Finite Group Databasebeta

← C2×#13074411 #14920800

Subgroups — C2×#13074411 #14920800

Order 2816.

3110 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic, complemented
3#13074411C2116yesmaximal, direct product factor
4C2×#10622290C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622606C211yesmaximal, characteristic, complemented
7C2×#10622285C212yesmaximal, complemented
8C2×#10622574C212yesmaximal, complemented
9C2×#10622570C212yesmaximal, complemented
10C2×#10622260C212yesmaximal, complemented
11C2×#10622280C211yesmaximal, characteristic, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2212yes—
32C2×#66945—28no—
33C2×#66945C2218yescomplemented
34C2×#66937—28no—
35C2×#66937C2218yes—
36C11×#397C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41#10622606C2218yescomplemented
42#10622574C22116yescomplemented
43#10622570C22116yescomplemented
44#10622562C2218yescomplemented
45#10622290C2218yescomplemented
46#10622285C22116yescomplemented
47#10622280C2218yescomplemented
48#10622260C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11—28no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11C2314yes—
61C22×C22⋊D11C2314yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C22×D44—24no—
67C22×D44—44no—
68C22×D44C2314yes—
69C22×C4×D11—28no—
70C22×C4×D11D418yes—
71C22×C4×D11C2314yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—44no—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2318yes—
78C2×C22⋊Dic11—44no—
79C2×C22⋊Dic11C2318yes—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—44no—
83C2×(C2×D11)⋊C4—44no—
84C2×(C2×D11)⋊C4—44no—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×C4⋊Dic11—24no—
91C2×C4⋊Dic11—44no—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2318yes—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—28no—
96C2×Dic11⋊C4—44no—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2318yes—
99C2×Dic11⋊C4C2318yes—
100C2×C4×Dic11—28no—
101C2×C4×Dic11C2318yes—
102#66945—232no—
103#66937—232no—
104C11×#95C2318yes—
105C11×#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C2×#2624—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C23×D11—24no—
117C23×D11—22no—
118C23×D11—24no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11—22no—
125C23×D11C2×D414yes—
126C23×D11C2412yes—
127C23×D11C2412yes—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2412yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2412yes—
142C2×C22⋊D11—28no—
143C2×C22⋊D11—216no—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—48no—
146C2×C22⋊D11—416no—
147C2×C22⋊D11—416no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11C2×D414yes—
157C22×Dic11#4118yes—
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2412yes—
162C2×D44—28no—
163C2×D44—48no—
164C2×D44—416no—
165C2×C4×D11—232no—
166C2×C4×D11—216no—
167C2×C4×D11C2×D4116yes—
168C11×C4⋊C4—28no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—48no—
171C22⋊Dic11—48no—
172(C2×D11)⋊C4—216no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—48no—
175(C2×D11)⋊C4—48no—
176(C2×D11)⋊C4—48no—
177C4⋊Dic11—28no—
178C4⋊Dic11—48no—
179Dic11⋊C4—28no—
180Dic11⋊C4—216no—
181Dic11⋊C4—48no—
182C4×Dic11—216no—
183C22×#121—111no—
184C22×#117—111no—
185#2624—1116no—
186C2×#399—111no—
187C2×#399—111no—
188C2×#397—111no—
189C2×#397D1111yescharacteristic, complemented
190C2×#394—112no—
191C2×#394—112no—
192C2×#390—112no—
193C2×#389—112no—
194C2×#380—111no—
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11C22×D412yes—
206C23×C11C2×#4114yes—
207C23×C11H(5,𝔽2)12yes—
208C23×C11H(5,𝔽2)14yes—
209C23×C112−1+412yes—
210C23×C11C2511yescharacteristic
211C22×D11—28no—
212C22×D11—28no—
213C22×D11—28no—
214C22×D11—24no—
215C22×D11—22no—
216C22×D11—24no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—24no—
220C22×D11—22no—
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—48no—
224C22×D11—48no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11—48no—
229C22×D11—48no—
230C22×D11C22×D414yes—
231C2×C4×C11—28no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—44no—
242C2×C4×C11—48no—
243C2×C4×C11—48no—
244C2×C4×C11C22×D414yes—
245C22⋊D11—416no—
246C22⋊D11—416no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—48no—
256C2×Dic11—44no—
257C2×Dic11—48no—
258C2×Dic11#123116yes—
259C2×Dic11C22×D414yes—
260C2×Dic11C2×#4118yes—
261D44—416no—
262C4×D11—232no—
263C23×D4—111no—
264C23×D4—111no—
265C23×D4—111no—
266C24×C4—111no—
267C2×#121—118no—
268C2×#121—228no—
269C2×#117—118no—
270C2×#117—228no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4—112no—
275C22×C4⋊C4—112no—
276C22×C4⋊C4C2×D1111yescharacteristic
277C22×C22⋊C4—112no—
278C22×C22⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4C2×D1111yescharacteristic
284C22×C22⋊C4C2×D1112yes—
285C22×C42—112no—
286#399—118no—
287#399—118no—
288#397—118no—
289#397C2×D1118yescomplemented
290#394—1116no—
291#394—1116no—
292#390—1116no—
293#389—1116no—
294#380—118no—
295C2×#95—112no—
296C2×#95—111no—
297C2×#95C2×D1112yes—
298C2×#95C2×D1111yescharacteristic
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—88no—
305C22×C11C2×#12314yes—
306C22×C11#53514yes—
307C22×C11#53714yes—
308C22×C11#54018yes—
309C22×C11#54218yes—
310C22×C11C23×D411yescharacteristic
311C22×C11C22×#4112yes—
312C22×C11C2×H(5,𝔽2)11yescharacteristic
313C22×C11C2×H(5,𝔽2)12yes—
314C22×C11C2×2−1+411yescharacteristic
315C2×D11—24no—
316C2×D11—24no—
317C2×D11—24no—
318C2×D11—416no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—88no—
327C4×C11—24no—
328C4×C11—42no—
329C4×C11—44no—
330C4×C11—44no—
331Dic11—44no—
332Dic11—42no—
333Dic11—44no—
334Dic11C2×#12318yes—
335C25—111no—
336C25—111no—
337C25C22×D1111yescharacteristic
338C22×D4—114no—
339C22×D4—114no—
340C22×D4—114no—
341C22×D4—224no—
342C22×D4—224no—
343C22×D4—228no—
344C22×D4—224no—
345C22×D4—444no—
346C22×D4—444no—
347C23×C4—111no—
348C23×C4—118no—
349C23×C4—114no—
350C23×C4—112no—
351C23×C4—112no—
352C23×C4—111no—
353C23×C4—228no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1112yes—
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1111yescharacteristic
358#121—2232no—
359#117—2232no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—118no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—228no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—444no—
370C2×C4⋊C4—444no—
371C2×C4⋊C4C22×D1114yes—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—228no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—444no—
383C2×C22⋊C4—444no—
384C2×C22⋊C4—444no—
385C2×C22⋊C4—444no—
386C2×C22⋊C4C22×D1114yes—
387C2×C22⋊C4C22×D1118yes—
388C2×C42—118no—
389C2×C42—228no—
390#95—114no—
391#95—118no—
392#95C22×D1114yes—
393#95C22×D1118yes—
394C2×C11—82no—
395C2×C11#262418yescomplemented
396C2×C11C22×#12311yescharacteristic
397C2×C11C2×#53511yescharacteristic
398C2×C11C2×#53711yescharacteristic
399C2×C11C2×#54012yes—
400C2×C11C2×#54212yes—
401D11—44no—
402D11—82no—
403C24—22no—
404C24—22no—
405C24—24no—
406C24—24no—
407C24—22no—
408C24—114no—
409C24—112no—
410C24—112no—
411C24—222no—
412C24—224no—
413C24—224no—
414C24—222no—
415C24—222no—
416C24—222no—
417C24—224no—
418C24—224no—
419C24—222no—
420C24C23×D1112yes—
421C24C23×D1111yescharacteristic
422C2×D4—228no—
423C2×D4—228no—
424C2×D4—2216no—
425C2×D4—228no—
426C2×D4—448no—
427C2×D4—4416no—
428C2×D4—4416no—
429C2×D4—448no—
430C2×D4—4416no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—114no—
441C22×C4—118no—
442C22×C4—112no—
443C22×C4—1116no—
444C22×C4—114no—
445C22×C4—112no—
446C22×C4—114no—
447C22×C4—2232no—
448C22×C4—2216no—
449C22×C4—224no—
450C22×C4—222no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4D4×D1114yes—
458C22×C4C23×D1114yes—
459C22×C4C23×D1114yes—
460C22×C4C23×D1112yes—
461C22×C4C23×D1112yes—
462C4⋊C4—28no—
463C4⋊C4—228no—
464C4⋊C4—2216no—
465C4⋊C4—228no—
466C4⋊C4—448no—
467C4⋊C4—448no—
468C22⋊C4—28no—
469C22⋊C4—48no—
470C22⋊C4—2216no—
471C22⋊C4—228no—
472C22⋊C4—448no—
473C22⋊C4—448no—
474C22⋊C4—448no—
475C22⋊C4—448no—
476C42—2216no—
477C11C2×#262411yescharacteristic, complemented, Sylow
478C23—22no—
479C23—22no—
480C23—24no—
481C23—24no—
482C23—22no—
483C23—48no—
484C23—44no—
485C23—44no—
486C23—48no—
487C23—44no—
488C23—114no—
489C23—228no—
490C23—228no—
491C23—222no—
492C23—224no—
493C23—224no—
494C23—222no—
495C23—228no—
496C23—222no—
497C23—222no—
498C23—224no—
499C23—224no—
500C23—222no—
501C23—448no—
502C23—448no—
503C23—448no—
504C23—444no—
505C23—444no—
506C23—448no—
507C23—444no—
508C23C2×D4×D1112yes—
509C23#6703712yes—
510C23#41×D1114yes—
511C23#6704214yes—
512C23#6704312yes—
513C23C24×D1111yescharacteristic
514D4—4416no—
515D4—4416no—
516D4—4416no—
517C2×C4—28no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—48no—
528C2×C4—48no—
529C2×C4—44no—
530C2×C4—1116no—
531C2×C4—114no—
532C2×C4—118no—
533C2×C4—2232no—
534C2×C4—224no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—448no—
543C2×C4—444no—
544C2×C4—448no—
545C2×C4C2×D4×D1114yes—
546C22—42no—
547C22—42no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—88no—
552C22—224no—
553C22—224no—
554C22—224no—
555C22—444no—
556C22—444no—
557C22—4416no—
558C22—442no—
559C22—442no—
560C22—444no—
561C22—444no—
562C22—442no—
563C22—888no—
564C22#1062313914yes—
565C22D11×#12314yes—
566C22#1062319418yes—
567C22#1062320514yes—
568C22#1062324118yes—
569C22C22×D4×D1111yescharacteristic
570C22C2×#6703711yescharacteristic
571C22C2×#41×D1112yes—
572C22C2×#6704212yes—
573C22C2×#6704311yescharacteristic
574C4—24no—
575C4—42no—
576C4—44no—
577C4—44no—
578C4—118no—
579C4—442no—
580C4—444no—
581C4—444no—
582C2—82no—
583C2—444no—
584C2—882no—
585C2#1307441118yesdirect product factor
586C2C2×D11×#12311yescharacteristic
587C2C2×#1062320511yescharacteristic
588C2C2×#1062313911yescharacteristic
589C2C2×#1062319412yes—
590C2C2×#1062324112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#397D11
hypocenterC11C2×#2624
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C22×#66945C2semidirect
3. #13074411C2direct (N × H)
4. C2×#10622290C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622606C2semidirect
7. C2×#10622285C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622260C2semidirect
11. C2×#10622280C2semidirect
12. C2×C11×#397C2semidirect
33. C2×#66945C22semidirect
36. C11×#397C22semidirect
41. #10622606C22semidirect
42. #10622574C22semidirect
43. #10622570C22semidirect
44. #10622562C22semidirect
45. #10622290C22semidirect
46. #10622285C22semidirect
47. #10622280C22semidirect
48. #10622260C22semidirect
189. C2×#397D11semidirect
289. #397C2×D11semidirect
395. C2×C11#2624semidirect
477. C11C2×#2624semidirect
585. C2#13074411direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×#669452
#130744112
C2×#106222902
C2×#106225622
C2×#106226062
C2×#106222852
C2×#106225742
C2×#106225702
C2×#106222602
C2×#106222802
C2×C11×#3972
C2×#262411