Finite Group Databasebeta

← C2×#13081320 #15633421

Subgroups — C2×#13081320 #15633421

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×#10623221C211yesmaximal, characteristic, complemented
2C2×#10623249C211yesmaximal, characteristic, complemented
3#13081320C2116yesmaximal, direct product factor
4C2×#10622377C211yesmaximal, characteristic, complemented
5C2×#10622373C211yesmaximal, characteristic, complemented
6C2×#10622376C211yesmaximal, characteristic, complemented
7C2×#10622679C211yesmaximal, characteristic, complemented
8C2×#10622374C211yesmaximal, characteristic, complemented
9C2×#10622399C211yesmaximal, characteristic, complemented
10C2×#10622399C211yesmaximal, characteristic, complemented
11C2×#10622685C211yesmaximal, characteristic, complemented
12C2×#10622314C211yesmaximal, characteristic, complemented
13C2×#10622324C211yesmaximal, characteristic, complemented
14C2×#10622398C211yesmaximal, characteristic, complemented
15C2×#10622369C211yesmaximal, characteristic, complemented
16C2×C11×#490C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C2×#66992—21no—
23C2×#66992—21no—
24C2×#66991—21no—
25C2×D4×Dic11C2211yescharacteristic
26C2×D4×Dic11C2211yescharacteristic
27C22×#4323C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C22×D88C2211yescharacteristic
30#10623249—24no—
31#10623249C2218yescomplemented
32#10623221—24no—
33#10623221C2218yescomplemented
34C2×#66950—21no—
35C2×#66949—21no—
36C2×#66949—21no—
37C2×#66946C2211yescharacteristic
38C2×#66946C2211yescharacteristic
39C2×C4⋊C4×D11—21no—
40C2×#66943C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#490C2218yescomplemented
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66881C2211yescharacteristic
56C2×#66879C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic
59C2×C8×Dic11C2211yescharacteristic
60#10622685C2218yescomplemented
61#10622679C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622399C2218yescomplemented
68#10622399C2218yescomplemented
69#10622398C2218yescomplemented
70#10622377C2218yescomplemented
71#10622376C2218yescomplemented
72#10622374C2218yescomplemented
73#10622373C2218yescomplemented
74#10622369C2218yescomplemented
75#10622324C2218yescomplemented
76#10622314C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C23×Dic11—21no—
87C2×#4341—28no—
88C2×#4341—48no—
89C22×D44C2311yescharacteristic
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×Dic22—21no—
96C22×Dic22D411yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C11×#127—22no—
100C11×#127C2314yes—
101C11×#125—22no—
102C11×#125C2314yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110#66993—22no—
111#66993—22no—
112#66993C2314yes—
113#66993C2314yes—
114#66992—28no—
115#66992—28no—
116#66991—28no—
117D4×Dic11—22no—
118D4×Dic11—22no—
119D4×Dic11C2314yes—
120D4×Dic11C2314yes—
121C2×#4323—24no—
122C2×#4323—24no—
123C2×#4323C2314yes—
124C2×#4323C2314yes—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11D411yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4D411yescharacteristic
136C2×Dic11⋊C4D411yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141C2×D88—24no—
142C2×D88C2314yes—
143#66950—28no—
144#66949—28no—
145#66949—28no—
146#66946—22no—
147#66946—22no—
148#66946C2314yes—
149#66946C2314yes—
150C4⋊C4×D11—28no—
151#66943—22no—
152#66943C2314yes—
153#66941—22no—
154#66941C2314yes—
155C4×D44—22no—
156C4×D44—22no—
157C4×D44C2314yes—
158C4×D44C2314yes—
159C4×Dic22D414yes—
160C4×Dic22C2314yes—
161C11×#102C2314yes—
162C11×#102C2314yes—
163C11×#102C2314yes—
164C11×#102C2314yes—
165C11×#97C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168#66885C2314yes—
169#66885C2314yes—
170#66881C2314yes—
171#66879C2314yes—
172Dic11⋊C8C2314yes—
173Dic11⋊C8C2314yes—
174C8×Dic11C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66872C2314yes—
178#66871C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C2×#3366—111nomaximal, Sylow
181C24×C11—21no—
182C24×C11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—44no—
194C2×D4×C11—82no—
195C2×D4×C11C2412yes—
196C2×D4×C11C2412yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11—82no—
209C2×C22⋊D11—82no—
210C22×Dic11—24no—
211C22×Dic11—24no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220#4341—432no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—22no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44#4114yescomplemented
227C2×D44C2412yes—
228C2×D44C2412yes—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—24no—
232C2×C4×D11—24no—
233C2×C4×D11—44no—
234C2×C4×D11—44no—
235C2×C4×D11—82no—
236C2×C4×D11—82no—
237C2×Dic22—24no—
238C2×Dic22—24no—
239C2×Dic22—82no—
240C2×Dic22C2×D414yes—
241C2×C8×C11—22no—
242C2×C8×C11—22no—
243C2×C8×C11C2412yes—
244C2×C8×C11C2412yes—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4C2412yes—
250C11×C4⋊C4C2412yes—
251C42×C11C2×D412yes—
252C42×C11C2412yes—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255#4323—28no—
256#4323—28no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261C4⋊Dic11—24no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11C2×D414yes—
265C4⋊Dic11C2412yes—
266C4⋊Dic11C2412yes—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4C2×D414yes—
270Dic11⋊C4C2×D414yes—
271C4×Dic11C2×D412yes—
272C4×Dic11C2×D412yes—
273C4×Dic11C2412yes—
274C4×Dic11C2412yes—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279D88—28no—
280C2×#554—111no—
281C2×#550—111no—
282#3366—1116no—
283C2×#490—111no—
284C2×#490D1111yescharacteristic, complemented
285C2×#486—111no—
286C2×#478—111no—
287C2×#478—111no—
288C2×#476—111no—
289C2×#459—111no—
290C2×#459—111no—
291C2×#459—111no—
292C2×#446—111no—
293C2×#442—111no—
294C2×#442—111no—
295C2×C4×D8—111no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11C22×D411yescharacteristic
305C22×D11—24no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313D4×C11—22no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—48no—
318D4×C11—42no—
319D4×C11—42no—
320D4×C11—84no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C2×#4112yes—
331C2×C4×C112−1+412yes—
332C2×C4×C11C2511yescharacteristic
333C22⋊D11—48no—
334C22⋊D11—48no—
335C22⋊D11—84no—
336C22⋊D11—84no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—48no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—48no—
346C2×Dic11AGL(1,ℤ/8)14yes—
347C2×Dic11C22×D412yes—
348C2×Dic11C22×D412yes—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351D44—24no—
352D44—22no—
353D44—22no—
354D44—22no—
355D44—42no—
356D44C2×#4114yescomplemented
357C4×D11—48no—
358C4×D11—48no—
359C4×D11—84no—
360C4×D11—84no—
361Dic22—28no—
362Dic22—84no—
363C8×C11—22no—
364C8×C11—22no—
365C11⋊C8—22no—
366C11⋊C8—22no—
367C22×#41—221no—
368C22×D8—111no—
369C22×D8—111no—
370C22×D8—111no—
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×#125C2×D1111yescharacteristic
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×D4—111no—
394C22×C4⋊C4—221no—
395#490—118no—
396#490C2×D1118yescomplemented
397#486—118no—
398#478—118no—
399#478—118no—
400#476—118no—
401#459—118no—
402#459—118no—
403#459—118no—
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⋊C8—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102C2×D1111yescharacteristic
421C2×#102C2×D1111yescharacteristic
422C2×#102C2×D1111yescharacteristic
423C2×#102C2×D1111yescharacteristic
424C2×#97—111no—
425C2×#97C2×D1111yescharacteristic
426C2×C4×C8—111no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—84no—
434C22×C11—84no—
435C22×C11#54812yes—
436C22×C11C2×AGL(1,ℤ/8)12yes—
437C22×C11#57612yes—
438C22×C11C23×D411yescharacteristic
439C2×D11—24no—
440C2×D11—48no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—84no—
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11#54812yes—
452C4×C11C22×#4111yescharacteristic
453C4×C11C2×2−1+411yescharacteristic
454Dic11—22no—
455Dic11—22no—
456Dic11—22no—
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—111no—
468C22×D4—221no—
469C22×D4—221no—
470C22×D4—221no—
471C22×D4—221no—
472C22×D4C22×D1111yescharacteristic
473C22×D4C22×D1111yescharacteristic
474C23×C4—221no—
475C23×C4—221no—
476C23×C4—221no—
477C23×C4—221no—
478C23×C4—221no—
479C23×C4—221no—
480C2×D8—114no—
481C2×D8—114no—
482C2×D8—114no—
483C2×D8—224no—
484C2×D8—224no—
485C2×D8—224no—
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—22no—
499#125—114no—
500#125—222no—
501#125C22×D1114yes—
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—114no—
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×D4—222no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—228no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C22⋊C4—221no—
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⋊C8—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554#102—114no—
555#102—114no—
556#102C22×D1114yes—
557#102C22×D1114yes—
558#102C22×D1114yes—
559#102C22×D1114yes—
560#97—114no—
561#97C22×D1114yes—
562C4×C8—114no—
563C2×C11—82no—
564C2×C11—82no—
565C2×C11#336614yescomplemented
566C2×C11C2×#54811yescharacteristic
567C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
568C2×C11C2×#57611yescharacteristic
569D11—44no—
570D11—82no—
571C24—21no—
572C24—21no—
573C24—221no—
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—24no—
583C2×D4—24no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—44no—
589C2×D4—82no—
590C2×D4—114no—
591C2×D4—112no—
592C2×D4—112no—
593C2×D4—224no—
594C2×D4—224no—
595C2×D4—224no—
596C2×D4—224no—
597C2×D4—221no—
598C2×D4—221no—
599C2×D4—222no—
600C2×D4—222no—
601C2×D4—222no—
602C2×D4—444no—
603C2×D4—444no—
604C2×D4—882no—
605C2×D4—882no—
606C2×D4C23×D1112yes—
607C2×D4C23×D1112yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4—224no—
617C22×C4—224no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—224no—
621C22×C4—224no—
622C22×C4—444no—
623C22×C4—444no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4—882no—
627C22×C4—882no—
628C22×C4D4×D1111yescharacteristic
629C22×C4D4×D1111yescharacteristic
630C22×C4C23×D1111yescharacteristic
631D8—228no—
632D8—228no—
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—24no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—114no—
647C4⋊C4—114no—
648C4⋊C4—114no—
649C4⋊C4—112no—
650C4⋊C4—112no—
651C4⋊C4—224no—
652C4⋊C4—224no—
653C4⋊C4—224no—
654C4⋊C4—221no—
655C4⋊C4—221no—
656C4⋊C4C23×D1112yes—
657C4⋊C4C23×D1112yes—
658C22⋊C4—224no—
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—22no—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—222no—
680C23—224no—
681C23—222no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23C2×D4×D1111yescharacteristic
688Q8—228no—
689Q8—884no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—42no—
696D4—42no—
697D4—84no—
698D4—114no—
699D4—222no—
700D4—222no—
701D4—222no—
702D4—224no—
703D4—448no—
704D4—448no—
705D4—442no—
706D4—884no—
707D4—884no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—114no—
715C2×C4—112no—
716C2×C4—112no—
717C2×C4—112no—
718C2×C4—112no—
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—884no—
731C2×C4—884no—
732C2×C4C2×D4×D1112yes—
733C2×C4C2×D4×D1112yes—
734C2×C4C2×D4×D1111yescharacteristic
735C2×C4#41×D1112yes—
736C2×C4#6704312yes—
737C2×C4C24×D1111yescharacteristic
738C8—22no—
739C8—22no—
740C8—222no—
741C8—222no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—84no—
750C22—224no—
751C22—442no—
752C22—448no—
753C22—442no—
754C22—442no—
755C22—442no—
756C22—442no—
757C22—884no—
758C22#1062320812yes—
759C22D11×AGL(1,ℤ/8)12yes—
760C22#1062330512yes—
761C22C22×D4×D1111yescharacteristic
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—114no—
767C4—222no—
768C4—222no—
769C4—222no—
770C4—442no—
771C4—442no—
772C4#1062320812yes—
773C4C2×#41×D1111yescharacteristic
774C4C2×#6704311yescharacteristic
775C2—82no—
776C2—82no—
777C2—444no—
778C2—882no—
779C2#1308132014yesdirect product factor
780C2C2×#1062320811yescharacteristic
781C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
782C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#490C2
socleC23×C11C22×D4
hypercenterC2×#490D11
hypocenterC11C2×#3366
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#10623221C2semidirect
2. C2×#10623249C2semidirect
3. #13081320C2direct (N × H)
4. C2×#10622377C2semidirect
5. C2×#10622373C2semidirect
6. C2×#10622376C2semidirect
7. C2×#10622679C2semidirect
8. C2×#10622374C2semidirect
9. C2×#10622399C2semidirect
10. C2×#10622399C2semidirect
11. C2×#10622685C2semidirect
12. C2×#10622314C2semidirect
13. C2×#10622324C2semidirect
14. C2×#10622398C2semidirect
15. C2×#10622369C2semidirect
16. C2×C11×#490C2semidirect
31. #10623249C22semidirect
33. #10623221C22semidirect
45. C11×#490C22semidirect
60. #10622685C22semidirect
61. #10622679C22semidirect
67. #10622399C22semidirect
68. #10622399C22semidirect
69. #10622398C22semidirect
70. #10622377C22semidirect
71. #10622376C22semidirect
72. #10622374C22semidirect
73. #10622373C22semidirect
74. #10622369C22semidirect
75. #10622324C22semidirect
76. #10622314C22semidirect
226. C2×D44#41semidirect
284. C2×#490D11semidirect
356. D44C2×#41semidirect
396. #490C2×D11semidirect
565. C2×C11#3366semidirect
670. C11C2×#3366semidirect
779. C2#13081320direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232212
C2×#106232492
#130813202
C2×#106223772
C2×#106223732
C2×#106223762
C2×#106226792
C2×#106223742
C2×#106223992
C2×#106226852
C2×#106223142
C2×#106223242
C2×#106223982
C2×#106223692
C2×C11×#4902
C2×#336611