Finite Group Databasebeta

← C2×#13078539 #15621551

Subgroups — C2×#13078539 #15621551

Order 2816.

2650 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13078539C2116yesmaximal, direct product factor
3C2×#10622583C212yesmaximal, complemented
4C2×#10622581C212yesmaximal, complemented
5C2×#10622584C212yesmaximal, complemented
6C2×#10622580C212yesmaximal, complemented
7C2×#10622577C212yesmaximal, complemented
8C2×#10622579C212yesmaximal, complemented
9C2×#10622820C211yesmaximal, characteristic, complemented
10C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
11C24×C4×C11—21no—
12C24×C4×C11C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C22×C11×C4⋊C4—24no—
15C22×C11×C4⋊C4—21no—
16C22×C11×C4⋊C4—21no—
17C22×C11×C4⋊C4—21no—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C4⋊C4C2218yescomplemented
22C2×#67006—21no—
23#10623322—24no—
24#10623322C2218yes—
25C2×#66983C2211yescharacteristic
26C2×#66983C2211yescharacteristic
27C2×#66982—21no—
28C2×C4×C22⋊D11—21no—
29C2×C4×C22⋊D11—21no—
30C2×#66979C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C2×#66977C2211yescharacteristic
33C22×#4318C2212yes—
34#10622820C2218yescomplemented
35C2×C22⋊(C11⋊C8)C2212yes—
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622584C22116yescomplemented
38#10622583C22116yescomplemented
39C2×#66874C2214yescomplemented
40#10622581C22116yescomplemented
41#10622580C22116yescomplemented
42#10622579C22116yescomplemented
43C2×#66873C2214yescomplemented
44#10622577C22116yescomplemented
45C2×#66872C2214yescomplemented
46C2×#66871C2214yescomplemented
47C25×C11D411yescharacteristic
48C23×C4×C11—28no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—28no—
53C23×C4×C11—48no—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D414yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2314yes—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×C22⋊D11—21no—
64C22×C22⋊D11—21no—
65C2×#4339—22no—
66C2×#4339—28no—
67C2×#4339C2314yes—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×Dic22C2311yescharacteristic
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—28no—
78C2×C11×C4⋊C4—28no—
79C2×C11×C4⋊C4—28no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C11×C4⋊C4C2318yes—
83C2×C11×C4⋊C4C2318yes—
84#67006—28no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#66983—22no—
89#66983—22no—
90#66983C2314yes—
91#66983C2314yes—
92#66982—28no—
93C4×C22⋊D11—28no—
94C4×C22⋊D11—28no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97#66979—22no—
98#66979C2314yes—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101#66977—22no—
102#66977—22no—
103#66977C2314yes—
104#66977C2314yes—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×C4×Dic11—21no—
108C2×#4318—28no—
109C2×#4318C2318yes—
110C22×C11⋊C8C2314yes—
111C22⋊(C11⋊C8)C2318yes—
112C22⋊(C11⋊C8)C2318yes—
113#66874C23116yescomplemented
114#66873C23116yescomplemented
115#66872C23116yescomplemented
116#66871C23116yescomplemented
117C2×#3092—111nomaximal, Sylow
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11C2×D414yes—
122C24×C11C2×D411yescharacteristic
123C24×C11C2×D411yescharacteristic
124C24×C11C2×D411yescharacteristic
125C23×D11—21no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—216no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—216no—
133C22×C4×C11—28no—
134C22×C4×C11—28no—
135C22×C4×C11—28no—
136C22×C4×C11—24no—
137C22×C4×C11—48no—
138C22×C4×C11—48no—
139C22×C4×C11—432no—
140C22×C4×C11—48no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11#4118yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2411yescharacteristic
154C22×C4×C11C2412yes—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—24no—
158C2×C22⋊D11—44no—
159C2×C22⋊D11—44no—
160C2×C22⋊D11—44no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164#4339—216no—
165#4339—48no—
166C2×D44—21no—
167C2×D44—24no—
168C2×D44C2412yes—
169C2×C4×D11—24no—
170C2×C4×D11—44no—
171C2×Dic22—21no—
172C2×Dic22—24no—
173C2×Dic22C2412yes—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4C2418yes—
179C22⋊Dic11—24no—
180C22⋊Dic11—24no—
181C22⋊Dic11—24no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—24no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C2412yes—
187C4⋊Dic11C2412yes—
188Dic11⋊C4—24no—
189Dic11⋊C4—24no—
190C4×Dic11—24no—
191#4318—216no—
192C2×C11⋊C8—28no—
193C2×C11⋊C8C2418yes—
194C2×#525—111no—
195C23×C4⋊C4D1111yescharacteristic, complemented
196#3092—1116no—
197C2×#484—112no—
198C2×#481—112no—
199C2×#483—112no—
200C2×#480—112no—
201C2×#428—112no—
202C2×#417—112no—
203C2×#407—111no—
204C23×C11—232no—
205C23×C11—28no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—28no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—28no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11#12314yes—
215C23×C11AGL(1,ℤ/8)14yes—
216C23×C11#13714yes—
217C23×C11C22×D412yes—
218C23×C11C22×D412yes—
219C23×C11C22×D412yes—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C2×C4×C11—28no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—28no—
231C2×C4×C11—28no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—28no—
235C2×C4×C11—416no—
236C2×C4×C11—416no—
237C2×C4×C11—416no—
238C2×C4×C11—48no—
239C2×C4×C11#12314yes—
240C2×C4×C11#12318yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D412yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4114yes—
246C2×C4×C11C2×#4118yes—
247C2×C4×C11C2511yescharacteristic
248C22⋊D11—48no—
249C22⋊D11—48no—
250C22⋊D11—48no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257D44—24no—
258D44—42no—
259C4×D11—48no—
260Dic22—24no—
261Dic22—42no—
262C11⋊C8—28no—
263C22×#41—111no—
264C24×C4—21no—
265C24×C4C2×D1111yescharacteristic
266C22×M16—112no—
267#525—118no—
268#525—224no—
269C2×#123—221no—
270C2×C22⋊Q8—111no—
271C2×C22⋊Q8—111no—
272C2×#121—111no—
273C2×#121—111no—
274C2×#120—221no—
275C2×C4×D4—221no—
276C2×C4×D4—221no—
277C2×#117—111no—
278C22×C4⋊C4—24no—
279C22×C4⋊C4—21no—
280C22×C4⋊C4—21no—
281C22×C4⋊C4—21no—
282C22×C4⋊C4C2×D1112yes—
283C22×C4⋊C4C2×D1112yes—
284C22×C4⋊C4C2×D1112yes—
285C22×C4⋊C4C2×D1118yescomplemented
286#484—1116no—
287#483—1116no—
288#481—1116no—
289#480—1116no—
290#428—1116no—
291C2×#107—114no—
292C2×#106—114no—
293#417—1116no—
294C2×#103—114no—
295C2×#102—114no—
296#407—118no—
297C2×C22⋊C8—112no—
298C2×C22⋊C8—112no—
299C22×C11—232no—
300C22×C11—28no—
301C22×C11—28no—
302C22×C11—28no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11C2×#12314yes—
310C22×C11C2×#12312yes—
311C22×C11C2×AGL(1,ℤ/8)14yes—
312C22×C11C2×AGL(1,ℤ/8)12yes—
313C22×C11C2×#13714yes—
314C22×C11C2×#13712yes—
315C22×C11C23×D411yescharacteristic
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—84no—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—48no—
323C4×C11C2×#12312yes—
324C4×C11C2×#12314yes—
325C4×C11C22×#4112yes—
326Dic11—42no—
327Dic11—42no—
328Dic11—42no—
329C25C22⋊D1111yescharacteristic
330C2×#41—114no—
331C2×#41—222no—
332C2×#41—228no—
333C22×Q8—111no—
334C22×D4—111no—
335C22×D4—221no—
336C22×D4—221no—
337C22×D4—221no—
338C23×C4—28no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—28no—
343C23×C4—48no—
344C23×C4—221no—
345C23×C4C22⋊D1111yescharacteristic
346C23×C4C22⋊D1111yescharacteristic
347C23×C4C22⋊D1111yescharacteristic
348C23×C4C22⋊D1114yes—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1114yes—
352C23×C4C22×D1111yescharacteristic
353C2×M16—118no—
354C2×M16—228no—
355C22×C8—114no—
356#123—228no—
357C22⋊Q8—114no—
358C22⋊Q8—114no—
359C22⋊Q8—222no—
360C22⋊Q8—222no—
361#121—114no—
362#121—114no—
363#121—222no—
364#121—222no—
365#120—228no—
366C4×D4—228no—
367C4×D4—228no—
368#117—114no—
369#117—222no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22×D1114yes—
384C2×C4⋊C4C22×D1118yes—
385C2×C4⋊C4C22×D1118yes—
386C2×C4⋊C4C22×D1118yes—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—221no—
393#107—1116no—
394#106—1116no—
395#103—1116no—
396#102—1116no—
397C22⋊C8—118no—
398C22⋊C8—118no—
399C2×C11—24no—
400C2×C11—24no—
401C2×C11—24no—
402C2×C11#309214yescomplemented
403C2×C11C22×#12311yescharacteristic
404C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
405C2×C11C22×#13711yescharacteristic
406D11—82no—
407C24—24no—
408C24—24no—
409C24—24no—
410C24—221no—
411C24C2×C22⋊D1114yes—
412C24C2×C22⋊D1111yescharacteristic
413C24C2×C22⋊D1111yescharacteristic
414C24C2×C22⋊D1111yescharacteristic
415#41—2216no—
416#41—448no—
417C2×Q8—112no—
418C2×Q8—221no—
419C2×Q8—224no—
420C2×D4—112no—
421C2×D4—224no—
422C2×D4—224no—
423C2×D4—224no—
424C2×D4—224no—
425C2×D4—221no—
426C2×D4—444no—
427C2×D4—444no—
428C2×D4—444no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—216no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—216no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—24no—
440C22×C4—48no—
441C22×C4—48no—
442C22×C4—432no—
443C22×C4—48no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—224no—
448C22×C4—444no—
449C22×C4#433918yes—
450C22×C4C2×C22⋊D1114yes—
451C22×C4C2×C22⋊D1114yes—
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1112yes—
454C22×C4C2×C22⋊D1114yes—
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1112yes—
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C23×D1112yes—
460C22×C4C23×D1112yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1111yescharacteristic
463M16—2216no—
464C2×C8—118no—
465C2×C8—228no—
466C4⋊C4—28no—
467C4⋊C4—28no—
468C4⋊C4—28no—
469C4⋊C4—24no—
470C4⋊C4—112no—
471C4⋊C4—112no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—224no—
475C4⋊C4—224no—
476C4⋊C4C23×D1118yes—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C42—224no—
483C11C2×#309211yescharacteristic, complemented, Sylow
484C23—232no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—28no—
489C23—22no—
490C23—22no—
491C23—28no—
492C23—22no—
493C23—22no—
494C23—222no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23#6698214yes—
499C23#6698514yes—
500C23#6699514yes—
501C23C22×C22⋊D1112yes—
502C23C22×C22⋊D1112yes—
503C23C22×C22⋊D1112yes—
504C23C22×C22⋊D1111yescharacteristic
505Q8—224no—
506Q8—442no—
507D4—224no—
508D4—448no—
509D4—448no—
510D4—448no—
511D4—442no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—28no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—28no—
522C2×C4—416no—
523C2×C4—416no—
524C2×C4—416no—
525C2×C4—48no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—448no—
533C2×C4#6698214yes—
534C2×C4#6698218yes—
535C2×C4C2×#433914yes—
536C2×C4C2×#433918yes—
537C2×C4C22×C22⋊D1112yes—
538C2×C4C22×C22⋊D1112yes—
539C2×C4C22×C22⋊D1112yes—
540C2×C4C22×C22⋊D1111yescharacteristic
541C2×C4C24×D1111yescharacteristic
542C8—228no—
543C22—232no—
544C22—28no—
545C22—28no—
546C22—28no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—884no—
557C22C2×#6698214yes—
558C22C2×#6698212yes—
559C22C2×#6698514yes—
560C22C2×#6698512yes—
561C22C2×#6699514yes—
562C22C2×#6699512yes—
563C22C23×C22⋊D1111yescharacteristic
564C4—22no—
565C4—22no—
566C4—48no—
567C4—442no—
568C4—442no—
569C4—442no—
570C4C2×#6698214yes—
571C4C2×#6698212yes—
572C4C22×#433912yes—
573C2—24no—
574C2—24no—
575C2—24no—
576C2—882no—
577C2#1307853914yesdirect product factor
578C2C22×#6698211yescharacteristic
579C2C22×#6698511yescharacteristic
580C2C22×#6699511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC23×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
hypercenterC23×C4⋊C4D11
hypocenterC11C2×#3092
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13078539C2direct (N × H)
3. C2×#10622583C2semidirect
4. C2×#10622581C2semidirect
5. C2×#10622584C2semidirect
6. C2×#10622580C2semidirect
7. C2×#10622577C2semidirect
8. C2×#10622579C2semidirect
9. C2×#10622820C2semidirect
10. C23×C11×C4⋊C4C2semidirect
21. C22×C11×C4⋊C4C22semidirect
34. #10622820C22semidirect
37. #10622584C22semidirect
38. #10622583C22semidirect
39. C2×#66874C22semidirect
40. #10622581C22semidirect
41. #10622580C22semidirect
42. #10622579C22semidirect
43. C2×#66873C22semidirect
44. #10622577C22semidirect
45. C2×#66872C22semidirect
46. C2×#66871C22semidirect
113. #66874C23semidirect
114. #66873C23semidirect
115. #66872C23semidirect
116. #66871C23semidirect
195. C23×C4⋊C4D11semidirect
285. C22×C4⋊C4C2×D11semidirect
402. C2×C11#3092semidirect
483. C11C2×#3092semidirect
577. C2#13078539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233222
#130785392
C2×#106225832
C2×#106225812
C2×#106225842
C2×#106225802
C2×#106225772
C2×#106225792
C2×#106228202
C23×C11×C4⋊C42
C2×#309211