Finite Group Databasebeta

← C2×#13067052 #14720198

Subgroups — C2×#13067052 #14720198

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic, complemented
3C2×C4×#4313C211yesmaximal, characteristic, complemented
4#13067052C218yesmaximal, 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×#4313—21no—
15C22×#4313—21no—
16C4×#4341—22no—
17C4×#4341—22no—
18C4×#4341C414yes—
19C4×#4341C2214yes—
20C2×#66945C411yescharacteristic
21C2×#66940C411yescharacteristic
22C2×(C22⋊D11)⋊C4—21no—
23C2×#66930—21no—
24C2×C42×D11C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66879—21no—
29C2×Dic11⋊C8—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622450—22no—
33#10622450C2214yescomplemented
34C4×#4313—22no—
35C4×#4313C2214yescomplemented
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—
81C2×#4313—28no—
82C2×#4313—24no—
83C2×#4313—24no—
84C2×#4313—44no—
85#66945—22no—
86#66945C2×C414yes—
87#66940—22no—
88#66940C2×C414yes—
89(C22⋊D11)⋊C4—24no—
90(C22⋊D11)⋊C4—24no—
91#66930—24no—
92#66930—24no—
93C42×D11C2×C412yes—
94C42×D11D412yes—
95C42×D11D412yes—
96C42×D11C2312yes—
97C4×Dic22—21no—
98C4×Dic22—21no—
99C4×Dic22C2×C412yes—
100C4×Dic22C2312yes—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C4×C8×C11—21no—
104C4×C8×C11C2312yes—
105#66879—24no—
106Dic11⋊C8—24no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2312yes—
109C4×C11⋊C8—21no—
110C4×C11⋊C8C2312yes—
111C2×#1489—111nomaximal, Sylow
112C24×C11—21no—
113C23×D11C22⋊C411yescharacteristic
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11M1614yescomplemented
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—28no—
127C2×C22⋊D11—24no—
128C22×Dic11—28no—
129C22×Dic11—24no—
130C22×Dic11—24no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—44no—
134C22×Dic11C22⋊C411yescharacteristic
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C411yescharacteristic
137#4341—216no—
138#4341—28no—
139#4341—28no—
140C2×C4×D11—24no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11C22⋊C412yes—
146C2×C4×D11C22⋊C412yes—
147C2×C4×D11C22⋊C412yes—
148C2×C4×D11C22×C412yes—
149C2×C4×D11C2×D412yes—
150C2×C4×D11C2×D412yes—
151C2×Dic22—21no—
152C2×Dic22—22no—
153C2×Dic22M1614yescomplemented
154C2×Dic22C22×C412yes—
155C2×C8×C11—24no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—42no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4C22×C412yes—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C42×C11C22×C411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2411yescharacteristic
167C22⋊Dic11—24no—
168(C2×D11)⋊C4—24no—
169C4⋊Dic11—21no—
170C4⋊Dic11C22×C412yes—
171Dic11⋊C4—24no—
172Dic11⋊C4—22no—
173Dic11⋊C4—22no—
174C4×Dic11—24no—
175C4×Dic11—24no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C4×Dic11C22⋊C412yes—
179C4×Dic11C22⋊C412yes—
180C4×Dic11C22⋊C412yes—
181C4×Dic11C22×C412yes—
182C4×Dic11C2×D412yes—
183C4×Dic11C2×D412yes—
184C2×C11⋊C8—24no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—42no—
188#4313—216no—
189#4313—48no—
190C2×C4×#41—111no—
191C2×#423—111no—
192C2×C4×M16—111no—
193#1489—118no—
194C2×Q8⋊C8—111no—
195C2×Q8⋊C8—111no—
196C2×D4⋊C8—111no—
197C2×D4⋊C8D1111yescharacteristic, complemented
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11C2×C22⋊C411yescharacteristic
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11C2×C22⋊C412yes—
207D4×C11—22no—
208D4×C11—24no—
209D4×C11C2×M1614yescomplemented
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11C2×C22⋊C411yescharacteristic
217C2×C4×C11C2×C22⋊C411yescharacteristic
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C2×M1612yes—
220C2×C4×C11C2×M1612yes—
221C2×C4×C11AGL(1,ℤ/8)12yes—
222C2×C4×C11#13712yes—
223C2×C4×C11C23×C411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C22⋊D11—216no—
227C2×Dic11—216no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—42no—
234C2×Dic11—48no—
235C2×Dic11#10414yes—
236C2×Dic11C2×C22⋊C412yes—
237C2×Dic11C2×C22⋊C412yes—
238C2×Dic11C2×C22⋊C412yes—
239C4×D11—22no—
240C4×D11—22no—
241C4×D11—22no—
242C4×D11—22no—
243C4×D11—24no—
244C4×D11—24no—
245C4×D11—24no—
246C4×D11—24no—
247Dic22—22no—
248Dic22—24no—
249Dic22C2×M1614yescomplemented
250C8×C11—24no—
251C8×C11—42no—
252C11⋊C8—24no—
253C11⋊C8—42no—
254C22×#41—111no—
255C22×M16—221no—
256C22×M16—221no—
257C4×#41—114no—
258C4×#41—114no—
259C4×#41—222no—
260C4×#41—222no—
261C2×C4×Q8—111no—
262C2×C4×Q8—111no—
263C2×C4×D4—111no—
264C2×C4×D4—221no—
265C2×C4×D4—221no—
266C2×C4×D4C2×D1111yescharacteristic
267C2×#117—111no—
268C2×#117—221no—
269C22×C42—111no—
270C22×C42—221no—
271#423—114no—
272#423—222no—
273C2×C4⋊C8—111no—
274C2×C4⋊C8—221no—
275C2×C4⋊C8C2×D1111yescharacteristic
276C4×M16—114no—
277C4×M16—222no—
278C2×#97—221no—
279C2×C4×C8—111no—
280C2×C4×C8C2×D1111yescharacteristic
281Q8⋊C8—114no—
282Q8⋊C8—114no—
283D4⋊C8—114no—
284D4⋊C8C2×D1114yescomplemented
285C22×C11—24no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—48no—
289C22×C11#40712yes—
290C22×C11#41712yes—
291C22×C11C2×#10412yes—
292C22×C11C22×C22⋊C411yescharacteristic
293C2×D11—22no—
294C2×D11—22no—
295C2×D11—22no—
296C2×D11—44no—
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—42no—
300C4×C11#40712yes—
301C4×C11#41712yes—
302C4×C11C22×M1611yescharacteristic
303C4×C11C22×M1611yescharacteristic
304C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C11C2×#13711yescharacteristic
306Dic11—24no—
307Dic11—22no—
308Dic11—22no—
309Dic11—42no—
310Dic11C2×#10414yes—
311C2×#41—114no—
312C2×#41—222no—
313C2×#41—224no—
314C2×#41—224no—
315C22×Q8—111no—
316C22×D4—221no—
317C22×D4C4×D1111yescharacteristic
318C23×C4—21no—
319C23×C4—111no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—221no—
323C23×C4—221no—
324C2×M16—224no—
325C2×M16—228no—
326C2×M16—224no—
327C2×M16—444no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—221no—
331C22×C8—221no—
332C4×Q8—114no—
333C4×Q8—112no—
334C4×Q8—112no—
335C4×Q8—222no—
336C4×Q8—221no—
337C4×Q8—221no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—114no—
341C4×D4—222no—
342C4×D4—224no—
343C4×D4—224no—
344C4×D4—224no—
345C4×D4—224no—
346C4×D4C4×D1112yes—
347C4×D4C22×D1112yes—
348#117—114no—
349#117—224no—
350#117—224no—
351#117—222no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4C4×D1111yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—221no—
359C2×C42—111no—
360C2×C42—111no—
361C2×C42—111no—
362C2×C42—112no—
363C2×C42—112no—
364C2×C42—112no—
365C2×C42—112no—
366C2×C42—224no—
367C2×C42—224no—
368C2×C42—221no—
369C2×C42—221no—
370C2×C42—221no—
371C2×C42C22×D1111yescharacteristic
372C4⋊C8—21no—
373C4⋊C8—112no—
374C4⋊C8—224no—
375C4⋊C8—221no—
376C4⋊C8C22×D1112yes—
377#97—224no—
378C4×C8—21no—
379C4×C8—112no—
380C4×C8—221no—
381C4×C8C22×D1112yes—
382C2×C11—44no—
383C2×C11#148914yescomplemented
384C2×C11C2×#40711yescharacteristic
385C2×C11C2×#41711yescharacteristic
386C2×C11C22×#10411yescharacteristic
387D11—42no—
388C24—21no—
389C24—111no—
390#41—228no—
391#41—2216no—
392#41—228no—
393C2×Q8—114no—
394C2×Q8—112no—
395C2×Q8—221no—
396C2×Q8—222no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—224no—
400C2×D4—228no—
401C2×D4#431314yescomplemented
402C2×D4C2×C4×D1112yes—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—111no—
409C22×C4—111no—
410C22×C4—111no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—228no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4—444no—
428C22×C4C2×C4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431M16—2216no—
432M16—448no—
433C2×C8—24no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—42no—
437C2×C8—224no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—442no—
441C4⋊C4—21no—
442C4⋊C4—112no—
443C4⋊C4—224no—
444C4⋊C4—221no—
445C4⋊C4—222no—
446C4⋊C4—222no—
447C4⋊C4C2×C4×D1112yes—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—224no—
451C22⋊C4—224no—
452C42—112no—
453C42—112no—
454C42—112no—
455C42—112no—
456C42—112no—
457C42—112no—
458C42—224no—
459C42—224no—
460C42—222no—
461C42—222no—
462C42C2×C4×D1111yescharacteristic
463C42D4×D1111yescharacteristic
464C42D4×D1111yescharacteristic
465C42C23×D1111yescharacteristic
466C11C2×#148911yescharacteristic, complemented, Sylow
467C23—22no—
468C23—24no—
469C23—42no—
470C23—42no—
471C23—112no—
472C23—222no—
473C23—222no—
474C23—222no—
475C23C22⋊C4×D1111yescharacteristic
476Q8—114no—
477Q8—222no—
478Q8—224no—
479D4—22no—
480D4—24no—
481D4—2216no—
482D4C2×#431314yescomplemented
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—44no—
489C2×C4—112no—
490C2×C4—114no—
491C2×C4—112no—
492C2×C4—112no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—2216no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—222no—
507C2×C4—448no—
508C2×C4—442no—
509C2×C4C22⋊C4×D1111yescharacteristic
510C2×C4C22⋊C4×D1111yescharacteristic
511C2×C4C22⋊C4×D1111yescharacteristic
512C2×C4C2×#431312yes—
513C2×C4M16×D1112yes—
514C2×C4#6696412yes—
515C2×C4#6696812yes—
516C2×C4C22×C4×D1111yescharacteristic
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C8—24no—
520C8—42no—
521C8—224no—
522C8—442no—
523C22—24no—
524C22—48no—
525C22—42no—
526C22—42no—
527C22—222no—
528C22—222no—
529C22—222no—
530C22—444no—
531C22#1062233912yes—
532C22#1062238412yes—
533C22D11×#10412yes—
534C22C2×C22⋊C4×D1111yescharacteristic
535C4—21no—
536C4—21no—
537C4—42no—
538C4—114no—
539C4—222no—
540C4—224no—
541C4—222no—
542C4—442no—
543C4#1062233912yes—
544C4#1062238412yes—
545C4C22×#431311yescharacteristic
546C4C2×M16×D1111yescharacteristic
547C4C2×#6696411yescharacteristic
548C4C2×#6696811yescharacteristic
549C2—44no—
550C2—442no—
551C2#1306705214yesdirect product factor
552C2C2×#1062233911yescharacteristic
553C2C2×#1062238411yescharacteristic
554C2C2×D11×#10411yescharacteristic
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×#1489
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×#10622450C2semidirect
3. C2×C4×#4313C2semidirect
4. #13067052C2direct (N × H)
5. C2×#10622094C2semidirect
6. C2×#10622122C2semidirect
7. C2×D4⋊(C11⋊C8)C2semidirect
8. C2×C11×D4⋊C8C2semidirect
33. #10622450C22semidirect
35. C4×#4313C22semidirect
36. C11×D4⋊C8C22semidirect
37. D4⋊(C11⋊C8)C22semidirect
38. #10622122C22semidirect
39. #10622094C22semidirect
116. C2×D4×C11M16semidirect
153. C2×Dic22M16semidirect
197. C2×D4⋊C8D11semidirect
209. D4×C11C2×M16semidirect
249. Dic22C2×M16semidirect
284. D4⋊C8C2×D11semidirect
383. C2×C11#1489semidirect
401. C2×D4#4313semidirect
466. C11C2×#1489semidirect
482. D4C2×#4313semidirect
551. C2#13067052direct (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×#106224502
C2×C4×#43132
#130670522
C2×#106220942
C2×#106221222
C2×D4⋊(C11⋊C8)2
C2×C11×D4⋊C82
C2×#148911