Finite Group Databasebeta

← C2×#13078970 #15623009

Subgroups — C2×#13078970 #15623009

Order 2816.

2262 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2#13078970C2116yesmaximal, direct product factor
3C2×#10622684C212yesmaximal, complemented
4C2×#10622668C212yesmaximal, complemented
5C2×#10622669C212yesmaximal, complemented
6C2×#10622683C212yesmaximal, complemented
7C2×#10622845C211yesmaximal, characteristic, complemented
8C2×#10622828C211yesmaximal, characteristic, complemented
9C2×#10622846C211yesmaximal, characteristic, complemented
10C22×#66896C211yesmaximal, characteristic, complemented
11C2×#10622610C211yesmaximal, characteristic, complemented
12C2×C11×#535C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C11×#535—24no—
16C11×#535C2218yes—
17C2×C11×#127C2212yes—
18C2×C11×#124C2212yes—
19C2×C11×#121—21no—
20C2×C11×#121—21no—
21C2×C11×#120—22no—
22C2×C11×#117C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623050—24no—
28#10623050C2218yescomplemented
29C2×#66943—21no—
30C2×#66941—21no—
31C2×#66931—22no—
32C2×#66923C2212yescomplemented
33C2×#66922C2212yescomplemented
34#10622846C2218yescomplemented
35#10622845C2218yescomplemented
36C2×#66899C2211yescharacteristic, complemented
37C2×#66899C2211yescharacteristic, complemented
38C2×#66899C2212yescomplemented
39#10622828C2218yescomplemented
40C2×#66896C2212yes—
41C2×#66896C2212yes—
42C2×#66896C2212yes—
43C2×#66896C2212yes—
44C2×#66896C2218yescomplemented
45C2×#66896C2211yescharacteristic, complemented
46C2×#66896C2211yescharacteristic, complemented
47C2×#66896C2212yescomplemented
48#10622684C22116yescomplemented
49#10622683C22116yescomplemented
50#10622669C22116yescomplemented
51#10622668C22116yescomplemented
52#10622610C2218yescomplemented
53C2×#66867C2212yescomplemented
54C2×C4×C11⋊C8C2212yescomplemented
55C25×C11—21no—
56C2×C11×#41—22no—
57C2×C11×#41—24no—
58C2×C11×#41—24no—
59C2×C11×#41C2314yes—
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—24no—
67C22×D4×C11—24no—
68C22×D4×C11C2312yes—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2314yes—
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C23×Dic11—21no—
74C22×Dic22—22no—
75C11×#127—24no—
76C11×#127C2318yes—
77C11×#124—24no—
78C11×#124C2318yes—
79C11×#121—28no—
80C11×#121—28no—
81C11×#120—216no—
82C11×#117D414yes—
83C11×#117C2314yes—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D412yes—
89C2×C42×C11C2312yes—
90C2×C22⋊Dic11—21no—
91#66979—22no—
92#66979C2314yes—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×C4×Dic11—21no—
103C2×#4318—24no—
104C2×#4318C2314yes—
105C22×C11⋊C8—24no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2314yes—
110#66943—28no—
111#66941—28no—
112#66931—216no—
113#66923—24no—
114#66923C2318yescomplemented
115#66922—24no—
116#66922C2318yescomplemented
117#66899C2318yescomplemented
118#66899C2314yescomplemented
119#66899C2314yescomplemented
120#66896C2318yes—
121#66896C2318yes—
122#66896C2318yes—
123#66896C2318yes—
124#66896C2318yescomplemented
125#66896C2314yescomplemented
126#66896C2314yescomplemented
127#66867C2318yescomplemented
128C4×C11⋊C8C2318yescomplemented
129C2×#3136—111nomaximal, Sylow
130C24×C11—22no—
131C24×C11—21no—
132C24×C11—24no—
133C24×C11—44no—
134C24×C11—82no—
135C24×C11—82no—
136C24×C11C2×D411yescharacteristic
137C11×#41—28no—
138C11×#41—28no—
139C11×#41—48no—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11C2412yes—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—28no—
149C2×D4×C11—28no—
150C2×D4×C11—24no—
151C2×D4×C11—24no—
152C2×D4×C11—28no—
153C2×D4×C11—28no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—44no—
157C2×D4×C11—44no—
158C2×D4×C11—48no—
159C2×D4×C11—84no—
160C2×D4×C11—84no—
161C2×D4×C11C2414yes—
162C2×D4×C11C2412yes—
163C22×C4×C11—21no—
164C22×C4×C11—24no—
165C22×C4×C11—44no—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D412yes—
170C22×C4×C11#4114yes—
171C22×C4×C11#4114yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2412yes—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—22no—
177C22×Dic11—24no—
178C22×Dic11—82no—
179C2×Dic22—28no—
180C2×Dic22—84no—
181C11×C4⋊C4C2×D414yes—
182C11×C4⋊C4C2×D414yes—
183C11×C22⋊C4—28no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4C2×D418yes—
186C42×C11C2×D414yes—
187C42×C11C2414yes—
188C22⋊Dic11—24no—
189C4⋊Dic11—21no—
190C4⋊Dic11—22no—
191C4⋊Dic11—28no—
192C4⋊Dic11—21no—
193C4⋊Dic11—24no—
194C4⋊Dic11C2412yes—
195C4⋊Dic11C2414yes—
196C4⋊Dic11C2412yes—
197Dic11⋊C4—28no—
198Dic11⋊C4—28no—
199C4×Dic11—24no—
200#4318—28no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—28no—
204C2×C11⋊C8—24no—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2414yes—
207C2×C11⋊C8C2412yes—
208C2×#544—111no—
209C2×#535D1111yescharacteristic
210#3136—1116no—
211C2×#490—112no—
212C2×#489—112no—
213C2×#488—112no—
214C2×#486—112no—
215C2×#417—111no—
216C2×#418—111no—
217C2×#416—111no—
218C22×#102—111no—
219C2×#405—111no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—22no—
224C23×C11—42no—
225C23×C11—48no—
226C23×C11—44no—
227C23×C11—42no—
228C23×C11—44no—
229C23×C11—42no—
230C23×C11—44no—
231C23×C11—84no—
232C23×C11—84no—
233C23×C11—816no—
234C23×C11#12414yes—
235C23×C11C22×D412yes—
236C23×C11C22×D411yescharacteristic
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—42no—
240D4×C11—24no—
241D4×C11—24no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—48no—
245D4×C11—48no—
246D4×C11—44no—
247D4×C11—42no—
248D4×C11—88no—
249D4×C11—88no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—42no—
254C2×C4×C11—48no—
255C2×C4×C11#12414yes—
256C2×C4×C11#12418yes—
257C2×C4×C11C22×D414yes—
258C2×C4×C11C22×D414yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4112yes—
262C2×C4×C11C2×#4112yes—
263C2×C4×C11C2×#4114yes—
264C2×C4×C11C2×#4114yes—
265C2×C4×C11C2511yescharacteristic
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—42no—
270C2×Dic11—44no—
271C2×Dic11—42no—
272C2×Dic11—84no—
273Dic22—88no—
274C11⋊C8—22no—
275C11⋊C8—22no—
276C11⋊C8—24no—
277C22×#41C2×D1111yescharacteristic
278C23×D4C2×D1111yescharacteristic
279C22×M16—111no—
280C23×C8—111no—
281#544—118no—
282#544—224no—
283#535—24no—
284#535C2×D1118yes—
285C2×C4⋊Q8—112no—
286C2×C4⋊Q8—221no—
287C2×#127C2×D1112yes—
288C2×#125—112no—
289C2×#125—221no—
290C2×#124C2×D1112yes—
291C2×C22⋊Q8—222no—
292C2×#121—21no—
293C2×#121—21no—
294C2×#120—22no—
295C2×#117—111no—
296C2×#117C2×D1111yescharacteristic
297C22×C4⋊C4—111no—
298#490—1116no—
299#489—1116no—
300#488—1116no—
301#486—1116no—
302#418—118no—
303#417—118no—
304#416—118no—
305C2×#103—111no—
306C2×#103—112no—
307C2×#103—111no—
308C2×#102—111no—
309C2×#102—112no—
310C2×#102—112no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—111no—
315C2×#102—118no—
316#405—118no—
317C2×#97—112no—
318C2×C4×C8—112no—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—42no—
323C22×C11—44no—
324C22×C11—42no—
325C22×C11—44no—
326C22×C11—42no—
327C22×C11—44no—
328C22×C11—816no—
329C22×C11—84no—
330C22×C11—88no—
331C22×C11C2×#12414yes—
332C22×C11C2×#12412yes—
333C22×C11#57612yes—
334C22×C11#57712yes—
335C22×C11C23×D411yescharacteristic
336C4×C11—24no—
337C4×C11—24no—
338C4×C11—42no—
339C4×C11C2×#12414yes—
340C4×C11C2×#12412yes—
341C4×C11C22×#4111yescharacteristic
342C4×C11C22×#4111yescharacteristic
343Dic11—42no—
344Dic11—44no—
345Dic11—42no—
346C25—21no—
347C2×#41—22no—
348C2×#41—24no—
349C2×#41—24no—
350C2×#41C22×D1114yes—
351C22×Q8—222no—
352C22×Q8C22×D1111yescharacteristic
353C22×D4—21no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4C22×D1112yes—
361C22×D4C22×D1111yescharacteristic
362C22×D4C22×D1114yes—
363C23×C4—21no—
364C23×C4—221no—
365C23×C4C22×D1111yescharacteristic
366C2×M16—114no—
367C2×M16—224no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—114no—
371C22×C8—112no—
372C22×C8—224no—
373C4⋊Q8—118no—
374C4⋊Q8—228no—
375C4⋊Q8—224no—
376#127—24no—
377#127C22×D1118yes—
378#125—118no—
379#125—228no—
380#125—224no—
381#124—24no—
382#124C22×D1118yes—
383C22⋊Q8—2216no—
384#121—28no—
385#121—28no—
386#120—216no—
387#117—114no—
388#117—222no—
389#117C22⋊D1114yes—
390#117C22×D1114yes—
391C2×C4⋊C4—112no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4C22⋊D1111yescharacteristic
401C2×C4⋊C4C22⋊D1111yescharacteristic
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4C22⋊D1112yes—
406C2×C42—221no—
407C2×C42C22×D1112yes—
408#103—114no—
409#103—114no—
410#103—118no—
411#102—118no—
412#102—118no—
413#102—118no—
414#102—118no—
415#102—114no—
416#102—114no—
417#102—118no—
418#97—118no—
419C4×C8—118no—
420C2×C11—24no—
421C2×C11—82no—
422C2×C11—84no—
423C2×C11#313614yescomplemented
424C2×C11C22×#12411yescharacteristic
425C2×C11C2×#57611yescharacteristic
426C2×C11C2×#57711yescharacteristic
427C24—22no—
428C24—21no—
429C24—24no—
430C24—44no—
431C24—82no—
432C24—82no—
433C24C2×C22⋊D1111yescharacteristic
434#41—28no—
435#41—28no—
436#41—48no—
437C2×Q8—21no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—228no—
441C2×Q8—884no—
442C2×Q8C23×D1112yes—
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—24no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—48no—
458C2×D4—84no—
459C2×D4—84no—
460C2×D4C23×D1114yes—
461C2×D4C23×D1112yes—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—44no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—224no—
469C22×C4—882no—
470C22×C4#434114yes—
471C22×C4#434114yes—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C2×C22⋊D1112yes—
474C22×C4C2×C22⋊D1112yes—
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C23×D1112yes—
477C22×C4C23×D1111yescharacteristic
478M16—228no—
479C2×C8—112no—
480C2×C8—114no—
481C2×C8—112no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—228no—
485C2×C8—224no—
486C4⋊C4—114no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—224no—
490C4⋊C4—222no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—228no—
494C4⋊C4—228no—
495C4⋊C4—228no—
496C4⋊C4C2×C22⋊D1114yes—
497C4⋊C4C2×C22⋊D1114yes—
498C22⋊C4—28no—
499C22⋊C4—28no—
500C22⋊C4—224no—
501C22⋊C4C2×C22⋊D1118yes—
502C42—224no—
503C42C2×C22⋊D1114yes—
504C42C23×D1114yes—
505C11C2×#313611yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—24no—
509C23—22no—
510C23—42no—
511C23—48no—
512C23—44no—
513C23—42no—
514C23—44no—
515C23—42no—
516C23—44no—
517C23—84no—
518C23—84no—
519C23—816no—
520C23#6698914yes—
521C23C22×C22⋊D1112yes—
522C23C22×C22⋊D1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—42no—
526Q8—888no—
527D4—24no—
528D4—24no—
529D4—22no—
530D4—22no—
531D4—48no—
532D4—48no—
533D4—44no—
534D4—42no—
535D4—88no—
536D4—88no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—42no—
541C2×C4—48no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—224no—
545C2×C4—444no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—884no—
549C2×C4#6698914yes—
550C2×C4#6698918yes—
551C2×C4C2×#434112yes—
552C2×C4C2×#434112yes—
553C2×C4C2×#434114yes—
554C2×C4C2×#434114yes—
555C2×C4C22×C22⋊D1114yes—
556C2×C4C22×C22⋊D1114yes—
557C2×C4C22×C22⋊D1112yes—
558C2×C4C22×C22⋊D1111yescharacteristic
559C2×C4C24×D1111yescharacteristic
560C8—222no—
561C8—222no—
562C8—224no—
563C22—28no—
564C22—22no—
565C22—22no—
566C22—42no—
567C22—44no—
568C22—42no—
569C22—44no—
570C22—42no—
571C22—44no—
572C22—816no—
573C22—88no—
574C22—84no—
575C22C2×#6698914yes—
576C22C2×#6698912yes—
577C22#1062336612yes—
578C22#1062336712yes—
579C22C23×C22⋊D1111yescharacteristic
580C4—24no—
581C4—24no—
582C4—42no—
583C4—444no—
584C4—442no—
585C4—442no—
586C4C2×#6698914yes—
587C4C2×#6698912yes—
588C4C22×#434111yescharacteristic
589C4C22×#434111yescharacteristic
590C2—24no—
591C2—84no—
592C2—82no—
593C2#1307897014yesdirect product factor
594C2C22×#6698911yescharacteristic
595C2C2×#1062336611yescharacteristic
596C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#535C2
socleC23×C11C22×D4
hypercenterC2×#535D11
hypocenterC11C2×#3136
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
2. #13078970C2direct (N × H)
3. C2×#10622684C2semidirect
4. C2×#10622668C2semidirect
5. C2×#10622669C2semidirect
6. C2×#10622683C2semidirect
7. C2×#10622845C2semidirect
8. C2×#10622828C2semidirect
9. C2×#10622846C2semidirect
10. C22×#66896C2semidirect
11. C2×#10622610C2semidirect
28. #10623050C22semidirect
32. C2×#66923C22semidirect
33. C2×#66922C22semidirect
34. #10622846C22semidirect
35. #10622845C22semidirect
36. C2×#66899C22semidirect
37. C2×#66899C22semidirect
38. C2×#66899C22semidirect
39. #10622828C22semidirect
44. C2×#66896C22semidirect
45. C2×#66896C22semidirect
46. C2×#66896C22semidirect
47. C2×#66896C22semidirect
48. #10622684C22semidirect
49. #10622683C22semidirect
50. #10622669C22semidirect
51. #10622668C22semidirect
52. #10622610C22semidirect
53. C2×#66867C22semidirect
54. C2×C4×C11⋊C8C22semidirect
114. #66923C23semidirect
116. #66922C23semidirect
117. #66899C23semidirect
118. #66899C23semidirect
119. #66899C23semidirect
124. #66896C23semidirect
125. #66896C23semidirect
126. #66896C23semidirect
127. #66867C23semidirect
128. C4×C11⋊C8C23semidirect
423. C2×C11#3136semidirect
505. C11C2×#3136semidirect
593. C2#13078970direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
#130789702
C2×#106226842
C2×#106226682
C2×#106226692
C2×#106226832
C2×#106228452
C2×#106228282
C2×#106228462
C22×#668962
C2×#106226102
C2×C11×#5352
C2×#313611