Finite Group Databasebeta

← C2×#13067122 #14720916

Subgroups — C2×#13067122 #14720916

Order 2816.

1410 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic, complemented
3C2×#10622261C211yesmaximal, characteristic, complemented
4#13067122C218yesmaximal, direct product factor
5C2×#10622108C211yesmaximal, characteristic, complemented
6C2×#10622175C211yesmaximal, characteristic, complemented
7C2×#10622089C211yesmaximal, characteristic, complemented
8C2×C11×#327C211yesmaximal, characteristic, complemented
9C22×#4341—21no—
10C2×C11×#121C2211yescharacteristic
11C2×#66993C411yescharacteristic, complemented
12C2×#66992—21no—
13C2×D4×Dic11C411yescharacteristic, complemented
14C2×#66983C2211yescharacteristic
15C22×C4×Dic11—21no—
16C22×C4×Dic11C2211yescharacteristic
17#10623127—22no—
18#10623127—22no—
19#10623127C414yescomplemented
20#10623127C2214yes—
21C2×#66946C411yescharacteristic, complemented
22C2×#66941C411yescharacteristic, complemented
23C2×#66938—21no—
24C2×(C22⋊D11)⋊C4—21no—
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11⋊#95—21no—
28C2×C11⋊#95C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66879—21no—
31C2×Dic11⋊C8—21no—
32#10622332—22no—
33#10622332C2214yescomplemented
34#10622261—22no—
35#10622261C2214yescomplemented
36C11×#327C2214yescomplemented
37#10622175C2214yescomplemented
38#10622108C2214yescomplemented
39#10622089C2214yescomplemented
40C22×D4×C11—21no—
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C22×C22⋊D11—21no—
46C22×C22⋊D11—21no—
47C23×Dic11—21no—
48C23×Dic11—21no—
49C23×Dic11D411yescharacteristic
50C23×Dic11D411yescharacteristic
51C2×#4341—24no—
52C2×#4341—24no—
53C2×#4341—44no—
54C2×#4341—44no—
55C22×D44C2×C411yescharacteristic
56C22×C4×D11—21no—
57C22×Dic22—21no—
58C22×C8×C11—21no—
59C11×#121—21no—
60C11×#121—21no—
61C11×#121C2×C412yes—
62C11×#121C2312yes—
63C2×C11×C4⋊C4C2×C411yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C22⋊Dic11—21no—
66#66993—22no—
67#66993C2×C414yescomplemented
68#66992—24no—
69#66992—24no—
70D4×Dic11—22no—
71D4×Dic11C2×C414yescomplemented
72#66983—21no—
73#66983—21no—
74#66983C2×C412yes—
75#66983C2312yes—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—28no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2×C412yes—
85C2×C4×Dic11D412yes—
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11D412yes—
89C2×C4×Dic11C2312yes—
90C22×C11⋊C8—21no—
91#66946—22no—
92#66946C2×C414yescomplemented
93#66941—22no—
94#66941C2×C414yescomplemented
95#66938—24no—
96#66938—24no—
97(C22⋊D11)⋊C4—24no—
98(C22⋊D11)⋊C4—24no—
99C11×C22⋊C8—21no—
100C11×C22⋊C8C2312yes—
101C11×#95—21no—
102C11×#95C2312yes—
103C11⋊#95—21no—
104C11⋊#95—24no—
105C11⋊#95C2312yes—
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)C2312yes—
108#66879—24no—
109Dic11⋊C8—24no—
110C2×#1505—111nomaximal, Sylow
111C24×C11—21no—
112C24×C11C2×D411yescharacteristic
113C23×D11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11C22×C412yes—
121C22×C4×C11—24no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—24no—
134C2×C22⋊D11—24no—
135C2×C22⋊D11—22no—
136C2×C22⋊D11—22no—
137C2×C22⋊D11—44no—
138C2×C22⋊D11—44no—
139C2×C22⋊D11—42no—
140C2×C22⋊D11—42no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—42no—
149C22×Dic11—44no—
150C22×Dic11—42no—
151C22×Dic11C22⋊C411yescharacteristic
152C22×Dic11C22⋊C412yes—
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C22×Dic11C22⋊C412yes—
156C22×Dic11C22⋊C411yescharacteristic
157C22×Dic11C2×D412yes—
158C22×Dic11C2×D412yes—
159#4341—48no—
160#4341—48no—
161#4341—416no—
162C2×D44—21no—
163C2×D44—42no—
164C2×D44C22×C412yes—
165C2×C4×D11—24no—
166C2×C4×D11—44no—
167C2×Dic22—24no—
168C2×Dic22—44no—
169C2×C8×C11—22no—
170C2×C8×C11—42no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C412yes—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C22⋊Dic11—24no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—22no—
178(C2×D11)⋊C4—22no—
179C4⋊Dic11—21no—
180C4⋊Dic11C22×C412yes—
181Dic11⋊C4—24no—
182C4×Dic11—216no—
183C4×Dic11C22⋊C412yes—
184C4×Dic11C22⋊C412yes—
185C4×Dic11C22⋊C412yes—
186C4×Dic11C22⋊C412yes—
187C4×Dic11C22×C412yes—
188C4×Dic11C22×C412yes—
189C4×Dic11C2×D412yes—
190C4×Dic11C2×D412yes—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—42no—
193C2×#532—111no—
194C2×#432—111no—
195C2×#376—111no—
196#1505—118no—
197C2×#327—111no—
198C2×#327—111no—
199C2×#327—111no—
200C2×#327D1111yescharacteristic, complemented
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11C2×C22⋊C411yescharacteristic
208C23×C11C2×C22⋊C411yescharacteristic
209C23×C11AGL(1,ℤ/8)12yes—
210C23×C11AGL(1,ℤ/8)12yes—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216D4×C11—42no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—44no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—48no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C2×C22⋊C411yescharacteristic
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C22⋊D11—48no—
238C22⋊D11—42no—
239C22⋊D11—42no—
240C22⋊D11—44no—
241C22⋊D11—48no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—48no—
253C2×Dic11—42no—
254C2×Dic11—48no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11#10414yes—
258C2×Dic11C2×C22⋊C412yes—
259C2×Dic11C2×C22⋊C412yes—
260C2×Dic11C2×C22⋊C412yes—
261C2×Dic11C2×C22⋊C412yes—
262D44—42no—
263D44—42no—
264C4×D11—48no—
265Dic22—48no—
266C8×C11—42no—
267C11⋊C8—42no—
268C22×#41—221no—
269#532—114no—
270#532—114no—
271#532—222no—
272#532—222no—
273C2×C4⋊Q8—111no—
274C2×#127—111no—
275C2×#124—221no—
276C2×#121—111no—
277C2×#121—221no—
278C2×#121C2×D1111yescharacteristic
279C2×C4×D4—111no—
280C2×C4×D4—111no—
281C2×C4×D4—221no—
282C22×C42—111no—
283C22×C42—221no—
284#432—114no—
285#432—222no—
286C2×C4⋊C8—221no—
287C2×C22⋊C8—111no—
288C2×C22⋊C8C2×D1111yescharacteristic
289C2×#97—221no—
290#376—114no—
291#376—222no—
292C2×#95—111no—
293C2×#95—221no—
294C2×#95C2×D1111yescharacteristic
295#327—114no—
296#327—114no—
297#327—114no—
298#327C2×D1114yescomplemented
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—84no—
309C22×C11#41012yes—
310C22×C11#41812yes—
311C22×C11#41812yes—
312C22×C11C2×#10412yes—
313C22×C11C22×C22⋊C411yescharacteristic
314C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—84no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—44no—
325C4×C11—42no—
326Dic11—22no—
327Dic11—22no—
328Dic11—22no—
329Dic11—44no—
330Dic11—42no—
331Dic11C2×#10414yes—
332C2×#41—224no—
333C2×#41—224no—
334C2×#41—444no—
335C2×#41—444no—
336C22×Q8—221no—
337C22×D4—21no—
338C22×D4—111no—
339C22×D4—221no—
340C22×D4—221no—
341C22×D4—221no—
342C22×D4C4×D1111yescharacteristic
343C23×C4—21no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—221no—
347C23×C4—221no—
348C23×C4—221no—
349C23×C4C22×D1111yescharacteristic
350C22×C8—21no—
351C22×C8—221no—
352C4⋊Q8—114no—
353C4⋊Q8—222no—
354#127—114no—
355#127—222no—
356#124—224no—
357#124—224no—
358#121—21no—
359#121—21no—
360#121—112no—
361#121—112no—
362#121—224no—
363#121—224no—
364#121—221no—
365#121—221no—
366#121C4×D1112yes—
367#121C22×D1112yes—
368C4×D4—114no—
369C4×D4—114no—
370C4×D4—224no—
371C4×D4—224no—
372C4×D4—222no—
373C4×D4—222no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C4×D1111yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—112no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—112no—
387C2×C42—112no—
388C2×C42—112no—
389C2×C42—224no—
390C2×C42—228no—
391C4⋊C8—224no—
392C22⋊C8—21no—
393C22⋊C8—112no—
394C22⋊C8—221no—
395C22⋊C8C22×D1112yes—
396#97—224no—
397#95—21no—
398#95—112no—
399#95—224no—
400#95—221no—
401#95C22×D1112yes—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—22no—
405C2×C11—82no—
406C2×C11#150514yescomplemented
407C2×C11C2×#41011yescharacteristic
408C2×C11C2×#41811yescharacteristic
409C2×C11C22×#10411yescharacteristic
410D11—82no—
411C24—21no—
412C24—221no—
413C24D4×D1111yescharacteristic
414#41—448no—
415#41—448no—
416#41—4416no—
417C2×Q8—224no—
418C2×Q8—444no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—112no—
426C2×D4—224no—
427C2×D4—224no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—221no—
431C2×D4—442no—
432C2×D4—444no—
433C2×D4—444no—
434C2×D4—442no—
435C2×D4—442no—
436C2×D4C2×C4×D1112yes—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—111no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—224no—
457C22×C4—221no—
458C22×C4—222no—
459C22×C4—444no—
460C22×C4—444no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4D4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C2×C8—22no—
470C2×C8—42no—
471C2×C8—222no—
472C2×C8—442no—
473C4⋊C4—21no—
474C4⋊C4—112no—
475C4⋊C4—224no—
476C4⋊C4—221no—
477C4⋊C4C2×C4×D1112yes—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—222no—
483C22⋊C4—222no—
484C42—112no—
485C42—112no—
486C42—112no—
487C42—112no—
488C42—112no—
489C42—112no—
490C42—112no—
491C42—112no—
492C42—2216no—
493C11C2×#150511yescharacteristic, complemented, Sylow
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—222no—
501C23—442no—
502C23—442no—
503C23—442no—
504C23C22⋊C4×D1111yescharacteristic
505C23C22⋊C4×D1111yescharacteristic
506C23#6696412yes—
507C23#6696712yes—
508C23C2×D4×D1111yescharacteristic
509Q8—448no—
510D4—42no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—44no—
515D4—442no—
516D4—442no—
517D4—448no—
518D4—448no—
519D4—442no—
520D4—442no—
521D4—444no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—48no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—112no—
535C2×C4—114no—
536C2×C4—112no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—222no—
549C2×C4—448no—
550C2×C4—448no—
551C2×C4—442no—
552C2×C4—448no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4C22⋊C4×D1111yescharacteristic
556C2×C4C22⋊C4×D1111yescharacteristic
557C2×C4C22×C4×D1111yescharacteristic
558C2×C4C2×D4×D1111yescharacteristic
559C8—42no—
560C8—442no—
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—21no—
566C22—21no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—84no—
571C22—442no—
572C22—442no—
573C22—442no—
574C22—884no—
575C22#1062235312yes—
576C22#1062238312yes—
577C22#1062238312yes—
578C22D11×#10412yes—
579C22C2×C22⋊C4×D1111yescharacteristic
580C22C2×#6696411yescharacteristic
581C22C2×#6696711yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—44no—
587C4—42no—
588C4—114no—
589C4—222no—
590C4—222no—
591C4—222no—
592C4—444no—
593C4—442no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—82no—
598C2—882no—
599C2#1306712214yesdirect product factor
600C2C2×#1062235311yescharacteristic
601C2C2×#1062238311yescharacteristic
602C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623127C2
cosocleC22×C4×C11C24
hypercenterC2×#327D11
hypocenterC11C2×#1505
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. C2×#10622261C2semidirect
4. #13067122C2direct (N × H)
5. C2×#10622108C2semidirect
6. C2×#10622175C2semidirect
7. C2×#10622089C2semidirect
8. C2×C11×#327C2semidirect
11. C2×#66993C4semidirect
13. C2×D4×Dic11C4semidirect
19. #10623127C4semidirect
21. C2×#66946C4semidirect
22. C2×#66941C4semidirect
33. #10622332C22semidirect
35. #10622261C22semidirect
36. C11×#327C22semidirect
37. #10622175C22semidirect
38. #10622108C22semidirect
39. #10622089C22semidirect
67. #66993C2×C4semidirect
71. D4×Dic11C2×C4semidirect
92. #66946C2×C4semidirect
94. #66941C2×C4semidirect
200. C2×#327D11semidirect
298. #327C2×D11semidirect
406. C2×C11#1505semidirect
493. C11C2×#1505semidirect
599. C2#13067122direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231272
C2×#106223322
C2×#106222612
#130671222
C2×#106221082
C2×#106221752
C2×#106220892
C2×C11×#3272
C2×#150511