109C23×D11—42no—
110C23×D11—42no—
111C23×D11C22×C412yes—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—216no—
122C2×C22⋊D11—216no—
123C2×C22⋊D11—24no—
124C2×C22⋊D11—24no—
125C2×C22⋊D11—24no—
126C2×C22⋊D11—24no—
127C2×C22⋊D11—24no—
128C2×C22⋊D11M1618yescomplemented
129C22×Dic11—24no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—42no—
138C22×Dic11—44no—
139C22×Dic11—44no—
140C22×Dic11—44no—
141C22×Dic11—44no—
142C22×Dic11—44no—
143C22×Dic11—44no—
144C22×Dic11C22⋊C412yes—
145C22×Dic11C22⋊C412yes—
146C22×Dic11C22⋊C411yescharacteristic
147C22×Dic11C22⋊C411yescharacteristic
148C22×Dic11C22⋊C411yescharacteristic
149C22×Dic11C22⋊C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C412yes—
154C22×Dic11C22×C411yescharacteristic
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—44no—
160C2×C4×D11—44no—
161C2×C4×D11—44no—
162C2×C4×D11—44no—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C11×M16—44no—
166C2×C8×C11—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4—24no—
173C4×Dic11C22⋊C412yes—
174C4×Dic11C22⋊C412yes—
175C4×Dic11C22⋊C412yes—
176C4×Dic11C22⋊C412yes—
177C4×Dic11C2×D412yes—
178C4×Dic11C2×D412yes—
179C4×Dic11C2×D412yes—
180C4×Dic11C2×D412yes—
181#4318—44no—
182C2×C11⋊C8—24no—
183C22×C4×D4—111no—
184#2920—112no—
185#1466—114no—
186#1462—112no—
187#1462—111no—
188#1462D1111yescharacteristic, complemented
189#1460—114no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—416no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11C2×C22⋊C411yescharacteristic
205C23×C11C2×C22⋊C411yescharacteristic
206C23×C11C2×M1614yes—
207C23×C11C23×C411yescharacteristic
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—42no—
213C22×D11—416no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11C2×M1614yes—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11C22×D412yes—
230C22⋊D11—216no—
231C22⋊D11—216no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—44no—
242C2×Dic11—44no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—44no—
246C2×Dic11—44no—
247C2×Dic11—42no—
248C2×Dic11#10014yes—
249C2×Dic11C2×C22⋊C412yes—
250C2×Dic11C2×C22⋊C411yescharacteristic
251C2×Dic11C2×C22⋊C411yescharacteristic
252C2×Dic11C2×C22⋊C412yes—
253C2×Dic11C2×C22⋊C411yescharacteristic
254C2×Dic11C2×C22⋊C411yescharacteristic
255C2×Dic11C2×M1614yes—
256C4×D11—44no—
257C4×D11—44no—
258C4×D11—44no—
259C4×D11—44no—
260C8×C11—44no—
261C11⋊C8—44no—
262C23×D4—111no—
263C24×C4—111no—
264C24×C4—111no—
265C2×C4×D4—112no—
266C2×C4×D4—112no—
267C2×C4×D4—112no—
268C2×C4×D4—112no—
269C2×C4×D4—222no—
270C2×C4×D4—222no—
271C2×C4×D4—222no—
272C2×C4×D4—222no—
273C22×C4⋊C4—111no—
274C22×C22⋊C4—111no—
275C22×C22⋊C4C2×D1111yescharacteristic
276C22×C42—111no—
277#432—114no—
278#432—222no—
279#431—114no—
280#431—222no—
281#423—222no—
282#407—112no—
283#407C2×D1112yes—
284C4×M16—222no—
285#323—114no—
286#323—118no—
287#323C2×D1114yescomplemented
288C22×C11—28no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—24no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—48no—
299C22×C11—48no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11#41012yes—
303C22×C11C2×#10012yes—
304C22×C11C22×C22⋊C411yescharacteristic
305C22×C11C22×M1612yes—
306C2×D11—24no—
307C2×D11—44no—
308C2×D11—48no—
309C2×D11—48no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—44no—
313C4×C11—22no—
314C4×C11—22no—
315C4×C11—42no—
316Dic11—22no—
317Dic11—21no—
318Dic11—21no—
319Dic11—42no—
320Dic11#40714yes—
321Dic11C2×#10012yes—
322Dic11C2×#10012yes—
323C25—111no—
324C25C4×D1111yescharacteristic
325C22×D4—112no—
326C22×D4—112no—
327C22×D4—222no—
328C22×D4—222no—
329C22×D4—228no—
330C23×C4—111no—
331C23×C4—111no—
332C23×C4—111no—
333C23×C4—112no—
334C23×C4—112no—
335C23×C4—112no—
336C23×C4—112no—
337C23×C4—221no—
338C23×C4—221no—
339C23×C4—221no—
340C23×C4—221no—
341C23×C4—221no—
342C23×C4—221no—
343C23×C4—221no—
344C23×C4—221no—
345C23×C4—444no—
346C23×C4—444no—
347C23×C4C4×D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C2×M16—22no—
350C2×M16—222no—
351C4×D4—224no—
352C4×D4—224no—
353C4×D4—224no—
354C4×D4—224no—
355C4×D4—224no—
356C4×D4—224no—
357C4×D4—224no—
358C4×D4—224no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—112no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4C4×D1112yes—
370C2×C22⋊C4C22×D1112yes—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—112no—
374C2×C42—112no—
375C2×C42—112no—
376C2×C42—112no—
377C2×C42—111no—
378C2×C42—111no—
379C4⋊C8—224no—
380C4⋊C8—224no—
381C22⋊C8—22no—
382C22⋊C8—114no—
383C22⋊C8—222no—
384C22⋊C8C22×D1114yes—
385#97—224no—
386C4×C8—224no—
387C2×C11—22no—
388C2×C11—22no—
389C2×C11—22no—
390C2×C11—44no—
391C2×C11C2×#40711yescharacteristic
392C2×C11C2×#41011yescharacteristic
393C2×C11C22×#10011yescharacteristic
394D11—44no—
395C24—21no—
396C24—21no—
397C24—24no—
398C24—42no—
399C24—42no—
400C24—112no—
401C24—224no—
402C24—221no—
403C24—221no—
404C24—442no—
405C24—442no—
406C24C2×C4×D1111yescharacteristic
407C24C2×C4×D1112yes—
408C2×D4—118no—
409C2×D4—224no—
410C2×D4—224no—
411C2×D4—224no—
412C2×D4—224no—
413C2×D4—2216no—
414C2×D4—2216no—
415C2×D4—224no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—112no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—444no—
444C22×C4—444no—
445C22×C4—444no—
446C22×C4—444no—
447C22×C4—444no—
448C22×C4—444no—
449C22×C4—444no—
450C22×C4—444no—
451C22×C4—444no—
452C22×C4—444no—
453C22×C4—444no—
454C22×C4—444no—
455C22×C4—442no—
456C22×C4C2×C4×D1112yes—
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4D4×D1112yes—
459C22×C4D4×D1112yes—
460C22×C4C23×D1111yescharacteristic
461M16—44no—
462M16—444no—
463C2×C8—24no—
464C2×C8—224no—
465C4⋊C4—224no—
466C4⋊C4—224no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C42—112no—
472C42—112no—
473C42—112no—
474C42—112no—
475C42—112no—
476C42—112no—
477C42—112no—
478C42—112no—
479C11#1736411yescharacteristic, complemented, Sylow
480C23—22no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—24no—
485C23—22no—
486C23—22no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—416no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—114no—
495C23—224no—
496C23—224no—
497C23—222no—
498C23—222no—
499C23—442no—
500C23—442no—
501C23—442no—
502C23—4416no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23C22⋊C4×D1111yescharacteristic
507C23C22⋊C4×D1111yescharacteristic
508C23M16×D1114yes—
509C23C22×C4×D1111yescharacteristic
510D4—2216no—
511D4—2216no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—112no—
521C2×C4—111no—
522C2×C4—111no—
523C2×C4—114no—
524C2×C4—114no—
525C2×C4—112no—
526C2×C4—111no—
527C2×C4—111no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—444no—
538C2×C4—444no—
539C2×C4—444no—
540C2×C4—444no—
541C2×C4—444no—
542C2×C4—444no—
543C2×C4—444no—
544C2×C4—444no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4C22⋊C4×D1112yes—
549C2×C4C2×D4×D1112yes—
550C8—44no—
551C8—444no—
552C22—28no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—24no—
560C22—44no—
561C22—44no—
562C22—48no—
563C22—48no—
564C22—42no—
565C22—42no—
566C22—224no—
567C22—444no—
568C22—444no—
569C22—448no—
570C22—448no—
571C22—442no—
572C22—442no—
573C22#1062235312yes—
574C22D11×#10012yes—
575C22C2×C22⋊C4×D1111yescharacteristic
576C22C2×M16×D1112yes—
577C4—22no—
578C4—22no—
579C4—42no—
580C4—114no—
581C4—112no—
582C4—112no—
583C4—222no—
584C4—221no—
585C4—221no—
586C4—442no—
587C2—22no—
588C2—22no—
589C2—22no—
590C2—44no—
591C2—444no—
592C2D11×#40711yescharacteristic
593C2C2×#1062235311yescharacteristic
594C2C2×D11×#10011yescharacteristic
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#17364
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. #13077245C2semidirect
3. #13066955C2semidirect
4. #13066943C2semidirect
5. #13066942C2semidirect
6. #13066935C2semidirect
7. C11×#1462C2semidirect
28. #10622332C22semidirect
30. #10622331C22semidirect
31. C11×#323C22semidirect
32. #10622163C22semidirect
33. #10622106C22semidirect
128. C2×C22⋊D11M16semidirect
188. #1462D11semidirect
287. #323C2×D11semidirect
479. C11#17364semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
#130772452
#130669552
#130669432
#130669422
#130669352
C11×#14622
#1736411