Finite Group Databasebeta

← C2×#13069712 #14780825

Subgroups — C2×#13069712 #14780825

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×Dic44C211yesmaximal, characteristic, complemented
2C23×#4324C211yesmaximal, characteristic
3C22×#66989C211yesmaximal, characteristic
4C22×#66874C211yesmaximal, characteristic, complemented
5C2×#10622587C211yesmaximal, characteristic, complemented
6#13069712C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C22⋊Dic11—22no—
15C2×#66989—24no—
16C2×#66989—24no—
17C2×#66989—22no—
18C2×#66989C2214yes—
19C22×#4324—24no—
20C22×#4324—24no—
21C22×#4324—24no—
22C22×#4324C2214yes—
23C22×C4×Dic11C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C22×Dic44—24no—
26C22×Dic44—24no—
27C22×Dic44—24no—
28C22×Dic44C2214yescomplemented
29C2×C11×#102—24no—
30C2×C11×#102C2214yes—
31C2×C11⋊#95—22no—
32#10622587—22no—
33#10622587C2214yescomplemented
34C2×#66874—24no—
35C2×#66874C2214yescomplemented
36#10622188C2214yescomplemented
37C25×C11—21no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—21no—
43C22×D4×C11—22no—
44C22×D4×C11D414yes—
45C22×D4×C11C2312yes—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11—21no—
50C23×Dic11D412yes—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—22no—
59C22×Dic22—22no—
60C22×Dic22—21no—
61C22×Dic22—21no—
62C22×Dic22—22no—
63C22×Dic22D414yes—
64C22×Dic22D414yes—
65C22×Dic22C2312yes—
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—
75C2×C22⋊Dic11—216no—
76C2×C22⋊Dic11—28no—
77#66989—216no—
78#66989—28no—
79#66989—28no—
80C2×#4324—232no—
81C2×#4324—28no—
82C2×#4324—28no—
83C2×#4324—28no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11D412yes—
87C2×C4×Dic11C2312yes—
88C22×C11⋊C8—22no—
89C22×C11⋊C8—22no—
90C22×C11⋊C8D414yes—
91C22×C11⋊C8C2312yes—
92C2×Dic44—232no—
93C2×Dic44—28no—
94C2×Dic44—28no—
95C2×Dic44—28no—
96C11×#102—28no—
97C11⋊#95—28no—
98#66874—28no—
99C2×#2015—111nomaximal, Sylow
100C24×C11—24no—
101C24×C11—22no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11—44no—
105C24×C11—44no—
106C24×C11C2×D411yescharacteristic
107C2×D4×C11—28no—
108C2×D4×C11—24no—
109C2×D4×C11—28no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11C2×D414yes—
120C22×C4×C11—22no—
121C22×C4×C11—42no—
122C22×C4×C11—44no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11C2×D414yes—
143C2×Dic22—28no—
144C2×Dic22—28no—
145C2×Dic22—28no—
146C2×Dic22—24no—
147C2×Dic22—28no—
148C2×Dic22—24no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—44no—
160C2×Dic22—42no—
161C2×Dic22—44no—
162C2×Dic22—42no—
163C2×Dic22—44no—
164C2×Dic22—44no—
165C2×Dic22—42no—
166C2×Dic22—42no—
167C2×Dic22C2×D414yes—
168C2×Dic22C2×D414yes—
169C2×C8×C11—28no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11C2×D414yes—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—42no—
176C22⋊Dic11—232no—
177#4324—232no—
178C4×Dic11—24no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C2×C11⋊C8—28no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8C2×D414yes—
185Dic44—232no—
186C23×Q16—111no—
187C23×SD16—111no—
188C22×#124—111no—
189C22×#103—111no—
190C22×#102D1111yescharacteristic
191C2×#391—111no—
192#2015—118no—
193C2×#336—111no—
194C23×C11—24no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—48no—
200C23×C11—416no—
201C23×C11—88no—
202C23×C11—84no—
203C23×C11—84no—
204C23×C11#12012yes—
205C23×C11#12112yes—
206C23×C11#12712yes—
207C23×C11#13514yes—
208C23×C11#13714yes—
209C23×C11C22×D411yescharacteristic
210D4×C11—24no—
211D4×C11—24no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—48no—
215C2×C4×C11—42no—
216C2×C4×C11—44no—
217C2×C4×C11—84no—
218C2×C4×C11#12014yes—
219C2×C4×C11#12012yes—
220C2×C4×C11#12014yes—
221C2×C4×C11#12114yes—
222C2×C4×C11#12112yes—
223C2×C4×C11#12114yes—
224C2×C4×C11#12712yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—48no—
241C2×Dic11—48no—
242C2×Dic11—48no—
243Dic22—24no—
244Dic22—24no—
245Dic22—24no—
246Dic22—24no—
247Dic22—42no—
248Dic22—42no—
249Dic22—42no—
250Dic22—42no—
251Dic22—48no—
252Dic22—48no—
253C8×C11—24no—
254C11⋊C8—24no—
255C23×Q8—111no—
256C23×Q8—111no—
257C23×D4C2×D1111yescharacteristic
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×C8C2×D1111yescharacteristic
268C2×#124—114no—
269C2×#124—222no—
270C2×#124—224no—
271C2×#124—224no—
272C22×C4⋊C4C2×D1111yescharacteristic
273C22×C22⋊C4—222no—
274C22×C42—111no—
275C2×#103—114no—
276C2×#103—224no—
277C2×#102—24no—
278C2×#102C2×D1114yes—
279#391—114no—
280#391—222no—
281C2×#95—222no—
282#336—114no—
283C22×C11—44no—
284C22×C11—48no—
285C22×C11—82no—
286C22×C11—82no—
287C22×C11—84no—
288C22×C11—816no—
289C22×C11#39214yes—
290C22×C11#45218yes—
291C22×C11#46418yes—
292C22×C11#49514yes—
293C22×C11#49714yes—
294C22×C11C2×#12011yescharacteristic
295C22×C11C2×#12111yescharacteristic
296C22×C11C2×#12711yescharacteristic
297C22×C11C2×#13512yes—
298C22×C11C2×#13712yes—
299C4×C11—82no—
300C4×C11#39214yes—
301C4×C11C2×#12011yescharacteristic
302C4×C11C2×#12011yescharacteristic
303C4×C11C2×#12111yescharacteristic
304C4×C11C2×#12111yescharacteristic
305Dic11—44no—
306Dic11—44no—
307Dic11—44no—
308C25—21no—
309C22×Q8—114no—
310C22×Q8—114no—
311C22×Q8—112no—
312C22×Q8—112no—
313C22×Q8—222no—
314C22×Q8—222no—
315C22×Q8—221no—
316C22×Q8—221no—
317C22×Q8—222no—
318C22×Q8—222no—
319C22×Q8—222no—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×Q8—222no—
324C22×Q8—222no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—21no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4D4414yes—
332C22×D4C22×D1112yes—
333C23×C4—21no—
334C23×C4—112no—
335C23×C4—221no—
336C23×C4—221no—
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—22no—
347C22×C8—22no—
348C22×C8—114no—
349C22×C8—112no—
350C22×C8—222no—
351C22×C8—222no—
352C22×C8C22⋊D1114yes—
353C22×C8C22×D1112yes—
354#124—228no—
355#124—2216no—
356#124—228no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C22×D1112yes—
361C2×C22⋊C4—228no—
362C2×C22⋊C4—2216no—
363C2×C42—112no—
364C2×C42—112no—
365C2×C42—222no—
366C2×C42—222no—
367#103—228no—
368#102—28no—
369#95—228no—
370C2×C11—84no—
371C2×C11#201518yescomplemented
372C2×C11C2×#39211yescharacteristic
373C2×C11C2×#45212yes—
374C2×C11C2×#46412yes—
375C2×C11C2×#49511yescharacteristic
376C2×C11C2×#49711yescharacteristic
377C24—24no—
378C24—22no—
379C24—42no—
380C24—44no—
381C24—44no—
382C24—42no—
383C24D4×D1111yescharacteristic
384C2×Q8—114no—
385C2×Q8—114no—
386C2×Q8—224no—
387C2×Q8—224no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×Q8—228no—
391C2×Q8—228no—
392C2×Q8—228no—
393C2×Q8—228no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8—222no—
402C2×Q8—442no—
403C2×Q8—444no—
404C2×Q8—442no—
405C2×Q8—444no—
406C2×Q8—444no—
407C2×Q8—444no—
408C2×Q8—442no—
409C2×Q8—442no—
410C2×D4—28no—
411C2×D4—24no—
412C2×D4—28no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—44no—
419C2×D4—42no—
420C2×D4—44no—
421C2×D4—42no—
422C2×D4C2×D4414yes—
423C22×C4—22no—
424C22×C4—44no—
425C22×C4—42no—
426C22×C4—114no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4—442no—
437C22×C4—442no—
438C22×C4C2×D4412yes—
439C22×C4#433912yes—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1112yes—
442C22×C4D4×D1112yes—
443C22×C4D4×D1112yes—
444C22×C4C2×C22⋊D1112yes—
445C22×C4C23×D1111yescharacteristic
446Q16—2232no—
447SD16—2232no—
448C2×C8—28no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—114no—
452C2×C8—228no—
453C2×C8—222no—
454C2×C8—222no—
455C2×C8C2×C22⋊D1114yes—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C22⋊C4—2232no—
460C42—224no—
461C42—222no—
462C42—222no—
463C11C2×#201511yescharacteristic, complemented, Sylow
464C23—24no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—42no—
469C23—48no—
470C23—416no—
471C23—84no—
472C23—84no—
473C23—88no—
474C23#6693512yes—
475C23#6693712yes—
476C23#6696514yes—
477C23#6696814yes—
478C23#6699312yes—
479C23C2×D4×D1111yescharacteristic
480Q8—224no—
481Q8—224no—
482Q8—224no—
483Q8—224no—
484Q8—442no—
485Q8—442no—
486Q8—442no—
487Q8—442no—
488Q8—448no—
489Q8—448no—
490D4—24no—
491D4—24no—
492D4—42no—
493D4—42no—
494D4—48no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—84no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—448no—
508C2×C4—448no—
509C2×C4—448no—
510C2×C4#6693514yes—
511C2×C4#6693512yes—
512C2×C4#6693714yes—
513C2×C4#6693712yes—
514C2×C4#6698314yes—
515C2×C4#6699014yes—
516C2×C4#6699312yes—
517C2×C4C22×D4411yescharacteristic
518C2×C4C2×#433911yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C22×C22⋊D1111yescharacteristic
523C8—24no—
524C8—224no—
525C22—48no—
526C22—44no—
527C22—82no—
528C22—84no—
529C22—816no—
530C22—82no—
531C22#1062238018yes—
532C22#1062239618yes—
533C22#1062257314yes—
534C22#1062276814yes—
535C22#1062278014yes—
536C22C2×#6693511yescharacteristic
537C22C2×#6693711yescharacteristic
538C22C2×#6696512yes—
539C22C2×#6696812yes—
540C22C2×#6699311yescharacteristic
541C4—82no—
542C4—444no—
543C4—444no—
544C4—444no—
545C4#1062257314yes—
546C4C2×#6693511yescharacteristic
547C4C2×#6693711yescharacteristic
548C4C2×#6698311yescharacteristic
549C4C2×#6699011yescharacteristic
550C2—84no—
551C2#1306971218yesdirect product factor
552C2C2×#1062257311yescharacteristic
553C2C2×#1062239612yes—
554C2C2×#1062238012yes—
555C2C2×#1062276811yescharacteristic
556C2C2×#1062278011yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC22×#102D11
hypocenterC11C2×#2015
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C23×Dic44C2semidirect
4. C22×#66874C2semidirect
5. C2×#10622587C2semidirect
6. #13069712C2direct (N × H)
7. C2×#10622188C2semidirect
28. C22×Dic44C22semidirect
33. #10622587C22semidirect
35. C2×#66874C22semidirect
36. #10622188C22semidirect
371. C2×C11#2015semidirect
463. C11C2×#2015semidirect
551. C2#13069712direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic442
C23×#43242
C22×#669892
C22×#668742
C2×#106225872
#130697122
C2×#106221882
C22×C11×#1022
C2×#201511