Finite Group Databasebeta

← C2×#13067812 #14729682

Subgroups — C2×#13067812 #14729682

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×#10622307C211yesmaximal, characteristic, complemented
3C2×#10622620C211yesmaximal, characteristic, complemented
4C2×#10622462C211yesmaximal, characteristic, complemented
5#13067812C218yesmaximal, direct product factor
6C2×#10622123C211yesmaximal, characteristic, complemented
7C2×#10622094C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#4339—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66993—21no—
12C2×#66983—21no—
13C22×Dic44—21no—
14#10623084—22no—
15#10623084—22no—
16#10623084—22no—
17#10623084C2214yes—
18C2×#66946—21no—
19C2×#66937—22no—
20C2×#66927C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66896—21no—
26C2×#66885—22no—
27C2×#66880—21no—
28#10622620—22no—
29#10622620C2214yescomplemented
30C2×#66871—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622462—22no—
33#10622462C2214yescomplemented
34#10622307—22no—
35#10622307C2214yescomplemented
36C11×D4⋊C8C2214yescomplemented
37#10622123C2214yescomplemented
38#10622094C2214yescomplemented
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C22×C22⋊D11—22no—
42C22×C22⋊D11—22no—
43C2×#4339—24no—
44C2×#4339—24no—
45C2×#4339—44no—
46C2×#4339—44no—
47C22×D44—21no—
48C22×D44—21no—
49C22×D44D412yes—
50C22×C4×D11—22no—
51C22×Dic22—21no—
52C22×Dic22D411yescharacteristic
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11D412yes—
58C4×D4×C11C2312yes—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62#66993—24no—
63#66993—24no—
64#66983—24no—
65#66983—24no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×Dic11⋊C4—21no—
71C2×C4×Dic11—21no—
72C22×C11⋊C8—21no—
73C2×Dic44—24no—
74C2×Dic44—44no—
75#66946—24no—
76#66946—24no—
77#66937—28no—
78#66937—28no—
79#66927—21no—
80#66927—21no—
81#66927D412yes—
82#66927C2312yes—
83#66922—21no—
84#66922—21no—
85#66922—21no—
86#66922C2312yes—
87C4×Dic22—21no—
88C4×Dic22—21no—
89C4×Dic22D412yes—
90C4×Dic22C2312yes—
91C11×C4⋊C8—21no—
92C11×C4⋊C8C2312yes—
93C4×C8×C11—21no—
94C4×C8×C11C2312yes—
95#66896—24no—
96#66885—28no—
97#66880—24no—
98#66871—24no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C2×#1641—111nomaximal, Sylow
102C24×C11—21no—
103C23×D11—22no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11C2×D412yes—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C2×C22⋊D11—28no—
117C2×C22⋊D11—28no—
118C2×C22⋊D11—48no—
119C2×C22⋊D11—84no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—41no—
123#4339—48no—
124#4339—416no—
125#4339—48no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—44no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—42no—
135C2×D44—42no—
136C2×D44C2×D414yes—
137C2×C4×D11—28no—
138C2×C4×D11—48no—
139C2×Dic22—21no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—41no—
143C2×Dic22—42no—
144C2×Dic22—42no—
145C2×Dic22D814yes—
146C2×Dic22C2×D412yes—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C2×C8×C11—42no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2411yescharacteristic
159(C2×D11)⋊C4—28no—
160C4⋊Dic11—21no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—41no—
164C4⋊Dic11—41no—
165C4⋊Dic11C2×D412yes—
166Dic11⋊C4—22no—
167Dic11⋊C4—22no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172Dic44—48no—
173C2×#550—111no—
174C2×#486—111no—
175C2×#474—111no—
176C2×#462—111no—
177#1641—118no—
178C2×#331—111no—
179C2×Q8⋊C8—111no—
180C2×D4⋊C8D1111yescharacteristic, complemented
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—
190D4×C11—22no—
191D4×C11—22no—
192D4×C11—42no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—44no—
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11C2×D812yes—
203C2×C4×C11#13512yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C22⋊D11—416no—
210C22⋊D11—88no—
211C2×Dic11—22no—
212C2×Dic11—24no—
213C2×Dic11—22no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—82no—
217D44—44no—
218D44—42no—
219D44—42no—
220D44—42no—
221D44—42no—
222D44—44no—
223D44—44no—
224D44—82no—
225C4×D11—416no—
226Dic22—22no—
227Dic22—24no—
228Dic22—42no—
229Dic22—42no—
230Dic22—82no—
231Dic22C2×D814yes—
232C8×C11—42no—
233C8×C11—42no—
234C11⋊C8—42no—
235C22×#41—221no—
236C22×Q16—221no—
237#550—114no—
238#550—222no—
239#550—222no—
240#550—222no—
241C2×C4⋊Q8—111no—
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#474—114no—
252#474—222no—
253#462—114no—
254#462—222no—
255C2×#107—221no—
256C2×C4⋊C8—111no—
257C2×C4⋊C8C2×D1111yescharacteristic
258C2×#103—221no—
259C2×#102—222no—
260C2×#102—221no—
261C2×C4×C8C2×D1111yescharacteristic
262#331—114no—
263Q8⋊C8—114no—
264D4⋊C8C2×D1114yescomplemented
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—84no—
269C22×C11#44712yes—
270C22×C11#45212yes—
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#44712yes—
281C4×C11#45212yes—
282C4×C11C22×D811yescharacteristic
283C4×C11C2×#13511yescharacteristic
284C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C4×C11C2×#13711yescharacteristic
286Dic11—24no—
287Dic11—42no—
288Dic11—82no—
289C2×#41—224no—
290C2×#41—224no—
291C2×#41—444no—
292C2×#41—444no—
293C22×Q8—111no—
294C22×Q8—221no—
295C22×D4—112no—
296C22×D4—222no—
297C22×D4—222no—
298C22×D4—221no—
299C22×D4—221no—
300C22×D4D4411yescharacteristic
301C23×C4—21no—
302C23×C4—222no—
303C2×Q16—224no—
304C2×Q16—444no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—221no—
308C4⋊Q8—112no—
309C4⋊Q8—221no—
310C4⋊Q8—221no—
311C4⋊Q8—221no—
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×D4D4412yes—
331C4×D4C22×D1112yes—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4D4411yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—222no—
339C2×C42—221no—
340C2×C42C22×D1111yescharacteristic
341#107—224no—
342C4⋊C8—21no—
343C4⋊C8—112no—
344C4⋊C8—221no—
345C4⋊C8C22×D1112yes—
346#103—224no—
347#102—228no—
348#102—224no—
349C4×C8—21no—
350C4×C8C22×D1112yes—
351C2×C11—82no—
352C2×C11#164114yescomplemented
353C2×C11C2×#44711yescharacteristic
354C2×C11C2×#45211yescharacteristic
355C2×C11C2×#45511yescharacteristic
356D11—84no—
357C24—21no—
358C24—222no—
359#41—448no—
360#41—448no—
361#41—4416no—
362C2×Q8—114no—
363C2×Q8—112no—
364C2×Q8—221no—
365C2×Q8—222no—
366C2×Q8—222no—
367C2×Q8—441no—
368C2×Q8—442no—
369C2×Q8—442no—
370C2×D4—21no—
371C2×D4—22no—
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×D4412yes—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—228no—
395C22×C4—221no—
396C22×C4—221no—
397C22×C4—448no—
398C22×C4—441no—
399C22×C4C2×D4411yescharacteristic
400C22×C4D4×D1111yescharacteristic
401C22×C4D4×D1111yescharacteristic
402Q16—448no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—42no—
406C2×C8—42no—
407C2×C8—222no—
408C2×C8—442no—
409C4⋊C4—21no—
410C4⋊C4—112no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4C2×D4412yes—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—228no—
422C42—222no—
423C42—222no—
424C42C2×D4411yescharacteristic
425C42D4×D1111yescharacteristic
426C42D4×D1111yescharacteristic
427C42C23×D1111yescharacteristic
428C11C2×#164111yescharacteristic, complemented, Sylow
429C23—22no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—224no—
434C23—444no—
435C23—444no—
436C23—444no—
437C23#6693511yescharacteristic
438Q8—114no—
439Q8—222no—
440Q8—224no—
441Q8—442no—
442Q8—442no—
443Q8—882no—
444D4—22no—
445D4—22no—
446D4—42no—
447D4—444no—
448D4—4416no—
449D4—442no—
450D4—442no—
451D4—442no—
452D4—442no—
453D4—444no—
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—222no—
464C2×C4—224no—
465C2×C4—222no—
466C2×C4—4416no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—882no—
470C2×C4#6693511yescharacteristic
471C2×C4#6693511yescharacteristic
472C2×C4#6693511yescharacteristic
473C2×C4#6695712yes—
474C2×C4#6696212yes—
475C2×C4D8×D1112yes—
476C2×C4#6696712yes—
477C2×C4C22×D4411yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C8—42no—
481C8—42no—
482C8—442no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—84no—
487C22—444no—
488C22—444no—
489C22—444no—
490C22—888no—
491C22#1062234612yes—
492C22#1062238612yes—
493C22#1062243812yes—
494C22C2×#6693511yescharacteristic
495C4—21no—
496C4—21no—
497C4—42no—
498C4—224no—
499C4—442no—
500C4—882no—
501C4#1062234612yes—
502C4#1062238612yes—
503C4C2×#6695711yescharacteristic
504C4C2×#6696211yescharacteristic
505C4C2×D8×D1111yescharacteristic
506C4C2×#6696711yescharacteristic
507C2—82no—
508C2—884no—
509C2#1306781214yesdirect product factor
510C2C2×#1062238611yescharacteristic
511C2C2×#1062234611yescharacteristic
512C2C2×#1062243811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11#120
prime radicalC2×#10623084C2
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1641
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622307C2semidirect
3. C2×#10622620C2semidirect
4. C2×#10622462C2semidirect
5. #13067812C2direct (N × H)
6. C2×#10622123C2semidirect
7. C2×#10622094C2semidirect
8. C2×C11×D4⋊C8C2semidirect
29. #10622620C22semidirect
33. #10622462C22semidirect
35. #10622307C22semidirect
36. C11×D4⋊C8C22semidirect
37. #10622123C22semidirect
38. #10622094C22semidirect
180. C2×D4⋊C8D11semidirect
264. D4⋊C8C2×D11semidirect
352. C2×C11#1641semidirect
428. C11C2×#1641semidirect
509. C2#13067812direct (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×#106223072
C2×#106226202
C2×#106224622
#130678122
C2×#106221232
C2×#106220942
C2×C11×D4⋊C82
C2×#164111