Finite Group Databasebeta

← C2×#13081363 #15633516

Subgroups — C2×#13081363 #15633516

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×#10623110C211yesmaximal, characteristic, complemented
2#13081363C2116yesmaximal, direct product factor
3C2×#10622684C211yesmaximal, characteristic, complemented
4C2×#10622668C211yesmaximal, characteristic, complemented
5C2×#10622669C211yesmaximal, characteristic, complemented
6C2×#10622635C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622620C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622670C211yesmaximal, characteristic, complemented
11C2×#10622685C211yesmaximal, characteristic
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622627C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×C4×#4323C211yesmaximal, characteristic, complemented
16C2×C11×#559C211yesmaximal, characteristic, complemented
17C11×#559—24no—
18C11×#559C2218yescomplemented
19C2×C11×#127C2211yescharacteristic
20C2×C11×#124—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×#123—21no—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×#66999—21no—
31C22×#4325C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34#10623110—24no—
35#10623110C2218yescomplemented
36C2×#66949—21no—
37C2×#66949—21no—
38C2×C4⋊C4×D11—21no—
39C2×C4×D44C2211yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×C4×D44C2211yescharacteristic
42C2×#66923C2211yescharacteristic
43C2×#66923C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C2×#66899C2211yescharacteristic
46C2×#66899C2211yescharacteristic
47C2×#66899C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622685C2218yes—
55#10622684C2218yescomplemented
56#10622670C2218yescomplemented
57#10622670C2218yescomplemented
58#10622669C2218yescomplemented
59#10622668C2218yescomplemented
60#10622639C2218yescomplemented
61#10622637C2218yescomplemented
62#10622635C2218yescomplemented
63#10622627C2218yescomplemented
64C4×#4323C2218yescomplemented
65#10622622C2218yescomplemented
66#10622620C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×C4⋊(C11⋊C8)C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×Dic22—21no—
90C11×#127—22no—
91C11×#127C2314yes—
92C11×#124—28no—
93C11×#124—22no—
94C11×#124—22no—
95C11×#124C2314yes—
96C11×#124C2314yes—
97C11×#123—28no—
98C11×#123—28no—
99C4×Q8×C11—22no—
100C4×Q8×C11D414yes—
101C4×Q8×C11C2314yes—
102C4×Q8×C11C2314yes—
103C4×D4×C11—28no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11C2314yes—
107C4×D4×C11C2314yes—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4D411yescharacteristic
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⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C42×C11—21no—
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123#66999—28no—
124C2×#4325—24no—
125C2×#4325C2314yes—
126C2×#4323—24no—
127C2×#4323—24no—
128C2×#4323C2314yes—
129C2×#4323C2314yes—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145#66949—28no—
146#66949—28no—
147C4⋊C4×D11—28no—
148C4×D44—22no—
149C4×D44—22no—
150C4×D44—22no—
151C4×D44C2314yes—
152C4×D44C2314yes—
153C4×D44C2314yes—
154#66923—22no—
155#66923—22no—
156#66923C2314yes—
157#66923C2314yes—
158#66922—22no—
159#66922C2314yes—
160#66899C2314yes—
161#66899C2314yes—
162#66899C2314yes—
163#66896C2314yes—
164#66896C2314yes—
165#66896C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169#66873C2314yes—
170#66872C2314yes—
171#66871C2314yes—
172#66871C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174C4⋊(C11⋊C8)C2314yes—
175C4⋊(C11⋊C8)C2314yes—
176#66867C2314yes—
177#66867C2314yes—
178C4×C11⋊C8C2314yes—
179C2×#3370—111nomaximal, Sylow
180C24×C11—21no—
181C24×C11—21no—
182C23×D11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11—42no—
187C2×Q8×C11C2×D414yes—
188C2×Q8×C11C2412yes—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—44no—
198C2×D4×C11—82no—
199C2×D4×C11C2412yes—
200C2×D4×C11C2412yes—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—24no—
204C22×C4×C11—24no—
205C22×C4×C11—82no—
206C22×C4×C11—82no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C2×D44—21no—
218C2×D44—22no—
219C2×D44#4114yes—
220C2×D44C2412yes—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—44no—
225C2×C4×D11—82no—
226C2×C4×D11—82no—
227C2×Dic22—24no—
228C2×Dic22—82no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4C2×D414yes—
232C11×C4⋊C4C2×D414yes—
233C11×C4⋊C4C2×D414yes—
234C11×C4⋊C4C2412yes—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C42×C11—24no—
242C42×C11C2×D412yes—
243C42×C11C2×D412yes—
244C42×C11C2×D412yes—
245C42×C11C2412yes—
246C42×C11C2412yes—
247C42×C11C2412yes—
248#4325—28no—
249#4323—28no—
250#4323—28no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260C4⋊Dic11C2412yes—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8C2412yes—
270C2×C11⋊C8C2412yes—
271C2×C11⋊C8C2412yes—
272C2×C11⋊C8C2412yes—
273C2×#559D1111yescharacteristic, complemented
274C2×#554—111no—
275#3370—1116no—
276C2×#490—111no—
277C2×#489—111no—
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—22no—
291C23×C11—42no—
292C23×C11—42no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11C22×D411yescharacteristic
298C22×D11—24no—
299C22×D11—22no—
300C22×D11—42no—
301C22×D11—42no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—44no—
305Q8×C11—42no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—48no—
311D4×C11—42no—
312D4×C11—42no—
313D4×C11—84no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—84no—
325C2×C4×C11—84no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4112yes—
334C2×C4×C112−1+412yes—
335C2×C4×C11C2511yescharacteristic
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342D44—24no—
343D44—22no—
344D44C2×#4114yes—
345C4×D11—48no—
346C4×D11—84no—
347C4×D11—84no—
348Dic22—84no—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C11⋊C8—22no—
352C11⋊C8—22no—
353C22×SD16—111no—
354C22×D8—111no—
355C22×D8—111no—
356#559—24no—
357#559C2×D1118yescomplemented
358#554—118no—
359#554—224no—
360C2×C4⋊Q8—111no—
361C2×#127C2×D1111yescharacteristic
362C2×#125—111no—
363C2×#125—111no—
364C2×#124—21no—
365C2×#124C2×D1111yescharacteristic
366C2×#124C2×D1111yescharacteristic
367C2×#123—21no—
368C2×#123—21no—
369C2×C22⋊Q8—221no—
370C2×C22⋊Q8—221no—
371C2×C22⋊Q8—221no—
372C2×C4×Q8C2×D1111yescharacteristic
373C2×C4×Q8C2×D1111yescharacteristic
374C2×C4×D4—21no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4—111no—
378C2×C4×D4C2×D1111yescharacteristic
379C2×C4×D4C2×D1111yescharacteristic
380C22×C4⋊C4—221no—
381#490—118no—
382#489—118no—
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×#103—111no—
402C2×#103—111no—
403C2×#102—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×#97—111no—
411C2×#97—111no—
412C2×C4×C8—111no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—84no—
420C22×C11—84no—
421C22×C11#54812yes—
422C22×C11#57512yes—
423C22×C11#57612yes—
424C22×C11C23×D411yescharacteristic
425C2×D11—24no—
426C2×D11—48no—
427C2×D11—42no—
428C2×D11—42no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—22no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11#54812yes—
438C4×C11C22×#4111yescharacteristic
439C4×C11C2×2−1+411yescharacteristic
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443C22×Q8—221no—
444C22×Q8C22⋊D1111yescharacteristic
445C22×Q8C22×D1111yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—111no—
449C22×D4C22×D1111yescharacteristic
450C22×D4C22×D1111yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
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×C8—111no—
465C22×C8—111no—
466C4⋊Q8—114no—
467C4⋊Q8—222no—
468#127—22no—
469#127C22×D1114yes—
470#125—114no—
471#125—114no—
472#125—222no—
473#125—222no—
474#124—28no—
475#124—22no—
476#124—22no—
477#124C22×D1114yes—
478#124C22×D1114yes—
479#123—28no—
480#123—28no—
481C22⋊Q8—228no—
482C22⋊Q8—228no—
483C22⋊Q8—228no—
484C4×Q8—22no—
485C4×Q8C22⋊D1114yes—
486C4×Q8C22×D1114yes—
487C4×Q8C22×D1114yes—
488C4×D4—28no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—114no—
492C4×D4—114no—
493C4×D4—114no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—222no—
497C4×D4C22×D1114yes—
498C4×D4C22×D1114yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—228no—
509C2×C4⋊C4C22⋊D1111yescharacteristic
510C2×C4⋊C4C22⋊D1111yescharacteristic
511C2×C4⋊C4C22⋊D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C42—21no—
523C2×C42C22×D1111yescharacteristic
524C2×C42C22×D1111yescharacteristic
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#103—114no—
534#103—114no—
535#102—114no—
536#102—114no—
537#102—114no—
538#102—114no—
539#102—114no—
540#102—114no—
541#102—114no—
542#97—114no—
543#97—114no—
544C4×C8—114no—
545C2×C11—82no—
546C2×C11—82no—
547C2×C11#337014yescomplemented
548C2×C11C2×#54811yescharacteristic
549C2×C11C2×#57511yescharacteristic
550C2×C11C2×#57611yescharacteristic
551D11—44no—
552C24—21no—
553C24—21no—
554C24—221no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—42no—
559C2×Q8—224no—
560C2×Q8—882no—
561C2×Q8C2×C22⋊D1114yes—
562C2×Q8C23×D1112yes—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—44no—
572C2×D4—82no—
573C2×D4—114no—
574C2×D4—112no—
575C2×D4—222no—
576C2×D4—221no—
577C2×D4C23×D1112yes—
578C2×D4C23×D1112yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—224no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—444no—
592C22×C4—882no—
593C22×C4—882no—
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C23×D1111yescharacteristic
601SD16—228no—
602D8—228no—
603D8—228no—
604C2×C8—112no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—112no—
608C2×C8—222no—
609C2×C8—222no—
610C2×C8—222no—
611C2×C8—222no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—112no—
615C4⋊C4—112no—
616C4⋊C4—112no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4C2×C22⋊D1114yes—
626C4⋊C4C2×C22⋊D1114yes—
627C4⋊C4C2×C22⋊D1114yes—
628C4⋊C4C23×D1112yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—24no—
639C42C2×C22⋊D1112yes—
640C42C2×C22⋊D1112yes—
641C42C2×C22⋊D1112yes—
642C42C23×D1112yes—
643C42C23×D1112yes—
644C42C23×D1112yes—
645C11C2×#337011yescharacteristic, complemented, Sylow
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—224no—
655C23—222no—
656C23—442no—
657C23—442no—
658C23C22×C22⋊D1111yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—44no—
662Q8—42no—
663Q8—884no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670D4—42no—
671D4—84no—
672D4—114no—
673D4—224no—
674D4—222no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—448no—
691C2×C4—442no—
692C2×C4—442no—
693C2×C4—442no—
694C2×C4—884no—
695C2×C4—884no—
696C2×C4#41×D1112yes—
697C2×C4#6704312yes—
698C2×C4C22×C22⋊D1112yes—
699C2×C4C22×C22⋊D1112yes—
700C2×C4C22×C22⋊D1112yes—
701C2×C4C22×C22⋊D1112yes—
702C2×C4C22×C22⋊D1112yes—
703C2×C4C22×C22⋊D1112yes—
704C2×C4C22×C22⋊D1111yescharacteristic
705C2×C4C24×D1111yescharacteristic
706C8—222no—
707C8—222no—
708C8—222no—
709C8—222no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—84no—
718C22—224no—
719C22—448no—
720C22—442no—
721C22—442no—
722C22#1062335312yes—
723C22#1062336212yes—
724C22#1062336612yes—
725C22C23×C22⋊D1111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4#1062336212yes—
738C4C2×#41×D1111yescharacteristic
739C4C2×#6704311yescharacteristic
740C2—82no—
741C2—82no—
742C2—444no—
743C2#1308136314yesdirect product factor
744C2C2×#1062336211yescharacteristic
745C2C2×#1062335311yescharacteristic
746C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenterC2×#559D11
hypocenterC11C2×#3370
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
2. #13081363C2direct (N × H)
3. C2×#10622684C2semidirect
4. C2×#10622668C2semidirect
5. C2×#10622669C2semidirect
6. C2×#10622635C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622620C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622670C2semidirect
12. C2×#10622637C2semidirect
13. C2×#10622627C2semidirect
14. C2×#10622639C2semidirect
15. C2×C4×#4323C2semidirect
16. C2×C11×#559C2semidirect
18. C11×#559C22semidirect
35. #10623110C22semidirect
55. #10622684C22semidirect
56. #10622670C22semidirect
57. #10622670C22semidirect
58. #10622669C22semidirect
59. #10622668C22semidirect
60. #10622639C22semidirect
61. #10622637C22semidirect
62. #10622635C22semidirect
63. #10622627C22semidirect
64. C4×#4323C22semidirect
65. #10622622C22semidirect
66. #10622620C22semidirect
273. C2×#559D11semidirect
357. #559C2×D11semidirect
547. C2×C11#3370semidirect
645. C11C2×#3370semidirect
743. C2#13081363direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
#130813632
C2×#106226842
C2×#106226682
C2×#106226692
C2×#106226352
C2×#106226222
C2×#106226202
C2×#106226702
C2×#106226852
C2×#106226372
C2×#106226272
C2×#106226392
C2×C4×#43232
C2×C11×#5592
C2×#337011