Finite Group Databasebeta

← C2×#13067049 #14720177

Subgroups — C2×#13067049 #14720177

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×#4343C211yesmaximal, characteristic
2C2×#10622448C211yesmaximal, characteristic, complemented
3C2×#10622298C211yesmaximal, characteristic, complemented
4#13067049C218yesmaximal, direct product factor
5C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6C2×#10622097C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C22×#4343C411yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×Q8×Dic11C411yescharacteristic
12C4×#4343—22no—
13C4×#4343—22no—
14C4×#4343C414yes—
15C4×#4343C2214yes—
16C2×#66946—21no—
17C2×#66946C411yescharacteristic
18C2×#66945—21no—
19C2×#66945C411yescharacteristic
20C2×C4×D44—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C42×D11—21no—
23C2×C42×D11C2211yescharacteristic
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×Q8⋊C8C2214yescomplemented
37Q8⋊(C11⋊C8)C2214yescomplemented
38#10622121C2214yescomplemented
39#10622097C2214yescomplemented
40C22×Q8×C11C2×C411yescharacteristic
41C2×#4343—24no—
42C2×#4343—24no—
43C2×#4343—22no—
44C2×#4343C2×C414yes—
45C22×D44—21no—
46C22×D44C2×C411yescharacteristic
47C22×C4×D11—21no—
48C22×C4×D11—21no—
49C22×C4×D11—21no—
50C22×C4×D11C2×C411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11C2×C412yes—
58C4×Q8×C11C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63Q8×Dic11—22no—
64Q8×Dic11C2×C414yes—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2×C411yescharacteristic
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—
77#66946—24no—
78#66946—24no—
79#66946—22no—
80#66946C2×C414yes—
81#66945—22no—
82#66945—24no—
83#66945—24no—
84#66945C2×C414yes—
85C4×D44—24no—
86C4×D44—24no—
87C4×D44—21no—
88C4×D44—21no—
89C4×D44C2×C412yes—
90C4×D44C2312yes—
91C42×D11—24no—
92C42×D11—24no—
93C42×D11C2×C412yes—
94C42×D11D412yes—
95C42×D11D412yes—
96C42×D11C2312yes—
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
110C23×D11—21no—
111C23×D11C22⋊C411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11M1614yes—
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×Dic11C22⋊C411yescharacteristic
123C22×Dic11C22⋊C411yescharacteristic
124C22×Dic11C22⋊C411yescharacteristic
125#4343—216no—
126#4343—28no—
127#4343—28no—
128C2×D44—28no—
129C2×D44—24no—
130C2×D44—21no—
131C2×D44—22no—
132C2×D44M1614yes—
133C2×D44C22×C412yes—
134C2×C4×D11—28no—
135C2×C4×D11—24no—
136C2×C4×D11—24no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—42no—
144C2×C4×D11—44no—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11C22⋊C412yes—
148C2×C4×D11C22⋊C412yes—
149C2×C4×D11C22⋊C412yes—
150C2×C4×D11C22×C412yes—
151C2×C4×D11C2×D412yes—
152C2×C4×D11C2×D412yes—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—42no—
156C2×C8×C11—42no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C22×C412yes—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11C22×C411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2411yescharacteristic
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—22no—
170(C2×D11)⋊C4—22no—
171C4⋊Dic11—24no—
172C4⋊Dic11—21no—
173C4⋊Dic11C22×C412yes—
174C4×Dic11—24no—
175C4×Dic11—24no—
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⋊C8D1111yescharacteristic, complemented
192C2×D4⋊C8—111no—
193C2×D4⋊C8—111no—
194C23×C11C2×C22⋊C411yescharacteristic
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—24no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11C2×C22⋊C412yes—
203Q8×C11—22no—
204Q8×C11—24no—
205Q8×C11C2×M1614yes—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—42no—
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C2×M1612yes—
215C2×C4×C11C2×M1612yes—
216C2×C4×C11#13512yes—
217C2×C4×C11#13512yes—
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—42no—
226C2×Dic11C2×C22⋊C412yes—
227C2×Dic11C2×C22⋊C412yes—
228C2×Dic11C2×C22⋊C412yes—
229D44—216no—
230D44—22no—
231D44—24no—
232D44C2×M1614yes—
233C4×D11—216no—
234C4×D11—22no—
235C4×D11—22no—
236C4×D11—22no—
237C4×D11—22no—
238C4×D11—24no—
239C4×D11—24no—
240C4×D11—42no—
241C4×D11—42no—
242C4×D11—48no—
243C4×D11—42no—
244C4×D11—42no—
245C4×D11—44no—
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×Q8C2×D1111yescharacteristic
257C2×C4×D4—111no—
258C2×C4×D4—111no—
259C2×C4×D4—221no—
260C2×C4×D4—221no—
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⋊C8C2×D1114yescomplemented
279D4⋊C8—114no—
280D4⋊C8—114no—
281C22×C11#40712yes—
282C22×C11#41612yes—
283C22×C11#42112yes—
284C22×C11C22×C22⋊C411yescharacteristic
285C2×D11—24no—
286C2×D11—22no—
287C2×D11—22no—
288C2×D11—22no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—44no—
292C2×D11—48no—
293C4×C11—24no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—42no—
297C4×C11#40712yes—
298C4×C11#41612yes—
299C4×C11C22×M1611yescharacteristic
300C4×C11C22×M1611yescharacteristic
301C4×C11C2×#13511yescharacteristic
302C4×C11C2×#13511yescharacteristic
303Dic11—22no—
304Dic11—22no—
305Dic11—22no—
306Dic11—42no—
307C2×#41—114no—
308C2×#41—222no—
309C2×#41—224no—
310C2×#41—224no—
311C22×Q8C4×D1111yescharacteristic
312C22×D4—111no—
313C22×D4—221no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—221no—
318C23×C4—221no—
319C23×C4—221no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—221no—
323C22×C8—221no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—114no—
327C4×Q8—222no—
328C4×Q8C4×D1112yes—
329C4×Q8C22×D1112yes—
330C4×D4—114no—
331C4×D4—112no—
332C4×D4—112no—
333C4×D4—224no—
334C4×D4—224no—
335C4×D4—222no—
336C4×D4—224no—
337C4×D4—224no—
338C4×D4—221no—
339C4×D4—221no—
340#117—114no—
341#117—224no—
342#117—224no—
343#117—222no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4C4×D1111yescharacteristic
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C42—21no—
352C2×C42—111no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—112no—
356C2×C42—112no—
357C2×C42—112no—
358C2×C42—112no—
359C2×C42—224no—
360C2×C42—224no—
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#148814yescomplemented
377C2×C11C2×#40711yescharacteristic
378C2×C11C2×#41611yescharacteristic
379C2×C11C2×#42111yescharacteristic
380D11—42no—
381D11—44no—
382C24—111no—
383C24—221no—
384#41—228no—
385#41—2216no—
386#41—228no—
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8#431314yes—
390C2×Q8C2×C4×D1112yes—
391C2×D4—114no—
392C2×D4—112no—
393C2×D4—224no—
394C2×D4—228no—
395C2×D4—221no—
396C2×D4—222no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—111no—
400C22×C4—111no—
401C22×C4—111no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—228no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—221no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—442no—
419C22×C4—444no—
420C22×C4—442no—
421C22×C4—442no—
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—22no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—112no—
437C4⋊C4—224no—
438C4⋊C4—221no—
439C4⋊C4C2×C4×D1112yes—
440C22⋊C4—224no—
441C22⋊C4—224no—
442C22⋊C4—222no—
443C22⋊C4—222no—
444C42—22no—
445C42—22no—
446C42—112no—
447C42—112no—
448C42—112no—
449C42—112no—
450C42—112no—
451C42—112no—
452C42—224no—
453C42—224no—
454C42C2×C4×D1111yescharacteristic
455C42D4×D1111yescharacteristic
456C42D4×D1111yescharacteristic
457C42C23×D1111yescharacteristic
458C11C2×#148811yescharacteristic, complemented, Sylow
459C23—112no—
460C23—222no—
461C23—224no—
462C23—222no—
463C23—222no—
464C23—222no—
465C23—442no—
466C23—442no—
467C23C22⋊C4×D1111yescharacteristic
468Q8—22no—
469Q8—24no—
470Q8C2×#431314yes—
471D4—114no—
472D4—2216no—
473D4—222no—
474D4—224no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—42no—
480C2×C4—112no—
481C2×C4—112no—
482C2×C4—112no—
483C2×C4—2216no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—222no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—448no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—444no—
501C2×C4C22⋊C4×D1111yescharacteristic
502C2×C4C22⋊C4×D1111yescharacteristic
503C2×C4C22⋊C4×D1111yescharacteristic
504C2×C4C2×#431312yes—
505C2×C4M16×D1112yes—
506C2×C4#6696912yes—
507C2×C4#6697212yes—
508C2×C4C22×C4×D1111yescharacteristic
509C2×C4C2×D4×D1111yescharacteristic
510C2×C4C2×D4×D1111yescharacteristic
511C8—42no—
512C8—42no—
513C8—442no—
514C8—442no—
515C22—224no—
516C22—222no—
517C22—222no—
518C22—222no—
519C22—444no—
520C22—448no—
521C22—442no—
522C22—442no—
523C22#1062233912yes—
524C22#1062241712yes—
525C22#1062243412yes—
526C22C2×C22⋊C4×D1111yescharacteristic
527C4—24no—
528C4—21no—
529C4—21no—
530C4—42no—
531C4—222no—
532C4—222no—
533C4—222no—
534C4—442no—
535C4#1062233912yes—
536C4#1062241712yes—
537C4C22×#431311yescharacteristic
538C4C2×M16×D1111yescharacteristic
539C4C2×#6696911yescharacteristic
540C4C2×#6697211yescharacteristic
541C2—442no—
542C2—444no—
543C2#1306704914yesdirect product factor
544C2C2×#1062233911yescharacteristic
545C2C2×#1062241711yescharacteristic
546C2C2×#1062243411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#4343C4
cosocleC42×C11C24
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1488
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
2. C2×#10622448C2semidirect
3. C2×#10622298C2semidirect
4. #13067049C2direct (N × H)
5. C2×Q8⋊(C11⋊C8)C2semidirect
6. C2×#10622097C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
33. #10622448C22semidirect
35. #10622298C22semidirect
36. C11×Q8⋊C8C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. #10622121C22semidirect
39. #10622097C22semidirect
191. C2×Q8⋊C8D11semidirect
278. Q8⋊C8C2×D11semidirect
376. C2×C11#1488semidirect
458. C11C2×#1488semidirect
543. C2#13067049direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#43432
C2×#106224482
C2×#106222982
#130670492
C2×Q8⋊(C11⋊C8)2
C2×#106220972
C2×#106221212
C2×C11×Q8⋊C82
C2×#148811