Finite Group Databasebeta

← C2×#13079663 #15625101

Subgroups — C2×#13079663 #15625101

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623093C211yesmaximal, characteristic, complemented
2C2×#10623205C211yesmaximal, characteristic, complemented
3#13079663C2116yesmaximal, direct product factor
4C2×#10622789C211yesmaximal, characteristic, complemented
5C2×#10622764C211yesmaximal, characteristic, complemented
6C2×#10622377C211yesmaximal, characteristic, complemented
7C2×#10622413C211yesmaximal, characteristic, complemented
8C2×#10622670C211yesmaximal, characteristic, complemented
9C2×#10622456C211yesmaximal, characteristic, complemented
10C2×#10622628C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622785C211yesmaximal, characteristic, complemented
13C2×#10622386C211yesmaximal, characteristic, complemented
14C2×#10622769C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic, complemented
20C22×C11×D8C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic, complemented
23C2×#67000C2211yescharacteristic
24C22×#4325C2211yescharacteristic, complemented
25C2×#66993C2211yescharacteristic
26C2×#66993C2211yescharacteristic, complemented
27C2×#66991C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C22×#4323C2211yescharacteristic, complemented
31C2×#66983—21no—
32C2×#66982—21no—
33C22×D88C2211yescharacteristic
34C22×D88C2211yescharacteristic, complemented
35#10623205—24no—
36#10623205C2218yescomplemented
37#10623093—24no—
38#10623093C2218yescomplemented
39C2×#66948C2211yescharacteristic
40C2×#66943C2211yescharacteristic, complemented
41C2×#66937—21no—
42C2×#66937—21no—
43C2×#66937—21no—
44C2×#66936—21no—
45C2×#66935—21no—
46C2×#66935—21no—
47C2×#66927C2211yescharacteristic
48C2×C4×D44C2211yescharacteristic, complemented
49C2×#66925C2211yescharacteristic
50C11×#463C2218yescomplemented
51C2×C11×C4⋊C8C2211yescharacteristic, complemented
52C2×C11×#103C2211yescharacteristic, complemented
53C2×C11×#102C2211yescharacteristic
54C2×#66899C2211yescharacteristic, complemented
55C2×#66896C2211yescharacteristic
56#10622789C2218yescomplemented
57#10622785C2218yescomplemented
58#10622769C2218yescomplemented
59#10622764C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic, complemented
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66879C2211yescharacteristic, complemented
65C2×C8×Dic11C2211yescharacteristic, complemented
66#10622670C2218yescomplemented
67#10622628C2218yescomplemented
68C2×#66873C2211yescharacteristic
69C2×#66873C2211yescharacteristic, complemented
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622456C2218yescomplemented
72#10622453C2218yescomplemented
73#10622424C2218yescomplemented
74#10622413C2218yescomplemented
75#10622386C2218yescomplemented
76#10622377C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C2×#4343—22no—
89C2×#4343—42no—
90C2×#4343—42no—
91C2×#4343C2314yes—
92C2×D4×D11—22no—
93C2×D4×D11—42no—
94C2×D4×D11—42no—
95C2×D4×D11C2314yes—
96C22×D44—21no—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44C2311yescharacteristic
101C22×D44C2311yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C2×C11×SD16—42no—
107C2×C11×SD16C2314yescomplemented
108C2×C11×D8—42no—
109C2×C11×D8C2314yes—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C11×#124—22no—
113C11×#124C2314yes—
114C4×D4×C11—22no—
115C4×D4×C11C2314yescomplemented
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C42×C11C2311yescharacteristic
121C2×C22⋊Dic11—21no—
122#67000—22no—
123#67000C2314yes—
124C2×#4325—42no—
125C2×#4325C2314yescomplemented
126#66993—22no—
127#66993—22no—
128#66993C2314yes—
129#66993C2314yescomplemented
130#66991—22no—
131#66991C2314yes—
132C2×#4323—42no—
133C2×#4323—42no—
134C2×#4323—42no—
135C2×#4323C2314yes—
136C2×#4323C2314yes—
137C2×#4323C2314yescomplemented
138#66983—28no—
139#66982—28no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4D411yescharacteristic
145C2×(C2×D11)⋊C4D411yescharacteristic
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4D411yescharacteristic
150C2×Dic11⋊C4D411yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C2×D88—42no—
155C2×D88—42no—
156C2×D88C2314yes—
157C2×D88C2314yescomplemented
158#66948—22no—
159#66948C2314yes—
160#66943—22no—
161#66943C2314yescomplemented
162#66937—28no—
163#66937—28no—
164#66937—28no—
165#66936—28no—
166#66935—28no—
167#66935—28no—
168#66927—22no—
169#66927C2314yes—
170C4×D44—22no—
171C4×D44C2314yescomplemented
172#66925D414yes—
173#66925C2314yes—
174C11×C4⋊C8C2314yescomplemented
175C11×#103C2314yescomplemented
176C11×#102C2314yes—
177#66899C2314yescomplemented
178#66896C2314yes—
179#66885C2314yes—
180#66885C2314yescomplemented
181(C2×D11)⋊C8C2314yes—
182(C2×D11)⋊C8C2314yes—
183#66879C2314yescomplemented
184C8×Dic11C2314yescomplemented
185#66873C2314yes—
186#66873C2314yescomplemented
187C4⋊(C11⋊C8)C2314yescomplemented
188C2×#3220—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—24no—
195C23×D11—44no—
196C23×D11—82no—
197C23×D11—82no—
198C23×D11C2×D411yescharacteristic
199C2×Q8×C11—21no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11C2412yes—
203C2×D4×C11—21no—
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11C2412yes—
210C2×D4×C11C2412yes—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—24no—
214C22×C4×C11—82no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—82no—
226C2×C22⋊D11—82no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11—82no—
229C2×C22⋊D11—82no—
230C22×Dic11—21no—
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234#4343—44no—
235#4343—44no—
236#4343—48no—
237D4×D11—44no—
238D4×D11—44no—
239D4×D11—48no—
240C2×D44—24no—
241C2×D44—24no—
242C2×D44—21no—
243C2×D44—21no—
244C2×D44—21no—
245C2×D44—24no—
246C2×D44—24no—
247C2×D44—22no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—44no—
254C2×D44—82no—
255C2×D44—82no—
256C2×D44—82no—
257C2×D44C2412yes—
258C2×D44C2412yes—
259C2×D44C2412yes—
260C2×C4×D11—24no—
261C2×C4×D11—24no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—44no—
265C2×C4×D11—82no—
266C2×C4×D11C2×D412yes—
267C2×C4×D11C2412yes—
268C11×SD16—44no—
269C11×D8—44no—
270C2×C8×C11—22no—
271C2×C8×C11—22no—
272C2×C8×C11C2412yes—
273C2×C8×C11C2412yes—
274C11×C4⋊C4—21no—
275C11×C4⋊C4C2412yes—
276C11×C22⋊C4—24no—
277C11×C22⋊C4—24no—
278C11×C22⋊C4—24no—
279C42×C11C2×D412yes—
280C42×C11C2412yes—
281C22⋊Dic11—24no—
282#4325—44no—
283#4323—44no—
284#4323—44no—
285#4323—44no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4—24no—
290(C2×D11)⋊C4C2×D414yes—
291(C2×D11)⋊C4C2×D414yes—
292C4⋊Dic11—24no—
293C4⋊Dic11—21no—
294C4⋊Dic11C2412yes—
295Dic11⋊C4—24no—
296Dic11⋊C4C2×D414yes—
297Dic11⋊C4C2×D414yes—
298C4×Dic11C2×D412yes—
299C4×Dic11C2412yes—
300C2×C11⋊C8—22no—
301C2×C11⋊C8—22no—
302C2×C11⋊C8C2412yes—
303C2×C11⋊C8C2412yes—
304D88—44no—
305D88—44no—
306C2×#540—111no—
307C2×#535—111no—
308#3220—1116no—
309C2×#496—111no—
310C2×#493—111no—
311C2×#490—111no—
312C2×#488—111no—
313C2×#463—111no—
314C2×#463D1111yescharacteristic, complemented
315C2×#459—111no—
316C2×#459—111no—
317C2×#449—111no—
318C2×#449—111no—
319C2×#447—111no—
320C2×#447—111no—
321C2×#433—111no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11C22×D411yescharacteristic
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—48no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—84no—
348C22×D11—84no—
349C22×D11—816no—
350C22×D11C22×D412yes—
351Q8×C11—22no—
352Q8×C11—22no—
353Q8×C11—42no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—42no—
359D4×C11—42no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—42no—
365C2×C4×C11—42no—
366C2×C4×C11—84no—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11H(5,𝔽2)12yes—
371C2×C4×C11H(5,𝔽2)12yes—
372C2×C4×C11C2511yescharacteristic
373C22⋊D11—48no—
374C22⋊D11—84no—
375C22⋊D11—84no—
376C22⋊D11—84no—
377C22⋊D11—84no—
378C22⋊D11—84no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—42no—
384C2×Dic11C22×D412yes—
385C2×Dic11C22×D412yes—
386C2×Dic11C22×D412yes—
387D44—22no—
388D44—22no—
389D44—22no—
390D44—22no—
391D44—22no—
392D44—22no—
393D44—48no—
394D44—42no—
395D44—42no—
396D44—42no—
397D44—84no—
398D44—84no—
399D44—84no—
400C4×D11—24no—
401C4×D11—22no—
402C4×D11—22no—
403C4×D11—48no—
404C4×D11—84no—
405C8×C11—22no—
406C8×C11—22no—
407C11⋊C8—22no—
408C11⋊C8—22no—
409C22×#41—111no—
410C23×D4—111no—
411C22×SD16—111no—
412C22×SD16C2×D1111yescharacteristic, complemented
413C22×D8—111no—
414C22×D8—111no—
415C22×D8—111no—
416C22×D8—111no—
417C22×D8—111no—
418C22×D8C2×D1111yescharacteristic
419#540—118no—
420#540—224no—
421#535—118no—
422#535—224no—
423C2×#127—111no—
424C2×#127—111no—
425C2×#127—111no—
426C2×#125—111no—
427C2×#124—111no—
428C2×#124C2×D1111yescharacteristic
429C2×#123—221no—
430C2×#123—221no—
431C2×#121—111no—
432C2×#121—111no—
433C2×#121—221no—
434C2×#121—221no—
435C2×#121—221no—
436C2×#121—221no—
437C2×#120—221no—
438C2×#120—221no—
439C2×C4×D4—111no—
440C2×C4×D4C2×D1111yescharacteristic, complemented
441C2×#117—111no—
442#496—118no—
443#493—118no—
444#490—118no—
445#488—118no—
446#463—118no—
447#463C2×D1118yescomplemented
448#459—118no—
449#459—118no—
450#449—118no—
451#449—118no—
452#447—118no—
453#447—118no—
454#433—118no—
455C2×C4⋊C8—111no—
456C2×C4⋊C8C2×D1111yescharacteristic, complemented
457C2×#103—111no—
458C2×#103C2×D1111yescharacteristic, complemented
459C2×#102—111no—
460C2×#102—111no—
461C2×#102—111no—
462C2×#102—111no—
463C2×#102—111no—
464C2×#102C2×D1111yescharacteristic
465C2×C22⋊C8—111no—
466C2×C22⋊C8—111no—
467C2×#97—111no—
468C2×C4×C8—111no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—84no—
476C22×C11—84no—
477C22×C11#53512yes—
478C22×C11#57612yes—
479C22×C11#57612yes—
480C22×C11C23×D411yescharacteristic
481C2×D11—22no—
482C2×D11—22no—
483C2×D11—22no—
484C2×D11—44no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—816no—
495C2×D11—84no—
496C2×D11—84no—
497C2×D11—84no—
498C4×C11—22no—
499C4×C11—22no—
500C4×C11—42no—
501C4×C11—42no—
502C4×C11#53512yes—
503C4×C11C2×H(5,𝔽2)11yescharacteristic
504C4×C11C2×H(5,𝔽2)11yescharacteristic
505Dic11—22no—
506Dic11—22no—
507Dic11—22no—
508Dic11—42no—
509C25—221no—
510C2×#41—114no—
511C2×#41—222no—
512C2×#41—442no—
513C2×#41—442no—
514C22×Q8C22×D1111yescharacteristic
515C22×D4—114no—
516C22×D4—111no—
517C22×D4—111no—
518C22×D4—111no—
519C22×D4—221no—
520C22×D4—221no—
521C22×D4—222no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4—221no—
527C22×D4—221no—
528C22×D4—221no—
529C22×D4—221no—
530C22×D4—442no—
531C22×D4—442no—
532C22×D4C22×D1111yescharacteristic
533C22×D4C22×D1111yescharacteristic
534C23×C4—21no—
535C23×C4—111no—
536C23×C4—221no—
537C23×C4—221no—
538C2×SD16—42no—
539C2×SD16—114no—
540C2×SD16—442no—
541C2×SD16C22×D1114yescomplemented
542C2×D8—42no—
543C2×D8—114no—
544C2×D8—114no—
545C2×D8—114no—
546C2×D8—114no—
547C2×D8—114no—
548C2×D8—442no—
549C2×D8—442no—
550C2×D8—442no—
551C2×D8—442no—
552C2×D8—442no—
553C2×D8C22×D1114yes—
554C22×C8—111no—
555C22×C8—111no—
556C22×C8C22×D1111yescharacteristic
557C22×C8C22×D1111yescharacteristic
558#127—114no—
559#127—114no—
560#127—114no—
561#127—222no—
562#127—222no—
563#127—222no—
564#125—114no—
565#125—222no—
566#124—22no—
567#124—114no—
568#124—222no—
569#124C22×D1114yes—
570#123—228no—
571#123—228no—
572#121—114no—
573#121—114no—
574#121—228no—
575#121—228no—
576#121—228no—
577#121—228no—
578#121—222no—
579#121—222no—
580#120—228no—
581#120—228no—
582C4×D4—22no—
583C4×D4—114no—
584C4×D4—222no—
585C4×D4C22×D1114yescomplemented
586#117—114no—
587#117—114no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4C22×D1111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—111no—
598C2×C22⋊C4—111no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C42—111no—
605C2×C42C22×D1111yescharacteristic
606C4⋊C8—114no—
607C4⋊C8C22×D1114yescomplemented
608#103—114no—
609#103C22×D1114yescomplemented
610#102—114no—
611#102—114no—
612#102—114no—
613#102—114no—
614#102—114no—
615#102C22×D1114yes—
616C22⋊C8—114no—
617C22⋊C8—114no—
618#97—114no—
619C4×C8—114no—
620C2×C11—82no—
621C2×C11—82no—
622C2×C11#322014yescomplemented
623C2×C11C2×#53511yescharacteristic
624C2×C11C2×#57611yescharacteristic
625C2×C11C2×#57611yescharacteristic
626D11—42no—
627D11—82no—
628D11—82no—
629D11—82no—
630C24—21no—
631C24—21no—
632C24—111no—
633C24—224no—
634C24—221no—
635C24—221no—
636C24—221no—
637C24—444no—
638C24—882no—
639C24—882no—
640#41—444no—
641#41—444no—
642#41—448no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8C23×D1112yes—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—112no—
654C2×D4—112no—
655C2×D4—112no—
656C2×D4—224no—
657C2×D4—224no—
658C2×D4—224no—
659C2×D4—224no—
660C2×D4—224no—
661C2×D4—224no—
662C2×D4—224no—
663C2×D4—224no—
664C2×D4—221no—
665C2×D4—221no—
666C2×D4—221no—
667C2×D4—224no—
668C2×D4—224no—
669C2×D4—222no—
670C2×D4—222no—
671C2×D4—222no—
672C2×D4—222no—
673C2×D4—222no—
674C2×D4—222no—
675C2×D4—444no—
676C2×D4—444no—
677C2×D4—444no—
678C2×D4—448no—
679C2×D4—444no—
680C2×D4—882no—
681C2×D4—882no—
682C2×D4—882no—
683C2×D4—882no—
684C2×D4—882no—
685C2×D4—882no—
686C2×D4—882no—
687C2×D4—882no—
688C2×D4C23×D1112yes—
689C2×D4C23×D1112yes—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—82no—
694C22×C4—111no—
695C22×C4—111no—
696C22×C4—111no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—224no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—221no—
703C22×C4—224no—
704C22×C4—444no—
705C22×C4—882no—
706C22×C4D4×D1111yescharacteristic
707C22×C4D4×D1111yescharacteristic
708C22×C4C23×D1111yescharacteristic
709SD16—44no—
710SD16—444no—
711D8—44no—
712D8—444no—
713D8—444no—
714D8—444no—
715D8—444no—
716D8—444no—
717C2×C8—22no—
718C2×C8—22no—
719C2×C8—112no—
720C2×C8—112no—
721C2×C8—222no—
722C2×C8—222no—
723C2×C8C23×D1112yes—
724C2×C8C23×D1112yes—
725C4⋊C4—21no—
726C4⋊C4—114no—
727C4⋊C4—114no—
728C4⋊C4—112no—
729C4⋊C4—224no—
730C4⋊C4—224no—
731C4⋊C4—221no—
732C4⋊C4C23×D1112yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—114no—
737C22⋊C4—114no—
738C22⋊C4—224no—
739C22⋊C4—224no—
740C22⋊C4—224no—
741C22⋊C4—224no—
742C22⋊C4—224no—
743C42—112no—
744C42—112no—
745C42D4×D1112yes—
746C42C23×D1112yes—
747C11C2×#322011yescharacteristic, complemented, Sylow
748C23—22no—
749C23—22no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—112no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—448no—
764C23—442no—
765C23—442no—
766C23—442no—
767C23—442no—
768C23—442no—
769C23—442no—
770C23—442no—
771C23—442no—
772C23—442no—
773C23—884no—
774C23—884no—
775C23—8816no—
776C23C2×D4×D1111yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—42no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—42no—
785D4—42no—
786D4—222no—
787D4—222no—
788D4—222no—
789D4—222no—
790D4—222no—
791D4—222no—
792D4—448no—
793D4—448no—
794D4—442no—
795D4—442no—
796D4—442no—
797D4—884no—
798D4—884no—
799D4—884no—
800D4—884no—
801D4—884no—
802D4—884no—
803D4—884no—
804D4—884no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—84no—
812C2×C4—112no—
813C2×C4—112no—
814C2×C4—112no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—224no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—448no—
823C2×C4—442no—
824C2×C4—884no—
825C2×C4C2×D4×D1112yes—
826C2×C4C2×D4×D1112yes—
827C2×C4C2×D4×D1111yescharacteristic
828C2×C4#6703712yes—
829C2×C4#6704212yes—
830C2×C4C24×D1111yescharacteristic
831C8—22no—
832C8—22no—
833C8—222no—
834C8—222no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—84no—
842C22—84no—
843C22—222no—
844C22—222no—
845C22—222no—
846C22—444no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—442no—
855C22—442no—
856C22—8816no—
857C22—884no—
858C22—884no—
859C22—884no—
860C22#1062313812yes—
861C22#1062330012yes—
862C22#1062330512yes—
863C22C22×D4×D1111yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—42no—
868C4—222no—
869C4—222no—
870C4—222no—
871C4—442no—
872C4#1062313812yes—
873C4C2×#6703711yescharacteristic
874C4C2×#6704211yescharacteristic
875C2—82no—
876C2—82no—
877C2—442no—
878C2—882no—
879C2—882no—
880C2—882no—
881C2#1307966314yesdirect product factor
882C2C2×#1062313811yescharacteristic
883C2C2×#1062330011yescharacteristic
884C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
hypercenterC2×#463D11
hypocenterC11C2×#3220
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#10623093C2semidirect
2. C2×#10623205C2semidirect
3. #13079663C2direct (N × H)
4. C2×#10622789C2semidirect
5. C2×#10622764C2semidirect
6. C2×#10622377C2semidirect
7. C2×#10622413C2semidirect
8. C2×#10622670C2semidirect
9. C2×#10622456C2semidirect
10. C2×#10622628C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622785C2semidirect
13. C2×#10622386C2semidirect
14. C2×#10622769C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#463C2semidirect
19. C22×C11×SD16C22semidirect
22. C2×C4×D4×C11C22semidirect
24. C22×#4325C22semidirect
26. C2×#66993C22semidirect
30. C22×#4323C22semidirect
34. C22×D88C22semidirect
36. #10623205C22semidirect
38. #10623093C22semidirect
40. C2×#66943C22semidirect
48. C2×C4×D44C22semidirect
50. C11×#463C22semidirect
51. C2×C11×C4⋊C8C22semidirect
52. C2×C11×#103C22semidirect
54. C2×#66899C22semidirect
56. #10622789C22semidirect
57. #10622785C22semidirect
58. #10622769C22semidirect
59. #10622764C22semidirect
61. C2×#66885C22semidirect
64. C2×#66879C22semidirect
65. C2×C8×Dic11C22semidirect
66. #10622670C22semidirect
67. #10622628C22semidirect
69. C2×#66873C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622456C22semidirect
72. #10622453C22semidirect
73. #10622424C22semidirect
74. #10622413C22semidirect
75. #10622386C22semidirect
76. #10622377C22semidirect
107. C2×C11×SD16C23semidirect
115. C4×D4×C11C23semidirect
125. C2×#4325C23semidirect
129. #66993C23semidirect
137. C2×#4323C23semidirect
157. C2×D88C23semidirect
161. #66943C23semidirect
171. C4×D44C23semidirect
174. C11×C4⋊C8C23semidirect
175. C11×#103C23semidirect
177. #66899C23semidirect
180. #66885C23semidirect
183. #66879C23semidirect
184. C8×Dic11C23semidirect
186. #66873C23semidirect
187. C4⋊(C11⋊C8)C23semidirect
314. C2×#463D11semidirect
412. C22×SD16C2×D11semidirect
440. C2×C4×D4C2×D11semidirect
447. #463C2×D11semidirect
456. C2×C4⋊C8C2×D11semidirect
458. C2×#103C2×D11semidirect
541. C2×SD16C22×D11semidirect
585. C4×D4C22×D11semidirect
607. C4⋊C8C22×D11semidirect
609. #103C22×D11semidirect
622. C2×C11#3220semidirect
747. C11C2×#3220semidirect
881. C2#13079663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230932
C2×#106232052
#130796632
C2×#106227892
C2×#106227642
C2×#106223772
C2×#106224132
C2×#106226702
C2×#106224562
C2×#106226282
C2×#106224242
C2×#106227852
C2×#106223862
C2×#106227692
C2×#106224532
C2×C11×#4632
C2×#322011