Finite Group Databasebeta

← C2×#13074545 #14920210

Subgroups — C2×#13074545 #14920210

Order 2816.

3326 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic
3#13074545C2116yesmaximal, direct product factor
4C2×#10622271C212yesmaximal, complemented
5C2×#10622287C211yesmaximal, characteristic, complemented
6C2×#10622566C211yesmaximal, characteristic, complemented
7C2×#10622572C212yesmaximal, complemented
8C2×#10622844C211yesmaximal, characteristic, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#393C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×D44C2211yescharacteristic
17C23×C4×D11C2212yes—
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C2×#66999—28no—
23C2×#66999C2218yescomplemented
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C2×#66937—28no—
32C2×#66937C2218yes—
33C11×#393C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2212yes—
36#10622844C2218yescomplemented
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622572C22116yescomplemented
43#10622569C22116yescomplemented
44#10622566C2218yescomplemented
45#10622287C2218yescomplemented
46#10622278C22116yescomplemented
47D11×#95C2218yescomplemented
48#10622271C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C22×Q8×C11—24no—
53C22×Q8×C11—44no—
54C22×Q8×C11C2314yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—24no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11—24no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11C2314yes—
64C22×C22⋊D11C2314yes—
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C22×D44—24no—
70C22×D44—28no—
71C22×D44C2314yes—
72C22×C4×D11—28no—
73C22×C4×D11—44no—
74C22×C4×D11—44no—
75C22×C4×D11—44no—
76C22×C4×D11D418yes—
77C22×C4×D11C2318yes—
78C22×C4×D11C2314yes—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11C2318yes—
85#66999—232no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11C2314yes—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—28no—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2318yes—
100#66937—232no—
101C11×#95C2318yes—
102C11×#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C2×#2639—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—22no—
112C24×C11—24no—
113C24×C11—22no—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C23×D11—24no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—22no—
124C23×D11C2×D414yes—
125C23×D11#4118yes—
126C23×D11C2412yes—
127C23×D11C2412yes—
128C2×Q8×C11—28no—
129C2×Q8×C11—48no—
130C2×Q8×C11—416no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2412yes—
145C2×C22⋊D11—28no—
146C2×C22⋊D11—28no—
147C2×C22⋊D11—216no—
148C2×C22⋊D11—48no—
149C2×C22⋊D11—416no—
150C2×C22⋊D11—416no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11C2×D414yes—
161C22×Dic11C2412yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C2×D44—28no—
166C2×D44—216no—
167C2×D44—416no—
168C2×C4×D11—216no—
169C2×C4×D11—416no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11—432no—
174C2×C4×D11C2×D4116yes—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—48no—
177C22⋊Dic11—48no—
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182C4⋊Dic11—28no—
183Dic11⋊C4—28no—
184Dic11⋊C4—216no—
185C22×C22⋊Q8—111no—
186C22×#121—111no—
187#2639—1116no—
188C2×#400—112no—
189C2×#397—111no—
190C2×#397—111no—
191C2×#394—112no—
192C2×#393—111no—
193C2×#393D1111yescharacteristic, complemented
194C2×#386—112no—
195C2×#386—112no—
196C22×#95—111no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11C22×D412yes—
208C23×C11C2×#4114yes—
209C23×C11H(5,𝔽2)14yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C112−1+412yes—
212C23×C11C2511yescharacteristic
213C22×D11—28no—
214C22×D11—28no—
215C22×D11—216no—
216C22×D11—216no—
217C22×D11—24no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—24no—
224C22×D11—22no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11—48no—
229C22×D11—48no—
230C22×D11#124116yes—
231C22×D11C22×D414yes—
232C22×D11C2×#4118yes—
233Q8×C11—416no—
234C2×C4×C11—28no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—44no—
245C2×C4×C11—48no—
246C2×C4×C11—48no—
247C2×C4×C11C22×D414yes—
248C22⋊D11—416no—
249C22⋊D11—416no—
250C2×Dic11—28no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—44no—
261C2×Dic11—48no—
262C2×Dic11—48no—
263C2×Dic11C22×D414yes—
264D44—416no—
265C4×D11—416no—
266C4×D11—432no—
267C23×Q8C2×D1111yescharacteristic
268C23×D4—111no—
269C23×D4—111no—
270C23×D4—111no—
271C24×C4—111no—
272C24×C4—112no—
273C2×C22⋊Q8—118no—
274C2×C22⋊Q8—228no—
275C2×#121—118no—
276C2×#121—228no—
277C22×C4⋊C4—112no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4—111no—
280C22×C22⋊C4—111no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4C2×D1112yes—
287#400—1116no—
288#397—118no—
289#397—118no—
290#394—1116no—
291#393—118no—
292#393C2×D1118yescomplemented
293#386—1116no—
294#386—1116no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—118no—
301C2×#95C2×D1111yescharacteristic
302C2×#95C2×D1112yes—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—88no—
309C22×C11C2×#12414yes—
310C22×C11#53414yes—
311C22×C11#53714yes—
312C22×C11#53818yes—
313C22×C11#53918yes—
314C22×C11C23×D411yescharacteristic
315C22×C11C22×#4112yes—
316C22×C11C2×H(5,𝔽2)12yes—
317C22×C11C2×H(5,𝔽2)11yescharacteristic
318C22×C11C2×2−1+411yescharacteristic
319C2×D11—232no—
320C2×D11—24no—
321C2×D11—24no—
322C2×D11—28no—
323C2×D11—28no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—88no—
330C2×D11C2×#12418yes—
331C4×C11—24no—
332C4×C11—42no—
333C4×C11—44no—
334C4×C11—44no—
335Dic11—24no—
336Dic11—42no—
337Dic11—44no—
338Dic11—44no—
339C25—111no—
340C25—111no—
341C25C22×D1111yescharacteristic
342C22×Q8—24no—
343C22×Q8—44no—
344C22×Q8C22×D1114yes—
345C22×D4—114no—
346C22×D4—114no—
347C22×D4—114no—
348C22×D4—224no—
349C22×D4—228no—
350C22×D4—224no—
351C22×D4—224no—
352C22×D4—228no—
353C22×D4—444no—
354C23×C4—111no—
355C23×C4—118no—
356C23×C4—114no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—111no—
360C23×C4—118no—
361C23×C4—228no—
362C23×C4—444no—
363C23×C4—444no—
364C23×C4—444no—
365C23×C4C22×D1112yes—
366C23×C4C22×D1112yes—
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C22⋊Q8—2232no—
370#121—2232no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—228no—
376C2×C4⋊C4—224no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—228no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—444no—
387C2×C22⋊C4—444no—
388C2×C22⋊C4—444no—
389C2×C22⋊C4C22×D1114yes—
390C2×C22⋊C4C22×D1118yes—
391#95—114no—
392#95—118no—
393#95—118no—
394#95—118no—
395#95—118no—
396#95C22×D1114yes—
397#95C22×D1118yes—
398C2×C11—82no—
399C2×C11#263918yescomplemented
400C2×C11C22×#12411yescharacteristic
401C2×C11C2×#53411yescharacteristic
402C2×C11C2×#53711yescharacteristic
403C2×C11C2×#53812yes—
404C2×C11C2×#53912yes—
405D11—28no—
406D11—82no—
407C24—22no—
408C24—24no—
409C24—22no—
410C24—24no—
411C24—22no—
412C24—114no—
413C24—118no—
414C24—112no—
415C24—112no—
416C24—224no—
417C24—222no—
418C24—222no—
419C24—222no—
420C24—224no—
421C24—222no—
422C24—224no—
423C24—222no—
424C24C23×D1112yes—
425C24C23×D1111yescharacteristic
426C2×Q8—28no—
427C2×Q8—48no—
428C2×Q8—416no—
429C2×D4—228no—
430C2×D4—2216no—
431C2×D4—228no—
432C2×D4—228no—
433C2×D4—2216no—
434C2×D4—4416no—
435C2×D4—448no—
436C2×D4—4416no—
437C2×D4—4416no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—114no—
448C22×C4—112no—
449C22×C4—1116no—
450C22×C4—114no—
451C22×C4—112no—
452C22×C4—114no—
453C22×C4—2216no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—4416no—
464C22×C4—448no—
465C22×C4—448no—
466C22×C4—448no—
467C22×C4—4432no—
468C22×C4D4×D1114yes—
469C22×C4C23×D1114yes—
470C22×C4C23×D1112yes—
471C22×C4C23×D1114yes—
472C22×C4C23×D1112yes—
473C4⋊C4—228no—
474C4⋊C4—2216no—
475C4⋊C4—228no—
476C22⋊C4—28no—
477C22⋊C4—48no—
478C22⋊C4—2216no—
479C22⋊C4—228no—
480C22⋊C4—448no—
481C22⋊C4—448no—
482C22⋊C4—448no—
483C11C2×#263911yescharacteristic, complemented, Sylow
484C23—22no—
485C23—24no—
486C23—22no—
487C23—24no—
488C23—22no—
489C23—44no—
490C23—44no—
491C23—48no—
492C23—44no—
493C23—48no—
494C23—114no—
495C23—118no—
496C23—1116no—
497C23—228no—
498C23—228no—
499C23—2216no—
500C23—224no—
501C23—222no—
502C23—222no—
503C23—2216no—
504C23—222no—
505C23—224no—
506C23—222no—
507C23—224no—
508C23—222no—
509C23—444no—
510C23—444no—
511C23—448no—
512C23—444no—
513C23—448no—
514C23C2×D4×D1112yes—
515C23#6703714yes—
516C23#6704012yes—
517C23#41×D1114yes—
518C23#6704212yes—
519C23C24×D1111yescharacteristic
520Q8—416no—
521D4—4416no—
522D4—4416no—
523D4—4416no—
524C2×C4—28no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—48no—
535C2×C4—44no—
536C2×C4—48no—
537C2×C4—114no—
538C2×C4—228no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—4416no—
549C2×C4—4432no—
550C2×C4—448no—
551C2×C4—444no—
552C2×C4—448no—
553C2×C4C2×D4×D1114yes—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—44no—
558C22—44no—
559C22—88no—
560C22—118no—
561C22—224no—
562C22—224no—
563C22—228no—
564C22—228no—
565C22—2232no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—444no—
570C22—444no—
571C22—888no—
572C22#1062312014yes—
573C22#1062316014yes—
574C22#1062316918yes—
575C22D11×#12414yes—
576C22#1062320918yes—
577C22C22×D4×D1111yescharacteristic
578C22C2×#6703712yes—
579C22C2×#6704011yescharacteristic
580C22C2×#41×D1112yes—
581C22C2×#6704211yescharacteristic
582C4—24no—
583C4—42no—
584C4—44no—
585C4—44no—
586C4—224no—
587C4—442no—
588C4—444no—
589C4—444no—
590C2—82no—
591C2—228no—
592C2—882no—
593C2#1307454518yesdirect product factor
594C2C2×D11×#12411yescharacteristic
595C2C2×#1062312011yescharacteristic
596C2C2×#1062316011yescharacteristic
597C2C2×#1062320912yes—
598C2C2×#1062316912yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#393D11
hypocenterC11C2×#2639
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#66999C2semidirect
3. #13074545C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622287C2semidirect
6. C2×#10622566C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622844C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622569C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#393C2semidirect
23. C2×#66999C22semidirect
33. C11×#393C22semidirect
36. #10622844C22semidirect
42. #10622572C22semidirect
43. #10622569C22semidirect
44. #10622566C22semidirect
45. #10622287C22semidirect
46. #10622278C22semidirect
47. D11×#95C22semidirect
48. #10622271C22semidirect
193. C2×#393D11semidirect
292. #393C2×D11semidirect
399. C2×C11#2639semidirect
483. C11C2×#2639semidirect
593. C2#13074545direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×#669372
#130745452
C2×#106222712
C2×#106222872
C2×#106225662
C2×#106225722
C2×#106228442
C2×#106222782
C2×#106225692
C2×D11×#952
C2×C11×#3932
C2×#263911