Finite Group Databasebeta

← C2×#13067043 #14720170

Subgroups — C2×#13067043 #14720170

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic
3C2×#10622450C211yesmaximal, characteristic
4#13067043C218yesmaximal, direct product factor
5C2×#10622094C211yesmaximal, characteristic, complemented
6C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622122C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C22×Q8×D11C411yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×Q8×Dic11C411yescharacteristic
12C22×#4313—21no—
13C4×Q8×D11—22no—
14C4×Q8×D11—22no—
15C4×Q8×D11C414yes—
16C4×Q8×D11C2214yes—
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11C411yescharacteristic
19C2×#66940—21no—
20C2×#66940C411yescharacteristic
21C2×C42×D11—21no—
22C2×C42×D11C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×(C2×D11)⋊C8—21no—
28C2×Dic11⋊C8—21no—
29C2×Dic11⋊C8—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622450—22no—
33#10622450C2214yes—
34#10622298—22no—
35#10622298C2214yes—
36C11×Q8⋊C8C2214yescomplemented
37Q8⋊(C11⋊C8)C2214yescomplemented
38#10622122C2214yescomplemented
39#10622094C2214yescomplemented
40C22×Q8×C11C2×C411yescharacteristic
41C2×Q8×D11—24no—
42C2×Q8×D11—22no—
43C2×Q8×D11—24no—
44C2×Q8×D11C2×C414yes—
45C22×C4×D11—21no—
46C22×C4×D11—21no—
47C22×C4×D11C2×C411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×Dic22—21no—
51C22×Dic22C2×C411yescharacteristic
52C22×C8×C11—21no—
53C22×C8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11C2×C412yes—
57C4×Q8×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62Q8×Dic11—22no—
63Q8×Dic11C2×C414yes—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2×C411yescharacteristic
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—21no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77C2×#4313—24no—
78C2×#4313—44no—
79C4⋊C4×D11—24no—
80C4⋊C4×D11—22no—
81C4⋊C4×D11—24no—
82C4⋊C4×D11C2×C414yes—
83#66940—24no—
84#66940—22no—
85#66940—24no—
86#66940C2×C414yes—
87C42×D11—24no—
88C42×D11—24no—
89C42×D11C2×C412yes—
90C42×D11D412yes—
91C42×D11D412yes—
92C42×D11C2312yes—
93C4×Dic22—21no—
94C4×Dic22—21no—
95C4×Dic22—24no—
96C4×Dic22—24no—
97C4×Dic22C2×C412yes—
98C4×Dic22C2312yes—
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2312yes—
101C4×C8×C11—21no—
102C4×C8×C11C2312yes—
103(C2×D11)⋊C8—24no—
104Dic11⋊C8—24no—
105Dic11⋊C8—24no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8C2312yes—
110C2×#1487—111nomaximal, Sylow
111C23×D11C22⋊C411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11M1614yescomplemented
115C2×Q8×C11C22×C412yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11C22⋊C411yescharacteristic
124C22×Dic11C22⋊C411yescharacteristic
125C22×Dic11C22⋊C411yescharacteristic
126Q8×D11—216no—
127Q8×D11—28no—
128Q8×D11—28no—
129C2×C4×D11—28no—
130C2×C4×D11—24no—
131C2×C4×D11—24no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—42no—
135C2×C4×D11—44no—
136C2×C4×D11C22⋊C412yes—
137C2×C4×D11C22⋊C412yes—
138C2×C4×D11C22⋊C412yes—
139C2×C4×D11SD1614yes—
140C2×C4×D11Q1614yes—
141C2×C4×D11C22×C412yes—
142C2×C4×D11C2×D412yes—
143C2×C4×D11C2×D412yes—
144C2×Dic22—28no—
145C2×Dic22—24no—
146C2×Dic22—21no—
147C2×Dic22—22no—
148C2×Dic22M1614yescomplemented
149C2×Dic22C22×C412yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—42no—
153C2×C8×C11—42no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4C22×C412yes—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11C22×C411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2411yescharacteristic
164C4⋊Dic11—24no—
165C4⋊Dic11—21no—
166C4⋊Dic11C22×C412yes—
167Dic11⋊C4—24no—
168Dic11⋊C4—24no—
169Dic11⋊C4—22no—
170Dic11⋊C4—22no—
171C4×Dic11—24no—
172C4×Dic11—24no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11C22⋊C412yes—
176C4×Dic11C22⋊C412yes—
177C4×Dic11C22⋊C412yes—
178C4×Dic11C22×C412yes—
179C4×Dic11C2×D412yes—
180C4×Dic11C2×D412yes—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—42no—
184C2×C11⋊C8—42no—
185#4313—48no—
186C22×C4×Q8—111no—
187C2×#431—111no—
188C2×#423—111no—
189#1487—118no—
190C2×Q8⋊C8—111no—
191C2×Q8⋊C8—111no—
192C2×Q8⋊C8—111no—
193C2×Q8⋊C8D1111yescharacteristic, complemented
194C23×C11C2×C22⋊C411yescharacteristic
195C22×D11—22no—
196C22×D11—22no—
197C22×D11#10314yes—
198C22×D11C2×C22⋊C412yes—
199Q8×C11—22no—
200Q8×C11—24no—
201Q8×C11C2×M1614yescomplemented
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—42no—
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×M1612yes—
211C2×C4×C11C2×M1612yes—
212C2×C4×C11C2×SD1612yes—
213C2×C4×C11C2×Q1612yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—42no—
223C2×Dic11#10314yes—
224C2×Dic11C2×C22⋊C412yes—
225C2×Dic11C2×C22⋊C412yes—
226C2×Dic11C2×C22⋊C412yes—
227C4×D11—216no—
228C4×D11—22no—
229C4×D11—22no—
230C4×D11—24no—
231C4×D11—42no—
232C4×D11—42no—
233C4×D11—48no—
234C4×D11#10318yes—
235C4×D11C2×SD1614yes—
236C4×D11C2×Q1614yes—
237Dic22—216no—
238Dic22—22no—
239Dic22—24no—
240Dic22C2×M1614yescomplemented
241C8×C11—42no—
242C8×C11—42no—
243C11⋊C8—42no—
244C11⋊C8—42no—
245C23×Q8—111no—
246C22×M16—221no—
247C2×C4×Q8—111no—
248C2×C4×Q8—114no—
249C2×C4×Q8—114no—
250C2×C4×Q8—111no—
251C2×C4×Q8—111no—
252C2×C4×Q8—221no—
253C2×C4×Q8—221no—
254C2×C4×Q8—222no—
255C2×C4×Q8—222no—
256C2×C4×Q8C2×D1111yescharacteristic
257C22×C4⋊C4—111no—
258C22×C4⋊C4—221no—
259C22×C42—111no—
260C22×C42—221no—
261#431—114no—
262#431—222no—
263#423—114no—
264#423—222no—
265C2×C4⋊C8—111no—
266C2×C4⋊C8—221no—
267C2×C4⋊C8—221no—
268C2×C4⋊C8C2×D1111yescharacteristic
269C2×C22⋊C8—221no—
270C2×C4×C8—111no—
271C2×C4×C8C2×D1111yescharacteristic
272Q8⋊C8—114no—
273Q8⋊C8—114no—
274Q8⋊C8—114no—
275Q8⋊C8C2×D1114yescomplemented
276C22×C11#40712yes—
277C22×C11C2×#10312yes—
278C22×C11#42112yes—
279C22×C11C22×C22⋊C411yescharacteristic
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—28no—
283C2×D11C2×#10314yes—
284C4×C11—24no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—42no—
288C4×C11#40712yes—
289C4×C11C2×#10312yes—
290C4×C11C22×M1611yescharacteristic
291C4×C11C22×M1611yescharacteristic
292C4×C11C22×SD1611yescharacteristic
293C4×C11C22×Q1611yescharacteristic
294Dic11—22no—
295Dic11—24no—
296Dic11—22no—
297Dic11—42no—
298Dic11C2×#10314yes—
299C22×Q8—114no—
300C22×Q8—111no—
301C22×Q8—221no—
302C22×Q8—222no—
303C22×Q8—224no—
304C22×Q8—224no—
305C22×Q8C4×D1111yescharacteristic
306C23×C4—111no—
307C23×C4—111no—
308C23×C4—111no—
309C23×C4—221no—
310C23×C4—221no—
311C2×M16—224no—
312C2×M16—444no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—221no—
316C22×C8—221no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—114no—
320C4×Q8—114no—
321C4×Q8—112no—
322C4×Q8—112no—
323C4×Q8—224no—
324C4×Q8—224no—
325C4×Q8—224no—
326C4×Q8—222no—
327C4×Q8—224no—
328C4×Q8—222no—
329C4×Q8—221no—
330C4×Q8—221no—
331C4×Q8C4×D1112yes—
332C4×Q8C22×D1112yes—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—224no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4C4×D1111yescharacteristic
344C2×C42—21no—
345C2×C42—111no—
346C2×C42—111no—
347C2×C42—111no—
348C2×C42—112no—
349C2×C42—112no—
350C2×C42—112no—
351C2×C42—112no—
352C2×C42—224no—
353C2×C42—224no—
354C2×C42—221no—
355C2×C42—221no—
356C2×C42—221no—
357C2×C42C22×D1111yescharacteristic
358C4⋊C8—21no—
359C4⋊C8—112no—
360C4⋊C8—224no—
361C4⋊C8—224no—
362C4⋊C8—221no—
363C4⋊C8C22×D1112yes—
364C22⋊C8—224no—
365C4×C8—21no—
366C4×C8—112no—
367C4×C8—221no—
368C4×C8C22×D1112yes—
369C2×C11#148714yescomplemented
370C2×C11C2×#40711yescharacteristic
371C2×C11C22×#10311yescharacteristic
372C2×C11C2×#42111yescharacteristic
373D11—24no—
374C24—111no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—114no—
378C2×Q8—112no—
379C2×Q8—224no—
380C2×Q8—228no—
381C2×Q8—228no—
382C2×Q8—2216no—
383C2×Q8—228no—
384C2×Q8—221no—
385C2×Q8—222no—
386C2×Q8#431314yescomplemented
387C2×Q8C2×C4×D1112yes—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—111no—
391C22×C4—112no—
392C22×C4—114no—
393C22×C4—114no—
394C22×C4—112no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—112no—
398C22×C4—112no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—224no—
402C22×C4—228no—
403C22×C4—224no—
404C22×C4—221no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—221no—
408C22×C4—442no—
409C22×C4—444no—
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413M16—448no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—42no—
417C2×C8—42no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—442no—
421C2×C8—442no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—112no—
426C4⋊C4—224no—
427C4⋊C4—224no—
428C4⋊C4—224no—
429C4⋊C4—221no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C4⋊C4C2×C4×D1112yes—
433C42—22no—
434C42—22no—
435C42—112no—
436C42—112no—
437C42—112no—
438C42—112no—
439C42—112no—
440C42—112no—
441C42—224no—
442C42—224no—
443C42—222no—
444C42—222no—
445C42C2×C4×D1111yescharacteristic
446C42D4×D1111yescharacteristic
447C42D4×D1111yescharacteristic
448C42C23×D1111yescharacteristic
449C11C2×#148711yescharacteristic, complemented, Sylow
450C23—112no—
451C23—114no—
452C23—222no—
453C23—222no—
454C23C22⋊C4×D1111yescharacteristic
455Q8—22no—
456Q8—24no—
457Q8—114no—
458Q8—2216no—
459Q8—222no—
460Q8—224no—
461Q8C2×#431314yescomplemented
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—42no—
467C2×C4—112no—
468C2×C4—114no—
469C2×C4—114no—
470C2×C4—114no—
471C2×C4—118no—
472C2×C4—112no—
473C2×C4—112no—
474C2×C4—2216no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—224no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—224no—
482C2×C4—222no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—448no—
486C2×C4—442no—
487C2×C4C22⋊C4×D1111yescharacteristic
488C2×C4C22⋊C4×D1111yescharacteristic
489C2×C4C22⋊C4×D1111yescharacteristic
490C2×C4C2×#431312yes—
491C2×C4M16×D1112yes—
492C2×C4SD16×D1112yes—
493C2×C4Q16×D1112yes—
494C2×C4C22×C4×D1111yescharacteristic
495C2×C4C2×D4×D1111yescharacteristic
496C2×C4C2×D4×D1111yescharacteristic
497C8—42no—
498C8—42no—
499C8—442no—
500C8—442no—
501C22—114no—
502C22—228no—
503C22—222no—
504C22—222no—
505C22#1062233912yes—
506C22D11×#10312yes—
507C22#1062243412yes—
508C22C2×C22⋊C4×D1111yescharacteristic
509C4—24no—
510C4—21no—
511C4—21no—
512C4—42no—
513C4—114no—
514C4—222no—
515C4—224no—
516C4—222no—
517C4—442no—
518C4#1062233912yes—
519C4D11×#10312yes—
520C4C22×#431311yescharacteristic
521C4C2×M16×D1111yescharacteristic
522C4C2×SD16×D1111yescharacteristic
523C4C2×Q16×D1111yescharacteristic
524C2—224no—
525C2#1306704314yesdirect product factor
526C2C2×#1062233911yescharacteristic
527C2C2×D11×#10311yescharacteristic
528C2C2×#1062243411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1487
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #13067043C2direct (N × H)
5. C2×#10622094C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
7. C2×#10622122C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
36. C11×Q8⋊C8C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. #10622122C22semidirect
39. #10622094C22semidirect
114. C2×Q8×C11M16semidirect
148. C2×Dic22M16semidirect
193. C2×Q8⋊C8D11semidirect
201. Q8×C11C2×M16semidirect
240. Dic22C2×M16semidirect
275. Q8⋊C8C2×D11semidirect
369. C2×C11#1487semidirect
386. C2×Q8#4313semidirect
449. C11C2×#1487semidirect
461. Q8C2×#4313semidirect
525. C2#13067043direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
C2×#106222982
C2×#106224502
#130670432
C2×#106220942
C2×Q8⋊(C11⋊C8)2
C2×#106221222
C2×C11×Q8⋊C82
C2×#148711