Finite Group Databasebeta

← C2×#13081416 #15633481

Subgroups — C2×#13081416 #15633481

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623216C211yesmaximal, characteristic
2C2×#10623252C211yesmaximal, characteristic
3#13081416C2116yesmaximal, direct product factor
4C2×#10622410C211yesmaximal, characteristic
5C2×#10622405C211yesmaximal, characteristic
6C2×#10622412C211yesmaximal, characteristic
7C2×#10622676C211yesmaximal, characteristic
8C2×#10622404C211yesmaximal, characteristic
9C2×#10622406C211yesmaximal, characteristic
10C2×#10622406C211yesmaximal, characteristic
11C2×#10622703C211yesmaximal, characteristic
12C2×#10622314C211yesmaximal, characteristic
13C2×#10622329C211yesmaximal, characteristic
14C2×#10622402C211yesmaximal, characteristic
15C2×#10622403C211yesmaximal, characteristic
16C2×C11×#491C211yesmaximal, characteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22C2×#66997C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C22×Dic44C2211yescharacteristic
26#10623252—24no—
27#10623252C2218yes—
28#10623216—24no—
29#10623216C2218yes—
30C2×#66943—21no—
31C2×#66943C2211yescharacteristic
32C2×#66942—21no—
33C2×#66942—21no—
34C2×#66942—21no—
35C2×#66942—21no—
36C2×#66941—21no—
37C2×#66941C2211yescharacteristic
38C2×#66940—21no—
39C2×#66940—21no—
40C2×#66940C2211yescharacteristic
41C2×#66940C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#491C2218yes—
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66881C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×#66879C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic
59C2×C8×Dic11C2211yescharacteristic
60#10622703C2218yes—
61#10622676C2218yes—
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622412C2218yes—
68#10622410C2218yes—
69#10622406C2218yes—
70#10622406C2218yes—
71#10622405C2218yes—
72#10622404C2218yes—
73#10622403C2218yes—
74#10622402C2218yes—
75#10622329C2218yes—
76#10622314C2218yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Dic22—21no—
80C22×Dic22D411yescharacteristic
81C22×Dic22C2311yescharacteristic
82C22×Dic22C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×C4⋊Q8—22no—
86C11×C4⋊Q8C2314yes—
87C11×#125—22no—
88C11×#125C2314yes—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96Q8×Dic11—22no—
97Q8×Dic11—22no—
98Q8×Dic11C2314yes—
99Q8×Dic11C2314yes—
100#66997—22no—
101#66997—22no—
102#66997C2314yes—
103#66997C2314yes—
104C2×#4326—24no—
105C2×#4326—24no—
106C2×#4326C2314yes—
107C2×#4326C2314yes—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11D411yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
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×Dic11—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×Dic44—24no—
137C2×Dic44C2314yes—
138#66943—28no—
139#66943—22no—
140#66943C2314yes—
141#66942—28no—
142#66942—28no—
143#66942—28no—
144#66942—28no—
145#66941—28no—
146#66941—22no—
147#66941C2314yes—
148#66940—28no—
149#66940—28no—
150#66940—22no—
151#66940—22no—
152#66940C2314yes—
153#66940C2314yes—
154C4×Dic22—22no—
155C4×Dic22—22no—
156C4×Dic22D414yes—
157C4×Dic22C2314yes—
158C4×Dic22C2314yes—
159C4×Dic22C2314yes—
160C11×#103C2314yes—
161C11×#103C2314yes—
162C11×#103C2314yes—
163C11×#103C2314yes—
164C11×#97C2314yes—
165#66899C2314yes—
166#66899C2314yes—
167#66881C2314yes—
168#66880C2314yes—
169#66880C2314yes—
170#66879C2314yes—
171Dic11⋊C8C2314yes—
172Dic11⋊C8C2314yes—
173C8×Dic11C2314yes—
174#66874C2314yes—
175#66874C2314yes—
176#66872C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C2×#3374—111nomaximal, Sylow
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—22no—
183C2×Q8×C11—22no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11C2412yes—
187C2×Q8×C11C2412yes—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201C22×Dic11C2×D411yescharacteristic
202C22×Dic11C2×D411yescharacteristic
203C2×Dic22—24no—
204C2×Dic22—24no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—22no—
208C2×Dic22—22no—
209C2×Dic22—22no—
210C2×Dic22—44no—
211C2×Dic22C2×D414yes—
212C2×Dic22#4114yes—
213C2×Dic22C2412yes—
214C2×Dic22C2412yes—
215C2×C8×C11—22no—
216C2×C8×C11—22no—
217C2×C8×C11C2412yes—
218C2×C8×C11C2412yes—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4C2412yes—
226C11×C4⋊C4C2412yes—
227C42×C11C2×D412yes—
228C42×C11C2412yes—
229#4326—28no—
230#4326—28no—
231C4⋊Dic11—24no—
232C4⋊Dic11—24no—
233C4⋊Dic11—24no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11C2×D414yes—
237C4⋊Dic11C2412yes—
238C4⋊Dic11C2412yes—
239Dic11⋊C4—24no—
240Dic11⋊C4—24no—
241Dic11⋊C4—24no—
242Dic11⋊C4—24no—
243Dic11⋊C4—24no—
244Dic11⋊C4—24no—
245Dic11⋊C4—24no—
246Dic11⋊C4—24no—
247Dic11⋊C4—24no—
248Dic11⋊C4—24no—
249Dic11⋊C4C2×D414yes—
250Dic11⋊C4C2×D414yes—
251C4×Dic11—24no—
252C4×Dic11—24no—
253C4×Dic11—24no—
254C4×Dic11—24no—
255C4×Dic11—24no—
256C4×Dic11—24no—
257C4×Dic11C2×D412yes—
258C4×Dic11C2×D412yes—
259C4×Dic11C2412yes—
260C4×Dic11C2412yes—
261C2×C11⋊C8—22no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8C2412yes—
264C2×C11⋊C8C2412yes—
265Dic44—28no—
266C2×#557—111no—
267C2×#557—111no—
268#3374—1116no—
269C2×#491—111no—
270C2×#491D1111yescharacteristic
271C2×#487—111no—
272C2×#479—111no—
273C2×#479—111no—
274C2×#475—111no—
275C2×#462—111no—
276C2×#462—111no—
277C2×#462—111no—
278C2×#446—111no—
279C2×#441—111no—
280C2×#441—111no—
281C2×C4×Q16—111no—
282C23×C11C22×D411yescharacteristic
283Q8×C11—22no—
284Q8×C11—22no—
285Q8×C11—22no—
286Q8×C11—22no—
287Q8×C11—42no—
288Q8×C11—42no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11C22×D412yes—
300C2×C4×C11C22×D412yes—
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4112yes—
303C2×C4×C112−1+412yes—
304C2×C4×C11C2511yescharacteristic
305C2×Dic11—24no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—42no—
314C2×Dic11—42no—
315C2×Dic11—42no—
316C2×Dic11#13714yes—
317C2×Dic11C22×D412yes—
318C2×Dic11C22×D412yes—
319C2×Dic11C22×D412yes—
320C2×Dic11C22×D412yes—
321Dic22—24no—
322Dic22—22no—
323Dic22—28no—
324Dic22—22no—
325Dic22—22no—
326Dic22—42no—
327Dic22—48no—
328Dic22C2×#4114yes—
329C8×C11—22no—
330C8×C11—22no—
331C11⋊C8—22no—
332C11⋊C8—22no—
333C22×Q16—111no—
334C22×Q16—111no—
335C22×Q16—111no—
336#557—118no—
337#557—118no—
338#557—224no—
339#557—224no—
340C2×C4⋊Q8—111no—
341C2×C4⋊Q8—111no—
342C2×C4⋊Q8—111no—
343C2×C4⋊Q8—221no—
344C2×C4⋊Q8C2×D1111yescharacteristic
345C2×#125—111no—
346C2×#125—221no—
347C2×#125—221no—
348C2×#125—221no—
349C2×#125—221no—
350C2×#125—221no—
351C2×#125C2×D1111yescharacteristic
352C2×C4×Q8—111no—
353C2×C4×Q8—111no—
354C2×C4×Q8—111no—
355C2×C4×Q8—111no—
356C2×C4×Q8—111no—
357C2×C4×Q8—111no—
358C2×C4×Q8—111no—
359C2×C4×Q8—221no—
360C2×C4×Q8—221no—
361#491—118no—
362#491C2×D1118yes—
363#487—118no—
364#479—118no—
365#479—118no—
366#475—118no—
367#462—118no—
368#462—118no—
369#462—118no—
370#446—118no—
371#441—118no—
372#441—118no—
373C4×Q16—118no—
374C2×#107—111no—
375C2×#106—111no—
376C2×#106—111no—
377C2×C4⋊C8—111no—
378C2×C4⋊C8—111no—
379C2×C4⋊C8—111no—
380C2×#103—111no—
381C2×#103—111no—
382C2×#103—111no—
383C2×#103—111no—
384C2×#103—111no—
385C2×#103—111no—
386C2×#103C2×D1111yescharacteristic
387C2×#103C2×D1111yescharacteristic
388C2×#103C2×D1111yescharacteristic
389C2×#103C2×D1111yescharacteristic
390C2×#97—111no—
391C2×#97C2×D1111yescharacteristic
392C2×C4×C8—111no—
393C22×C11#54812yes—
394C22×C11C2×#13712yes—
395C22×C11#57812yes—
396C22×C11C23×D411yescharacteristic
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—42no—
400C4×C11—42no—
401C4×C11—42no—
402C4×C11—42no—
403C4×C11#54812yes—
404C4×C11C22×#4111yescharacteristic
405C4×C11C2×2−1+411yescharacteristic
406Dic11—24no—
407Dic11—22no—
408Dic11—22no—
409Dic11—22no—
410Dic11—42no—
411Dic11—42no—
412Dic11—42no—
413Dic11C2×#13714yes—
414C22×Q8—111no—
415C22×Q8—111no—
416C22×Q8—111no—
417C22×Q8—221no—
418C22×Q8C22×D1111yescharacteristic
419C22×Q8C22×D1111yescharacteristic
420C2×Q16—114no—
421C2×Q16—114no—
422C2×Q16—114no—
423C2×Q16—224no—
424C2×Q16—224no—
425C2×Q16—224no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8C22×D1111yescharacteristic
429C22×C8C22×D1111yescharacteristic
430C4⋊Q8—22no—
431C4⋊Q8—114no—
432C4⋊Q8—114no—
433C4⋊Q8—114no—
434C4⋊Q8—222no—
435C4⋊Q8—222no—
436C4⋊Q8—222no—
437C4⋊Q8—228no—
438C4⋊Q8C22×D1114yes—
439#125—22no—
440#125—114no—
441#125—222no—
442#125—228no—
443#125—228no—
444#125—228no—
445#125—228no—
446#125—228no—
447#125C22×D1114yes—
448C4×Q8—114no—
449C4×Q8—114no—
450C4×Q8—114no—
451C4×Q8—114no—
452C4×Q8—114no—
453C4×Q8—114no—
454C4×Q8—114no—
455C4×Q8—114no—
456C4×Q8—222no—
457C4×Q8—222no—
458C4×Q8—222no—
459C4×Q8—222no—
460C4×Q8—228no—
461C4×Q8—228no—
462C4×Q8—222no—
463C4×Q8—222no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C42—111no—
489C2×C42—111no—
490C2×C42—221no—
491C2×C42—221no—
492C2×C42—221no—
493C2×C42—221no—
494C2×C42—221no—
495C2×C42—221no—
496C2×C42C22×D1111yescharacteristic
497#107—114no—
498#106—114no—
499#106—114no—
500C4⋊C8—114no—
501C4⋊C8—114no—
502C4⋊C8—114no—
503#103—114no—
504#103—114no—
505#103—114no—
506#103—114no—
507#103—114no—
508#103—114no—
509#103C22×D1114yes—
510#103C22×D1114yes—
511#103C22×D1114yes—
512#103C22×D1114yes—
513#97—114no—
514#97C22×D1114yes—
515C4×C8—114no—
516C2×C11#337414yescomplemented
517C2×C11C2×#54811yescharacteristic
518C2×C11C22×#13711yescharacteristic
519C2×C11C2×#57811yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—114no—
527C2×Q8—114no—
528C2×Q8—112no—
529C2×Q8—112no—
530C2×Q8—224no—
531C2×Q8—224no—
532C2×Q8—221no—
533C2×Q8—221no—
534C2×Q8—222no—
535C2×Q8—222no—
536C2×Q8—222no—
537C2×Q8—444no—
538C2×Q8C23×D1112yes—
539C2×Q8C23×D1112yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—111no—
545C22×C4—111no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4D4×D1111yescharacteristic
553C22×C4D4×D1111yescharacteristic
554C22×C4C23×D1111yescharacteristic
555Q16—228no—
556Q16—228no—
557Q16—228no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—112no—
561C2×C8—112no—
562C2×C8—222no—
563C2×C8—222no—
564C2×C8C23×D1112yes—
565C2×C8C23×D1112yes—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—114no—
573C4⋊C4—114no—
574C4⋊C4—114no—
575C4⋊C4—112no—
576C4⋊C4—112no—
577C4⋊C4—224no—
578C4⋊C4—224no—
579C4⋊C4—224no—
580C4⋊C4—224no—
581C4⋊C4—224no—
582C4⋊C4—224no—
583C4⋊C4—224no—
584C4⋊C4—224no—
585C4⋊C4—224no—
586C4⋊C4—224no—
587C4⋊C4—224no—
588C4⋊C4—221no—
589C4⋊C4—221no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4C23×D1112yes—
593C4⋊C4C23×D1112yes—
594C42—112no—
595C42—112no—
596C42—112no—
597C42—112no—
598C42—224no—
599C42—224no—
600C42—224no—
601C42—224no—
602C42—224no—
603C42—224no—
604C42D4×D1112yes—
605C42C23×D1112yes—
606C11C2×#337411yescharacteristic, complemented, Sylow
607C23C2×D4×D1111yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—42no—
613Q8—42no—
614Q8—114no—
615Q8—228no—
616Q8—222no—
617Q8—224no—
618Q8—222no—
619Q8—222no—
620Q8—448no—
621Q8—442no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—114no—
633C2×C4—112no—
634C2×C4—112no—
635C2×C4—112no—
636C2×C4—112no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—224no—
642C2×C4—222no—
643C2×C4—222no—
644C2×C4—222no—
645C2×C4—442no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4C2×D4×D1112yes—
649C2×C4C2×D4×D1112yes—
650C2×C4C2×D4×D1111yescharacteristic
651C2×C4#41×D1112yes—
652C2×C4#6704312yes—
653C2×C4C24×D1111yescharacteristic
654C8—22no—
655C8—22no—
656C8—222no—
657C8—222no—
658C22#1062320812yes—
659C22D11×#13712yes—
660C22#1062331012yes—
661C22C22×D4×D1111yescharacteristic
662C4—22no—
663C4—22no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—114no—
669C4—222no—
670C4—224no—
671C4—222no—
672C4—222no—
673C4—442no—
674C4—442no—
675C4—442no—
676C4#1062320812yes—
677C4C2×#41×D1111yescharacteristic
678C4C2×#6704311yescharacteristic
679C2#1308141614yesdirect product factor
680C2C2×#1062320811yescharacteristic
681C2C2×D11×#13711yescharacteristic
682C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#491C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#491D11
hypocenterC11C2×#3374
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
3. #13081416C2direct (N × H)
516. C2×C11#3374semidirect
606. C11C2×#3374semidirect
679. C2#13081416direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232162
C2×#106232522
#130814162
C2×#106224102
C2×#106224052
C2×#106224122
C2×#106226762
C2×#106224042
C2×#106224062
C2×#106227032
C2×#106223142
C2×#106223292
C2×#106224022
C2×#106224032
C2×C11×#4912
C2×#337411