Finite Group Databasebeta

← C2×#13081549 #15634287

Subgroups — C2×#13081549 #15634287

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic22C211yesmaximal, characteristic
2C2×#10623100C211yesmaximal, characteristic
3#13081549C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic
5C2×#10622469C211yesmaximal, characteristic
6C2×#10622468C211yesmaximal, characteristic
7C2×#10622409C211yesmaximal, characteristic
8C2×#10622635C211yesmaximal, characteristic
9C2×#10622407C211yesmaximal, characteristic
10C2×#10622633C211yesmaximal, characteristic
11C2×#10622404C211yesmaximal, characteristic
12C2×#10622404C211yesmaximal, characteristic
13C2×#10622314C211yesmaximal, characteristic
14C2×#10622797C211yesmaximal, characteristic
15C2×Q16×Dic11C211yesmaximal, characteristic
16C2×C11×#441C211yesmaximal, characteristic
17C22×C11×Q16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24#10623100—24no—
25#10623100C2218yes—
26Q8×Dic22—24no—
27Q8×Dic22C2218yes—
28C2×#66943—21no—
29C2×#66943C2211yescharacteristic
30C2×#66941—21no—
31C2×#66941—21no—
32C2×#66941—21no—
33C2×#66941C2211yescharacteristic
34C2×#66941C2211yescharacteristic
35C2×#66941C2211yescharacteristic
36C2×#66923—21no—
37C2×#66923C2211yescharacteristic
38C2×#66922—21no—
39C2×#66922C2211yescharacteristic
40C2×C4×Dic22—21no—
41C2×C4×Dic22—21no—
42C2×C4×Dic22C2211yescharacteristic
43C11×#441C2218yes—
44C2×C11×#106C2211yescharacteristic
45C2×C11×#103C2211yescharacteristic
46C2×C11×#103C2211yescharacteristic
47C2×C11×#97C2211yescharacteristic
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52#10622797C2218yes—
53Q16×Dic11C2218yes—
54C2×#66882C2211yescharacteristic
55C2×#66882C2211yescharacteristic
56C2×#66881C2211yescharacteristic
57C2×#66881C2211yescharacteristic
58C2×#66879C2211yescharacteristic
59C2×Dic11⋊C8C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62#10622635C2218yes—
63#10622633C2218yes—
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622469C2218yes—
70#10622468C2218yes—
71#10622409C2218yes—
72#10622407C2218yes—
73#10622404C2218yes—
74#10622404C2218yes—
75#10622315C2218yes—
76#10622314C2218yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Dic22—21no—
80C22×Dic22—21no—
81C22×Dic22—21no—
82C22×Dic22—21no—
83C22×Dic22D411yescharacteristic
84C2×C11×Q16Q818yescomplemented
85C2×C11×Q16C2314yes—
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11C2314yes—
91C4×Q8×C11C2314yes—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11—21no—
98C2×C42×C11C2311yescharacteristic
99Q8×Dic11—22no—
100Q8×Dic11—22no—
101Q8×Dic11—22no—
102Q8×Dic11—22no—
103Q8×Dic11C2314yes—
104Q8×Dic11C2314yes—
105Q8×Dic11C2314yes—
106Q8×Dic11C2314yes—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11D411yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4D411yescharacteristic
125C2×Dic11⋊C4D411yescharacteristic
126C2×C4×Dic11—21no—
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134#66943—28no—
135#66943—22no—
136#66943C2314yes—
137#66941—28no—
138#66941—28no—
139#66941—28no—
140#66941—22no—
141#66941—22no—
142#66941—22no—
143#66941C2314yes—
144#66941C2314yes—
145#66941C2314yes—
146#66923—22no—
147#66923—28no—
148#66923C2314yes—
149#66922—22no—
150#66922—28no—
151#66922C2314yes—
152C4×Dic22—28no—
153C4×Dic22—28no—
154C4×Dic22D414yes—
155C4×Dic22C2314yes—
156C11×#106C2314yes—
157C11×#103C2314yes—
158C11×#103C2314yes—
159C11×#97C2314yes—
160#66899C2314yes—
161#66899C2314yes—
162#66899C2314yes—
163#66899C2314yes—
164#66882C2314yes—
165#66882C2314yes—
166#66881C2314yes—
167#66881C2314yes—
168#66879C2314yes—
169Dic11⋊C8C2314yes—
170Dic11⋊C8C2314yes—
171C8×Dic11C2314yes—
172#66872C2314yes—
173#66872C2314yes—
174#66872C2314yes—
175#66871C2314yes—
176C4⋊(C11⋊C8)C2314yes—
177C2×#3387—111nomaximal, Sylow
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—22no—
181C2×Q8×C11—22no—
182C2×Q8×C11C2×Q814yes—
183C2×Q8×C11C2×Q814yes—
184C2×Q8×C11C2412yes—
185C2×Q8×C11C2412yes—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11C2×D411yescharacteristic
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201C2×Dic22—24no—
202C2×Dic22—24no—
203C2×Dic22—24no—
204C2×Dic22—24no—
205C2×Dic22—24no—
206C2×Dic22—44no—
207C2×Dic22—82no—
208C2×Dic22—82no—
209C2×Dic22—82no—
210C2×Dic22C2×D414yes—
211C11×Q16C2×Q8116yescomplemented
212C2×C8×C11—22no—
213C2×C8×C11C2×Q814yes—
214C2×C8×C11C2412yes—
215C2×C8×C11C2412yes—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4C2412yes—
221C11×C4⋊C4C2412yes—
222C42×C11—24no—
223C42×C11—24no—
224C42×C11C2×D412yes—
225C42×C11C2412yes—
226C4⋊Dic11—24no—
227C4⋊Dic11—24no—
228C4⋊Dic11—24no—
229C4⋊Dic11—24no—
230C4⋊Dic11—24no—
231C4⋊Dic11—24no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11C2×D414yes—
237C4⋊Dic11C2412yes—
238C4⋊Dic11C2412yes—
239C4⋊Dic11C2412yes—
240C4⋊Dic11C2412yes—
241Dic11⋊C4—24no—
242Dic11⋊C4—24no—
243Dic11⋊C4—24no—
244Dic11⋊C4—24no—
245Dic11⋊C4—24no—
246Dic11⋊C4—24no—
247Dic11⋊C4C2×D414yes—
248Dic11⋊C4C2×D414yes—
249C4×Dic11—24no—
250C4×Dic11—24no—
251C4×Dic11—24no—
252C4×Dic11—24no—
253C4×Dic11C2×D412yes—
254C4×Dic11C2×D412yes—
255C4×Dic11C2412yes—
256C4×Dic11C2412yes—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—22no—
259C2×C11⋊C8C2412yes—
260C2×C11⋊C8C2412yes—
261C2×Q82—111no—
262C2×#557—111no—
263#3387—1116no—
264C2×#501—111no—
265C2×#501—111no—
266C2×#498—111no—
267C2×#479—111no—
268C2×#479—111no—
269C2×#477—111no—
270C2×#475—111no—
271C2×#475—111no—
272C2×#475—111no—
273C2×#446—111no—
274C2×#441—111no—
275C2×#441D1111yescharacteristic
276C2×C4×Q16—111no—
277C23×C11C22×D411yescharacteristic
278Q8×C11—24no—
279Q8×C11—24no—
280Q8×C11—22no—
281Q8×C11—22no—
282Q8×C11C22×Q814yes—
283Q8×C11C22×Q814yes—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11C22×D412yes—
295C2×C4×C11C22×D412yes—
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×Q812yes—
298C2×C4×C112−1+412yes—
299C2×C4×C11C2511yescharacteristic
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11#13714yes—
312C2×Dic11C22×D412yes—
313C2×Dic11C22×D412yes—
314C2×Dic11C22×D412yes—
315C2×Dic11C22×D412yes—
316Dic22—28no—
317Dic22—48no—
318Dic22—84no—
319Dic22—84no—
320Dic22—84no—
321C8×C11—22no—
322C8×C11C22×Q814yes—
323C11⋊C8—22no—
324C11⋊C8—22no—
325C22×Q16C2×D1111yescharacteristic
326Q82—118no—
327Q82—224no—
328#557—118no—
329#557—224no—
330C2×C4⋊Q8—111no—
331C2×C4⋊Q8—111no—
332C2×C4⋊Q8—111no—
333C2×C4⋊Q8—111no—
334C2×C4⋊Q8—221no—
335C2×C4⋊Q8—221no—
336C2×C4⋊Q8—221no—
337C2×C4⋊Q8—221no—
338C2×#125—111no—
339C2×#125—111no—
340C2×#125—221no—
341C2×#125—221no—
342C2×C4×Q8—111no—
343C2×C4×Q8—111no—
344C2×C4×Q8—111no—
345C2×C4×Q8—111no—
346C2×C4×Q8—111no—
347C2×C4×Q8—221no—
348C2×C4×Q8—221no—
349C2×C4×Q8C2×D1111yescharacteristic
350C2×C4×Q8C2×D1111yescharacteristic
351#501—118no—
352#501—118no—
353#498—118no—
354#479—118no—
355#479—118no—
356#477—118no—
357#475—118no—
358#475—118no—
359#475—118no—
360#446—118no—
361#441—118no—
362#441C2×D1118yes—
363C4×Q16—118no—
364C2×#107—111no—
365C2×#107—111no—
366C2×#107—111no—
367C2×#106—111no—
368C2×#106—111no—
369C2×#106—111no—
370C2×#106—111no—
371C2×#106—111no—
372C2×#106C2×D1111yescharacteristic
373C2×C4⋊C8—111no—
374C2×C4⋊C8—111no—
375C2×C4⋊C8—111no—
376C2×#103—111no—
377C2×#103—111no—
378C2×#103—111no—
379C2×#103—111no—
380C2×#103C2×D1111yescharacteristic
381C2×#103C2×D1111yescharacteristic
382C2×#97—111no—
383C2×#97C2×D1111yescharacteristic
384C2×C4×C8—111no—
385C22×C11D4×Q812yes—
386C22×C11C2×#13712yes—
387C22×C11#57712yes—
388C22×C11C23×D411yescharacteristic
389C4×C11—24no—
390C4×C11—24no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11D4×Q812yes—
396C4×C11C23×Q811yescharacteristic
397C4×C11C2×2−1+411yescharacteristic
398Dic11—22no—
399Dic11—22no—
400Dic11—22no—
401Dic11—42no—
402Dic11—42no—
403Dic11—42no—
404Dic11—42no—
405Dic11C2×#13714yes—
406C22×Q8—111no—
407C22×Q8—221no—
408C22×Q8—221no—
409C22×Q8—221no—
410C22×Q8—221no—
411C22×Q8C22×D1111yescharacteristic
412C22×Q8C22×D1111yescharacteristic
413C2×Q16Dic2218yescomplemented
414C2×Q16C22×D1114yes—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C4⋊Q8—114no—
420C4⋊Q8—114no—
421C4⋊Q8—114no—
422C4⋊Q8—114no—
423C4⋊Q8—228no—
424C4⋊Q8—222no—
425C4⋊Q8—222no—
426C4⋊Q8—222no—
427C4⋊Q8—228no—
428C4⋊Q8—228no—
429C4⋊Q8—228no—
430C4⋊Q8—222no—
431#125—114no—
432#125—114no—
433#125—228no—
434#125—222no—
435#125—228no—
436#125—222no—
437C4×Q8—22no—
438C4×Q8—22no—
439C4×Q8—114no—
440C4×Q8—114no—
441C4×Q8—114no—
442C4×Q8—114no—
443C4×Q8—114no—
444C4×Q8—114no—
445C4×Q8—228no—
446C4×Q8—228no—
447C4×Q8—222no—
448C4×Q8—222no—
449C4×Q8—222no—
450C4×Q8—222no—
451C4×Q8C22×D1114yes—
452C4×Q8C22×D1114yes—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—111no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—221no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4C22×D1111yescharacteristic
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—111no—
479C2×C42—111no—
480C2×C42—221no—
481C2×C42—221no—
482C2×C42—221no—
483C2×C42—221no—
484C2×C42C22×D1111yescharacteristic
485#107—114no—
486#107—114no—
487#107—114no—
488#106—114no—
489#106—114no—
490#106—114no—
491#106—114no—
492#106—114no—
493#106C22×D1114yes—
494C4⋊C8—114no—
495C4⋊C8—114no—
496C4⋊C8—114no—
497#103—114no—
498#103—114no—
499#103—114no—
500#103—114no—
501#103C22×D1114yes—
502#103C22×D1114yes—
503#97—114no—
504#97C22×D1114yes—
505C4×C8—114no—
506C2×C11#338714yescomplemented
507C2×C11C2×D4×Q811yescharacteristic
508C2×C11C22×#13711yescharacteristic
509C2×C11C2×#57711yescharacteristic
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—114no—
515C2×Q8—224no—
516C2×Q8—224no—
517C2×Q8—224no—
518C2×Q8—224no—
519C2×Q8—224no—
520C2×Q8—444no—
521C2×Q8—882no—
522C2×Q8—882no—
523C2×Q8—882no—
524C2×Q8C2×Dic2214yes—
525C2×Q8C2×Dic2214yes—
526C2×Q8C23×D1112yes—
527C2×Q8C23×D1112yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—111no—
533C22×C4—111no—
534C22×C4—111no—
535C22×C4—111no—
536C22×C4—221no—
537C22×C4—221no—
538C22×C4—221no—
539C22×C4—221no—
540C22×C4D4×D1111yescharacteristic
541C22×C4D4×D1111yescharacteristic
542C22×C4C23×D1111yescharacteristic
543Q16C2×Dic22116yescomplemented
544C2×C8—22no—
545C2×C8—112no—
546C2×C8—112no—
547C2×C8—222no—
548C2×C8—222no—
549C2×C8C2×Dic2214yes—
550C2×C8C23×D1112yes—
551C2×C8C23×D1112yes—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—114no—
557C4⋊C4—114no—
558C4⋊C4—114no—
559C4⋊C4—112no—
560C4⋊C4—112no—
561C4⋊C4—112no—
562C4⋊C4—112no—
563C4⋊C4—224no—
564C4⋊C4—224no—
565C4⋊C4—224no—
566C4⋊C4—224no—
567C4⋊C4—224no—
568C4⋊C4—224no—
569C4⋊C4—224no—
570C4⋊C4—224no—
571C4⋊C4—224no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—221no—
575C4⋊C4—221no—
576C4⋊C4—224no—
577C4⋊C4—224no—
578C4⋊C4—224no—
579C4⋊C4C23×D1112yes—
580C4⋊C4C23×D1112yes—
581C42—24no—
582C42—24no—
583C42—112no—
584C42—112no—
585C42—112no—
586C42—112no—
587C42—224no—
588C42—224no—
589C42—224no—
590C42—224no—
591C42D4×D1112yes—
592C42C23×D1112yes—
593C11C2×#338711yescharacteristic, complemented, Sylow
594C23C2×D4×D1111yescharacteristic
595Q8—24no—
596Q8—24no—
597Q8—22no—
598Q8—22no—
599Q8—228no—
600Q8—448no—
601Q8—884no—
602Q8—884no—
603Q8—884no—
604Q8C22×Dic2214yes—
605Q8C22×Dic2214yes—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—114no—
617C2×C4—112no—
618C2×C4—112no—
619C2×C4—112no—
620C2×C4—112no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4C22×Dic2212yes—
633C2×C4C2×D4×D1112yes—
634C2×C4C2×D4×D1112yes—
635C2×C4C2×D4×D1111yescharacteristic
636C2×C4#6704312yes—
637C2×C4C24×D1111yescharacteristic
638C8—22no—
639C8—222no—
640C8—222no—
641C8C22×Dic2214yes—
642C22D4×Dic2212yes—
643C22D11×#13712yes—
644C22#1062330912yes—
645C22C22×D4×D1111yescharacteristic
646C4—22no—
647C4—24no—
648C4—24no—
649C4—22no—
650C4—42no—
651C4—42no—
652C4—114no—
653C4—222no—
654C4—222no—
655C4—222no—
656C4—442no—
657C4—442no—
658C4—442no—
659C4—442no—
660C4D4×Dic2212yes—
661C4C23×Dic2211yescharacteristic
662C4C2×#6704311yescharacteristic
663C2#1308154914yesdirect product factor
664C2C2×D4×Dic2211yescharacteristic
665C2C2×D11×#13711yescharacteristic
666C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#441C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#441D11
hypocenterC11C2×#3387
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #13081549C2direct (N × H)
84. C2×C11×Q16Q8semidirect
211. C11×Q16C2×Q8semidirect
413. C2×Q16Dic22semidirect
506. C2×C11#3387semidirect
543. Q16C2×Dic22semidirect
593. C11C2×#3387semidirect
663. C2#13081549direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic222
C2×#106231002
#130815492
C2×#106223152
C2×#106224692
C2×#106224682
C2×#106224092
C2×#106226352
C2×#106224072
C2×#106226332
C2×#106224042
C2×#106223142
C2×#106227972
C2×Q16×Dic112
C2×C11×#4412
C2×#338711