Finite Group Databasebeta

← C2×#13069700 #14780831

Subgroups — C2×#13069700 #14780831

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4314C211yesmaximal, characteristic
2C23×#4325C211yesmaximal, characteristic
3C22×#66997C211yesmaximal, characteristic, complemented
4C22×#66874C211yesmaximal, characteristic, complemented
5C2×#10622601C211yesmaximal, characteristic
6#13069700C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#103C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66997—24no—
15C2×#66997—24no—
16C2×#66997—22no—
17C2×#66997C2214yescomplemented
18C22×#4325—24no—
19C22×#4325—24no—
20C22×#4325—24no—
21C22×#4325C2214yes—
22C22×(C2×D11)⋊C4—22no—
23C22×Dic11⋊C4—22no—
24C22×C4×Dic11C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C22×#4314—24no—
27C22×#4314—24no—
28C22×#4314—24no—
29C22×#4314C2214yes—
30C2×C11×#103—24no—
31C2×C11×#103C2214yescomplemented
32#10622601—22no—
33#10622601C2214yes—
34C2×#66874—24no—
35C2×#66874C2214yescomplemented
36#10622188C2214yescomplemented
37C24×D11—21no—
38C22×Q8×C11—22no—
39C22×Q8×C11—21no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11D414yes—
45C22×Q8×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—21no—
50C23×Dic11D412yes—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—21no—
56C22×D44—22no—
57C22×D44D414yes—
58C22×D44C2312yes—
59C22×Dic22—22no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—22no—
64C22×Dic22—21no—
65C22×Dic22D414yes—
66C22×Dic22C2312yes—
67C22×C8×C11—22no—
68C22×C8×C11—22no—
69C22×C8×C11D414yes—
70C22×C8×C11C2312yes—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2312yes—
75#66997—216no—
76#66997—28no—
77#66997—28no—
78C2×#4325—232no—
79C2×#4325—28no—
80C2×#4325—28no—
81C2×#4325—28no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—48no—
84C2×Dic11⋊C4—216no—
85C2×Dic11⋊C4—28no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11D412yes—
89C2×C4×Dic11C2312yes—
90C22×C11⋊C8—22no—
91C22×C11⋊C8—22no—
92C22×C11⋊C8D414yes—
93C22×C11⋊C8C2312yes—
94C2×#4314—232no—
95C2×#4314—28no—
96C2×#4314—28no—
97C2×#4314—28no—
98C11×#103—28no—
99#66874—28no—
100C2×#2013—111nomaximal, Sylow
101C24×C11C2×D411yescharacteristic
102C23×D11—24no—
103C23×D11—22no—
104C23×D11—42no—
105C23×D11—42no—
106C23×D11—44no—
107C23×D11—44no—
108C2×Q8×C11—24no—
109C2×Q8×C11—22no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—44no—
117C2×Q8×C11—42no—
118C2×Q8×C11—44no—
119C2×Q8×C11—42no—
120C2×Q8×C11C2×D414yes—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—44no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—22no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11SD1618yescomplemented
143C22×Dic11C2×D414yes—
144C2×D44—28no—
145C2×D44—28no—
146C2×D44—24no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—42no—
153C2×D44—44no—
154C2×D44—44no—
155C2×D44—42no—
156C2×D44C2×D414yes—
157C2×Dic22—28no—
158C2×Dic22—24no—
159C2×Dic22—28no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—44no—
166C2×Dic22—42no—
167C2×Dic22—44no—
168C2×Dic22—42no—
169C2×Dic22C2×D414yes—
170C2×C8×C11—28no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11C2×D414yes—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—42no—
177#4325—232no—
178(C2×D11)⋊C4—416no—
179Dic11⋊C4—232no—
180C4×Dic11—24no—
181C4×Dic11—22no—
182C4×Dic11—22no—
183C2×C11⋊C8—28no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8C2×D414yes—
187#4314—232no—
188C23×SD16—111no—
189C23×SD16—111no—
190C22×C4⋊Q8—111no—
191C22×#103—111no—
192C22×#103D1111yescharacteristic, complemented
193C2×#390—111no—
194#2013—118no—
195C2×#336—111no—
196C23×C11#12012yes—
197C23×C11#12112yes—
198C23×C11#12712yes—
199C23×C11C2×SD1614yes—
200C23×C11#13714yes—
201C23×C11C22×D411yescharacteristic
202C22×D11—24no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11—48no—
208C22×D11—416no—
209C22×D11—88no—
210C22×D11—84no—
211C22×D11—84no—
212Q8×C11—24no—
213Q8×C11—24no—
214Q8×C11—42no—
215Q8×C11—42no—
216Q8×C11—48no—
217C2×C4×C11—24no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—48no—
221C2×C4×C11—42no—
222C2×C4×C11—44no—
223C2×C4×C11—84no—
224C2×C4×C11#12014yes—
225C2×C4×C11#12012yes—
226C2×C4×C11#12014yes—
227C2×C4×C11#12114yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12114yes—
230C2×C4×C11#12712yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—216no—
240C2×Dic11—24no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—48no—
244C2×Dic11C2×SD1618yescomplemented
245D44—24no—
246D44—24no—
247D44—42no—
248D44—42no—
249D44—48no—
250Dic22—24no—
251Dic22—24no—
252Dic22—42no—
253Dic22—42no—
254Dic22—48no—
255C8×C11—24no—
256C11⋊C8—24no—
257C23×Q8—111no—
258C23×Q8C2×D1111yescharacteristic
259C23×D4—111no—
260C22×SD16—114no—
261C22×SD16—114no—
262C22×SD16—224no—
263C22×SD16—224no—
264C22×SD16—224no—
265C22×SD16—224no—
266C22×SD16—224no—
267C22×SD16—224no—
268C23×C8—111no—
269C23×C8C2×D1111yescharacteristic
270C2×C4⋊Q8—114no—
271C2×C4⋊Q8—222no—
272C2×C4⋊Q8—224no—
273C2×C4⋊Q8—224no—
274C22×C4⋊C4—222no—
275C22×C4⋊C4C2×D1111yescharacteristic
276C22×C22⋊C4—222no—
277C22×C42—111no—
278C2×#103—24no—
279C2×#103—114no—
280C2×#103—224no—
281C2×#103C2×D1114yescomplemented
282#390—114no—
283#390—222no—
284#336—114no—
285C22×C11#39214yes—
286C22×C11#44818yes—
287C22×C11#46118yes—
288C22×C11#49214yes—
289C22×C11#49714yes—
290C22×C11C2×#12011yescharacteristic
291C22×C11C2×#12111yescharacteristic
292C22×C11C2×#12711yescharacteristic
293C22×C11C22×SD1612yes—
294C22×C11C2×#13712yes—
295C2×D11—44no—
296C2×D11—48no—
297C2×D11—82no—
298C2×D11—82no—
299C2×D11—84no—
300C2×D11—816no—
301C4×C11—44no—
302C4×C11—82no—
303C4×C11#39214yes—
304C4×C11C2×#12011yescharacteristic
305C4×C11C2×#12011yescharacteristic
306C4×C11C2×#12111yescharacteristic
307C4×C11C2×#12111yescharacteristic
308Dic11—28no—
309Dic11—44no—
310C25—221no—
311C22×Q8—22no—
312C22×Q8—21no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—114no—
318C22×Q8—112no—
319C22×Q8—222no—
320C22×Q8—221no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×Q8—222no—
324C22×Q8—222no—
325C22×Q8D4414yes—
326C22×Q8C22×D1112yes—
327C22×D4—114no—
328C22×D4—112no—
329C22×D4—222no—
330C22×D4—222no—
331C22×D4—222no—
332C22×D4—222no—
333C22×D4—221no—
334C22×D4—222no—
335C23×C4—21no—
336C23×C4—21no—
337C23×C4—112no—
338C23×C4—221no—
339C23×C4C22×D1111yescharacteristic
340C2×SD16—228no—
341C2×SD16—228no—
342C2×SD16—2232no—
343C2×SD16—228no—
344C2×SD16—228no—
345C2×SD16—2232no—
346C2×SD16—228no—
347C2×SD16—228no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—114no—
351C22×C8—112no—
352C22×C8—222no—
353C22×C8—222no—
354C22×C8C22⋊D1114yes—
355C22×C8C22×D1112yes—
356C4⋊Q8—228no—
357C4⋊Q8—2216no—
358C4⋊Q8—228no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—228no—
363C2×C4⋊C4—2216no—
364C2×C4⋊C4C22×D1112yes—
365C2×C22⋊C4—228no—
366C2×C22⋊C4—448no—
367C2×C42—112no—
368C2×C42—112no—
369C2×C42—222no—
370C2×C42—222no—
371#103—28no—
372#103—228no—
373C2×C11#201318yescomplemented
374C2×C11C2×#39211yescharacteristic
375C2×C11C2×#44812yes—
376C2×C11C2×#46112yes—
377C2×C11C2×#49211yescharacteristic
378C2×C11C2×#49711yescharacteristic
379D11—84no—
380C24—224no—
381C24—222no—
382C24—442no—
383C24—444no—
384C24—444no—
385C24—442no—
386C24D4×D1111yescharacteristic
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—28no—
390C2×Q8—28no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—42no—
396C2×Q8—44no—
397C2×Q8—44no—
398C2×Q8—42no—
399C2×Q8—114no—
400C2×Q8—224no—
401C2×Q8—222no—
402C2×Q8—228no—
403C2×Q8—228no—
404C2×Q8—222no—
405C2×Q8—222no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8—444no—
409C2×Q8—442no—
410C2×Q8—444no—
411C2×Q8—442no—
412C2×Q8C2×D4414yes—
413C2×D4—114no—
414C2×D4—228no—
415C2×D4—224no—
416C2×D4—228no—
417C2×D4—222no—
418C2×D4—222no—
419C2×D4—222no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—442no—
423C2×D4—444no—
424C2×D4—444no—
425C2×D4—442no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—44no—
432C22×C4—42no—
433C22×C4—118no—
434C22×C4—114no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—442no—
440C22×C4—442no—
441C22×C4C2×D4412yes—
442C22×C4#433912yes—
443C22×C4D4×D1111yescharacteristic
444C22×C4D4×D1112yes—
445C22×C4D4×D1112yes—
446C22×C4D4×D1112yes—
447C22×C4C2×C22⋊D1112yes—
448C22×C4C23×D1111yescharacteristic
449SD16—2232no—
450SD16—2232no—
451C2×C8—28no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—114no—
455C2×C8—228no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8C2×C22⋊D1114yes—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—42no—
462C4⋊C4—2232no—
463C22⋊C4—4416no—
464C42—224no—
465C42—222no—
466C42—222no—
467C11C2×#201311yescharacteristic, complemented, Sylow
468C23—224no—
469C23—442no—
470C23—444no—
471C23—444no—
472C23—442no—
473C23—448no—
474C23—4416no—
475C23—884no—
476C23—884no—
477C23—888no—
478C23#6693512yes—
479C23#6693712yes—
480C23SD16×D1114yes—
481C23#6697114yes—
482C23#6699312yes—
483C23C2×D4×D1111yescharacteristic
484Q8—24no—
485Q8—24no—
486Q8—42no—
487Q8—42no—
488Q8—48no—
489Q8—224no—
490Q8—224no—
491Q8—442no—
492Q8—442no—
493Q8—448no—
494D4—224no—
495D4—224no—
496D4—442no—
497D4—442no—
498D4—448no—
499C2×C4—24no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—48no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—84no—
506C2×C4—118no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—2216no—
510C2×C4—224no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—448no—
514C2×C4#6693514yes—
515C2×C4#6693512yes—
516C2×C4#6693714yes—
517C2×C4#6693712yes—
518C2×C4#6698314yes—
519C2×C4#6699014yes—
520C2×C4#6699312yes—
521C2×C4C22×D4411yescharacteristic
522C2×C4C2×#433911yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4C22×C22⋊D1111yescharacteristic
527C8—24no—
528C8—224no—
529C22—448no—
530C22—444no—
531C22—882no—
532C22—884no—
533C22—8816no—
534C22—882no—
535C22#1062241918yes—
536C22#1062243118yes—
537C22#1062257314yes—
538C22#1062278814yes—
539C22#1062280314yes—
540C22C2×#6693511yescharacteristic
541C22C2×#6693711yescharacteristic
542C22C2×SD16×D1112yes—
543C22C2×#6697112yes—
544C22C2×#6699311yescharacteristic
545C4—44no—
546C4—82no—
547C4—228no—
548C4—444no—
549C4#1062257314yes—
550C4C2×#6693511yescharacteristic
551C4C2×#6693711yescharacteristic
552C4C2×#6698311yescharacteristic
553C4C2×#6699011yescharacteristic
554C2—884no—
555C2#1306970018yesdirect product factor
556C2C2×#1062257311yescharacteristic
557C2C2×#1062241912yes—
558C2C2×#1062243112yes—
559C2C2×#1062278811yescharacteristic
560C2C2×#1062280311yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC22×#103D11
hypocenterC11C2×#2013
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C22×#66997C2semidirect
4. C22×#66874C2semidirect
6. #13069700C2direct (N × H)
7. C2×#10622188C2semidirect
8. C22×C11×#103C2semidirect
17. C2×#66997C22semidirect
31. C2×C11×#103C22semidirect
35. C2×#66874C22semidirect
36. #10622188C22semidirect
142. C22×Dic11SD16semidirect
192. C22×#103D11semidirect
244. C2×Dic11C2×SD16semidirect
281. C2×#103C2×D11semidirect
373. C2×C11#2013semidirect
467. C11C2×#2013semidirect
555. C2#13069700direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43142
C23×#43252
C22×#669972
C22×#668742
C2×#106226012
#130697002
C2×#106221882
C22×C11×#1032
C2×#201311