Finite Group Databasebeta

← C2×#13069991 #14782358

Subgroups — C2×#13069991 #14782358

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66872C211yesmaximal, characteristic, complemented
2C22×Dic11⋊C8C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic
4C22×#66873C211yesmaximal, characteristic
5C2×#10622601C211yesmaximal, characteristic
6C2×#10622586C211yesmaximal, characteristic, complemented
7#13069991C218yesmaximal, direct product factor
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⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4—21no—
17C22×C4×Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×C11⋊#95—21no—
20C2×#66885—24no—
21C2×#66885C2214yes—
22C2×Dic11⋊C8—24no—
23C2×Dic11⋊C8C2214yescomplemented
24#10622601—22no—
25#10622601C2214yes—
26#10622586—22no—
27#10622586C2214yescomplemented
28C2×#66873—24no—
29C2×#66873C2214yes—
30C2×#66872—24no—
31C2×#66872C2214yescomplemented
32C11×#340C2214yescomplemented
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—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
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—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11D414yes—
67C2×C4⋊Dic11C2312yes—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—44no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11D412yes—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—22no—
76C22×C11⋊C8D414yes—
77C22×C11⋊C8C2312yes—
78C11⋊#95—24no—
79#66885—28no—
80Dic11⋊C8—28no—
81#66873—28no—
82#66872—28no—
83C2×#2065—111nomaximal, Sylow
84C24×C11C2×D411yescharacteristic
85C23×D11—24no—
86C23×D11—22no—
87C23×D11—42no—
88C23×D11—42no—
89C23×D11—42no—
90C23×D11—42no—
91C23×D11—42no—
92C23×D11—42no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×Q812yes—
105C22×C4×C11#4112yes—
106C22×C4×C11#4112yes—
107C22×C4×C11#4112yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—42no—
117C22×Dic11—42no—
118C22×Dic11SD1614yes—
119C22×Dic11C2×D412yes—
120C22×Dic11C2×D412yes—
121C2×D44—24no—
122C2×D44—28no—
123C2×D44—28no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—44no—
130C2×D44—42no—
131C2×D44—42no—
132C2×D44—44no—
133C2×D44C2×Q814yes—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—44no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144(C2×D11)⋊C4—48no—
145(C2×D11)⋊C4—48no—
146C4⋊Dic11—24no—
147C4⋊Dic11—22no—
148C4⋊Dic11C2×D414yes—
149Dic11⋊C4—48no—
150C4×Dic11—24no—
151C4×Dic11—22no—
152C4×Dic11—22no—
153C2×C11⋊C8—28no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8C2×D414yes—
157C22×#106—111no—
158C22×C4⋊C8—111no—
159C22×#102—111no—
160C22×#102—111no—
161C2×#390—111no—
162C2×#389—111no—
163#2065—118no—
164C2×#340D1111yescharacteristic, complemented
165C23×C11#12112yes—
166C23×C11#12112yes—
167C23×C11C22⋊Q812yes—
168C23×C11C2×SD1612yes—
169C23×C11#13512yes—
170C23×C11AGL(1,ℤ/8)12yes—
171C23×C11AGL(1,ℤ/8)12yes—
172C23×C11C22×D411yescharacteristic
173C22×D11—24no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—48no—
181C22×D11—48no—
182C22×D11—48no—
183C22×D11—84no—
184C22×D11—84no—
185C22×D11—84no—
186C22×D11—84no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—84no—
194C2×C4×C11—84no—
195C2×C4×C11#12114yes—
196C2×C4×C11#12112yes—
197C2×C4×C11#12112yes—
198C2×C4×C11C22⋊Q814yes—
199C2×C4×C11C22⋊Q814yes—
200C2×C4×C11C22⋊Q812yes—
201C2×C4×C11#12614yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×Q811yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—28no—
211C2×Dic11—22no—
212C2×Dic11—24no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—48no—
218C2×Dic11—44no—
219C2×Dic11C2×SD1614yes—
220D44—24no—
221D44—24no—
222D44—42no—
223D44—42no—
224D44—48no—
225C8×C11—42no—
226C11⋊C8—24no—
227C23×D4—111no—
228C23×C8—111no—
229C23×C8C2×D1111yescharacteristic
230C22×C4⋊C4—111no—
231C22×C4⋊C4—221no—
232C22×C4⋊C4C2×D1111yescharacteristic
233C22×C4⋊C4C2×D1111yescharacteristic
234C22×C22⋊C4—221no—
235C22×C22⋊C4—221no—
236C22×C42—111no—
237C2×#106—114no—
238C2×#106—224no—
239C2×C4⋊C8—114no—
240C2×C4⋊C8—224no—
241C2×#102—114no—
242C2×#102—114no—
243C2×#102—224no—
244C2×#102—224no—
245#390—114no—
246#390—222no—
247#389—114no—
248#389—222no—
249C2×#95—221no—
250#340C2×D1114yescomplemented
251C22×C11#39614yes—
252C22×C11#46014yes—
253C22×C11#46314yes—
254C22×C11#46514yes—
255C22×C11#46914yes—
256C22×C11#47614yes—
257C22×C11#47814yes—
258C22×C11C2×#12111yescharacteristic
259C22×C11C2×#12111yescharacteristic
260C22×C11C2×C22⋊Q811yescharacteristic
261C22×C11C22×SD1611yescharacteristic
262C22×C11C2×#13511yescharacteristic
263C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C2×D11—44no—
266C2×D11—44no—
267C2×D11—44no—
268C2×D11—816no—
269C2×D11—82no—
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—82no—
273C4×C11—82no—
274C4×C11—82no—
275C4×C11#39614yes—
276C4×C11C2×#12111yescharacteristic
277C4×C11C2×C22⋊Q811yescharacteristic
278C4×C11C2×C22⋊Q811yescharacteristic
279C4×C11C2×#12611yescharacteristic
280Dic11—24no—
281Dic11—44no—
282Dic11—42no—
283C25—221no—
284C22×D4—114no—
285C22×D4—112no—
286C22×D4—222no—
287C22×D4—222no—
288C22×D4—222no—
289C22×D4—222no—
290C22×D4—222no—
291C22×D4—221no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—111no—
295C23×C4—111no—
296C23×C4—221no—
297C23×C4C22×D1111yescharacteristic
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—114no—
302C22×C8—112no—
303C22×C8—222no—
304C22×C8—222no—
305C22×C8C22×D1112yes—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—114no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—224no—
317C2×C4⋊C4—444no—
318C2×C4⋊C4C22×D1112yes—
319C2×C4⋊C4C22×D1112yes—
320C2×C22⋊C4—224no—
321C2×C22⋊C4—224no—
322C2×C22⋊C4—444no—
323C2×C22⋊C4—444no—
324C2×C42—112no—
325C2×C42—112no—
326C2×C42—222no—
327C2×C42—222no—
328#106—228no—
329C4⋊C8—228no—
330#102—228no—
331#102—228no—
332#95—224no—
333C2×C11#206518yescomplemented
334C2×C11C2×#39611yescharacteristic
335C2×C11C2×#46311yescharacteristic
336C2×C11C2×#46011yescharacteristic
337C2×C11C2×#46511yescharacteristic
338C2×C11C2×#46911yescharacteristic
339C2×C11C2×#47611yescharacteristic
340C2×C11C2×#47811yescharacteristic
341D11—84no—
342C24—224no—
343C24—222no—
344C24—442no—
345C24—442no—
346C24—442no—
347C24—442no—
348C24—442no—
349C24—442no—
350C24D4×D1111yescharacteristic
351C2×D4—114no—
352C2×D4—228no—
353C2×D4—228no—
354C2×D4—224no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—444no—
361C2×D4—444no—
362C2×D4—442no—
363C2×D4—442no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—114no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—224no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—442no—
383C22×C4—442no—
384C22×C4#433912yes—
385C22×C4#433912yes—
386C22×C4#433912yes—
387C22×C4D4×D1111yescharacteristic
388C22×C4D4×D1112yes—
389C22×C4D4×D1112yes—
390C22×C4Q8×D1112yes—
391C22×C4C23×D1111yescharacteristic
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—44no—
396C2×C8—114no—
397C2×C8—228no—
398C2×C8—222no—
399C2×C8—222no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—114no—
407C4⋊C4—224no—
408C4⋊C4—222no—
409C4⋊C4—448no—
410C22⋊C4—448no—
411C22⋊C4—448no—
412C42—224no—
413C42—222no—
414C42—222no—
415C11C2×#206511yescharacteristic, complemented, Sylow
416C23—224no—
417C23—448no—
418C23—448no—
419C23—442no—
420C23—442no—
421C23—442no—
422C23—442no—
423C23—442no—
424C23—442no—
425C23—448no—
426C23—884no—
427C23—884no—
428C23—884no—
429C23—884no—
430C23#6693712yes—
431C23#6693712yes—
432C23#6694912yes—
433C23#6696412yes—
434C23SD16×D1112yes—
435C23#6696712yes—
436C23#6697212yes—
437C23C2×D4×D1111yescharacteristic
438D4—224no—
439D4—224no—
440D4—442no—
441D4—442no—
442D4—448no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—84no—
450C2×C4—84no—
451C2×C4—114no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—228no—
455C2×C4—222no—
456C2×C4—224no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—444no—
462C2×C4—448no—
463C2×C4#6692914yes—
464C2×C4#6693714yes—
465C2×C4#6693712yes—
466C2×C4#6693712yes—
467C2×C4#6694914yes—
468C2×C4#6694914yes—
469C2×C4#6694912yes—
470C2×C4C2×#433911yescharacteristic
471C2×C4C2×#433911yescharacteristic
472C2×C4C2×#433911yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4C2×Q8×D1111yescharacteristic
476C8—42no—
477C8—224no—
478C22—444no—
479C22—444no—
480C22—444no—
481C22—882no—
482C22—882no—
483C22—882no—
484C22—8816no—
485C22—882no—
486C22#1062228914yes—
487C22#1062237514yes—
488C22#1062239514yes—
489C22#1062242014yes—
490C22#1062243214yes—
491C22#1062248314yes—
492C22#1062250414yes—
493C22C2×#6693711yescharacteristic
494C22C2×#6693711yescharacteristic
495C22C2×#6694911yescharacteristic
496C22C2×#6696411yescharacteristic
497C22C2×SD16×D1111yescharacteristic
498C22C2×#6696711yescharacteristic
499C22C2×#6697211yescharacteristic
500C4—82no—
501C4—82no—
502C4—224no—
503C4—444no—
504C4—442no—
505C4#1062228914yes—
506C4C2×#6692911yescharacteristic
507C4C2×#6693711yescharacteristic
508C4C2×#6694911yescharacteristic
509C4C2×#6694911yescharacteristic
510C2—884no—
511C2#1306999118yesdirect product factor
512C2C2×#1062228911yescharacteristic
513C2C2×#1062243211yescharacteristic
514C2C2×#1062237511yescharacteristic
515C2C2×#1062242011yescharacteristic
516C2C2×#1062239511yescharacteristic
517C2C2×#1062248311yescharacteristic
518C2C2×#1062250411yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC23×D44C22
hypercenterC2×#340D11
hypocenterC11C2×#2065
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×#66872C2semidirect
2. C22×Dic11⋊C8C2semidirect
6. C2×#10622586C2semidirect
7. #13069991C2direct (N × H)
8. C2×C11×#340C2semidirect
23. C2×Dic11⋊C8C22semidirect
27. #10622586C22semidirect
31. C2×#66872C22semidirect
32. C11×#340C22semidirect
164. C2×#340D11semidirect
250. #340C2×D11semidirect
333. C2×C11#2065semidirect
415. C11C2×#2065semidirect
511. C2#13069991direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668722
C22×Dic11⋊C82
C22×#668852
C22×#668732
C2×#106226012
C2×#106225862
#130699912
C2×C11×#3402
C2×#206511