Finite Group Databasebeta

← C2×#13081414 #15633479

Subgroups — C2×#13081414 #15633479

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×#10623100C211yesmaximal, characteristic
2C2×#10623252C211yesmaximal, characteristic
3#13081414C2116yesmaximal, direct product factor
4C2×#10622695C211yesmaximal, characteristic
5C2×#10622410C211yesmaximal, characteristic
6C2×#10622405C211yesmaximal, characteristic
7C2×#10622409C211yesmaximal, characteristic
8C2×#10622442C211yesmaximal, characteristic
9C2×#10622404C211yesmaximal, characteristic
10C2×#10622795C211yesmaximal, characteristic
11C2×#10622795C211yesmaximal, characteristic
12C2×#10622441C211yesmaximal, characteristic
13C2×#10622797C211yesmaximal, characteristic
14C2×#10622643C211yesmaximal, characteristic
15C2×Q16×Dic11C211yesmaximal, characteristic
16C2×C11×#462C211yesmaximal, characteristic
17C22×C11×Q16C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C2×#66997C2211yescharacteristic
27C22×#4326C2211yescharacteristic
28#10623252—24no—
29#10623252C2218yes—
30#10623100—24no—
31#10623100C2218yes—
32C2×#66943—21no—
33C2×#66943—21no—
34C2×#66943C2211yescharacteristic
35C2×#66942—21no—
36C2×#66942—21no—
37C2×#66941—21no—
38C2×#66941C2211yescharacteristic
39C2×#66940—21no—
40C2×#66923—21no—
41C2×#66923C2211yescharacteristic
42C2×C4×Dic22—21no—
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#462C2218yes—
46C2×C11×C4⋊C8C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54#10622797C2218yes—
55Q16×Dic11C2218yes—
56#10622795C2218yes—
57#10622795C2218yes—
58C2×#66882C2211yescharacteristic
59C2×#66881C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622695C2218yes—
67#10622643C2218yes—
68C2×#66874C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66867C2211yescharacteristic
71#10622442C2218yes—
72#10622441C2218yes—
73#10622410C2218yes—
74#10622409C2218yes—
75#10622405C2218yes—
76#10622404C2218yes—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×Dic22—21no—
81C22×Dic22D411yescharacteristic
82C22×Dic22C2311yescharacteristic
83C2×C11×Q16—24no—
84C2×C11×Q16—24no—
85C2×C11×Q16C2314yes—
86C2×C11×Q16C2314yes—
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×C4⋊Q8—22no—
90C11×C4⋊Q8C2314yes—
91C4×Q8×C11—22no—
92C4×Q8×C11C2314yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
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—
107#66997—22no—
108#66997—22no—
109#66997C2314yes—
110#66997C2314yes—
111C2×#4326—24no—
112C2×#4326C2314yes—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11D411yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4D411yescharacteristic
132C2×Dic11⋊C4D411yescharacteristic
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142#66943—28no—
143#66943—28no—
144#66943—22no—
145#66943C2314yes—
146#66942—28no—
147#66942—28no—
148#66941—28no—
149#66941—22no—
150#66941C2314yes—
151#66940—28no—
152#66923—22no—
153#66923—28no—
154#66923C2314yes—
155C4×Dic22—22no—
156C4×Dic22—28no—
157C4×Dic22D414yes—
158C4×Dic22C2314yes—
159C4×Dic22C2314yes—
160C11×C4⋊C8C2314yes—
161C11×#103C2314yes—
162C11×#103C2314yes—
163#66899C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66899C2314yes—
167#66899C2314yes—
168#66882C2314yes—
169#66881C2314yes—
170#66880C2314yes—
171#66880C2314yes—
172#66879C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175C8×Dic11C2314yes—
176#66874C2314yes—
177#66872C2314yes—
178#66867C2314yes—
179C2×#3374—111nomaximal, Sylow
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—22no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11#4114yes—
189C2×Q8×C11C2412yes—
190C2×Q8×C11C2412yes—
191C2×Q8×C11C2412yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C2×Dic22—24no—
208C2×Dic22—24no—
209C2×Dic22—21no—
210C2×Dic22—22no—
211C2×Dic22—22no—
212C2×Dic22—44no—
213C2×Dic22C2×D414yes—
214C2×Dic22C2412yes—
215C11×Q16—28no—
216C11×Q16—28no—
217C2×C8×C11—22no—
218C2×C8×C11—22no—
219C2×C8×C11C2412yes—
220C2×C8×C11C2412yes—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4C2412yes—
226C42×C11—24no—
227C42×C11C2×D412yes—
228C42×C11C2412yes—
229#4326—28no—
230C4⋊Dic11—24no—
231C4⋊Dic11—24no—
232C4⋊Dic11—24no—
233C4⋊Dic11—24no—
234C4⋊Dic11—24no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11C2×D414yes—
239C4⋊Dic11C2412yes—
240C4⋊Dic11C2412yes—
241C4⋊Dic11C2412yes—
242Dic11⋊C4—24no—
243Dic11⋊C4—24no—
244Dic11⋊C4—24no—
245Dic11⋊C4—24no—
246Dic11⋊C4—24no—
247Dic11⋊C4—24no—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250Dic11⋊C4—24no—
251Dic11⋊C4C2×D414yes—
252Dic11⋊C4C2×D414yes—
253C4×Dic11—24no—
254C4×Dic11—24no—
255C4×Dic11—24no—
256C4×Dic11—24no—
257C4×Dic11—24no—
258C4×Dic11C2×D412yes—
259C4×Dic11C2×D412yes—
260C4×Dic11C2412yes—
261C4×Dic11C2412yes—
262C2×C11⋊C8—22no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8C2412yes—
265C2×C11⋊C8C2412yes—
266C2×#557—111no—
267C2×#557—111no—
268#3374—1116no—
269C2×#491—111no—
270C2×#491—111no—
271C2×#487—111no—
272C2×#479—111no—
273C2×#479—111no—
274C2×#475—111no—
275C2×#462—111no—
276C2×#462—111no—
277C2×#462D1111yescharacteristic
278C2×#446—111no—
279C2×#441—111no—
280C2×#441—111no—
281C2×C4×Q16—111no—
282C23×C11C22×D411yescharacteristic
283Q8×C11—24no—
284Q8×C11—22no—
285Q8×C11—22no—
286Q8×C11—22no—
287Q8×C11—22no—
288Q8×C11—22no—
289Q8×C11—42no—
290Q8×C11—42no—
291Q8×C11C2×#4114yes—
292C2×C4×C11—24no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11C22×D412yes—
303C2×C4×C11C22×D412yes—
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C2×#4112yes—
306C2×C4×C112−1+412yes—
307C2×C4×C11C2511yescharacteristic
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11#13714yes—
320C2×Dic11C22×D412yes—
321C2×Dic11C22×D412yes—
322C2×Dic11C22×D412yes—
323C2×Dic11C22×D412yes—
324Dic22—28no—
325Dic22—22no—
326Dic22—22no—
327Dic22—42no—
328Dic22—48no—
329C8×C11—22no—
330C8×C11—22no—
331C11⋊C8—22no—
332C11⋊C8—22no—
333C22×Q16—111no—
334C22×Q16C2×D1111yescharacteristic
335C22×Q16C2×D1111yescharacteristic
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—111no—
347C2×#125—221no—
348C2×#125—221no—
349C2×#125—221no—
350C2×#125—221no—
351C2×#125—221no—
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—221no—
359C2×C4×Q8—221no—
360C2×C4×Q8C2×D1111yescharacteristic
361#491—118no—
362#491—118no—
363#487—118no—
364#479—118no—
365#479—118no—
366#475—118no—
367#462—118no—
368#462—118no—
369#462C2×D1118yes—
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⋊C8C2×D1111yescharacteristic
380C2×#103—111no—
381C2×#103—111no—
382C2×#103—111no—
383C2×#103—111no—
384C2×#103—111no—
385C2×#103—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#103C2×D1111yescharacteristic
389C2×#103C2×D1111yescharacteristic
390C2×#97—111no—
391C2×#97—111no—
392C2×C4×C8—111no—
393C22×C11#54812yes—
394C22×C11C2×#13712yes—
395C22×C11#57812yes—
396C22×C11C23×D411yescharacteristic
397C4×C11—24no—
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—42no—
401C4×C11—42no—
402C4×C11—42no—
403C4×C11#54812yes—
404C4×C11C22×#4111yescharacteristic
405C4×C11C2×2−1+411yescharacteristic
406Dic11—22no—
407Dic11—22no—
408Dic11—22no—
409Dic11—42no—
410Dic11—42no—
411Dic11—42no—
412Dic11—42no—
413Dic11C2×#13714yes—
414C22×Q8—111no—
415C22×Q8—111no—
416C22×Q8—221no—
417C22×Q8C22×D1111yescharacteristic
418C22×Q8C22×D1111yescharacteristic
419C22×Q8C22×D1111yescharacteristic
420C2×Q16—24no—
421C2×Q16—24no—
422C2×Q16—114no—
423C2×Q16—224no—
424C2×Q16C22×D1114yes—
425C2×Q16C22×D1114yes—
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—114no—
440#125—114no—
441#125—228no—
442#125—222no—
443#125—228no—
444#125—228no—
445#125—228no—
446#125—228no—
447#125—222no—
448C4×Q8—22no—
449C4×Q8—114no—
450C4×Q8—114no—
451C4×Q8—114no—
452C4×Q8—114no—
453C4×Q8—114no—
454C4×Q8—114no—
455C4×Q8—114no—
456C4×Q8—228no—
457C4×Q8—222no—
458C4×Q8—222no—
459C4×Q8—222no—
460C4×Q8—222no—
461C4×Q8—228no—
462C4×Q8—222no—
463C4×Q8C22×D1114yes—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—111no—
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⋊C4—221no—
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C42—21no—
489C2×C42—111no—
490C2×C42—111no—
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⋊C8C22×D1114yes—
503#103—114no—
504#103—114no—
505#103—114no—
506#103—114no—
507#103—114no—
508#103—114no—
509#103—114no—
510#103—114no—
511#103C22×D1114yes—
512#103C22×D1114yes—
513#97—114no—
514#97—114no—
515C4×C8—114no—
516C2×C11#337414yescomplemented
517C2×C11C2×#54811yescharacteristic
518C2×C11C22×#13711yescharacteristic
519C2×C11C2×#57811yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—114no—
529C2×Q8—112no—
530C2×Q8—224no—
531C2×Q8—224no—
532C2×Q8—221no—
533C2×Q8—222no—
534C2×Q8—222no—
535C2×Q8—444no—
536C2×Q8#434114yes—
537C2×Q8C23×D1112yes—
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—28no—
556Q16—28no—
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—21no—
570C4⋊C4—114no—
571C4⋊C4—114no—
572C4⋊C4—114no—
573C4⋊C4—112no—
574C4⋊C4—112no—
575C4⋊C4—112no—
576C4⋊C4—224no—
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—221no—
588C4⋊C4—221no—
589C4⋊C4—221no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4—224no—
593C4⋊C4C23×D1112yes—
594C42—24no—
595C42—112no—
596C42—112no—
597C42—112no—
598C42—112no—
599C42—224no—
600C42—224no—
601C42—224no—
602C42—224no—
603C42—224no—
604C42D4×D1112yes—
605C42C23×D1112yes—
606C11C2×#337411yescharacteristic, complemented, Sylow
607C23C2×D4×D1111yescharacteristic
608Q8—24no—
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—42no—
615Q8—42no—
616Q8—228no—
617Q8—222no—
618Q8—222no—
619Q8—448no—
620Q8—442no—
621Q8C2×#434114yes—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
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—222no—
642C2×C4—222no—
643C2×C4—222no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4C2×D4×D1112yes—
649C2×C4C2×D4×D1112yes—
650C2×C4C2×D4×D1111yescharacteristic
651C2×C4C2×#434112yes—
652C2×C4#6704312yes—
653C2×C4C24×D1111yescharacteristic
654C8—22no—
655C8—22no—
656C8—222no—
657C8—222no—
658C22#1062312912yes—
659C22#1062329712yes—
660C22D11×#13712yes—
661C22C22×D4×D1111yescharacteristic
662C4—22no—
663C4—24no—
664C4—22no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—114no—
669C4—222no—
670C4—222no—
671C4—222no—
672C4—442no—
673C4—442no—
674C4—442no—
675C4—442no—
676C4#1062312912yes—
677C4C22×#434111yescharacteristic
678C4C2×#6704311yescharacteristic
679C2#1308141414yesdirect product factor
680C2C2×#1062312911yescharacteristic
681C2C2×D11×#13711yescharacteristic
682C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#462D11
hypocenterC11C2×#3374
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #13081414C2direct (N × H)
516. C2×C11#3374semidirect
606. C11C2×#3374semidirect
679. C2#13081414direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231002
C2×#106232522
#130814142
C2×#106226952
C2×#106224102
C2×#106224052
C2×#106224092
C2×#106224422
C2×#106224042
C2×#106227952
C2×#106224412
C2×#106227972
C2×#106226432
C2×Q16×Dic112
C2×C11×#4622
C2×#337411