Finite Group Databasebeta

← C2×#13079296 #15623654

Subgroups — C2×#13079296 #15623654

Order 2816.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623213C211yesmaximal, characteristic, complemented
2C2×#10623250C211yesmaximal, characteristic, complemented
3#13079296C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622669C211yesmaximal, characteristic, complemented
6C2×#10622683C211yesmaximal, characteristic, complemented
7C2×#10622772C211yesmaximal, characteristic, complemented
8C2×#10622787C211yesmaximal, characteristic, complemented
9C2×#10622770C211yesmaximal, characteristic, complemented
10C2×#10622784C211yesmaximal, characteristic, complemented
11C2×#10622765C211yesmaximal, characteristic, complemented
12C2×#10622777C211yesmaximal, characteristic, complemented
13C2×SD16×Dic11C211yesmaximal, characteristic, complemented
14C2×D8×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622321C211yesmaximal, characteristic, complemented
16C2×C11×#496C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#127C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66992—21no—
26C2×#66992—21no—
27C2×#66991C2211yescharacteristic
28C2×#66991C2211yescharacteristic
29C2×#66991C2211yescharacteristic
30C2×#66988—21no—
31C2×#66988—21no—
32C2×D4×Dic11C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C2×D4×Dic11C2211yescharacteristic
35C22×#4313C2211yescharacteristic
36C22×C8×D11C2211yescharacteristic
37#10623250—24no—
38#10623250C2218yescomplemented
39#10623213—24no—
40#10623213C2218yescomplemented
41C2×#66939—21no—
42C2×#66938—21no—
43C2×#66932—21no—
44C2×#66931—21no—
45C2×#66925C2211yescharacteristic
46C2×#66923C2211yescharacteristic
47C2×#66922C2211yescharacteristic
48C11×#496C2218yescomplemented
49C2×C11×#97C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×#66896C2211yescharacteristic
58#10622787C2218yescomplemented
59#10622784C2218yescomplemented
60#10622777C2218yescomplemented
61SD16×Dic11C2218yescomplemented
62#10622772C2218yescomplemented
63#10622770C2218yescomplemented
64#10622765C2218yescomplemented
65D8×Dic11C2218yescomplemented
66C2×#66882C2211yescharacteristic
67C2×#66882C2211yescharacteristic
68C2×#66881C2211yescharacteristic
69C2×#66881C2211yescharacteristic
70C2×#66879C2211yescharacteristic
71C2×C8×Dic11C2211yescharacteristic
72#10622683C2218yescomplemented
73#10622669C2218yescomplemented
74C2×C4×C11⋊C8C2211yescharacteristic
75#10622321C2218yescomplemented
76#10622315C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11—21no—
87C23×Dic11—21no—
88C23×Dic11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×Dic22—21no—
91C2×C11×SD16—24no—
92C2×C11×SD16—24no—
93C2×C11×SD16C2314yes—
94C2×C11×SD16C2314yes—
95C2×C11×D8—24no—
96C2×C11×D8—24no—
97C2×C11×D8C2314yes—
98C2×C11×D8C2314yes—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×#127—22no—
102C11×#127C2314yes—
103C11×#124—22no—
104C11×#124C2314yes—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114#66999—22no—
115#66999C2314yes—
116Q8×Dic11—22no—
117Q8×Dic11C2314yes—
118#66992—28no—
119#66992—28no—
120#66991—22no—
121#66991—22no—
122#66991—22no—
123#66991C2314yes—
124#66991C2314yes—
125#66991C2314yes—
126#66988—28no—
127#66988—28no—
128D4×Dic11—22no—
129D4×Dic11—22no—
130D4×Dic11—22no—
131D4×Dic11C2314yes—
132D4×Dic11C2314yes—
133D4×Dic11C2314yes—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4D411yescharacteristic
136C2×(C2×D11)⋊C4D411yescharacteristic
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4D411yescharacteristic
147C2×Dic11⋊C4D411yescharacteristic
148C2×C4×Dic11—21no—
149C2×C4×Dic11C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C2×#4313—24no—
153C2×#4313C2314yes—
154C2×C8×D11—24no—
155C2×C8×D11C2314yes—
156#66939—28no—
157#66938—28no—
158#66932—28no—
159#66931—28no—
160#66925D414yes—
161#66925C2314yes—
162#66923—22no—
163#66923C2314yes—
164#66922—22no—
165#66922C2314yes—
166C11×#97C2314yes—
167#66899C2314yes—
168#66899C2314yes—
169#66896C2314yes—
170#66896C2314yes—
171#66896C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66882C2314yes—
176#66882C2314yes—
177#66881C2314yes—
178#66881C2314yes—
179#66879C2314yes—
180C8×Dic11C2314yes—
181C4×C11⋊C8C2314yes—
182C2×#3179—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C23×D11C2×D411yescharacteristic
187C2×Q8×C11—21no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11C2412yes—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—24no—
195C2×D4×C11—24no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—82no—
203C2×D4×C11—82no—
204C2×D4×C11C2412yes—
205C2×D4×C11C2412yes—
206C2×D4×C11C2412yes—
207C22×C4×C11—21no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—24no—
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—82no—
215C2×C22⋊D11—82no—
216C2×C22⋊D11—82no—
217C22×Dic11—24no—
218C22×Dic11—24no—
219C22×Dic11—24no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—82no—
225C22×Dic11—82no—
226C22×Dic11—82no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11C2×D412yes—
233C2×C4×D11C2412yes—
234C2×Dic22—24no—
235C2×Dic22—82no—
236C11×SD16—28no—
237C11×SD16—28no—
238C11×D8—28no—
239C11×D8—28no—
240C2×C8×C11#4114yes—
241C2×C8×C11#4114yes—
242C2×C8×C11C2412yes—
243C2×C8×C11C2412yes—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C42×C11C2×D412yes—
247C42×C11C2412yes—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4C2×D414yes—
256(C2×D11)⋊C4C2×D414yes—
257C4⋊Dic11—24no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—24no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266C4⋊Dic11C2412yes—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4C2×D414yes—
271Dic11⋊C4C2×D414yes—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2412yes—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279#4313—28no—
280C8×D11—28no—
281C2×#542—111no—
282C2×#540—111no—
283#3179—1116no—
284C2×#501—111no—
285C2×#496D1111yescharacteristic, complemented
286C2×#488—111no—
287C2×#486—111no—
288C2×#469—111no—
289C2×#468—111no—
290C2×#466—111no—
291C2×#465—111no—
292C2×#442—111no—
293C2×#440—111no—
294C2×C4×SD16—111no—
295C2×C4×D8—111no—
296C2×#405—111no—
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×C11—42no—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11C22×D412yes—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—42no—
317D4×C11—22no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—42no—
324D4×C11—42no—
325D4×C11—42no—
326D4×C11—84no—
327D4×C11—84no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—42no—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4112yes—
336C2×C4×C11C2×#4112yes—
337C2×C4×C11C2511yescharacteristic
338C22⋊D11—84no—
339C22⋊D11—84no—
340C22⋊D11—84no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—84no—
353C2×Dic11—84no—
354C2×Dic11—84no—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358C4×D11—24no—
359C4×D11—22no—
360C4×D11—22no—
361Dic22—84no—
362C8×C11C2×#4114yes—
363C8×C11C2×#4114yes—
364C11⋊C8—22no—
365C11⋊C8—22no—
366C22×SD16C2×D1111yescharacteristic
367C22×SD16C2×D1111yescharacteristic
368C22×D8C2×D1111yescharacteristic
369C22×D8C2×D1111yescharacteristic
370C22×M16—111no—
371C23×C8—111no—
372#542—118no—
373#542—224no—
374#540—118no—
375#540—224no—
376C2×C4⋊Q8—111no—
377C2×#127C2×D1111yescharacteristic
378C2×#126—221no—
379C2×#125—111no—
380C2×#124—221no—
381C2×#124C2×D1111yescharacteristic
382C2×#123—221no—
383C2×#123—221no—
384C2×#123—221no—
385C2×C22⋊Q8—111no—
386C2×C22⋊Q8—221no—
387C2×#121—111no—
388C2×#121—111no—
389C2×#121—111no—
390C2×#121—221no—
391C2×#121—221no—
392C2×C4×Q8—111no—
393C2×C4×D4—111no—
394C2×C4×D4—111no—
395C2×C4×D4—111no—
396C2×#117—111no—
397#501—118no—
398#496C2×D1118yescomplemented
399#488—118no—
400#486—118no—
401#469—118no—
402#468—118no—
403#466—118no—
404#465—118no—
405#442—118no—
406#440—118no—
407C4×SD16—118no—
408C4×D8—118no—
409C2×#107—111no—
410C2×#107—111no—
411C2×#106—111no—
412C2×#106—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421#405—118no—
422C2×#97—111no—
423C2×#97C2×D1111yescharacteristic
424C2×C4×C8—111no—
425C2×C4×C8—111no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—84no—
436C22×C11—84no—
437C22×C11—84no—
438C22×C11#53212yes—
439C22×C11#57612yes—
440C22×C11#57712yes—
441C22×C11C23×D411yescharacteristic
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—22no—
445C2×D11—44no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—42no—
449C4×C11#53212yes—
450C4×C11C22×#4111yescharacteristic
451C4×C11C22×#4111yescharacteristic
452Dic11—22no—
453Dic11—22no—
454Dic11—22no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459C22×Q8—221no—
460C22×Q8C22×D1111yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—221no—
464C22×D4—221no—
465C22×D4—221no—
466C22×D4C22×D1111yescharacteristic
467C22×D4C22×D1111yescharacteristic
468C22×D4C22×D1111yescharacteristic
469C23×C4—111no—
470C23×C4—221no—
471C23×C4—221no—
472C23×C4—221no—
473C2×SD16—24no—
474C2×SD16—24no—
475C2×SD16C22×D1114yes—
476C2×SD16C22×D1114yes—
477C2×D8—24no—
478C2×D8—24no—
479C2×D8C22×D1114yes—
480C2×D8C22×D1114yes—
481C2×M16—114no—
482C2×M16—224no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—114no—
486C22×C8—224no—
487C22×C8C22×D1111yescharacteristic
488C22×C8C22×D1111yescharacteristic
489C4⋊Q8—114no—
490C4⋊Q8—222no—
491#127—22no—
492#127C22×D1114yes—
493#126—228no—
494#125—114no—
495#125—222no—
496#124—22no—
497#124—228no—
498#124C22×D1114yes—
499#123—228no—
500#123—228no—
501#123—228no—
502C22⋊Q8—114no—
503C22⋊Q8—228no—
504C22⋊Q8—222no—
505#121—114no—
506#121—114no—
507#121—114no—
508#121—228no—
509#121—228no—
510#121—222no—
511#121—222no—
512#121—222no—
513C4×Q8—114no—
514C4×Q8—222no—
515C4×D4—114no—
516C4×D4—114no—
517C4×D4—114no—
518C4×D4—222no—
519C4×D4—222no—
520C4×D4—222no—
521#117—114no—
522#117—114no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—111no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C42—111no—
546C2×C42—221no—
547C2×C42C22×D1111yescharacteristic
548#107—114no—
549#107—114no—
550#106—114no—
551#106—114no—
552#103—114no—
553#103—114no—
554#102—114no—
555#102—114no—
556#102—114no—
557#102—114no—
558#102—114no—
559#102—114no—
560#97—114no—
561#97C22×D1114yes—
562C4×C8—114no—
563C4×C8—114no—
564C2×C11—82no—
565C2×C11—82no—
566C2×C11—82no—
567C2×C11#317914yescomplemented
568C2×C11C2×#53211yescharacteristic
569C2×C11C2×#57611yescharacteristic
570C2×C11C2×#57711yescharacteristic
571D11—42no—
572C24—21no—
573C24—21no—
574C24—21no—
575C24—111no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—224no—
580C2×Q8—882no—
581C2×Q8C23×D1112yes—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—82no—
594C2×D4—82no—
595C2×D4—224no—
596C2×D4—224no—
597C2×D4—224no—
598C2×D4—882no—
599C2×D4—882no—
600C2×D4—882no—
601C2×D4C23×D1112yes—
602C2×D4C23×D1112yes—
603C2×D4C23×D1112yes—
604C22×C4—21no—
605C22×C4—111no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—112no—
609C22×C4—112no—
610C22×C4—224no—
611C22×C4—224no—
612C22×C4—224no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—882no—
620C22×C4—882no—
621C22×C4—882no—
622C22×C4D4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4C23×D1111yescharacteristic
625SD16—28no—
626SD16—28no—
627D8—28no—
628D8—28no—
629M16—228no—
630C2×C8—112no—
631C2×C8—112no—
632C2×C8—222no—
633C2×C8—222no—
634C2×C8—228no—
635C2×C8#434114yes—
636C2×C8#434114yes—
637C2×C8C23×D1112yes—
638C2×C8C23×D1112yes—
639C4⋊C4—114no—
640C4⋊C4—114no—
641C4⋊C4—112no—
642C4⋊C4—112no—
643C4⋊C4—112no—
644C4⋊C4—112no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—221no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—224no—
652C4⋊C4—224no—
653C4⋊C4—224no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—114no—
657C22⋊C4—114no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C42—112no—
666C42—112no—
667C42—224no—
668C42D4×D1112yes—
669C42C23×D1112yes—
670C11C2×#317911yescharacteristic, complemented, Sylow
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—112no—
684C23—222no—
685C23—222no—
686C23—222no—
687C23C2×D4×D1111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—884no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—84no—
702D4—84no—
703D4—884no—
704D4—884no—
705D4—884no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—112no—
711C2×C4—112no—
712C2×C4—112no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—224no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—884no—
728C2×C4—884no—
729C2×C4—884no—
730C2×C4C2×D4×D1112yes—
731C2×C4C2×D4×D1112yes—
732C2×C4C2×D4×D1111yescharacteristic
733C2×C4C2×#434112yes—
734C2×C4C2×#434112yes—
735C2×C4C24×D1111yescharacteristic
736C8—222no—
737C8—222no—
738C8C2×#434114yes—
739C8C2×#434114yes—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22—84no—
751C22—84no—
752C22—222no—
753C22—222no—
754C22—222no—
755C22—444no—
756C22#1062324712yes—
757C22#1062330512yes—
758C22#1062330612yes—
759C22C22×D4×D1111yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—222no—
764C4—222no—
765C4—222no—
766C4—442no—
767C4—442no—
768C4—442no—
769C4—442no—
770C4#1062324712yes—
771C4C22×#434111yescharacteristic
772C4C22×#434111yescharacteristic
773C2—82no—
774C2—82no—
775C2—82no—
776C2—442no—
777C2#1307929614yesdirect product factor
778C2C2×#1062324711yescharacteristic
779C2C2×#1062330511yescharacteristic
780C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#496C2
socleC23×C11C22×D4
hypercenterC2×#496D11
hypocenterC11C2×#3179
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#10623213C2semidirect
2. C2×#10623250C2semidirect
3. #13079296C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622669C2semidirect
6. C2×#10622683C2semidirect
7. C2×#10622772C2semidirect
8. C2×#10622787C2semidirect
9. C2×#10622770C2semidirect
10. C2×#10622784C2semidirect
11. C2×#10622765C2semidirect
12. C2×#10622777C2semidirect
13. C2×SD16×Dic11C2semidirect
14. C2×D8×Dic11C2semidirect
15. C2×#10622321C2semidirect
16. C2×C11×#496C2semidirect
38. #10623250C22semidirect
40. #10623213C22semidirect
48. C11×#496C22semidirect
58. #10622787C22semidirect
59. #10622784C22semidirect
60. #10622777C22semidirect
61. SD16×Dic11C22semidirect
62. #10622772C22semidirect
63. #10622770C22semidirect
64. #10622765C22semidirect
65. D8×Dic11C22semidirect
72. #10622683C22semidirect
73. #10622669C22semidirect
75. #10622321C22semidirect
76. #10622315C22semidirect
285. C2×#496D11semidirect
398. #496C2×D11semidirect
567. C2×C11#3179semidirect
670. C11C2×#3179semidirect
777. C2#13079296direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232132
C2×#106232502
#130792962
C2×#106223152
C2×#106226692
C2×#106226832
C2×#106227722
C2×#106227872
C2×#106227702
C2×#106227842
C2×#106227652
C2×#106227772
C2×SD16×Dic112
C2×D8×Dic112
C2×#106223212
C2×C11×#4962
C2×#317911