Finite Group Databasebeta

← C2×#13067814 #14729686

Subgroups — C2×#13067814 #14729686

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic
2C2×#10622701C211yesmaximal, characteristic, complemented
3C2×#10622707C211yesmaximal, characteristic, complemented
4#13067814C218yesmaximal, direct product factor
5C2×#10622123C211yesmaximal, characteristic, complemented
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×C11×#461C211yesmaximal, characteristic, complemented
9C22×#4339—21no—
10C22×C11×SD16—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66993—21no—
14C2×#66983—21no—
15#10623084—22no—
16#10623084—22no—
17#10623084—22no—
18#10623084C2214yes—
19C2×#66946—21no—
20C2×#66937—22no—
21C2×#66927C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#461—22no—
24C11×#461C2214yescomplemented
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103—21no—
27#10622707—22no—
28#10622707C2214yescomplemented
29#10622701—22no—
30#10622701C2214yescomplemented
31C2×#66874—21no—
32C2×#66873—22no—
33C2×#66872—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36D4⋊(C11⋊C8)C2214yescomplemented
37#10622123C2214yescomplemented
38#10622122C2214yescomplemented
39C22×Q8×C11—21no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C22×C22⋊D11—22no—
43C22×C22⋊D11—22no—
44C2×#4339—24no—
45C2×#4339—24no—
46C2×#4339—44no—
47C2×#4339—44no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44D412yes—
51C22×C4×D11—22no—
52C22×Dic22D411yescharacteristic
53C2×C11×SD16—24no—
54C2×C11×SD16—44no—
55C22×C8×C11—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8C2312yes—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11D412yes—
63C4×D4×C11C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69#66993—24no—
70#66993—24no—
71#66983—24no—
72#66983—24no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4⋊Dic11D411yescharacteristic
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C22×C11⋊C8—21no—
78C22×C11⋊C8—21no—
79#66946—24no—
80#66946—24no—
81#66937—28no—
82#66937—28no—
83#66927—21no—
84#66927—21no—
85#66927D412yes—
86#66927C2312yes—
87C4×Dic22—21no—
88C4×Dic22—21no—
89C4×Dic22D412yes—
90C4×Dic22C2312yes—
91C11×C4⋊C8—21no—
92C11×C4⋊C8C2312yes—
93C11×#103—24no—
94#66874—24no—
95#66873—28no—
96#66872—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4×C11⋊C8—21no—
100C4×C11⋊C8C2312yes—
101C2×#1642—111nomaximal, Sylow
102C24×C11—21no—
103C23×D11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—41no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C2×D4×C11—21no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11C2×D412yes—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—41no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—28no—
122C2×C22⋊D11—28no—
123C2×C22⋊D11—48no—
124C2×C22⋊D11—84no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127#4339—48no—
128#4339—416no—
129#4339—48no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—44no—
136C2×D44—42no—
137C2×D44—42no—
138C2×D44—42no—
139C2×D44—42no—
140C2×D44C2×D414yes—
141C2×C4×D11—28no—
142C2×C4×D11—48no—
143C2×Dic22—21no—
144C2×Dic22—22no—
145C2×Dic22SD1614yescomplemented
146C2×Dic22C2×D412yes—
147C11×SD16—48no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2411yescharacteristic
162(C2×D11)⋊C4—28no—
163C4⋊Dic11—21no—
164C4⋊Dic11C2×D412yes—
165Dic11⋊C4—22no—
166Dic11⋊C4—22no—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172C2×C11⋊C8—42no—
173C2×#550—111no—
174C2×#486—111no—
175C2×#475—111no—
176C2×#461D1111yescharacteristic, complemented
177#1642—118no—
178C2×#331—111no—
179C2×Q8⋊C8—111no—
180C2×D4⋊C8—111no—
181C23×C11—22no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11#12011yescharacteristic
186C22×D11—24no—
187C22×D11—44no—
188C22×D11—44no—
189C22×D11—44no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—82no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—42no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—44no—
202C2×C4×C11—42no—
203C2×C4×C11—82no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11C2×SD1612yes—
208C2×C4×C11#13512yes—
209C2×C4×C11AGL(1,ℤ/8)12yes—
210C2×C4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—416no—
215C22⋊D11—88no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—22no—
219C2×Dic11—42no—
220D44—44no—
221D44—42no—
222D44—42no—
223D44—42no—
224D44—42no—
225D44—44no—
226D44—44no—
227D44—82no—
228C4×D11—416no—
229Dic22—22no—
230Dic22—24no—
231Dic22C2×SD1614yescomplemented
232C8×C11—42no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C22×#41—221no—
236C22×SD16—21no—
237#550—114no—
238#550—222no—
239#550—222no—
240#550—222no—
241C2×C4⋊Q8C2×D1111yescharacteristic
242C2×#127—111no—
243C2×#127—221no—
244C2×#121—222no—
245C2×#121—221no—
246C2×C4×Q8—111no—
247C2×C4×D4—221no—
248C2×C4×D4C2×D1111yescharacteristic
249#486—114no—
250#486—222no—
251#475—114no—
252#475—222no—
253#461—22no—
254#461C2×D1114yescomplemented
255C2×#106—221no—
256C2×C4⋊C8—111no—
257C2×C4⋊C8C2×D1111yescharacteristic
258C2×#103—21no—
259C2×#103—221no—
260C2×#102—222no—
261C2×C4×C8—111no—
262#331—114no—
263Q8⋊C8—114no—
264D4⋊C8—114no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—84no—
269C22×C11#44912yes—
270C22×C11#45012yes—
271C22×C11#45512yes—
272C22×C11C2×#12011yescharacteristic
273C2×D11—44no—
274C2×D11—44no—
275C2×D11—44no—
276C2×D11—88no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—42no—
280C4×C11—82no—
281C4×C11#44912yes—
282C4×C11#45012yes—
283C4×C11C22×SD1611yescharacteristic
284C4×C11C2×#13511yescharacteristic
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
287Dic11—24no—
288Dic11—42no—
289C2×#41—224no—
290C2×#41—224no—
291C2×#41—444no—
292C2×#41—444no—
293C22×Q8—21no—
294C22×Q8—111no—
295C22×D4—112no—
296C22×D4—222no—
297C22×D4—222no—
298C22×D4—221no—
299C22×D4—221no—
300C22×D4C22⋊D1111yescharacteristic
301C23×C4—21no—
302C23×C4—222no—
303C2×SD16—24no—
304C2×SD16—44no—
305C22×C8—21no—
306C22×C8—221no—
307C22×C8—221no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8C22×D1112yes—
312#127—112no—
313#127—112no—
314#127—224no—
315#127—224no—
316#127—221no—
317#127—221no—
318#121—228no—
319#121—228no—
320#121—224no—
321#121—224no—
322C4×Q8—112no—
323C4×Q8—112no—
324C4×Q8—221no—
325C4×Q8—221no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—224no—
329C4×D4—224no—
330C4×D4C22⋊D1112yes—
331C4×D4C22×D1112yes—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4C22⋊D1111yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—222no—
339C2×C42—221no—
340C2×C42C22×D1111yescharacteristic
341#106—224no—
342C4⋊C8—21no—
343C4⋊C8—112no—
344C4⋊C8—221no—
345C4⋊C8C22×D1112yes—
346#103—24no—
347#103—224no—
348#102—228no—
349C4×C8—112no—
350C4×C8—221no—
351C2×C11—82no—
352C2×C11#164214yescomplemented
353C2×C11C2×#45011yescharacteristic
354C2×C11C2×#44911yescharacteristic
355C2×C11C2×#45511yescharacteristic
356D11—84no—
357C24—21no—
358C24—222no—
359#41—448no—
360#41—448no—
361#41—4416no—
362C2×Q8—22no—
363C2×Q8—41no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8—114no—
367C2×Q8—112no—
368C2×Q8—222no—
369C2×Q8—221no—
370C2×D4—22no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—114no—
374C2×D4—228no—
375C2×D4—228no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—444no—
382C2×D4—448no—
383C2×D4—442no—
384C2×D4—442no—
385C2×D4—442no—
386C2×D4—442no—
387C2×D4—884no—
388C2×D4C2×C22⋊D1112yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—41no—
395C22×C4—228no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—448no—
399C22×C4D4×D1111yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402SD16—48no—
403C2×C8—22no—
404C2×C8—42no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—442no—
408C2×C8—442no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—112no—
415C4⋊C4—221no—
416C4⋊C4—222no—
417C4⋊C4—222no—
418C4⋊C4C2×C22⋊D1112yes—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—228no—
422C42—222no—
423C42—222no—
424C42D4×D1111yescharacteristic
425C42D4×D1111yescharacteristic
426C42C2×C22⋊D1111yescharacteristic
427C42C23×D1111yescharacteristic
428C11C2×#164211yescharacteristic, complemented, Sylow
429C23—22no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—224no—
434C23—444no—
435C23—444no—
436C23—444no—
437C23#6699011yescharacteristic
438Q8—42no—
439Q8—42no—
440Q8—82no—
441Q8—114no—
442Q8—222no—
443Q8—224no—
444D4—22no—
445D4—22no—
446D4—42no—
447D4—444no—
448D4—4416no—
449D4—442no—
450D4—442no—
451D4—444no—
452D4—442no—
453D4—442no—
454D4—444no—
455D4—882no—
456D4—888no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—82no—
465C2×C4—224no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—4416no—
469C2×C4—442no—
470C2×C4SD16×D1112yes—
471C2×C4#6696712yes—
472C2×C4#6698512yes—
473C2×C4#6699011yescharacteristic
474C2×C4#6699011yescharacteristic
475C2×C4#6699011yescharacteristic
476C2×C4#6700312yes—
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C22×C22⋊D1111yescharacteristic
480C8—42no—
481C8—442no—
482C8—442no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—84no—
487C22—444no—
488C22—444no—
489C22—444no—
490C22—888no—
491C22#1062265012yes—
492C22#1062278212yes—
493C22#1062281512yes—
494C22C2×#6699011yescharacteristic
495C4—21no—
496C4—21no—
497C4—42no—
498C4—82no—
499C4—224no—
500C4—442no—
501C4#1062265012yes—
502C4#1062278212yes—
503C4C2×SD16×D1111yescharacteristic
504C4C2×#6696711yescharacteristic
505C4C2×#6698511yescharacteristic
506C4C2×#6700311yescharacteristic
507C2—82no—
508C2—884no—
509C2#1306781414yesdirect product factor
510C2C2×#1062278211yescharacteristic
511C2C2×#1062265011yescharacteristic
512C2C2×#1062281511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#461C2
socleC23×C11#120
prime radicalC2×#10623084C2
hypercenterC2×#461D11
hypocenterC11C2×#1642
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. C2×#10622701C2semidirect
3. C2×#10622707C2semidirect
4. #13067814C2direct (N × H)
5. C2×#10622123C2semidirect
6. C2×#10622122C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
8. C2×C11×#461C2semidirect
24. C11×#461C22semidirect
28. #10622707C22semidirect
30. #10622701C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622123C22semidirect
38. #10622122C22semidirect
145. C2×Dic22SD16semidirect
176. C2×#461D11semidirect
231. Dic22C2×SD16semidirect
254. #461C2×D11semidirect
352. C2×C11#1642semidirect
428. C11C2×#1642semidirect
509. C2#13067814direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106227012
C2×#106227072
#130678142
C2×#106221232
C2×#106221222
C2×D4⋊(C11⋊C8)2
C2×C11×#4612
C2×#164211