Finite Group Databasebeta

← C2×#13069934 #14781710

Subgroups — C2×#13069934 #14781710

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×#4314C211yesmaximal, characteristic
2C22×#66880C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic
4C2×#10622542C211yesmaximal, characteristic, complemented
5C2×#10622552C211yesmaximal, characteristic
6#13069934C218yesmaximal, direct product factor
7C2×#10622189C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C8C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×(C2×D11)⋊C4—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×#4314—24no—
19C22×#4314—24no—
20C22×#4314—24no—
21C22×#4314C2214yes—
22C2×C11×C4⋊C8—24no—
23C2×C11×C4⋊C8C2214yescomplemented
24C2×C11⋊#95—21no—
25C2×C11⋊#95—21no—
26C2×#66885—24no—
27C2×#66885C2214yes—
28C2×#66880—24no—
29C2×#66880C2214yescomplemented
30#10622552—22no—
31#10622552C2214yes—
32#10622542—22no—
33#10622542C2214yescomplemented
34#10622189C2214yescomplemented
35C24×D11—21no—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11—21no—
40C23×Dic11—21no—
41C23×Dic11—21no—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—21no—
47C22×D44—22no—
48C22×D44D414yes—
49C22×D44C2312yes—
50C22×Dic22—22no—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—21no—
55C22×Dic22—22no—
56C22×Dic22D414yes—
57C22×Dic22C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11—22no—
63C22×C8×C11D414yes—
64C22×C8×C11C2312yes—
65C22×C8×C11C2312yes—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11D412yes—
69C2×C42×C11C2312yes—
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—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2312yes—
82C2×#4314—232no—
83C2×#4314—28no—
84C2×#4314—28no—
85C2×#4314—28no—
86C11×C4⋊C8—28no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89#66885—28no—
90#66880—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—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11SD1614yescomplemented
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4112yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—42no—
122C22×Dic11—42no—
123C22×Dic11—42no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C2×D44—28no—
130C2×D44—24no—
131C2×D44—28no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—42no—
138C2×D44—42no—
139C2×D44—44no—
140C2×D44—44no—
141C2×D44C2×D414yes—
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—
155C2×C8×C11—28no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—44no—
162C2×C8×C11C2×D414yes—
163C42×C11—24no—
164C42×C11—22no—
165C42×C11—22no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—42no—
173C4⋊Dic11—42no—
174#4314—232no—
175C23×SD16—111no—
176C22×C4⋊C8D1111yescharacteristic, complemented
177C22×#103—111no—
178C22×#102—111no—
179C2×#391—111no—
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—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—28no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—44no—
212C2×C4×C11#12014yes—
213C2×C4×C11#12112yes—
214C2×C4×C11#12112yes—
215C2×C4×C11#12112yes—
216C2×C4×C11#12314yes—
217C2×C4×C11#12314yes—
218C2×C4×C11#12414yes—
219C2×C4×C11C2×SD1614yescomplemented
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×Dic11—24no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—48no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—84no—
237C2×Dic11—84no—
238D44—24no—
239D44—24no—
240D44—42no—
241D44—42no—
242D44—48no—
243Dic22—24no—
244Dic22—24no—
245Dic22—42no—
246Dic22—42no—
247Dic22—48no—
248C8×C11—24no—
249C8×C11—42no—
250C23×Q8—111no—
251C23×D4—111no—
252C22×SD16—114no—
253C22×SD16—224no—
254C22×SD16—224no—
255C22×SD16—224no—
256C23×C8C2×D1111yescharacteristic
257C23×C8C2×D1111yescharacteristic
258C22×C4⋊C4—111no—
259C22×C4⋊C4—111no—
260C22×C22⋊C4—221no—
261C22×C22⋊C4—221no—
262C22×C42C2×D1111yescharacteristic
263C2×C4⋊C8—24no—
264C2×C4⋊C8C2×D1114yescomplemented
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#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—42no—
300C4×C11#39414yes—
301C4×C11C2×#12011yescharacteristic
302C4×C11C2×#12311yescharacteristic
303C4×C11C2×#12311yescharacteristic
304C4×C11C2×#12411yescharacteristic
305Dic11—44no—
306Dic11—82no—
307Dic11—82no—
308C25—221no—
309C22×Q8—114no—
310C22×Q8—112no—
311C22×Q8—221no—
312C22×Q8—222no—
313C22×Q8—222no—
314C22×Q8—222no—
315C22×Q8—222no—
316C22×Q8—222no—
317C22×D4—114no—
318C22×D4—112no—
319C22×D4—221no—
320C22×D4—222no—
321C22×D4—222no—
322C22×D4—222no—
323C22×D4—222no—
324C22×D4—222no—
325C23×C4—221no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4D4411yescharacteristic
329C23×C4D4411yescharacteristic
330C23×C4C22×D1111yescharacteristic
331C2×SD16—228no—
332C2×SD16—228no—
333C2×SD16—2232no—
334C2×SD16—228no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8—22no—
340C22×C8C22⋊D1114yes—
341C22×C8C22×D1112yes—
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—22no—
356C2×C42—22no—
357C2×C42D4412yes—
358C2×C42C22×D1112yes—
359C4⋊C8—28no—
360#103—228no—
361#102—228no—
362#95—224no—
363#95—224no—
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×D4411yescharacteristic
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—442no—
393C2×Q8—442no—
394C2×Q8—444no—
395C2×D4—114no—
396C2×D4—228no—
397C2×D4—224no—
398C2×D4—228no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—444no—
405C2×D4—442no—
406C2×D4—442no—
407C2×D4—444no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—224no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—442no—
418C22×C4—442no—
419C22×C4—442no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4#431414yescomplemented
426C22×C4C2×D4412yes—
427C22×C4C2×D4412yes—
428C22×C4C2×D4411yescharacteristic
429C22×C4#433912yes—
430C22×C4D4×D1112yes—
431C22×C4D4×D1112yes—
432C22×C4#434312yes—
433C22×C4#434312yes—
434C22×C4C2×C22⋊D1112yes—
435C22×C4C23×D1111yescharacteristic
436SD16—2232no—
437C2×C8—28no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—44no—
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—24no—
454C42—22no—
455C42—22no—
456C11C2×#205511yescharacteristic, complemented, Sylow
457C23—224no—
458C23—442no—
459C23—442no—
460C23—442no—
461C23—442no—
462C23—442no—
463C23—442no—
464C23—448no—
465C23—448no—
466C23—448no—
467C23—884no—
468C23—884no—
469C23—884no—
470C23—884no—
471C23#6694812yes—
472C23#6694812yes—
473C23C2×#431412yes—
474C23#6695712yes—
475C23#6696112yes—
476C23#6696212yes—
477C23#6698312yes—
478C23C22×D4411yescharacteristic
479Q8—224no—
480Q8—224no—
481Q8—442no—
482Q8—442no—
483Q8—448no—
484D4—224no—
485D4—224no—
486D4—442no—
487D4—442no—
488D4—448no—
489C2×C4—28no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—44no—
496C2×C4—224no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—448no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—884no—
507C2×C4—884no—
508C2×C4#6694714yes—
509C2×C4#6694714yes—
510C2×C4#6694812yes—
511C2×C4#6694812yes—
512C2×C4C2×#431414yescomplemented
513C2×C4#6698312yes—
514C2×C4#6699014yes—
515C2×C4#6700014yes—
516C2×C4C2×#433911yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×#434311yescharacteristic
520C2×C4C2×#434311yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—24no—
523C8—42no—
524C22—444no—
525C22—444no—
526C22—444no—
527C22—882no—
528C22—882no—
529C22—8816no—
530C22—882no—
531C22—882no—
532C22#1062245414yes—
533C22#1062245714yes—
534C22#1062245814yes—
535C22#1062246114yes—
536C22#1062260414yes—
537C22#1062272714yes—
538C22#1062274714yes—
539C22C2×#6694811yescharacteristic
540C22C2×#6694811yescharacteristic
541C22C22×#431411yescharacteristic
542C22C2×#6695711yescharacteristic
543C22C2×#6696111yescharacteristic
544C22C2×#6696211yescharacteristic
545C22C2×#6698311yescharacteristic
546C4—24no—
547C4—42no—
548C4—444no—
549C4—882no—
550C4—882no—
551C4#1062260414yes—
552C4C2×#6694711yescharacteristic
553C4C2×#6694711yescharacteristic
554C4C2×#6699011yescharacteristic
555C4C2×#6700011yescharacteristic
556C2—884no—
557C2#1306993418yesdirect product factor
558C2C2×#1062260411yescharacteristic
559C2C2×#1062245411yescharacteristic
560C2C2×#1062245711yescharacteristic
561C2C2×#1062246111yescharacteristic
562C2C2×#1062245811yescharacteristic
563C2C2×#1062272711yescharacteristic
564C2C2×#1062274711yescharacteristic
subgroupG/H
centerC24C2×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C4⋊C8C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC22×C4⋊C8D11
hypocenterC11C2×#2055
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#66880C2semidirect
4. C2×#10622542C2semidirect
6. #13069934C2direct (N × H)
7. C2×#10622189C2semidirect
8. C22×C11×C4⋊C8C2semidirect
23. C2×C11×C4⋊C8C22semidirect
29. C2×#66880C22semidirect
33. #10622542C22semidirect
34. #10622189C22semidirect
106. C22×C4×C11SD16semidirect
176. C22×C4⋊C8D11semidirect
219. C2×C4×C11C2×SD16semidirect
264. C2×C4⋊C8C2×D11semidirect
364. C2×C11#2055semidirect
425. C22×C4#4314semidirect
456. C11C2×#2055semidirect
512. C2×C4C2×#4314semidirect
557. C2#13069934direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43142
C22×#668802
C22×#668852
C2×#106225422
C2×#106225522
#130699342
C2×#106221892
C22×C11×C4⋊C82
C2×#205511