Finite Group Databasebeta

← C2×#13069861 #14781454

Subgroups — C2×#13069861 #14781454

Order 2816.

1542 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic
2C22×#66880C211yesmaximal, characteristic
3C22×#66899C211yesmaximal, characteristic
4C22×#66874C211yesmaximal, characteristic
5C2×#10622598C211yesmaximal, characteristic
6#13069861C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic
8C22×C11×#103C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66997—24no—
14C2×#66997—24no—
15C2×#66997—22no—
16C2×#66997C2214yes—
17C22×C4⋊Dic11—21no—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4—21no—
20C22×Dic11⋊C4—21no—
21C22×C4×Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C11×#103—24no—
24C2×C11×#103C2214yes—
25C2×#66899—24no—
26C2×#66899C2214yes—
27C2×C11⋊#95—21no—
28C2×#66880—24no—
29C2×#66880C2214yes—
30#10622598—22no—
31#10622598C2214yes—
32C2×#66874—24no—
33C2×#66874C2214yes—
34#10622188C2214yes—
35C22×Q8×C11—22no—
36C22×Q8×C11—21no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11D414yes—
42C22×Q8×C11C2312yes—
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11—21no—
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×Dic22—22no—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—21no—
56C22×Dic22D414yes—
57C22×Dic22C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D414yes—
65C2×C11×C4⋊C4C2312yes—
66#66997—216no—
67#66997—28no—
68#66997—28no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—44no—
74C2×C4⋊Dic11C2312yes—
75C2×Dic11⋊C4—28no—
76C2×Dic11⋊C4—28no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11D412yes—
82C2×C4×Dic11C2312yes—
83C22×C11⋊C8—22no—
84C22×C11⋊C8—22no—
85C22×C11⋊C8—22no—
86C22×C11⋊C8C2312yes—
87C11×#103—28no—
88#66899—28no—
89C11⋊#95—24no—
90#66880—28no—
91#66874—28no—
92C2×#2043—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C2×Q8×C11—24no—
95C2×Q8×C11—22no—
96C2×Q8×C11—28no—
97C2×Q8×C11—28no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—42no—
103C2×Q8×C11—44no—
104C2×Q8×C11—44no—
105C2×Q8×C11—42no—
106C2×Q8×C11C2×D414yes—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—24no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—42no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135C22×Dic11SD1614yes—
136C22×Dic11Q1614yes—
137C22×Dic11C2×D412yes—
138C22×Dic11C2×D412yes—
139C2×Dic22—24no—
140C2×Dic22—28no—
141C2×Dic22—28no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—44no—
148C2×Dic22—42no—
149C2×Dic22—44no—
150C2×Dic22—42no—
151C2×Dic22C2×D414yes—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—44no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C2×D414yes—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—48no—
162C4⋊Dic11—42no—
163Dic11⋊C4—216no—
164Dic11⋊C4—216no—
165C4×Dic11—24no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—44no—
172C22×C4⋊Q8—111no—
173C22×#103—111no—
174C22×#103—111no—
175C22×#103—111no—
176C22×#103D1111yescharacteristic
177C2×#389—111no—
178#2043—118no—
179C2×#336—111no—
180C23×C11#12012yes—
181C23×C11#12112yes—
182C23×C11#12412yes—
183C23×C11C2×SD1612yes—
184C23×C11C2×Q1612yes—
185C23×C11#13712yes—
186C23×C11#13712yes—
187C23×C11C22×D411yescharacteristic
188Q8×C11—24no—
189Q8×C11—24no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—48no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—48no—
200C2×C4×C11—48no—
201C2×C4×C11#12012yes—
202C2×C4×C11#12114yes—
203C2×C4×C11#12114yes—
204C2×C4×C11#12112yes—
205C2×C4×C11#12314yes—
206C2×C4×C11#12314yes—
207C2×C4×C11#12412yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—28no—
219C2×Dic11—28no—
220C2×Dic11—24no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—48no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—84no—
228C2×Dic11C2×SD1614yes—
229C2×Dic11C2×Q1614yes—
230Dic22—24no—
231Dic22—24no—
232Dic22—42no—
233Dic22—42no—
234Dic22—48no—
235C8×C11—42no—
236C11⋊C8—42no—
237C23×Q8—111no—
238C23×Q8C2×D1111yescharacteristic
239C23×C8—111no—
240C23×C8C2×D1111yescharacteristic
241C2×C4⋊Q8—114no—
242C2×C4⋊Q8—222no—
243C2×C4⋊Q8—224no—
244C2×C4⋊Q8—224no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4—221no—
247C22×C4⋊C4—221no—
248C22×C4⋊C4—221no—
249C22×C4⋊C4C2×D1111yescharacteristic
250C22×C42—111no—
251C2×#103—24no—
252C2×#103—114no—
253C2×#103—114no—
254C2×#103—114no—
255C2×#103—224no—
256C2×#103—224no—
257C2×#103—224no—
258C2×#103C2×D1114yes—
259#389—114no—
260#389—222no—
261C2×#95—221no—
262#336—114no—
263C22×C11#39414yes—
264C22×C11#44814yes—
265C22×C11#45114yes—
266C22×C11#46114yes—
267C22×C11#46214yes—
268C22×C11#48714yes—
269C22×C11#49114yes—
270C22×C11C2×#12011yescharacteristic
271C22×C11C2×#12111yescharacteristic
272C22×C11C2×#12411yescharacteristic
273C22×C11C22×SD1611yescharacteristic
274C22×C11C22×Q1611yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C22×C11C2×#13711yescharacteristic
277C4×C11—44no—
278C4×C11—44no—
279C4×C11#39414yes—
280C4×C11C2×#12111yescharacteristic
281C4×C11C2×#12111yescharacteristic
282C4×C11C2×#12311yescharacteristic
283C4×C11C2×#12311yescharacteristic
284Dic11—24no—
285Dic11—24no—
286Dic11—44no—
287Dic11—82no—
288C22×Q8—22no—
289C22×Q8—21no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—114no—
295C22×Q8—112no—
296C22×Q8—222no—
297C22×Q8—221no—
298C22×Q8—222no—
299C22×Q8—222no—
300C22×Q8—222no—
301C22×Q8—222no—
302C22×Q8D4414yes—
303C22×Q8C22×D1112yes—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—221no—
309C23×C4—221no—
310C23×C4C22×D1111yescharacteristic
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—112no—
315C22×C8—222no—
316C22×C8—222no—
317C22×C8—222no—
318C22×C8C22×D1112yes—
319C4⋊Q8—228no—
320C4⋊Q8—2216no—
321C4⋊Q8—228no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—224no—
326C2×C4⋊C4—224no—
327C2×C4⋊C4—228no—
328C2×C4⋊C4—228no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—224no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—444no—
334C2×C4⋊C4C22⋊D1114yes—
335C2×C4⋊C4C22×D1112yes—
336C2×C42—112no—
337C2×C42—112no—
338C2×C42—222no—
339C2×C42—222no—
340#103—28no—
341#103—228no—
342#103—228no—
343#103—228no—
344#95—224no—
345C2×C11#204318yescomplemented
346C2×C11C2×#39411yescharacteristic
347C2×C11C2×#44811yescharacteristic
348C2×C11C2×#45111yescharacteristic
349C2×C11C2×#46111yescharacteristic
350C2×C11C2×#46211yescharacteristic
351C2×C11C2×#48711yescharacteristic
352C2×C11C2×#49111yescharacteristic
353C24D4×D1111yescharacteristic
354C2×Q8—24no—
355C2×Q8—22no—
356C2×Q8—28no—
357C2×Q8—28no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—44no—
363C2×Q8—42no—
364C2×Q8—44no—
365C2×Q8—42no—
366C2×Q8—114no—
367C2×Q8—224no—
368C2×Q8—222no—
369C2×Q8—228no—
370C2×Q8—228no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8—222no—
374C2×Q8—222no—
375C2×Q8—442no—
376C2×Q8—444no—
377C2×Q8—444no—
378C2×Q8—442no—
379C2×Q8C2×D4414yes—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—114no—
389C22×C4—114no—
390C22×C4—112no—
391C22×C4—112no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—224no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—442no—
400C22×C4—442no—
401C22×C4—442no—
402C22×C4—442no—
403C22×C4—442no—
404C22×C4C2×D4412yes—
405C22×C4#433912yes—
406C22×C4D4×D1111yescharacteristic
407C22×C4D4×D1112yes—
408C22×C4#434112yes—
409C22×C4#434112yes—
410C22×C4C2×C22⋊D1112yes—
411C22×C4C23×D1111yescharacteristic
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—44no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—444no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—2216no—
423C4⋊C4—2216no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C4⋊C4—448no—
427C4⋊C4—442no—
428C4⋊C4C2×C22⋊D1114yes—
429C42—224no—
430C42—222no—
431C42—222no—
432C11C2×#204311yescharacteristic, complemented, Sylow
433C23#6693512yes—
434C23#6693812yes—
435C23SD16×D1112yes—
436C23#6696812yes—
437C23Q16×D1112yes—
438C23#6697112yes—
439C23#6699212yes—
440C23C2×D4×D1111yescharacteristic
441Q8—24no—
442Q8—24no—
443Q8—42no—
444Q8—42no—
445Q8—48no—
446Q8—224no—
447Q8—224no—
448Q8—442no—
449Q8—442no—
450Q8—448no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—42no—
454C2×C4—48no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—48no—
459C2×C4—114no—
460C2×C4—114no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—228no—
466C2×C4—228no—
467C2×C4—224no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—448no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—884no—
475C2×C4#6693512yes—
476C2×C4#6693614yes—
477C2×C4#6693812yes—
478C2×C4#6693914yes—
479C2×C4#6698314yes—
480C2×C4#6699114yes—
481C2×C4#6699212yes—
482C2×C4C22×D4411yescharacteristic
483C2×C4C2×#433911yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×#434111yescharacteristic
486C2×C4C2×#434111yescharacteristic
487C2×C4C22×C22⋊D1111yescharacteristic
488C8—42no—
489C8—442no—
490C22#1062240514yes—
491C22#1062241014yes—
492C22#1062241914yes—
493C22#1062242114yes—
494C22#1062257414yes—
495C22#1062277514yes—
496C22#1062279514yes—
497C22C2×#6693511yescharacteristic
498C22C2×#6693811yescharacteristic
499C22C2×SD16×D1111yescharacteristic
500C22C2×#6696811yescharacteristic
501C22C2×Q16×D1111yescharacteristic
502C22C2×#6697111yescharacteristic
503C22C2×#6699211yescharacteristic
504C4—44no—
505C4—44no—
506C4—224no—
507C4—224no—
508C4—444no—
509C4—882no—
510C4#1062257414yes—
511C4C2×#6693611yescharacteristic
512C4C2×#6693911yescharacteristic
513C4C2×#6698311yescharacteristic
514C4C2×#6699111yescharacteristic
515C2#1306986118yesdirect product factor
516C2C2×#1062257411yescharacteristic
517C2C2×#1062241911yescharacteristic
518C2C2×#1062242111yescharacteristic
519C2C2×#1062277511yescharacteristic
520C2C2×#1062279511yescharacteristic
521C2C2×#1062240511yescharacteristic
522C2C2×#1062241011yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socle, prime radicalC24×C11C2×D4
hypercenterC22×#103D11
hypocenterC11C2×#2043
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
6. #13069861C2direct (N × H)
345. C2×C11#2043semidirect
432. C11C2×#2043semidirect
515. C2#13069861direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669972
C22×#668802
C22×#668992
C22×#668742
C2×#106225982
#130698612
C2×#106221882
C22×C11×#1032
C2×#204311