Finite Group Databasebeta

← C2×#13069275 #14756309

Subgroups — C2×#13069275 #14756309

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622577C211yesmaximal, characteristic, complemented
2C2×#10622828C211yesmaximal, characteristic
3C22×#66897C211yesmaximal, characteristic
4C2×#10622714C211yesmaximal, characteristic, complemented
5#13069275C218yesmaximal, direct product factor
6C2×#10622168C211yesmaximal, characteristic, complemented
7C2×#10622190C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C2×C11×#102—21no—
17C2×C11×#102—21no—
18C2×C11×#102—22no—
19C2×C11×#102C2214yes—
20C2×#66897C418yescomplemented
21C2×#66897C2214yes—
22#10622828—22no—
23#10622828C2214yes—
24C2×#66896—21no—
25C2×#66896—21no—
26#10622714—22no—
27#10622714C2214yescomplemented
28C2×#66879—21no—
29C2×C8×Dic11—21no—
30#10622577—22no—
31#10622577C2214yescomplemented
32C2×#66872—21no—
33C2×#66871—21no—
34#10622190C2214yescomplemented
35#10622168C2214yescomplemented
36C25×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11—22no—
45C22×D4×C11C2×C414yes—
46C22×D4×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C8×C11—22no—
50C22×C8×C11—22no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C22×C8×C11D412yes—
54C22×C8×C11C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2312yes—
61C2×C22⋊Dic11—21no—
62#66979—21no—
63#66979—21no—
64#66979D412yes—
65#66979C2312yes—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4×Dic11—21no—
69C2×#4318—21no—
70C2×#4318—21no—
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318—21no—
74C2×#4318—22no—
75C2×#4318—22no—
76C2×#4318C2×C414yes—
77C2×#4318C2×C414yes—
78C2×#4318C2312yes—
79C2×#4318C2312yes—
80C2×#4318C2312yes—
81C22×C11⋊C8—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C11×#102—24no—
85C11×#102—24no—
86#66897C2×C4116yescomplemented
87#66896—24no—
88#66896—24no—
89#66879—24no—
90C8×Dic11—24no—
91#66872—24no—
92#66871—24no—
93C2×#1931—111nomaximal, Sylow
94C24×C11—24no—
95C24×C11—22no—
96C24×C11—41no—
97C24×C11—41no—
98C24×C11—42no—
99C24×C11—82no—
100C24×C11—82no—
101C24×C11#4111yescharacteristic
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—41no—
113C2×D4×C11—41no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11C22×C414yes—
120C22×C4×C11—22no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—82no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—24no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11C2×D412yes—
142C2×C8×C11C2×D412yes—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C22⋊Dic11—22no—
148C22⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11C2×D412yes—
152C4⋊Dic11C2×D412yes—
153C4×Dic11—22no—
154C4×Dic11—22no—
155#4318—24no—
156#4318—24no—
157#4318—22no—
158#4318—22no—
159#4318—22no—
160#4318—22no—
161#4318—42no—
162#4318C22×C414yes—
163#4318C22×C414yes—
164C2×C11⋊C8—24no—
165C2×C11⋊C8—24no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170C2×#428—111no—
171C2×#418—111no—
172C22×#102D1111yescharacteristic
173C22×#100—111no—
174C2×#405—111no—
175#1931—118no—
176C2×#343—111no—
177C2×#341—111no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—24no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—44no—
184C23×C11—44no—
185C23×C11—88no—
186C23×C11—82no—
187C23×C11—82no—
188C23×C11—88no—
189C23×C11—82no—
190C23×C11—82no—
191C23×C11—82no—
192C23×C11—82no—
193C23×C11#11712yes—
194C23×C11#12111yescharacteristic
195C23×C11#12111yescharacteristic
196C23×C11#12612yes—
197C23×C11C2×#4111yescharacteristic
198D4×C11—24no—
199D4×C11—24no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—44no—
204C2×C4×C11—42no—
205C2×C4×C11—82no—
206C2×C4×C11—82no—
207C2×C4×C11—82no—
208C2×C4×C11#11712yes—
209C2×C4×C11C4×D412yes—
210C2×C4×C11C4×D412yes—
211C2×C4×C11C4×D412yes—
212C2×C4×C11C4×D412yes—
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12312yes—
216C2×C4×C11#12312yes—
217C2×C4×C11#12412yes—
218C2×C4×C11#12412yes—
219C2×C4×C11#12612yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C8×C11—22no—
231C8×C11—22no—
232C11⋊C8—24no—
233C11⋊C8—24no—
234C11⋊C8—42no—
235C23×D4C2×D1111yescharacteristic
236C22×M16—111no—
237C22×M16—111no—
238C22×M16—111no—
239C23×C8C2×D1111yescharacteristic
240C2×#117—111no—
241C22×C4⋊C4C2×D1111yescharacteristic
242#428—114no—
243#428—222no—
244C2×#107—221no—
245C2×#106—221no—
246#418—114no—
247#418—222no—
248C2×#102—21no—
249C2×#102—21no—
250C2×#102—22no—
251C2×#102—221no—
252C2×#102—221no—
253C2×#102C2×D1114yes—
254C2×#100—114no—
255C2×#100—118no—
256#405—114no—
257#405—222no—
258C2×#97—221no—
259C2×C4×C8—221no—
260#343—114no—
261#341—114no—
262C22×C11—24no—
263C22×C11—24no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—44no—
269C22×C11—84no—
270C22×C11—84no—
271C22×C11—88no—
272C22×C11—88no—
273C22×C11—82no—
274C22×C11—82no—
275C22×C11#38812yes—
276C22×C11#38812yes—
277C22×C11#47112yes—
278C22×C11#47212yes—
279C22×C11C2×#11711yescharacteristic
280C22×C11C2×#12111yescharacteristic
281C22×C11C2×#12611yescharacteristic
282C4×C11—82no—
283C4×C11#38812yes—
284C4×C11#38812yes—
285C4×C11C2×C4×D411yescharacteristic
286C4×C11C2×C4×D411yescharacteristic
287C4×C11C2×#12311yescharacteristic
288C4×C11C2×#12411yescharacteristic
289Dic11—42no—
290Dic11—42no—
291C25—21no—
292C22×D4—22no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—22no—
296C22×D4—21no—
297C22×D4—22no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C4×D1114yes—
301C22×D4C22×D1112yes—
302C23×C4—21no—
303C23×C4C22×D1111yescharacteristic
304C2×M16—114no—
305C2×M16—114no—
306C2×M16—112no—
307C2×M16—112no—
308C2×M16—112no—
309C2×M16—222no—
310C2×M16—221no—
311C2×M16—222no—
312C2×M16—221no—
313C2×M16—221no—
314C2×M16—222no—
315C2×M16—222no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—221no—
319C22×C8—221no—
320C22×C8—221no—
321C22×C8C22⋊D1111yescharacteristic
322C22×C8C22⋊D1111yescharacteristic
323C22×C8C22⋊D1112yes—
324C22×C8C22×D1112yes—
325#117—112no—
326#117—112no—
327#117—221no—
328#117—221no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4C22×D1112yes—
337C2×C22⋊C4—221no—
338C2×C42—221no—
339#107—224no—
340#106—224no—
341#102—24no—
342#102—24no—
343#102—224no—
344#102—224no—
345#100—1116no—
346#97—224no—
347C4×C8—224no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—84no—
352C2×C11#193114yescomplemented
353C2×C11C2×#38811yescharacteristic
354C2×C11C2×#47111yescharacteristic
355C2×C11C2×#47211yescharacteristic
356C24—24no—
357C24—22no—
358C24—42no—
359C24—41no—
360C24—41no—
361C24—82no—
362C24—82no—
363C24#434111yescharacteristic
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—24no—
367C2×D4—24no—
368C2×D4—24no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4C2×C4×D1114yes—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—82no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4C2×C4×D1112yes—
389C22×C4#433912yes—
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4#434111yescharacteristic
393C22×C4#434112yes—
394C22×C4#434112yes—
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C23×D1111yescharacteristic
398M16—114no—
399M16—114no—
400M16—224no—
401M16—224no—
402M16—222no—
403M16—222no—
404M16—222no—
405M16—222no—
406M16—442no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—24no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—224no—
413C2×C8—224no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—222no—
417C2×C8—442no—
418C2×C8C2×C22⋊D1112yes—
419C2×C8C2×C22⋊D1112yes—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—112no—
425C4⋊C4—112no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C22⋊C4—222no—
429C22⋊C4—222no—
430C42—222no—
431C42—222no—
432C11C2×#193111yescharacteristic, complemented, Sylow
433C23—22no—
434C23—22no—
435C23—24no—
436C23—42no—
437C23—44no—
438C23—44no—
439C23—42no—
440C23—82no—
441C23—82no—
442C23—88no—
443C23—82no—
444C23—82no—
445C23—88no—
446C23—82no—
447C23—82no—
448C23#6693012yes—
449C23#6693212yes—
450C23#6699111yescharacteristic
451C23#6699111yescharacteristic
452C23C2×#434111yescharacteristic
453D4—24no—
454D4—24no—
455D4—42no—
456D4—44no—
457D4—44no—
458D4—42no—
459C2×C4—42no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4#6693012yes—
468C2×C4#6693212yes—
469C2×C4(C22⋊D11)⋊C412yes—
470C2×C4(C22⋊D11)⋊C412yes—
471C2×C4#6693812yes—
472C2×C4#6693812yes—
473C2×C4C4×C22⋊D1112yes—
474C2×C4C4×C22⋊D1112yes—
475C2×C4#6698812yes—
476C2×C4#6698812yes—
477C2×C4#6699111yescharacteristic
478C2×C4#6699111yescharacteristic
479C2×C4C22×C4×D1111yescharacteristic
480C2×C4C2×#433911yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C2×C4C2×#434111yescharacteristic
483C2×C4C2×#434111yescharacteristic
484C2×C4C22×C22⋊D1111yescharacteristic
485C8—22no—
486C8—22no—
487C8—224no—
488C8—224no—
489C8—442no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—24no—
495C22—24no—
496C22—44no—
497C22—84no—
498C22—84no—
499C22—88no—
500C22—82no—
501C22—82no—
502C22—88no—
503C22#1062255712yes—
504C22#1062255712yes—
505C22#1062277312yes—
506C22#1062279012yes—
507C22C2×#6693011yescharacteristic
508C22C2×#6693211yescharacteristic
509C22C2×#6699111yescharacteristic
510C4—82no—
511C4—442no—
512C4—442no—
513C4#1062255712yes—
514C4#1062255712yes—
515C4C2×(C22⋊D11)⋊C411yescharacteristic
516C4C2×#6693811yescharacteristic
517C4C2×C4×C22⋊D1111yescharacteristic
518C4C2×#6698811yescharacteristic
519C2—21no—
520C2—21no—
521C2—22no—
522C2—84no—
523C2#1306927514yesdirect product factor
524C2C2×#1062255711yescharacteristic
525C2C2×#1062279011yescharacteristic
526C2C2×#1062277311yescharacteristic
subgroupG/H
centerC23#66991
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC23×C11#121
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC22×#102D11
hypocenterC11C2×#1931
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C2×#10622577C2semidirect
4. C2×#10622714C2semidirect
5. #13069275C2direct (N × H)
6. C2×#10622168C2semidirect
7. C2×#10622190C2semidirect
20. C2×#66897C4semidirect
27. #10622714C22semidirect
31. #10622577C22semidirect
34. #10622190C22semidirect
35. #10622168C22semidirect
86. #66897C2×C4semidirect
352. C2×C11#1931semidirect
432. C11C2×#1931semidirect
523. C2#13069275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106225772
C2×#106228282
C22×#668972
C2×#106227142
#130692752
C2×#106221682
C2×#106221902
C22×C11×#1022
C2×#193111