Finite Group Databasebeta

← C2×#13080766 #15630453

Subgroups — C2×#13080766 #15630453

Order 2816.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic, complemented
2#13080766C2116yesmaximal, direct product factor
3C2×#10622702C211yesmaximal, characteristic, complemented
4C2×#10622609C211yesmaximal, characteristic, complemented
5C2×#10622616C211yesmaximal, characteristic, complemented
6C2×#10622700C211yesmaximal, characteristic, complemented
7C2×#10622655C211yesmaximal, characteristic, complemented
8C2×#10622651C211yesmaximal, characteristic, complemented
9C2×#10622629C211yesmaximal, characteristic, complemented
10C2×#10622650C211yesmaximal, characteristic, complemented
11C2×#10622649C211yesmaximal, characteristic, complemented
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622614C211yesmaximal, characteristic, complemented
15C2×#10622615C211yesmaximal, characteristic, complemented
16C2×C11×#555C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C11×#555—24no—
20C11×#555C2218yescomplemented
21C2×C11×C4⋊Q8C2211yescharacteristic, complemented
22C2×C11×#124—21no—
23C2×C11×#124—21no—
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic, complemented
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C2×C11×#117—21no—
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic, complemented
32C2×#66990—21no—
33C22×#4324C2211yescharacteristic, complemented
34C22×#4323C2211yescharacteristic
35C22×#4323C2211yescharacteristic
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C23×C11⋊C8C2211yescharacteristic, complemented
40#10623081—24no—
41#10623081C2218yescomplemented
42C2×#66947—21no—
43C2×#66937—21no—
44C2×C22⋊C4×D11—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66896C2211yescharacteristic, complemented
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
50#10622702C2218yescomplemented
51#10622700C2218yescomplemented
52#10622655C2218yescomplemented
53#10622651C2218yescomplemented
54#10622650C2218yescomplemented
55#10622649C2218yescomplemented
56#10622629C2218yescomplemented
57#10622627C2218yescomplemented
58#10622624C2218yescomplemented
59#10622616C2218yescomplemented
60#10622615C2218yescomplemented
61#10622614C2218yescomplemented
62#10622609C2218yescomplemented
63C2×#66874C2211yescharacteristic, complemented
64C2×#66874C2211yescharacteristic, complemented
65C2×#66874C2211yescharacteristic, complemented
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66873C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71C2×#66873C2211yescharacteristic
72C2×#66872C2211yescharacteristic, complemented
73C2×#66871C2211yescharacteristic, complemented
74C2×#66871C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×#66867C2211yescharacteristic, complemented
77C24×D11—21no—
78C22×Q8×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11D411yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C2×#4339—22no—
89C2×#4339—24no—
90C2×#4339—42no—
91C2×#4339C2314yes—
92C22×D44—24no—
93C22×D44—21no—
94C22×D44—22no—
95C22×D44—42no—
96C22×D44C2311yescharacteristic
97C22×D44C2314yes—
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×Dic22C2311yescharacteristic
102C11×C4⋊Q8—22no—
103C11×C4⋊Q8C2314yescomplemented
104C11×#124—28no—
105C11×#124—28no—
106C11×#121—28no—
107C11×#121—22no—
108C11×#121—22no—
109C11×#121C2314yes—
110C11×#121C2314yescomplemented
111C4×D4×C11—22no—
112C4×D4×C11D414yes—
113C4×D4×C11C2314yes—
114C4×D4×C11C2314yescomplemented
115C11×#117—22no—
116C11×#117—22no—
117C11×#117—28no—
118C11×#117C2314yes—
119C11×#117C2314yescomplemented
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C22⋊C4—21no—
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4D411yescharacteristic
131C2×C11×C22⋊C4D411yescharacteristic
132C2×C42×C11—21no—
133C2×C42×C11—21no—
134C2×C42×C11C2311yescharacteristic
135C2×C22⋊Dic11—21no—
136#66990—28no—
137C2×#4324—42no—
138C2×#4324C2314yescomplemented
139C2×#4323—24no—
140C2×#4323—42no—
141C2×#4323C2314yes—
142C2×#4323C2314yes—
143#66983—22no—
144#66983C2314yes—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×C4⋊Dic11C2311yescharacteristic
150#66977—22no—
151#66977C2314yes—
152C2×Dic11⋊C4—21no—
153C2×#4318—42no—
154C2×#4318C2314yes—
155C22×C11⋊C8—42no—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2314yescomplemented
161#66947—28no—
162#66937—28no—
163C22⋊C4×D11—28no—
164#66928—22no—
165#66928C2314yes—
166C4×D44—22no—
167C4×D44C2314yes—
168#66896C2314yescomplemented
169C22⋊(C11⋊C8)C2314yes—
170C22⋊(C11⋊C8)C2314yescomplemented
171#66874C2314yescomplemented
172#66874C2314yescomplemented
173#66874C2314yescomplemented
174#66873C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182#66871C2314yescomplemented
183C4⋊(C11⋊C8)C2314yescomplemented
184#66867C2314yescomplemented
185C2×#3319—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—24no—
192C23×D11—44no—
193C23×D11—44no—
194C23×D11—82no—
195C2×Q8×C11—24no—
196C2×Q8×C11—82no—
197C2×D4×C11—24no—
198C2×D4×C11—24no—
199C2×D4×C11—21no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—42no—
203C2×D4×C11—82no—
204C2×D4×C11—82no—
205C2×D4×C11C2×D414yes—
206C2×D4×C11C2412yes—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—24no—
215C22×C4×C11—44no—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—82no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231#4339—28no—
232#4339—44no—
233#4339—48no—
234C2×D44—28no—
235C2×D44—21no—
236C2×D44—21no—
237C2×D44—24no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44—44no—
242C2×D44—44no—
243C2×D44—48no—
244C2×D44#4114yes—
245C2×D44C2412yes—
246C2×D44C2412yes—
247C2×C4×D11—24no—
248C2×C4×D11—24no—
249C2×C4×D11—44no—
250C2×C4×D11—82no—
251C2×Dic22—21no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22C2412yes—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—21no—
258C11×C4⋊C4—21no—
259C11×C4⋊C4C2×D414yes—
260C11×C4⋊C4C2412yes—
261C11×C4⋊C4C2412yes—
262C11×C4⋊C4C2412yes—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4C2×D414yes—
269C11×C22⋊C4C2×D414yes—
270C42×C11—24no—
271C42×C11—24no—
272C42×C11C2×D412yes—
273C42×C11C2412yes—
274C22⋊Dic11—24no—
275#4324—44no—
276#4323—28no—
277#4323—44no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282C4⋊Dic11—21no—
283C4⋊Dic11C2412yes—
284Dic11⋊C4—24no—
285#4318—44no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—44no—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295C2×#555D1111yescharacteristic, complemented
296C2×#546—111no—
297#3319—1116no—
298C2×#489—111no—
299C2×#485—111no—
300C2×#482—111no—
301C2×#474—111no—
302C2×#468—111no—
303C2×#466—111no—
304C2×#463—111no—
305C2×#449—111no—
306C2×#447—111no—
307C2×#442—111no—
308C2×#435—111no—
309C2×#418—111no—
310C2×#416—111no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11C22×D412yes—
322C23×C11C22×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—24no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—48no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—48no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—84no—
335C22×D11—816no—
336Q8×C11—84no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—44no—
340D4×C11—42no—
341D4×C11—84no—
342D4×C11—84no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—24no—
348C2×C4×C11—24no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—48no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×C4×C11C22×D412yes—
361C2×C4×C11C22×D412yes—
362C2×C4×C11C22×D412yes—
363C2×C4×C11C22×D412yes—
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C2×#4112yes—
366C2×C4×C11H(5,𝔽2)12yes—
367C2×C4×C11C2511yescharacteristic
368C22⋊D11—48no—
369C22⋊D11—84no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374D44—24no—
375D44—22no—
376D44—22no—
377D44—22no—
378D44—48no—
379D44—42no—
380D44C2×#4114yes—
381C4×D11—48no—
382C4×D11—84no—
383Dic22—22no—
384Dic22—22no—
385Dic22—42no—
386C11⋊C8—22no—
387C11⋊C8—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C22×#41—111no—
391C23×D4—111no—
392C22×SD16—111no—
393C22×D8—111no—
394C22×D8—111no—
395C22×M16—111no—
396C23×C8—111no—
397#555—24no—
398#555C2×D1118yescomplemented
399#546—118no—
400#546—224no—
401C2×C4⋊Q8C2×D1111yescharacteristic, complemented
402C2×#124—21no—
403C2×#124—21no—
404C2×#124—111no—
405C2×#123—221no—
406C2×C22⋊Q8—111no—
407C2×#121—21no—
408C2×#121—111no—
409C2×#121—221no—
410C2×#121C2×D1111yescharacteristic
411C2×#121C2×D1111yescharacteristic, complemented
412C2×#120—221no—
413C2×C4×D4—111no—
414C2×C4×D4C2×D1111yescharacteristic
415C2×C4×D4C2×D1111yescharacteristic, complemented
416C2×#117—21no—
417C2×#117C2×D1111yescharacteristic
418C2×#117C2×D1111yescharacteristic, complemented
419C22×C22⋊C4—221no—
420#489—118no—
421#485—118no—
422#482—118no—
423#474—118no—
424#468—118no—
425#466—118no—
426#463—118no—
427#449—118no—
428#447—118no—
429#442—118no—
430#435—118no—
431C2×#107—111no—
432C2×#107—111no—
433C2×#106—111no—
434C2×C4⋊C8—111no—
435#418—118no—
436#416—118no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103—111no—
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×C22⋊C8—111no—
448C2×C22⋊C8—111no—
449C2×#97—111no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—44no—
457C22×C11—44no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—84no—
462C22×C11#54612yes—
463C22×C11#57512yes—
464C22×C11#57612yes—
465C22×C11C23×D411yescharacteristic
466C2×D11—24no—
467C2×D11—48no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—816no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11—22no—
479C4×C11—42no—
480C4×C11—42no—
481C4×C11—42no—
482C4×C11#54612yes—
483C4×C11C22×#4111yescharacteristic
484C4×C11C2×H(5,𝔽2)11yescharacteristic
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C2×#41—114no—
489C2×#41—224no—
490C2×#41—222no—
491C2×#41—442no—
492C22×Q8—21no—
493C22×Q8—111no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—114no—
499C22×D4—224no—
500C22×D4—221no—
501C22×D4—221no—
502C22×D4—221no—
503C22×D4—222no—
504C22×D4—442no—
505C22×D4C22⋊D1111yescharacteristic
506C22×D4C22×D1111yescharacteristic
507C23×C4—21no—
508C23×C4—221no—
509C23×C4—221no—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512C2×SD16—114no—
513C2×SD16—442no—
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—224no—
517C2×D8—442no—
518C2×M16—114no—
519C2×M16—442no—
520C22×C8—111no—
521C22×C8—111no—
522C22×C8—111no—
523C22×C8—111no—
524C22×C8—114no—
525C22×C8—442no—
526C4⋊Q8—22no—
527C4⋊Q8C22×D1114yescomplemented
528#124—28no—
529#124—28no—
530#124—114no—
531#124—222no—
532#123—228no—
533C22⋊Q8—114no—
534C22⋊Q8—222no—
535#121—28no—
536#121—22no—
537#121—22no—
538#121—114no—
539#121—222no—
540#121—228no—
541#121C22×D1114yes—
542#121C22×D1114yescomplemented
543#120—228no—
544C4×D4—22no—
545C4×D4—114no—
546C4×D4—222no—
547C4×D4C22⋊D1114yes—
548C4×D4C22×D1114yes—
549C4×D4C22×D1114yescomplemented
550#117—22no—
551#117—22no—
552#117—28no—
553#117C22×D1114yes—
554#117C22×D1114yescomplemented
555C2×C4⋊C4—21no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—221no—
558C2×C4⋊C4C22⋊D1111yescharacteristic
559C2×C4⋊C4C22×D1111yescharacteristic
560C2×C4⋊C4C22×D1111yescharacteristic
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—228no—
573C2×C22⋊C4C22⋊D1111yescharacteristic
574C2×C22⋊C4C22⋊D1111yescharacteristic
575C2×C42—21no—
576C2×C42—21no—
577C2×C42C22×D1111yescharacteristic
578#107—114no—
579#107—114no—
580#106—114no—
581C4⋊C8—114no—
582#103—114no—
583#103—114no—
584#103—114no—
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590#102—114no—
591#102—114no—
592C22⋊C8—114no—
593C22⋊C8—114no—
594#97—114no—
595C2×C11—42no—
596C2×C11—42no—
597C2×C11—82no—
598C2×C11#331914yescomplemented
599C2×C11C2×#54611yescharacteristic
600C2×C11C2×#57511yescharacteristic
601C2×C11C2×#57611yescharacteristic
602D11—44no—
603D11—82no—
604C24—21no—
605C24—221no—
606C24—221no—
607C24—224no—
608C24—444no—
609C24—444no—
610C24—882no—
611C24C2×C22⋊D1111yescharacteristic
612C24C2×C22⋊D1111yescharacteristic
613#41—228no—
614#41—444no—
615#41—448no—
616C2×Q8—24no—
617C2×Q8—82no—
618C2×Q8—112no—
619C2×Q8—221no—
620C2×Q8—222no—
621C2×Q8—222no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—82no—
629C2×D4—82no—
630C2×D4—114no—
631C2×D4—112no—
632C2×D4—112no—
633C2×D4—228no—
634C2×D4—224no—
635C2×D4—224no—
636C2×D4—222no—
637C2×D4—222no—
638C2×D4—222no—
639C2×D4—221no—
640C2×D4—224no—
641C2×D4—221no—
642C2×D4—444no—
643C2×D4—448no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—882no—
647C2×D4C2×C22⋊D1114yes—
648C2×D4C23×D1112yes—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—44no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—444no—
663C22×C4—882no—
664C22×C4C2×C22⋊D1112yes—
665C22×C4C2×C22⋊D1112yes—
666C22×C4C2×C22⋊D1111yescharacteristic
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669C22×C4C2×C22⋊D1111yescharacteristic
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—444no—
674D8—228no—
675D8—444no—
676M16—444no—
677C2×C8—112no—
678C2×C8—112no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—222no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8—222no—
685C2×C8—444no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—112no—
691C4⋊C4—221no—
692C4⋊C4—224no—
693C4⋊C4C2×C22⋊D1114yes—
694C4⋊C4C23×D1112yes—
695C4⋊C4C23×D1112yes—
696C4⋊C4C23×D1112yes—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4C2×C22⋊D1114yes—
708C22⋊C4C2×C22⋊D1114yes—
709C42—24no—
710C42—24no—
711C42C2×C22⋊D1112yes—
712C42C23×D1112yes—
713C11C2×#331911yescharacteristic, complemented, Sylow
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—224no—
725C23—222no—
726C23—222no—
727C23—448no—
728C23—448no—
729C23—442no—
730C23—442no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23—884no—
735C23—8816no—
736C23C22×C22⋊D1112yes—
737C23C22×C22⋊D1112yes—
738C23C22×C22⋊D1111yescharacteristic
739Q8—84no—
740Q8—222no—
741Q8—222no—
742Q8—442no—
743D4—22no—
744D4—22no—
745D4—44no—
746D4—42no—
747D4—84no—
748D4—84no—
749D4—114no—
750D4—224no—
751D4—222no—
752D4—222no—
753D4—222no—
754D4—448no—
755D4—448no—
756D4—442no—
757D4—884no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—48no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—448no—
778C2×C4—442no—
779C2×C4—442no—
780C2×C4—884no—
781C2×C4#41×D1112yes—
782C2×C4#6704212yes—
783C2×C4C22×C22⋊D1112yes—
784C2×C4C22×C22⋊D1112yes—
785C2×C4C22×C22⋊D1112yes—
786C2×C4C22×C22⋊D1112yes—
787C2×C4C22×C22⋊D1111yescharacteristic
788C2×C4C24×D1111yescharacteristic
789C8—222no—
790C8—222no—
791C8—222no—
792C8—222no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—84no—
805C22—224no—
806C22—448no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—442no—
812C22—8816no—
813C22—884no—
814C22#1062335312yes—
815C22#1062336012yes—
816C22#1062336612yes—
817C22C23×C22⋊D1111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—442no—
826C4—442no—
827C4#1062336012yes—
828C4C2×#41×D1111yescharacteristic
829C4C2×#6704211yescharacteristic
830C2—42no—
831C2—42no—
832C2—82no—
833C2—444no—
834C2—882no—
835C2#1308076614yesdirect product factor
836C2C2×#1062336011yescharacteristic
837C2C2×#1062335311yescharacteristic
838C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11C2×#3319
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#10623081C2semidirect
2. #13080766C2direct (N × H)
3. C2×#10622702C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622700C2semidirect
7. C2×#10622655C2semidirect
8. C2×#10622651C2semidirect
9. C2×#10622629C2semidirect
10. C2×#10622650C2semidirect
11. C2×#10622649C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622614C2semidirect
15. C2×#10622615C2semidirect
16. C2×C11×#555C2semidirect
20. C11×#555C22semidirect
21. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×#121C22semidirect
28. C2×C4×D4×C11C22semidirect
31. C2×C11×#117C22semidirect
33. C22×#4324C22semidirect
39. C23×C11⋊C8C22semidirect
41. #10623081C22semidirect
47. C2×#66896C22semidirect
49. C2×C22⋊(C11⋊C8)C22semidirect
50. #10622702C22semidirect
51. #10622700C22semidirect
52. #10622655C22semidirect
53. #10622651C22semidirect
54. #10622650C22semidirect
55. #10622649C22semidirect
56. #10622629C22semidirect
57. #10622627C22semidirect
58. #10622624C22semidirect
59. #10622616C22semidirect
60. #10622615C22semidirect
61. #10622614C22semidirect
62. #10622609C22semidirect
63. C2×#66874C22semidirect
64. C2×#66874C22semidirect
65. C2×#66874C22semidirect
72. C2×#66872C22semidirect
73. C2×#66871C22semidirect
74. C2×#66871C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×#66867C22semidirect
103. C11×C4⋊Q8C23semidirect
110. C11×#121C23semidirect
114. C4×D4×C11C23semidirect
119. C11×#117C23semidirect
138. C2×#4324C23semidirect
160. C22×C11⋊C8C23semidirect
168. #66896C23semidirect
170. C22⋊(C11⋊C8)C23semidirect
171. #66874C23semidirect
172. #66874C23semidirect
173. #66874C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
182. #66871C23semidirect
183. C4⋊(C11⋊C8)C23semidirect
184. #66867C23semidirect
295. C2×#555D11semidirect
398. #555C2×D11semidirect
401. C2×C4⋊Q8C2×D11semidirect
411. C2×#121C2×D11semidirect
415. C2×C4×D4C2×D11semidirect
418. C2×#117C2×D11semidirect
527. C4⋊Q8C22×D11semidirect
542. #121C22×D11semidirect
549. C4×D4C22×D11semidirect
554. #117C22×D11semidirect
598. C2×C11#3319semidirect
713. C11C2×#3319semidirect
835. C2#13080766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230812
#130807662
C2×#106227022
C2×#106226092
C2×#106226162
C2×#106227002
C2×#106226552
C2×#106226512
C2×#106226292
C2×#106226502
C2×#106226492
C2×#106226272
C2×#106226242
C2×#106226142
C2×#106226152
C2×C11×#5552
C2×#331911