Finite Group Databasebeta

← C2×#13078568 #15621594

Subgroups — C2×#13078568 #15621594

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic, complemented
2#13078568C2116yesmaximal, direct product factor
3C2×#10622647C212yesmaximal, complemented
4C2×#10622648C212yesmaximal, complemented
5C2×#10622648C212yesmaximal, complemented
6C2×#10622646C212yesmaximal, complemented
7C2×#10622608C211yesmaximal, characteristic, complemented
8C2×#10622611C211yesmaximal, characteristic, complemented
9C2×#10622828C211yesmaximal, characteristic, complemented
10C22×#66896C211yesmaximal, characteristic, complemented
11C2×#10622847C211yesmaximal, characteristic, complemented
12C2×C11×#535C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C11×#535—24no—
16C11×#535C2218yes—
17C2×C11×#127—21no—
18C2×C11×#124—21no—
19C2×C11×#121C2212yes—
20C2×C11×#121C2212yes—
21C2×C11×#120—22no—
22C2×C11×#117C2211yescharacteristic
23#10623358—24no—
24#10623358C2218yescomplemented
25C2×Q8×Dic11—21no—
26C2×D4×Dic11—21no—
27C2×D4×Dic11—22no—
28C2×#66979C2211yescharacteristic
29C2×#66979C2212yescomplemented
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2212yescomplemented
32C22×#4318C2211yescharacteristic
33C23×C11⋊C8C2211yescharacteristic
34#10622847C2218yescomplemented
35#10622828C2218yescomplemented
36C2×#66896C2212yes—
37C2×#66896C2212yes—
38C2×#66896C2212yes—
39C2×#66896C2212yes—
40C2×#66896C2218yescomplemented
41C2×C22⋊(C11⋊C8)C2212yescomplemented
42C2×C22⋊(C11⋊C8)C2212yescomplemented
43#10622648C22116yescomplemented
44#10622648C22116yescomplemented
45#10622647C22116yescomplemented
46#10622646C22116yescomplemented
47#10622611C2218yescomplemented
48#10622608C2218yescomplemented
49C2×#66872C2211yescharacteristic, complemented
50C2×#66872C2211yescharacteristic, complemented
51C2×#66872C2212yescomplemented
52C2×#66871C2211yescharacteristic, complemented
53C2×#66871C2211yescharacteristic, complemented
54C2×#66871C2212yescomplemented
55C25×C11—21no—
56C2×C11×#41—24no—
57C2×C11×#41—24no—
58C2×C11×#41D414yes—
59C2×C11×#41C2314yes—
60C22×Q8×C11D411yescharacteristic
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—24no—
66C22×D4×C11—24no—
67C22×D4×C11D412yes—
68C22×D4×C11D411yescharacteristic
69C22×D4×C11C2312yes—
70C22×D4×C11C2314yes—
71C23×C4×C11C2312yes—
72C23×C4×C11C2311yescharacteristic
73C23×Dic11—21no—
74C23×Dic11—22no—
75C11×#127—28no—
76C11×#124—28no—
77C11×#121—24no—
78C11×#121—24no—
79C11×#121C2318yes—
80C11×#121C2318yes—
81C11×#120—216no—
82C11×#117—22no—
83C11×#117C2314yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C42×C11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—22no—
92Q8×Dic11—28no—
93D4×Dic11—28no—
94D4×Dic11—216no—
95#66979—22no—
96#66979—24no—
97#66979C2314yes—
98#66979C2318yescomplemented
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2314yes—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2318yescomplemented
108C2×C4×Dic11—21no—
109C2×C4×Dic11—22no—
110C2×#4318—24no—
111C2×#4318C2314yes—
112C22×C11⋊C8—24no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2314yes—
116C22×C11⋊C8C2312yes—
117#66896C2318yes—
118#66896C2318yes—
119#66896C2318yes—
120#66896C2318yes—
121C22⋊(C11⋊C8)C2318yescomplemented
122C22⋊(C11⋊C8)C2318yescomplemented
123#66872C2318yescomplemented
124#66872C2314yescomplemented
125#66872C2314yescomplemented
126#66871C2318yescomplemented
127#66871C2314yescomplemented
128#66871C2314yescomplemented
129C2×#3096—111nomaximal, Sylow
130C24×C11—22no—
131C24×C11—24no—
132C24×C11—44no—
133C24×C11—82no—
134C24×C11—82no—
135C24×C11C2×D412yes—
136C24×C11C2×D411yescharacteristic
137C11×#41—216no—
138C11×#41—28no—
139C11×#41—28no—
140C2×Q8×C11—24no—
141C2×Q8×C11C2×D414yes—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—28no—
145C2×D4×C11—24no—
146C2×D4×C11—22no—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—28no—
151C2×D4×C11—28no—
152C2×D4×C11—44no—
153C2×D4×C11—48no—
154C2×D4×C11—84no—
155C2×D4×C11—84no—
156C2×D4×C11C2×D418yes—
157C2×D4×C11C2×D414yes—
158C2×D4×C11C2414yes—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4114yes—
168C22×C4×C11#4114yes—
169C22×C4×C11C2414yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2412yes—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—22no—
175C22×Dic11—24no—
176C22×Dic11—28no—
177C22×Dic11—82no—
178C22×Dic11—84no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C2412yes—
182C11×C4⋊C4C2412yes—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—28no—
186C42×C11—24no—
187C22⋊Dic11—24no—
188C22⋊Dic11—28no—
189C4⋊Dic11—22no—
190C4⋊Dic11—21no—
191C4⋊Dic11—24no—
192C4⋊Dic11—28no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2414yes—
195C4⋊Dic11C2412yes—
196C4⋊Dic11C2412yes—
197C4×Dic11—24no—
198C4×Dic11—28no—
199#4318—28no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—28no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8C2412yes—
205C2×C11⋊C8C2414yes—
206C2×C11⋊C8C2412yes—
207C2×#535D1111yescharacteristic
208C2×#520—111no—
209#3096—1116no—
210C2×#481—112no—
211C2×#482—112no—
212C2×#482—112no—
213C2×#480—112no—
214C2×#428—111no—
215C2×#427—111no—
216C2×#418—111no—
217C22×#102—111no—
218C2×#408—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—48no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11—44no—
229C23×C11—84no—
230C23×C11—84no—
231C23×C11—816no—
232C23×C11#12314yes—
233C23×C11C22×D414yes—
234C23×C11C22×D412yes—
235C23×C11C22×D411yescharacteristic
236Q8×C11—28no—
237D4×C11—216no—
238D4×C11—28no—
239D4×C11—24no—
240D4×C11—24no—
241D4×C11—44no—
242D4×C11—48no—
243D4×C11—88no—
244D4×C11—88no—
245C2×C4×C11—24no—
246C2×C4×C11—28no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11#12314yes—
254C2×C4×C11#12318yes—
255C2×C4×C11C22×D414yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4112yes—
259C2×C4×C11C2×#4112yes—
260C2×C4×C11C2×#4114yes—
261C2×C4×C11C2×#4114yes—
262C2×C4×C11C2511yescharacteristic
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—42no—
267C2×Dic11—44no—
268C2×Dic11—42no—
269C2×Dic11—84no—
270C2×Dic11—88no—
271C11⋊C8—22no—
272C11⋊C8—22no—
273C11⋊C8—24no—
274C22×#41C2×D1111yescharacteristic
275C23×D4C2×D1111yescharacteristic
276C22×M16—111no—
277C23×C8—111no—
278#535—24no—
279#535C2×D1118yes—
280C2×#127—21no—
281C2×#124—21no—
282C2×#121C2×D1112yes—
283C2×#121C2×D1112yes—
284C2×#120—22no—
285#520—118no—
286#520—224no—
287C2×C4×Q8—221no—
288C2×C4×D4—222no—
289C2×C4×D4—221no—
290C2×#117—112no—
291C2×#117—111no—
292C2×#117C2×D1111yescharacteristic
293C22×C4⋊C4—112no—
294C22×C4⋊C4—111no—
295#482—1116no—
296#482—1116no—
297#481—1116no—
298#480—1116no—
299#428—118no—
300#427—118no—
301C2×#107—111no—
302C2×#107—112no—
303C2×#107—111no—
304C2×#106—111no—
305C2×#106—112no—
306C2×#106—111no—
307#418—118no—
308C2×#102—112no—
309C2×#102—112no—
310C2×#102—112no—
311C2×#102—112no—
312C2×#102—118no—
313#408—118no—
314C2×C22⋊C8—112no—
315C2×C22⋊C8—112no—
316C22×C11—28no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—48no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—816no—
327C22×C11—88no—
328C22×C11C2×#12314yes—
329C22×C11C2×#12312yes—
330C22×C11#57612yes—
331C22×C11#57712yes—
332C22×C11C23×D411yescharacteristic
333C4×C11—24no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11C2×#12312yes—
337C4×C11C2×#12314yes—
338C4×C11C22×#4111yescharacteristic
339C4×C11C22×#4111yescharacteristic
340Dic11—42no—
341Dic11—44no—
342Dic11—42no—
343C25—21no—
344C2×#41—24no—
345C2×#41—24no—
346C2×#41C22⋊D1114yes—
347C2×#41C22×D1114yes—
348C22×Q8C22⋊D1111yescharacteristic
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—21no—
354C22×D4—22no—
355C22×D4C22⋊D1112yes—
356C22×D4C22⋊D1111yescharacteristic
357C22×D4C22×D1112yes—
358C22×D4C22×D1114yes—
359C23×C4—222no—
360C23×C4—221no—
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C2×M16—114no—
364C2×M16—224no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8—114no—
368C22×C8—112no—
369C22×C8—224no—
370#127—28no—
371#124—28no—
372#121—24no—
373#121—24no—
374#121C22×D1118yes—
375#121C22×D1118yes—
376#120—216no—
377C4×Q8—228no—
378C4×D4—2216no—
379C4×D4—228no—
380#117—22no—
381#117—114no—
382#117—118no—
383#117—224no—
384#117—222no—
385#117C22×D1114yes—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—118no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—224no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—221no—
402C2×C42—21no—
403C2×C42—222no—
404C2×C42—221no—
405#107—114no—
406#107—114no—
407#107—118no—
408#106—114no—
409#106—114no—
410#106—118no—
411#102—118no—
412#102—118no—
413#102—118no—
414#102—118no—
415C22⋊C8—118no—
416C22⋊C8—118no—
417C2×C11—24no—
418C2×C11—44no—
419C2×C11—84no—
420C2×C11#309614yescomplemented
421C2×C11C22×#12311yescharacteristic
422C2×C11C2×#57611yescharacteristic
423C2×C11C2×#57711yescharacteristic
424C24—22no—
425C24—24no—
426C24—44no—
427C24—82no—
428C24—82no—
429C24C2×C22⋊D1112yes—
430C24C2×C22⋊D1111yescharacteristic
431#41—216no—
432#41—28no—
433#41—28no—
434C2×Q8—24no—
435C2×Q8C2×C22⋊D1114yes—
436C2×D4—28no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—24no—
442C2×D4—28no—
443C2×D4—28no—
444C2×D4—22no—
445C2×D4—24no—
446C2×D4—44no—
447C2×D4—48no—
448C2×D4—84no—
449C2×D4—84no—
450C2×D4C2×C22⋊D1118yes—
451C2×D4C2×C22⋊D1114yes—
452C2×D4C23×D1114yes—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—221no—
458C22×C4—222no—
459C22×C4—221no—
460C22×C4—228no—
461C22×C4—224no—
462C22×C4—882no—
463C22×C4—884no—
464C22×C4#434114yes—
465C22×C4#434114yes—
466C22×C4C2×C22⋊D1114yes—
467C22×C4C2×C22⋊D1112yes—
468C22×C4C2×C22⋊D1112yes—
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C23×D1114yes—
471C22×C4C23×D1112yes—
472C22×C4C23×D1111yescharacteristic
473M16—228no—
474C2×C8—112no—
475C2×C8—114no—
476C2×C8—112no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8—228no—
480C2×C8—224no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—114no—
484C4⋊C4—112no—
485C4⋊C4—112no—
486C4⋊C4—221no—
487C4⋊C4—222no—
488C4⋊C4—228no—
489C4⋊C4—224no—
490C4⋊C4—221no—
491C4⋊C4C23×D1112yes—
492C4⋊C4C23×D1112yes—
493C22⋊C4—24no—
494C22⋊C4—28no—
495C22⋊C4—28no—
496C22⋊C4—228no—
497C22⋊C4—224no—
498C42—24no—
499C42—228no—
500C42—224no—
501C11C2×#309611yescharacteristic, complemented, Sylow
502C23—22no—
503C23—22no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—48no—
509C23—44no—
510C23—44no—
511C23—44no—
512C23—84no—
513C23—84no—
514C23—816no—
515C23#6698814yes—
516C23C22×C22⋊D1114yes—
517C23C22×C22⋊D1112yes—
518C23C22×C22⋊D1111yescharacteristic
519Q8—28no—
520D4—216no—
521D4—28no—
522D4—24no—
523D4—24no—
524D4—44no—
525D4—48no—
526D4—88no—
527D4—88no—
528C2×C4—24no—
529C2×C4—28no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—222no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—444no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—884no—
543C2×C4—888no—
544C2×C4#6698814yes—
545C2×C4#6698818yes—
546C2×C4C2×#434112yes—
547C2×C4C2×#434112yes—
548C2×C4C2×#434114yes—
549C2×C4C2×#434114yes—
550C2×C4C22×C22⋊D1114yes—
551C2×C4C22×C22⋊D1112yes—
552C2×C4C22×C22⋊D1111yescharacteristic
553C2×C4C24×D1111yescharacteristic
554C8—222no—
555C8—222no—
556C8—224no—
557C22—28no—
558C22—22no—
559C22—22no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—48no—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—816no—
568C22—88no—
569C22C2×#6698814yes—
570C22C2×#6698812yes—
571C22#1062336612yes—
572C22#1062336712yes—
573C22C23×C22⋊D1111yescharacteristic
574C4—24no—
575C4—42no—
576C4—42no—
577C4—444no—
578C4—442no—
579C4—442no—
580C4C2×#6698812yes—
581C4C2×#6698814yes—
582C4C22×#434111yescharacteristic
583C4C22×#434111yescharacteristic
584C2—24no—
585C2—44no—
586C2—84no—
587C2#1307856814yesdirect product factor
588C2C22×#6698811yescharacteristic
589C2C2×#1062336611yescharacteristic
590C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#535C2
socleC23×C11C22×D4
hypercenterC2×#535D11
hypocenterC11C2×#3096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#10623358C2semidirect
2. #13078568C2direct (N × H)
3. C2×#10622647C2semidirect
4. C2×#10622648C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622646C2semidirect
7. C2×#10622608C2semidirect
8. C2×#10622611C2semidirect
9. C2×#10622828C2semidirect
10. C22×#66896C2semidirect
11. C2×#10622847C2semidirect
24. #10623358C22semidirect
29. C2×#66979C22semidirect
31. C22×C4⋊Dic11C22semidirect
34. #10622847C22semidirect
35. #10622828C22semidirect
40. C2×#66896C22semidirect
41. C2×C22⋊(C11⋊C8)C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
43. #10622648C22semidirect
44. #10622648C22semidirect
45. #10622647C22semidirect
46. #10622646C22semidirect
47. #10622611C22semidirect
48. #10622608C22semidirect
49. C2×#66872C22semidirect
50. C2×#66872C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
53. C2×#66871C22semidirect
54. C2×#66871C22semidirect
98. #66979C23semidirect
107. C2×C4⋊Dic11C23semidirect
121. C22⋊(C11⋊C8)C23semidirect
122. C22⋊(C11⋊C8)C23semidirect
123. #66872C23semidirect
124. #66872C23semidirect
125. #66872C23semidirect
126. #66871C23semidirect
127. #66871C23semidirect
128. #66871C23semidirect
420. C2×C11#3096semidirect
501. C11C2×#3096semidirect
587. C2#13078568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233582
#130785682
C2×#106226472
C2×#106226482
C2×#106226462
C2×#106226082
C2×#106226112
C2×#106228282
C22×#668962
C2×#106228472
C2×C11×#5352
C2×#309611