Finite Group Databasebeta

← C2×#13069760 #14781047

Subgroups — C2×#13069760 #14781047

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×#66896C211yesmaximal, characteristic
3C2×#10622834C211yesmaximal, characteristic
4#13069760C218yesmaximal, direct product factor
5C2×#10622189C211yesmaximal, characteristic, complemented
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C22⋊Dic11—21no—
13C22×C22⋊Dic11—21no—
14C22×C4⋊Dic11—21no—
15C22×C4⋊Dic11C2211yescharacteristic
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×C11×#102—24no—
25C2×C11×#102C2214yes—
26#10622834—22no—
27#10622834C2214yes—
28C2×#66896—24no—
29C2×#66896C2214yes—
30#10622189C2214yescomplemented
31#10622188C2214yescomplemented
32#10622167C2214yescomplemented
33C25×C11—21no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11Q814yes—
41C22×D4×C11C2312yes—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C23×Dic11—21no—
46C23×Dic11D411yescharacteristic
47C23×Dic11D411yescharacteristic
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⋊C4D414yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—44no—
59C2×C22⋊Dic11—44no—
60C2×C4⋊Dic11—28no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—24no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D414yes—
68C2×C4⋊Dic11C2312yes—
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—
83C11×#102—28no—
84#66896—28no—
85C2×#2025—111nomaximal, Sylow
86C24×C11—24no—
87C24×C11—22no—
88C24×C11—42no—
89C24×C11—42no—
90C24×C11—42no—
91C24×C11—42no—
92C24×C11—42no—
93C24×C11—42no—
94C24×C11C2×D411yescharacteristic
95C2×D4×C11—28no—
96C2×D4×C11—28no—
97C2×D4×C11—24no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—42no—
104C2×D4×C11—44no—
105C2×D4×C11—42no—
106C2×D4×C11—44no—
107C2×D4×C11C2×Q814yes—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×Q812yes—
116C22×C4×C11#4112yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—24no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—42no—
130C22×Dic11—42no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11C2×D412yes—
135C22×Dic11C2×D412yes—
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⋊C4C2×D414yes—
143C22⋊Dic11—48no—
144C22⋊Dic11—48no—
145C4⋊Dic11—216no—
146C4⋊Dic11—24no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—42no—
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×#102D1111yescharacteristic
163C2×#390—111no—
164#2025—118no—
165C2×#340—111no—
166C2×#340—111no—
167C2×#336—111no—
168C23×C11—24no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—48no—
176C23×C11—48no—
177C23×C11—48no—
178C23×C11—84no—
179C23×C11—84no—
180C23×C11—84no—
181C23×C11—84no—
182C23×C11#12012yes—
183C23×C11C22⋊Q812yes—
184C23×C11#12412yes—
185C23×C11#13512yes—
186C23×C11#13512yes—
187C23×C11AGL(1,ℤ/8)12yes—
188C23×C11AGL(1,ℤ/8)12yes—
189C23×C11C22×D411yescharacteristic
190D4×C11—24no—
191D4×C11—24no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—48no—
195C2×C4×C11—24no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—48no—
199C2×C4×C11#12012yes—
200C2×C4×C11C22⋊Q814yes—
201C2×C4×C11C22⋊Q812yes—
202C2×C4×C11C22⋊Q814yes—
203C2×C4×C11#12414yes—
204C2×C4×C11#12412yes—
205C2×C4×C11#12414yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×Q811yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—24no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—44no—
222C2×Dic11—44no—
223C2×Dic11—48no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—84no—
228C8×C11—42no—
229C11⋊C8—42no—
230C23×D4C2×D1111yescharacteristic
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—111no—
239C22×C4⋊C4—221no—
240C22×C4⋊C4—221no—
241C22×C4⋊C4C2×D1111yescharacteristic
242C22×C22⋊C4—221no—
243C22×C22⋊C4—221no—
244C22×C42—111no—
245C2×#102—24no—
246C2×#102—114no—
247C2×#102—224no—
248C2×#102C2×D1114yes—
249#390—114no—
250#390—222no—
251#340—114no—
252#340—114no—
253#336—114no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—816no—
262C22×C11#39314yes—
263C22×C11#44914yes—
264C22×C11#44914yes—
265C22×C11#47814yes—
266C22×C11#47814yes—
267C22×C11#48814yes—
268C22×C11#49014yes—
269C22×C11C2×#12011yescharacteristic
270C22×C11C2×C22⋊Q811yescharacteristic
271C22×C11C2×#12411yescharacteristic
272C22×C11C2×#13511yescharacteristic
273C22×C11C2×#13511yescharacteristic
274C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
276C4×C11—44no—
277C4×C11#39314yes—
278C4×C11C2×C22⋊Q811yescharacteristic
279C4×C11C2×C22⋊Q811yescharacteristic
280C4×C11C2×#12411yescharacteristic
281C4×C11C2×#12411yescharacteristic
282Dic11—42no—
283Dic11—42no—
284Dic11—44no—
285Dic11—82no—
286C25—21no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—21no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4Dic2214yes—
294C22×D4C22×D1112yes—
295C23×C4—21no—
296C23×C4—111no—
297C23×C4—111no—
298C23×C4—221no—
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—114no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4—224no—
319C2×C4⋊C4—228no—
320C2×C4⋊C4—228no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4C22⋊D1114yes—
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—28no—
337#102—228no—
338C2×C11—84no—
339C2×C11#202518yescomplemented
340C2×C11C2×#39311yescharacteristic
341C2×C11C2×#44911yescharacteristic
342C2×C11C2×#44911yescharacteristic
343C2×C11C2×#47811yescharacteristic
344C2×C11C2×#47811yescharacteristic
345C2×C11C2×#48811yescharacteristic
346C2×C11C2×#49011yescharacteristic
347C24—24no—
348C24—22no—
349C24—42no—
350C24—42no—
351C24—42no—
352C24—42no—
353C24—42no—
354C24—42no—
355C24D4×D1111yescharacteristic
356C2×D4—28no—
357C2×D4—24no—
358C2×D4—28no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—44no—
365C2×D4—42no—
366C2×D4—44no—
367C2×D4—42no—
368C2×D4C2×Dic2214yes—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—224no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—442no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4C2×Dic2212yes—
390C22×C4#433912yes—
391C22×C4D4×D1111yescharacteristic
392C22×C4D4×D1112yes—
393C22×C4#434112yes—
394C22×C4#434112yes—
395C22×C4C2×C22⋊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—114no—
408C4⋊C4—2216no—
409C4⋊C4—2216no—
410C4⋊C4—224no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—442no—
415C4⋊C4C2×C22⋊D1114yes—
416C22⋊C4—448no—
417C22⋊C4—448no—
418C42—224no—
419C42—222no—
420C42—222no—
421C11C2×#202511yescharacteristic, complemented, Sylow
422C23—24no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—48no—
429C23—42no—
430C23—48no—
431C23—48no—
432C23—84no—
433C23—84no—
434C23—84no—
435C23—84no—
436C23#6693112yes—
437C23#6693812yes—
438C23#6696412yes—
439C23#6696512yes—
440C23#6696712yes—
441C23#6696912yes—
442C23#6699012yes—
443C23C2×D4×D1111yescharacteristic
444D4—24no—
445D4—24no—
446D4—42no—
447D4—48no—
448D4—42no—
449C2×C4—24no—
450C2×C4—48no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—224no—
460C2×C4—444no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—444no—
464C2×C4—448no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—884no—
469C2×C4#6693114yes—
470C2×C4#6693112yes—
471C2×C4#6693814yes—
472C2×C4#6693812yes—
473C2×C4#6697714yes—
474C2×C4#6698914yes—
475C2×C4#6699012yes—
476C2×C4C22×Dic2211yescharacteristic
477C2×C4C2×#433911yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C2×#434111yescharacteristic
480C2×C4C2×#434111yescharacteristic
481C2×C4C22×C22⋊D1111yescharacteristic
482C8—42no—
483C8—442no—
484C22—44no—
485C22—44no—
486C22—44no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22—816no—
492C22#1062237614yes—
493C22#1062237714yes—
494C22#1062237914yes—
495C22#1062238114yes—
496C22#1062256014yes—
497C22#1062277114yes—
498C22#1062278514yes—
499C22C2×#6693111yescharacteristic
500C22C2×#6693811yescharacteristic
501C22C2×#6696411yescharacteristic
502C22C2×#6696511yescharacteristic
503C22C2×#6696711yescharacteristic
504C22C2×#6696911yescharacteristic
505C22C2×#6699011yescharacteristic
506C4—44no—
507C4—442no—
508C4—442no—
509C4—444no—
510C4—882no—
511C4#1062256014yes—
512C4C2×#6693111yescharacteristic
513C4C2×#6693811yescharacteristic
514C4C2×#6697711yescharacteristic
515C4C2×#6698911yescharacteristic
516C2—84no—
517C2#1306976018yesdirect product factor
518C2C2×#1062256011yescharacteristic
519C2C2×#1062277111yescharacteristic
520C2C2×#1062278511yescharacteristic
521C2C2×#1062237911yescharacteristic
522C2C2×#1062237611yescharacteristic
523C2C2×#1062238111yescharacteristic
524C2C2×#1062237711yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
hypercenterC22×#102D11
hypocenterC11C2×#2025
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. C22×#66943C2semidirect
4. #13069760C2direct (N × H)
5. C2×#10622189C2semidirect
6. C2×#10622167C2semidirect
7. C2×#10622188C2semidirect
23. C2×#66943C22semidirect
30. #10622189C22semidirect
31. #10622188C22semidirect
32. #10622167C22semidirect
339. C2×C11#2025semidirect
421. C11C2×#2025semidirect
517. C2#13069760direct (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×#668962
C2×#106228342
#130697602
C2×#106221892
C2×#106221672
C2×#106221882
C22×C11×#1022
C2×#202511