Finite Group Databasebeta

← C2×#13081368 #15633521

Subgroups — C2×#13081368 #15633521

Order 2816.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623212C211yesmaximal, characteristic, complemented
2C2×#10623261C211yesmaximal, characteristic, complemented
3#13081368C2116yesmaximal, direct product factor
4C2×#10622377C211yesmaximal, characteristic, complemented
5C2×#10622413C211yesmaximal, characteristic, complemented
6C2×#10622412C211yesmaximal, characteristic, complemented
7C2×#10622376C211yesmaximal, characteristic, complemented
8C2×#10622700C211yesmaximal, characteristic, complemented
9C2×#10622432C211yesmaximal, characteristic, complemented
10C2×#10622670C211yesmaximal, characteristic, complemented
11C2×#10622399C211yesmaximal, characteristic
12C2×#10622314C211yesmaximal, characteristic, complemented
13C2×#10622324C211yesmaximal, characteristic, complemented
14C2×#10622430C211yesmaximal, characteristic, complemented
15C2×#10622369C211yesmaximal, characteristic, complemented
16C2×C11×#489C211yesmaximal, characteristic, complemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×#66999—21no—
21C2×#66999—21no—
22C2×Q8×Dic11C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66993C2211yescharacteristic
25C2×D4×Dic11C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C22×D88C2211yescharacteristic
28#10623261—24no—
29#10623261C2218yescomplemented
30#10623212—24no—
31#10623212C2218yescomplemented
32C2×#66950—21no—
33C2×#66946C2211yescharacteristic
34C2×#66946C2211yescharacteristic
35C2×C4⋊C4×D11—21no—
36C2×#66943C2211yescharacteristic
37C2×#66943C2211yescharacteristic
38C2×#66939—21no—
39C2×#66938—21no—
40C2×#66936—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#489C2218yescomplemented
46C2×C11×#103C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66881C2211yescharacteristic
56C2×#66879C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic
59C2×C8×Dic11C2211yescharacteristic
60#10622700C2218yescomplemented
61#10622670C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622432C2218yescomplemented
68#10622430C2218yescomplemented
69#10622413C2218yescomplemented
70#10622412C2218yescomplemented
71#10622399C2218yes—
72#10622377C2218yescomplemented
73#10622376C2218yescomplemented
74#10622369C2218yescomplemented
75#10622324C2218yescomplemented
76#10622314C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C23×Dic11—21no—
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×Dic22D411yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C11×C4⋊Q8—22no—
93C11×C4⋊Q8C2314yes—
94C11×#124—22no—
95C11×#124C2314yes—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103#67000—22no—
104#67000C2314yes—
105#66999—28no—
106#66999—28no—
107Q8×Dic11—22no—
108Q8×Dic11C2314yes—
109C2×#4325—24no—
110C2×#4325C2314yes—
111#66993—22no—
112#66993C2314yes—
113D4×Dic11—22no—
114D4×Dic11C2314yes—
115C2×#4323—24no—
116C2×#4323C2314yes—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11D411yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4D411yescharacteristic
132C2×Dic11⋊C4D411yescharacteristic
133C2×C4×Dic11—21no—
134C2×C4×Dic11C2311yescharacteristic
135C2×C4×Dic11C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×D88—24no—
139C2×D88C2314yes—
140#66950—28no—
141#66946—22no—
142#66946—22no—
143#66946C2314yes—
144#66946C2314yes—
145C4⋊C4×D11—28no—
146#66943—22no—
147#66943—22no—
148#66943C2314yes—
149#66943C2314yes—
150#66939—28no—
151#66938—28no—
152#66936—28no—
153(C22⋊D11)⋊C4—28no—
154C4×D44—22no—
155C4×D44—22no—
156C4×D44C2314yes—
157C4×D44C2314yes—
158C4×Dic22D414yes—
159C4×Dic22C2314yes—
160C11×#103C2314yes—
161C11×#103C2314yes—
162C11×#102C2314yes—
163C11×#102C2314yes—
164C11×#97C2314yes—
165#66899C2314yes—
166#66896C2314yes—
167#66885C2314yes—
168#66885C2314yes—
169#66881C2314yes—
170#66879C2314yes—
171Dic11⋊C8C2314yes—
172Dic11⋊C8C2314yes—
173C8×Dic11C2314yes—
174#66873C2314yes—
175#66873C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C2×#3370—111nomaximal, Sylow
180C24×C11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—24no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—82no—
188C2×Q8×C11C2412yes—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11C2412yes—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11—82no—
203C22×Dic11—24no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—82no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44#4114yes—
217C2×D44C2412yes—
218C2×D44C2412yes—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—44no—
224C2×C4×D11—82no—
225C2×C4×D11—82no—
226C2×C4×D11—82no—
227C2×Dic22—42no—
228C2×Dic22C2×D414yes—
229C2×C8×C11—22no—
230C2×C8×C11—22no—
231C2×C8×C11C2412yes—
232C2×C8×C11C2412yes—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4C2412yes—
237C11×C4⋊C4C2412yes—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C42×C11C2×D412yes—
241C42×C11C2412yes—
242C22⋊Dic11—24no—
243#4325—28no—
244#4323—28no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2×D414yes—
257C4⋊Dic11C2412yes—
258C4⋊Dic11C2412yes—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4C2×D414yes—
262Dic11⋊C4C2×D414yes—
263C4×Dic11—24no—
264C4×Dic11C2×D412yes—
265C4×Dic11C2×D412yes—
266C4×Dic11C2412yes—
267C4×Dic11C2412yes—
268C2×C11⋊C8—22no—
269C2×C11⋊C8—22no—
270C2×C11⋊C8C2412yes—
271C2×C11⋊C8C2412yes—
272D88—28no—
273C2×#559—111no—
274C2×#554—111no—
275#3370—1116no—
276C2×#490—111no—
277C2×#489D1111yescharacteristic, complemented
278C2×#488—111no—
279C2×#479—111no—
280C2×#478—111no—
281C2×#474—111no—
282C2×#463—111no—
283C2×#463—111no—
284C2×#459—111no—
285C2×#446—111no—
286C2×#442—111no—
287C2×#440—111no—
288C2×C4×D8—111no—
289C23×C11—22no—
290C23×C11—42no—
291C23×C11—42no—
292C23×C11—42no—
293C23×C11C22×D411yescharacteristic
294C22×D11—24no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11—42no—
300C22×D11—42no—
301C22×D11—42no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—42no—
305Q8×C11—84no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—42no—
309C2×C4×C11—22no—
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—42no—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D412yes—
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4112yes—
321C2×C4×C112−1+412yes—
322C2×C4×C11C2511yescharacteristic
323C22⋊D11—48no—
324C22⋊D11—84no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—84no—
334C2×Dic11C22×D412yes—
335C2×Dic11C22×D412yes—
336C2×Dic11C22×D412yes—
337C2×Dic11C22×D412yes—
338D44—24no—
339D44—22no—
340D44—22no—
341D44—22no—
342D44—42no—
343D44C2×#4114yes—
344C4×D11—48no—
345C4×D11—84no—
346C4×D11—84no—
347C4×D11—84no—
348Dic22—44no—
349C8×C11—22no—
350C8×C11—22no—
351C11⋊C8—22no—
352C11⋊C8—22no—
353C22×SD16—111no—
354C22×D8—111no—
355C22×D8—111no—
356#559—118no—
357#559—224no—
358#554—118no—
359#554—224no—
360C2×C4⋊Q8C2×D1111yescharacteristic
361C2×#127—111no—
362C2×#125—111no—
363C2×#125—111no—
364C2×#124—111no—
365C2×#124—221no—
366C2×#124C2×D1111yescharacteristic
367C2×#123—221no—
368C2×#123—221no—
369C2×C22⋊Q8—221no—
370C2×C22⋊Q8—221no—
371C2×C22⋊Q8—221no—
372C2×C4×Q8—111no—
373C2×C4×Q8—111no—
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4—111no—
378C2×C4×D4—111no—
379C2×C4×D4—221no—
380C22×C4⋊C4—221no—
381#490—118no—
382#489C2×D1118yescomplemented
383#488—118no—
384#479—118no—
385#478—118no—
386#474—118no—
387#463—118no—
388#463—118no—
389#459—118no—
390#446—118no—
391#442—118no—
392#440—118no—
393C4×D8—118no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#106—111no—
397C2×C4⋊C8—111no—
398C2×C4⋊C8—111no—
399C2×C4⋊C8—111no—
400C2×#103—111no—
401C2×#103C2×D1111yescharacteristic
402C2×#103C2×D1111yescharacteristic
403C2×#102—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#102C2×D1111yescharacteristic
409C2×#102C2×D1111yescharacteristic
410C2×#97—111no—
411C2×#97C2×D1111yescharacteristic
412C2×C4×C8—111no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—84no—
417C22×C11#54812yes—
418C22×C11#57512yes—
419C22×C11#57612yes—
420C22×C11C23×D411yescharacteristic
421C2×D11—24no—
422C2×D11—48no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—84no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11#54812yes—
435C4×C11C22×#4111yescharacteristic
436C4×C11C2×2−1+411yescharacteristic
437Dic11—22no—
438Dic11—22no—
439Dic11—22no—
440Dic11—22no—
441Dic11—42no—
442Dic11—42no—
443C22×Q8—21no—
444C22×Q8—111no—
445C22×Q8C22×D1111yescharacteristic
446C22×D4—111no—
447C22×D4—111no—
448C22×D4—221no—
449C22×D4—221no—
450C22×D4C22×D1111yescharacteristic
451C23×C4—221no—
452C23×C4—221no—
453C23×C4—221no—
454C23×C4—221no—
455C23×C4—221no—
456C2×SD16—114no—
457C2×SD16—224no—
458C2×D8—114no—
459C2×D8—114no—
460C2×D8—224no—
461C2×D8—224no—
462C22×C8—111no—
463C22×C8—111no—
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466C4⋊Q8—22no—
467C4⋊Q8C22×D1114yes—
468#127—114no—
469#127—222no—
470#125—114no—
471#125—114no—
472#125—222no—
473#125—222no—
474#124—22no—
475#124—114no—
476#124—222no—
477#124—228no—
478#124C22×D1114yes—
479#123—228no—
480#123—228no—
481C22⋊Q8—228no—
482C22⋊Q8—228no—
483C22⋊Q8—228no—
484C4×Q8—114no—
485C4×Q8—114no—
486C4×Q8—114no—
487C4×Q8—222no—
488C4×D4—114no—
489C4×D4—114no—
490C4×D4—114no—
491C4×D4—114no—
492C4×D4—114no—
493C4×D4—222no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—228no—
497C4×D4—222no—
498C4×D4—222no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—228no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C42—111no—
523C2×C42—111no—
524C2×C42—221no—
525C2×C42C22×D1111yescharacteristic
526#107—114no—
527#107—114no—
528#106—114no—
529C4⋊C8—114no—
530C4⋊C8—114no—
531C4⋊C8—114no—
532#103—114no—
533#103C22×D1114yes—
534#103C22×D1114yes—
535#102—114no—
536#102—114no—
537#102—114no—
538#102—114no—
539#102—114no—
540#102C22×D1114yes—
541#102C22×D1114yes—
542#97—114no—
543#97C22×D1114yes—
544C4×C8—114no—
545C2×C11—82no—
546C2×C11#337014yescomplemented
547C2×C11C2×#54811yescharacteristic
548C2×C11C2×#57511yescharacteristic
549C2×C11C2×#57611yescharacteristic
550D11—44no—
551D11—82no—
552C24—21no—
553C24—221no—
554C24—221no—
555C2×Q8—21no—
556C2×Q8—24no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—82no—
560C2×Q8—114no—
561C2×Q8—442no—
562C2×Q8C23×D1112yes—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—114no—
567C2×D4—112no—
568C2×D4—112no—
569C2×D4—224no—
570C2×D4—224no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—222no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—444no—
577C2×D4—882no—
578C2×D4C23×D1112yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—111no—
585C22×C4—111no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—224no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—224no—
592C22×C4—224no—
593C22×C4—444no—
594C22×C4—882no—
595C22×C4—882no—
596C22×C4—882no—
597C22×C4—882no—
598C22×C4D4×D1111yescharacteristic
599C22×C4D4×D1111yescharacteristic
600C22×C4C23×D1111yescharacteristic
601SD16—228no—
602D8—228no—
603D8—228no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—112no—
607C2×C8—112no—
608C2×C8—222no—
609C2×C8—222no—
610C2×C8C23×D1112yes—
611C2×C8C23×D1112yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—114no—
616C4⋊C4—114no—
617C4⋊C4—114no—
618C4⋊C4—112no—
619C4⋊C4—112no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4C23×D1112yes—
628C4⋊C4C23×D1112yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—112no—
639C42—112no—
640C42—112no—
641C42—112no—
642C42—224no—
643C42D4×D1112yes—
644C42C23×D1112yes—
645C11C2×#337011yescharacteristic, complemented, Sylow
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—222no—
651C23—224no—
652C23—222no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23C2×D4×D1111yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—84no—
663Q8—444no—
664D4—22no—
665D4—22no—
666D4—42no—
667D4—114no—
668D4—222no—
669D4—222no—
670D4—222no—
671D4—224no—
672D4—448no—
673D4—442no—
674D4—884no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—112no—
684C2×C4—112no—
685C2×C4—112no—
686C2×C4—112no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—448no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—884no—
697C2×C4—884no—
698C2×C4—884no—
699C2×C4—884no—
700C2×C4C2×D4×D1112yes—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1111yescharacteristic
703C2×C4#41×D1112yes—
704C2×C4#6704312yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—222no—
709C8—222no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—224no—
715C22—448no—
716C22—442no—
717C22—442no—
718C22—442no—
719C22—442no—
720C22—442no—
721C22—884no—
722C22#1062320812yes—
723C22#1062330512yes—
724C22#1062330812yes—
725C22C22×D4×D1111yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—222no—
732C4—222no—
733C4—222no—
734C4—222no—
735C4—442no—
736C4—442no—
737C4#1062320812yes—
738C4C2×#41×D1111yescharacteristic
739C4C2×#6704311yescharacteristic
740C2—82no—
741C2—444no—
742C2—882no—
743C2#1308136814yesdirect product factor
744C2C2×#1062320811yescharacteristic
745C2C2×#1062330811yescharacteristic
746C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
prime radicalC2×#10622399C2
hypercenterC2×#489D11
hypocenterC11C2×#3370
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#10623212C2semidirect
2. C2×#10623261C2semidirect
3. #13081368C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622413C2semidirect
6. C2×#10622412C2semidirect
7. C2×#10622376C2semidirect
8. C2×#10622700C2semidirect
9. C2×#10622432C2semidirect
10. C2×#10622670C2semidirect
12. C2×#10622314C2semidirect
13. C2×#10622324C2semidirect
14. C2×#10622430C2semidirect
15. C2×#10622369C2semidirect
16. C2×C11×#489C2semidirect
29. #10623261C22semidirect
31. #10623212C22semidirect
45. C11×#489C22semidirect
60. #10622700C22semidirect
61. #10622670C22semidirect
67. #10622432C22semidirect
68. #10622430C22semidirect
69. #10622413C22semidirect
70. #10622412C22semidirect
72. #10622377C22semidirect
73. #10622376C22semidirect
74. #10622369C22semidirect
75. #10622324C22semidirect
76. #10622314C22semidirect
277. C2×#489D11semidirect
382. #489C2×D11semidirect
546. C2×C11#3370semidirect
645. C11C2×#3370semidirect
743. C2#13081368direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232122
C2×#106232612
#130813682
C2×#106223772
C2×#106224132
C2×#106224122
C2×#106223762
C2×#106227002
C2×#106224322
C2×#106226702
C2×#106223992
C2×#106223142
C2×#106223242
C2×#106224302
C2×#106223692
C2×C11×#4892
C2×#337011