Finite Group Databasebeta

← C2×#13067047 #14720175

Subgroups — C2×#13067047 #14720175

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2C2×#10622448C211yesmaximal, characteristic, complemented
3C2×#10622298C211yesmaximal, characteristic, complemented
4#13067047C218yesmaximal, direct product factor
5C2×#10622094C211yesmaximal, characteristic, complemented
6C2×#10622122C211yesmaximal, characteristic, complemented
7C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#4341C411yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×D4×Dic11C411yescharacteristic
12C2×C4×C22⋊D11—21no—
13C22×C4×Dic11—21no—
14C4×#4341—22no—
15C4×#4341—22no—
16C4×#4341C414yes—
17C4×#4341C2214yes—
18C2×#66945C411yescharacteristic
19C2×#66940C411yescharacteristic
20C2×(C22⋊D11)⋊C4—21no—
21C2×#66930—21no—
22C2×C42×D11C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×(C2×D11)⋊C8—21no—
27C2×(C2×D11)⋊C8—21no—
28C2×#66879—21no—
29C2×Dic11⋊C8—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622448—22no—
33#10622448C2214yescomplemented
34#10622298—22no—
35#10622298C2214yescomplemented
36C11×D4⋊C8C2214yescomplemented
37D4⋊(C11⋊C8)C2214yescomplemented
38#10622122C2214yescomplemented
39#10622094C2214yescomplemented
40C22×D4×C11C2×C411yescharacteristic
41C23×C4×C11—21no—
42C22×C22⋊D11—21no—
43C23×Dic11—21no—
44C23×Dic11—21no—
45C2×#4341—24no—
46C2×#4341—22no—
47C2×#4341—24no—
48C2×#4341C2×C414yes—
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×Dic22C2×C411yescharacteristic
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11C2×C412yes—
58C4×D4×C11C2312yes—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—21no—
63D4×Dic11—22no—
64D4×Dic11C2×C414yes—
65C4×C22⋊D11—24no—
66C4×C22⋊D11—24no—
67C2×(C2×D11)⋊C4—21no—
68C2×C4⋊Dic11C2×C411yescharacteristic
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C22×C11⋊C8—21no—
80C22×C11⋊C8—21no—
81#66945—22no—
82#66945C2×C414yes—
83#66940—22no—
84#66940C2×C414yes—
85(C22⋊D11)⋊C4—24no—
86(C22⋊D11)⋊C4—24no—
87#66930—24no—
88#66930—24no—
89C42×D11C2×C412yes—
90C42×D11D412yes—
91C42×D11D412yes—
92C42×D11C2312yes—
93C4×Dic22—21no—
94C4×Dic22—21no—
95C4×Dic22C2×C412yes—
96C4×Dic22C2312yes—
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2312yes—
99C4×C8×C11—21no—
100C4×C8×C11C2312yes—
101(C2×D11)⋊C8—24no—
102(C2×D11)⋊C8—24no—
103#66879—24no—
104Dic11⋊C8—24no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8C2312yes—
109C2×#1488—111nomaximal, Sylow
110C24×C11—21no—
111C23×D11C22⋊C411yescharacteristic
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11M1614yes—
115C2×D4×C11C22×C412yes—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—28no—
125C2×C22⋊D11—24no—
126C22×Dic11—28no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—44no—
132C22×Dic11C22⋊C411yescharacteristic
133C22×Dic11C22⋊C411yescharacteristic
134C22×Dic11C22⋊C411yescharacteristic
135#4341—216no—
136#4341—28no—
137#4341—28no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—42no—
143C2×C4×D11C22⋊C412yes—
144C2×C4×D11C22⋊C412yes—
145C2×C4×D11C22⋊C412yes—
146C2×C4×D11C22×C412yes—
147C2×C4×D11C2×D412yes—
148C2×C4×D11C2×D412yes—
149C2×Dic22—21no—
150C2×Dic22—22no—
151C2×Dic22M1614yes—
152C2×Dic22C22×C412yes—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—42no—
156C2×C8×C11—42no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4C22×C412yes—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C42×C11C22×C411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2411yescharacteristic
165C22⋊Dic11—24no—
166(C2×D11)⋊C4—24no—
167C4⋊Dic11—21no—
168C4⋊Dic11C22×C412yes—
169Dic11⋊C4—24no—
170Dic11⋊C4—22no—
171Dic11⋊C4—22no—
172C4×Dic11—24no—
173C4×Dic11—24no—
174C4×Dic11—22no—
175C4×Dic11—22no—
176C4×Dic11C22⋊C412yes—
177C4×Dic11C22⋊C412yes—
178C4×Dic11C22⋊C412yes—
179C4×Dic11C22×C412yes—
180C4×Dic11C2×D412yes—
181C4×Dic11C2×D412yes—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—42no—
185C2×C11⋊C8—42no—
186C2×C4×#41—111no—
187C2×#432—111no—
188C2×#431—111no—
189#1488—118no—
190C2×Q8⋊C8—111no—
191C2×Q8⋊C8—111no—
192C2×D4⋊C8—111no—
193C2×D4⋊C8D1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11C2×C22⋊C411yescharacteristic
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11C2×C22⋊C412yes—
203D4×C11—22no—
204D4×C11—24no—
205D4×C11C2×M1614yes—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—44no—
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11C2×M1612yes—
216C2×C4×C11C2×M1612yes—
217C2×C4×C11#13512yes—
218C2×C4×C11#13512yes—
219C2×C4×C11C23×C411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C22⋊D11—216no—
223C2×Dic11—216no—
224C2×Dic11—22no—
225C2×Dic11—24no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—48no—
231C2×Dic11—42no—
232C2×Dic11C2×C22⋊C412yes—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235C4×D11—22no—
236C4×D11—22no—
237C4×D11—22no—
238C4×D11—22no—
239C4×D11—24no—
240C4×D11—24no—
241C4×D11—42no—
242C4×D11—42no—
243Dic22—22no—
244Dic22—24no—
245Dic22C2×M1614yes—
246C8×C11—42no—
247C8×C11—42no—
248C11⋊C8—42no—
249C11⋊C8—42no—
250C22×#41—111no—
251C4×#41—114no—
252C4×#41—114no—
253C4×#41—222no—
254C4×#41—222no—
255C2×C4×Q8—111no—
256C2×C4×Q8—111no—
257C2×C4×D4—111no—
258C2×C4×D4—221no—
259C2×C4×D4—221no—
260C2×C4×D4C2×D1111yescharacteristic
261C2×#117—111no—
262C2×#117—221no—
263C22×C42—111no—
264C22×C42—221no—
265#432—114no—
266#432—222no—
267#431—114no—
268#431—222no—
269C2×C4⋊C8—111no—
270C2×C4⋊C8—221no—
271C2×C4⋊C8C2×D1111yescharacteristic
272C2×C22⋊C8—221no—
273C2×C22⋊C8—221no—
274C2×#97—221no—
275C2×C4×C8—111no—
276C2×C4×C8C2×D1111yescharacteristic
277Q8⋊C8—114no—
278Q8⋊C8—114no—
279D4⋊C8—114no—
280D4⋊C8C2×D1114yescomplemented
281C22×C11—24no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—48no—
285C22×C11#40712yes—
286C22×C11#41612yes—
287C22×C11#42112yes—
288C22×C11C22×C22⋊C411yescharacteristic
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—22no—
292C2×D11—44no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—42no—
296C4×C11#40712yes—
297C4×C11#41612yes—
298C4×C11C22×M1611yescharacteristic
299C4×C11C22×M1611yescharacteristic
300C4×C11C2×#13511yescharacteristic
301C4×C11C2×#13511yescharacteristic
302Dic11—24no—
303Dic11—22no—
304Dic11—22no—
305Dic11—22no—
306Dic11—42no—
307C2×#41—114no—
308C2×#41—222no—
309C2×#41—224no—
310C2×#41—224no—
311C22×Q8—111no—
312C22×D4—221no—
313C22×D4C4×D1111yescharacteristic
314C23×C4—21no—
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—221no—
319C23×C4—221no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—221no—
323C22×C8—221no—
324C4×Q8—114no—
325C4×Q8—112no—
326C4×Q8—112no—
327C4×Q8—222no—
328C4×Q8—221no—
329C4×Q8—221no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—114no—
333C4×D4—222no—
334C4×D4—224no—
335C4×D4—224no—
336C4×D4—224no—
337C4×D4—224no—
338C4×D4C4×D1112yes—
339C4×D4C22×D1112yes—
340#117—114no—
341#117—224no—
342#117—224no—
343#117—222no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4C4×D1111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42—112no—
355C2×C42—112no—
356C2×C42—112no—
357C2×C42—112no—
358C2×C42—224no—
359C2×C42—224no—
360C2×C42—221no—
361C2×C42—221no—
362C2×C42—221no—
363C2×C42C22×D1111yescharacteristic
364C4⋊C8—21no—
365C4⋊C8—112no—
366C4⋊C8—224no—
367C4⋊C8—221no—
368C4⋊C8C22×D1112yes—
369C22⋊C8—224no—
370C22⋊C8—224no—
371#97—224no—
372C4×C8—21no—
373C4×C8—112no—
374C4×C8—221no—
375C4×C8C22×D1112yes—
376C2×C11—44no—
377C2×C11#148814yescomplemented
378C2×C11C2×#40711yescharacteristic
379C2×C11C2×#41611yescharacteristic
380C2×C11C2×#42111yescharacteristic
381D11—42no—
382C24—21no—
383C24—111no—
384#41—228no—
385#41—2216no—
386#41—228no—
387C2×Q8—114no—
388C2×Q8—112no—
389C2×Q8—221no—
390C2×Q8—222no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4—224no—
394C2×D4—228no—
395C2×D4#431314yes—
396C2×D4C2×C4×D1112yes—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—228no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4—442no—
421C22×C4—444no—
422C22×C4C2×C4×D1111yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4D4×D1111yescharacteristic
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—42no—
428C2×C8—42no—
429C2×C8—222no—
430C2×C8—222no—
431C2×C8—442no—
432C2×C8—442no—
433C4⋊C4—21no—
434C4⋊C4—112no—
435C4⋊C4—224no—
436C4⋊C4—221no—
437C4⋊C4—222no—
438C4⋊C4—222no—
439C4⋊C4C2×C4×D1112yes—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—224no—
443C22⋊C4—224no—
444C42—112no—
445C42—112no—
446C42—112no—
447C42—112no—
448C42—112no—
449C42—112no—
450C42—224no—
451C42—224no—
452C42—222no—
453C42—222no—
454C42C2×C4×D1111yescharacteristic
455C42D4×D1111yescharacteristic
456C42D4×D1111yescharacteristic
457C42C23×D1111yescharacteristic
458C11C2×#148811yescharacteristic, complemented, Sylow
459C23—22no—
460C23—24no—
461C23—42no—
462C23—42no—
463C23—112no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23C22⋊C4×D1111yescharacteristic
468Q8—114no—
469Q8—222no—
470Q8—224no—
471D4—22no—
472D4—24no—
473D4—2216no—
474D4C2×#431314yes—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—112no—
482C2×C4—112no—
483C2×C4—112no—
484C2×C4—2216no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—224no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—448no—
500C2×C4—442no—
501C2×C4C22⋊C4×D1111yescharacteristic
502C2×C4C22⋊C4×D1111yescharacteristic
503C2×C4C22⋊C4×D1111yescharacteristic
504C2×C4C2×#431312yes—
505C2×C4M16×D1112yes—
506C2×C4#6696512yes—
507C2×C4#6696912yes—
508C2×C4C22×C4×D1111yescharacteristic
509C2×C4C2×D4×D1111yescharacteristic
510C2×C4C2×D4×D1111yescharacteristic
511C8—42no—
512C8—42no—
513C8—442no—
514C8—442no—
515C22—24no—
516C22—48no—
517C22—42no—
518C22—42no—
519C22—222no—
520C22—222no—
521C22—222no—
522C22—444no—
523C22#1062233912yes—
524C22#1062238512yes—
525C22#1062243412yes—
526C22C2×C22⋊C4×D1111yescharacteristic
527C4—21no—
528C4—21no—
529C4—42no—
530C4—222no—
531C4—224no—
532C4—222no—
533C4—222no—
534C4—442no—
535C4#1062233912yes—
536C4#1062238512yes—
537C4C22×#431311yescharacteristic
538C4C2×M16×D1111yescharacteristic
539C4C2×#6696511yescharacteristic
540C4C2×#6696911yescharacteristic
541C2—44no—
542C2—442no—
543C2#1306704714yesdirect product factor
544C2C2×#1062233911yescharacteristic
545C2C2×#1062238511yescharacteristic
546C2C2×#1062243411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#4341C4
cosocleC42×C11C24
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1488
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622448C2semidirect
3. C2×#10622298C2semidirect
4. #13067047C2direct (N × H)
5. C2×#10622094C2semidirect
6. C2×#10622122C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
8. C2×C11×D4⋊C8C2semidirect
33. #10622448C22semidirect
35. #10622298C22semidirect
36. C11×D4⋊C8C22semidirect
37. D4⋊(C11⋊C8)C22semidirect
38. #10622122C22semidirect
39. #10622094C22semidirect
193. C2×D4⋊C8D11semidirect
280. D4⋊C8C2×D11semidirect
377. C2×C11#1488semidirect
458. C11C2×#1488semidirect
543. C2#13067047direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C2×#106224482
C2×#106222982
#130670472
C2×#106220942
C2×#106221222
C2×D4⋊(C11⋊C8)2
C2×C11×D4⋊C82
C2×#148811