Finite Group Databasebeta

← C2×#13081676 #15634773

Subgroups — C2×#13081676 #15634773

Order 2816.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2#13081676C2116yesmaximal, direct product factor
3C2×#10622673C211yesmaximal, characteristic, complemented
4C2×#10622687C211yesmaximal, characteristic
5C2×#10622672C211yesmaximal, characteristic, complemented
6C2×#10622641C211yesmaximal, characteristic, complemented
7C2×#10622667C211yesmaximal, characteristic, complemented
8C2×#10622688C211yesmaximal, characteristic, complemented
9C2×#10622629C211yesmaximal, characteristic, complemented
10C2×#10622670C211yesmaximal, characteristic, complemented
11C2×#10622632C211yesmaximal, characteristic, complemented
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622627C211yesmaximal, characteristic, complemented
14C2×#10622643C211yesmaximal, characteristic, complemented
15C2×C4×#4324C211yesmaximal, characteristic, complemented
16C2×C11×#559C211yesmaximal, characteristic, complemented
17C11×#559—24no—
18C11×#559C2218yescomplemented
19C2×C11×#127C2211yescharacteristic
20C2×C11×#124—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×#123—21no—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×#66999—21no—
31C22×#4326C2211yescharacteristic
32C22×#4326C2211yescharacteristic
33C22×#4325C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C22×#4324C2211yescharacteristic
36C22×#4324C2211yescharacteristic
37C22×#4324C2211yescharacteristic
38C22×#4323C2211yescharacteristic
39C22×#4323C2211yescharacteristic
40#10623115—24no—
41#10623115C2218yescomplemented
42C2×#66951—21no—
43C2×#66951—21no—
44C2×#66945—21no—
45C2×#66928C2211yescharacteristic
46C2×#66928C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48C2×#66922C2211yescharacteristic
49C2×C4×Dic22C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622688C2218yescomplemented
55#10622687C2218yes—
56#10622673C2218yescomplemented
57#10622672C2218yescomplemented
58#10622670C2218yescomplemented
59#10622667C2218yescomplemented
60#10622643C2218yescomplemented
61#10622641C2218yescomplemented
62#10622637C2218yescomplemented
63#10622632C2218yescomplemented
64C4×#4324C2218yescomplemented
65#10622629C2218yescomplemented
66#10622627C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66874C2211yescharacteristic
69C2×#66873C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×C4⋊(C11⋊C8)C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×Dic22C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C11×#127—22no—
90C11×#127C2314yes—
91C11×#124—28no—
92C11×#124—22no—
93C11×#124—22no—
94C11×#124C2314yes—
95C11×#124C2314yes—
96C11×#123—28no—
97C11×#123—28no—
98C4×Q8×C11—22no—
99C4×Q8×C11D414yes—
100C4×Q8×C11C2314yes—
101C4×Q8×C11C2314yes—
102C4×D4×C11—28no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11C2314yes—
106C4×D4×C11C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122#66999—28no—
123C2×#4326—24no—
124C2×#4326—42no—
125C2×#4326C2314yes—
126C2×#4326C2314yes—
127C2×#4325—42no—
128C2×#4325C2314yes—
129C2×#4324—24no—
130C2×#4324—42no—
131C2×#4324—42no—
132C2×#4324—42no—
133C2×#4324C2314yes—
134C2×#4324C2314yes—
135C2×#4324C2314yes—
136C2×#4324C2314yes—
137C2×#4323—24no—
138C2×#4323—42no—
139C2×#4323C2314yes—
140C2×#4323C2314yes—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157#66951—28no—
158#66951—28no—
159#66945—28no—
160#66928—22no—
161#66928—22no—
162#66928C2314yes—
163#66928C2314yes—
164C4×D44—22no—
165C4×D44C2314yes—
166#66922—22no—
167#66922C2314yes—
168C4×Dic22—22no—
169C4×Dic22—22no—
170C4×Dic22C2314yes—
171C4×Dic22C2314yes—
172#66899C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66874C2314yes—
176#66874C2314yes—
177#66873C2314yes—
178#66872C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C4⋊(C11⋊C8)C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182#66867C2314yes—
183#66867C2314yes—
184C4×C11⋊C8C2314yes—
185C2×#3401—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C23×D11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11—42no—
193C2×Q8×C11C2×D414yes—
194C2×Q8×C11C2412yes—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—24no—
198C2×D4×C11—24no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—44no—
204C2×D4×C11—82no—
205C2×D4×C11C2412yes—
206C2×D4×C11C2412yes—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—24no—
210C22×C4×C11—24no—
211C22×C4×C11—82no—
212C22×C4×C11—82no—
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C2×D44—21no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44C2412yes—
227C2×C4×D11—24no—
228C2×C4×D11—44no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—22no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22—22no—
235C2×Dic22C2412yes—
236C2×Dic22C2412yes—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4C2×D414yes—
240C11×C4⋊C4C2×D414yes—
241C11×C4⋊C4C2×D414yes—
242C11×C4⋊C4C2412yes—
243C11×C22⋊C4—24no—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C42×C11—24no—
250C42×C11C2×D412yes—
251C42×C11C2×D412yes—
252C42×C11C2×D412yes—
253C42×C11C2412yes—
254C42×C11C2412yes—
255C42×C11C2412yes—
256#4326—28no—
257#4326—44no—
258#4325—44no—
259#4324—28no—
260#4324—44no—
261#4324—44no—
262#4324—44no—
263#4323—28no—
264#4323—44no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270C4⋊Dic11—21no—
271C4⋊Dic11—24no—
272C4⋊Dic11—24no—
273C4⋊Dic11C2412yes—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276C4×Dic11—24no—
277C4×Dic11—24no—
278C2×C11⋊C8—22no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8#4114yes—
282C2×C11⋊C8C2412yes—
283C2×C11⋊C8C2412yes—
284C2×C11⋊C8C2412yes—
285C2×C11⋊C8C2412yes—
286C2×#559D1111yescharacteristic, complemented
287C2×#556—111no—
288#3401—1116no—
289C2×#497—111no—
290C2×#496—111no—
291C2×#495—111no—
292C2×#464—111no—
293C2×#464—111no—
294C2×#460—111no—
295C2×#463—111no—
296C2×#463—111no—
297C2×#461—111no—
298C2×#446—111no—
299C2×#442—111no—
300C2×#441—111no—
301C2×C4×SD16—111no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11C22×D411yescharacteristic
311C22×D11—22no—
312C22×D11—42no—
313C22×D11—42no—
314C22×D11—42no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—44no—
318Q8×C11—42no—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—48no—
324D4×C11—42no—
325D4×C11—42no—
326D4×C11—84no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—84no—
338C2×C4×C11—84no—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D412yes—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C2×#4112yes—
347C2×C4×C11H(5,𝔽2)12yes—
348C2×C4×C11C2511yescharacteristic
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355D44—22no—
356D44—22no—
357D44—42no—
358C4×D11—48no—
359Dic22—22no—
360Dic22—22no—
361Dic22—22no—
362Dic22—22no—
363Dic22—42no—
364Dic22—42no—
365C11⋊C8—22no—
366C11⋊C8—22no—
367C11⋊C8—22no—
368C11⋊C8C2×#4114yes—
369C22×Q16—111no—
370C22×Q16—111no—
371C22×SD16—111no—
372C22×SD16—111no—
373C22×SD16—111no—
374C22×SD16—111no—
375C22×SD16—111no—
376C22×D8—111no—
377C22×D8—111no—
378#559—24no—
379#559C2×D1118yescomplemented
380#556—118no—
381#556—224no—
382C2×C4⋊Q8—111no—
383C2×#127C2×D1111yescharacteristic
384C2×#126—221no—
385C2×#126—221no—
386C2×#124—21no—
387C2×#124—111no—
388C2×#124—111no—
389C2×#124C2×D1111yescharacteristic
390C2×#124C2×D1111yescharacteristic
391C2×#123—21no—
392C2×#123—21no—
393C2×C22⋊Q8—221no—
394C2×C4×Q8—111no—
395C2×C4×Q8—111no—
396C2×C4×Q8C2×D1111yescharacteristic
397C2×C4×Q8C2×D1111yescharacteristic
398C2×C4×D4—21no—
399C2×C4×D4—111no—
400C2×C4×D4C2×D1111yescharacteristic
401C2×C4×D4C2×D1111yescharacteristic
402C2×#117—221no—
403#497—118no—
404#496—118no—
405#495—118no—
406#464—118no—
407#464—118no—
408#463—118no—
409#463—118no—
410#461—118no—
411#460—118no—
412#446—118no—
413#442—118no—
414#441—118no—
415C4×SD16—118no—
416C2×#106—111no—
417C2×C4⋊C8—111no—
418C2×C4⋊C8—111no—
419C2×C4⋊C8—111no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#97—111no—
427C2×#97—111no—
428C2×C4×C8—111no—
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#55012yes—
438C22×C11#57512yes—
439C22×C11#57712yes—
440C22×C11C23×D411yescharacteristic
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—84no—
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11#55012yes—
454C4×C11C22×#4111yescharacteristic
455C4×C11C2×H(5,𝔽2)11yescharacteristic
456Dic11—42no—
457Dic11—42no—
458Dic11—42no—
459C22×Q8—111no—
460C22×Q8—111no—
461C22×Q8C22⋊D1111yescharacteristic
462C22×Q8C22×D1111yescharacteristic
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—111no—
466C22×D4C22×D1111yescharacteristic
467C22×D4C22×D1111yescharacteristic
468C23×C4—21no—
469C23×C4—21no—
470C23×C4—221no—
471C2×Q16—114no—
472C2×Q16—114no—
473C2×Q16—224no—
474C2×Q16—442no—
475C2×SD16—114no—
476C2×SD16—114no—
477C2×SD16—114no—
478C2×SD16—114no—
479C2×SD16—114no—
480C2×SD16—224no—
481C2×SD16—442no—
482C2×SD16—442no—
483C2×SD16—442no—
484C2×SD16—442no—
485C2×D8—114no—
486C2×D8—114no—
487C2×D8—224no—
488C2×D8—442no—
489C22×C8—111no—
490C22×C8—111no—
491C22×C8—111no—
492C22×C8—111no—
493C4⋊Q8—114no—
494C4⋊Q8—222no—
495#127—22no—
496#127C22×D1114yes—
497#126—228no—
498#126—228no—
499#124—28no—
500#124—22no—
501#124—22no—
502#124—114no—
503#124—114no—
504#124—222no—
505#124—222no—
506#124C22×D1114yes—
507#124C22×D1114yes—
508#123—28no—
509#123—28no—
510C22⋊Q8—228no—
511C4×Q8—22no—
512C4×Q8—114no—
513C4×Q8—114no—
514C4×Q8—222no—
515C4×Q8—222no—
516C4×Q8C22⋊D1114yes—
517C4×Q8C22×D1114yes—
518C4×Q8C22×D1114yes—
519C4×D4—28no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—114no—
523C4×D4—222no—
524C4×D4C22×D1114yes—
525C4×D4C22×D1114yes—
526#117—228no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4C22⋊D1111yescharacteristic
534C2×C4⋊C4C22⋊D1111yescharacteristic
535C2×C4⋊C4C22⋊D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C42—21no—
549C2×C42—221no—
550C2×C42—221no—
551C2×C42C22×D1111yescharacteristic
552C2×C42C22×D1111yescharacteristic
553C2×C42C22×D1111yescharacteristic
554#106—114no—
555C4⋊C8—114no—
556C4⋊C8—114no—
557C4⋊C8—114no—
558#103—114no—
559#103—114no—
560#103—114no—
561#102—114no—
562#102—114no—
563#102—114no—
564#97—114no—
565#97—114no—
566C4×C8—114no—
567C2×C11—82no—
568C2×C11—82no—
569C2×C11#340114yescomplemented
570C2×C11C2×#55011yescharacteristic
571C2×C11C2×#57511yescharacteristic
572C2×C11C2×#57711yescharacteristic
573D11—82no—
574C24—21no—
575C24—21no—
576C24—221no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—42no—
581C2×Q8—112no—
582C2×Q8—112no—
583C2×Q8—221no—
584C2×Q8—221no—
585C2×Q8—222no—
586C2×Q8—222no—
587C2×Q8—222no—
588C2×Q8—222no—
589C2×Q8C2×C22⋊D1114yes—
590C2×Q8C23×D1112yes—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—44no—
600C2×D4—82no—
601C2×D4—112no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—221no—
605C2×D4C23×D1112yes—
606C2×D4C23×D1112yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—224no—
617C22×C4—444no—
618C22×C4C2×C22⋊D1111yescharacteristic
619C22×C4C2×C22⋊D1111yescharacteristic
620C22×C4C2×C22⋊D1111yescharacteristic
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C23×D1111yescharacteristic
625Q16—228no—
626Q16—444no—
627SD16—228no—
628SD16—444no—
629SD16—444no—
630SD16—444no—
631SD16—444no—
632D8—228no—
633D8—444no—
634C2×C8—114no—
635C2×C8—112no—
636C2×C8—112no—
637C2×C8—112no—
638C2×C8—112no—
639C2×C8—222no—
640C2×C8—222no—
641C2×C8—222no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—112no—
645C4⋊C4—221no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4C2×C22⋊D1114yes—
651C4⋊C4C2×C22⋊D1114yes—
652C4⋊C4C2×C22⋊D1114yes—
653C4⋊C4C23×D1112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C42—24no—
666C42—224no—
667C42—224no—
668C42C2×C22⋊D1112yes—
669C42C2×C22⋊D1112yes—
670C42C2×C22⋊D1112yes—
671C42C23×D1112yes—
672C42C23×D1112yes—
673C42C23×D1112yes—
674C11C2×#340111yescharacteristic, complemented, Sylow
675C23—22no—
676C23—22no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—222no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23C22×C22⋊D1111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—44no—
691Q8—42no—
692Q8—222no—
693Q8—222no—
694Q8—222no—
695Q8—222no—
696Q8—442no—
697Q8—442no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—42no—
704D4—42no—
705D4—84no—
706D4—222no—
707D4—222no—
708D4—442no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—448no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4#41×D1112yes—
729C2×C4#6704212yes—
730C2×C4C22×C22⋊D1112yes—
731C2×C4C22×C22⋊D1112yes—
732C2×C4C22×C22⋊D1112yes—
733C2×C4C22×C22⋊D1112yes—
734C2×C4C22×C22⋊D1112yes—
735C2×C4C22×C22⋊D1112yes—
736C2×C4C22×C22⋊D1111yescharacteristic
737C2×C4C24×D1111yescharacteristic
738C8—114no—
739C8—222no—
740C8—222no—
741C8—222no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—84no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—884no—
754C22#1062335312yes—
755C22#1062336512yes—
756C22#1062336712yes—
757C22C23×C22⋊D1111yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—442no—
767C4—442no—
768C4—442no—
769C4#1062336512yes—
770C4C2×#41×D1111yescharacteristic
771C4C2×#6704211yescharacteristic
772C2—82no—
773C2—82no—
774C2—882no—
775C2#1308167614yesdirect product factor
776C2C2×#1062336511yescharacteristic
777C2C2×#1062335311yescharacteristic
778C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×#10622687C2
hypercenterC2×#559D11
hypocenterC11C2×#3401
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#10623115C2semidirect
2. #13081676C2direct (N × H)
3. C2×#10622673C2semidirect
5. C2×#10622672C2semidirect
6. C2×#10622641C2semidirect
7. C2×#10622667C2semidirect
8. C2×#10622688C2semidirect
9. C2×#10622629C2semidirect
10. C2×#10622670C2semidirect
11. C2×#10622632C2semidirect
12. C2×#10622637C2semidirect
13. C2×#10622627C2semidirect
14. C2×#10622643C2semidirect
15. C2×C4×#4324C2semidirect
16. C2×C11×#559C2semidirect
18. C11×#559C22semidirect
41. #10623115C22semidirect
54. #10622688C22semidirect
56. #10622673C22semidirect
57. #10622672C22semidirect
58. #10622670C22semidirect
59. #10622667C22semidirect
60. #10622643C22semidirect
61. #10622641C22semidirect
62. #10622637C22semidirect
63. #10622632C22semidirect
64. C4×#4324C22semidirect
65. #10622629C22semidirect
66. #10622627C22semidirect
286. C2×#559D11semidirect
379. #559C2×D11semidirect
569. C2×C11#3401semidirect
674. C11C2×#3401semidirect
775. C2#13081676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
#130816762
C2×#106226732
C2×#106226872
C2×#106226722
C2×#106226412
C2×#106226672
C2×#106226882
C2×#106226292
C2×#106226702
C2×#106226322
C2×#106226372
C2×#106226272
C2×#106226432
C2×C4×#43242
C2×C11×#5592
C2×#340111