Finite Group Databasebeta

← C2×#13079975 #15626614

Subgroups — C2×#13079975 #15626614

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic, complemented
2C2×#10623211C211yesmaximal, characteristic, complemented
3#13079975C2116yesmaximal, direct product factor
4C2×#10622404C211yesmaximal, characteristic, complemented
5C2×#10622460C211yesmaximal, characteristic, complemented
6C2×#10622622C211yesmaximal, characteristic, complemented
7C2×#10622372C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622772C211yesmaximal, characteristic, complemented
10C2×#10622425C211yesmaximal, characteristic, complemented
11C2×#10622787C211yesmaximal, characteristic, complemented
12C2×#10622776C211yesmaximal, characteristic, complemented
13C2×#10622670C211yesmaximal, characteristic, complemented
14C2×#10622763C211yesmaximal, characteristic, complemented
15C2×#10622450C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66993C2211yescharacteristic
26C2×#66991C2211yescharacteristic
27C2×#66991C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C2×C4×C22⋊D11—21no—
31C22×#4313C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33#10623211—24no—
34#10623211C2218yescomplemented
35#10623079—24no—
36#10623079C2218yescomplemented
37C2×#66948C2211yescharacteristic
38C2×#66941C2211yescharacteristic
39C2×#66938—21no—
40C2×#66937—21no—
41C2×#66936—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×#66932—21no—
44C2×#66930—21no—
45C2×C4×D44C2211yescharacteristic
46C2×C42×D11C2211yescharacteristic
47C2×#66923C2211yescharacteristic
48C11×#463C2218yescomplemented
49C2×C11×C4⋊C8C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622787C2218yescomplemented
57#10622776C2218yescomplemented
58#10622772C2218yescomplemented
59#10622763C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×#66882C2211yescharacteristic
63C2×#66881C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66#10622670C2218yescomplemented
67#10622622C2218yescomplemented
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic
71#10622460C2218yescomplemented
72#10622450C2218yescomplemented
73#10622425C2218yescomplemented
74#10622404C2218yescomplemented
75#10622395C2218yescomplemented
76#10622372C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C2×#4339—28no—
87C2×#4339—48no—
88C22×D44—21no—
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×C4×D11D411yescharacteristic
92C22×C4×D11D411yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C22×Dic22—21no—
95C2×C11×SD16—42no—
96C2×C11×SD16C2314yes—
97C2×C11×D8—42no—
98C2×C11×D8C2314yes—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×#124—22no—
102C11×#124C2314yes—
103C4×D4×C11—22no—
104C4×D4×C11C2314yes—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C42×C11C2311yescharacteristic
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113#66999—22no—
114#66999C2314yes—
115Q8×Dic11—22no—
116Q8×Dic11C2314yes—
117C2×#4325—42no—
118C2×#4325C2314yes—
119#66993—22no—
120#66993C2314yes—
121#66991—22no—
122#66991—22no—
123#66991C2314yes—
124#66991C2314yes—
125D4×Dic11—22no—
126D4×Dic11C2314yes—
127C2×#4323—42no—
128C2×#4323C2314yes—
129C4×C22⋊D11—28no—
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—
141C2×C4×Dic11—21no—
142C2×C4×Dic11D411yescharacteristic
143C2×C4×Dic11D411yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C2×#4313—42no—
148C2×#4313—42no—
149C2×#4313C2314yes—
150C2×#4313C2314yes—
151#66948—22no—
152#66948C2314yes—
153#66941—22no—
154#66941C2314yes—
155#66938—28no—
156#66937—28no—
157#66936—28no—
158(C22⋊D11)⋊C4—28no—
159#66932—28no—
160#66930—28no—
161C4×D44—22no—
162C4×D44C2314yes—
163C42×D11D414yes—
164C42×D11C2314yes—
165#66923—22no—
166#66923C2314yes—
167C11×C4⋊C8C2314yes—
168C11×#103C2314yes—
169C11×#102C2314yes—
170#66899C2314yes—
171#66896C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66882C2314yes—
177#66881C2314yes—
178Dic11⋊C8C2314yes—
179Dic11⋊C8C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C4⋊(C11⋊C8)C2314yes—
183C2×#3251—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11—21no—
186C23×D11—21no—
187C23×D11C2×D411yescharacteristic
188C2×Q8×C11—21no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11C2412yes—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11C2412yes—
199C2×D4×C11C2412yes—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—44no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—44no—
215C22×Dic11—24no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—44no—
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223#4339—432no—
224C2×D44—24no—
225C2×D44—21no—
226C2×D44—22no—
227C2×D44—22no—
228C2×D44—44no—
229C2×D44C2412yes—
230C2×C4×D11—24no—
231C2×C4×D11—24no—
232C2×C4×D11—22no—
233C2×C4×D11—22no—
234C2×C4×D11—42no—
235C2×C4×D11—44no—
236C2×C4×D11C2×D412yes—
237C2×C4×D11C2×D414yes—
238C2×C4×D11C2×D414yes—
239C2×C4×D11C2412yes—
240C2×Dic22—24no—
241C2×Dic22—44no—
242C11×SD16—44no—
243C11×D8—44no—
244C2×C8×C11—22no—
245C2×C8×C11—22no—
246C2×C8×C11C2412yes—
247C2×C8×C11C2412yes—
248C11×C4⋊C4—21no—
249C11×C4⋊C4C2412yes—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C42×C11C2×D412yes—
254C42×C11C2412yes—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258#4325—44no—
259#4323—44no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263C4⋊Dic11—24no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11C2412yes—
268C4⋊Dic11C2412yes—
269C4⋊Dic11C2412yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274C4×Dic11—24no—
275C4×Dic11C2×D412yes—
276C4×Dic11C2×D414yes—
277C4×Dic11C2×D414yes—
278C4×Dic11C2412yes—
279C2×C11⋊C8—22no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8C2412yes—
282C2×C11⋊C8C2412yes—
283#4313—44no—
284#4313—44no—
285C2×#532—111no—
286C2×#529—111no—
287#3251—1116no—
288C2×#475—111no—
289C2×#478—111no—
290C2×#478—111no—
291C2×#474—111no—
292C2×#469—111no—
293C2×#469—111no—
294C2×#468—111no—
295C2×#468—111no—
296C2×#460—111no—
297C2×#463—111no—
298C2×#463D1111yescharacteristic, complemented
299C2×#459—111no—
300C2×#423—111no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11C22×D412yes—
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—42no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—22no—
325D4×C11—42no—
326D4×C11—42no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—48no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11H(5,𝔽2)12yes—
338C2×C4×C112−1+412yes—
339C2×C4×C11C2511yescharacteristic
340C22⋊D11—48no—
341C22⋊D11—48no—
342C22⋊D11—48no—
343C22⋊D11—48no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—48no—
353C2×Dic11AGL(1,ℤ/8)14yes—
354C2×Dic11C22×D412yes—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357D44—22no—
358D44—22no—
359D44—48no—
360D44—42no—
361C4×D11—24no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—28no—
365C4×D11—44no—
366C4×D11—48no—
367Dic22—48no—
368C8×C11—22no—
369C8×C11—22no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C22×#41—221no—
373C22×SD16—111no—
374C22×SD16C2×D1111yescharacteristic
375C22×D8—111no—
376C22×D8C2×D1111yescharacteristic
377C22×M16—111no—
378C22×M16—111no—
379#532—118no—
380#532—224no—
381C2×C4⋊Q8—111no—
382C2×#127—111no—
383#529—118no—
384#529—224no—
385C2×#126—221no—
386C2×#125—111no—
387C2×#124—221no—
388C2×#124C2×D1111yescharacteristic
389C2×#123—221no—
390C2×C22⋊Q8—111no—
391C2×#121—111no—
392C2×#121—111no—
393C2×#121—111no—
394C2×#121—221no—
395C2×C4×Q8—111no—
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4—221no—
399C2×C4×D4—221no—
400C2×C4×D4C2×D1111yescharacteristic
401C2×#117—221no—
402C22×C42—111no—
403#478—118no—
404#478—118no—
405#475—118no—
406#474—118no—
407#469—118no—
408#469—118no—
409#468—118no—
410#468—118no—
411#463—118no—
412#463C2×D1118yescomplemented
413#460—118no—
414#459—118no—
415C2×#107—111no—
416C2×#107—111no—
417C2×#106—111no—
418C2×#106—111no—
419#423—118no—
420C2×C4⋊C8—111no—
421C2×C4⋊C8—111no—
422C2×C4⋊C8—111no—
423C2×C4⋊C8C2×D1111yescharacteristic
424C2×#103—111no—
425C2×#103C2×D1111yescharacteristic
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102C2×D1111yescharacteristic
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—84no—
439C22×C11—84no—
440C22×C11#53712yes—
441C22×C11C2×AGL(1,ℤ/8)12yes—
442C22×C11#57512yes—
443C22×C11C23×D411yescharacteristic
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—44no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—84no—
452C4×C11—22no—
453C4×C11—22no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11#53712yes—
457C4×C11C2×H(5,𝔽2)11yescharacteristic
458C4×C11C2×2−1+411yescharacteristic
459Dic11—22no—
460Dic11—22no—
461Dic11—42no—
462Dic11—42no—
463Dic11—42no—
464Dic11C2×AGL(1,ℤ/8)14yes—
465C2×#41—228no—
466C2×#41—448no—
467C22×Q8—221no—
468C22×Q8C22×D1111yescharacteristic
469C22×D4—111no—
470C22×D4—221no—
471C22×D4—221no—
472C22×D4—221no—
473C22×D4—221no—
474C22×D4—221no—
475C22×D4C22×D1111yescharacteristic
476C22×D4C22×D1111yescharacteristic
477C23×C4—21no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—221no—
482C23×C4—221no—
483C2×SD16—42no—
484C2×SD16—114no—
485C2×SD16—442no—
486C2×SD16C22×D1114yes—
487C2×D8—42no—
488C2×D8—114no—
489C2×D8—442no—
490C2×D8C22×D1114yes—
491C2×M16—114no—
492C2×M16—114no—
493C2×M16—442no—
494C2×M16—442no—
495C22×C8—111no—
496C22×C8—111no—
497C22×C8C22×D1111yescharacteristic
498C22×C8C22×D1111yescharacteristic
499C4⋊Q8—114no—
500C4⋊Q8—222no—
501#127—114no—
502#127—222no—
503#126—228no—
504#125—114no—
505#125—222no—
506#124—22no—
507#124—228no—
508#124C22×D1114yes—
509#123—228no—
510C22⋊Q8—114no—
511C22⋊Q8—222no—
512#121—114no—
513#121—114no—
514#121—114no—
515#121—228no—
516#121—222no—
517#121—222no—
518#121—222no—
519C4×Q8—114no—
520C4×Q8—222no—
521C4×D4—22no—
522C4×D4—114no—
523C4×D4—114no—
524C4×D4—228no—
525C4×D4—222no—
526C4×D4—228no—
527C4×D4—222no—
528C4×D4C22×D1114yes—
529#117—228no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C42—111no—
549C2×C42—111no—
550C2×C42—111no—
551C2×C42—114no—
552C2×C42—114no—
553C2×C42—221no—
554C2×C42C22×D1111yescharacteristic
555#107—114no—
556#107—114no—
557#106—114no—
558#106—114no—
559C4⋊C8—114no—
560C4⋊C8—114no—
561C4⋊C8—114no—
562C4⋊C8C22×D1114yes—
563#103—114no—
564#103C22×D1114yes—
565#102—114no—
566#102—114no—
567#102—114no—
568#102—114no—
569#102—114no—
570#102C22×D1114yes—
571C2×C11—82no—
572C2×C11—82no—
573C2×C11#325114yescomplemented
574C2×C11C2×#53711yescharacteristic
575C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
576C2×C11C2×#57511yescharacteristic
577D11—42no—
578D11—82no—
579C24—21no—
580C24—21no—
581C24—111no—
582C24—221no—
583#41—4432no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—224no—
588C2×Q8—444no—
589C2×Q8C23×D1112yes—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—112no—
597C2×D4—224no—
598C2×D4—224no—
599C2×D4—224no—
600C2×D4—224no—
601C2×D4—224no—
602C2×D4—221no—
603C2×D4—222no—
604C2×D4—222no—
605C2×D4—444no—
606C2×D4—444no—
607C2×D4—444no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4C23×D1112yes—
611C2×D4C23×D1112yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—24no—
615C22×C4—44no—
616C22×C4—111no—
617C22×C4—111no—
618C22×C4—111no—
619C22×C4—114no—
620C22×C4—112no—
621C22×C4—112no—
622C22×C4—114no—
623C22×C4—224no—
624C22×C4—224no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—224no—
631C22×C4—442no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4D4×D1111yescharacteristic
635C22×C4D4×D1111yescharacteristic
636C22×C4C23×D1111yescharacteristic
637SD16—44no—
638SD16—444no—
639D8—44no—
640D8—444no—
641M16—444no—
642M16—444no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—112no—
646C2×C8—112no—
647C2×C8—222no—
648C2×C8—222no—
649C2×C8C23×D1112yes—
650C2×C8C23×D1112yes—
651C4⋊C4—21no—
652C4⋊C4—112no—
653C4⋊C4—112no—
654C4⋊C4—112no—
655C4⋊C4—224no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4—221no—
659C4⋊C4—221no—
660C4⋊C4—221no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4C23×D1112yes—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—224no—
668C22⋊C4—224no—
669C22⋊C4—224no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C42—114no—
674C42—114no—
675C42—112no—
676C42—112no—
677C42—224no—
678C42D4×D1112yes—
679C42C23×D1112yes—
680C11C2×#325111yescharacteristic, complemented, Sylow
681C23—22no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—112no—
690C23—222no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23C2×D4×D1111yescharacteristic
698Q8—22no—
699Q8—22no—
700Q8—42no—
701Q8—448no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—222no—
709D4—222no—
710D4—448no—
711D4—448no—
712D4—448no—
713D4—448no—
714D4—448no—
715D4—442no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—114no—
724C2×C4—112no—
725C2×C4—112no—
726C2×C4—112no—
727C2×C4—228no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—224no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—444no—
737C2×C4—448no—
738C2×C4—448no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4C2×D4×D1112yes—
743C2×C4C2×D4×D1112yes—
744C2×C4C2×D4×D1111yescharacteristic
745C2×C4#6703712yes—
746C2×C4#6704312yes—
747C2×C4C24×D1111yescharacteristic
748C8—22no—
749C8—22no—
750C8—222no—
751C8—222no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—84no—
759C22—84no—
760C22—222no—
761C22—222no—
762C22—222no—
763C22—444no—
764C22—442no—
765C22—442no—
766C22—442no—
767C22—884no—
768C22#1062313912yes—
769C22#1062329912yes—
770C22D11×AGL(1,ℤ/8)12yes—
771C22C22×D4×D1111yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—114no—
777C4—222no—
778C4—222no—
779C4—442no—
780C4—442no—
781C4—442no—
782C4#1062313912yes—
783C4C2×#6703711yescharacteristic
784C4C2×#6704311yescharacteristic
785C2—82no—
786C2—82no—
787C2—442no—
788C2—882no—
789C2#1307997514yesdirect product factor
790C2C2×#1062313911yescharacteristic
791C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
792C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
hypercenterC2×#463D11
hypocenterC11C2×#3251
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×#10623079C2semidirect
2. C2×#10623211C2semidirect
3. #13079975C2direct (N × H)
4. C2×#10622404C2semidirect
5. C2×#10622460C2semidirect
6. C2×#10622622C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622772C2semidirect
10. C2×#10622425C2semidirect
11. C2×#10622787C2semidirect
12. C2×#10622776C2semidirect
13. C2×#10622670C2semidirect
14. C2×#10622763C2semidirect
15. C2×#10622450C2semidirect
16. C2×C11×#463C2semidirect
34. #10623211C22semidirect
36. #10623079C22semidirect
48. C11×#463C22semidirect
56. #10622787C22semidirect
57. #10622776C22semidirect
58. #10622772C22semidirect
59. #10622763C22semidirect
66. #10622670C22semidirect
67. #10622622C22semidirect
71. #10622460C22semidirect
72. #10622450C22semidirect
73. #10622425C22semidirect
74. #10622404C22semidirect
75. #10622395C22semidirect
76. #10622372C22semidirect
298. C2×#463D11semidirect
412. #463C2×D11semidirect
573. C2×C11#3251semidirect
680. C11C2×#3251semidirect
789. C2#13079975direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×#106232112
#130799752
C2×#106224042
C2×#106224602
C2×#106226222
C2×#106223722
C2×#106223952
C2×#106227722
C2×#106224252
C2×#106227872
C2×#106227762
C2×#106226702
C2×#106227632
C2×#106224502
C2×C11×#4632
C2×#325111