Finite Group Databasebeta

← C2×D11×#380 #14912029

Subgroups — C2×D11×#380 #14912029

Order 2816.

8670 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D11C211yesmaximal, characteristic
2C22×C4⋊C4×D11C212yesmaximal, complemented
3C22×C22⋊C4×D11C212yesmaximal
4C2×#10622825C211yesmaximal, characteristic, complemented
5C2×#10622280C212yesmaximal, complemented
6C2×#10622555C212yesmaximal, complemented
7C2×#10622600C212yesmaximal, complemented
8D11×#380C2116yesmaximal, direct product factor
9C2×D11×#95C212yesmaximal, complemented
10C2×C11×#380C211yesmaximal, characteristic, complemented
11C25×D11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C23×C4×D11—216no—
15C23×C4×D11C4116yescomplemented
16C23×C4×D11C2214yes—
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2218yes—
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C4⋊C4C2212yescomplemented
23C22×C11×C22⋊C4C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×(C2×D11)⋊C4C2214yes—
26C22×C4⋊Dic11C2212yescomplemented
27C22×Dic11⋊C4C2214yescomplemented
28C2×C4⋊C4×D11—216no—
29C2×C4⋊C4×D11C22116yescomplemented
30C2×C22⋊C4×D11—216no—
31C2×C22⋊C4×D11C22116yes—
32C11×#380C2218yescomplemented
33C2×C11×#95C2212yescomplemented
34#10622825C2218yescomplemented
35C2×C11⋊#95C2214yescomplemented
36C2×C11⋊#95C2212yescomplemented
37#10622600C22116yescomplemented
38#10622555C22116yescomplemented
39#10622280C22116yescomplemented
40D11×#95C22116yescomplemented
41C25×C11C2311yescharacteristic
42C24×D11—28no—
43C24×D11—28no—
44C24×D11C2×C418yes—
45C24×D11D418yes—
46C24×D11Q818yes—
47C24×D11C2314yes—
48C24×D11C2311yescharacteristic
49C24×D11C2311yescharacteristic
50C23×C4×C11—28no—
51C23×C4×C11C2×C418yescomplemented
52C23×C4×C11C2314yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2314yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—28no—
57C23×Dic11C2×C418yescomplemented
58C23×Dic11C2314yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2314yes—
61C23×Dic11C2311yescharacteristic
62C22×C4×D11—28no—
63C22×C4×D11—28no—
64C22×C4×D11—28no—
65C22×C4×D11—2128no—
66C22×C4×D11—264no—
67C22×C4×D11—216no—
68C22×C4×D11—216no—
69C22×C4×D11—216no—
70C22×C4×D11C2×C418yes—
71C22×C4×D11C2×C418yes—
72C22×C4×D11C2×C4164yescomplemented
73C22×C4×D11C2×C418yescomplemented
74C22×C4×D11C2×C418yescomplemented
75C22×C4×D11D4116yes—
76C22×C4×D11C23116yes—
77C22×C4×D11C2314yes—
78C22×C4×D11C2314yes—
79C22×C4×D11C2314yes—
80C22×C4×D11C2314yes—
81C2×C11×C4⋊C4—28no—
82C2×C11×C4⋊C4C2318yescomplemented
83C2×C11×C22⋊C4—28no—
84C2×C11×C22⋊C4C2318yes—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11C2318yes—
87C2×(C2×D11)⋊C4—216no—
88C2×(C2×D11)⋊C4C23116yes—
89C2×C4⋊Dic11—28no—
90C2×C4⋊Dic11C2318yescomplemented
91C2×Dic11⋊C4—216no—
92C2×Dic11⋊C4C23116yescomplemented
93C4⋊C4×D11—264no—
94C22⋊C4×D11—264no—
95C11×#95C2318yescomplemented
96C11⋊#95C2318yescomplemented
97C11⋊#95C23116yescomplemented
98C22×#380—111nomaximal, Sylow
99C24×C11—24no—
100C24×C11—24no—
101C24×C11C22×C414yes—
102C24×C11C2×D414yes—
103C24×C11C2×Q814yes—
104C24×C11C2412yes—
105C24×C11C2411yescharacteristic
106C23×D11—24no—
107C23×D11—24no—
108C23×D11—232no—
109C23×D11—232no—
110C23×D11—264no—
111C23×D11—264no—
112C23×D11—216no—
113C23×D11—216no—
114C23×D11C4⋊C4164yescomplemented
115C23×D11C22×C414yes—
116C23×D11C22×C4116yes—
117C23×D11C22×C414yes—
118C23×D11C2×D4116yes—
119C23×D11C2×D414yes—
120C23×D11C2×D418yes—
121C23×D11C2×D414yes—
122C23×D11C2×Q814yes—
123C23×D11C2×Q8116yes—
124C23×D11C2×Q814yes—
125C23×D11#4118yes—
126C23×D11C2412yes—
127C23×D11C2412yes—
128C22×C4×C11—24no—
129C22×C4×C11—232no—
130C22×C4×C11—216no—
131C22×C4×C11—28no—
132C22×C4×C11—28no—
133C22×C4×C11—28no—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C4116yescomplemented
137C22×C4×C11C2×D418yes—
138C22×C4×C11C2418yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×Dic11—232no—
142C22×Dic11—216no—
143C22×Dic11—24no—
144C22×Dic11—28no—
145C22×Dic11—28no—
146C22×Dic11—28no—
147C22×Dic11C22×C414yes—
148C22×Dic11C22×C414yes—
149C22×Dic11C22×C4116yescomplemented
150C22×Dic11C2×D418yes—
151C22×Dic11C2418yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C2×C4×D11—232no—
155C2×C4×D11—216no—
156C2×C4×D11—2256no—
157C2×C4×D11—232no—
158C2×C4×D11—216no—
159C2×C4×D11—232no—
160C2×C4×D11—232no—
161C2×C4×D11—232no—
162C2×C4×D11—232no—
163C2×C4×D11—216no—
164C2×C4×D11—464no—
165C2×C4×D11C22⋊C4164yescomplemented
166C2×C4×D11C22×C4116yes—
167C2×C4×D11C22×C4116yes—
168C2×C4×D11C22×C4116yescomplemented
169C2×C4×D11C22×C4116yescomplemented
170C2×C4×D11C2×D4132yes—
171C11×C4⋊C4—216no—
172C11×C22⋊C4—216no—
173C22⋊Dic11—216no—
174(C2×D11)⋊C4—232no—
175C4⋊Dic11—216no—
176Dic11⋊C4—232no—
177C25×C4—111no—
178C23×C4⋊C4—112no—
179C23×C22⋊C4—112no—
180C2×#380—1116no—
181C2×#380—112no—
182C2×#380—111no—
183C2×#380—112no—
184C2×#380—112no—
185C2×#380D1111yescharacteristic, direct product factor
186C22×#95—112no—
187C23×C11—28no—
188C23×C11—28no—
189C23×C11—216no—
190C23×C11—216no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11C2×C4⋊C4116yescomplemented
194C23×C11C23×C414yes—
195C23×C11C23×C412yes—
196C23×C11C22×D414yes—
197C23×C11C22×D414yes—
198C23×C11C22×D412yes—
199C23×C11C22×Q814yes—
200C23×C11C22×Q812yes—
201C23×C11C2×#4114yes—
202C23×C11C2511yescharacteristic
203C22×D11—28no—
204C22×D11—28no—
205C22×D11—216no—
206C22×D11—216no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—232no—
210C22×D11—232no—
211C22×D11—264no—
212C22×D11—264no—
213C22×D11—2256no—
214C22×D11C2×C22⋊C4116yes—
215C22×D11C2×C4⋊C4116yes—
216C22×D11C2×C4⋊C4164yescomplemented
217C22×D11C2×C4⋊C4116yescomplemented
218C22×D11#117116yes—
219C22×D11#121132yes—
220C22×D11C22⋊Q8132yes—
221C22×D11C23×C414yes—
222C22×D11C23×C414yes—
223C22×D11C22×D414yes—
224C22×D11C22×D418yes—
225C22×D11C22×D414yes—
226C22×D11C22×Q814yes—
227C22×D11C22×Q814yes—
228C22×D11C2×#4118yes—
229C2×C4×C11—28no—
230C2×C4×C11—24no—
231C2×C4×C11—232no—
232C2×C4×C11—28no—
233C2×C4×C11—28no—
234C2×C4×C11—28no—
235C2×C4×C11—416no—
236C2×C4×C11C2×C22⋊C4116yescomplemented
237C2×C4×C11C23×C414yes—
238C2×C4×C11C23×C414yes—
239C2×C4×C11C22×D418yes—
240C2×Dic11—28no—
241C2×Dic11—24no—
242C2×Dic11—232no—
243C2×Dic11—28no—
244C2×Dic11—28no—
245C2×Dic11—28no—
246C2×Dic11—416no—
247C2×Dic11C2×C22⋊C4116yescomplemented
248C2×Dic11C23×C414yes—
249C2×Dic11C23×C414yes—
250C2×Dic11C22×D418yes—
251C4×D11—232no—
252C4×D11—232no—
253C4×D11—232no—
254C4×D11—464no—
255C4×D11C2×C22⋊C4164yescomplemented
256C26—111no—
257C24×C4—111no—
258C24×C4—111no—
259C24×C4—111no—
260C24×C4—111no—
261C24×C4—118no—
262C24×C4—111no—
263C24×C4—1116no—
264C24×C4—114no—
265C24×C4—2216no—
266C24×C4C2×D1111yescharacteristic
267C22×C4⋊C4—114no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4—1116no—
270C22×C4⋊C4—2216no—
271C22×C4⋊C4C2×D1112yescomplemented
272C22×C22⋊C4—112no—
273C22×C22⋊C4—114no—
274C22×C22⋊C4—1116no—
275C22×C22⋊C4—2216no—
276C22×C22⋊C4C2×D1112yes—
277#380—118no—
278#380—1116no—
279#380—1116no—
280#380—1116no—
281#380C2×D1118yesdirect product factor
282C2×#95—114no—
283C2×#95—112no—
284C2×#95—1116no—
285C2×#95C2×D1112yescomplemented
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—28no—
289C22×C11—28no—
290C22×C11—232no—
291C22×C11C22×C22⋊C414yes—
292C22×C11C22×C4⋊C414yes—
293C22×C11C22×C4⋊C418yescomplemented
294C22×C11C2×#11714yes—
295C22×C11C2×#12118yes—
296C22×C11C2×C22⋊Q818yes—
297C22×C11C24×C411yescharacteristic
298C22×C11C23×D412yes—
299C22×C11C23×D411yescharacteristic
300C22×C11C23×Q811yescharacteristic
301C22×C11C22×#4112yes—
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—28no—
305C2×D11—28no—
306C2×D11—232no—
307C2×D11—2128no—
308C2×D11#380164yesdirect product factor
309C2×D11C22×C22⋊C418yes—
310C2×D11C22×C4⋊C418yes—
311C2×D11C22×C4⋊C418yescomplemented
312C2×D11C2×#11718yes—
313C2×D11C2×#121116yes—
314C2×D11C2×C22⋊Q8116yes—
315C4×C11—24no—
316C4×C11—48no—
317C4×C11C22×C22⋊C418yescomplemented
318Dic11—24no—
319Dic11—48no—
320Dic11C22×C22⋊C418yescomplemented
321C25—111no—
322C25—118no—
323C25—118no—
324C25—118no—
325C25—114no—
326C25—111no—
327C25—228no—
328C25—228no—
329C25C22×D1111yescharacteristic
330C23×C4—28no—
331C23×C4—111no—
332C23×C4—118no—
333C23×C4—1116no—
334C23×C4—114no—
335C23×C4—118no—
336C23×C4—114no—
337C23×C4—111no—
338C23×C4—118no—
339C23×C4—118no—
340C23×C4—118no—
341C23×C4—1164no—
342C23×C4—114no—
343C23×C4—114no—
344C23×C4—114no—
345C23×C4—114no—
346C23×C4—1116no—
347C23×C4—228no—
348C23×C4—22128no—
349C23×C4—2264no—
350C23×C4—228no—
351C23×C4—2216no—
352C23×C4—2216no—
353C23×C4—2216no—
354C23×C4—228no—
355C23×C4—228no—
356C23×C4C4×D1118yescomplemented
357C23×C4C22×D1114yes—
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1114yes—
360C23×C4C22×D1111yescharacteristic
361C2×C4⋊C4—28no—
362C2×C4⋊C4—1116no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—2264no—
365C2×C4⋊C4—2216no—
366C2×C4⋊C4—228no—
367C2×C4⋊C4C22×D1118yescomplemented
368C2×C22⋊C4—28no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—1116no—
371C2×C22⋊C4—2264no—
372C2×C22⋊C4—2216no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4C22×D1118yes—
375#95—1116no—
376#95—118no—
377#95C22×D1118yescomplemented
378C2×C11—28no—
379C2×C11C2×#38018yescomplemented
380C2×C11C23×C22⋊C411yescharacteristic
381C2×C11C23×C4⋊C411yescharacteristic
382C2×C11C22×#11711yescharacteristic
383C2×C11C22×#12112yes—
384C2×C11C22×C22⋊Q812yes—
385D11—28no—
386D11C2×#380116yesdirect product factor
387C24—24no—
388C24—24no—
389C24—114no—
390C24—118no—
391C24—114no—
392C24—114no—
393C24—118no—
394C24—112no—
395C24—1164no—
396C24—1116no—
397C24—114no—
398C24—1116no—
399C24—114no—
400C24—1116no—
401C24—114no—
402C24—112no—
403C24—2232no—
404C24—2216no—
405C24—2232no—
406C24—2264no—
407C24—2264no—
408C24—2216no—
409C24—224no—
410C24—224no—
411C24C2×C4×D1114yes—
412C24D4×D1114yes—
413C24Q8×D1114yes—
414C24C23×D1112yes—
415C24C23×D1111yescharacteristic
416C22×C4—24no—
417C22×C4—232no—
418C22×C4—216no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—114no—
423C22×C4—118no—
424C22×C4—112no—
425C22×C4—1164no—
426C22×C4—1116no—
427C22×C4—1132no—
428C22×C4—114no—
429C22×C4—1116no—
430C22×C4—112no—
431C22×C4—1116no—
432C22×C4—1116no—
433C22×C4—1116no—
434C22×C4—118no—
435C22×C4—2232no—
436C22×C4—2216no—
437C22×C4—22256no—
438C22×C4—2232no—
439C22×C4—2216no—
440C22×C4—2232no—
441C22×C4—2232no—
442C22×C4—2232no—
443C22×C4—2232no—
444C22×C4—2216no—
445C22×C4—224no—
446C22×C4—2232no—
447C22×C4—2216no—
448C22×C4—228no—
449C22×C4—228no—
450C22×C4—228no—
451C22×C4—4464no—
452C22×C4C2×C4×D1114yes—
453C22×C4C2×C4×D1114yes—
454C22×C4C2×C4×D11116yescomplemented
455C22×C4D4×D1118yes—
456C22×C4C23×D1118yes—
457C22×C4C23×D1112yes—
458C22×C4C23×D1112yes—
459C4⋊C4—216no—
460C4⋊C4—2232no—
461C4⋊C4—2216no—
462C22⋊C4—216no—
463C22⋊C4—2232no—
464C22⋊C4—2216no—
465C11C22×#38011yescharacteristic, complemented, Sylow
466C23—28no—
467C23—28no—
468C23—216no—
469C23—216no—
470C23—24no—
471C23—24no—
472C23—1116no—
473C23—1116no—
474C23—1116no—
475C23—1132no—
476C23—1132no—
477C23—114no—
478C23—118no—
479C23—114no—
480C23—114no—
481C23—118no—
482C23—1116no—
483C23—1164no—
484C23—114no—
485C23—114no—
486C23—114no—
487C23—2232no—
488C23—22256no—
489C23—2232no—
490C23—2264no—
491C23—2264no—
492C23—228no—
493C23—228no—
494C23—2216no—
495C23—2216no—
496C23—224no—
497C23—224no—
498C23C4⋊C4×D11116yescomplemented
499C23C22×C4×D1114yes—
500C23C22×C4×D1112yes—
501C23C2×D4×D1114yes—
502C23C2×D4×D1114yes—
503C23C2×D4×D1112yes—
504C23C2×Q8×D1114yes—
505C23C2×Q8×D1112yes—
506C23#41×D1114yes—
507C23C24×D1111yescharacteristic
508C2×C4—28no—
509C2×C4—24no—
510C2×C4—232no—
511C2×C4—28no—
512C2×C4—28no—
513C2×C4—28no—
514C2×C4—416no—
515C2×C4—1116no—
516C2×C4—114no—
517C2×C4—118no—
518C2×C4—1164no—
519C2×C4—114no—
520C2×C4—2232no—
521C2×C4—2232no—
522C2×C4—2232no—
523C2×C4—228no—
524C2×C4—224no—
525C2×C4—2232no—
526C2×C4—228no—
527C2×C4—228no—
528C2×C4—228no—
529C2×C4—4464no—
530C2×C4—4416no—
531C2×C4C22⋊C4×D11116yescomplemented
532C2×C4C22×C4×D1114yes—
533C2×C4C22×C4×D1114yes—
534C2×C4C2×D4×D1118yes—
535C22—232no—
536C22—24no—
537C22—24no—
538C22—28no—
539C22—28no—
540C22—1164no—
541C22—118no—
542C22—118no—
543C22—118no—
544C22—1116no—
545C22—1116no—
546C22—118no—
547C22—22128no—
548C22—2232no—
549C22—224no—
550C22—224no—
551C22—228no—
552C22—228no—
553C22C2×C22⋊C4×D1114yes—
554C22C2×C4⋊C4×D1114yes—
555C22C2×C4⋊C4×D1118yescomplemented
556C22D11×#11714yes—
557C22D11×#12118yes—
558C22D11×C22⋊Q818yes—
559C22C23×C4×D1111yescharacteristic
560C22C22×D4×D1112yes—
561C22C22×D4×D1111yescharacteristic
562C22C22×Q8×D1111yescharacteristic
563C22C2×#41×D1112yes—
564C4—24no—
565C4—48no—
566C4—118no—
567C4—224no—
568C4—448no—
569C4C2×C22⋊C4×D1118yescomplemented
570C2—28no—
571C2—1116no—
572C2—228no—
573C2D11×#38018yesdirect product factor
574C2C22×C22⋊C4×D1111yescharacteristic
575C2C22×C4⋊C4×D1111yescharacteristic
576C2C2×D11×#11711yescharacteristic
577C2C2×D11×#12112yes—
578C2C2×D11×C22⋊Q812yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC25×D11C22
cosocleC23×C11C25
hypercenterC2×#380D11
hypocenterC11C22×#380
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
4. C2×#10622825C2semidirect
5. C2×#10622280C2semidirect
6. C2×#10622555C2semidirect
7. C2×#10622600C2semidirect
8. D11×#380C2direct (N × H)
9. C2×D11×#95C2semidirect
10. C2×C11×#380C2semidirect
15. C23×C4×D11C4semidirect
22. C22×C11×C4⋊C4C22semidirect
26. C22×C4⋊Dic11C22semidirect
27. C22×Dic11⋊C4C22semidirect
29. C2×C4⋊C4×D11C22semidirect
32. C11×#380C22semidirect
33. C2×C11×#95C22semidirect
34. #10622825C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. #10622600C22semidirect
38. #10622555C22semidirect
39. #10622280C22semidirect
40. D11×#95C22semidirect
51. C23×C4×C11C2×C4semidirect
57. C23×Dic11C2×C4semidirect
72. C22×C4×D11C2×C4semidirect
73. C22×C4×D11C2×C4semidirect
74. C22×C4×D11C2×C4semidirect
82. C2×C11×C4⋊C4C23semidirect
90. C2×C4⋊Dic11C23semidirect
92. C2×Dic11⋊C4C23semidirect
95. C11×#95C23semidirect
96. C11⋊#95C23semidirect
97. C11⋊#95C23semidirect
114. C23×D11C4⋊C4semidirect
136. C22×C4×C11C22×C4semidirect
149. C22×Dic11C22×C4semidirect
165. C2×C4×D11C22⋊C4semidirect
168. C2×C4×D11C22×C4semidirect
169. C2×C4×D11C22×C4semidirect
185. C2×#380D11direct (N × H)
193. C23×C11C2×C4⋊C4semidirect
216. C22×D11C2×C4⋊C4semidirect
217. C22×D11C2×C4⋊C4semidirect
236. C2×C4×C11C2×C22⋊C4semidirect
247. C2×Dic11C2×C22⋊C4semidirect
255. C4×D11C2×C22⋊C4semidirect
271. C22×C4⋊C4C2×D11semidirect
281. #380C2×D11direct (N × H)
285. C2×#95C2×D11semidirect
293. C22×C11C22×C4⋊C4semidirect
308. C2×D11#380direct (N × H)
311. C2×D11C22×C4⋊C4semidirect
317. C4×C11C22×C22⋊C4semidirect
320. Dic11C22×C22⋊C4semidirect
356. C23×C4C4×D11semidirect
367. C2×C4⋊C4C22×D11semidirect
377. #95C22×D11semidirect
379. C2×C11C2×#380semidirect
386. D11C2×#380direct (N × H)
454. C22×C4C2×C4×D11semidirect
465. C11C22×#380semidirect
498. C23C4⋊C4×D11semidirect
531. C2×C4C22⋊C4×D11semidirect
555. C22C2×C4⋊C4×D11semidirect
569. C4C2×C22⋊C4×D11semidirect
573. C2D11×#380direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D112
C22×C4⋊C4×D112
C22×C22⋊C4×D112
C2×#106228252
C2×#106222802
C2×#106225552
C2×#106226002
D11×#3802
C2×D11×#952
C2×C11×#3802
C22×#38011