Finite Group Databasebeta

← C2×#13067686 #14729388

Subgroups — C2×#13067686 #14729388

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2C2×#10622689C211yesmaximal, characteristic, complemented
3C2×#10622688C211yesmaximal, characteristic, complemented
4#13067686C218yesmaximal, direct product factor
5C2×#10622119C211yesmaximal, characteristic, complemented
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×C11×#459C211yesmaximal, characteristic
9C22×C11×D8—21no—
10C2×C11×#127C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11—21no—
13C22×#4324—21no—
14C22×#4324—22no—
15C22×C4⋊Dic11—21no—
16C2×#66977—21no—
17#10623074—22no—
18#10623074—22no—
19#10623074—22no—
20#10623074C2214yescomplemented
21C2×#66943—21no—
22C2×#66931—22no—
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#459—22no—
26C11×#459C2214yes—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#102—21no—
29C2×#66896—21no—
30#10622689—22no—
31#10622689C2214yescomplemented
32#10622688—22no—
33#10622688C2214yescomplemented
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36D4⋊(C11⋊C8)C2214yescomplemented
37#10622122C2214yescomplemented
38#10622119C2214yescomplemented
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11D411yescharacteristic
43C23×C4×C11—21no—
44C23×Dic11—22no—
45C22×Dic22D411yescharacteristic
46C22×Dic22D412yes—
47C2×C11×D8—24no—
48C2×C11×D8—44no—
49C22×C8×C11—21no—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127C2312yes—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11D412yes—
57C4×D4×C11C2312yes—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62D4×Dic11—24no—
63D4×Dic11—24no—
64C2×#4324—24no—
65C2×#4324—28no—
66C2×#4324—48no—
67C2×#4324—44no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—24no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11D411yescharacteristic
74#66977—24no—
75#66977—24no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8—21no—
80C22×C11⋊C8—21no—
81#66943—24no—
82#66943—24no—
83#66931—28no—
84#66931—28no—
85#66922—21no—
86#66922—21no—
87#66922D412yes—
88#66922C2312yes—
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×#1622—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11—41no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—44no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11SD1614yescomplemented
118C2×D4×C11C2×D412yes—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×Dic11—28no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—84no—
132C2×Dic22—21no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—44no—
137C2×Dic22C2×D412yes—
138C2×Dic22C2×D414yes—
139C11×D8—48no—
140C2×C8×C11—22no—
141C2×C8×C11—42no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4C2×D412yes—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2411yescharacteristic
150C22⋊Dic11—28no—
151#4324—416no—
152#4324—48no—
153C4⋊Dic11—28no—
154C4⋊Dic11—21no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11C2×D412yes—
160Dic11⋊C4—28no—
161Dic11⋊C4—22no—
162Dic11⋊C4—22no—
163C4×Dic11—22no—
164C4×Dic11—22no—
165C2×C11⋊C8—24no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—42no—
169C2×#554—111no—
170C2×#492—111no—
171C2×#460—111no—
172C2×#459D1111yescharacteristic
173#1622—118no—
174C2×#333—111no—
175C2×Q8⋊C8—111no—
176C2×D4⋊C8—111no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—82no—
183C23×C11—82no—
184C23×C11—82no—
185C23×C11#12011yescharacteristic
186D4×C11—22no—
187D4×C11—24no—
188D4×C11—44no—
189D4×C11—42no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—82no—
194D4×C11—82no—
195D4×C11—82no—
196D4×C11C2×SD1614yescomplemented
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—44no—
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11C2×SD1612yes—
207C2×C4×C11#13512yes—
208C2×C4×C11AGL(1,ℤ/8)12yes—
209C2×C4×C11#13712yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—24no—
216C2×Dic11—42no—
217C2×Dic11—44no—
218C2×Dic11—42no—
219C2×Dic11—88no—
220Dic22—22no—
221Dic22—22no—
222Dic22—42no—
223Dic22—44no—
224Dic22—82no—
225C8×C11—42no—
226C11⋊C8—24no—
227C11⋊C8—42no—
228C22×SD16—222no—
229C22×SD16—221no—
230C22×D8—21no—
231#554—114no—
232#554—222no—
233#554—222no—
234#554—222no—
235C2×C4⋊Q8—111no—
236C2×#127C2×D1111yescharacteristic
237C2×#125—221no—
238C2×C22⋊Q8—222no—
239C2×C22⋊Q8—221no—
240C2×C4×Q8—111no—
241C2×C4×D4—221no—
242C2×C4×D4C2×D1111yescharacteristic
243C22×C4⋊C4—221no—
244#492—114no—
245#492—222no—
246#460—114no—
247#460—222no—
248#459—22no—
249#459C2×D1114yes—
250C2×C4⋊C8—111no—
251C2×C4⋊C8C2×D1111yescharacteristic
252C2×#102—21no—
253C2×#102—221no—
254C2×C4×C8—111no—
255#333—114no—
256Q8⋊C8—114no—
257D4⋊C8—114no—
258C22×C11—24no—
259C22×C11—48no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—164no—
266C22×C11#44812yes—
267C22×C11#44912yes—
268C22×C11#45312yes—
269C22×C11C2×#12011yescharacteristic
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—42no—
273C4×C11#44812yes—
274C4×C11#44912yes—
275C4×C11C22×SD1611yescharacteristic
276C4×C11C2×#13511yescharacteristic
277C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
278C4×C11C2×#13711yescharacteristic
279Dic11—42no—
280Dic11—44no—
281Dic11—42no—
282C22×Q8—111no—
283C22×Q8—112no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4C22⋊D1111yescharacteristic
288C23×C4—21no—
289C23×C4—222no—
290C2×SD16—224no—
291C2×SD16—228no—
292C2×SD16—448no—
293C2×SD16—444no—
294C2×D8—24no—
295C2×D8—44no—
296C22×C8—21no—
297C22×C8—221no—
298C22×C8—221no—
299C4⋊Q8—112no—
300C4⋊Q8—112no—
301C4⋊Q8—221no—
302C4⋊Q8—221no—
303#127—21no—
304#127—21no—
305#127—21no—
306#127C22×D1112yes—
307#125—224no—
308#125—224no—
309C22⋊Q8—228no—
310C22⋊Q8—228no—
311C22⋊Q8—224no—
312C22⋊Q8—224no—
313C4×Q8—112no—
314C4×Q8—112no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—224no—
320C4×D4—224no—
321C4×D4C22⋊D1112yes—
322C4×D4C22×D1112yes—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—224no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—224no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4C22⋊D1111yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—222no—
334C2×C42—221no—
335C2×C42C22×D1111yescharacteristic
336C4⋊C8—21no—
337C4⋊C8—112no—
338C4⋊C8—221no—
339C4⋊C8C22×D1112yes—
340#102—24no—
341#102—224no—
342C4×C8—112no—
343C4×C8—221no—
344C2×C11—44no—
345C2×C11—162no—
346C2×C11#162214yescomplemented
347C2×C11C2×#44811yescharacteristic
348C2×C11C2×#44911yescharacteristic
349C2×C11C2×#45311yescharacteristic
350C24—21no—
351C24—41no—
352C2×Q8—112no—
353C2×Q8—114no—
354C2×Q8—221no—
355C2×Q8—222no—
356C2×Q8—222no—
357C2×Q8—222no—
358C2×Q8—444no—
359C2×D4—21no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—44no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—42no—
372C2×D4#432414yescomplemented
373C2×D4C2×C22⋊D1112yes—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—222no—
382C22×C4—228no—
383C22×C4—884no—
384C22×C4D4×D1111yescharacteristic
385C22×C4D4×D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387SD16—4416no—
388SD16—448no—
389D8—48no—
390C2×C8—22no—
391C2×C8—42no—
392C2×C8—224no—
393C2×C8—222no—
394C2×C8—222no—
395C2×C8—442no—
396C4⋊C4—21no—
397C4⋊C4—112no—
398C4⋊C4—228no—
399C4⋊C4—228no—
400C4⋊C4—221no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4C2×C22⋊D1112yes—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—228no—
411C42—222no—
412C42—222no—
413C42D4×D1111yescharacteristic
414C42D4×D1111yescharacteristic
415C42C2×C22⋊D1111yescharacteristic
416C42C23×D1111yescharacteristic
417C11C2×#162211yescharacteristic, complemented, Sylow
418C23—22no—
419C23—24no—
420C23—42no—
421C23—42no—
422C23—42no—
423C23—82no—
424C23—82no—
425C23—82no—
426C23#6699011yescharacteristic
427Q8—222no—
428Q8—222no—
429Q8—444no—
430Q8—442no—
431Q8—882no—
432D4—22no—
433D4—24no—
434D4—44no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—42no—
439D4—82no—
440D4—82no—
441D4—82no—
442D4C2×#432414yescomplemented
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—224no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—444no—
455C2×C4—888no—
456C2×C4#6696412yes—
457C2×C4#6696512yes—
458C2×C4C2×#432412yes—
459C2×C4#6699011yescharacteristic
460C2×C4#6699011yescharacteristic
461C2×C4#6699011yescharacteristic
462C2×C4#6700412yes—
463C2×C4C2×D4×D1111yescharacteristic
464C2×C4C2×D4×D1111yescharacteristic
465C2×C4C22×C22⋊D1111yescharacteristic
466C8—42no—
467C8—224no—
468C8—442no—
469C22—24no—
470C22—42no—
471C22—48no—
472C22—42no—
473C22—82no—
474C22—82no—
475C22—82no—
476C22—164no—
477C22#1062265312yes—
478C22#1062277112yes—
479C22#1062281112yes—
480C22C2×#6699011yescharacteristic
481C4—21no—
482C4—21no—
483C4—42no—
484C4—442no—
485C4—442no—
486C4—444no—
487C4#1062265312yes—
488C4#1062277112yes—
489C4C2×#6696411yescharacteristic
490C4C2×#6696511yescharacteristic
491C4C22×#432411yescharacteristic
492C4C2×#6700411yescharacteristic
493C2—44no—
494C2—162no—
495C2#1306768614yesdirect product factor
496C2C2×#1062265311yescharacteristic
497C2C2×#1062277111yescharacteristic
498C2C2×#1062281111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11#120
hypercenterC2×#459D11
hypocenterC11C2×#1622
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. C2×#10622689C2semidirect
3. C2×#10622688C2semidirect
4. #13067686C2direct (N × H)
5. C2×#10622119C2semidirect
6. C2×#10622122C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
20. #10623074C22semidirect
31. #10622689C22semidirect
33. #10622688C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622122C22semidirect
38. #10622119C22semidirect
117. C2×D4×C11SD16semidirect
196. D4×C11C2×SD16semidirect
346. C2×C11#1622semidirect
372. C2×D4#4324semidirect
417. C11C2×#1622semidirect
442. D4C2×#4324semidirect
495. C2#13067686direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106226892
C2×#106226882
#130676862
C2×#106221192
C2×#106221222
C2×D4⋊(C11⋊C8)2
C2×C11×#4592
C2×#162211