Finite Group Databasebeta

← C2×#13078574 #15621600

Subgroups — C2×#13078574 #15621600

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×#10623361C211yesmaximal, characteristic
2#13078574C2116yesmaximal, direct product factor
3C2×#10622581C212yesmaximal, complemented
4C2×#10622616C212yesmaximal, complemented
5C2×#10622616C212yesmaximal, complemented
6C2×#10622580C212yesmaximal, complemented
7C2×#10622577C211yesmaximal, characteristic, complemented
8C2×#10622611C211yesmaximal, characteristic, complemented
9C2×#10622614C211yesmaximal, characteristic, complemented
10C22×#66873C211yesmaximal, characteristic, complemented
11C2×#10622847C211yesmaximal, characteristic, complemented
12C2×C11×#520C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×D44C2211yescharacteristic
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×#117C2212yescomplemented
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2212yescomplemented
24#10623361—24no—
25#10623361C2218yes—
26C2×#67000—21no—
27C2×#66993—21no—
28C2×#66990—22no—
29C2×#66983C2212yes—
30C2×#66983C2212yes—
31C2×#66979C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C23×C11⋊C8C2211yescharacteristic
34#10622847C2218yescomplemented
35C2×C22⋊(C11⋊C8)C2212yescomplemented
36C2×C22⋊(C11⋊C8)C2212yescomplemented
37#10622616C22116yescomplemented
38#10622616C22116yescomplemented
39#10622614C2218yescomplemented
40#10622611C2218yescomplemented
41#10622581C22116yescomplemented
42#10622580C22116yescomplemented
43C2×#66873C2212yes—
44C2×#66873C2212yes—
45C2×#66873C2212yes—
46C2×#66873C2212yes—
47C2×#66873C2218yescomplemented
48#10622577C2218yescomplemented
49C2×#66872C2211yescharacteristic, complemented
50C2×#66872C2211yescharacteristic, complemented
51C2×#66872C2212yescomplemented
52C2×#66871C2211yescharacteristic, complemented
53C2×#66871C2211yescharacteristic, complemented
54C2×#66871C2212yescomplemented
55C24×D11—21no—
56C2×C11×#41—24no—
57C2×C11×#41—24no—
58C2×C11×#41D414yes—
59C2×C11×#41C2314yes—
60C22×Q8×C11D411yescharacteristic
61C22×D4×C11D412yes—
62C22×D4×C11D411yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—22no—
65C23×C4×C11C2312yes—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×D44—24no—
70C22×D44—24no—
71C22×D44—21no—
72C22×D44—22no—
73C22×D44C2312yes—
74C22×D44C2314yes—
75C4×Q8×C11—28no—
76C4×D4×C11—28no—
77C4×D4×C11—216no—
78C11×#117—22no—
79C11×#117—24no—
80C11×#117C2314yes—
81C11×#117C2318yescomplemented
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2318yescomplemented
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—22no—
93C2×C42×C11—21no—
94C2×C42×C11—22no—
95C2×C22⋊Dic11—21no—
96#67000—28no—
97#66993—28no—
98#66990—216no—
99#66983—24no—
100#66983—24no—
101#66983C2318yes—
102#66983C2318yes—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105#66979—22no—
106#66979C2314yes—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4×Dic11—21no—
110C2×#4318—24no—
111C2×#4318C2314yes—
112C22×C11⋊C8—24no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2314yes—
116C22×C11⋊C8C2312yes—
117C22⋊(C11⋊C8)C2318yescomplemented
118C22⋊(C11⋊C8)C2318yescomplemented
119#66873C2318yes—
120#66873C2318yes—
121#66873C2318yes—
122#66873C2318yes—
123#66872C2318yescomplemented
124#66872C2314yescomplemented
125#66872C2314yescomplemented
126#66871C2318yescomplemented
127#66871C2314yescomplemented
128#66871C2314yescomplemented
129C2×#3096—111nomaximal, Sylow
130C24×C11C2×D412yes—
131C24×C11C2×D411yescharacteristic
132C23×D11—22no—
133C23×D11—24no—
134C23×D11—44no—
135C23×D11—82no—
136C23×D11—82no—
137C11×#41—216no—
138C11×#41—28no—
139C11×#41—28no—
140C2×Q8×C11—24no—
141C2×Q8×C11C2×D414yes—
142C2×D4×C11—28no—
143C2×D4×C11—24no—
144C2×D4×C11C2×D418yes—
145C2×D4×C11C2×D414yes—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—28no—
153C22×C4×C11—82no—
154C22×C4×C11—84no—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4114yes—
160C22×C4×C11#4114yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C2411yescharacteristic
163C22×C4×C11C2412yes—
164C2×C22⋊D11—28no—
165C2×C22⋊D11—28no—
166C2×C22⋊D11—84no—
167C2×C22⋊D11—84no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C2×D44—22no—
171C2×D44—24no—
172C2×D44—24no—
173C2×D44—24no—
174C2×D44—28no—
175C2×D44—28no—
176C2×D44—44no—
177C2×D44—48no—
178C2×D44C2414yes—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—28no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C2414yes—
185C11×C4⋊C4C2412yes—
186C11×C4⋊C4C2412yes—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—28no—
189C42×C11—24no—
190C42×C11—28no—
191C22⋊Dic11—24no—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—28no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2412yes—
197C4⋊Dic11C2412yes—
198C4×Dic11—24no—
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×#535—111no—
208C2×#520D1111yescharacteristic, complemented
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#12314yes—
225C23×C11C22×D414yes—
226C23×C11C22×D412yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—24no—
229C22×D11—48no—
230C22×D11—44no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—84no—
234C22×D11—84no—
235C22×D11—816no—
236Q8×C11—28no—
237D4×C11—216no—
238D4×C11—28no—
239C2×C4×C11—24no—
240C2×C4×C11—28no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—42no—
249C2×C4×C11—84no—
250C2×C4×C11—88no—
251C2×C4×C11#12314yes—
252C2×C4×C11#12318yes—
253C2×C4×C11C22×D414yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4112yes—
257C2×C4×C11C2×#4112yes—
258C2×C4×C11C2×#4114yes—
259C2×C4×C11C2×#4114yes—
260C2×C4×C11C2511yescharacteristic
261C22⋊D11—88no—
262C22⋊D11—88no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267D44—24no—
268D44—24no—
269D44—44no—
270D44—48no—
271C11⋊C8—22no—
272C11⋊C8—22no—
273C11⋊C8—24no—
274C22×#41C2×D1111yescharacteristic
275C23×D4—111no—
276C22×M16—111no—
277C23×C8—111no—
278#535—118no—
279#535—224no—
280C2×#127—221no—
281C2×#124—221no—
282C2×#121—112no—
283C2×#121—112no—
284C2×#120—222no—
285#520—24no—
286#520C2×D1118yescomplemented
287C2×C4×Q8—21no—
288C2×C4×D4—21no—
289C2×C4×D4—22no—
290C2×#117—111no—
291C2×#117C2×D1111yescharacteristic
292C2×#117C2×D1112yescomplemented
293C22×C4⋊C4C2×D1111yescharacteristic
294C22×C4⋊C4C2×D1112yescomplemented
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×C11C2×#12314yes—
324C22×C11C2×#12312yes—
325C22×C11#57612yes—
326C22×C11#57712yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—816no—
332C2×D11—88no—
333C4×C11—24no—
334C4×C11—42no—
335C4×C11—44no—
336C4×C11—42no—
337C4×C11C2×#12312yes—
338C4×C11C2×#12314yes—
339C4×C11C22×#4111yescharacteristic
340C4×C11C22×#4111yescharacteristic
341Dic11—42no—
342Dic11—42no—
343C25—221no—
344C2×#41—24no—
345C2×#41—24no—
346C2×#41C22⋊D1114yes—
347C2×#41C22×D1114yes—
348C22×Q8C22⋊D1111yescharacteristic
349C22×D4—112no—
350C22×D4—114no—
351C22×D4—222no—
352C22×D4—222no—
353C22×D4—224no—
354C22×D4—224no—
355C22×D4—221no—
356C22×D4—222no—
357C22×D4C22⋊D1112yes—
358C22×D4C22⋊D1111yescharacteristic
359C23×C4—21no—
360C23×C4—22no—
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—228no—
371#124—228no—
372#121—118no—
373#121—118no—
374#121—224no—
375#121—224no—
376#120—2216no—
377C4×Q8—28no—
378C4×D4—28no—
379C4×D4—216no—
380#117—22no—
381#117—24no—
382#117—114no—
383#117—222no—
384#117C22×D1114yes—
385#117C22×D1118yescomplemented
386C2×C4⋊C4—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4C22×D1112yes—
393C2×C4⋊C4C22×D1114yes—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1118yescomplemented
397C2×C22⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—222no—
402C2×C42—21no—
403C2×C42—22no—
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#309614yescomplemented
420C2×C11C22×#12311yescharacteristic
421C2×C11C2×#57611yescharacteristic
422C2×C11C2×#57711yescharacteristic
423D11—84no—
424C24—222no—
425C24—224no—
426C24—444no—
427C24—882no—
428C24—882no—
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—24no—
438C2×D4—114no—
439C2×D4—228no—
440C2×D4—228no—
441C2×D4—224no—
442C2×D4—224no—
443C2×D4—228no—
444C2×D4—228no—
445C2×D4—222no—
446C2×D4—224no—
447C2×D4—444no—
448C2×D4—448no—
449C2×D4—884no—
450C2×D4—884no—
451C2×D4C2×C22⋊D1118yes—
452C2×D4C2×C22⋊D1114yes—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—28no—
460C22×C4—82no—
461C22×C4—84no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4#433914yes—
465C22×C4#433914yes—
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—22no—
482C4⋊C4—21no—
483C4⋊C4—24no—
484C4⋊C4—28no—
485C4⋊C4—21no—
486C4⋊C4—112no—
487C4⋊C4—112no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4C23×D1114yes—
491C4⋊C4C23×D1112yes—
492C4⋊C4C23×D1112yes—
493C22⋊C4—24no—
494C22⋊C4—28no—
495C22⋊C4—224no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C42—24no—
499C42—28no—
500C42—224no—
501C11C2×#309611yescharacteristic, complemented, Sylow
502C23—22no—
503C23—22no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—224no—
508C23—448no—
509C23—444no—
510C23—444no—
511C23—444no—
512C23—884no—
513C23—884no—
514C23—8816no—
515C23#6698214yes—
516C23C22×C22⋊D1114yes—
517C23C22×C22⋊D1112yes—
518C23C22×C22⋊D1111yescharacteristic
519Q8—28no—
520D4—216no—
521D4—28no—
522D4—224no—
523D4—224no—
524D4—444no—
525D4—448no—
526D4—888no—
527D4—888no—
528C2×C4—24no—
529C2×C4—28no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—84no—
539C2×C4—88no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4#6698214yes—
545C2×C4#6698218yes—
546C2×C4C2×#433912yes—
547C2×C4C2×#433912yes—
548C2×C4C2×#433914yes—
549C2×C4C2×#433914yes—
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—444no—
565C22—444no—
566C22—444no—
567C22—8816no—
568C22—888no—
569C22C2×#6698214yes—
570C22C2×#6698212yes—
571C22#1062336612yes—
572C22#1062336812yes—
573C22C23×C22⋊D1111yescharacteristic
574C4—24no—
575C4—42no—
576C4—44no—
577C4—42no—
578C4—442no—
579C4—442no—
580C4C2×#6698212yes—
581C4C2×#6698214yes—
582C4C22×#433911yescharacteristic
583C4C22×#433911yescharacteristic
584C2—24no—
585C2—44no—
586C2—884no—
587C2#1307857414yesdirect product factor
588C2C22×#6698211yescharacteristic
589C2C2×#1062336611yescharacteristic
590C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#520C2
socleC23×C11C22×D4
prime radicalC2×#10623361C2
hypercenterC2×#520D11
hypocenterC11C2×#3096
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. #13078574C2direct (N × H)
3. C2×#10622581C2semidirect
4. C2×#10622616C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622580C2semidirect
7. C2×#10622577C2semidirect
8. C2×#10622611C2semidirect
9. C2×#10622614C2semidirect
10. C22×#66873C2semidirect
11. C2×#10622847C2semidirect
12. C2×C11×#520C2semidirect
16. C11×#520C22semidirect
21. C2×C11×#117C22semidirect
23. C22×C11×C4⋊C4C22semidirect
34. #10622847C22semidirect
35. C2×C22⋊(C11⋊C8)C22semidirect
36. C2×C22⋊(C11⋊C8)C22semidirect
37. #10622616C22semidirect
38. #10622616C22semidirect
39. #10622614C22semidirect
40. #10622611C22semidirect
41. #10622581C22semidirect
42. #10622580C22semidirect
47. C2×#66873C22semidirect
48. #10622577C22semidirect
49. C2×#66872C22semidirect
50. C2×#66872C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
53. C2×#66871C22semidirect
54. C2×#66871C22semidirect
81. C11×#117C23semidirect
90. C2×C11×C4⋊C4C23semidirect
117. C22⋊(C11⋊C8)C23semidirect
118. C22⋊(C11⋊C8)C23semidirect
123. #66872C23semidirect
124. #66872C23semidirect
125. #66872C23semidirect
126. #66871C23semidirect
127. #66871C23semidirect
128. #66871C23semidirect
208. C2×#520D11semidirect
286. #520C2×D11semidirect
292. C2×#117C2×D11semidirect
294. C22×C4⋊C4C2×D11semidirect
385. #117C22×D11semidirect
396. C2×C4⋊C4C22×D11semidirect
419. C2×C11#3096semidirect
501. C11C2×#3096semidirect
587. C2#13078574direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233612
#130785742
C2×#106225812
C2×#106226162
C2×#106225802
C2×#106225772
C2×#106226112
C2×#106226142
C22×#668732
C2×#106228472
C2×C11×#5202
C2×#309611