Finite Group Databasebeta

← C2×#13079863 #15625956

Subgroups — C2×#13079863 #15625956

Order 2816.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2#13079863C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622677C211yesmaximal, characteristic, complemented
5C2×#10622684C211yesmaximal, characteristic, complemented
6C2×#10622683C211yesmaximal, characteristic, complemented
7C2×#10622647C211yesmaximal, characteristic, complemented
8C2×#10622648C211yesmaximal, characteristic, complemented
9C2×#10622648C211yesmaximal, characteristic, complemented
10C2×#10622646C211yesmaximal, characteristic, complemented
11C2×#10622622C211yesmaximal, characteristic, complemented
12C2×#10622622C211yesmaximal, characteristic, complemented
13C2×#10622621C211yesmaximal, characteristic, complemented
14C2×#10622620C211yesmaximal, characteristic, complemented
15C2×#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#540C211yesmaximal, characteristic
17C11×#540—24no—
18C11×#540C2218yes—
19C2×C11×#127C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#123—21no—
23C2×C11×#121—21no—
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32#10623050—24no—
33#10623050C2218yescomplemented
34C2×#66943—21no—
35C2×#66941—21no—
36C2×#66931—21no—
37C2×#66931—21no—
38C2×#66923C2211yescharacteristic
39C2×#66923C2211yescharacteristic
40C2×#66922C2211yescharacteristic
41C2×#66922C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52#10622684C2218yescomplemented
53#10622683C2218yescomplemented
54#10622678C2218yescomplemented
55#10622677C2218yescomplemented
56#10622648C2218yescomplemented
57#10622648C2218yescomplemented
58#10622647C2218yescomplemented
59#10622646C2218yescomplemented
60#10622622C2218yescomplemented
61#10622622C2218yescomplemented
62#10622621C2218yescomplemented
63#10622620C2218yescomplemented
64#10622613C2218yescomplemented
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C23×Dic11—21no—
87C22×Dic22—21no—
88C22×Dic22—21no—
89C11×#127—22no—
90C11×#127C2314yes—
91C11×#125—22no—
92C11×#125C2314yes—
93C11×#123—28no—
94C11×#123—28no—
95C11×#121—22no—
96C11×#121—22no—
97C11×#121—28no—
98C11×#121—28no—
99C11×#121C2314yes—
100C11×#121C2314yes—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11C2314yes—
104C4×D4×C11C2314yes—
105C11×#117D414yes—
106C11×#117C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C22⋊Dic11—21no—
122#66979—22no—
123#66979C2314yes—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2314yes—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×C4×Dic11—21no—
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142#66943—28no—
143#66941—28no—
144#66931—28no—
145#66931—28no—
146#66923—22no—
147#66923—22no—
148#66923C2314yes—
149#66923C2314yes—
150#66922—22no—
151#66922—22no—
152#66922C2314yes—
153#66922C2314yes—
154#66896C2314yes—
155#66896C2314yes—
156#66896C2314yes—
157#66896C2314yes—
158#66896C2314yes—
159#66896C2314yes—
160#66896C2314yes—
161#66896C2314yes—
162C22⋊(C11⋊C8)C2314yes—
163C22⋊(C11⋊C8)C2314yes—
164#66872C2314yes—
165#66872C2314yes—
166#66872C2314yes—
167#66872C2314yes—
168#66871C2314yes—
169#66871C2314yes—
170#66871C2314yes—
171#66871C2314yes—
172C4⋊(C11⋊C8)C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174#66867C2314yes—
175C4×C11⋊C8C2314yes—
176C2×#3241—111nomaximal, Sylow
177C24×C11—21no—
178C24×C11—21no—
179C24×C11C2×D411yescharacteristic
180C2×D4×C11—24no—
181C2×D4×C11—24no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—24no—
185C2×D4×C11—24no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—82no—
191C2×D4×C11—82no—
192C2×D4×C11—82no—
193C2×D4×C11—82no—
194C2×D4×C11C2412yes—
195C2×D4×C11C2412yes—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—82no—
203C22×C4×C11—82no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2411yescharacteristic
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—24no—
217C22×Dic11—82no—
218C2×Dic22—24no—
219C2×Dic22—24no—
220C2×Dic22—82no—
221C2×Dic22—82no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4C2×D414yes—
227C11×C4⋊C4C2×D414yes—
228C11×C4⋊C4C2412yes—
229C11×C4⋊C4C2412yes—
230C11×C22⋊C4—24no—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4C2×D414yes—
235C11×C22⋊C4C2×D414yes—
236C42×C11C2×D412yes—
237C42×C11C2×D412yes—
238C42×C11C2412yes—
239C42×C11C2412yes—
240C22⋊Dic11—24no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—24no—
245C4⋊Dic11—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11—24no—
248C4⋊Dic11C2412yes—
249C4⋊Dic11C2412yes—
250C4⋊Dic11C2412yes—
251C4⋊Dic11C2412yes—
252Dic11⋊C4—24no—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256C4×Dic11—24no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—22no—
259C2×C11⋊C8—22no—
260C2×C11⋊C8—22no—
261C2×C11⋊C8C2412yes—
262C2×C11⋊C8C2412yes—
263C2×C11⋊C8C2412yes—
264C2×C11⋊C8C2412yes—
265C2×#544—111no—
266C2×#540D1111yescharacteristic
267#3241—1116no—
268C2×#501—111no—
269C2×#499—111no—
270C2×#490—111no—
271C2×#486—111no—
272C2×#481—111no—
273C2×#482—111no—
274C2×#482—111no—
275C2×#480—111no—
276C2×#478—111no—
277C2×#478—111no—
278C2×#476—111no—
279C2×#474—111no—
280C2×#433—111no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—42no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11—42no—
290C23×C11—42no—
291C23×C11—42no—
292C23×C11C22×D412yes—
293C23×C11C22×D411yescharacteristic
294D4×C11—22no—
295D4×C11—22no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—42no—
299D4×C11—42no—
300D4×C11—84no—
301D4×C11—84no—
302D4×C11—84no—
303D4×C11—84no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—84no—
317C2×C4×C11—84no—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C112−1+412yes—
325C2×C4×C112−1+412yes—
326C2×C4×C11C2511yescharacteristic
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—84no—
336Dic22—84no—
337Dic22—84no—
338C11⋊C8—22no—
339C11⋊C8—22no—
340C11⋊C8—22no—
341C11⋊C8—22no—
342#544—118no—
343#544—224no—
344#540—24no—
345#540C2×D1118yes—
346C2×C4⋊Q8—111no—
347C2×C4⋊Q8—111no—
348C2×C4⋊Q8—221no—
349C2×#127C2×D1111yescharacteristic
350C2×#125—111no—
351C2×#125—111no—
352C2×#125—221no—
353C2×#125C2×D1111yescharacteristic
354C2×#123—21no—
355C2×#123—21no—
356C2×C22⋊Q8—221no—
357C2×C22⋊Q8—221no—
358C2×#121—21no—
359C2×#121—21no—
360C2×#121C2×D1111yescharacteristic
361C2×#121C2×D1111yescharacteristic
362C2×C4×D4C2×D1111yescharacteristic
363C2×C4×D4C2×D1111yescharacteristic
364C2×#117—111no—
365C2×#117C2×D1111yescharacteristic
366C22×C4⋊C4—111no—
367#501—118no—
368#499—118no—
369#490—118no—
370#486—118no—
371#482—118no—
372#482—118no—
373#481—118no—
374#480—118no—
375#478—118no—
376#478—118no—
377#476—118no—
378#474—118no—
379#433—118no—
380C2×#107—111no—
381C2×#107—111no—
382C2×#107—111no—
383C2×#107—111no—
384C2×#106—111no—
385C2×#106—111no—
386C2×#106—111no—
387C2×#106—111no—
388C2×C4⋊C8—111no—
389C2×C4⋊C8—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×#102—111no—
397C2×#102—111no—
398C2×C22⋊C8—111no—
399C2×C22⋊C8—111no—
400C2×#97—111no—
401C2×C4×C8—111no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—44no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—84no—
413C22×C11—84no—
414C22×C11#53612yes—
415C22×C11#57612yes—
416C22×C11#57712yes—
417C22×C11C23×D411yescharacteristic
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—22no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11#53612yes—
426C4×C11C2×2−1+411yescharacteristic
427C4×C11C2×2−1+411yescharacteristic
428Dic11—42no—
429Dic11—42no—
430Dic11—42no—
431Dic11—42no—
432C22×Q8—221no—
433C22×Q8—221no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C22×D1111yescharacteristic
439C22×D4C22×D1111yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—221no—
443C23×C4C22×D1111yescharacteristic
444C22×C8—111no—
445C22×C8—111no—
446C22×C8—111no—
447C22×C8—111no—
448C4⋊Q8—114no—
449C4⋊Q8—114no—
450C4⋊Q8—228no—
451C4⋊Q8—222no—
452C4⋊Q8—222no—
453#127—22no—
454#127C22×D1114yes—
455#125—22no—
456#125—114no—
457#125—114no—
458#125—228no—
459#125—222no—
460#125—222no—
461#125C22×D1114yes—
462#123—28no—
463#123—28no—
464C22⋊Q8—228no—
465C22⋊Q8—228no—
466#121—22no—
467#121—22no—
468#121—28no—
469#121—28no—
470#121C22×D1114yes—
471#121C22×D1114yes—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4C22×D1114yes—
475C4×D4C22×D1114yes—
476#117—114no—
477#117—222no—
478#117C22⋊D1114yes—
479#117C22×D1114yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4—222no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4C22⋊D1111yescharacteristic
496C2×C4⋊C4C22⋊D1111yescharacteristic
497C2×C4⋊C4C22×D1111yescharacteristic
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4C22⋊D1111yescharacteristic
505C2×C22⋊C4C22⋊D1111yescharacteristic
506C2×C42—221no—
507C2×C42C22×D1111yescharacteristic
508C2×C42C22×D1111yescharacteristic
509#107—114no—
510#107—114no—
511#107—114no—
512#107—114no—
513#106—114no—
514#106—114no—
515#106—114no—
516#106—114no—
517C4⋊C8—114no—
518C4⋊C8—114no—
519#102—114no—
520#102—114no—
521#102—114no—
522#102—114no—
523#102—114no—
524#102—114no—
525#102—114no—
526#102—114no—
527C22⋊C8—114no—
528C22⋊C8—114no—
529#97—114no—
530C4×C8—114no—
531C2×C11—42no—
532C2×C11—82no—
533C2×C11—82no—
534C2×C11#324114yescomplemented
535C2×C11C2×#53611yescharacteristic
536C2×C11C2×#57611yescharacteristic
537C2×C11C2×#57711yescharacteristic
538C24—21no—
539C24—21no—
540C24C2×C22⋊D1111yescharacteristic
541C2×Q8—224no—
542C2×Q8—224no—
543C2×Q8—882no—
544C2×Q8—882no—
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4C23×D1112yes—
560C2×D4C23×D1112yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—82no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—224no—
574C22×C4—882no—
575C22×C4C2×C22⋊D1112yes—
576C22×C4C2×C22⋊D1111yescharacteristic
577C22×C4C2×C22⋊D1111yescharacteristic
578C22×C4C2×C22⋊D1111yescharacteristic
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C2×C22⋊D1111yescharacteristic
581C22×C4C23×D1112yes—
582C22×C4C23×D1111yescharacteristic
583C2×C8—112no—
584C2×C8—112no—
585C2×C8—112no—
586C2×C8—112no—
587C2×C8—222no—
588C2×C8—222no—
589C2×C8—222no—
590C2×C8—222no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—112no—
596C4⋊C4—112no—
597C4⋊C4—112no—
598C4⋊C4—112no—
599C4⋊C4—224no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—224no—
605C4⋊C4—224no—
606C4⋊C4—224no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4C2×C22⋊D1114yes—
611C4⋊C4C2×C22⋊D1114yes—
612C4⋊C4C23×D1112yes—
613C4⋊C4C23×D1112yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—224no—
619C22⋊C4C2×C22⋊D1114yes—
620C22⋊C4C2×C22⋊D1114yes—
621C42—224no—
622C42C2×C22⋊D1112yes—
623C42C2×C22⋊D1112yes—
624C42C23×D1112yes—
625C42C23×D1112yes—
626C11C2×#324111yescharacteristic, complemented, Sylow
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C22×C22⋊D1112yes—
639C23C22×C22⋊D1111yescharacteristic
640Q8—884no—
641Q8—884no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—84no—
649D4—84no—
650D4—84no—
651D4—84no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—442no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—884no—
675C2×C4#6704312yes—
676C2×C4#6704312yes—
677C2×C4C22×C22⋊D1112yes—
678C2×C4C22×C22⋊D1112yes—
679C2×C4C22×C22⋊D1112yes—
680C2×C4C22×C22⋊D1112yes—
681C2×C4C22×C22⋊D1112yes—
682C2×C4C22×C22⋊D1111yescharacteristic
683C2×C4C24×D1111yescharacteristic
684C8—222no—
685C8—222no—
686C8—222no—
687C8—222no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—84no—
699C22—84no—
700C22#1062335612yes—
701C22#1062336612yes—
702C22#1062336712yes—
703C22C23×C22⋊D1111yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—442no—
712C4—442no—
713C4—442no—
714C4—442no—
715C4#1062335612yes—
716C4C2×#6704311yescharacteristic
717C4C2×#6704311yescharacteristic
718C2—42no—
719C2—82no—
720C2—82no—
721C2#1307986314yesdirect product factor
722C2C2×#1062335611yescharacteristic
723C2C2×#1062336611yescharacteristic
724C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#540C2
socleC23×C11C22×D4
hypercenterC2×#540D11
hypocenterC11C2×#3241
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
2. #13079863C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622677C2semidirect
5. C2×#10622684C2semidirect
6. C2×#10622683C2semidirect
7. C2×#10622647C2semidirect
8. C2×#10622648C2semidirect
9. C2×#10622648C2semidirect
10. C2×#10622646C2semidirect
11. C2×#10622622C2semidirect
12. C2×#10622622C2semidirect
13. C2×#10622621C2semidirect
14. C2×#10622620C2semidirect
15. C2×#10622613C2semidirect
33. #10623050C22semidirect
52. #10622684C22semidirect
53. #10622683C22semidirect
54. #10622678C22semidirect
55. #10622677C22semidirect
56. #10622648C22semidirect
57. #10622648C22semidirect
58. #10622647C22semidirect
59. #10622646C22semidirect
60. #10622622C22semidirect
61. #10622622C22semidirect
62. #10622621C22semidirect
63. #10622620C22semidirect
64. #10622613C22semidirect
534. C2×C11#3241semidirect
626. C11C2×#3241semidirect
721. C2#13079863direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
#130798632
C2×#106226782
C2×#106226772
C2×#106226842
C2×#106226832
C2×#106226472
C2×#106226482
C2×#106226462
C2×#106226222
C2×#106226212
C2×#106226202
C2×#106226132
C2×C11×#5402
C2×#324111