Finite Group Databasebeta

← C2×#13067031 #14720289

Subgroups — C2×#13067031 #14720289

Order 2816.

1354 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic, complemented
3C2×C4×#4313C211yesmaximal, characteristic, complemented
4#13067031C218yesmaximal, direct product factor
5C2×#10622097C211yesmaximal, characteristic, complemented
6C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#4339—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66993C411yescharacteristic
12C2×#66991C411yescharacteristic
13C2×C4×C22⋊D11—21no—
14C22×#4313—21no—
15#10623079—22no—
16#10623079—22no—
17#10623079C414yes—
18#10623079C2214yes—
19C2×#66948C411yescharacteristic
20C2×#66941C411yescharacteristic
21C2×#66938—21no—
22C2×#66937—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×(C2×D11)⋊C8—21no—
28C2×#66879—21no—
29C2×C8×Dic11—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622446—22no—
33#10622446C2214yescomplemented
34C4×#4313—22no—
35C4×#4313C2214yescomplemented
36C11×D4⋊C8C2214yescomplemented
37D4⋊(C11⋊C8)C2214yescomplemented
38#10622121C2214yescomplemented
39#10622097C2214yescomplemented
40C22×D4×C11C2×C411yescharacteristic
41C23×C4×C11—21no—
42C22×C22⋊D11—21no—
43C22×C22⋊D11—21no—
44C22×C22⋊D11—21no—
45C2×#4339—24no—
46C2×#4339—24no—
47C2×#4339—44no—
48C2×#4339—44no—
49C22×D44—21no—
50C22×D44C2×C411yescharacteristic
51C22×C4×D11—21no—
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×Dic22—21no—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11C2×C412yes—
61C4×D4×C11C2312yes—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—21no—
66#66993—22no—
67#66993C2×C414yes—
68#66991—22no—
69#66991C2×C414yes—
70C4×C22⋊D11—24no—
71C4×C22⋊D11—24no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C22×C11⋊C8—21no—
80C22×C11⋊C8—21no—
81C2×#4313—28no—
82C2×#4313—24no—
83#66948—22no—
84#66948C2×C414yes—
85#66941—22no—
86#66941C2×C414yes—
87#66938—24no—
88#66938—24no—
89#66937—24no—
90#66937—24no—
91C4×D44—21no—
92C4×D44—21no—
93C4×D44C2×C412yes—
94C4×D44C2312yes—
95C42×D11C2×C412yes—
96C42×D11D412yes—
97C42×D11D412yes—
98C42×D11C2312yes—
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2312yes—
101C4×C8×C11—21no—
102C4×C8×C11C2312yes—
103(C2×D11)⋊C8—24no—
104#66879—24no—
105C8×Dic11—24no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8C2312yes—
110C2×#1484—111nomaximal, Sylow
111C24×C11—21no—
112C23×D11—21no—
113C23×D11C22⋊C411yescharacteristic
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C22×C412yes—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—24no—
127C2×C22⋊D11—24no—
128C2×C22⋊D11—24no—
129C2×C22⋊D11—44no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—44no—
132C22×Dic11—21no—
133C22×Dic11C22⋊C411yescharacteristic
134C22×Dic11C22⋊C411yescharacteristic
135C22×Dic11C22⋊C411yescharacteristic
136#4339—48no—
137#4339—48no—
138#4339—416no—
139C2×D44—24no—
140C2×D44—21no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44—44no—
144C2×D44C22×C412yes—
145C2×C4×D11—24no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11C22⋊C412yes—
155C2×C4×D11C22⋊C412yes—
156C2×C4×D11C22⋊C412yes—
157C2×C4×D11C22×C412yes—
158C2×C4×D11C2×D412yes—
159C2×C4×D11C2×D412yes—
160C2×Dic22—24no—
161C2×Dic22—44no—
162C2×C8×C11—24no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—42no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4C22×C412yes—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C42×C11C22×C411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2411yescharacteristic
174C22⋊Dic11—24no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—22no—
177(C2×D11)⋊C4—22no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22×C412yes—
180Dic11⋊C4—24no—
181C4×Dic11C22⋊C412yes—
182C4×Dic11C22⋊C412yes—
183C4×Dic11C22⋊C412yes—
184C4×Dic11C22×C412yes—
185C4×Dic11C2×D412yes—
186C4×Dic11C2×D412yes—
187C2×C11⋊C8—24no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—42no—
191#4313—216no—
192C2×#532—111no—
193C2×#431—111no—
194C2×C4×M16—111no—
195#1484—118no—
196C2×D4⋊C8—111no—
197C2×D4⋊C8—111no—
198C2×D4⋊C8—111no—
199C2×D4⋊C8D1111yescharacteristic, complemented
200C23×C11—22no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11C2×C22⋊C411yescharacteristic
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11C2×C22⋊C412yes—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—42no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11#13112yes—
226C2×C4×C11#13112yes—
227C2×C4×C11AGL(1,ℤ/8)12yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C23×C411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C22⋊D11—48no—
233C22⋊D11—48no—
234C22⋊D11—48no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—42no—
239C2×Dic11#10414yes—
240C2×Dic11C2×C22⋊C412yes—
241C2×Dic11C2×C22⋊C412yes—
242C2×Dic11C2×C22⋊C412yes—
243D44—22no—
244D44—22no—
245D44—48no—
246D44—42no—
247C4×D11—22no—
248C4×D11—22no—
249C4×D11—22no—
250C4×D11—22no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—24no—
254C4×D11—24no—
255C4×D11—42no—
256C4×D11—42no—
257C4×D11—44no—
258Dic22—48no—
259C8×C11—24no—
260C8×C11—42no—
261C11⋊C8—24no—
262C11⋊C8—42no—
263C22×#41—221no—
264C22×M16—221no—
265#532—114no—
266#532—114no—
267#532—222no—
268#532—222no—
269C2×C4⋊Q8—111no—
270C2×#127—111no—
271C2×#124—221no—
272C2×#121—111no—
273C2×#121—111no—
274C2×#121—221no—
275C2×C4×D4—111no—
276C2×C4×D4—221no—
277C2×C4×D4C2×D1111yescharacteristic
278C22×C42—111no—
279#431—114no—
280#431—222no—
281C2×C4⋊C8—111no—
282C2×C4⋊C8C2×D1111yescharacteristic
283C2×C22⋊C8—221no—
284C4×M16—114no—
285C4×M16—222no—
286C2×#97—221no—
287C2×C4×C8—111no—
288C2×C4×C8—221no—
289C2×C4×C8C2×D1111yescharacteristic
290D4⋊C8—114no—
291D4⋊C8—114no—
292D4⋊C8—114no—
293D4⋊C8C2×D1114yescomplemented
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—84no—
298C22×C11#40812yes—
299C22×C11#41812yes—
300C22×C11C2×#10412yes—
301C22×C11C22×C22⋊C411yescharacteristic
302C2×D11—22no—
303C2×D11—22no—
304C2×D11—22no—
305C2×D11—44no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—84no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—42no—
313C4×C11#40812yes—
314C4×C11#41812yes—
315C4×C11C2×#13111yescharacteristic
316C4×C11C2×#13111yescharacteristic
317C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
319Dic11—22no—
320Dic11—22no—
321Dic11—42no—
322Dic11C2×#10414yes—
323C2×#41—224no—
324C2×#41—224no—
325C2×#41—444no—
326C2×#41—444no—
327C22×Q8—221no—
328C22×D4—111no—
329C22×D4—221no—
330C22×D4—221no—
331C22×D4—221no—
332C22×D4—221no—
333C22×D4C4×D1111yescharacteristic
334C23×C4—21no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—221no—
339C2×M16—224no—
340C2×M16—228no—
341C22×C8—21no—
342C22×C8—21no—
343C22×C8—221no—
344C22×C8—221no—
345C4⋊Q8—114no—
346C4⋊Q8—222no—
347#127—114no—
348#127—222no—
349#124—224no—
350#124—224no—
351#121—114no—
352#121—114no—
353#121—224no—
354#121—224no—
355#121—222no—
356#121—222no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—112no—
360C4×D4—112no—
361C4×D4—224no—
362C4×D4—224no—
363C4×D4—221no—
364C4×D4—221no—
365C4×D4C4×D1112yes—
366C4×D4C22×D1112yes—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4C4×D1111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—112no—
378C2×C42—112no—
379C2×C42—112no—
380C2×C42—112no—
381C2×C42C22×D1111yescharacteristic
382C4⋊C8—21no—
383C4⋊C8—112no—
384C4⋊C8—221no—
385C4⋊C8C22×D1112yes—
386C22⋊C8—224no—
387#97—224no—
388C4×C8—21no—
389C4×C8—112no—
390C4×C8—224no—
391C4×C8—221no—
392C4×C8C22×D1112yes—
393C2×C11—82no—
394C2×C11#148414yescomplemented
395C2×C11C2×#40811yescharacteristic
396C2×C11C2×#41811yescharacteristic
397C2×C11C22×#10411yescharacteristic
398D11—42no—
399D11—82no—
400C24—21no—
401C24—111no—
402C24—221no—
403#41—448no—
404#41—448no—
405#41—4416no—
406C2×Q8—224no—
407C2×Q8—444no—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—112no—
412C2×D4—224no—
413C2×D4—224no—
414C2×D4—224no—
415C2×D4—224no—
416C2×D4—221no—
417C2×D4—222no—
418C2×D4—222no—
419C2×D4—444no—
420C2×D4—444no—
421C2×D4—444no—
422C2×D4—444no—
423C2×D4C2×C4×D1112yes—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—221no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1111yescharacteristic
451M16—2216no—
452C2×C8—24no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—42no—
456C2×C8—224no—
457C2×C8—222no—
458C2×C8—222no—
459C2×C8—442no—
460C4⋊C4—21no—
461C4⋊C4—112no—
462C4⋊C4—224no—
463C4⋊C4—221no—
464C4⋊C4C2×C4×D1112yes—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—224no—
468C22⋊C4—224no—
469C22⋊C4—222no—
470C22⋊C4—222no—
471C42—112no—
472C42—112no—
473C42—112no—
474C42—112no—
475C42—112no—
476C42—112no—
477C42C2×C4×D1111yescharacteristic
478C42D4×D1111yescharacteristic
479C42D4×D1111yescharacteristic
480C42C23×D1111yescharacteristic
481C11C2×#148411yescharacteristic, complemented, Sylow
482C23—22no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—112no—
487C23—222no—
488C23—222no—
489C23—222no—
490C23—222no—
491C23—442no—
492C23—442no—
493C23—442no—
494C23C22⋊C4×D1111yescharacteristic
495Q8—448no—
496D4—22no—
497D4—22no—
498D4—42no—
499D4—222no—
500D4—222no—
501D4—448no—
502D4—448no—
503D4—448no—
504D4—448no—
505D4—442no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—44no—
512C2×C4—112no—
513C2×C4—114no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—222no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—444no—
531C2×C4C22⋊C4×D1111yescharacteristic
532C2×C4C22⋊C4×D1111yescharacteristic
533C2×C4C22⋊C4×D1111yescharacteristic
534C2×C4#6695412yes—
535C2×C4#6696012yes—
536C2×C4#6696412yes—
537C2×C4#6696712yes—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C8—24no—
542C8—42no—
543C8—224no—
544C8—442no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—84no—
549C22—222no—
550C22—222no—
551C22—222no—
552C22—444no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—884no—
557C22#1062234012yes—
558C22#1062238312yes—
559C22D11×#10412yes—
560C22C2×C22⋊C4×D1111yescharacteristic
561C4—21no—
562C4—21no—
563C4—42no—
564C4—114no—
565C4—222no—
566C4—222no—
567C4—442no—
568C4#1062234012yes—
569C4#1062238312yes—
570C4C2×#6695411yescharacteristic
571C4C2×#6696011yescharacteristic
572C4C2×#6696411yescharacteristic
573C4C2×#6696711yescharacteristic
574C2—82no—
575C2—442no—
576C2—882no—
577C2#1306703114yesdirect product factor
578C2C2×#1062234011yescharacteristic
579C2C2×#1062238311yescharacteristic
580C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623079C2
cosocleC42×C11C24
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1484
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×#10622446C2semidirect
3. C2×C4×#4313C2semidirect
4. #13067031C2direct (N × H)
5. C2×#10622097C2semidirect
6. C2×D4⋊(C11⋊C8)C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×D4⋊C8C2semidirect
33. #10622446C22semidirect
35. C4×#4313C22semidirect
36. C11×D4⋊C8C22semidirect
37. D4⋊(C11⋊C8)C22semidirect
38. #10622121C22semidirect
39. #10622097C22semidirect
199. C2×D4⋊C8D11semidirect
293. D4⋊C8C2×D11semidirect
394. C2×C11#1484semidirect
481. C11C2×#1484semidirect
577. C2#13067031direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×#106224462
C2×C4×#43132
#130670312
C2×#106220972
C2×D4⋊(C11⋊C8)2
C2×#106221212
C2×C11×D4⋊C82
C2×#148411