Finite Group Databasebeta

← C2×#13068726 #14753635

Subgroups — C2×#13068726 #14753635

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623052C211yesmaximal, characteristic
2C22×#66887C211yesmaximal, characteristic
3C22×#66887C211yesmaximal, characteristic
4#13068726C218yesmaximal, direct product factor
5C2×#10622197C211yesmaximal, characteristic, complemented
6C2×#10622194C211yesmaximal, characteristic, complemented
7C2×#10622171C211yesmaximal, characteristic, complemented
8C2×C11×#344C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16#10623052—22no—
17#10623052—22no—
18#10623052C414yes—
19#10623052C2214yes—
20C2×#66946—22no—
21C2×C22⋊C4×D11C414yes—
22C2×C4×D44—22no—
23C2×#66887—22no—
24C2×#66887—22no—
25C2×#66887—22no—
26C2×#66887—22no—
27C2×#66887C2214yes—
28C2×#66887C2214yes—
29C11×#344C2214yescomplemented
30#10622197C2214yescomplemented
31#10622194C2214yescomplemented
32#10622171C2214yescomplemented
33C24×D11C2×C412yes—
34C23×C4×C11C2311yescharacteristic
35C22×D44—21no—
36C22×D44—21no—
37C22×D44—21no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×D44C2×C412yes—
44C22×D44D412yes—
45C22×D44D412yes—
46C22×D44D412yes—
47C22×D44D412yes—
48C22×D44C2312yes—
49C22×C4×D11—24no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16C2312yes—
61C2×C11×M16C2312yes—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117C2×C412yes—
67C11×#117C2312yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C22⋊C4C2×C412yes—
70C2×C42×C11—21no—
71C2×C22⋊Dic11C2×C412yes—
72C2×(C2×D11)⋊C4—24no—
73#66979—21no—
74#66979—21no—
75#66979C2×C412yes—
76#66979C2312yes—
77C2×C4⋊Dic11—21no—
78C2×C4×Dic11—21no—
79C2×#4318—21no—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318C2312yes—
90C2×#4318C2312yes—
91C22×C11⋊C8—21no—
92C22×C11⋊C8—21no—
93#66946—28no—
94#66946—28no—
95C22⋊C4×D11—28no—
96C22⋊C4×D11C2×C4116yes—
97C4×D44—28no—
98C4×D44—28no—
99#66887—28no—
100#66887—28no—
101C2×#1829—111nomaximal, Sylow
102C24×C11C22×C411yescharacteristic
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—84no—
108C23×D11C22⋊C414yes—
109C23×D11C22⋊C414yes—
110C23×D11C22×C414yes—
111C22×C4×C11—22no—
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44C22⋊C414yes—
152C2×D44C22⋊C414yes—
153C2×D44C2×D414yes—
154C2×D44C2×D414yes—
155C2×C4×D11—216no—
156C2×C4×D11—88no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—41no—
162C11×M16—41no—
163C11×M16—41no—
164C11×M16—41no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—41no—
168C2×C8×C11—41no—
169C2×C8×C11—41no—
170C2×C8×C11—41no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4C22×C414yes—
175C42×C11—22no—
176C42×C11—22no—
177C22⋊Dic11—22no—
178C22⋊Dic11C22×C414yes—
179(C2×D11)⋊C4—216no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—41no—
189#4318—41no—
190#4318—41no—
191#4318—41no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—41no—
195C2×C11⋊C8—41no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×#518—111no—
199C22×#100—111no—
200C22×#100—111no—
201#1829—118no—
202C2×#344—111no—
203C2×#344—111no—
204C2×#344—111no—
205C2×#344D1111yescharacteristic, complemented
206C23×C11—42no—
207C23×C11C2×C22⋊C411yescharacteristic
208C23×C11C2×C22⋊C411yescharacteristic
209C23×C11#11711yescharacteristic
210C23×C11#11711yescharacteristic
211C23×C11#11711yescharacteristic
212C23×C11#11711yescharacteristic
213C23×C11C23×C411yescharacteristic
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—48no—
221C22×D11—84no—
222C22×D11—84no—
223C22×D11—84no—
224C22×D11—84no—
225C22×D11—84no—
226C22×D11—84no—
227C22×D11C2×C22⋊C418yes—
228C2×C4×C11—24no—
229C2×C4×C11—44no—
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×C4×C11#11711yescharacteristic
233C2×C4×C11#11711yescharacteristic
234C2×C4×C11#11711yescharacteristic
235C2×C4×C11#11711yescharacteristic
236C2×C4×C11#12311yescharacteristic
237C2×C4×C11#12311yescharacteristic
238C2×C4×C11#12311yescharacteristic
239C2×C4×C11#12311yescharacteristic
240C2×C4×C11#12311yescharacteristic
241C2×C4×C11#12311yescharacteristic
242C2×C4×C11#12311yescharacteristic
243C2×C4×C11#12311yescharacteristic
244C2×C4×C11#12311yescharacteristic
245C2×C4×C11#12311yescharacteristic
246C2×C4×C11#12311yescharacteristic
247C2×C4×C11#12311yescharacteristic
248C2×C4×C11#12311yescharacteristic
249C2×C4×C11#12311yescharacteristic
250C2×C4×C11#12311yescharacteristic
251C2×C4×C11#12311yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×Dic11—24no—
259C2×Dic11—44no—
260D44—24no—
261D44—24no—
262D44—24no—
263D44—24no—
264D44—24no—
265D44—24no—
266D44—24no—
267D44—24no—
268C4×D11—816no—
269C8×C11—42no—
270C8×C11—42no—
271C11⋊C8—42no—
272C11⋊C8—42no—
273C23×D4—111no—
274C22×M16—111no—
275C22×M16—111no—
276C22×M16C2×D1111yescharacteristic
277C22×M16C2×D1111yescharacteristic
278#518—114no—
279#518—114no—
280#518—222no—
281#518—222no—
282C2×C4×D4—222no—
283C2×C4×D4—222no—
284C2×#117—111no—
285C2×#117C2×D1111yescharacteristic
286C22×C22⋊C4—114no—
287C2×#100—114no—
288C2×#100—114no—
289C2×#100—222no—
290C2×#100—222no—
291C2×#100—222no—
292C2×#100—222no—
293#344—114no—
294#344—114no—
295#344—114no—
296#344C2×D1114yescomplemented
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11#38111yescharacteristic
305C22×C11#38111yescharacteristic
306C22×C11#38111yescharacteristic
307C22×C11#38111yescharacteristic
308C22×C11C22×C22⋊C411yescharacteristic
309C22×C11C2×#11711yescharacteristic
310C22×C11C2×#11711yescharacteristic
311C2×D11—28no—
312C2×D11—48no—
313C2×D11—48no—
314C2×D11—48no—
315C2×D11—84no—
316C2×D11—84no—
317C2×D11—84no—
318C2×D11—84no—
319C4×C11—44no—
320C4×C11#38111yescharacteristic
321C4×C11#38111yescharacteristic
322C4×C11#38111yescharacteristic
323C4×C11#38111yescharacteristic
324C4×C11C2×#12311yescharacteristic
325C4×C11C2×#12311yescharacteristic
326C4×C11C2×#12311yescharacteristic
327C4×C11C2×#12311yescharacteristic
328Dic11—44no—
329C25—112no—
330C22×D4—112no—
331C22×D4—112no—
332C22×D4—112no—
333C22×D4—112no—
334C22×D4—112no—
335C22×D4—112no—
336C22×D4—221no—
337C22×D4—221no—
338C22×D4—221no—
339C22×D4—221no—
340C22×D4—221no—
341C22×D4—221no—
342C22×D4—221no—
343C22×D4—221no—
344C23×C4—224no—
345C23×C4C22×D1111yescharacteristic
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—112no—
357C2×M16—112no—
358C2×M16—221no—
359C2×M16—221no—
360C2×M16—221no—
361C2×M16—221no—
362C2×M16—221no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16C22×D1112yes—
369C2×M16C22×D1112yes—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—221no—
373C22×C8—221no—
374C4×D4—228no—
375C4×D4—228no—
376C4×D4—228no—
377C4×D4—228no—
378#117—21no—
379#117—21no—
380#117—112no—
381#117—112no—
382#117—221no—
383#117—221no—
384#117C4×D1112yes—
385#117C22×D1112yes—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—221no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4—1116no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4C4×D1112yes—
393C2×C42—21no—
394C2×C42—221no—
395#100—228no—
396#100—228no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—21no—
403C2×C11#182912yescomplemented
404C2×C11C2×#38111yescharacteristic
405D11—48no—
406C24—114no—
407C24—114no—
408C24—114no—
409C24—222no—
410C24—222no—
411C24—222no—
412C24—222no—
413C24—884no—
414C24C2×C4×D1111yescharacteristic
415C2×D4—114no—
416C2×D4—114no—
417C2×D4—114no—
418C2×D4—114no—
419C2×D4—222no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—222no—
441C2×D4—222no—
442C2×D4—222no—
443C22×C4—22no—
444C22×C4—2216no—
445C22×C4—222no—
446C22×C4—888no—
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4#433911yescharacteristic
449C22×C4#433911yescharacteristic
450C22×C4#433911yescharacteristic
451C22×C4#433911yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4#434111yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4#434311yescharacteristic
459C22×C4#434311yescharacteristic
460C22×C4C23×D1111yescharacteristic
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—222no—
470M16—222no—
471M16—222no—
472M16—222no—
473M16—441no—
474M16—441no—
475M16—441no—
476M16—441no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8—441no—
486C2×C8—441no—
487C2×C8—441no—
488C2×C8—441no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C22⋊C4—22no—
494C22⋊C4—114no—
495C22⋊C4—2216no—
496C22⋊C4—222no—
497C22⋊C4C2×C4×D1114yes—
498C42—22no—
499C42—22no—
500C42—222no—
501C42—222no—
502C11C2×#182911yescharacteristic, complemented, Sylow
503C23—42no—
504C23—118no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—224no—
511C23—448no—
512C23—884no—
513C23—884no—
514C23—884no—
515C23—884no—
516C23—884no—
517C23—884no—
518C23#6692511yescharacteristic
519C23#6692511yescharacteristic
520C23C22⋊C4×D1111yescharacteristic
521C23C22⋊C4×D1111yescharacteristic
522C23#6694511yescharacteristic
523C23#6694511yescharacteristic
524C23C22×C4×D1111yescharacteristic
525D4—224no—
526D4—224no—
527D4—224no—
528D4—224no—
529D4—224no—
530D4—224no—
531D4—224no—
532D4—224no—
533C2×C4—24no—
534C2×C4—44no—
535C2×C4—224no—
536C2×C4—444no—
537C2×C4—8816no—
538C2×C4#6692511yescharacteristic
539C2×C4#6692511yescharacteristic
540C2×C4C22⋊C4×D1111yescharacteristic
541C2×C4C22⋊C4×D1111yescharacteristic
542C2×C4#6693611yescharacteristic
543C2×C4#6693611yescharacteristic
544C2×C4#6693611yescharacteristic
545C2×C4#6693611yescharacteristic
546C2×C4#6693611yescharacteristic
547C2×C4#6693611yescharacteristic
548C2×C4#6693611yescharacteristic
549C2×C4#6693611yescharacteristic
550C2×C4#6694511yescharacteristic
551C2×C4#6694511yescharacteristic
552C2×C4#6694711yescharacteristic
553C2×C4#6694711yescharacteristic
554C2×C4#6694711yescharacteristic
555C2×C4#6694711yescharacteristic
556C2×C4#6694711yescharacteristic
557C2×C4#6694711yescharacteristic
558C2×C4#6694711yescharacteristic
559C2×C4#6694711yescharacteristic
560C2×C4C2×#433911yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×#434111yescharacteristic
565C2×C4C2×#434311yescharacteristic
566C8—42no—
567C8—42no—
568C8—442no—
569C8—442no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—228no—
578C22—448no—
579C22—448no—
580C22—448no—
581C22—884no—
582C22—884no—
583C22—884no—
584C22—884no—
585C22#1062227711yescharacteristic
586C22#1062227711yescharacteristic
587C22#1062227711yescharacteristic
588C22#1062227711yescharacteristic
589C22C2×#6692511yescharacteristic
590C22C2×C22⋊C4×D1111yescharacteristic
591C22C2×#6694511yescharacteristic
592C4—44no—
593C4—444no—
594C4#1062227711yescharacteristic
595C4#1062227711yescharacteristic
596C4#1062227711yescharacteristic
597C4#1062227711yescharacteristic
598C4C2×#6693611yescharacteristic
599C4C2×#6693611yescharacteristic
600C4C2×#6694711yescharacteristic
601C4C2×#6694711yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—448no—
609C2#1306872612yesdirect product factor
610C2C2×#1062227711yescharacteristic
subgroupG/H
centerC22#10622277
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#344C2
socleC22×C11#381
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterC2×#344D11
hypocenterC11C2×#1829
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. #13068726C2direct (N × H)
5. C2×#10622197C2semidirect
6. C2×#10622194C2semidirect
7. C2×#10622171C2semidirect
8. C2×C11×#344C2semidirect
29. C11×#344C22semidirect
30. #10622197C22semidirect
31. #10622194C22semidirect
32. #10622171C22semidirect
205. C2×#344D11semidirect
296. #344C2×D11semidirect
403. C2×C11#1829semidirect
502. C11C2×#1829semidirect
609. C2#13068726direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230522
C22×#668872
#130687262
C2×#106221972
C2×#106221942
C2×#106221712
C2×C11×#3442
C2×#182911