Finite Group Databasebeta

← C2×#13069931 #14781707

Subgroups — C2×#13069931 #14781707

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×#4325C211yesmaximal, characteristic
2C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C22×#66899C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic
5C2×#10622552C211yesmaximal, characteristic
6#13069931C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C2×C11×#391C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×#4325—24no—
14C22×#4325—24no—
15C22×#4325—24no—
16C22×#4325C2214yes—
17C22×(C2×D11)⋊C4—21no—
18C22×(C2×D11)⋊C4—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C11×#391—22no—
23C11×#391C2214yescomplemented
24C2×C11×#95—21no—
25C2×C11×#95—21no—
26C2×#66899—24no—
27C2×#66899C2214yescomplemented
28C2×#66873—24no—
29C2×#66873C2214yes—
30#10622552—22no—
31#10622552C2214yes—
32C2×C4⋊(C11⋊C8)—24no—
33C2×C4⋊(C11⋊C8)C2214yescomplemented
34#10622167C2214yescomplemented
35C24×D11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11D414yes—
43C22×Q8×C11C2312yes—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—21no—
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—22no—
56C22×D44D414yes—
57C22×D44C2312yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2312yes—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11D412yes—
65C2×C42×C11C2312yes—
66C2×#4325—232no—
67C2×#4325—28no—
68C2×#4325—28no—
69C2×#4325—28no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—44no—
73C2×(C2×D11)⋊C4—44no—
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—
86C11×#95—24no—
87C11×#95—24no—
88#66899—28no—
89#66873—28no—
90C4⋊(C11⋊C8)—28no—
91C2×#2055—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C23×D11—24no—
94C23×D11—22no—
95C23×D11—42no—
96C23×D11—42no—
97C23×D11—42no—
98C23×D11—42no—
99C23×D11—42no—
100C23×D11—42no—
101C2×Q8×C11—24no—
102C2×Q8×C11—22no—
103C2×Q8×C11—28no—
104C2×Q8×C11—28no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C2×Q8×C11—44no—
112C2×Q8×C11—44no—
113C2×Q8×C11C2×D414yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11SD1614yescomplemented
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—22no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C2×D44—28no—
143C2×D44—24no—
144C2×D44—28no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—42no—
151C2×D44—42no—
152C2×D44—44no—
153C2×D44—44no—
154C2×D44C2×D414yes—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C42×C11—24no—
159C42×C11—22no—
160C42×C11—22no—
161#4325—232no—
162(C2×D11)⋊C4—48no—
163(C2×D11)⋊C4—48no—
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×#391D1111yescharacteristic, complemented
180C2×#390—111no—
181#2055—118no—
182C2×#340—111no—
183C23×C11#12112yes—
184C23×C11#12112yes—
185C23×C11#12112yes—
186C23×C11C2×SD1612yes—
187C23×C11#13512yes—
188C23×C11AGL(1,ℤ/8)12yes—
189C23×C11#13712yes—
190C23×C11C22×D411yescharacteristic
191C22×D11—24no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—48no—
199C22×D11—48no—
200C22×D11—48no—
201C22×D11—84no—
202C22×D11—84no—
203C22×D11—84no—
204C22×D11—84no—
205Q8×C11—24no—
206Q8×C11—24no—
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—48no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—48no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—84no—
225C2×C4×C11#12014yes—
226C2×C4×C11#12112yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12314yes—
230C2×C4×C11#12314yes—
231C2×C4×C11#12414yes—
232C2×C4×C11C2×SD1614yescomplemented
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—84no—
243D44—24no—
244D44—24no—
245D44—42no—
246D44—42no—
247D44—48no—
248C11⋊C8—24no—
249C11⋊C8—42no—
250C23×Q8C2×D1111yescharacteristic
251C23×D4—111no—
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—221no—
261C22×C22⋊C4—221no—
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—22no—
270#391C2×D1114yescomplemented
271#390—114no—
272#390—222no—
273C2×#95—21no—
274C2×#95—21no—
275#340—114no—
276C22×C11#39414yes—
277C22×C11#46014yes—
278C22×C11#46114yes—
279C22×C11#46314yes—
280C22×C11#46414yes—
281C22×C11#46514yes—
282C22×C11#46814yes—
283C22×C11C2×#12111yescharacteristic
284C22×C11C2×#12111yescharacteristic
285C22×C11C2×#12111yescharacteristic
286C22×C11C22×SD1611yescharacteristic
287C22×C11C2×#13511yescharacteristic
288C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C11C2×#13711yescharacteristic
290C2×D11—44no—
291C2×D11—44no—
292C2×D11—44no—
293C2×D11—816no—
294C2×D11—82no—
295C2×D11—82no—
296C2×D11—82no—
297C2×D11—82no—
298C4×C11—24no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11—82no—
302C4×C11#39414yes—
303C4×C11C2×#12011yescharacteristic
304C4×C11C2×#12311yescharacteristic
305C4×C11C2×#12311yescharacteristic
306C4×C11C2×#12411yescharacteristic
307Dic11—82no—
308C25—221no—
309C22×Q8—22no—
310C22×Q8—21no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8D4414yes—
316C22×Q8C22×D1112yes—
317C22×D4—114no—
318C22×D4—112no—
319C22×D4—222no—
320C22×D4—222no—
321C22×D4—222no—
322C22×D4—222no—
323C22×D4—222no—
324C22×D4—221no—
325C23×C4—21no—
326C23×C4—21no—
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—224no—
352C2×C22⋊C4—224no—
353C2×C22⋊C4—444no—
354C2×C22⋊C4—444no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42C22⋊D1112yes—
358C2×C42C22×D1112yes—
359C4⋊C8—228no—
360#103—228no—
361#102—228no—
362#95—24no—
363#95—24no—
364C2×C11#205518yescomplemented
365C2×C11C2×#39411yescharacteristic
366C2×C11C2×#46111yescharacteristic
367C2×C11C2×#46311yescharacteristic
368C2×C11C2×#46011yescharacteristic
369C2×C11C2×#46411yescharacteristic
370C2×C11C2×#46511yescharacteristic
371C2×C11C2×#46811yescharacteristic
372D11—84no—
373C24—224no—
374C24—222no—
375C24—442no—
376C24—442no—
377C24—442no—
378C24—442no—
379C24—442no—
380C24—442no—
381C24C2×C22⋊D1111yescharacteristic
382C2×Q8—24no—
383C2×Q8—22no—
384C2×Q8—28no—
385C2×Q8—28no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—44no—
391C2×Q8—44no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8C2×D4414yes—
395C2×D4—114no—
396C2×D4—228no—
397C2×D4—228no—
398C2×D4—224no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—444no—
405C2×D4—444no—
406C2×D4—442no—
407C2×D4—442no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—222no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4#432514yescomplemented
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—448no—
452C22⋊C4—448no—
453C42—24no—
454C42—22no—
455C42—22no—
456C11C2×#205511yescharacteristic, complemented, Sylow
457C23—224no—
458C23—442no—
459C23—442no—
460C23—442no—
461C23—442no—
462C23—448no—
463C23—442no—
464C23—442no—
465C23—448no—
466C23—448no—
467C23—884no—
468C23—884no—
469C23—884no—
470C23—884no—
471C23#6698312yes—
472C23#6699112yes—
473C23#6699212yes—
474C23C2×#432512yes—
475C23#6699512yes—
476C23#6700212yes—
477C23#6700312yes—
478C23C22×C22⋊D1111yescharacteristic
479Q8—24no—
480Q8—24no—
481Q8—42no—
482Q8—42no—
483Q8—48no—
484D4—224no—
485D4—224no—
486D4—442no—
487D4—442no—
488D4—448no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—28no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—48no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—84no—
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×C4#6699112yes—
514C2×C4#6699212yes—
515C2×C4C2×#432514yescomplemented
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—444no—
525C22—444no—
526C22—444no—
527C22—882no—
528C22—882no—
529C22—8816no—
530C22—882no—
531C22—882no—
532C22#1062257414yes—
533C22#1062264014yes—
534C22#1062264114yes—
535C22#1062266114yes—
536C22#1062266214yes—
537C22#1062267014yes—
538C22#1062269614yes—
539C22C2×#6698311yescharacteristic
540C22C2×#6699111yescharacteristic
541C22C2×#6699211yescharacteristic
542C22C22×#432511yescharacteristic
543C22C2×#6699511yescharacteristic
544C22C2×#6700211yescharacteristic
545C22C2×#6700311yescharacteristic
546C4—24no—
547C4—42no—
548C4—44no—
549C4—82no—
550C4—882no—
551C4#1062257414yes—
552C4C2×#6693511yescharacteristic
553C4C2×#6693611yescharacteristic
554C4C2×#6693811yescharacteristic
555C4C2×#6693911yescharacteristic
556C2—884no—
557C2#1306993118yesdirect product factor
558C2C2×#1062257411yescharacteristic
559C2C2×#1062269611yescharacteristic
560C2C2×#1062267011yescharacteristic
561C2C2×#1062264011yescharacteristic
562C2C2×#1062264111yescharacteristic
563C2C2×#1062266111yescharacteristic
564C2C2×#1062266211yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#391C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC2×#391D11
hypocenterC11C2×#2055
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊(C11⋊C8)C2semidirect
3. C22×#66899C2semidirect
6. #13069931C2direct (N × H)
7. C2×#10622167C2semidirect
8. C2×C11×#391C2semidirect
23. C11×#391C22semidirect
27. C2×#66899C22semidirect
33. C2×C4⋊(C11⋊C8)C22semidirect
34. #10622167C22semidirect
127. C22×C4×C11SD16semidirect
179. C2×#391D11semidirect
232. C2×C4×C11C2×SD16semidirect
270. #391C2×D11semidirect
364. C2×C11#2055semidirect
425. C22×C4#4325semidirect
456. C11C2×#2055semidirect
515. C2×C4C2×#4325semidirect
557. C2#13069931direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43252
C22×C4⋊(C11⋊C8)2
C22×#668992
C22×#668732
C2×#106225522
#130699312
C2×#106221672
C2×C11×#3912
C2×#205511