Finite Group Databasebeta

← C2×#13079468 #15624426

Subgroups — C2×#13079468 #15624426

Order 2816.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic, complemented
2#13079468C2116yesmaximal, direct product factor
3C2×#10622647C211yesmaximal, characteristic, complemented
4C2×#10622609C211yesmaximal, characteristic, complemented
5C2×#10622616C211yesmaximal, characteristic, complemented
6C2×#10622646C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622655C211yesmaximal, characteristic, complemented
9C2×#10622651C211yesmaximal, characteristic, complemented
10C2×#10622654C211yesmaximal, characteristic, complemented
11C2×#10622650C211yesmaximal, characteristic, complemented
12C2×#10622650C211yesmaximal, characteristic, complemented
13C2×#10622831C211yesmaximal, characteristic, complemented
14C2×#10622830C211yesmaximal, characteristic, complemented
15C2×#10622847C211yesmaximal, characteristic, complemented
16C2×C11×#535C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×#4339C2211yescharacteristic, complemented
20C11×#535—24no—
21C11×#535C2218yescomplemented
22C2×C11×#127—21no—
23C2×C11×#124—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#120—21no—
29C2×C11×#120—21no—
30C2×C11×#117C2211yescharacteristic
31#10623364—24no—
32#10623364C2218yescomplemented
33C2×#66999—21no—
34C2×#66992—21no—
35C2×#66992—21no—
36C2×#66991—21no—
37C22×#4324C2211yescharacteristic
38C22×#4324C2211yescharacteristic
39C22×#4323C2211yescharacteristic
40C22×#4323C2211yescharacteristic
41C2×#66983C2211yescharacteristic
42C2×#66983C2211yescharacteristic, complemented
43C22×C4⋊Dic11C2211yescharacteristic, complemented
44C2×#66977C2211yescharacteristic
45C2×#66977C2211yescharacteristic, complemented
46C22×#4318C2211yescharacteristic, complemented
47C23×C11⋊C8C2211yescharacteristic, complemented
48#10622847C2218yescomplemented
49#10622831C2218yescomplemented
50#10622830C2218yescomplemented
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56C2×C22⋊(C11⋊C8)C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622655C2218yescomplemented
60#10622654C2218yescomplemented
61#10622652C2218yescomplemented
62#10622651C2218yescomplemented
63#10622650C2218yescomplemented
64#10622650C2218yescomplemented
65#10622647C2218yescomplemented
66#10622646C2218yescomplemented
67#10622616C2218yescomplemented
68#10622609C2218yescomplemented
69C2×#66874C2211yescharacteristic, complemented
70C2×#66874C2211yescharacteristic, complemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66873C2211yescharacteristic, complemented
73C2×#66872C2211yescharacteristic, complemented
74C2×#66872C2211yescharacteristic, complemented
75C2×#66871C2211yescharacteristic, complemented
76C2×#66871C2211yescharacteristic, complemented
77C25×C11—21no—
78C2×C11×#41—42no—
79C2×C11×#41—42no—
80C2×C11×#41D414yes—
81C2×C11×#41C2314yes—
82C22×Q8×C11D411yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—22no—
89C22×D4×C11—42no—
90C22×D4×C11—42no—
91C22×D4×C11D411yescharacteristic
92C22×D4×C11D411yescharacteristic
93C22×D4×C11D411yescharacteristic
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2311yescharacteristic
96C22×D4×C11C2314yes—
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C22×C22⋊D11—21no—
101C22×C22⋊D11—21no—
102C22×C22⋊D11—21no—
103C23×Dic11—21no—
104C2×#4339—22no—
105C2×#4339—42no—
106C2×#4339—42no—
107C2×#4339C2314yescomplemented
108C22×D44C2311yescharacteristic
109C22×C4×D11—21no—
110C22×Dic22C2311yescharacteristic
111C11×#127—28no—
112C11×#124—28no—
113C11×#121—22no—
114C11×#121—22no—
115C11×#121—22no—
116C11×#121—22no—
117C11×#121C2314yes—
118C11×#121C2314yes—
119C11×#121C2314yes—
120C11×#121C2314yes—
121C11×#120—28no—
122C11×#120—28no—
123C11×#117—22no—
124C11×#117C2314yes—
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4—21no—
128C2×C11×C22⋊C4—21no—
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C42×C11—21no—
133C2×C22⋊Dic11—21no—
134C2×C22⋊Dic11—21no—
135#66999—28no—
136#66992—28no—
137#66992—28no—
138#66991—28no—
139C2×#4324—42no—
140C2×#4324—42no—
141C2×#4324C2314yes—
142C2×#4324C2314yes—
143C2×#4323—42no—
144C2×#4323—42no—
145C2×#4323C2314yes—
146C2×#4323C2314yes—
147#66983—22no—
148#66983—22no—
149#66983C2314yes—
150#66983C2314yescomplemented
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153C2×C4⋊Dic11—21no—
154C2×C4⋊Dic11—22no—
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2311yescharacteristic
157C2×C4⋊Dic11C2314yescomplemented
158#66977—22no—
159#66977—22no—
160#66977C2314yes—
161#66977C2314yescomplemented
162C2×Dic11⋊C4—21no—
163C2×Dic11⋊C4—21no—
164C2×#4318—42no—
165C2×#4318C2314yescomplemented
166C22×C11⋊C8—42no—
167C22×C11⋊C8C2311yescharacteristic
168C22×C11⋊C8C2311yescharacteristic
169C22×C11⋊C8C2311yescharacteristic
170C22×C11⋊C8C2311yescharacteristic
171C22×C11⋊C8C2314yescomplemented
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176C22⋊(C11⋊C8)C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yescomplemented
179C22⋊(C11⋊C8)C2314yescomplemented
180#66874C2314yescomplemented
181#66874C2314yescomplemented
182#66873C2314yescomplemented
183#66873C2314yescomplemented
184#66872C2314yescomplemented
185#66872C2314yescomplemented
186#66871C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3198—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—24no—
192C24×C11—44no—
193C24×C11—82no—
194C24×C11—82no—
195C24×C11C2×D411yescharacteristic
196C24×C11C2×D411yescharacteristic
197C24×C11C2×D411yescharacteristic
198C23×D11—21no—
199C11×#41—48no—
200C11×#41—44no—
201C11×#41—44no—
202C2×Q8×C11—42no—
203C2×Q8×C11C2×D414yes—
204C2×D4×C11—24no—
205C2×D4×C11—24no—
206C2×D4×C11—24no—
207C2×D4×C11—24no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—24no—
211C2×D4×C11—22no—
212C2×D4×C11—22no—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—44no—
216C2×D4×C11—44no—
217C2×D4×C11—42no—
218C2×D4×C11—42no—
219C2×D4×C11—42no—
220C2×D4×C11—44no—
221C2×D4×C11—48no—
222C2×D4×C11—82no—
223C2×D4×C11—82no—
224C2×D4×C11—82no—
225C2×D4×C11—82no—
226C2×D4×C11C2×D414yes—
227C2×D4×C11C2×D414yes—
228C2×D4×C11C2×D414yes—
229C2×D4×C11C2412yes—
230C2×D4×C11C2412yes—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C2×C22⋊D11—24no—
250C2×C22⋊D11—24no—
251C2×C22⋊D11—24no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—82no—
254C2×C22⋊D11—82no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—24no—
259C22×Dic11—82no—
260#4339—44no—
261#4339—44no—
262#4339—48no—
263C2×D44—21no—
264C2×D44—22no—
265C2×D44—22no—
266C2×D44C2412yes—
267C2×C4×D11—24no—
268C2×C4×D11—44no—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—22no—
272C2×Dic22C2412yes—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4C2412yes—
276C11×C4⋊C4C2412yes—
277C11×C22⋊C4—24no—
278C11×C22⋊C4—24no—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C42×C11—24no—
283C22⋊Dic11—24no—
284C22⋊Dic11—24no—
285#4324—44no—
286#4324—44no—
287#4323—44no—
288#4323—44no—
289(C2×D11)⋊C4—24no—
290(C2×D11)⋊C4—24no—
291C4⋊Dic11—21no—
292C4⋊Dic11—21no—
293C4⋊Dic11—24no—
294C4⋊Dic11C2412yes—
295C4⋊Dic11C2412yes—
296Dic11⋊C4—24no—
297Dic11⋊C4—24no—
298#4318—44no—
299C2×C11⋊C8—22no—
300C2×C11⋊C8—22no—
301C2×C11⋊C8—22no—
302C2×C11⋊C8—22no—
303C2×C11⋊C8—44no—
304C2×C11⋊C8C2412yes—
305C2×C11⋊C8C2412yes—
306C2×C11⋊C8C2412yes—
307C2×C11⋊C8C2412yes—
308C2×#537—111no—
309C2×#535D1111yescharacteristic, complemented
310#3198—1116no—
311C2×#481—111no—
312C2×#485—111no—
313C2×#482—111no—
314C2×#480—111no—
315C2×#469—111no—
316C2×#468—111no—
317C2×#466—111no—
318C2×#465—111no—
319C2×#449—111no—
320C2×#449—111no—
321C2×#450—111no—
322C2×#447—111no—
323C2×#408—111no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—48no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11—42no—
340C23×C11—42no—
341C23×C11—42no—
342C23×C11—84no—
343C23×C11—84no—
344C23×C11—816no—
345C23×C11C22×D412yes—
346C23×C11C22×D412yes—
347C23×C11C22×D412yes—
348C23×C11C22×D411yescharacteristic
349C22×D11—22no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353Q8×C11—44no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—44no—
359D4×C11—44no—
360D4×C11—44no—
361D4×C11—48no—
362D4×C11—42no—
363D4×C11—42no—
364D4×C11—84no—
365D4×C11—84no—
366D4×C11—84no—
367D4×C11—84no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—24no—
372C2×C4×C11—24no—
373C2×C4×C11—24no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—42no—
383C2×C4×C11—42no—
384C2×C4×C11C22×D412yes—
385C2×C4×C11C22×D412yes—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11H(5,𝔽2)12yes—
389C2×C4×C11H(5,𝔽2)12yes—
390C2×C4×C11C2511yescharacteristic
391C22⋊D11—48no—
392C22⋊D11—84no—
393C22⋊D11—84no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399C2×Dic11—42no—
400C2×Dic11—84no—
401D44—22no—
402D44—22no—
403D44—42no—
404C4×D11—48no—
405Dic22—22no—
406Dic22—22no—
407Dic22—42no—
408C11⋊C8—22no—
409C11⋊C8—22no—
410C11⋊C8—22no—
411C11⋊C8—22no—
412C22×#41—111no—
413C22×#41C2×D1111yescharacteristic
414C23×D4C2×D1111yescharacteristic
415C22×SD16—111no—
416C22×SD16—111no—
417C22×D8—111no—
418C22×D8—111no—
419C22×M16—111no—
420C23×C8—111no—
421#537—118no—
422#537—224no—
423#535—24no—
424#535C2×D1118yescomplemented
425C2×#127—21no—
426C2×#124—21no—
427C2×C22⋊Q8—111no—
428C2×C22⋊Q8—111no—
429C2×C22⋊Q8—221no—
430C2×#121—111no—
431C2×#121—111no—
432C2×#121—221no—
433C2×#121—221no—
434C2×#121—221no—
435C2×#121C2×D1111yescharacteristic
436C2×#121C2×D1111yescharacteristic
437C2×#121C2×D1111yescharacteristic
438C2×#121C2×D1111yescharacteristic
439C2×#120—21no—
440C2×#120—21no—
441C2×#117C2×D1111yescharacteristic
442C22×C4⋊C4—111no—
443#485—118no—
444#482—118no—
445#481—118no—
446#480—118no—
447#469—118no—
448#468—118no—
449#466—118no—
450#465—118no—
451#450—118no—
452#449—118no—
453#449—118no—
454#447—118no—
455C2×#107—111no—
456C2×#107—111no—
457C2×#106—111no—
458C2×#106—111no—
459C2×#103—111no—
460C2×#103—111no—
461C2×#102—111no—
462C2×#102—111no—
463C2×#102—111no—
464C2×#102—111no—
465C2×#102—111no—
466C2×#102—111no—
467#408—118no—
468C2×C22⋊C8—111no—
469C2×C22⋊C8—111no—
470C2×C22⋊C8—111no—
471C2×C22⋊C8—111no—
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—44no—
482C22×C11—44no—
483C22×C11—44no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—816no—
491C22×C11—84no—
492C22×C11—84no—
493C22×C11#53412yes—
494C22×C11#57612yes—
495C22×C11#57712yes—
496C22×C11C23×D411yescharacteristic
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—84no—
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11#53412yes—
507C4×C11C2×H(5,𝔽2)11yescharacteristic
508C4×C11C2×H(5,𝔽2)11yescharacteristic
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—21no—
513C2×#41—42no—
514C2×#41—42no—
515C2×#41—114no—
516C2×#41—222no—
517C2×#41—442no—
518C2×#41—442no—
519C2×#41C22⋊D1114yes—
520C2×#41C22×D1114yes—
521C22×Q8—111no—
522C22×Q8C22⋊D1111yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—42no—
530C22×D4—42no—
531C22×D4—111no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4—221no—
535C22×D4C22⋊D1111yescharacteristic
536C22×D4C22⋊D1111yescharacteristic
537C22×D4C22⋊D1111yescharacteristic
538C22×D4C22×D1111yescharacteristic
539C22×D4C22×D1111yescharacteristic
540C22×D4C22×D1114yes—
541C23×C4—221no—
542C23×C4—221no—
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C2×SD16—114no—
547C2×SD16—114no—
548C2×SD16—442no—
549C2×SD16—442no—
550C2×D8—114no—
551C2×D8—114no—
552C2×D8—442no—
553C2×D8—442no—
554C2×M16—114no—
555C2×M16—442no—
556C22×C8—111no—
557C22×C8—111no—
558C22×C8—111no—
559C22×C8—111no—
560C22×C8—114no—
561C22×C8—442no—
562#127—28no—
563#124—28no—
564C22⋊Q8—114no—
565C22⋊Q8—114no—
566C22⋊Q8—228no—
567C22⋊Q8—222no—
568C22⋊Q8—222no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—114no—
574#121—114no—
575#121—228no—
576#121—228no—
577#121—228no—
578#121—222no—
579#121—222no—
580#121C22×D1114yes—
581#121C22×D1114yes—
582#121C22×D1114yes—
583#121C22×D1114yes—
584#120—28no—
585#120—28no—
586#117—22no—
587#117C22×D1114yes—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—114no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C4⋊C4C22×D1111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C22⋊C4—221no—
606C2×C42—21no—
607#107—114no—
608#107—114no—
609#106—114no—
610#106—114no—
611#103—114no—
612#103—114no—
613#102—114no—
614#102—114no—
615#102—114no—
616#102—114no—
617#102—114no—
618#102—114no—
619C22⋊C8—114no—
620C22⋊C8—114no—
621C22⋊C8—114no—
622C22⋊C8—114no—
623C2×C11—42no—
624C2×C11—42no—
625C2×C11—42no—
626C2×C11—82no—
627C2×C11—82no—
628C2×C11#319814yescomplemented
629C2×C11C2×#53411yescharacteristic
630C2×C11C2×#57611yescharacteristic
631C2×C11C2×#57711yescharacteristic
632D11—82no—
633C24—21no—
634C24—21no—
635C24—24no—
636C24—44no—
637C24—82no—
638C24—82no—
639C24—221no—
640C24C2×C22⋊D1111yescharacteristic
641C24C2×C22⋊D1111yescharacteristic
642C24C2×C22⋊D1111yescharacteristic
643#41—44no—
644#41—44no—
645#41—48no—
646#41—444no—
647#41—444no—
648#41—448no—
649C2×Q8—42no—
650C2×Q8—112no—
651C2×Q8—221no—
652C2×Q8—222no—
653C2×Q8—222no—
654C2×Q8C2×C22⋊D1114yes—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—24no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—44no—
672C2×D4—48no—
673C2×D4—82no—
674C2×D4—82no—
675C2×D4—82no—
676C2×D4—82no—
677C2×D4—112no—
678C2×D4—224no—
679C2×D4—224no—
680C2×D4—224no—
681C2×D4—222no—
682C2×D4—222no—
683C2×D4—221no—
684C2×D4—444no—
685C2×D4—882no—
686C2×D4—882no—
687C2×D4C2×C22⋊D1114yes—
688C2×D4C2×C22⋊D1114yes—
689C2×D4C2×C22⋊D1114yes—
690C2×D4C23×D1112yes—
691C2×D4C23×D1112yes—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—224no—
704C22×C4—224no—
705C22×C4—444no—
706C22×C4—882no—
707C22×C4C2×C22⋊D1112yes—
708C22×C4C2×C22⋊D1112yes—
709C22×C4C2×C22⋊D1112yes—
710C22×C4C2×C22⋊D1111yescharacteristic
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C23×D1112yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717SD16—444no—
718SD16—444no—
719D8—444no—
720D8—444no—
721M16—444no—
722C2×C8—112no—
723C2×C8—112no—
724C2×C8—112no—
725C2×C8—112no—
726C2×C8—222no—
727C2×C8—222no—
728C2×C8—222no—
729C2×C8—222no—
730C2×C8—444no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—112no—
734C4⋊C4—112no—
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—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C42—24no—
752C11C2×#319811yescharacteristic, complemented, Sylow
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—48no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—84no—
772C23—84no—
773C23—816no—
774C23—222no—
775C23—442no—
776C23—442no—
777C23—442no—
778C23C22×C22⋊D1112yes—
779C23C22×C22⋊D1112yes—
780C23C22×C22⋊D1112yes—
781C23C22×C22⋊D1111yescharacteristic
782Q8—44no—
783Q8—222no—
784Q8—222no—
785Q8—442no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—44no—
792D4—44no—
793D4—48no—
794D4—42no—
795D4—42no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800D4—222no—
801D4—222no—
802D4—448no—
803D4—442no—
804D4—884no—
805D4—884no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—448no—
826C2×C4—442no—
827C2×C4—442no—
828C2×C4—442no—
829C2×C4—884no—
830C2×C4#6703712yes—
831C2×C4#6703712yes—
832C2×C4C22×C22⋊D1112yes—
833C2×C4C22×C22⋊D1112yes—
834C2×C4C22×C22⋊D1112yes—
835C2×C4C22×C22⋊D1111yescharacteristic
836C2×C4C24×D1111yescharacteristic
837C8—222no—
838C8—222no—
839C8—222no—
840C8—222no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—816no—
860C22—84no—
861C22—84no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—884no—
866C22#1062333512yes—
867C22#1062336612yes—
868C22#1062336712yes—
869C22C23×C22⋊D1111yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—442no—
876C4—442no—
877C4—442no—
878C4#1062333512yes—
879C4C2×#6703711yescharacteristic
880C4C2×#6703711yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—82no—
886C2—882no—
887C2#1307946814yesdirect product factor
888C2C2×#1062333511yescharacteristic
889C2C2×#1062336611yescharacteristic
890C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#535C2
socleC23×C11C22×D4
hypercenterC2×#535D11
hypocenterC11C2×#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#10623364C2semidirect
2. #13079468C2direct (N × H)
3. C2×#10622647C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622646C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622655C2semidirect
9. C2×#10622651C2semidirect
10. C2×#10622654C2semidirect
11. C2×#10622650C2semidirect
12. C2×#10622650C2semidirect
13. C2×#10622831C2semidirect
14. C2×#10622830C2semidirect
15. C2×#10622847C2semidirect
16. C2×C11×#535C2semidirect
19. C22×#4339C22semidirect
21. C11×#535C22semidirect
32. #10623364C22semidirect
42. C2×#66983C22semidirect
43. C22×C4⋊Dic11C22semidirect
45. C2×#66977C22semidirect
46. C22×#4318C22semidirect
47. C23×C11⋊C8C22semidirect
48. #10622847C22semidirect
49. #10622831C22semidirect
50. #10622830C22semidirect
57. C2×C22⋊(C11⋊C8)C22semidirect
58. C2×C22⋊(C11⋊C8)C22semidirect
59. #10622655C22semidirect
60. #10622654C22semidirect
61. #10622652C22semidirect
62. #10622651C22semidirect
63. #10622650C22semidirect
64. #10622650C22semidirect
65. #10622647C22semidirect
66. #10622646C22semidirect
67. #10622616C22semidirect
68. #10622609C22semidirect
69. C2×#66874C22semidirect
70. C2×#66874C22semidirect
71. C2×#66873C22semidirect
72. C2×#66873C22semidirect
73. C2×#66872C22semidirect
74. C2×#66872C22semidirect
75. C2×#66871C22semidirect
76. C2×#66871C22semidirect
107. C2×#4339C23semidirect
150. #66983C23semidirect
157. C2×C4⋊Dic11C23semidirect
161. #66977C23semidirect
165. C2×#4318C23semidirect
171. C22×C11⋊C8C23semidirect
178. C22⋊(C11⋊C8)C23semidirect
179. C22⋊(C11⋊C8)C23semidirect
180. #66874C23semidirect
181. #66874C23semidirect
182. #66873C23semidirect
183. #66873C23semidirect
184. #66872C23semidirect
185. #66872C23semidirect
186. #66871C23semidirect
187. #66871C23semidirect
309. C2×#535D11semidirect
424. #535C2×D11semidirect
628. C2×C11#3198semidirect
752. C11C2×#3198semidirect
887. C2#13079468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233642
#130794682
C2×#106226472
C2×#106226092
C2×#106226162
C2×#106226462
C2×#106226522
C2×#106226552
C2×#106226512
C2×#106226542
C2×#106226502
C2×#106228312
C2×#106228302
C2×#106228472
C2×C11×#5352
C2×#319811