Finite Group Databasebeta

← C2×#13069761 #14781048

Subgroups — C2×#13069761 #14781048

Order 2816.

1518 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic, complemented
2C22×#66885C211yesmaximal, characteristic
3C22×#66873C211yesmaximal, characteristic
4C2×#10622601C211yesmaximal, characteristic
5#13069761C218yesmaximal, direct product factor
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622188C211yesmaximal, characteristic, complemented
8C2×C11×#340C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4—21no—
14C22×(C2×D11)⋊C4—21no—
15C22×C4⋊Dic11—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4—21no—
18C22×C4×Dic11C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×#66943—24no—
21C2×#66943—24no—
22C2×#66943—22no—
23C2×#66943C2214yescomplemented
24C2×#66885—24no—
25C2×#66885C2214yes—
26#10622601—22no—
27#10622601C2214yes—
28C2×#66873—24no—
29C2×#66873C2214yes—
30C11×#340C2214yescomplemented
31#10622188C2214yescomplemented
32#10622167C2214yescomplemented
33C24×D11—21no—
34C23×C4×C11—21no—
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—21no—
38C23×Dic11D411yescharacteristic
39C23×Dic11D411yescharacteristic
40C22×D44—22no—
41C22×D44—22no—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—21no—
45C22×D44—22no—
46C22×D44Q814yes—
47C22×D44C2312yes—
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11—22no—
51C22×C8×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D414yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2312yes—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—44no—
63C2×(C2×D11)⋊C4—44no—
64C2×C4⋊Dic11—28no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—24no—
68C2×C4⋊Dic11D414yes—
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—28no—
71C2×Dic11⋊C4—24no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11D412yes—
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8—22no—
77C22×C11⋊C8—22no—
78C22×C11⋊C8—22no—
79C22×C11⋊C8C2312yes—
80#66943—216no—
81#66943—28no—
82#66943—28no—
83#66885—28no—
84#66873—28no—
85C2×#2025—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C23×D11—24no—
88C23×D11—22no—
89C23×D11—42no—
90C23×D11—42no—
91C23×D11—42no—
92C23×D11—42no—
93C23×D11—42no—
94C23×D11—42no—
95C22×C4×C11—24no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×Q812yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—24no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—42no—
120C22×Dic11—42no—
121C22×Dic11C2×D412yes—
122C22×Dic11C2×D412yes—
123C2×D44—24no—
124C2×D44—28no—
125C2×D44—28no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—42no—
132C2×D44—44no—
133C2×D44—44no—
134C2×D44—42no—
135C2×D44C2×Q814yes—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—44no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4C2×D414yes—
146(C2×D11)⋊C4—48no—
147(C2×D11)⋊C4—48no—
148C4⋊Dic11—216no—
149C4⋊Dic11—24no—
150C4⋊Dic11—22no—
151C4⋊Dic11C2×D414yes—
152Dic11⋊C4—216no—
153C4×Dic11—24no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—44no—
160C22×#125—111no—
161C22×#102—111no—
162C22×#102—111no—
163C2×#390—111no—
164#2025—118no—
165C2×#340—111no—
166C2×#340D1111yescharacteristic, complemented
167C2×#336—111no—
168C23×C11#12012yes—
169C23×C11C22⋊Q812yes—
170C23×C11#12412yes—
171C23×C11#13512yes—
172C23×C11#13512yes—
173C23×C11AGL(1,ℤ/8)12yes—
174C23×C11AGL(1,ℤ/8)12yes—
175C23×C11C22×D411yescharacteristic
176C22×D11—24no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—48no—
184C22×D11—48no—
185C22×D11—48no—
186C22×D11—84no—
187C22×D11—84no—
188C22×D11—84no—
189C22×D11—84no—
190C2×C4×C11—24no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—48no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—84no—
198C2×C4×C11#12012yes—
199C2×C4×C11C22⋊Q814yes—
200C2×C4×C11C22⋊Q812yes—
201C2×C4×C11C22⋊Q814yes—
202C2×C4×C11#12414yes—
203C2×C4×C11#12414yes—
204C2×C4×C11#12412yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—24no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—44no—
221C2×Dic11—44no—
222C2×Dic11—48no—
223D44—24no—
224D44—24no—
225D44—42no—
226D44—42no—
227D44—48no—
228C8×C11—42no—
229C11⋊C8—42no—
230C23×D4—111no—
231C23×C8—111no—
232C23×C8C2×D1111yescharacteristic
233C2×#125—114no—
234C2×#125—222no—
235C2×#125—224no—
236C2×#125—224no—
237C22×C4⋊C4—111no—
238C22×C4⋊C4—221no—
239C22×C4⋊C4—221no—
240C22×C4⋊C4C2×D1111yescharacteristic
241C22×C4⋊C4C2×D1111yescharacteristic
242C22×C22⋊C4—221no—
243C22×C22⋊C4—221no—
244C22×C42—111no—
245C2×#102—114no—
246C2×#102—114no—
247C2×#102—224no—
248C2×#102—224no—
249#390—114no—
250#390—222no—
251#340—114no—
252#340C2×D1114yescomplemented
253#336—114no—
254C22×C11#39314yes—
255C22×C11#44914yes—
256C22×C11#44914yes—
257C22×C11#47814yes—
258C22×C11#47814yes—
259C22×C11#48814yes—
260C22×C11#49014yes—
261C22×C11C2×#12011yescharacteristic
262C22×C11C2×C22⋊Q811yescharacteristic
263C22×C11C2×#12411yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11C2×#13511yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
268C2×D11—44no—
269C2×D11—44no—
270C2×D11—44no—
271C2×D11—82no—
272C2×D11—82no—
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—816no—
276C4×C11—44no—
277C4×C11—82no—
278C4×C11#39314yes—
279C4×C11C2×C22⋊Q811yescharacteristic
280C4×C11C2×C22⋊Q811yescharacteristic
281C4×C11C2×#12411yescharacteristic
282C4×C11C2×#12411yescharacteristic
283Dic11—42no—
284Dic11—42no—
285Dic11—44no—
286C25—221no—
287C22×D4—114no—
288C22×D4—112no—
289C22×D4—222no—
290C22×D4—222no—
291C22×D4—222no—
292C22×D4—222no—
293C22×D4—221no—
294C22×D4—222no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—221no—
300C23×C4C22×D1111yescharacteristic
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—112no—
305C22×C8—222no—
306C22×C8—222no—
307C22×C8—222no—
308C22×C8C22×D1112yes—
309#125—228no—
310#125—2216no—
311#125—228no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—114no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—224no—
320C2×C4⋊C4—224no—
321C2×C4⋊C4—228no—
322C2×C4⋊C4—228no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4D4414yes—
326C2×C4⋊C4C22×D1112yes—
327C2×C4⋊C4C22×D1112yes—
328C2×C22⋊C4—224no—
329C2×C22⋊C4—224no—
330C2×C22⋊C4—444no—
331C2×C22⋊C4—444no—
332C2×C42—112no—
333C2×C42—112no—
334C2×C42—222no—
335C2×C42—222no—
336#102—228no—
337#102—228no—
338C2×C11#202518yescomplemented
339C2×C11C2×#39311yescharacteristic
340C2×C11C2×#44911yescharacteristic
341C2×C11C2×#44911yescharacteristic
342C2×C11C2×#47811yescharacteristic
343C2×C11C2×#47811yescharacteristic
344C2×C11C2×#48811yescharacteristic
345C2×C11C2×#49011yescharacteristic
346D11—84no—
347C24—224no—
348C24—222no—
349C24—442no—
350C24—442no—
351C24—442no—
352C24—442no—
353C24—442no—
354C24—442no—
355C24D4×D1111yescharacteristic
356C2×D4—114no—
357C2×D4—228no—
358C2×D4—224no—
359C2×D4—228no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—222no—
364C2×D4—222no—
365C2×D4—444no—
366C2×D4—442no—
367C2×D4—444no—
368C2×D4—442no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—224no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4C2×D4412yes—
390C22×C4#433912yes—
391C22×C4#433912yes—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1112yes—
394C22×C4#434112yes—
395C22×C4Q8×D1112yes—
396C22×C4C23×D1111yescharacteristic
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—44no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—444no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—42no—
410C4⋊C4—114no—
411C4⋊C4—2216no—
412C4⋊C4—2216no—
413C4⋊C4—224no—
414C4⋊C4—222no—
415C4⋊C4C2×D4414yes—
416C22⋊C4—448no—
417C22⋊C4—448no—
418C42—224no—
419C42—222no—
420C42—222no—
421C11C2×#202511yescharacteristic, complemented, Sylow
422C23—224no—
423C23—448no—
424C23—448no—
425C23—442no—
426C23—442no—
427C23—442no—
428C23—442no—
429C23—442no—
430C23—442no—
431C23—448no—
432C23—884no—
433C23—884no—
434C23—884no—
435C23—884no—
436C23#6693512yes—
437C23#6693812yes—
438C23#6694912yes—
439C23#6696412yes—
440C23#6696712yes—
441C23#6696912yes—
442C23#6697212yes—
443C23C2×D4×D1111yescharacteristic
444D4—224no—
445D4—224no—
446D4—442no—
447D4—442no—
448D4—448no—
449C2×C4—24no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—48no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—84no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—224no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—444no—
467C2×C4—444no—
468C2×C4—448no—
469C2×C4#6692814yes—
470C2×C4#6693512yes—
471C2×C4#6693814yes—
472C2×C4#6693812yes—
473C2×C4#6694914yes—
474C2×C4#6694912yes—
475C2×C4#6695014yes—
476C2×C4C22×D4411yescharacteristic
477C2×C4C2×#433911yescharacteristic
478C2×C4C2×#433911yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4C2×#434111yescharacteristic
481C2×C4C2×Q8×D1111yescharacteristic
482C8—42no—
483C8—442no—
484C22—444no—
485C22—444no—
486C22—444no—
487C22—882no—
488C22—882no—
489C22—882no—
490C22—882no—
491C22—8816no—
492C22#1062228614yes—
493C22#1062237714yes—
494C22#1062239414yes—
495C22#1062241314yes—
496C22#1062242414yes—
497C22#1062248414yes—
498C22#1062250414yes—
499C22C2×#6693511yescharacteristic
500C22C2×#6693811yescharacteristic
501C22C2×#6694911yescharacteristic
502C22C2×#6696411yescharacteristic
503C22C2×#6696711yescharacteristic
504C22C2×#6696911yescharacteristic
505C22C2×#6697211yescharacteristic
506C4—44no—
507C4—82no—
508C4—442no—
509C4—442no—
510C4—444no—
511C4#1062228614yes—
512C4C2×#6692811yescharacteristic
513C4C2×#6693811yescharacteristic
514C4C2×#6694911yescharacteristic
515C4C2×#6695011yescharacteristic
516C2—884no—
517C2#1306976118yesdirect product factor
518C2C2×#1062228611yescharacteristic
519C2C2×#1062239411yescharacteristic
520C2C2×#1062242411yescharacteristic
521C2C2×#1062248411yescharacteristic
522C2C2×#1062250411yescharacteristic
523C2C2×#1062241311yescharacteristic
524C2C2×#1062237711yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC2×#340D11
hypocenterC11C2×#2025
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
5. #13069761C2direct (N × H)
6. C2×#10622167C2semidirect
7. C2×#10622188C2semidirect
8. C2×C11×#340C2semidirect
23. C2×#66943C22semidirect
30. C11×#340C22semidirect
31. #10622188C22semidirect
32. #10622167C22semidirect
166. C2×#340D11semidirect
252. #340C2×D11semidirect
338. C2×C11#2025semidirect
421. C11C2×#2025semidirect
517. C2#13069761direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669432
C22×#668852
C22×#668732
C2×#106226012
#130697612
C2×#106221672
C2×#106221882
C2×C11×#3402
C2×#202511