Finite Group Databasebeta

← C2×#13069929 #14781705

Subgroups — C2×#13069929 #14781705

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
1C22×Dic11⋊C8C211yesmaximal, characteristic, complemented
2C22×#66899C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic
4C2×#10622843C211yesmaximal, characteristic, complemented
5C2×#10622834C211yesmaximal, characteristic
6#13069929C218yesmaximal, direct product factor
7C2×#10622189C211yesmaximal, characteristic, complemented
8C23×C11×SD16C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×SD16—24no—
12C22×C11×SD16—24no—
13C22×C11×SD16—24no—
14C22×C11×SD16C2214yes—
15C23×C8×C11C2211yescharacteristic
16C22×C22⋊Dic11—21no—
17C22×C22⋊Dic11—21no—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22#10622843—22no—
23#10622843C2214yescomplemented
24C2×#66899—24no—
25C2×#66899C2214yescomplemented
26#10622834—22no—
27#10622834C2214yes—
28C2×#66896—24no—
29C2×#66896C2214yes—
30C2×C11⋊#95—21no—
31C2×C11⋊#95—21no—
32C2×Dic11⋊C8—24no—
33C2×Dic11⋊C8C2214yescomplemented
34#10622189C2214yescomplemented
35C25×C11—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—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—21no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11D414yes—
51C22×D4×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C23×Dic11—21no—
56C23×Dic11D411yescharacteristic
57C23×Dic11D411yescharacteristic
58C2×C11×SD16—232no—
59C2×C11×SD16—28no—
60C2×C11×SD16—28no—
61C2×C11×SD16—28no—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11D414yes—
65C22×C8×C11C2312yes—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—44no—
69C2×C22⋊Dic11—44no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2312yes—
77C2×C4⋊Dic11C2312yes—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11D412yes—
81C2×C4×Dic11C2312yes—
82C22×C11⋊C8—22no—
83C22×C11⋊C8—22no—
84C22×C11⋊C8—22no—
85C22×C11⋊C8C2312yes—
86#66899—28no—
87#66896—28no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90Dic11⋊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×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—
114C2×D4×C11—28no—
115C2×D4×C11—24no—
116C2×D4×C11—28no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11C2×D414yes—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11SD1614yescomplemented
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155C11×SD16—232no—
156C2×C8×C11—28no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11C2×D414yes—
160C22⋊Dic11—48no—
161C22⋊Dic11—48no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—42no—
167C4⋊Dic11—42no—
168C4×Dic11—24no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—44no—
175C23×SD16D1111yescharacteristic
176C22×C4⋊C8—111no—
177C22×#103—111no—
178C22×#102—111no—
179C2×#391—111no—
180C2×#390—111no—
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
205Q8×C11—24no—
206Q8×C11—24no—
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—48no—
210D4×C11—24no—
211D4×C11—24no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—48no—
215C2×C4×C11—24no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—48no—
219C2×C4×C11#12014yes—
220C2×C4×C11#12112yes—
221C2×C4×C11#12112yes—
222C2×C4×C11#12112yes—
223C2×C4×C11#12314yes—
224C2×C4×C11#12314yes—
225C2×C4×C11#12414yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—28no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—44no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—84no—
246C2×Dic11—84no—
247C2×Dic11C2×SD1614yescomplemented
248C8×C11—24no—
249C11⋊C8—42no—
250C23×Q8C2×D1111yescharacteristic
251C23×D4C2×D1111yescharacteristic
252C22×SD16—24no—
253C22×SD16—24no—
254C22×SD16—24no—
255C22×SD16C2×D1114yes—
256C23×C8—111no—
257C23×C8C2×D1111yescharacteristic
258C22×C4⋊C4—111no—
259C22×C4⋊C4—111no—
260C22×C22⋊C4—221no—
261C22×C22⋊C4—221no—
262C22×C42—111no—
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—114no—
272#390—222no—
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—44no—
299C4×C11#39414yes—
300C4×C11C2×#12011yescharacteristic
301C4×C11C2×#12311yescharacteristic
302C4×C11C2×#12311yescharacteristic
303C4×C11C2×#12411yescharacteristic
304Dic11—24no—
305Dic11—42no—
306Dic11—82no—
307Dic11—82no—
308C25—21no—
309C22×Q8—21no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8C22⋊D1114yes—
316C22×Q8C22×D1112yes—
317C22×D4—21no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4C22⋊D1114yes—
324C22×D4C22×D1112yes—
325C23×C4—21no—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4—221no—
329C23×C4—221no—
330C23×C4C22×D1111yescharacteristic
331C2×SD16—232no—
332C2×SD16—28no—
333C2×SD16—28no—
334C2×SD16—28no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—112no—
338C22×C8—222no—
339C22×C8—222no—
340C22×C8—222no—
341C22×C8C22⋊D1114yes—
342C22×C8C22×D1112yes—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C22⋊C4—224no—
352C2×C22⋊C4—224no—
353C2×C22⋊C4—444no—
354C2×C22⋊C4—444no—
355C2×C42—112no—
356C2×C42—112no—
357C2×C42—222no—
358C2×C42—222no—
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—
381C24D4×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×C22⋊D1114yes—
395C2×D4—28no—
396C2×D4—24no—
397C2×D4—28no—
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×C22⋊D1114yes—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—114no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4D4×D1111yescharacteristic
429C22×C4#434112yes—
430C22×C4#434112yes—
431C22×C4#434112yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C2×C22⋊D1112yes—
435C22×C4C23×D1111yescharacteristic
436SD16—232no—
437C2×C8—28no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—444no—
444C2×C8C2×C22⋊D1114yes—
445C4⋊C4—222no—
446C4⋊C4—222no—
447C4⋊C4—222no—
448C4⋊C4—222no—
449C4⋊C4—442no—
450C4⋊C4—442no—
451C22⋊C4—448no—
452C22⋊C4—448no—
453C42—224no—
454C42—222no—
455C42—222no—
456C11C2×#205511yescharacteristic, complemented, Sylow
457C23—24no—
458C23—48no—
459C23—42no—
460C23—48no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—48no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23SD16×D1112yes—
472C23#6696712yes—
473C23#6696812yes—
474C23#6696912yes—
475C23#6699112yes—
476C23#6699212yes—
477C23#6699212yes—
478C23C2×D4×D1111yescharacteristic
479Q8—24no—
480Q8—24no—
481Q8—42no—
482Q8—42no—
483Q8—48no—
484D4—24no—
485D4—24no—
486D4—42no—
487D4—42no—
488D4—48no—
489C2×C4—24no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—48no—
493C2×C4—114no—
494C2×C4—222no—
495C2×C4—228no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—444no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—884no—
508C2×C4—884no—
509C2×C4#6698814yes—
510C2×C4#6698814yes—
511C2×C4#6698914yes—
512C2×C4#6699112yes—
513C2×C4#6699212yes—
514C2×C4#6699212yes—
515C2×C4#6700614yes—
516C2×C4C2×#434111yescharacteristic
517C2×C4C2×#434111yescharacteristic
518C2×C4C2×#434111yescharacteristic
519C2×C4C22×C22⋊D1111yescharacteristic
520C2×C4C22×C22⋊D1111yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—24no—
523C8—442no—
524C22—44no—
525C22—44no—
526C22—44no—
527C22—82no—
528C22—82no—
529C22—816no—
530C22—82no—
531C22—82no—
532C22#1062277514yes—
533C22#1062277614yes—
534C22#1062277814yes—
535C22#1062277914yes—
536C22#1062278414yes—
537C22#1062278714yes—
538C22#1062283514yes—
539C22C2×SD16×D1111yescharacteristic
540C22C2×#6696711yescharacteristic
541C22C2×#6696811yescharacteristic
542C22C2×#6696911yescharacteristic
543C22C2×#6699111yescharacteristic
544C22C2×#6699211yescharacteristic
545C22C2×#6699211yescharacteristic
546C4—44no—
547C4—224no—
548C4—442no—
549C4—882no—
550C4—882no—
551C4#1062283514yes—
552C4C2×#6698811yescharacteristic
553C4C2×#6698811yescharacteristic
554C4C2×#6698911yescharacteristic
555C4C2×#6700611yescharacteristic
556C2—84no—
557C2#1306992918yesdirect product factor
558C2C2×#1062283511yescharacteristic
559C2C2×#1062277511yescharacteristic
560C2C2×#1062277811yescharacteristic
561C2C2×#1062277611yescharacteristic
562C2C2×#1062277911yescharacteristic
563C2C2×#1062278411yescharacteristic
564C2C2×#1062278711yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC23×C11×SD16C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC23×SD16D11
hypocenterC11C2×#2055
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×SD16

Complements

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

NH ≅ G/Ntype
1. C22×Dic11⋊C8C2semidirect
2. C22×#66899C2semidirect
4. C2×#10622843C2semidirect
6. #13069929C2direct (N × H)
7. C2×#10622189C2semidirect
23. #10622843C22semidirect
25. C2×#66899C22semidirect
33. C2×Dic11⋊C8C22semidirect
34. #10622189C22semidirect
152. C22×Dic11SD16semidirect
247. C2×Dic11C2×SD16semidirect
365. C2×C11#2055semidirect
456. C11C2×#2055semidirect
557. C2#13069929direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Dic11⋊C82
C22×#668992
C22×#668962
C2×#106228432
C2×#106228342
#130699292
C2×#106221892
C23×C11×SD162
C2×#205511