Finite Group Databasebeta

← C2×D11×#323 #14719557

Subgroups — C2×D11×#323 #14719557

Order 2816.

2878 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C211yesmaximal, characteristic
2C2×D11×C22⋊C8C212yesmaximal, complemented
3C2×#10622163C211yesmaximal, characteristic, complemented
4C2×#10622106C212yesmaximal, complemented
5D11×#323C218yesmaximal, direct product factor
6C2×C11×#323C211yesmaximal, characteristic, complemented
7C25×D11C411yescharacteristic
8C23×C4×D11C411yescharacteristic
9C23×C4×D11C2211yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C22⋊Dic11C411yescharacteristic
12C22×(C2×D11)⋊C4C411yescharacteristic
13C22×(C2×D11)⋊C4C2211yescharacteristic
14C22×C8×D11—22no—
15C2×C22⋊C4×D11—22no—
16C2×C22⋊C4×D11—22no—
17C2×C22⋊C4×D11—24no—
18C2×C22⋊C4×D11C414yes—
19C2×C22⋊C4×D11C2214yes—
20C2×C11×C22⋊C8C2212yescomplemented
21C2×C22⋊(C11⋊C8)C2212yescomplemented
22C2×(C2×D11)⋊C8—22no—
23D11×C22⋊C8—24no—
24D11×C22⋊C8C2218yescomplemented
25C11×#323C2214yescomplemented
26#10622163C2214yescomplemented
27#10622106C2218yescomplemented
28C25×C11C2×C411yescharacteristic
29C24×D11—22no—
30C24×D11—21no—
31C24×D11—21no—
32C24×D11—24no—
33C24×D11—44no—
34C24×D11—44no—
35C24×D11C818yescomplemented
36C24×D11C2×C411yescharacteristic
37C24×D11C2×C414yes—
38C24×D11C2×C411yescharacteristic
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2×C411yescharacteristic
42C23×Dic11C2×C411yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11—21no—
45C22×C4×D11—21no—
46C22×C4×D11—44no—
47C22×C4×D11—44no—
48C22×C4×D11C2×C414yes—
49C22×C4×D11C2×C412yes—
50C22×C4×D11D412yes—
51C22×C4×D11D412yes—
52C22×C4×D11D414yes—
53C22×C4×D11C2312yes—
54C22×C8×C11—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4C2×C412yes—
58C2×C11×C22⋊C4C2312yes—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11C2×C414yes—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4C2×C412yes—
67C2×(C2×D11)⋊C4C2×C414yes—
68C2×(C2×D11)⋊C4C2312yes—
69C22×C11⋊C8—22no—
70C2×C8×D11—28no—
71C2×C8×D11—48no—
72C22⋊C4×D11—28no—
73C22⋊C4×D11—28no—
74C22⋊C4×D11—28no—
75C22⋊C4×D11—28no—
76C11×C22⋊C8—22no—
77C11×C22⋊C8C2314yescomplemented
78C22⋊(C11⋊C8)—22no—
79C22⋊(C11⋊C8)C2314yescomplemented
80(C2×D11)⋊C8—28no—
81C22×#323—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—22no—
85C24×C11—42no—
86C24×C11—42no—
87C24×C11C2×C814yescomplemented
88C24×C11C22×C411yescharacteristic
89C24×C11C22×C412yes—
90C23×D11—24no—
91C23×D11—24no—
92C23×D11—21no—
93C23×D11—21no—
94C23×D11—22no—
95C23×D11—216no—
96C23×D11—28no—
97C23×D11—28no—
98C23×D11—24no—
99C23×D11—24no—
100C23×D11—28no—
101C23×D11—44no—
102C23×D11—44no—
103C23×D11—432no—
104C23×D11—48no—
105C23×D11—48no—
106C23×D11—432no—
107C23×D11—48no—
108C23×D11—48no—
109C23×D11—44no—
110C23×D11—44no—
111C23×D11—42no—
112C23×D11—42no—
113C23×D11C22⋊C411yescharacteristic
114C23×D11C22⋊C412yes—
115C23×D11C22⋊C411yescharacteristic
116C23×D11C2×C814yes—
117C23×D11C2×C8116yescomplemented
118C23×D11C2×C814yescomplemented
119C23×D11M1614yes—
120C23×D11C22×C412yes—
121C23×D11C22×C412yes—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C22×Dic11C22⋊C412yes—
136C22×Dic11C22⋊C412yes—
137C22×Dic11C22×C412yes—
138C22×Dic11C22×C412yes—
139C2×C4×D11—28no—
140C2×C4×D11—24no—
141C2×C4×D11—24no—
142C2×C4×D11—44no—
143C2×C4×D11—44no—
144C2×C4×D11—48no—
145C2×C4×D11—44no—
146C2×C4×D11—48no—
147C2×C4×D11—44no—
148C2×C4×D11—48no—
149C2×C4×D11—44no—
150C2×C4×D11C22⋊C414yes—
151C2×C4×D11C22⋊C414yes—
152C2×C4×D11C2×D414yes—
153C2×C4×D11C2×D414yes—
154C2×C8×C11—24no—
155C2×C8×C11—44no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—24no—
158C22⋊Dic11—28no—
159(C2×D11)⋊C4—28no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162C2×C11⋊C8—24no—
163C2×C11⋊C8—44no—
164C8×D11—416no—
165C23×C22⋊C4—111no—
166C22×C22⋊C8—112no—
167C2×#323—112no—
168C2×#323—118no—
169C2×#323—111no—
170C2×#323D1111yescharacteristic, direct product factor
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—48no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—48no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11C2×C22⋊C411yescharacteristic
186C23×C11C2×C22⋊C411yescharacteristic
187C23×C11C22×C812yes—
188C23×C11C22×C814yescomplemented
189C23×C11C2×M1612yes—
190C23×C11C23×C411yescharacteristic
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—216no—
194C22×D11—216no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—216no—
204C22×D11—216no—
205C22×D11—48no—
206C22×D11—48no—
207C22×D11—432no—
208C22×D11—464no—
209C22×D11—432no—
210C22×D11—432no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—48no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—432no—
217C22×D11—48no—
218C22×D11—48no—
219C22×D11—48no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11C22⋊C814yes—
223C22×D11C22⋊C818yes—
224C22×D11C22⋊C814yes—
225C22×D11#9914yes—
226C22×D11#10014yes—
227C22×D11C2×C22⋊C412yes—
228C22×D11C2×C22⋊C412yes—
229C22×D11C22×C814yes—
230C22×D11C22×C814yescomplemented
231C22×D11C2×M1614yes—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11C2×C22⋊C412yes—
241C2×C4×C11C22×D412yes—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11C2×C22⋊C414yes—
250C4×D11—28no—
251C4×D11—28no—
252C4×D11—44no—
253C4×D11—44no—
254C4×D11—48no—
255C4×D11—48no—
256C8×C11—44no—
257C11⋊C8—44no—
258C26—111no—
259C24×C4—111no—
260C24×C4—111no—
261C23×C8—222no—
262C22×C22⋊C4—111no—
263C22×C22⋊C4—111no—
264C22×C22⋊C4—111no—
265C22×C22⋊C4—114no—
266C22×C22⋊C4—114no—
267C22×C22⋊C4—222no—
268C22×C22⋊C4—224no—
269C22×C22⋊C4—222no—
270C22×C22⋊C4C2×D1111yescharacteristic
271C2×C22⋊C8—112no—
272C2×C22⋊C8—118no—
273C2×C22⋊C8—224no—
274C2×C22⋊C8—222no—
275C2×C22⋊C8C2×D1112yescomplemented
276#323—114no—
277#323—118no—
278#323C2×D1114yesdirect product factor
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—48no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—48no—
292C22×C11C2×C22⋊C812yes—
293C22×C11C2×C22⋊C812yes—
294C22×C11C2×#9912yes—
295C22×C11C2×#10012yes—
296C22×C11C22×C22⋊C411yescharacteristic
297C22×C11C23×C811yescharacteristic
298C22×C11C22×M1611yescharacteristic
299C2×D11—22no—
300C2×D11—22no—
301C2×D11—28no—
302C2×D11—216no—
303C2×D11—28no—
304C2×D11—28no—
305C2×D11—24no—
306C2×D11—432no—
307C2×D11—44no—
308C2×D11—48no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—48no—
312C2×D11—432no—
313C2×D11—44no—
314C2×D11#323116yesdirect product factor
315C2×D11C2×C22⋊C814yes—
316C2×D11C2×C22⋊C814yes—
317C2×D11C2×#9914yes—
318C2×D11C2×#10014yes—
319C4×C11—22no—
320C4×C11—22no—
321C4×C11—42no—
322Dic11—24no—
323Dic11—42no—
324C25—111no—
325C25—118no—
326C25—114no—
327C25—111no—
328C25—222no—
329C25—221no—
330C25—221no—
331C25—224no—
332C25—444no—
333C25—444no—
334C25C4×D1111yescharacteristic
335C23×C4—111no—
336C23×C4—112no—
337C23×C4—112no—
338C23×C4—112no—
339C23×C4—114no—
340C23×C4—112no—
341C23×C4—111no—
342C23×C4—114no—
343C23×C4—222no—
344C23×C4—221no—
345C23×C4—221no—
346C23×C4—444no—
347C23×C4—444no—
348C23×C4C4×D1111yescharacteristic
349C23×C4C22×D1111yescharacteristic
350C22×C8—22no—
351C22×C8—228no—
352C22×C8—222no—
353C22×C8—448no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—114no—
357C2×C22⋊C4—114no—
358C2×C22⋊C4—112no—
359C2×C22⋊C4—112no—
360C2×C22⋊C4—228no—
361C2×C22⋊C4—228no—
362C2×C22⋊C4—228no—
363C2×C22⋊C4—228no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4C4×D1112yes—
371C2×C22⋊C4C22×D1112yes—
372C22⋊C8—22no—
373C22⋊C8—114no—
374C22⋊C8—228no—
375C22⋊C8—222no—
376C22⋊C8C22×D1114yescomplemented
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—22no—
380C2×C11—44no—
381C2×C11C2×#32314yescomplemented
382C2×C11C22×C22⋊C811yescharacteristic
383C2×C11C22×#9911yescharacteristic
384C2×C11C22×#10011yescharacteristic
385D11—24no—
386D11—44no—
387D11C2×#32318yesdirect product factor
388C24—21no—
389C24—21no—
390C24—22no—
391C24—42no—
392C24—42no—
393C24—111no—
394C24—112no—
395C24—111no—
396C24—114no—
397C24—114no—
398C24—112no—
399C24—114no—
400C24—1116no—
401C24—112no—
402C24—224no—
403C24—224no—
404C24—224no—
405C24—224no—
406C24—228no—
407C24—228no—
408C24—2216no—
409C24—228no—
410C24—221no—
411C24—221no—
412C24—222no—
413C24—442no—
414C24—442no—
415C24—444no—
416C24—444no—
417C24—4432no—
418C24—448no—
419C24—448no—
420C24—448no—
421C24—448no—
422C24—4432no—
423C24—444no—
424C24—444no—
425C24C8×D1114yescomplemented
426C24C2×C4×D1111yescharacteristic
427C24C2×C4×D1112yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—114no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—228no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—444no—
446C22×C4—444no—
447C22×C4—448no—
448C22×C4—444no—
449C22×C4—444no—
450C22×C4—448no—
451C22×C4—444no—
452C22×C4—448no—
453C22×C4—442no—
454C22×C4—442no—
455C22×C4C2×C4×D1112yes—
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4D4×D1112yes—
458C22×C4D4×D1112yes—
459C22×C4C23×D1111yescharacteristic
460C2×C8—24no—
461C2×C8—44no—
462C2×C8—224no—
463C2×C8—4416no—
464C2×C8—444no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—228no—
468C22⋊C4—228no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C11C22×#32311yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—48no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—48no—
484C23—42no—
485C23—42no—
486C23—112no—
487C23—114no—
488C23—114no—
489C23—114no—
490C23—114no—
491C23—112no—
492C23—114no—
493C23—118no—
494C23—114no—
495C23—114no—
496C23—224no—
497C23—224no—
498C23—224no—
499C23—224no—
500C23—2216no—
501C23—2216no—
502C23—2216no—
503C23—2216no—
504C23—222no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—224no—
509C23—224no—
510C23—442no—
511C23—442no—
512C23—448no—
513C23—442no—
514C23—442no—
515C23—448no—
516C23—448no—
517C23—448no—
518C23—4432no—
519C23—4432no—
520C23—4432no—
521C23—4464no—
522C23—448no—
523C23—448no—
524C23—4432no—
525C23—442no—
526C23—442no—
527C23C22⋊C4×D1111yescharacteristic
528C23C22⋊C4×D1111yescharacteristic
529C23C2×C8×D1112yes—
530C23C2×C8×D1114yescomplemented
531C23M16×D1112yes—
532C23C22×C4×D1111yescharacteristic
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—114no—
542C2×C4—228no—
543C2×C4—228no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—444no—
547C2×C4—444no—
548C2×C4—448no—
549C2×C4—448no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4C22⋊C4×D1112yes—
556C2×C4C2×D4×D1112yes—
557C8—44no—
558C8—444no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—24no—
566C22—44no—
567C22—44no—
568C22—48no—
569C22—42no—
570C22—42no—
571C22—48no—
572C22—114no—
573C22—114no—
574C22—114no—
575C22—1116no—
576C22—114no—
577C22—228no—
578C22—228no—
579C22—2216no—
580C22—222no—
581C22—222no—
582C22—228no—
583C22—224no—
584C22—444no—
585C22—444no—
586C22—448no—
587C22—4432no—
588C22—4432no—
589C22—442no—
590C22—442no—
591C22—448no—
592C22D11×C22⋊C812yes—
593C22D11×C22⋊C812yes—
594C22D11×#9912yes—
595C22D11×#10012yes—
596C22C2×C22⋊C4×D1111yescharacteristic
597C22C22×C8×D1111yescharacteristic
598C22C2×M16×D1111yescharacteristic
599C4—22no—
600C4—22no—
601C4—42no—
602C4—224no—
603C4—442no—
604C2—21no—
605C2—21no—
606C2—22no—
607C2—44no—
608C2—118no—
609C2—224no—
610C2—444no—
611C2D11×#32314yesdirect product factor
612C2C2×D11×C22⋊C811yescharacteristic
613C2C2×D11×#9911yescharacteristic
614C2C2×D11×#10011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C11C23×C8
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC23×C11C2×C22⋊C4
prime radicalC25×D11C4
cosocleC22×C4×C11C24
hypercenterC2×#323D11
hypocenterC11C22×#323
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×D11×C22⋊C8C2semidirect
3. C2×#10622163C2semidirect
4. C2×#10622106C2semidirect
5. D11×#323C2direct (N × H)
6. C2×C11×#323C2semidirect
20. C2×C11×C22⋊C8C22semidirect
21. C2×C22⋊(C11⋊C8)C22semidirect
24. D11×C22⋊C8C22semidirect
25. C11×#323C22semidirect
26. #10622163C22semidirect
27. #10622106C22semidirect
35. C24×D11C8semidirect
77. C11×C22⋊C8C23semidirect
79. C22⋊(C11⋊C8)C23semidirect
87. C24×C11C2×C8semidirect
117. C23×D11C2×C8semidirect
118. C23×D11C2×C8semidirect
170. C2×#323D11direct (N × H)
188. C23×C11C22×C8semidirect
230. C22×D11C22×C8semidirect
275. C2×C22⋊C8C2×D11semidirect
278. #323C2×D11direct (N × H)
314. C2×D11#323direct (N × H)
376. C22⋊C8C22×D11semidirect
381. C2×C11C2×#323semidirect
387. D11C2×#323direct (N × H)
425. C24C8×D11semidirect
471. C11C22×#323semidirect
530. C23C2×C8×D11semidirect
611. C2D11×#323direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D112
C2×D11×C22⋊C82
C2×#106221632
C2×#106221062
D11×#3232
C2×C11×#3232
C22×#32311