Finite Group Databasebeta

← C2×#13080021 #15626677

Subgroups — C2×#13080021 #15626677

Order 2816.

1946 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×#10623065C211yesmaximal, characteristic, complemented
2#13080021C2116yesmaximal, direct product factor
3C2×#10622676C211yesmaximal, characteristic, complemented
4C2×#10622679C211yesmaximal, characteristic, complemented
5C2×#10622621C211yesmaximal, characteristic, complemented
6C2×#10622620C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622655C211yesmaximal, characteristic, complemented
9C2×#10622651C211yesmaximal, characteristic, complemented
10C2×#10622654C211yesmaximal, characteristic, complemented
11C2×#10622688C211yesmaximal, characteristic, complemented
12C2×#10622629C211yesmaximal, characteristic, complemented
13C2×#10622629C211yesmaximal, characteristic, complemented
14C2×#10622685C211yesmaximal, characteristic, complemented
15C2×#10622612C211yesmaximal, characteristic, complemented
16C2×C11×#540C211yesmaximal, characteristic, complemented
17C11×#540—24no—
18C11×#540C2218yescomplemented
19C2×C11×#127C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#123—21no—
23C2×C11×#121—21no—
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C22×#4324C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623065—24no—
39#10623065C2218yescomplemented
40C2×#66951—21no—
41C2×#66949—21no—
42C2×#66938—21no—
43C2×#66936—21no—
44C2×#66928C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52#10622688C2218yescomplemented
53#10622685C2218yescomplemented
54#10622679C2218yescomplemented
55#10622676C2218yescomplemented
56#10622655C2218yescomplemented
57#10622654C2218yescomplemented
58#10622652C2218yescomplemented
59#10622651C2218yescomplemented
60#10622629C2218yescomplemented
61#10622629C2218yescomplemented
62#10622621C2218yescomplemented
63#10622620C2218yescomplemented
64#10622612C2218yescomplemented
65C2×#66874C2211yescharacteristic
66C2×#66874C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×C4⋊(C11⋊C8)C2211yescharacteristic
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×Dic22—21no—
90C22×Dic22C2311yescharacteristic
91C11×#127—22no—
92C11×#127C2314yes—
93C11×#125—22no—
94C11×#125C2314yes—
95C11×#123—28no—
96C11×#123—28no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—28no—
100C11×#121—28no—
101C11×#121C2314yes—
102C11×#121C2314yes—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11C2314yes—
106C4×D4×C11C2314yes—
107C11×#117D414yes—
108C11×#117C2314yes—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C11×C22⋊C4D411yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11—21no—
124C2×#4324—42no—
125C2×#4324—42no—
126C2×#4324C2314yes—
127C2×#4324C2314yes—
128C2×#4323—42no—
129C2×#4323—42no—
130C2×#4323C2314yes—
131C2×#4323C2314yes—
132#66983—22no—
133#66983C2314yes—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141#66977—22no—
142#66977C2314yes—
143C2×Dic11⋊C4—21no—
144C2×Dic11⋊C4—21no—
145C2×C4×Dic11—21no—
146C2×#4318—42no—
147C2×#4318C2314yes—
148C22×C11⋊C8—42no—
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2314yes—
154#66951—28no—
155#66949—28no—
156#66938—28no—
157#66936—28no—
158#66928—22no—
159#66928C2314yes—
160C4×D44—22no—
161C4×D44C2314yes—
162#66922—22no—
163#66922C2314yes—
164C4×Dic22—22no—
165C4×Dic22C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169#66896C2314yes—
170#66874C2314yes—
171#66874C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C4⋊(C11⋊C8)C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3257—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C24×C11C2×D411yescharacteristic
186C23×D11—21no—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
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—82no—
198C2×D4×C11—82no—
199C2×D4×C11—82no—
200C2×D4×C11—82no—
201C2×D4×C11C2412yes—
202C2×D4×C11C2412yes—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—24no—
208C22×C4×C11—24no—
209C22×C4×C11—82no—
210C22×C4×C11—82no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C2×C22⋊D11—24no—
220C2×C22⋊D11—82no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C2×D44—21no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44C2412yes—
228C2×C4×D11—24no—
229C2×C4×D11—82no—
230C2×Dic22—21no—
231C2×Dic22—24no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22—82no—
235C2×Dic22C2412yes—
236C11×C4⋊C4—24no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4C2×D414yes—
241C11×C4⋊C4C2×D414yes—
242C11×C4⋊C4C2412yes—
243C11×C4⋊C4C2412yes—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4C2×D414yes—
249C11×C22⋊C4C2×D414yes—
250C42×C11C2×D412yes—
251C42×C11C2×D412yes—
252C42×C11C2412yes—
253C42×C11C2412yes—
254C22⋊Dic11—24no—
255#4324—44no—
256#4324—44no—
257#4323—44no—
258#4323—44no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—24no—
266C4⋊Dic11C2412yes—
267C4⋊Dic11C2412yes—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270C4×Dic11—24no—
271#4318—44no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—44no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281C2×#542—111no—
282C2×#540D1111yescharacteristic, complemented
283#3257—1116no—
284C2×#479—111no—
285C2×#478—111no—
286C2×#476—111no—
287C2×#474—111no—
288C2×#469—111no—
289C2×#468—111no—
290C2×#466—111no—
291C2×#465—111no—
292C2×#460—111no—
293C2×#463—111no—
294C2×#463—111no—
295C2×#459—111no—
296C2×#424—111no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11C22×D412yes—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11—42no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—22no—
318D4×C11—42no—
319D4×C11—42no—
320D4×C11—84no—
321D4×C11—84no—
322D4×C11—84no—
323D4×C11—84no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—24no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—84no—
337C2×C4×C11—84no—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D411yescharacteristic
344C2×C4×C11H(5,𝔽2)12yes—
345C2×C4×C112−1+412yes—
346C2×C4×C11C2511yescharacteristic
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354D44—22no—
355D44—22no—
356D44—42no—
357C4×D11—84no—
358Dic22—22no—
359Dic22—22no—
360Dic22—42no—
361Dic22—84no—
362C11⋊C8—22no—
363C11⋊C8—22no—
364C11⋊C8—22no—
365C11⋊C8—22no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×D8—111no—
369C22×D8—111no—
370C22×M16—111no—
371C23×C8—111no—
372#542—118no—
373#542—224no—
374#540—24no—
375#540C2×D1118yescomplemented
376C2×C4⋊Q8—111no—
377C2×#127C2×D1111yescharacteristic
378C2×#126—221no—
379C2×#125C2×D1111yescharacteristic
380C2×#124—111no—
381C2×#124—221no—
382C2×#123—21no—
383C2×#123—21no—
384C2×#123—221no—
385C2×C22⋊Q8—111no—
386C2×C22⋊Q8—221no—
387C2×#121—21no—
388C2×#121—21no—
389C2×#121—111no—
390C2×#121C2×D1111yescharacteristic
391C2×#121C2×D1111yescharacteristic
392C2×C4×Q8—111no—
393C2×C4×D4—111no—
394C2×C4×D4C2×D1111yescharacteristic
395C2×C4×D4C2×D1111yescharacteristic
396C2×#117C2×D1111yescharacteristic
397#479—118no—
398#478—118no—
399#476—118no—
400#474—118no—
401#469—118no—
402#468—118no—
403#466—118no—
404#465—118no—
405#463—118no—
406#463—118no—
407#460—118no—
408#459—118no—
409C2×#107—111no—
410C2×#107—111no—
411C2×#106—111no—
412C2×#106—111no—
413#424—118no—
414C2×C4⋊C8—111no—
415C2×C4⋊C8—111no—
416C2×C4⋊C8—111no—
417C2×C4⋊C8—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—44no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—84no—
437C22×C11—84no—
438C22×C11#53712yes—
439C22×C11#57612yes—
440C22×C11#57712yes—
441C22×C11C23×D411yescharacteristic
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—84no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11#53712yes—
454C4×C11C2×H(5,𝔽2)11yescharacteristic
455C4×C11C2×2−1+411yescharacteristic
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459C22×Q8—111no—
460C22×Q8—221no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—111no—
466C22×D4—221no—
467C22×D4C22×D1111yescharacteristic
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—221no—
472C23×C4C22×D1111yescharacteristic
473C2×SD16—114no—
474C2×SD16—114no—
475C2×SD16—442no—
476C2×SD16—442no—
477C2×D8—114no—
478C2×D8—114no—
479C2×D8—442no—
480C2×D8—442no—
481C2×M16—114no—
482C2×M16—442no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—111no—
486C22×C8—111no—
487C22×C8—114no—
488C22×C8—442no—
489C4⋊Q8—114no—
490C4⋊Q8—222no—
491#127—22no—
492#127C22×D1114yes—
493#126—228no—
494#125—22no—
495#125C22×D1114yes—
496#124—114no—
497#124—228no—
498#124—222no—
499#123—28no—
500#123—28no—
501#123—228no—
502C22⋊Q8—114no—
503C22⋊Q8—222no—
504C22⋊Q8—228no—
505#121—22no—
506#121—22no—
507#121—28no—
508#121—28no—
509#121—114no—
510#121—222no—
511#121C22×D1114yes—
512#121C22×D1114yes—
513C4×Q8—114no—
514C4×Q8—222no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—114no—
518C4×D4—222no—
519C4×D4C22×D1114yes—
520C4×D4C22×D1114yes—
521#117C22⋊D1114yes—
522#117C22×D1114yes—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4C22⋊D1111yescharacteristic
531C2×C4⋊C4C22⋊D1111yescharacteristic
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4C22⋊D1111yescharacteristic
544C2×C22⋊C4C22⋊D1111yescharacteristic
545C2×C42—221no—
546C2×C42C22×D1111yescharacteristic
547C2×C42C22×D1111yescharacteristic
548#107—114no—
549#107—114no—
550#106—114no—
551#106—114no—
552C4⋊C8—114no—
553C4⋊C8—114no—
554C4⋊C8—114no—
555C4⋊C8—114no—
556#103—114no—
557#103—114no—
558#102—114no—
559#102—114no—
560#102—114no—
561#102—114no—
562#102—114no—
563#102—114no—
564C2×C11—42no—
565C2×C11—82no—
566C2×C11—82no—
567C2×C11#325714yescomplemented
568C2×C11C2×#53711yescharacteristic
569C2×C11C2×#57611yescharacteristic
570C2×C11C2×#57711yescharacteristic
571D11—82no—
572C24—21no—
573C24—21no—
574C24—221no—
575C24C2×C22⋊D1111yescharacteristic
576C2×Q8—112no—
577C2×Q8—221no—
578C2×Q8—224no—
579C2×Q8—222no—
580C2×Q8—222no—
581C2×Q8—882no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—24no—
591C2×D4—24no—
592C2×D4—82no—
593C2×D4—82no—
594C2×D4—82no—
595C2×D4—82no—
596C2×D4—112no—
597C2×D4—224no—
598C2×D4—222no—
599C2×D4—222no—
600C2×D4—221no—
601C2×D4—882no—
602C2×D4C23×D1112yes—
603C2×D4C23×D1112yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—224no—
616C22×C4—882no—
617C22×C4C2×C22⋊D1112yes—
618C22×C4C2×C22⋊D1111yescharacteristic
619C22×C4C2×C22⋊D1111yescharacteristic
620C22×C4C2×C22⋊D1111yescharacteristic
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C23×D1112yes—
624C22×C4C23×D1111yescharacteristic
625SD16—444no—
626SD16—444no—
627D8—444no—
628D8—444no—
629M16—444no—
630C2×C8—112no—
631C2×C8—112no—
632C2×C8—112no—
633C2×C8—112no—
634C2×C8—222no—
635C2×C8—222no—
636C2×C8—222no—
637C2×C8—222no—
638C2×C8—444no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—112no—
644C4⋊C4—112no—
645C4⋊C4—221no—
646C4⋊C4—221no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4C2×C22⋊D1114yes—
651C4⋊C4C2×C22⋊D1114yes—
652C4⋊C4C23×D1112yes—
653C4⋊C4C23×D1112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4C2×C22⋊D1114yes—
664C22⋊C4C2×C22⋊D1114yes—
665C42—224no—
666C42C2×C22⋊D1112yes—
667C42C2×C22⋊D1112yes—
668C42C23×D1112yes—
669C42C23×D1112yes—
670C11C2×#325711yescharacteristic, complemented, Sylow
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—222no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23C22×C22⋊D1112yes—
687C23C22×C22⋊D1111yescharacteristic
688Q8—222no—
689Q8—222no—
690Q8—442no—
691Q8—884no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—84no—
699D4—84no—
700D4—84no—
701D4—84no—
702D4—222no—
703D4—222no—
704D4—442no—
705D4—884no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—884no—
727C2×C4#6704212yes—
728C2×C4#6704312yes—
729C2×C4C22×C22⋊D1112yes—
730C2×C4C22×C22⋊D1112yes—
731C2×C4C22×C22⋊D1112yes—
732C2×C4C22×C22⋊D1112yes—
733C2×C4C22×C22⋊D1112yes—
734C2×C4C22×C22⋊D1111yescharacteristic
735C2×C4C24×D1111yescharacteristic
736C8—222no—
737C8—222no—
738C8—222no—
739C8—222no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—84no—
752C22—442no—
753C22—442no—
754C22—442no—
755C22—884no—
756C22#1062336412yes—
757C22#1062336612yes—
758C22#1062336712yes—
759C22C23×C22⋊D1111yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—442no—
768C4—442no—
769C4—442no—
770C4#1062336412yes—
771C4C2×#6704211yescharacteristic
772C4C2×#6704311yescharacteristic
773C2—42no—
774C2—82no—
775C2—82no—
776C2—882no—
777C2#1308002114yesdirect product factor
778C2C2×#1062336411yescharacteristic
779C2C2×#1062336611yescharacteristic
780C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#540C2
socleC23×C11C22×D4
hypercenterC2×#540D11
hypocenterC11C2×#3257
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13080021C2direct (N × H)
3. C2×#10622676C2semidirect
4. C2×#10622679C2semidirect
5. C2×#10622621C2semidirect
6. C2×#10622620C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622655C2semidirect
9. C2×#10622651C2semidirect
10. C2×#10622654C2semidirect
11. C2×#10622688C2semidirect
12. C2×#10622629C2semidirect
13. C2×#10622629C2semidirect
14. C2×#10622685C2semidirect
15. C2×#10622612C2semidirect
16. C2×C11×#540C2semidirect
18. C11×#540C22semidirect
39. #10623065C22semidirect
52. #10622688C22semidirect
53. #10622685C22semidirect
54. #10622679C22semidirect
55. #10622676C22semidirect
56. #10622655C22semidirect
57. #10622654C22semidirect
58. #10622652C22semidirect
59. #10622651C22semidirect
60. #10622629C22semidirect
61. #10622629C22semidirect
62. #10622621C22semidirect
63. #10622620C22semidirect
64. #10622612C22semidirect
282. C2×#540D11semidirect
375. #540C2×D11semidirect
567. C2×C11#3257semidirect
670. C11C2×#3257semidirect
777. C2#13080021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230652
#130800212
C2×#106226762
C2×#106226792
C2×#106226212
C2×#106226202
C2×#106226522
C2×#106226552
C2×#106226512
C2×#106226542
C2×#106226882
C2×#106226292
C2×#106226852
C2×#106226122
C2×C11×#5402
C2×#325711