Finite Group Databasebeta

← C2×#13078241 #15620926

Subgroups — C2×#13078241 #15620926

Order 2816.

2898 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66968C211yesmaximal, characteristic, complemented
2C22×M16×D11C211yesmaximal, characteristic, complemented
3C2×#10623137C211yesmaximal, characteristic
4C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
5#13078241C2116yesmaximal, direct product factor
6C2×#10622750C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622655C211yesmaximal, characteristic, complemented
9C2×#10622500C211yesmaximal, characteristic, complemented
10C2×#10622426C211yesmaximal, characteristic, complemented
11C2×#10622391C211yesmaximal, characteristic, complemented
12C2×#10622784C211yesmaximal, characteristic, complemented
13C2×#10622494C211yesmaximal, characteristic, complemented
14C2×#10622384C211yesmaximal, characteristic, complemented
15C2×#10622415C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic, complemented
21C22×C11×M16C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C22×#4326C2211yescharacteristic, complemented
26C2×#66991C2211yescharacteristic
27C2×#66990—21no—
28C2×D4×Dic11—21no—
29C22×#4324C2211yescharacteristic, complemented
30C2×#66977C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C2×#66968—28no—
34C2×#66968C2218yescomplemented
35C2×M16×D11—28no—
36C2×M16×D11C2218yescomplemented
37C22×Dic44C2211yescharacteristic, complemented
38C22×#4313C2211yescharacteristic
39C22×#4313C2211yescharacteristic
40C22×C8×D11C2211yescharacteristic
41C22×C8×D11C2211yescharacteristic
42D11×C22⋊Q8—24no—
43D11×C22⋊Q8C2218yescomplemented
44#10623137—24no—
45#10623137C2218yes—
46C2×#66950C2211yescharacteristic
47C2×#66950C2211yescharacteristic
48C2×#66949—21no—
49C2×#66945C2211yescharacteristic
50C2×C4⋊C4×D11—21no—
51C2×C4⋊C4×D11C2211yescharacteristic
52C2×#66936—21no—
53C2×(C22⋊D11)⋊C4—21no—
54C2×C22⋊C4×D11—21no—
55C2×#66931—21no—
56C11×#468C2218yescomplemented
57C2×C11×#107C2211yescharacteristic, complemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic, complemented
60C2×#66899C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62#10622784C2218yescomplemented
63#10622750C2218yescomplemented
64C2×#66881C2211yescharacteristic, complemented
65C2×#66880C2211yescharacteristic, complemented
66C2×#66880C2211yescharacteristic, complemented
67#10622665C2218yescomplemented
68#10622655C2218yescomplemented
69C2×#66874C2211yescharacteristic, complemented
70C2×#66874C2211yescharacteristic, complemented
71C2×#66872C2211yescharacteristic, complemented
72C2×#66871C2211yescharacteristic, complemented
73#10622500C2218yescomplemented
74#10622494C2218yescomplemented
75#10622426C2218yescomplemented
76#10622415C2218yescomplemented
77#10622391C2218yescomplemented
78#10622384C2218yescomplemented
79C24×D11D411yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11—21no—
87C23×Dic11D411yescharacteristic
88C2×Q8×D11—22no—
89C2×Q8×D11—24no—
90C2×Q8×D11—24no—
91C2×Q8×D11C2314yes—
92C2×#4341—24no—
93C2×#4341—22no—
94C2×#4341—24no—
95C2×#4341C2314yes—
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11D411yescharacteristic
101C22×C4×D11D411yescharacteristic
102C22×C4×D11D414yes—
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2314yes—
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—21no—
107C22×Dic22C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C2×C11×SD16—24no—
110C2×C11×SD16C2314yescomplemented
111C2×C11×M16—24no—
112C2×C11×M16C2314yes—
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2311yescharacteristic
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8C2314yes—
117C11×#121—22no—
118C11×#121C2314yes—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127#66999—22no—
128#66999C2314yes—
129C2×#4326—24no—
130C2×#4326C2314yescomplemented
131#66991—22no—
132#66991C2314yes—
133#66990—28no—
134D4×Dic11—28no—
135C2×#4324—24no—
136C2×#4324C2314yescomplemented
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11—21no—
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145#66977—22no—
146#66977—22no—
147#66977C2314yes—
148#66977C2314yes—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×C4×Dic11—21no—
154C2×#4318—24no—
155C2×#4318C2314yes—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158#66968—232no—
159M16×D11—232no—
160C2×Dic44—24no—
161C2×Dic44C2314yescomplemented
162C2×#4313—24no—
163C2×#4313D418yescomplemented
164C2×#4313C2314yes—
165C2×#4313C2314yes—
166C2×C8×D11—24no—
167C2×C8×D11—24no—
168C2×C8×D11C2314yes—
169C2×C8×D11C2314yes—
170#66950—22no—
171#66950—22no—
172#66950C2314yes—
173#66950C2314yes—
174#66949—28no—
175#66945—22no—
176#66945C2314yes—
177C4⋊C4×D11—28no—
178C4⋊C4×D11—22no—
179C4⋊C4×D11C2314yes—
180#66936—28no—
181(C22⋊D11)⋊C4—28no—
182C22⋊C4×D11—28no—
183#66931—28no—
184C11×#107C2314yescomplemented
185C11×#103C2314yescomplemented
186C11×#102C2314yescomplemented
187#66899C2314yescomplemented
188#66896C2314yescomplemented
189#66881C2314yescomplemented
190#66880C2314yescomplemented
191#66880C2314yescomplemented
192#66874C2314yescomplemented
193#66874C2314yescomplemented
194#66872C2314yescomplemented
195#66871C2314yescomplemented
196C2×#3056—111nomaximal, Sylow
197C24×C11—21no—
198C24×C11C2×D411yescharacteristic
199C23×D11—24no—
200C23×D11—24no—
201C23×D11—42no—
202C23×D11C2×D414yes—
203C23×D11C2×D411yescharacteristic
204C23×D11C2×D411yescharacteristic
205C2×Q8×C11—21no—
206C2×Q8×C11—22no—
207C2×Q8×C11—22no—
208C2×Q8×C11C2412yes—
209C2×D4×C11—24no—
210C2×D4×C11—22no—
211C2×D4×C11—21no—
212C2×D4×C11—22no—
213C2×D4×C11—44no—
214C2×D4×C11C2412yes—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2411yescharacteristic
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C22×Dic11—24no—
229C22×Dic11—24no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—44no—
235C22×Dic11C2×D414yes—
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238Q8×D11—28no—
239Q8×D11—28no—
240Q8×D11—48no—
241#4341—28no—
242#4341—28no—
243#4341—48no—
244C2×C4×D11—24no—
245C2×C4×D11—216no—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—24no—
249C2×C4×D11—24no—
250C2×C4×D11—24no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11C2×D414yes—
256C2×C4×D11C2×D414yes—
257C2×C4×D11C2×D414yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2×D412yes—
260C2×C4×D11#4114yes—
261C2×C4×D11C2412yes—
262C2×C4×D11C2412yes—
263C2×Dic22—24no—
264C2×Dic22—22no—
265C2×Dic22—22no—
266C2×Dic22—21no—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×Dic22—44no—
271C2×Dic22C2412yes—
272C2×Dic22C2412yes—
273C11×SD16—28no—
274C11×M16—28no—
275C2×C8×C11—22no—
276C2×C8×C11C2×D414yes—
277C2×C8×C11C2412yes—
278C2×C8×C11C2412yes—
279C11×C4⋊C4—24no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4C2412yes—
283C11×C4⋊C4C2412yes—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C22⋊Dic11—24no—
287C22⋊Dic11—24no—
288C22⋊Dic11—24no—
289#4326—28no—
290#4324—28no—
291(C2×D11)⋊C4—24no—
292(C2×D11)⋊C4—24no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295C4⋊Dic11—24no—
296C4⋊Dic11—24no—
297C4⋊Dic11—21no—
298C4⋊Dic11—21no—
299C4⋊Dic11C2412yes—
300C4⋊Dic11C2412yes—
301Dic11⋊C4—24no—
302Dic11⋊C4—24no—
303Dic11⋊C4—24no—
304Dic11⋊C4—24no—
305C4×Dic11—24no—
306#4318—28no—
307C2×C11⋊C8—22no—
308C2×C11⋊C8C2×D414yes—
309C2×C11⋊C8C2412yes—
310C2×C11⋊C8C2412yes—
311Dic44—28no—
312#4313—28no—
313#4313C2×D4116yescomplemented
314C8×D11—28no—
315C8×D11—28no—
316C22×#137—111no—
317C23×M16—111no—
318C2×#525—111no—
319C22×C22⋊Q8—111no—
320#3056—1116no—
321C2×#470—111no—
322C2×#470—111no—
323C2×#468—111no—
324C2×#468D1111yescharacteristic, complemented
325C2×#467—111no—
326C2×#467—111no—
327C2×#465—111no—
328C2×#465—111no—
329C2×#428—111no—
330C2×#417—111no—
331C2×#419—111no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11C22×D412yes—
340C23×C11C22×D411yescharacteristic
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—44no—
348C22×D11—416no—
349C22×D11#12114yes—
350C22×D11#13714yescomplemented
351C22×D11C22×D412yes—
352C22×D11C22×D412yes—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—42no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—48no—
359D4×C11—42no—
360C2×C4×C11—22no—
361C2×C4×C11—24no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11—42no—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D412yes—
373C2×C4×C11C2×#4112yes—
374C2×C4×C11C2511yescharacteristic
375C22⋊D11—48no—
376C22⋊D11—48no—
377C2×Dic11—22no—
378C2×Dic11—28no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—42no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11—48no—
388C2×Dic11#12114yes—
389C2×Dic11C22×D412yes—
390C2×Dic11C22×D412yes—
391C4×D11—28no—
392C4×D11—24no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—28no—
396C4×D11—48no—
397C4×D11—48no—
398C4×D11#12118yes—
399C4×D11C22×D414yes—
400C4×D11C2×#4114yes—
401Dic22—22no—
402Dic22—22no—
403Dic22—22no—
404Dic22—22no—
405Dic22—42no—
406Dic22—42no—
407Dic22—48no—
408C8×C11—22no—
409C8×C11C22×D414yes—
410C11⋊C8—22no—
411C11⋊C8C22×D414yes—
412C22×#41—111no—
413C23×Q8—111no—
414C24×C4—111no—
415C2×#137—118no—
416C2×#137—228no—
417C22×Q16—111no—
418C22×Q16—111no—
419C22×SD16—111no—
420C22×SD16C2×D1111yescharacteristic, complemented
421C22×M16—111no—
422C22×M16—118no—
423C22×M16—111no—
424C22×M16—111no—
425C22×M16—228no—
426C22×M16C2×D1111yescharacteristic
427C23×C8—111no—
428C23×C8—111no—
429#525—118no—
430#525—224no—
431C2×#123—221no—
432C2×C22⋊Q8—111no—
433C2×C22⋊Q8—111no—
434C2×C22⋊Q8—111no—
435C2×C22⋊Q8—118no—
436C2×C22⋊Q8—111no—
437C2×C22⋊Q8—111no—
438C2×C22⋊Q8—221no—
439C2×C22⋊Q8—221no—
440C2×C22⋊Q8—224no—
441C2×C22⋊Q8C2×D1111yescharacteristic
442C2×#121—111no—
443C2×#121C2×D1111yescharacteristic
444C2×#120—221no—
445C2×C4×D4—221no—
446C2×C4×D4—221no—
447C2×#117—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—221no—
450C22×C22⋊C4—221no—
451#470—118no—
452#470—118no—
453#468—118no—
454#468C2×D1118yescomplemented
455#467—118no—
456#467—118no—
457#465—118no—
458#465—118no—
459#428—118no—
460C2×#107—111no—
461C2×#107C2×D1111yescharacteristic, complemented
462C2×#106—111no—
463C2×#106—111no—
464#419—118no—
465#417—118no—
466C2×#103—111no—
467C2×#103—111no—
468C2×#103—111no—
469C2×#103—111no—
470C2×#103—111no—
471C2×#103C2×D1111yescharacteristic, complemented
472C2×#102—111no—
473C2×#102C2×D1111yescharacteristic, complemented
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—44no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—84no—
482C22×C11C2×#12112yes—
483C22×C11C2×#13712yes—
484C22×C11#57512yes—
485C22×C11C23×D411yescharacteristic
486C2×D11—22no—
487C2×D11—28no—
488C2×D11—28no—
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—416no—
493C2×D11C2×#12114yes—
494C2×D11C2×#13714yescomplemented
495C4×C11—22no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11—42no—
499C4×C11C2×#12112yes—
500C4×C11C23×D411yescharacteristic
501C4×C11C22×#4111yescharacteristic
502Dic11—22no—
503Dic11—42no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507Dic11C2×#12114yes—
508C25—111no—
509C2×#41—114no—
510C2×#41—222no—
511C2×#41—224no—
512C2×#41—224no—
513C22×Q8—114no—
514C22×Q8—111no—
515C22×Q8—111no—
516C22×Q8—221no—
517C22×Q8—222no—
518C22×Q8—224no—
519C22×Q8—224no—
520C22×Q8C22×D1111yescharacteristic
521C22×D4—21no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4C22×D1111yescharacteristic
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—114no—
530C23×C4—111no—
531C23×C4—114no—
532C23×C4—224no—
533C23×C4—224no—
534C23×C4—221no—
535C23×C4—221no—
536C23×C4—221no—
537C23×C4C22×D1111yescharacteristic
538#137—2232no—
539C2×Q16—114no—
540C2×Q16—114no—
541C2×Q16—224no—
542C2×Q16—224no—
543C2×SD16—24no—
544C2×SD16—114no—
545C2×SD16—224no—
546C2×SD16C22×D1114yescomplemented
547C2×M16—24no—
548C2×M16—114no—
549C2×M16—118no—
550C2×M16—114no—
551C2×M16—114no—
552C2×M16—224no—
553C2×M16—224no—
554C2×M16—2232no—
555C2×M16C22×D1114yes—
556C22×C8—111no—
557C22×C8—111no—
558C22×C8—114no—
559C22×C8—114no—
560C22×C8—224no—
561C22×C8—224no—
562C22×C8C22×D1111yescharacteristic
563C22×C8C22×D1111yescharacteristic
564#123—228no—
565C22⋊Q8—22no—
566C22⋊Q8—114no—
567C22⋊Q8—114no—
568C22⋊Q8—114no—
569C22⋊Q8—114no—
570C22⋊Q8—114no—
571C22⋊Q8—228no—
572C22⋊Q8—228no—
573C22⋊Q8—222no—
574C22⋊Q8—222no—
575C22⋊Q8—222no—
576C22⋊Q8—222no—
577C22⋊Q8—222no—
578C22⋊Q8C22×D1114yes—
579#121—22no—
580#121—114no—
581#121—222no—
582#121C22×D1114yes—
583#120—228no—
584C4×D4—228no—
585C4×D4—228no—
586#117—114no—
587#117—222no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—114no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—228no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4—221no—
596C2×C4⋊C4—221no—
597C2×C4⋊C4—221no—
598C2×C4⋊C4—221no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4C22×D1111yescharacteristic
601C2×C4⋊C4C22×D1111yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—228no—
605C2×C22⋊C4—221no—
606C2×C22⋊C4—221no—
607C2×C22⋊C4—221no—
608C2×C22⋊C4—221no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C42—221no—
613#107—114no—
614#107C22×D1114yescomplemented
615#106—114no—
616#106—114no—
617#103—114no—
618#103—114no—
619#103—114no—
620#103—114no—
621#103—114no—
622#103C22×D1114yescomplemented
623#102—114no—
624#102C22×D1114yescomplemented
625C2×C11—42no—
626C2×C11—82no—
627C2×C11#305614yescomplemented
628C2×C11C22×#12111yescharacteristic
629C2×C11C22×#13711yescharacteristic
630C2×C11C2×#57511yescharacteristic
631D11—24no—
632D11—24no—
633C24—21no—
634C24—111no—
635C24—111no—
636C24—114no—
637C24—224no—
638C24—224no—
639C24—442no—
640C24D4×D1111yescharacteristic
641#41—228no—
642#41—228no—
643#41—448no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—112no—
648C2×Q8—112no—
649C2×Q8—224no—
650C2×Q8—228no—
651C2×Q8—228no—
652C2×Q8—221no—
653C2×Q8—221no—
654C2×Q8—222no—
655C2×Q8—222no—
656C2×Q8—222no—
657C2×Q8—222no—
658C2×Q8—444no—
659C2×Q8—448no—
660C2×Q8C23×D1112yes—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—21no—
664C2×D4—22no—
665C2×D4—44no—
666C2×D4—224no—
667C2×D4—224no—
668C2×D4—444no—
669C2×D4—444no—
670C2×D4C23×D1112yes—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—111no—
677C22×C4—112no—
678C22×C4—114no—
679C22×C4—114no—
680C22×C4—112no—
681C22×C4—114no—
682C22×C4—111no—
683C22×C4—114no—
684C22×C4—114no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—228no—
688C22×C4—224no—
689C22×C4—2216no—
690C22×C4—228no—
691C22×C4—224no—
692C22×C4—224no—
693C22×C4—224no—
694C22×C4—224no—
695C22×C4—224no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—444no—
703C22×C4—444no—
704C22×C4—444no—
705C22×C4D4×D1112yes—
706C22×C4D4×D1111yescharacteristic
707C22×C4C23×D1112yes—
708C22×C4C23×D1111yescharacteristic
709Q16—228no—
710Q16—228no—
711SD16—28no—
712SD16—228no—
713M16—28no—
714M16—1116no—
715M16—228no—
716M16—228no—
717C2×C8—22no—
718C2×C8—114no—
719C2×C8—112no—
720C2×C8—112no—
721C2×C8—228no—
722C2×C8—222no—
723C2×C8—228no—
724C2×C8D4×D1114yes—
725C2×C8C23×D1112yes—
726C2×C8C23×D1112yes—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—112no—
731C4⋊C4—112no—
732C4⋊C4—224no—
733C4⋊C4—224no—
734C4⋊C4—224no—
735C4⋊C4—224no—
736C4⋊C4—221no—
737C4⋊C4—221no—
738C4⋊C4—224no—
739C4⋊C4—224no—
740C4⋊C4C23×D1112yes—
741C4⋊C4C23×D1112yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—224no—
745C22⋊C4—224no—
746C22⋊C4—224no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C42—224no—
752C11C2×#305611yescharacteristic, complemented, Sylow
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—114no—
761C23—114no—
762C23—112no—
763C23—112no—
764C23—228no—
765C23—228no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—444no—
771C23—4416no—
772C23C2×D4×D1112yes—
773C23C2×D4×D1111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—42no—
777Q8—222no—
778Q8—222no—
779Q8—222no—
780Q8—222no—
781Q8—448no—
782Q8—442no—
783Q8—442no—
784D4—22no—
785D4—22no—
786D4—48no—
787D4—42no—
788D4—448no—
789D4—448no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—114no—
801C2×C4—112no—
802C2×C4—118no—
803C2×C4—114no—
804C2×C4—114no—
805C2×C4—112no—
806C2×C4—228no—
807C2×C4—228no—
808C2×C4—228no—
809C2×C4—222no—
810C2×C4—224no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—448no—
818C2×C4—448no—
819C2×C4—448no—
820C2×C4—442no—
821C2×C4—442no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4C2×D4×D1112yes—
825C2×C4C2×D4×D1111yescharacteristic
826C2×C4C2×D4×D1112yes—
827C2×C4#41×D1112yes—
828C2×C4C24×D1111yescharacteristic
829C8—22no—
830C8—114no—
831C8—222no—
832C8C2×D4×D1114yes—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—84no—
841C22—114no—
842C22—114no—
843C22—222no—
844C22—222no—
845C22—222no—
846C22—228no—
847C22—228no—
848C22—222no—
849C22—4416no—
850C22D11×#12112yes—
851C22#1062330412yes—
852C22D11×#13712yes—
853C22C22×D4×D1111yescharacteristic
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—114no—
859C4—222no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C4D11×#12112yes—
865C4C22×D4×D1111yescharacteristic
866C4C2×#41×D1111yescharacteristic
867C2—42no—
868C2—82no—
869C2—224no—
870C2—224no—
871C2#1307824114yesdirect product factor
872C2C2×D11×#12111yescharacteristic
873C2C2×D11×#13711yescharacteristic
874C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
prime radicalC2×#10623137C2
hypercenterC2×#468D11
hypocenterC11C2×#3056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×#66968C2semidirect
2. C22×M16×D11C2semidirect
4. C2×D11×C22⋊Q8C2semidirect
5. #13078241C2direct (N × H)
6. C2×#10622750C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622655C2semidirect
9. C2×#10622500C2semidirect
10. C2×#10622426C2semidirect
11. C2×#10622391C2semidirect
12. C2×#10622784C2semidirect
13. C2×#10622494C2semidirect
14. C2×#10622384C2semidirect
15. C2×#10622415C2semidirect
16. C2×C11×#468C2semidirect
20. C22×C11×SD16C22semidirect
25. C22×#4326C22semidirect
29. C22×#4324C22semidirect
34. C2×#66968C22semidirect
36. C2×M16×D11C22semidirect
37. C22×Dic44C22semidirect
43. D11×C22⋊Q8C22semidirect
56. C11×#468C22semidirect
57. C2×C11×#107C22semidirect
58. C2×C11×#103C22semidirect
59. C2×C11×#102C22semidirect
60. C2×#66899C22semidirect
61. C2×#66896C22semidirect
62. #10622784C22semidirect
63. #10622750C22semidirect
64. C2×#66881C22semidirect
65. C2×#66880C22semidirect
66. C2×#66880C22semidirect
67. #10622665C22semidirect
68. #10622655C22semidirect
69. C2×#66874C22semidirect
70. C2×#66874C22semidirect
71. C2×#66872C22semidirect
72. C2×#66871C22semidirect
73. #10622500C22semidirect
74. #10622494C22semidirect
75. #10622426C22semidirect
76. #10622415C22semidirect
77. #10622391C22semidirect
78. #10622384C22semidirect
110. C2×C11×SD16C23semidirect
130. C2×#4326C23semidirect
136. C2×#4324C23semidirect
161. C2×Dic44C23semidirect
163. C2×#4313D4semidirect
184. C11×#107C23semidirect
185. C11×#103C23semidirect
186. C11×#102C23semidirect
187. #66899C23semidirect
188. #66896C23semidirect
189. #66881C23semidirect
190. #66880C23semidirect
191. #66880C23semidirect
192. #66874C23semidirect
193. #66874C23semidirect
194. #66872C23semidirect
195. #66871C23semidirect
313. #4313C2×D4semidirect
324. C2×#468D11semidirect
350. C22×D11#137semidirect
420. C22×SD16C2×D11semidirect
454. #468C2×D11semidirect
461. C2×#107C2×D11semidirect
471. C2×#103C2×D11semidirect
473. C2×#102C2×D11semidirect
494. C2×D11C2×#137semidirect
546. C2×SD16C22×D11semidirect
614. #107C22×D11semidirect
622. #103C22×D11semidirect
624. #102C22×D11semidirect
627. C2×C11#3056semidirect
752. C11C2×#3056semidirect
871. C2#13078241direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C22×M16×D112
C2×#106231372
C2×D11×C22⋊Q82
#130782412
C2×#106227502
C2×#106226652
C2×#106226552
C2×#106225002
C2×#106224262
C2×#106223912
C2×#106227842
C2×#106224942
C2×#106223842
C2×#106224152
C2×C11×#4682
C2×#305611