Finite Group Databasebeta

← C2×#13067742 #14729635

Subgroups — C2×#13067742 #14729635

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic
2C2×#10622698C211yesmaximal, characteristic, complemented
3C2×#10622704C211yesmaximal, characteristic, complemented
4#13067742C218yesmaximal, direct product factor
5C2×#10622123C211yesmaximal, characteristic, complemented
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×C11×#476C211yesmaximal, characteristic, complemented
9C22×#4339—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C22×#4325—22no—
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×#476—22no—
24C11×#476C2214yescomplemented
25C2×C11×#106—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102—21no—
28#10622704—22no—
29#10622704C2214yescomplemented
30#10622698—22no—
31#10622698C2214yescomplemented
32C2×#66874—21no—
33C2×#66871—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
53C22×C8×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2312yes—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D412yes—
61C4×D4×C11C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4325—28no—
68C2×#4325—48no—
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×#106—24no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8C2312yes—
94C11×#102—24no—
95#66874—24no—
96#66871—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4×C11⋊C8—21no—
100C4×C11⋊C8C2312yes—
101C2×#1631—111nomaximal, Sylow
102C24×C11—21no—
103C23×D11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—44no—
106C2×Q8×C11—41no—
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11C2×D412yes—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—41no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C2×C22⋊D11—28no—
121C2×C22⋊D11—28no—
122C2×C22⋊D11—48no—
123C2×C22⋊D11—84no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126#4339—48no—
127#4339—416no—
128#4339—48no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—44no—
135C2×D44—42no—
136C2×D44—42no—
137C2×D44—42no—
138C2×D44—42no—
139C2×D44C2×D414yes—
140C2×C4×D11—28no—
141C2×C4×D11—48no—
142C2×Dic22—21no—
143C2×Dic22—22no—
144C2×Dic22SD1614yescomplemented
145C2×Dic22C2×D412yes—
146C2×C8×C11—22no—
147C2×C8×C11—42no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4C2×D412yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2411yescharacteristic
160#4325—416no—
161(C2×D11)⋊C4—28no—
162C4⋊Dic11—21no—
163C4⋊Dic11C2×D412yes—
164Dic11⋊C4—22no—
165Dic11⋊C4—22no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C2×C11⋊C8—24no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172C2×#550—111no—
173C2×#492—111no—
174C2×#477—111no—
175C2×#476D1111yescharacteristic, complemented
176#1631—118no—
177C2×#331—111no—
178C2×Q8⋊C8—111no—
179C2×D4⋊C8—111no—
180C23×C11—22no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11#12011yescharacteristic
185C22×D11—24no—
186C22×D11—44no—
187C22×D11—44no—
188C22×D11—44no—
189Q8×C11—44no—
190Q8×C11—82no—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—42no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—82no—
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11C2×SD1612yes—
206C2×C4×C11#13512yes—
207C2×C4×C11AGL(1,ℤ/8)12yes—
208C2×C4×C11#13712yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C22⋊D11—416no—
213C22⋊D11—88no—
214C2×Dic11—22no—
215C2×Dic11—24no—
216C2×Dic11—22no—
217C2×Dic11—42no—
218D44—44no—
219D44—42no—
220D44—42no—
221D44—42no—
222D44—42no—
223D44—44no—
224D44—44no—
225D44—82no—
226C4×D11—416no—
227Dic22—22no—
228Dic22—24no—
229Dic22C2×SD1614yescomplemented
230C8×C11—42no—
231C11⋊C8—24no—
232C11⋊C8—42no—
233C22×#41—221no—
234C22×SD16—222no—
235#550—114no—
236#550—222no—
237#550—222no—
238#550—222no—
239C2×C4⋊Q8C2×D1111yescharacteristic
240C2×#127—111no—
241C2×#127—221no—
242C2×#121—222no—
243C2×#121—221no—
244C2×C4×Q8—111no—
245C2×C4×D4—221no—
246C2×C4×D4C2×D1111yescharacteristic
247#492—114no—
248#492—222no—
249#477—114no—
250#477—222no—
251#476—22no—
252#476C2×D1114yescomplemented
253C2×#107—221no—
254C2×#106—21no—
255C2×C4⋊C8—111no—
256C2×C4⋊C8C2×D1111yescharacteristic
257C2×#103—221no—
258C2×#102—21no—
259C2×C4×C8—111no—
260#331—114no—
261Q8⋊C8—114no—
262D4⋊C8—114no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—84no—
267C22×C11#45012yes—
268C22×C11#45212yes—
269C22×C11#45312yes—
270C22×C11C2×#12011yescharacteristic
271C2×D11—44no—
272C2×D11—44no—
273C2×D11—44no—
274C2×D11—88no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—42no—
278C4×C11—82no—
279C4×C11#45012yes—
280C4×C11#45212yes—
281C4×C11C22×SD1611yescharacteristic
282C4×C11C2×#13511yescharacteristic
283C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
284C4×C11C2×#13711yescharacteristic
285Dic11—24no—
286Dic11—42no—
287C2×#41—224no—
288C2×#41—224no—
289C2×#41—444no—
290C2×#41—444no—
291C22×Q8—21no—
292C22×Q8—111no—
293C22×D4—112no—
294C22×D4—222no—
295C22×D4—222no—
296C22×D4—221no—
297C22×D4—221no—
298C22×D4C22⋊D1111yescharacteristic
299C23×C4—21no—
300C23×C4—222no—
301C2×SD16—228no—
302C2×SD16—448no—
303C22×C8—21no—
304C22×C8—221no—
305C22×C8—221no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8C22×D1112yes—
310#127—112no—
311#127—112no—
312#127—224no—
313#127—224no—
314#127—221no—
315#127—221no—
316#121—228no—
317#121—228no—
318#121—224no—
319#121—224no—
320C4×Q8—112no—
321C4×Q8—112no—
322C4×Q8—221no—
323C4×Q8—221no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—224no—
327C4×D4—224no—
328C4×D4C22⋊D1112yes—
329C4×D4C22×D1112yes—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—222no—
337C2×C42—221no—
338C2×C42C22×D1111yescharacteristic
339#107—224no—
340#106—24no—
341C4⋊C8—21no—
342C4⋊C8—112no—
343C4⋊C8—221no—
344C4⋊C8C22×D1112yes—
345#103—224no—
346#102—24no—
347C4×C8—112no—
348C4×C8—221no—
349C2×C11—82no—
350C2×C11#163114yescomplemented
351C2×C11C2×#45011yescharacteristic
352C2×C11C2×#45211yescharacteristic
353C2×C11C2×#45311yescharacteristic
354D11—84no—
355C24—21no—
356C24—222no—
357#41—448no—
358#41—448no—
359#41—4416no—
360C2×Q8—22no—
361C2×Q8—44no—
362C2×Q8—41no—
363C2×Q8—114no—
364C2×Q8—112no—
365C2×Q8—222no—
366C2×Q8—221no—
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—114no—
371C2×D4—228no—
372C2×D4—228no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—222no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—444no—
379C2×D4—448no—
380C2×D4—442no—
381C2×D4—442no—
382C2×D4—442no—
383C2×D4—442no—
384C2×D4—884no—
385C2×D4C2×C22⋊D1112yes—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—41no—
392C22×C4—228no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—448no—
396C22×C4D4×D1111yescharacteristic
397C22×C4D4×D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399SD16—4416no—
400C2×C8—22no—
401C2×C8—42no—
402C2×C8—224no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—442no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—112no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4C2×C22⋊D1112yes—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—228no—
419C42—222no—
420C42—222no—
421C42D4×D1111yescharacteristic
422C42D4×D1111yescharacteristic
423C42C2×C22⋊D1111yescharacteristic
424C42C23×D1111yescharacteristic
425C11C2×#163111yescharacteristic, complemented, Sylow
426C23—22no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23—224no—
431C23—444no—
432C23—444no—
433C23—444no—
434C23#6699011yescharacteristic
435Q8—44no—
436Q8—82no—
437Q8—114no—
438Q8—222no—
439Q8—224no—
440D4—22no—
441D4—22no—
442D4—42no—
443D4—444no—
444D4—4416no—
445D4—442no—
446D4—442no—
447D4—444no—
448D4—442no—
449D4—442no—
450D4—444no—
451D4—882no—
452D4—888no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—82no—
461C2×C4—224no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—4416no—
465C2×C4—442no—
466C2×C4SD16×D1112yes—
467C2×C4#6696712yes—
468C2×C4#6699011yescharacteristic
469C2×C4#6699011yescharacteristic
470C2×C4#6699011yescharacteristic
471C2×C4#6699512yes—
472C2×C4#6700312yes—
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—42no—
477C8—224no—
478C8—442no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—84no—
483C22—444no—
484C22—444no—
485C22—444no—
486C22—888no—
487C22#1062266012yes—
488C22#1062278212yes—
489C22#1062281112yes—
490C22C2×#6699011yescharacteristic
491C4—21no—
492C4—21no—
493C4—42no—
494C4—82no—
495C4—224no—
496C4—442no—
497C4#1062266012yes—
498C4#1062278212yes—
499C4C2×SD16×D1111yescharacteristic
500C4C2×#6696711yescharacteristic
501C4C2×#6699511yescharacteristic
502C4C2×#6700311yescharacteristic
503C2—82no—
504C2—884no—
505C2#1306774214yesdirect product factor
506C2C2×#1062278211yescharacteristic
507C2C2×#1062266011yescharacteristic
508C2C2×#1062281111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#476C2
socleC23×C11#120
prime radicalC2×#10623084C2
hypercenterC2×#476D11
hypocenterC11C2×#1631
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×#10622698C2semidirect
3. C2×#10622704C2semidirect
4. #13067742C2direct (N × H)
5. C2×#10622123C2semidirect
6. C2×#10622122C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
8. C2×C11×#476C2semidirect
24. C11×#476C22semidirect
29. #10622704C22semidirect
31. #10622698C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622123C22semidirect
38. #10622122C22semidirect
144. C2×Dic22SD16semidirect
175. C2×#476D11semidirect
229. Dic22C2×SD16semidirect
252. #476C2×D11semidirect
350. C2×C11#1631semidirect
425. C11C2×#1631semidirect
505. C2#13067742direct (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×#106226982
C2×#106227042
#130677422
C2×#106221232
C2×#106221222
C2×D4⋊(C11⋊C8)2
C2×C11×#4762
C2×#163111