Finite Group Databasebeta

← C2×#13081318 #15633419

Subgroups — C2×#13081318 #15633419

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623070C211yesmaximal, characteristic, complemented
2C2×#10623249C211yesmaximal, characteristic, complemented
3#13081318C2116yesmaximal, direct product factor
4C2×#10622684C211yesmaximal, characteristic, complemented
5C2×#10622377C211yesmaximal, characteristic, complemented
6C2×#10622373C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622379C211yesmaximal, characteristic, complemented
9C2×#10622374C211yesmaximal, characteristic, complemented
10C2×#10622763C211yesmaximal, characteristic, complemented
11C2×#10622763C211yesmaximal, characteristic, complemented
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622765C211yesmaximal, characteristic, complemented
14C2×#10622627C211yesmaximal, characteristic, complemented
15C2×D8×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#459C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×D8C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C2×C11×#127C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66993C2211yescharacteristic
23C2×#66993C2211yescharacteristic
24C2×#66992—21no—
25C2×#66992—21no—
26C2×#66991—21no—
27C2×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C2×#66977—21no—
33C22×Dic11⋊C4—21no—
34#10623249—24no—
35#10623249C2218yescomplemented
36#10623070—24no—
37#10623070C2218yescomplemented
38C2×#66943C2211yescharacteristic
39C2×#66941C2211yescharacteristic
40C2×#66931—21no—
41C2×#66931—21no—
42C2×C4×D44C2211yescharacteristic
43C2×#66923C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#459C2218yescomplemented
46C2×C11×C4⋊C8C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622765C2218yescomplemented
55#10622763C2218yescomplemented
56#10622763C2218yescomplemented
57D8×Dic11C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622684C2218yescomplemented
67#10622627C2218yescomplemented
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66867C2211yescharacteristic
71#10622460C2218yescomplemented
72#10622441C2218yescomplemented
73#10622379C2218yescomplemented
74#10622377C2218yescomplemented
75#10622374C2218yescomplemented
76#10622373C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C23×Dic11—21no—
88C23×Dic11—21no—
89C23×Dic11—21no—
90C23×Dic11—21no—
91C2×#4341—28no—
92C2×#4341—48no—
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C22×Dic22—21no—
96C22×Dic22D411yescharacteristic
97C2×C11×D8—24no—
98C2×C11×D8—24no—
99C2×C11×D8C2314yes—
100C2×C11×D8C2314yes—
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×#127—22no—
104C11×#127C2314yes—
105C4×D4×C11—22no—
106C4×D4×C11C2314yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C42×C11C2311yescharacteristic
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114#66993—22no—
115#66993—22no—
116#66993C2314yes—
117#66993C2314yes—
118#66992—28no—
119#66992—28no—
120#66991—28no—
121D4×Dic11—22no—
122D4×Dic11—22no—
123D4×Dic11—22no—
124D4×Dic11—22no—
125D4×Dic11C2314yes—
126D4×Dic11C2314yes—
127D4×Dic11C2314yes—
128D4×Dic11C2314yes—
129C2×#4323—24no—
130C2×#4323C2314yes—
131C2×(C2×D11)⋊C4—21no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11D411yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137#66977—28no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—28no—
143C2×Dic11⋊C4D411yescharacteristic
144C2×Dic11⋊C4D411yescharacteristic
145C2×C4×Dic11C2311yescharacteristic
146C2×C4×Dic11C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149#66943—22no—
150#66943C2314yes—
151#66941—22no—
152#66941C2314yes—
153#66931—28no—
154#66931—28no—
155C4×D44—22no—
156C4×D44C2314yes—
157#66923—22no—
158#66923C2314yes—
159C4×Dic22D414yes—
160C4×Dic22C2314yes—
161C11×C4⋊C8C2314yes—
162C11×#102C2314yes—
163C11×#102C2314yes—
164#66896C2314yes—
165#66896C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169#66885C2314yes—
170#66885C2314yes—
171#66882C2314yes—
172#66881C2314yes—
173#66879C2314yes—
174Dic11⋊C8C2314yes—
175Dic11⋊C8C2314yes—
176C8×Dic11C2314yes—
177#66873C2314yes—
178#66872C2314yes—
179#66867C2314yes—
180C2×#3366—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C23×D11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—44no—
196C2×D4×C11—82no—
197C2×D4×C11#4114yescomplemented
198C2×D4×C11C2412yes—
199C2×D4×C11C2412yes—
200C2×D4×C11C2412yes—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—82no—
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—82no—
214C2×C22⋊D11—82no—
215C22×Dic11—24no—
216C22×Dic11—24no—
217C22×Dic11—24no—
218C22×Dic11—24no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—44no—
223C22×Dic11—44no—
224C22×Dic11—44no—
225C22×Dic11—82no—
226C22×Dic11C2×D411yescharacteristic
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230#4341—432no—
231C2×D44—21no—
232C2×D44—22no—
233C2×D44—22no—
234C2×D44C2412yes—
235C2×C4×D11—24no—
236C2×C4×D11—44no—
237C2×Dic22—24no—
238C2×Dic22—24no—
239C2×Dic22—82no—
240C2×Dic22C2×D414yes—
241C11×D8—28no—
242C11×D8—28no—
243C2×C8×C11—22no—
244C2×C8×C11—22no—
245C2×C8×C11C2412yes—
246C2×C8×C11C2412yes—
247C11×C4⋊C4—21no—
248C11×C4⋊C4C2412yes—
249C11×C22⋊C4—24no—
250C42×C11C2×D412yes—
251C42×C11C2412yes—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256#4323—28no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11C2×D414yes—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4C2×D414yes—
271Dic11⋊C4C2×D414yes—
272C4×Dic11C2×D412yes—
273C4×Dic11C2×D412yes—
274C4×Dic11C2412yes—
275C4×Dic11C2412yes—
276C2×C11⋊C8—22no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280C2×#554—111no—
281C2×#550—111no—
282#3366—1116no—
283C2×#490—111no—
284C2×#490—111no—
285C2×#486—111no—
286C2×#478—111no—
287C2×#478—111no—
288C2×#476—111no—
289C2×#459—111no—
290C2×#459—111no—
291C2×#459D1111yescharacteristic, complemented
292C2×#446—111no—
293C2×#442—111no—
294C2×#442—111no—
295C2×C4×D8—111no—
296C23×C11—24no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11C22×D411yescharacteristic
309C22×D11—22no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313D4×C11—24no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—22no—
319D4×C11—48no—
320D4×C11—42no—
321D4×C11—42no—
322D4×C11—84no—
323D4×C11C2×#4114yescomplemented
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—42no—
328C2×C4×C11—84no—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4112yes—
333C2×C4×C112−1+412yes—
334C2×C4×C11C2511yescharacteristic
335C22⋊D11—48no—
336C22⋊D11—48no—
337C22⋊D11—84no—
338C22⋊D11—84no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—48no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—48no—
350C2×Dic11—48no—
351C2×Dic11—84no—
352C2×Dic11AGL(1,ℤ/8)14yes—
353C2×Dic11C22×D412yes—
354C2×Dic11C22×D412yes—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357D44—22no—
358D44—22no—
359D44—42no—
360C4×D11—48no—
361Dic22—28no—
362Dic22—84no—
363C8×C11—22no—
364C8×C11—22no—
365C11⋊C8—22no—
366C11⋊C8—22no—
367C22×#41—221no—
368C22×D8—111no—
369C22×D8C2×D1111yescharacteristic
370C22×D8C2×D1111yescharacteristic
371#554—118no—
372#554—224no—
373#550—118no—
374#550—224no—
375C2×C4⋊Q8—111no—
376C2×#127—111no—
377C2×#127—111no—
378C2×#127C2×D1111yescharacteristic
379C2×#125—111no—
380C2×#125—111no—
381C2×C22⋊Q8—221no—
382C2×C22⋊Q8—221no—
383C2×C22⋊Q8—221no—
384C2×#121—221no—
385C2×#121—221no—
386C2×#121—221no—
387C2×C4×Q8—111no—
388C2×C4×D4—111no—
389C2×C4×D4—111no—
390C2×C4×D4—111no—
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×C4×D4C2×D1111yescharacteristic
394C22×C4⋊C4—221no—
395#490—118no—
396#490—118no—
397#486—118no—
398#478—118no—
399#478—118no—
400#476—118no—
401#459—118no—
402#459—118no—
403#459C2×D1118yescomplemented
404#446—118no—
405#442—118no—
406#442—118no—
407C4×D8—118no—
408C2×#107—111no—
409C2×#106—111no—
410C2×#106—111no—
411C2×C4⋊C8—111no—
412C2×C4⋊C8—111no—
413C2×C4⋊C8C2×D1111yescharacteristic
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102C2×D1111yescharacteristic
423C2×#102C2×D1111yescharacteristic
424C2×#97—111no—
425C2×#97—111no—
426C2×C4×C8—111no—
427C22×C11—24no—
428C22×C11—48no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—84no—
438C22×C11—84no—
439C22×C11#54812yes—
440C22×C11C2×AGL(1,ℤ/8)12yes—
441C22×C11#57612yes—
442C22×C11C23×D411yescharacteristic
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—84no—
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—42no—
450C4×C11#54812yes—
451C4×C11C22×#4111yescharacteristic
452C4×C11C2×2−1+411yescharacteristic
453Dic11—22no—
454Dic11—22no—
455Dic11—22no—
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459Dic11C2×AGL(1,ℤ/8)14yes—
460C2×#41—228no—
461C2×#41—448no—
462C22×Q8—111no—
463C22×Q8—221no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—111no—
467C22×D4—221no—
468C22×D4—221no—
469C22×D4—221no—
470C22×D4—221no—
471C22×D4C22×D1111yescharacteristic
472C22×D4C22×D1111yescharacteristic
473C22×D4C22×D1111yescharacteristic
474C23×C4—21no—
475C23×C4—221no—
476C23×C4—221no—
477C23×C4—221no—
478C23×C4—221no—
479C23×C4—221no—
480C2×D8—24no—
481C2×D8—24no—
482C2×D8—114no—
483C2×D8—224no—
484C2×D8C22×D1114yes—
485C2×D8C22×D1114yes—
486C22×C8—111no—
487C22×C8—111no—
488C22×C8C22×D1111yescharacteristic
489C22×C8C22×D1111yescharacteristic
490C4⋊Q8—114no—
491C4⋊Q8—222no—
492#127—22no—
493#127—114no—
494#127—114no—
495#127—222no—
496#127—222no—
497#127C22×D1114yes—
498#125—114no—
499#125—114no—
500#125—222no—
501#125—222no—
502C22⋊Q8—228no—
503C22⋊Q8—228no—
504C22⋊Q8—228no—
505#121—228no—
506#121—228no—
507#121—228no—
508C4×Q8—114no—
509C4×Q8—114no—
510C4×D4—22no—
511C4×D4—114no—
512C4×D4—114no—
513C4×D4—114no—
514C4×D4—114no—
515C4×D4—114no—
516C4×D4—222no—
517C4×D4—222no—
518C4×D4—222no—
519C4×D4—222no—
520C4×D4—222no—
521C4×D4C22×D1114yes—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—228no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—221no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C42—111no—
542C2×C42—111no—
543C2×C42C22×D1111yescharacteristic
544#107—114no—
545#106—114no—
546#106—114no—
547C4⋊C8—114no—
548C4⋊C8—114no—
549C4⋊C8C22×D1114yes—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554#102—114no—
555#102—114no—
556#102—114no—
557#102—114no—
558#102C22×D1114yes—
559#102C22×D1114yes—
560#97—114no—
561#97—114no—
562C4×C8—114no—
563C2×C11—44no—
564C2×C11—82no—
565C2×C11—82no—
566C2×C11#336614yescomplemented
567C2×C11C2×#54811yescharacteristic
568C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
569C2×C11C2×#57611yescharacteristic
570D11—82no—
571C24—21no—
572C24—21no—
573C24—21no—
574C24—221no—
575#41—4432no—
576C2×Q8—114no—
577C2×Q8—224no—
578C2×Q8—224no—
579C2×Q8—882no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—44no—
591C2×D4—82no—
592C2×D4—112no—
593C2×D4—224no—
594C2×D4—224no—
595C2×D4—224no—
596C2×D4—224no—
597C2×D4—221no—
598C2×D4—222no—
599C2×D4—222no—
600C2×D4—444no—
601C2×D4—444no—
602C2×D4—882no—
603C2×D4—882no—
604C2×D4#434114yescomplemented
605C2×D4C23×D1112yes—
606C2×D4C23×D1112yes—
607C2×D4C23×D1112yes—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—82no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—224no—
616C22×C4—224no—
617C22×C4—224no—
618C22×C4—224no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—224no—
623C22×C4—444no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4—444no—
627C22×C4—882no—
628C22×C4D4×D1111yescharacteristic
629C22×C4D4×D1111yescharacteristic
630C22×C4C23×D1111yescharacteristic
631D8—28no—
632D8—28no—
633D8—228no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—112no—
637C2×C8—112no—
638C2×C8—222no—
639C2×C8—222no—
640C2×C8C23×D1112yes—
641C2×C8C23×D1112yes—
642C4⋊C4—21no—
643C4⋊C4—114no—
644C4⋊C4—114no—
645C4⋊C4—114no—
646C4⋊C4—112no—
647C4⋊C4—112no—
648C4⋊C4—112no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—221no—
655C4⋊C4—224no—
656C4⋊C4—224no—
657C4⋊C4C23×D1112yes—
658C22⋊C4—24no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C42—112no—
665C42—112no—
666C42—112no—
667C42—112no—
668C42D4×D1112yes—
669C42C23×D1112yes—
670C11C2×#336611yescharacteristic, complemented, Sylow
671C23—24no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—222no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23C2×D4×D1111yescharacteristic
688Q8—228no—
689Q8—884no—
690D4—24no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—42no—
698D4—42no—
699D4—84no—
700D4—222no—
701D4—222no—
702D4—448no—
703D4—448no—
704D4—442no—
705D4—884no—
706D4—884no—
707D4C2×#434114yescomplemented
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—84no—
713C2×C4—114no—
714C2×C4—112no—
715C2×C4—112no—
716C2×C4—112no—
717C2×C4—112no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—448no—
725C2×C4—448no—
726C2×C4—448no—
727C2×C4—448no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—884no—
732C2×C4C2×D4×D1112yes—
733C2×C4C2×D4×D1112yes—
734C2×C4C2×D4×D1111yescharacteristic
735C2×C4C2×#434112yes—
736C2×C4#6704312yes—
737C2×C4C24×D1111yescharacteristic
738C8—22no—
739C8—22no—
740C8—222no—
741C8—222no—
742C22—24no—
743C22—42no—
744C22—42no—
745C22—48no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—84no—
753C22—84no—
754C22—442no—
755C22—442no—
756C22—442no—
757C22—884no—
758C22#1062312912yes—
759C22#1062328812yes—
760C22D11×AGL(1,ℤ/8)12yes—
761C22C22×D4×D1111yescharacteristic
762C4—22no—
763C4—22no—
764C4—42no—
765C4—114no—
766C4—222no—
767C4—222no—
768C4—222no—
769C4—442no—
770C4—442no—
771C4—442no—
772C4#1062312912yes—
773C4C22×#434111yescharacteristic
774C4C2×#6704311yescharacteristic
775C2—44no—
776C2—82no—
777C2—82no—
778C2—882no—
779C2#1308131814yesdirect product factor
780C2C2×#1062312911yescharacteristic
781C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
782C2C2×#1062328811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3366
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623070C2semidirect
2. C2×#10623249C2semidirect
3. #13081318C2direct (N × H)
4. C2×#10622684C2semidirect
5. C2×#10622377C2semidirect
6. C2×#10622373C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622379C2semidirect
9. C2×#10622374C2semidirect
10. C2×#10622763C2semidirect
11. C2×#10622763C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622765C2semidirect
14. C2×#10622627C2semidirect
15. C2×D8×Dic11C2semidirect
16. C2×C11×#459C2semidirect
35. #10623249C22semidirect
37. #10623070C22semidirect
45. C11×#459C22semidirect
54. #10622765C22semidirect
55. #10622763C22semidirect
56. #10622763C22semidirect
57. D8×Dic11C22semidirect
66. #10622684C22semidirect
67. #10622627C22semidirect
71. #10622460C22semidirect
72. #10622441C22semidirect
73. #10622379C22semidirect
74. #10622377C22semidirect
75. #10622374C22semidirect
76. #10622373C22semidirect
197. C2×D4×C11#41semidirect
291. C2×#459D11semidirect
323. D4×C11C2×#41semidirect
403. #459C2×D11semidirect
566. C2×C11#3366semidirect
604. C2×D4#4341semidirect
670. C11C2×#3366semidirect
707. D4C2×#4341semidirect
779. C2#13081318direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230702
C2×#106232492
#130813182
C2×#106226842
C2×#106223772
C2×#106223732
C2×#106224602
C2×#106223792
C2×#106223742
C2×#106227632
C2×#106224412
C2×#106227652
C2×#106226272
C2×D8×Dic112
C2×C11×#4592
C2×#336611