Finite Group Databasebeta

← C2×#13067674 #14729404

Subgroups — C2×#13067674 #14729404

Order 2816.

1190 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×#10623116C211yesmaximal, characteristic, complemented
2C2×#10622686C211yesmaximal, characteristic
3C2×#10622688C211yesmaximal, characteristic, complemented
4#13067674C218yesmaximal, direct product factor
5C2×#10622123C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622122C211yesmaximal, characteristic, complemented
8C2×C11×#460C211yesmaximal, characteristic, complemented
9C22×C11×SD16—21no—
10C2×C11×#127C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×#67000—21no—
13C22×#4324—21no—
14C22×#4323—22no—
15#10623116—22no—
16#10623116—22no—
17#10623116—22no—
18#10623116C2214yescomplemented
19C2×#66947—22no—
20C2×#66946—21no—
21C2×#66928—21no—
22C2×#66927C2211yescharacteristic
23C2×C4×D44—21no—
24C2×C4×Dic22C2211yescharacteristic
25C11×#460—22no—
26C11×#460C2214yescomplemented
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#102—21no—
29C2×#66896—21no—
30#10622688—22no—
31#10622688C2214yescomplemented
32#10622686—22no—
33#10622686C2214yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36Q8⋊(C11⋊C8)C2214yescomplemented
37#10622123C2214yescomplemented
38#10622122C2214yescomplemented
39C22×Q8×C11D411yescharacteristic
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44D412yes—
46C22×C4×D11—22no—
47C22×Dic22D411yescharacteristic
48C2×C11×SD16—24no—
49C2×C11×SD16—44no—
50C22×C8×C11—21no—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127—21no—
54C11×#127C2312yes—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11D412yes—
58C4×Q8×C11C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#67000—24no—
64#67000—24no—
65C2×#4324—24no—
66C2×#4324—44no—
67C2×#4323—28no—
68C2×#4323—48no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11D411yescharacteristic
73C2×Dic11⋊C4—21no—
74C2×C4×Dic11—21no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77#66947—28no—
78#66947—28no—
79#66946—24no—
80#66946—24no—
81#66928—24no—
82#66928—24no—
83#66927—21no—
84#66927—21no—
85#66927D412yes—
86#66927C2312yes—
87C4×D44—24no—
88C4×D44—24no—
89C4×Dic22—21no—
90C4×Dic22—21no—
91C4×Dic22D412yes—
92C4×Dic22C2312yes—
93C11×C4⋊C8—21no—
94C11×C4⋊C8C2312yes—
95C11×#102—24no—
96#66896—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4×C11⋊C8—21no—
100C4×C11⋊C8C2312yes—
101C2×#1620—111nomaximal, Sylow
102C24×C11—41no—
103C23×D11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11C2×D412yes—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—44no—
112C2×D4×C11—41no—
113C2×D4×C11—41no—
114C2×D4×C11—41no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×Dic11—21no—
125C22×Dic11—21no—
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—84no—
139C2×Dic22—21no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22C2×D412yes—
143C11×SD16—48no—
144C2×C8×C11—22no—
145C2×C8×C11—42no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4C2×D412yes—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2411yescharacteristic
156#4324—48no—
157#4323—416no—
158(C2×D11)⋊C4—28no—
159(C2×D11)⋊C4—28no—
160(C2×D11)⋊C4—28no—
161C4⋊Dic11—21no—
162C4⋊Dic11C2×D412yes—
163Dic11⋊C4—22no—
164Dic11⋊C4—22no—
165C4×Dic11—22no—
166C4×Dic11—22no—
167C2×C11⋊C8—24no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—42no—
171C2×#559—111no—
172C2×#493—111no—
173C2×#460—111no—
174C2×#460D1111yescharacteristic, complemented
175#1620—118no—
176C2×#331—111no—
177C2×Q8⋊C8—111no—
178C2×Q8⋊C8—111no—
179C23×C11—42no—
180C23×C11—82no—
181C23×C11—82no—
182C23×C11—82no—
183C23×C11#12011yescharacteristic
184C22×D11—24no—
185C22×D11—44no—
186C22×D11—44no—
187C22×D11—44no—
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—42no—
191D4×C11—44no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—82no—
197D4×C11—82no—
198D4×C11—82no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#13512yes—
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
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218D44—44no—
219D44—42no—
220D44—42no—
221D44—42no—
222D44—42no—
223D44—44no—
224D44—44no—
225D44—82no—
226C4×D11—88no—
227Dic22—22no—
228Dic22—22no—
229Dic22—42no—
230C8×C11—42no—
231C11⋊C8—24no—
232C11⋊C8—42no—
233C22×SD16—21no—
234C22×SD16—221no—
235C22×D8—222no—
236#559—114no—
237#559—222no—
238#559—222no—
239#559—222no—
240C2×#127—111no—
241C2×#127C2×D1111yescharacteristic
242C2×#124—221no—
243C2×#124—221no—
244C2×#123—222no—
245C2×C4×Q8—111no—
246C2×C4×Q8C2×D1111yescharacteristic
247C2×C4×D4—221no—
248C2×C4×D4—221no—
249#493—114no—
250#493—222no—
251#460—22no—
252#460—114no—
253#460—222no—
254#460C2×D1114yescomplemented
255C2×C4⋊C8—111no—
256C2×C4⋊C8C2×D1111yescharacteristic
257C2×#102—21no—
258C2×#102—221no—
259C2×C4×C8—111no—
260#331—114no—
261Q8⋊C8—114no—
262Q8⋊C8—114no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—82no—
266C22×C11—164no—
267C22×C11#44912yes—
268C22×C11#44912yes—
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—42no—
279C4×C11#44912yes—
280C4×C11#44912yes—
281C4×C11C2×#13511yescharacteristic
282C4×C11C2×#13511yescharacteristic
283C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
284C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
285Dic11—42no—
286Dic11—42no—
287C22×Q8—111no—
288C22×Q8C22⋊D1111yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—112no—
293C22×D4—221no—
294C22×D4—221no—
295C23×C4—222no—
296C2×SD16—24no—
297C2×SD16—44no—
298C2×SD16—224no—
299C2×SD16—444no—
300C2×D8—228no—
301C2×D8—448no—
302C22×C8—21no—
303C22×C8—221no—
304C22×C8—221no—
305#127—21no—
306#127—21no—
307#127—21no—
308#127—112no—
309#127—112no—
310#127—221no—
311#127—221no—
312#127C22×D1112yes—
313#124—224no—
314#124—224no—
315#124—224no—
316#124—224no—
317#123—228no—
318#123—228no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—112no—
322C4×Q8—112no—
323C4×Q8—221no—
324C4×Q8—221no—
325C4×Q8C22⋊D1112yes—
326C4×Q8C22×D1112yes—
327C4×D4—224no—
328C4×D4—224no—
329C4×D4—224no—
330C4×D4—224no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C22⋊D1111yescharacteristic
335C2×C22⋊C4—222no—
336C2×C22⋊C4—222no—
337C2×C22⋊C4—222no—
338C2×C42—21no—
339C2×C42—221no—
340C2×C42C22×D1111yescharacteristic
341C4⋊C8—21no—
342C4⋊C8—112no—
343C4⋊C8—221no—
344C4⋊C8C22×D1112yes—
345#102—24no—
346#102—224no—
347C4×C8—112no—
348C4×C8—221no—
349C2×C11—162no—
350C2×C11#162014yescomplemented
351C2×C11C2×#44911yescharacteristic
352C2×C11C2×#44911yescharacteristic
353C2×C11C2×#45311yescharacteristic
354D11—84no—
355C24—41no—
356C24—222no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—112no—
361C2×Q8—221no—
362C2×Q8—222no—
363C2×Q8—222no—
364C2×Q8C2×C22⋊D1112yes—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—44no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—42no—
376C2×D4—114no—
377C2×D4—222no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—444no—
383C2×D4—442no—
384C2×D4—442no—
385C2×D4—442no—
386C2×D4—442no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—228no—
390C22×C4—221no—
391C22×C4—221no—
392C22×C4—884no—
393C22×C4D4×D1111yescharacteristic
394C22×C4D4×D1111yescharacteristic
395C22×C4C2×C22⋊D1111yescharacteristic
396SD16—48no—
397SD16—448no—
398D8—4416no—
399C2×C8—22no—
400C2×C8—42no—
401C2×C8—224no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—442no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—112no—
409C4⋊C4—221no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4C2×C22⋊D1112yes—
413C22⋊C4—228no—
414C22⋊C4—228no—
415C22⋊C4—228no—
416C42—22no—
417C42—22no—
418C42—222no—
419C42—222no—
420C42D4×D1111yescharacteristic
421C42D4×D1111yescharacteristic
422C42C2×C22⋊D1111yescharacteristic
423C42C23×D1111yescharacteristic
424C11C2×#162011yescharacteristic, complemented, Sylow
425C23—42no—
426C23—82no—
427C23—82no—
428C23—82no—
429C23—224no—
430C23—444no—
431C23—444no—
432C23—444no—
433C23#6699011yescharacteristic
434Q8—22no—
435Q8—22no—
436Q8—42no—
437Q8—222no—
438Q8—222no—
439Q8—442no—
440D4—44no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—82no—
446D4—82no—
447D4—82no—
448D4—444no—
449D4—442no—
450D4—442no—
451D4—444no—
452D4—442no—
453D4—442no—
454D4—444no—
455D4—882no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—888no—
466C2×C4#6696712yes—
467C2×C4#6696912yes—
468C2×C4#6698512yes—
469C2×C4#6699011yescharacteristic
470C2×C4#6699011yescharacteristic
471C2×C4#6699011yescharacteristic
472C2×C4#6700312yes—
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4C2×D4×D1111yescharacteristic
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—42no—
477C8—224no—
478C8—442no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—164no—
483C22—444no—
484C22—444no—
485C22—444no—
486C22—888no—
487C22#1062265012yes—
488C22#1062278512yes—
489C22#1062281112yes—
490C22C2×#6699011yescharacteristic
491C4—21no—
492C4—21no—
493C4—42no—
494C4—42no—
495C4—442no—
496C4—442no—
497C4#1062265012yes—
498C4#1062278512yes—
499C4C2×#6696711yescharacteristic
500C4C2×#6696911yescharacteristic
501C4C2×#6698511yescharacteristic
502C4C2×#6700311yescharacteristic
503C2—162no—
504C2—884no—
505C2#1306767414yesdirect product factor
506C2C2×#1062265011yescharacteristic
507C2C2×#1062278511yescharacteristic
508C2C2×#1062281111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#460C2
socleC23×C11#120
prime radicalC2×#10622686C2
hypercenterC2×#460D11
hypocenterC11C2×#1620
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
3. C2×#10622688C2semidirect
4. #13067674C2direct (N × H)
5. C2×#10622123C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
7. C2×#10622122C2semidirect
8. C2×C11×#460C2semidirect
18. #10623116C22semidirect
26. C11×#460C22semidirect
31. #10622688C22semidirect
36. Q8⋊(C11⋊C8)C22semidirect
37. #10622123C22semidirect
38. #10622122C22semidirect
174. C2×#460D11semidirect
254. #460C2×D11semidirect
350. C2×C11#1620semidirect
424. C11C2×#1620semidirect
505. C2#13067674direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106226862
C2×#106226882
#130676742
C2×#106221232
C2×Q8⋊(C11⋊C8)2
C2×#106221222
C2×C11×#4602
C2×#162011