Finite Group Databasebeta

← C2×#13078594 #15621622

Subgroups — C2×#13078594 #15621622

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2#13078594C2116yesmaximal, direct product factor
3C2×#10622583C212yesmaximal, complemented
4C2×#10622609C212yesmaximal, complemented
5C2×#10622616C212yesmaximal, complemented
6C2×#10622580C212yesmaximal, complemented
7C2×#10622608C211yesmaximal, characteristic, complemented
8C22×#66871C211yesmaximal, characteristic, complemented
9C2×#10622579C211yesmaximal, characteristic, complemented
10C2×#10622615C211yesmaximal, characteristic, complemented
11C2×#10622847C211yesmaximal, characteristic, complemented
12C2×C11×#520C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C22×#4339C2211yescharacteristic
15C11×#520—24no—
16C11×#520C2218yescomplemented
17C2×C4×Q8×C11—21no—
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11—22no—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2212yes—
24#10623364—24no—
25#10623364C2218yes—
26C2×#66999—21no—
27C2×#66992—22no—
28C2×#66991—21no—
29C2×#66983C2212yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C2×#66977C2212yes—
32C22×#4318C2211yescharacteristic
33C23×C11⋊C8C2211yescharacteristic
34#10622847C2218yescomplemented
35C2×C22⋊(C11⋊C8)C2212yes—
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622616C22116yescomplemented
38#10622615C2218yescomplemented
39#10622609C22116yescomplemented
40#10622608C2218yescomplemented
41#10622583C22116yescomplemented
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2212yes—
45#10622580C22116yescomplemented
46#10622579C2218yescomplemented
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2212yes—
50C2×#66872C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53C2×#66871C2212yes—
54C2×#66871C2218yescomplemented
55C2×C11×#41—24no—
56C2×C11×#41—24no—
57C2×C11×#41D414yes—
58C2×C11×#41C2314yes—
59C22×Q8×C11D411yescharacteristic
60C22×D4×C11D411yescharacteristic
61C22×D4×C11D412yes—
62C23×C4×C11—22no—
63C23×C4×C11—21no—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—22no—
68C23×Dic11—21no—
69C2×#4339—22no—
70C2×#4339—24no—
71C2×#4339—24no—
72C2×#4339C2314yes—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×Dic22C2311yescharacteristic
76C4×Q8×C11—28no—
77C4×D4×C11—28no—
78C4×D4×C11—216no—
79C11×#117—24no—
80C11×#117—22no—
81C11×#117C2314yes—
82C11×#117C2318yes—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2318yes—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—21no—
94C2×C42×C11—22no—
95C2×C42×C11—21no—
96C2×C22⋊Dic11—22no—
97#66999—28no—
98#66992—216no—
99#66991—28no—
100#66983—24no—
101#66983C2318yes—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2314yes—
107#66977—24no—
108#66977C2318yes—
109C2×Dic11⋊C4—22no—
110C2×#4318—24no—
111C2×#4318C2314yes—
112C22×C11⋊C8—24no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2314yes—
116C22×C11⋊C8C2312yes—
117C22⋊(C11⋊C8)C2318yes—
118C22⋊(C11⋊C8)C2318yes—
119#66874C2318yes—
120#66874C2314yes—
121#66874C2314yes—
122#66873C2318yes—
123#66873C2314yes—
124#66873C2314yes—
125#66872C2318yes—
126#66871C2318yes—
127#66871C2318yes—
128#66871C2318yes—
129C2×#3098—111nomaximal, Sylow
130C24×C11C2×D412yes—
131C24×C11C2×D411yescharacteristic
132C23×D11—21no—
133C11×#41—216no—
134C11×#41—28no—
135C11×#41—28no—
136C2×Q8×C11—24no—
137C2×Q8×C11C2×D414yes—
138C2×D4×C11—28no—
139C2×D4×C11—24no—
140C2×D4×C11C2×D414yes—
141C2×D4×C11C2×D418yes—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—28no—
148C22×C4×C11—24no—
149C22×C4×C11—82no—
150C22×C4×C11—84no—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4114yes—
156C22×C4×C11#4114yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2411yescharacteristic
159C22×C4×C11C2412yes—
160C2×C22⋊D11—24no—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—44no—
163C2×C22⋊D11—84no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—82no—
168#4339—28no—
169#4339—28no—
170#4339—48no—
171C2×D44—21no—
172C2×D44—22no—
173C2×D44—22no—
174C2×D44C2412yes—
175C2×C4×D11—24no—
176C2×C4×D11—44no—
177C2×Dic22—21no—
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22C2412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—28no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C2414yes—
187C11×C4⋊C4C2412yes—
188C11×C4⋊C4C2412yes—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—24no—
191C42×C11—28no—
192C42×C11—24no—
193C22⋊Dic11—28no—
194(C2×D11)⋊C4—28no—
195C4⋊Dic11—22no—
196C4⋊Dic11—24no—
197C4⋊Dic11C2414yes—
198Dic11⋊C4—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⋊C8C2412yes—
206C2×C11⋊C8C2414yes—
207C2×#537—111no—
208C2×#520D1111yescharacteristic, complemented
209#3098—1116no—
210C2×#484—112no—
211C2×#485—112no—
212C2×#482—112no—
213C2×#480—112no—
214C2×#428—111no—
215C22×#107—111no—
216C2×#417—111no—
217C2×#416—111no—
218C2×#408—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11#12314yes—
225C23×C11C22×D414yes—
226C23×C11C22×D412yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—22no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232Q8×C11—28no—
233D4×C11—216no—
234D4×C11—28no—
235C2×C4×C11—24no—
236C2×C4×C11—28no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—44no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—84no—
246C2×C4×C11—88no—
247C2×C4×C11#12314yes—
248C2×C4×C11#12318yes—
249C2×C4×C11C22×D414yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4112yes—
253C2×C4×C11C2×#4112yes—
254C2×C4×C11C2×#4114yes—
255C2×C4×C11C2×#4114yes—
256C2×C4×C11C2511yescharacteristic
257C22⋊D11—48no—
258C22⋊D11—88no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—42no—
262C2×Dic11—44no—
263C2×Dic11—84no—
264D44—22no—
265D44—22no—
266D44—42no—
267C4×D11—48no—
268Dic22—22no—
269Dic22—22no—
270Dic22—42no—
271C11⋊C8—22no—
272C11⋊C8—22no—
273C11⋊C8—24no—
274C22×#41—111no—
275C22×#41C2×D1111yescharacteristic
276C22×M16—111no—
277C23×C8—111no—
278#537—118no—
279#537—224no—
280C2×C22⋊Q8—112no—
281C2×C22⋊Q8—221no—
282C2×#121—112no—
283C2×#121—221no—
284C2×#121—222no—
285#520—24no—
286#520C2×D1118yescomplemented
287C2×C4×Q8—21no—
288C2×C4×D4—22no—
289C2×C4×D4—21no—
290C2×#117C2×D1112yes—
291C2×#117C2×D1111yescharacteristic
292C22×C4⋊C4—111no—
293C22×C4⋊C4C2×D1112yes—
294C22×C4⋊C4C2×D1111yescharacteristic
295#485—1116no—
296#484—1116no—
297#482—1116no—
298#480—1116no—
299#428—118no—
300C2×#107—112no—
301C2×#107—112no—
302C2×#107—112no—
303C2×#107—118no—
304C2×#106—112no—
305#417—118no—
306#416—118no—
307C2×#103—111no—
308C2×#103—112no—
309C2×#103—111no—
310C2×#102—111no—
311C2×#102—112no—
312C2×#102—111no—
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×C11C2×#12314yes—
324C22×C11C2×#12312yes—
325C22×C11#57612yes—
326C22×C11#57812yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—84no—
332C4×C11—24no—
333C4×C11—44no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11C2×#12312yes—
337C4×C11C2×#12314yes—
338C4×C11C22×#4111yescharacteristic
339C4×C11C22×#4111yescharacteristic
340Dic11—42no—
341Dic11—44no—
342C2×#41—24no—
343C2×#41—24no—
344C2×#41—114no—
345C2×#41—222no—
346C2×#41—224no—
347C2×#41—224no—
348C2×#41C22⋊D1114yes—
349C2×#41C22×D1114yes—
350C22×Q8—111no—
351C22×Q8C22⋊D1111yescharacteristic
352C22×D4—111no—
353C22×D4—221no—
354C22×D4—222no—
355C22×D4C22⋊D1112yes—
356C22×D4C22⋊D1111yescharacteristic
357C23×C4—22no—
358C23×C4—21no—
359C23×C4—221no—
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—
370C22⋊Q8—118no—
371C22⋊Q8—228no—
372C22⋊Q8—224no—
373#121—118no—
374#121—228no—
375#121—2216no—
376#121—224no—
377C4×Q8—28no—
378C4×D4—216no—
379C4×D4—28no—
380#117—24no—
381#117—22no—
382#117C22×D1114yes—
383#117C22×D1118yes—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—112no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1112yes—
395C2×C4⋊C4C22×D1114yes—
396C2×C4⋊C4C22×D1118yes—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—22no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—222no—
402C2×C42—22no—
403C2×C42—21no—
404#107—118no—
405#107—118no—
406#107—118no—
407#106—118no—
408#103—114no—
409#103—114no—
410#103—118no—
411#102—114no—
412#102—114no—
413#102—118no—
414C22⋊C8—118no—
415C22⋊C8—118no—
416C2×C11—24no—
417C2×C11—44no—
418C2×C11#309814yescomplemented
419C2×C11C22×#12311yescharacteristic
420C2×C11C2×#57611yescharacteristic
421C2×C11C2×#57811yescharacteristic
422D11—82no—
423C24—221no—
424C24C2×C22⋊D1112yes—
425C24C2×C22⋊D1111yescharacteristic
426#41—216no—
427#41—28no—
428#41—28no—
429#41—228no—
430#41—228no—
431#41—448no—
432C2×Q8—24no—
433C2×Q8—112no—
434C2×Q8—221no—
435C2×Q8—222no—
436C2×Q8—222no—
437C2×Q8C2×C22⋊D1114yes—
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—112no—
441C2×D4—224no—
442C2×D4—228no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—221no—
446C2×D4—444no—
447C2×D4—884no—
448C2×D4C2×C22⋊D1118yes—
449C2×D4C2×C22⋊D1114yes—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—28no—
456C22×C4—24no—
457C22×C4—82no—
458C22×C4—84no—
459C22×C4—222no—
460C22×C4—221no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—444no—
464C22×C4—882no—
465C22×C4#433914yes—
466C22×C4#433914yes—
467C22×C4C2×C22⋊D1114yes—
468C22×C4C2×C22⋊D1112yes—
469C22×C4C2×C22⋊D1112yes—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C23×D1114yes—
472C22×C4C23×D1112yes—
473C22×C4C23×D1111yescharacteristic
474M16—228no—
475C2×C8—114no—
476C2×C8—112no—
477C2×C8—112no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—228no—
481C2×C8—224no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—28no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—114no—
488C4⋊C4—224no—
489C4⋊C4—222no—
490C4⋊C4—228no—
491C4⋊C4C23×D1112yes—
492C4⋊C4C23×D1112yes—
493C4⋊C4C23×D1114yes—
494C22⋊C4—28no—
495C22⋊C4—24no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C42—28no—
499C42—24no—
500C11C2×#309811yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—222no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23#6698214yes—
511C23C22×C22⋊D1114yes—
512C23C22×C22⋊D1112yes—
513C23C22×C22⋊D1111yescharacteristic
514Q8—28no—
515Q8—222no—
516Q8—222no—
517Q8—442no—
518D4—216no—
519D4—28no—
520D4—222no—
521D4—222no—
522D4—448no—
523D4—442no—
524D4—888no—
525C2×C4—24no—
526C2×C4—28no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—84no—
536C2×C4—88no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—442no—
540C2×C4—444no—
541C2×C4—448no—
542C2×C4—884no—
543C2×C4#6698214yes—
544C2×C4#6698218yes—
545C2×C4C2×#433912yes—
546C2×C4C2×#433912yes—
547C2×C4C2×#433914yes—
548C2×C4C2×#433914yes—
549C2×C4C22×C22⋊D1114yes—
550C2×C4C22×C22⋊D1112yes—
551C2×C4C22×C22⋊D1111yescharacteristic
552C2×C4C24×D1111yescharacteristic
553C8—222no—
554C8—222no—
555C8—224no—
556C22—28no—
557C22—22no—
558C22—22no—
559C22—24no—
560C22—24no—
561C22—24no—
562C22—48no—
563C22—442no—
564C22—442no—
565C22—442no—
566C22—884no—
567C22C2×#6698214yes—
568C22C2×#6698212yes—
569C22#1062336612yes—
570C22#1062336912yes—
571C22C23×C22⋊D1111yescharacteristic
572C4—24no—
573C4—44no—
574C4—42no—
575C4—42no—
576C4—444no—
577C4—442no—
578C4C2×#6698212yes—
579C4C2×#6698214yes—
580C4C22×#433911yescharacteristic
581C4C22×#433911yescharacteristic
582C2—24no—
583C2—44no—
584C2—882no—
585C2#1307859414yesdirect product factor
586C2C22×#6698211yescharacteristic
587C2C2×#1062336611yescharacteristic
588C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC2×#520D11
hypocenterC11C2×#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. #13078594C2direct (N × H)
3. C2×#10622583C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622580C2semidirect
7. C2×#10622608C2semidirect
8. C22×#66871C2semidirect
9. C2×#10622579C2semidirect
10. C2×#10622615C2semidirect
11. C2×#10622847C2semidirect
12. C2×C11×#520C2semidirect
16. C11×#520C22semidirect
34. #10622847C22semidirect
37. #10622616C22semidirect
38. #10622615C22semidirect
39. #10622609C22semidirect
40. #10622608C22semidirect
41. #10622583C22semidirect
45. #10622580C22semidirect
46. #10622579C22semidirect
54. C2×#66871C22semidirect
208. C2×#520D11semidirect
286. #520C2×D11semidirect
418. C2×C11#3098semidirect
500. C11C2×#3098semidirect
585. C2#13078594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233642
#130785942
C2×#106225832
C2×#106226092
C2×#106226162
C2×#106225802
C2×#106226082
C22×#668712
C2×#106225792
C2×#106226152
C2×#106228472
C2×C11×#5202
C2×#309811