Finite Group Databasebeta

← C2×#13080053 #15626711

Subgroups — C2×#13080053 #15626711

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623250C211yesmaximal, characteristic, complemented
2C2×#10623093C211yesmaximal, characteristic, complemented
3#13080053C2116yesmaximal, direct product factor
4C2×#10622376C211yesmaximal, characteristic, complemented
5C2×#10622460C211yesmaximal, characteristic, complemented
6C2×#10622622C211yesmaximal, characteristic, complemented
7C2×#10622379C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622772C211yesmaximal, characteristic, complemented
10C2×#10622388C211yesmaximal, characteristic, complemented
11C2×#10622770C211yesmaximal, characteristic, complemented
12C2×#10622763C211yesmaximal, characteristic, complemented
13C2×#10622763C211yesmaximal, characteristic, complemented
14C2×#10622685C211yesmaximal, characteristic, complemented
15C2×#10622452C211yesmaximal, characteristic, complemented
16C2×C11×#459C211yesmaximal, characteristic, complemented
17C22×C11×D8C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C2×#66992—21no—
23C2×#66992—21no—
24C2×#66991C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C2×#66991C2211yescharacteristic
27C2×#66988—21no—
28C2×#66988—21no—
29C2×D4×Dic11C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C2×#66983—21no—
34C2×#66982—21no—
35C22×#4313C2211yescharacteristic
36C22×C8×D11C2211yescharacteristic
37#10623250—24no—
38#10623250C2218yescomplemented
39#10623093—24no—
40#10623093C2218yescomplemented
41C2×#66948C2211yescharacteristic
42C2×#66943C2211yescharacteristic
43C2×#66937—21no—
44C2×#66936—21no—
45C2×C4×D44C2211yescharacteristic
46C2×#66925C2211yescharacteristic
47C2×#66923C2211yescharacteristic
48C11×#459C2218yescomplemented
49C2×C11×C4⋊C8C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622772C2218yescomplemented
57#10622770C2218yescomplemented
58#10622763C2218yescomplemented
59#10622763C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×#66882C2211yescharacteristic
63C2×#66881C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66#10622685C2218yescomplemented
67#10622622C2218yescomplemented
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic
71#10622460C2218yescomplemented
72#10622452C2218yescomplemented
73#10622395C2218yescomplemented
74#10622388C2218yescomplemented
75#10622379C2218yescomplemented
76#10622376C2218yescomplemented
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—
87C22×C22⋊D11—21no—
88C23×Dic11—21no—
89C23×Dic11—21no—
90C22×D44—21no—
91C22×D44C2311yescharacteristic
92C22×C4×D11—21no—
93C22×C4×D11C2311yescharacteristic
94C2×C11×D8—42no—
95C2×C11×D8—42no—
96C2×C11×D8C2314yes—
97C2×C11×D8C2314yes—
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×#127—22no—
101C11×#127C2314yes—
102C4×D4×C11—22no—
103C4×D4×C11C2314yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112#66993—22no—
113#66993C2314yes—
114#66992—28no—
115#66992—28no—
116#66991—22no—
117#66991—22no—
118#66991—22no—
119#66991C2314yes—
120#66991C2314yes—
121#66991C2314yes—
122#66988—28no—
123#66988—28no—
124D4×Dic11—22no—
125D4×Dic11—22no—
126D4×Dic11C2314yes—
127D4×Dic11C2314yes—
128C2×#4323—42no—
129C2×#4323—42no—
130C2×#4323C2314yes—
131C2×#4323C2314yes—
132#66983—28no—
133#66982—28no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4D411yescharacteristic
137C2×(C2×D11)⋊C4D411yescharacteristic
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4D411yescharacteristic
146C2×Dic11⋊C4D411yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C2×#4313—42no—
151C2×#4313C2314yes—
152C2×C8×D11—42no—
153C2×C8×D11C2314yes—
154#66948—22no—
155#66948C2314yes—
156#66943—22no—
157#66943C2314yes—
158#66937—28no—
159#66936—28no—
160C4×D44—22no—
161C4×D44C2314yes—
162#66925D414yes—
163#66925C2314yes—
164#66923—22no—
165#66923C2314yes—
166C11×C4⋊C8C2314yes—
167C11×#102C2314yes—
168C11×#102C2314yes—
169#66896C2314yes—
170#66896C2314yes—
171#66896C2314yes—
172#66896C2314yes—
173#66885C2314yes—
174#66885C2314yes—
175#66882C2314yes—
176#66881C2314yes—
177Dic11⋊C8C2314yes—
178Dic11⋊C8C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3259—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C23×D11—21no—
187C23×D11C2×D411yescharacteristic
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—82no—
200C2×D4×C11—82no—
201C2×D4×C11C2412yes—
202C2×D4×C11C2412yes—
203C2×D4×C11C2412yes—
204C22×C4×C11—21no—
205C22×C4×C11—24no—
206C22×C4×C11—82no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2411yescharacteristic
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11—82no—
216C2×C22⋊D11—82no—
217C2×C22⋊D11—82no—
218C2×C22⋊D11—82no—
219C2×C22⋊D11—82no—
220C22×Dic11—24no—
221C22×Dic11—24no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—82no—
226C22×Dic11—82no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230C2×D44—24no—
231C2×D44—21no—
232C2×D44—22no—
233C2×D44—22no—
234C2×D44—82no—
235C2×D44C2412yes—
236C2×C4×D11—24no—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—82no—
240C2×C4×D11C2×D412yes—
241C2×C4×D11C2412yes—
242C11×D8—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—
251C42×C11C2×D412yes—
252C42×C11C2412yes—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258#4323—44no—
259#4323—44no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4C2×D414yes—
263(C2×D11)⋊C4C2×D414yes—
264C4⋊Dic11—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11C2412yes—
269C4⋊Dic11C2412yes—
270C4⋊Dic11C2412yes—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4C2×D414yes—
275Dic11⋊C4C2×D414yes—
276C4×Dic11C2×D412yes—
277C4×Dic11C2412yes—
278C2×C11⋊C8—22no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8C2412yes—
281C2×C11⋊C8C2412yes—
282#4313—44no—
283C8×D11—44no—
284C2×#540—111no—
285C2×#540—111no—
286#3259—1116no—
287C2×#478—111no—
288C2×#478—111no—
289C2×#478—111no—
290C2×#478—111no—
291C2×#469—111no—
292C2×#469—111no—
293C2×#466—111no—
294C2×#466—111no—
295C2×#459—111no—
296C2×#459—111no—
297C2×#459—111no—
298C2×#459D1111yescharacteristic, complemented
299C2×#424—111no—
300C23×C11—22no—
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×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11C22×D412yes—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—22no—
325D4×C11—22no—
326D4×C11—22no—
327D4×C11—42no—
328D4×C11—42no—
329D4×C11—42no—
330D4×C11—84no—
331D4×C11—84no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—42no—
336C2×C4×C11—84no—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11H(5,𝔽2)12yes—
341C2×C4×C112−1+412yes—
342C2×C4×C11C2511yescharacteristic
343C22⋊D11—84no—
344C22⋊D11—84no—
345C22⋊D11—84no—
346C22⋊D11—84no—
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—84no—
358C2×Dic11—84no—
359C2×Dic11C22×D412yes—
360C2×Dic11C22×D412yes—
361C2×Dic11C22×D412yes—
362D44—22no—
363D44—22no—
364D44—42no—
365D44—84no—
366C4×D11—24no—
367C4×D11—22no—
368C4×D11—22no—
369C4×D11—84no—
370C8×C11—22no—
371C8×C11—22no—
372C11⋊C8—22no—
373C11⋊C8—22no—
374C22×D8—111no—
375C22×D8—111no—
376C22×D8C2×D1111yescharacteristic
377C22×D8C2×D1111yescharacteristic
378C22×M16—111no—
379C23×C8—111no—
380#540—118no—
381#540—118no—
382#540—224no—
383#540—224no—
384C2×#127—111no—
385C2×#127C2×D1111yescharacteristic
386C2×#125—111no—
387C2×#125—111no—
388C2×#123—221no—
389C2×#123—221no—
390C2×#123—221no—
391C2×#123—221no—
392C2×#121—111no—
393C2×#121—111no—
394C2×#121—111no—
395C2×#121—111no—
396C2×#121—221no—
397C2×#121—221no—
398C2×#121—221no—
399C2×#121—221no—
400C2×C4×D4—111no—
401C2×C4×D4—111no—
402C2×C4×D4—111no—
403C2×C4×D4C2×D1111yescharacteristic
404C2×#117—111no—
405#478—118no—
406#478—118no—
407#478—118no—
408#478—118no—
409#469—118no—
410#469—118no—
411#466—118no—
412#466—118no—
413#459—118no—
414#459—118no—
415#459—118no—
416#459C2×D1118yescomplemented
417C2×#107—111no—
418C2×#107—111no—
419C2×#106—111no—
420C2×#106—111no—
421#424—118no—
422C2×C4⋊C8—111no—
423C2×C4⋊C8—111no—
424C2×C4⋊C8—111no—
425C2×C4⋊C8C2×D1111yescharacteristic
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102C2×D1111yescharacteristic
433C2×#102C2×D1111yescharacteristic
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—84no—
444C22×C11—84no—
445C22×C11—84no—
446C22×C11#53712yes—
447C22×C11#57612yes—
448C22×C11#57612yes—
449C22×C11C23×D411yescharacteristic
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—22no—
453C2×D11—44no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—84no—
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—42no—
461C4×C11#53712yes—
462C4×C11C2×H(5,𝔽2)11yescharacteristic
463C4×C11C2×2−1+411yescharacteristic
464Dic11—22no—
465Dic11—22no—
466Dic11—22no—
467Dic11—42no—
468Dic11—42no—
469Dic11—42no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—111no—
473C22×D4—221no—
474C22×D4—221no—
475C22×D4—221no—
476C22×D4—221no—
477C22×D4—221no—
478C22×D4—221no—
479C22×D4C22×D1111yescharacteristic
480C22×D4C22×D1111yescharacteristic
481C22×D4C22×D1111yescharacteristic
482C23×C4—21no—
483C23×C4—111no—
484C23×C4—221no—
485C23×C4—221no—
486C23×C4—221no—
487C2×D8—42no—
488C2×D8—42no—
489C2×D8—114no—
490C2×D8—114no—
491C2×D8—442no—
492C2×D8—442no—
493C2×D8C22×D1114yes—
494C2×D8C22×D1114yes—
495C2×M16—114no—
496C2×M16—442no—
497C22×C8—111no—
498C22×C8—111no—
499C22×C8—114no—
500C22×C8—442no—
501C22×C8C22×D1111yescharacteristic
502C22×C8C22×D1111yescharacteristic
503#127—22no—
504#127—114no—
505#127—222no—
506#127C22×D1114yes—
507#125—114no—
508#125—114no—
509#125—222no—
510#125—222no—
511#123—228no—
512#123—228no—
513#123—228no—
514#123—228no—
515#121—114no—
516#121—114no—
517#121—114no—
518#121—114no—
519#121—228no—
520#121—228no—
521#121—228no—
522#121—228no—
523#121—222no—
524#121—222no—
525#121—222no—
526#121—222no—
527C4×D4—22no—
528C4×D4—114no—
529C4×D4—114no—
530C4×D4—114no—
531C4×D4—222no—
532C4×D4—222no—
533C4×D4—222no—
534C4×D4C22×D1114yes—
535#117—114no—
536#117—114no—
537C2×C4⋊C4—111no—
538C2×C4⋊C4—111no—
539C2×C4⋊C4—111no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—221no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4C22×D1111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—111no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C42—111no—
558C2×C42C22×D1111yescharacteristic
559#107—114no—
560#107—114no—
561#106—114no—
562#106—114no—
563C4⋊C8—114no—
564C4⋊C8—114no—
565C4⋊C8—114no—
566C4⋊C8C22×D1114yes—
567#102—114no—
568#102—114no—
569#102—114no—
570#102—114no—
571#102—114no—
572#102—114no—
573#102C22×D1114yes—
574#102C22×D1114yes—
575C2×C11—82no—
576C2×C11—82no—
577C2×C11—82no—
578C2×C11#325914yescomplemented
579C2×C11C2×#53711yescharacteristic
580C2×C11C2×#57611yescharacteristic
581C2×C11C2×#57611yescharacteristic
582D11—42no—
583D11—82no—
584C24—21no—
585C24—21no—
586C24—21no—
587C24—111no—
588C24—221no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—24no—
593C2×D4—24no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—82no—
601C2×D4—82no—
602C2×D4—112no—
603C2×D4—224no—
604C2×D4—224no—
605C2×D4—224no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—221no—
610C2×D4—222no—
611C2×D4—222no—
612C2×D4—882no—
613C2×D4—882no—
614C2×D4—882no—
615C2×D4—882no—
616C2×D4—882no—
617C2×D4—882no—
618C2×D4C23×D1112yes—
619C2×D4C23×D1112yes—
620C2×D4C23×D1112yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—82no—
624C22×C4—111no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—224no—
630C22×C4—224no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—221no—
636C22×C4—224no—
637C22×C4—882no—
638C22×C4—882no—
639C22×C4—882no—
640C22×C4D4×D1111yescharacteristic
641C22×C4D4×D1111yescharacteristic
642C22×C4C23×D1111yescharacteristic
643D8—44no—
644D8—44no—
645D8—444no—
646D8—444no—
647M16—444no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—112no—
651C2×C8—112no—
652C2×C8—222no—
653C2×C8—222no—
654C2×C8—444no—
655C2×C8C23×D1112yes—
656C2×C8C23×D1112yes—
657C4⋊C4—21no—
658C4⋊C4—114no—
659C4⋊C4—114no—
660C4⋊C4—112no—
661C4⋊C4—112no—
662C4⋊C4—112no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—221no—
666C4⋊C4—221no—
667C4⋊C4—221no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4C23×D1112yes—
671C22⋊C4—24no—
672C22⋊C4—114no—
673C22⋊C4—114no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C42—112no—
682C42—112no—
683C42D4×D1112yes—
684C42C23×D1112yes—
685C11C2×#325911yescharacteristic, complemented, Sylow
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—112no—
699C23—222no—
700C23—222no—
701C23—222no—
702C23—222no—
703C23—442no—
704C23—442no—
705C23—442no—
706C23C2×D4×D1111yescharacteristic
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—84no—
717D4—84no—
718D4—222no—
719D4—222no—
720D4—442no—
721D4—884no—
722D4—884no—
723D4—884no—
724D4—884no—
725D4—884no—
726D4—884no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—42no—
731C2×C4—84no—
732C2×C4—112no—
733C2×C4—112no—
734C2×C4—112no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—884no—
748C2×C4—884no—
749C2×C4—884no—
750C2×C4C2×D4×D1112yes—
751C2×C4C2×D4×D1112yes—
752C2×C4C2×D4×D1111yescharacteristic
753C2×C4#6703712yes—
754C2×C4#6704312yes—
755C2×C4C24×D1111yescharacteristic
756C8—22no—
757C8—22no—
758C8—222no—
759C8—222no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—84no—
772C22—222no—
773C22—222no—
774C22—222no—
775C22—444no—
776C22—442no—
777C22—442no—
778C22—442no—
779C22—884no—
780C22#1062313912yes—
781C22#1062328812yes—
782C22#1062330512yes—
783C22C22×D4×D1111yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—222no—
788C4—222no—
789C4—222no—
790C4—442no—
791C4—442no—
792C4—442no—
793C4#1062313912yes—
794C4C2×#6703711yescharacteristic
795C4C2×#6704311yescharacteristic
796C2—82no—
797C2—82no—
798C2—82no—
799C2—442no—
800C2—882no—
801C2#1308005314yesdirect product factor
802C2C2×#1062313911yescharacteristic
803C2C2×#1062328811yescharacteristic
804C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3259
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×#10623250C2semidirect
2. C2×#10623093C2semidirect
3. #13080053C2direct (N × H)
4. C2×#10622376C2semidirect
5. C2×#10622460C2semidirect
6. C2×#10622622C2semidirect
7. C2×#10622379C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622772C2semidirect
10. C2×#10622388C2semidirect
11. C2×#10622770C2semidirect
12. C2×#10622763C2semidirect
13. C2×#10622763C2semidirect
14. C2×#10622685C2semidirect
15. C2×#10622452C2semidirect
16. C2×C11×#459C2semidirect
38. #10623250C22semidirect
40. #10623093C22semidirect
48. C11×#459C22semidirect
56. #10622772C22semidirect
57. #10622770C22semidirect
58. #10622763C22semidirect
59. #10622763C22semidirect
66. #10622685C22semidirect
67. #10622622C22semidirect
71. #10622460C22semidirect
72. #10622452C22semidirect
73. #10622395C22semidirect
74. #10622388C22semidirect
75. #10622379C22semidirect
76. #10622376C22semidirect
298. C2×#459D11semidirect
416. #459C2×D11semidirect
578. C2×C11#3259semidirect
685. C11C2×#3259semidirect
801. C2#13080053direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232502
C2×#106230932
#130800532
C2×#106223762
C2×#106224602
C2×#106226222
C2×#106223792
C2×#106223952
C2×#106227722
C2×#106223882
C2×#106227702
C2×#106227632
C2×#106226852
C2×#106224522
C2×C11×#4592
C2×#325911