Finite Group Databasebeta

← C2×#13069933 #14781709

Subgroups — C2×#13069933 #14781709

Order 2816.

1702 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4324C211yesmaximal, characteristic
2C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C22×#66874C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic
5C2×#10622542C211yesmaximal, characteristic, complemented
6#13069933C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C2×C11×#390C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4—21no—
13C22×C11×C22⋊C4—21no—
14C22×C42×C11C2211yescharacteristic
15C22×#4324—24no—
16C22×#4324—24no—
17C22×#4324—24no—
18C22×#4324C2214yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C11×#390—22no—
23C11×#390C2214yes—
24C2×#66896—24no—
25C2×#66896C2214yes—
26C2×C11⋊#95—21no—
27C2×C11⋊#95—21no—
28C2×#66874—24no—
29C2×#66874C2214yescomplemented
30#10622542—22no—
31#10622542C2214yescomplemented
32C2×C4⋊(C11⋊C8)—24no—
33C2×C4⋊(C11⋊C8)C2214yescomplemented
34#10622167C2214yescomplemented
35C25×C11—21no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—21no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11D414yes—
43C22×D4×C11C2312yes—
44C23×C4×C11—21no—
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11—21no—
50C22×Dic22—22no—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—21no—
55C22×Dic22—22no—
56C22×Dic22D414yes—
57C22×Dic22C2312yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—44no—
65C2×C11×C22⋊C4—44no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11D412yes—
69C2×C42×C11C2312yes—
70C2×#4324—232no—
71C2×#4324—28no—
72C2×#4324—28no—
73C2×#4324—28no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2312yes—
78C22×C11⋊C8—22no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8—22no—
83C22×C11⋊C8D414yes—
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2312yes—
86#66896—28no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89#66874—28no—
90C4⋊(C11⋊C8)—28no—
91C2×#2055—111nomaximal, Sylow
92C24×C11—24no—
93C24×C11—22no—
94C24×C11—42no—
95C24×C11—42no—
96C24×C11—42no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11C2×D411yescharacteristic
101C2×D4×C11—28no—
102C2×D4×C11—24no—
103C2×D4×C11—28no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—44no—
112C2×D4×C11—44no—
113C2×D4×C11C2×D414yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11SD1614yescomplemented
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C2×Dic22—28no—
143C2×Dic22—24no—
144C2×Dic22—28no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—42no—
151C2×Dic22—42no—
152C2×Dic22—44no—
153C2×Dic22—44no—
154C2×Dic22C2×D414yes—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C11×C22⋊C4—48no—
159C11×C22⋊C4—48no—
160C42×C11—24no—
161C42×C11—22no—
162C42×C11—22no—
163#4324—232no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—42no—
167C2×C11⋊C8—28no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—44no—
174C2×C11⋊C8C2×D414yes—
175C23×SD16—111no—
176C22×C4⋊C8—111no—
177C22×#103—111no—
178C22×#102—111no—
179C2×#391—111no—
180C2×#390D1111yescharacteristic
181#2055—118no—
182C2×#340—111no—
183C23×C11—24no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—48no—
191C23×C11—48no—
192C23×C11—48no—
193C23×C11—84no—
194C23×C11—84no—
195C23×C11—84no—
196C23×C11—84no—
197C23×C11#12112yes—
198C23×C11#12112yes—
199C23×C11#12112yes—
200C23×C11C2×SD1612yes—
201C23×C11#13512yes—
202C23×C11AGL(1,ℤ/8)12yes—
203C23×C11#13712yes—
204C23×C11C22×D411yescharacteristic
205D4×C11—24no—
206D4×C11—24no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—48no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—84no—
221C2×C4×C11#12014yes—
222C2×C4×C11#12112yes—
223C2×C4×C11#12112yes—
224C2×C4×C11#12112yes—
225C2×C4×C11#12314yes—
226C2×C4×C11#12314yes—
227C2×C4×C11#12414yes—
228C2×C4×C11C2×SD1614yescomplemented
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×Dic11—24no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—48no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—84no—
243Dic22—24no—
244Dic22—24no—
245Dic22—42no—
246Dic22—42no—
247Dic22—48no—
248C11⋊C8—24no—
249C11⋊C8—42no—
250C23×Q8—111no—
251C23×D4C2×D1111yescharacteristic
252C22×SD16—114no—
253C22×SD16—224no—
254C22×SD16—224no—
255C22×SD16—224no—
256C23×C8—111no—
257C23×C8—111no—
258C22×C4⋊C4—111no—
259C22×C4⋊C4C2×D1111yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262C22×C42C2×D1111yescharacteristic
263C2×C4⋊C8—114no—
264C2×C4⋊C8—224no—
265C2×#103—114no—
266C2×#103—224no—
267C2×#102—114no—
268C2×#102—224no—
269#391—114no—
270#391—222no—
271#390—22no—
272#390C2×D1114yes—
273C2×#95—221no—
274C2×#95—221no—
275#340—114no—
276C22×C11—44no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—816no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11—82no—
284C22×C11#39414yes—
285C22×C11#46014yes—
286C22×C11#46114yes—
287C22×C11#46314yes—
288C22×C11#46414yes—
289C22×C11#46514yes—
290C22×C11#46814yes—
291C22×C11C2×#12111yescharacteristic
292C22×C11C2×#12111yescharacteristic
293C22×C11C2×#12111yescharacteristic
294C22×C11C22×SD1611yescharacteristic
295C22×C11C2×#13511yescharacteristic
296C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C4×C11—24no—
299C4×C11—42no—
300C4×C11—82no—
301C4×C11#39414yes—
302C4×C11C2×#12011yescharacteristic
303C4×C11C2×#12311yescharacteristic
304C4×C11C2×#12311yescharacteristic
305C4×C11C2×#12411yescharacteristic
306Dic11—44no—
307Dic11—82no—
308C25—21no—
309C22×Q8—114no—
310C22×Q8—112no—
311C22×Q8—222no—
312C22×Q8—221no—
313C22×Q8—222no—
314C22×Q8—222no—
315C22×Q8—222no—
316C22×Q8—222no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—21no—
323C22×D4D4414yes—
324C22×D4C22×D1112yes—
325C23×C4—21no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4C22⋊D1111yescharacteristic
329C23×C4C22⋊D1111yescharacteristic
330C23×C4C22×D1111yescharacteristic
331C2×SD16—228no—
332C2×SD16—228no—
333C2×SD16—2232no—
334C2×SD16—228no—
335C22×C8—114no—
336C22×C8—112no—
337C22×C8—112no—
338C22×C8—222no—
339C22×C8—222no—
340C22×C8—222no—
341C22×C8—222no—
342C22×C8—222no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4C22×D1112yes—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42C22⋊D1112yes—
358C2×C42C22×D1112yes—
359C4⋊C8—228no—
360#103—228no—
361#102—228no—
362#95—224no—
363#95—224no—
364C2×C11—84no—
365C2×C11#205518yescomplemented
366C2×C11C2×#39411yescharacteristic
367C2×C11C2×#46111yescharacteristic
368C2×C11C2×#46311yescharacteristic
369C2×C11C2×#46011yescharacteristic
370C2×C11C2×#46411yescharacteristic
371C2×C11C2×#46511yescharacteristic
372C2×C11C2×#46811yescharacteristic
373C24—24no—
374C24—22no—
375C24—42no—
376C24—42no—
377C24—42no—
378C24—42no—
379C24—42no—
380C24—42no—
381C24C2×C22⋊D1111yescharacteristic
382C2×Q8—114no—
383C2×Q8—224no—
384C2×Q8—222no—
385C2×Q8—228no—
386C2×Q8—228no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—444no—
392C2×Q8—444no—
393C2×Q8—442no—
394C2×Q8—442no—
395C2×D4—28no—
396C2×D4—28no—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—44no—
404C2×D4—44no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4C2×D4414yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—224no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4#432414yescomplemented
426C22×C4C2×D4412yes—
427C22×C4#433912yes—
428C22×C4D4×D1112yes—
429C22×C4D4×D1112yes—
430C22×C4#434112yes—
431C22×C4#434112yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436SD16—2232no—
437C2×C8—114no—
438C2×C8—228no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—444no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—442no—
451C22⋊C4—48no—
452C22⋊C4—48no—
453C42—24no—
454C42—22no—
455C42—22no—
456C11C2×#205511yescharacteristic, complemented, Sylow
457C23—24no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—48no—
463C23—42no—
464C23—42no—
465C23—48no—
466C23—48no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23#6698312yes—
472C23#6698512yes—
473C23C2×#432412yes—
474C23#6699112yes—
475C23#6699212yes—
476C23#6700312yes—
477C23#6700412yes—
478C23C22×C22⋊D1111yescharacteristic
479Q8—224no—
480Q8—224no—
481Q8—442no—
482Q8—442no—
483Q8—448no—
484D4—24no—
485D4—24no—
486D4—42no—
487D4—42no—
488D4—48no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—28no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—84no—
500C2×C4—224no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—448no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—884no—
508C2×C4#6693514yes—
509C2×C4#6693614yes—
510C2×C4#6693814yes—
511C2×C4#6693914yes—
512C2×C4#6698312yes—
513C2×C4C2×#432414yescomplemented
514C2×C4#6699112yes—
515C2×C4#6699212yes—
516C2×C4C22×D4411yescharacteristic
517C2×C4C2×#433911yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4C2×#434111yescharacteristic
522C8—224no—
523C8—442no—
524C22—44no—
525C22—44no—
526C22—44no—
527C22—82no—
528C22—82no—
529C22—816no—
530C22—82no—
531C22—82no—
532C22#1062257414yes—
533C22#1062262914yes—
534C22#1062263214yes—
535C22#1062265414yes—
536C22#1062265514yes—
537C22#1062266714yes—
538C22#1062268814yes—
539C22C2×#6698311yescharacteristic
540C22C2×#6698511yescharacteristic
541C22C22×#432411yescharacteristic
542C22C2×#6699111yescharacteristic
543C22C2×#6699211yescharacteristic
544C22C2×#6700311yescharacteristic
545C22C2×#6700411yescharacteristic
546C4—24no—
547C4—42no—
548C4—82no—
549C4—444no—
550C4—882no—
551C4#1062257414yes—
552C4C2×#6693511yescharacteristic
553C4C2×#6693611yescharacteristic
554C4C2×#6693811yescharacteristic
555C4C2×#6693911yescharacteristic
556C2—84no—
557C2#1306993318yesdirect product factor
558C2C2×#1062257411yescharacteristic
559C2C2×#1062263211yescharacteristic
560C2C2×#1062262911yescharacteristic
561C2C2×#1062268811yescharacteristic
562C2C2×#1062266711yescharacteristic
563C2C2×#1062265411yescharacteristic
564C2C2×#1062265511yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#390C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11C2×#2055
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊(C11⋊C8)C2semidirect
3. C22×#66874C2semidirect
5. C2×#10622542C2semidirect
6. #13069933C2direct (N × H)
7. C2×#10622167C2semidirect
29. C2×#66874C22semidirect
31. #10622542C22semidirect
33. C2×C4⋊(C11⋊C8)C22semidirect
34. #10622167C22semidirect
123. C22×C4×C11SD16semidirect
228. C2×C4×C11C2×SD16semidirect
365. C2×C11#2055semidirect
425. C22×C4#4324semidirect
456. C11C2×#2055semidirect
513. C2×C4C2×#4324semidirect
557. C2#13069933direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43242
C22×C4⋊(C11⋊C8)2
C22×#668742
C22×#668962
C2×#106225422
#130699332
C2×#106221672
C2×C11×#3902
C2×#205511