Finite Group Databasebeta

← C2×#13069709 #14780822

Subgroups — C2×#13069709 #14780822

Order 2816.

2166 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4326C211yesmaximal, characteristic, complemented
2C23×#4325C211yesmaximal, characteristic
3C22×#66928C211yesmaximal, characteristic
4C22×#66874C211yesmaximal, characteristic, complemented
5C22×#66873C211yesmaximal, characteristic
6#13069709C218yesmaximal, direct product factor
7C2×#10622162C211yesmaximal, characteristic, complemented
8C2×C11×#391C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×#4326—24no—
15C22×#4326—24no—
16C22×#4326—24no—
17C22×#4326C2214yescomplemented
18C22×#4325—24no—
19C22×#4325—24no—
20C22×#4325—24no—
21C22×#4325C2214yes—
22C22×(C2×D11)⋊C4—22no—
23C23×C11⋊C8C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C2×#66928—24no—
26C2×#66928—24no—
27C2×#66928—22no—
28C2×#66928C2214yes—
29C11×#391—22no—
30C11×#391C2214yescomplemented
31C2×C11×#95—22no—
32C2×#66874—24no—
33C2×#66874C2214yescomplemented
34C2×#66873—24no—
35C2×#66873C2214yes—
36#10622162C2214yescomplemented
37C24×D11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—22no—
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×C11D412yes—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—21no—
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—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2312yes—
71C2×C42×C11—22no—
72C2×C42×C11—22no—
73C2×C42×C11D412yes—
74C2×C42×C11C2312yes—
75C2×#4326—232no—
76C2×#4326—28no—
77C2×#4326—28no—
78C2×#4326—28no—
79C2×#4325—232no—
80C2×#4325—28no—
81C2×#4325—28no—
82C2×#4325—28no—
83C2×(C2×D11)⋊C4—216no—
84C2×(C2×D11)⋊C4—28no—
85C22×C11⋊C8—22no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8D414yes—
90C22×C11⋊C8D414yes—
91C22×C11⋊C8C2312yes—
92C22×C11⋊C8C2312yes—
93#66928—216no—
94#66928—28no—
95#66928—28no—
96C11×#95—28no—
97#66874—28no—
98#66873—28no—
99C2×#2015—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C23×D11—24no—
102C23×D11—22no—
103C23×D11—42no—
104C23×D11—42no—
105C23×D11—44no—
106C23×D11—44no—
107C2×Q8×C11—24no—
108C2×Q8×C11—22no—
109C2×Q8×C11—28no—
110C2×Q8×C11—28no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—42no—
116C2×Q8×C11—44no—
117C2×Q8×C11—44no—
118C2×Q8×C11—42no—
119C2×Q8×C11C2×D414yes—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—44no—
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—42no—
142C22×Dic11—42no—
143C2×D44—24no—
144C2×D44—28no—
145C2×D44—28no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—44no—
152C2×D44—44no—
153C2×D44—42no—
154C2×D44—42no—
155C2×D44C2×D414yes—
156C2×Dic22—28no—
157C2×Dic22—24no—
158C2×Dic22—28no—
159C2×Dic22—22no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22—44no—
165C2×Dic22—44no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22C2×D414yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—42no—
172C42×C11—24no—
173C42×C11—22no—
174C42×C11—22no—
175#4326—232no—
176#4325—232no—
177(C2×D11)⋊C4—232no—
178C2×C11⋊C8—28no—
179C2×C11⋊C8—28no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8C2×D414yes—
185C2×C11⋊C8C2×D414yes—
186C23×Q16—111no—
187C23×SD16—111no—
188C22×#124—111no—
189C22×#103—111no—
190C22×#102—111no—
191C2×#391D1111yescharacteristic, complemented
192#2015—118no—
193C2×#336—111no—
194C23×C11#12012yes—
195C23×C11#12112yes—
196C23×C11#12712yes—
197C23×C11#13514yes—
198C23×C11#13714yes—
199C23×C11C22×D411yescharacteristic
200C22×D11—24no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11—48no—
206C22×D11—416no—
207C22×D11—88no—
208C22×D11—84no—
209C22×D11—84no—
210Q8×C11—24no—
211Q8×C11—24no—
212Q8×C11—42no—
213Q8×C11—42no—
214Q8×C11—48no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—48no—
222C2×C4×C11—48no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11—84no—
226C2×C4×C11#12014yes—
227C2×C4×C11#12014yes—
228C2×C4×C11#12012yes—
229C2×C4×C11#12114yes—
230C2×C4×C11#12114yes—
231C2×C4×C11#12112yes—
232C2×C4×C11#12712yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×Dic11—24no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—48no—
243D44—24no—
244D44—24no—
245D44—42no—
246D44—42no—
247D44—48no—
248Dic22—24no—
249Dic22—24no—
250Dic22—42no—
251Dic22—42no—
252Dic22—48no—
253C11⋊C8—24no—
254C11⋊C8—24no—
255C23×Q8—111no—
256C23×Q8C2×D1111yescharacteristic
257C23×D4—111no—
258C22×Q16—114no—
259C22×Q16—224no—
260C22×Q16—224no—
261C22×Q16—224no—
262C22×SD16—114no—
263C22×SD16—224no—
264C22×SD16—224no—
265C22×SD16—224no—
266C23×C8—111no—
267C23×C8—111no—
268C2×#124—114no—
269C2×#124—224no—
270C2×#124—224no—
271C2×#124—222no—
272C22×C4⋊C4C2×D1111yescharacteristic
273C22×C22⋊C4—222no—
274C22×C42C2×D1111yescharacteristic
275C2×#103—114no—
276C2×#103—224no—
277C2×#102—114no—
278C2×#102—224no—
279#391—22no—
280#391C2×D1114yescomplemented
281C2×#95—22no—
282#336—114no—
283C22×C11#39214yes—
284C22×C11#45218yes—
285C22×C11#46418yes—
286C22×C11#49514yes—
287C22×C11#49714yes—
288C22×C11C2×#12011yescharacteristic
289C22×C11C2×#12111yescharacteristic
290C22×C11C2×#12711yescharacteristic
291C22×C11C2×#13512yes—
292C22×C11C2×#13712yes—
293C2×D11—44no—
294C2×D11—48no—
295C2×D11—82no—
296C2×D11—82no—
297C2×D11—84no—
298C2×D11—816no—
299C4×C11—44no—
300C4×C11—44no—
301C4×C11—82no—
302C4×C11#39214yes—
303C4×C11C2×#12011yescharacteristic
304C4×C11C2×#12011yescharacteristic
305C4×C11C2×#12111yescharacteristic
306C4×C11C2×#12111yescharacteristic
307Dic11—44no—
308C25—221no—
309C22×Q8—22no—
310C22×Q8—21no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—114no—
316C22×Q8—112no—
317C22×Q8—222no—
318C22×Q8—221no—
319C22×Q8—222no—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×Q8D4414yes—
324C22×Q8C22×D1112yes—
325C22×D4—114no—
326C22×D4—112no—
327C22×D4—222no—
328C22×D4—222no—
329C22×D4—222no—
330C22×D4—222no—
331C22×D4—222no—
332C22×D4—221no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—221no—
336C23×C4C22⋊D1112yes—
337C23×C4C22×D1111yescharacteristic
338C2×Q16—228no—
339C2×Q16—228no—
340C2×Q16—2232no—
341C2×Q16—228no—
342C2×SD16—228no—
343C2×SD16—228no—
344C2×SD16—2232no—
345C2×SD16—228no—
346C22×C8—114no—
347C22×C8—114no—
348C22×C8—112no—
349C22×C8—112no—
350C22×C8—222no—
351C22×C8—222no—
352C22×C8—222no—
353C22×C8—222no—
354#124—228no—
355#124—228no—
356#124—2216no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C22×D1112yes—
361C2×C22⋊C4—2216no—
362C2×C22⋊C4—228no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42C22⋊D1112yes—
366C2×C42C22×D1112yes—
367#103—228no—
368#102—228no—
369#95—28no—
370C2×C11#201518yescomplemented
371C2×C11C2×#39211yescharacteristic
372C2×C11C2×#45212yes—
373C2×C11C2×#46412yes—
374C2×C11C2×#49511yescharacteristic
375C2×C11C2×#49711yescharacteristic
376D11—84no—
377C24—224no—
378C24—222no—
379C24—442no—
380C24—442no—
381C24—444no—
382C24—444no—
383C24C2×C22⋊D1111yescharacteristic
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—28no—
387C2×Q8—28no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—44no—
393C2×Q8—44no—
394C2×Q8—42no—
395C2×Q8—42no—
396C2×Q8—114no—
397C2×Q8—224no—
398C2×Q8—222no—
399C2×Q8—228no—
400C2×Q8—228no—
401C2×Q8—222no—
402C2×Q8—222no—
403C2×Q8—222no—
404C2×Q8—222no—
405C2×Q8—444no—
406C2×Q8—444no—
407C2×Q8—442no—
408C2×Q8—442no—
409C2×Q8C2×D4414yes—
410C2×D4—114no—
411C2×D4—228no—
412C2×D4—228no—
413C2×D4—224no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—222no—
418C2×D4—222no—
419C2×D4—444no—
420C2×D4—444no—
421C2×D4—442no—
422C2×D4—442no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—44no—
433C22×C4—224no—
434C22×C4—222no—
435C22×C4—442no—
436C22×C4—442no—
437C22×C4C2×D4412yes—
438C22×C4#433912yes—
439C22×C4D4×D1112yes—
440C22×C4D4×D1112yes—
441C22×C4D4×D1112yes—
442C22×C4D4×D1112yes—
443C22×C4C2×C22⋊D1114yes—
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
446Q16—2232no—
447SD16—2232no—
448C2×C8—114no—
449C2×C8—114no—
450C2×C8—228no—
451C2×C8—228no—
452C2×C8—222no—
453C2×C8—222no—
454C2×C8—222no—
455C2×C8—222no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C22⋊C4—2232no—
460C42—24no—
461C42—22no—
462C42—22no—
463C11C2×#201511yescharacteristic, complemented, Sylow
464C23—224no—
465C23—442no—
466C23—442no—
467C23—444no—
468C23—448no—
469C23—444no—
470C23—4416no—
471C23—888no—
472C23—884no—
473C23—884no—
474C23#6698312yes—
475C23#6699012yes—
476C23#6699312yes—
477C23#6699514yes—
478C23#6700314yes—
479C23C22×C22⋊D1111yescharacteristic
480Q8—24no—
481Q8—24no—
482Q8—42no—
483Q8—42no—
484Q8—48no—
485Q8—224no—
486Q8—224no—
487Q8—442no—
488Q8—442no—
489Q8—448no—
490D4—224no—
491D4—224no—
492D4—442no—
493D4—442no—
494D4—448no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—48no—
502C2×C4—48no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—84no—
506C2×C4—224no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—448no—
510C2×C4#6693514yes—
511C2×C4#6693514yes—
512C2×C4#6693714yes—
513C2×C4#6693714yes—
514C2×C4#6698312yes—
515C2×C4#6699012yes—
516C2×C4#6699312yes—
517C2×C4C22×D4411yescharacteristic
518C2×C4C2×#433911yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C8—224no—
524C8—224no—
525C22—448no—
526C22—444no—
527C22—882no—
528C22—884no—
529C22—8816no—
530C22—882no—
531C22#1062257314yes—
532C22#1062264118yes—
533C22#1062266018yes—
534C22#1062267214yes—
535C22#1062269914yes—
536C22C2×#6698311yescharacteristic
537C22C2×#6699011yescharacteristic
538C22C2×#6699311yescharacteristic
539C22C2×#6699512yes—
540C22C2×#6700312yes—
541C4—44no—
542C4—44no—
543C4—82no—
544C4—444no—
545C4#1062257314yes—
546C4C2×#6693511yescharacteristic
547C4C2×#6693511yescharacteristic
548C4C2×#6693711yescharacteristic
549C4C2×#6693711yescharacteristic
550C2—884no—
551C2#1306970918yesdirect product factor
552C2C2×#1062257311yescharacteristic
553C2C2×#1062266012yes—
554C2C2×#1062264112yes—
555C2C2×#1062267211yescharacteristic
556C2C2×#1062269911yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#391C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC2×#391D11
hypocenterC11C2×#2015
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
1. C23×#4326C2semidirect
4. C22×#66874C2semidirect
6. #13069709C2direct (N × H)
7. C2×#10622162C2semidirect
8. C2×C11×#391C2semidirect
17. C22×#4326C22semidirect
30. C11×#391C22semidirect
33. C2×#66874C22semidirect
36. #10622162C22semidirect
191. C2×#391D11semidirect
280. #391C2×D11semidirect
370. C2×C11#2015semidirect
463. C11C2×#2015semidirect
551. C2#13069709direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43262
C23×#43252
C22×#669282
C22×#668742
C22×#668732
#130697092
C2×#106221622
C2×C11×#3912
C2×#201511