Finite Group Databasebeta

← C2×#13066995 #14720122

Subgroups — C2×#13066995 #14720122

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic, complemented
3C2×C4×C8×D11C211yesmaximal, characteristic, complemented
4#13066995C218yesmaximal, 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—
14C22×C8×D11—21no—
15C4×#4341—22no—
16C4×#4341—22no—
17C4×#4341C414yes—
18C4×#4341C2214yes—
19C2×#66945C411yescharacteristic
20C2×#66940C411yescharacteristic
21C2×(C22⋊D11)⋊C4—21no—
22C2×#66930—21no—
23C2×C42×D11C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×(C2×D11)⋊C8—21no—
28C2×C8×Dic11—21no—
29C2×C8×Dic11—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622446—22no—
33#10622446C2214yescomplemented
34C4×C8×D11—22no—
35C4×C8×D11C2214yescomplemented
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—22no—
46C2×#4341—24no—
47C2×#4341C818yescomplemented
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—
81C2×C8×D11—28no—
82C2×C8×D11—24no—
83#66945—22no—
84#66945C2×C414yes—
85#66940—22no—
86#66940C2×C414yes—
87(C22⋊D11)⋊C4—24no—
88(C22⋊D11)⋊C4—24no—
89#66930—24no—
90#66930—24no—
91C42×D11C2×C412yes—
92C42×D11D412yes—
93C42×D11D412yes—
94C42×D11C2312yes—
95C4×Dic22—21no—
96C4×Dic22—21no—
97C4×Dic22C2×C412yes—
98C4×Dic22C2312yes—
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2312yes—
101C4×C8×C11—21no—
102C4×C8×C11C2312yes—
103(C2×D11)⋊C8—24no—
104C8×Dic11—24no—
105C8×Dic11—24no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8C2312yes—
110C2×#1476—111nomaximal, Sylow
111C24×C11—21no—
112C23×D11C22⋊C411yescharacteristic
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11C2×C814yescomplemented
116C2×D4×C11C22×C412yes—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C2×C22⋊D11—28no—
126C2×C22⋊D11—24no—
127C22×Dic11—28no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—44no—
133C22×Dic11C22⋊C411yescharacteristic
134C22×Dic11C22⋊C411yescharacteristic
135C22×Dic11C22⋊C411yescharacteristic
136#4341—216no—
137#4341—28no—
138#4341C2×C8116yescomplemented
139C2×C4×D11—24no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11C22⋊C412yes—
143C2×C4×D11C22⋊C412yes—
144C2×C4×D11C22⋊C412yes—
145C2×C4×D11C2×C814yes—
146C2×C4×D11M1614yes—
147C2×C4×D11C22×C412yes—
148C2×C4×D11C2×D412yes—
149C2×C4×D11C2×D412yes—
150C2×Dic22—21no—
151C2×Dic22—22no—
152C2×Dic22C2×C814yescomplemented
153C2×Dic22C22×C412yes—
154C2×C8×C11—24no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—42no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4C22×C412yes—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C42×C11C22×C411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2411yescharacteristic
166C22⋊Dic11—24no—
167(C2×D11)⋊C4—24no—
168C4⋊Dic11—21no—
169C4⋊Dic11C22×C412yes—
170Dic11⋊C4—24no—
171Dic11⋊C4—22no—
172Dic11⋊C4—22no—
173C4×Dic11—24no—
174C4×Dic11—24no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C4×Dic11C22⋊C412yes—
178C4×Dic11C22⋊C412yes—
179C4×Dic11C22⋊C412yes—
180C4×Dic11C22×C412yes—
181C4×Dic11C2×D412yes—
182C4×Dic11C2×D412yes—
183C2×C11⋊C8—24no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—42no—
187C8×D11—216no—
188C2×C4×#41—111no—
189C2×#431—111no—
190C22×C4×C8—111no—
191#1476—118no—
192C2×Q8⋊C8—111no—
193C2×Q8⋊C8—111no—
194C2×D4⋊C8—111no—
195C2×D4⋊C8D1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11C2×C22⋊C411yescharacteristic
201C22×D11—22no—
202C22×D11—22no—
203C22×D11C22⋊C814yes—
204C22×D11C2×C22⋊C412yes—
205D4×C11—22no—
206D4×C11—24no—
207D4×C11C22×C814yescomplemented
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11C2×C22⋊C411yescharacteristic
216C2×C4×C11C2×C22⋊C411yescharacteristic
217C2×C4×C11C22×C812yes—
218C2×C4×C11C2×M1612yes—
219C2×C4×C11#13512yes—
220C2×C4×C11#13512yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C22⋊D11—216no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—216no—
229C2×Dic11—22no—
230C2×Dic11—42no—
231C2×Dic11—48no—
232C2×Dic11C22⋊C814yes—
233C2×Dic11#10414yes—
234C2×Dic11C2×C22⋊C412yes—
235C2×Dic11C2×C22⋊C412yes—
236C2×Dic11C2×C22⋊C412yes—
237C4×D11—22no—
238C4×D11—22no—
239C4×D11—24no—
240C4×D11—24no—
241C4×D11—24no—
242C4×D11C22⋊C818yes—
243C4×D11C22×C814yes—
244C4×D11C2×M1614yes—
245Dic22—22no—
246Dic22—24no—
247Dic22C22×C814yescomplemented
248C8×C11—24no—
249C8×C11—42no—
250C11⋊C8—24no—
251C11⋊C8—42no—
252C22×#41—111no—
253C23×C8—221no—
254C4×#41—114no—
255C4×#41—114no—
256C4×#41—222no—
257C4×#41—222no—
258C2×C4×Q8—111no—
259C2×C4×Q8—111no—
260C2×C4×D4—111no—
261C2×C4×D4—221no—
262C2×C4×D4—221no—
263C2×C4×D4C2×D1111yescharacteristic
264C2×#117—111no—
265C2×#117—221no—
266C22×C42—111no—
267C22×C42—221no—
268#431—114no—
269#431—222no—
270C2×C4⋊C8—111no—
271C2×C4⋊C8C2×D1111yescharacteristic
272C2×C22⋊C8—221no—
273C2×C4×C8—111no—
274C2×C4×C8—114no—
275C2×C4×C8—222no—
276C2×C4×C8—221no—
277C2×C4×C8—221no—
278C2×C4×C8C2×D1111yescharacteristic
279Q8⋊C8—114no—
280Q8⋊C8—114no—
281D4⋊C8—114no—
282D4⋊C8C2×D1114yescomplemented
283C22×C11—24no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—48no—
287C22×C11C2×C22⋊C812yes—
288C22×C11#41612yes—
289C22×C11C2×#10412yes—
290C22×C11C22×C22⋊C411yescharacteristic
291C2×D11—22no—
292C2×D11—22no—
293C2×D11—28no—
294C2×D11C2×C22⋊C814yes—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—42no—
298C4×C11C2×C22⋊C812yes—
299C4×C11#41612yes—
300C4×C11C23×C811yescharacteristic
301C4×C11C22×M1611yescharacteristic
302C4×C11C2×#13511yescharacteristic
303C4×C11C2×#13511yescharacteristic
304Dic11—24no—
305Dic11—22no—
306Dic11—42no—
307Dic11C2×C22⋊C814yes—
308Dic11C2×#10414yes—
309C2×#41—118no—
310C2×#41—114no—
311C2×#41—222no—
312C2×#41—224no—
313C22×Q8—111no—
314C22×D4—221no—
315C22×D4C4×D1111yescharacteristic
316C23×C4—21no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—221no—
321C23×C4—221no—
322C22×C8—21no—
323C22×C8—21no—
324C22×C8—224no—
325C22×C8—228no—
326C22×C8—221no—
327C22×C8—221no—
328C4×Q8—114no—
329C4×Q8—112no—
330C4×Q8—112no—
331C4×Q8—222no—
332C4×Q8—221no—
333C4×Q8—221no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—114no—
337C4×D4—222no—
338C4×D4—224no—
339C4×D4—224no—
340C4×D4—224no—
341C4×D4—224no—
342C4×D4C4×D1112yes—
343C4×D4C22×D1112yes—
344#117—114no—
345#117—224no—
346#117—224no—
347#117—222no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C4×D1111yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42—111no—
358C2×C42—112no—
359C2×C42—112no—
360C2×C42—112no—
361C2×C42—112no—
362C2×C42—224no—
363C2×C42—224no—
364C2×C42—221no—
365C2×C42—221no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368C4⋊C8—21no—
369C4⋊C8—112no—
370C4⋊C8—221no—
371C4⋊C8C22×D1112yes—
372C22⋊C8—224no—
373C4×C8—21no—
374C4×C8—112no—
375C4×C8—224no—
376C4×C8—224no—
377C4×C8—221no—
378C4×C8C22×D1112yes—
379C2×C11—44no—
380C2×C11#147614yescomplemented
381C2×C11C22×C22⋊C811yescharacteristic
382C2×C11C2×#41611yescharacteristic
383C2×C11C22×#10411yescharacteristic
384D11—24no—
385C24—21no—
386C24—111no—
387#41—1116no—
388#41—228no—
389#41—2216no—
390C2×Q8—114no—
391C2×Q8—112no—
392C2×Q8—221no—
393C2×Q8—222no—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—224no—
397C2×D4—228no—
398C2×D4C8×D1114yescomplemented
399C2×D4C2×C4×D1112yes—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—111no—
406C22×C4—111no—
407C22×C4—112no—
408C22×C4—114no—
409C22×C4—114no—
410C22×C4—112no—
411C22×C4—111no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—228no—
419C22×C4—224no—
420C22×C4—221no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—444no—
425C22×C4C2×C4×D1111yescharacteristic
426C22×C4D4×D1111yescharacteristic
427C22×C4D4×D1111yescharacteristic
428C2×C8—24no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—42no—
432C2×C8—2216no—
433C2×C8—224no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—442no—
437C4⋊C4—21no—
438C4⋊C4—112no—
439C4⋊C4—224no—
440C4⋊C4—221no—
441C4⋊C4—222no—
442C4⋊C4—222no—
443C4⋊C4C2×C4×D1112yes—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—224no—
447C22⋊C4—224no—
448C42—112no—
449C42—112no—
450C42—112no—
451C42—112no—
452C42—112no—
453C42—112no—
454C42—224no—
455C42—224no—
456C42—222no—
457C42—222no—
458C42C2×C4×D1111yescharacteristic
459C42D4×D1111yescharacteristic
460C42D4×D1111yescharacteristic
461C42C23×D1111yescharacteristic
462C11C2×#147611yescharacteristic, complemented, Sylow
463C23—22no—
464C23—24no—
465C23—42no—
466C23—42no—
467C23—112no—
468C23—114no—
469C23—222no—
470C23—222no—
471C23C22⋊C4×D1111yescharacteristic
472Q8—114no—
473Q8—222no—
474Q8—224no—
475D4—22no—
476D4—24no—
477D4—2216no—
478D4C2×C8×D1114yescomplemented
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—112no—
486C2×C4—112no—
487C2×C4—114no—
488C2×C4—114no—
489C2×C4—114no—
490C2×C4—114no—
491C2×C4—118no—
492C2×C4—112no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—2216no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—224no—
502C2×C4—222no—
503C2×C4—448no—
504C2×C4—442no—
505C2×C4C22⋊C4×D1111yescharacteristic
506C2×C4C22⋊C4×D1111yescharacteristic
507C2×C4C22⋊C4×D1111yescharacteristic
508C2×C4C2×C8×D1112yes—
509C2×C4M16×D1112yes—
510C2×C4#6696512yes—
511C2×C4#6696912yes—
512C2×C4C22×C4×D1111yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C8—24no—
516C8—42no—
517C8—224no—
518C8—442no—
519C22—24no—
520C22—42no—
521C22—42no—
522C22—48no—
523C22—114no—
524C22—222no—
525C22—222no—
526C22—228no—
527C22D11×C22⋊C812yes—
528C22#1062238512yes—
529C22D11×#10412yes—
530C22C2×C22⋊C4×D1111yescharacteristic
531C4—21no—
532C4—21no—
533C4—42no—
534C4—114no—
535C4—114no—
536C4—224no—
537C4—222no—
538C4—442no—
539C4D11×C22⋊C812yes—
540C4#1062238512yes—
541C4C22×C8×D1111yescharacteristic
542C4C2×M16×D1111yescharacteristic
543C4C2×#6696511yescharacteristic
544C4C2×#6696911yescharacteristic
545C2—44no—
546C2—224no—
547C2#1306699514yesdirect product factor
548C2C2×D11×C22⋊C811yescharacteristic
549C2C2×#1062238511yescharacteristic
550C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#4341C4
cosocleC42×C11C24
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1476
LCSG ▷ 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×C8×D11C2semidirect
4. #13066995C2direct (N × H)
5. C2×#10622094C2semidirect
6. C2×#10622122C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
8. C2×C11×D4⋊C8C2semidirect
33. #10622446C22semidirect
35. C4×C8×D11C22semidirect
36. C11×D4⋊C8C22semidirect
37. D4⋊(C11⋊C8)C22semidirect
38. #10622122C22semidirect
39. #10622094C22semidirect
47. C2×#4341C8semidirect
115. C2×D4×C11C2×C8semidirect
138. #4341C2×C8semidirect
152. C2×Dic22C2×C8semidirect
195. C2×D4⋊C8D11semidirect
207. D4×C11C22×C8semidirect
247. Dic22C22×C8semidirect
282. D4⋊C8C2×D11semidirect
380. C2×C11#1476semidirect
398. C2×D4C8×D11semidirect
462. C11C2×#1476semidirect
478. D4C2×C8×D11semidirect
547. C2#13066995direct (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×#106224462
C2×C4×C8×D112
#130669952
C2×#106220942
C2×#106221222
C2×D4⋊(C11⋊C8)2
C2×C11×D4⋊C82
C2×#147611