Finite Group Databasebeta

← C2×#13078807 #15622011

Subgroups — C2×#13078807 #15622011

Order 2816.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623264C211yesmaximal, characteristic, complemented
2C2×#10623076C211yesmaximal, characteristic, complemented
3#13078807C2116yesmaximal, direct product factor
4C2×#10622501C211yesmaximal, characteristic, complemented
5C2×#10622498C211yesmaximal, characteristic, complemented
6C2×#10622697C211yesmaximal, characteristic, complemented
7C2×#10622457C211yesmaximal, characteristic, complemented
8C2×#10622629C211yesmaximal, characteristic, complemented
9C2×#10622389C211yesmaximal, characteristic, complemented
10C2×#10622386C211yesmaximal, characteristic
11C2×#10622398C211yesmaximal, characteristic, complemented
12C2×#10622502C211yesmaximal, characteristic, complemented
13C2×#10622371C211yesmaximal, characteristic, complemented
14C2×#10622485C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#474C211yesmaximal, characteristic, complemented
17C22×D4×D11C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×#67000—21no—
21C2×#66999—21no—
22C2×D4×Dic11C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C22×(C2×D11)⋊C4—21no—
27C22×D88C2211yescharacteristic
28C22×#4314C2211yescharacteristic
29#10623264—24no—
30#10623264C2218yescomplemented
31#10623076—24no—
32#10623076C2218yescomplemented
33C2×#66951—21no—
34C2×#66950C2211yescharacteristic
35C2×#66948C2211yescharacteristic
36C2×#66947—21no—
37C2×#66946C2211yescharacteristic
38C2×#66946C2211yescharacteristic, complemented
39C2×#66945C2211yescharacteristic
40C2×#66940C2211yescharacteristic, complemented
41C2×(C22⋊D11)⋊C4—21no—
42C2×C22⋊C4×D11—21no—
43C2×#66928C2211yescharacteristic, complemented
44C2×C4×D44C2211yescharacteristic
45C2×#66925C2211yescharacteristic
46C11×#474C2218yescomplemented
47C2×C11×#107C2211yescharacteristic, complemented
48C2×C11×#107C2211yescharacteristic, complemented
49C2×C11×C4⋊C8C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66885C2211yescharacteristic, complemented
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66880C2211yescharacteristic, complemented
56C2×#66879C2211yescharacteristic, complemented
57C2×C8×Dic11C2211yescharacteristic, complemented
58#10622697C2218yescomplemented
59#10622629C2218yescomplemented
60C2×#66874C2211yescharacteristic, complemented
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic, complemented
64C2×#66872C2211yescharacteristic, complemented
65C2×#66872C2211yescharacteristic, complemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
67#10622502C2218yescomplemented
68#10622501C2218yescomplemented
69#10622498C2218yescomplemented
70#10622485C2218yescomplemented
71#10622457C2218yescomplemented
72#10622453C2218yescomplemented
73#10622398C2218yescomplemented
74#10622389C2218yescomplemented
75#10622386C2218yes—
76#10622371C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C23×Dic11—21no—
83C2×D4×D11—24no—
84C2×D4×D11—24no—
85C2×D4×D11—22no—
86C2×D4×D11C2314yes—
87C22×D44—21no—
88C22×D44C2311yescharacteristic
89C22×D44C2311yescharacteristic
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11C2311yescharacteristic
94C22×Dic22C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C11×C4⋊Q8—22no—
98C11×C4⋊Q8C2314yescomplemented
99C4×D4×C11—22no—
100C4×D4×C11C2314yes—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108#67000—28no—
109#66999—28no—
110D4×Dic11—22no—
111D4×Dic11C2314yes—
112C2×#4324—24no—
113C2×#4324C2314yes—
114C2×#4323—24no—
115C2×#4323C2314yes—
116C4×C22⋊D11—28no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—28no—
126C2×(C2×D11)⋊C4D411yescharacteristic
127C2×(C2×D11)⋊C4D411yescharacteristic
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4D411yescharacteristic
132C2×Dic11⋊C4D411yescharacteristic
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×D88—24no—
139C2×D88C2314yes—
140C2×#4314—24no—
141C2×#4314C2314yes—
142#66951—28no—
143#66950—22no—
144#66950C2314yes—
145#66948—22no—
146#66948C2314yes—
147#66947—28no—
148#66946—22no—
149#66946—22no—
150#66946C2314yes—
151#66946C2314yescomplemented
152#66945—22no—
153#66945C2314yes—
154#66940—22no—
155#66940C2314yescomplemented
156(C22⋊D11)⋊C4—28no—
157C22⋊C4×D11—28no—
158#66928—22no—
159#66928C2314yescomplemented
160C4×D44—22no—
161C4×D44C2314yes—
162#66925D414yes—
163#66925C2314yes—
164C11×#107C2314yescomplemented
165C11×#107C2314yescomplemented
166C11×C4⋊C8C2314yescomplemented
167C11×#102C2314yes—
168C11×#102C2314yes—
169#66885C2314yescomplemented
170(C2×D11)⋊C8C2314yes—
171(C2×D11)⋊C8C2314yes—
172#66880C2314yescomplemented
173#66879C2314yescomplemented
174C8×Dic11C2314yescomplemented
175#66874C2314yescomplemented
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yescomplemented
179#66872C2314yescomplemented
180#66872C2314yescomplemented
181C4⋊(C11⋊C8)C2314yescomplemented
182C2×#3118—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11—28no—
186C23×D11—24no—
187C23×D11—21no—
188C23×D11—82no—
189C23×D11—82no—
190C23×D11C2×D411yescharacteristic
191C2×Q8×C11—24no—
192C2×Q8×C11—82no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11#4114yes—
196C2×D4×C11C2412yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—24no—
201C22×C4×C11—82no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—28no—
206C2×C22⋊D11—24no—
207C22×Dic11—24no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—82no—
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214D4×D11—216no—
215D4×D11—28no—
216D4×D11—28no—
217C2×D44—24no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—22no—
221C2×D44—22no—
222C2×D44—22no—
223C2×D44—82no—
224C2×D44#4114yes—
225C2×D44C2412yes—
226C2×D44C2412yes—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11—82no—
233C2×C4×D11—82no—
234C2×C4×D11—82no—
235C2×C4×D11C2×D412yes—
236C2×C4×D11C2412yes—
237C2×Dic22—21no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22C2412yes—
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—21no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4C2412yes—
250C11×C4⋊C4C2412yes—
251C11×C4⋊C4C2412yes—
252C11×C22⋊C4—24no—
253C42×C11C2×D412yes—
254C42×C11C2412yes—
255C22⋊Dic11—24no—
256#4324—28no—
257#4323—28no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4C2×D414yes—
267(C2×D11)⋊C4C2×D414yes—
268C4⋊Dic11—24no—
269C4⋊Dic11—21no—
270C4⋊Dic11C2412yes—
271Dic11⋊C4—24no—
272Dic11⋊C4C2×D414yes—
273Dic11⋊C4C2×D414yes—
274C4×Dic11—24no—
275C4×Dic11—24no—
276C4×Dic11C2×D412yes—
277C4×Dic11C2412yes—
278C2×C11⋊C8—22no—
279C2×C11⋊C8—22no—
280C2×C11⋊C8C2412yes—
281C2×C11⋊C8C2412yes—
282D88—28no—
283#4314—28no—
284C2×#542—111no—
285C2×#518—111no—
286#3118—1116no—
287C2×#485—111no—
288C2×#482—111no—
289C2×#476—111no—
290C2×#474D1111yescharacteristic, complemented
291C2×#463—111no—
292C2×#463—111no—
293C2×#450—111no—
294C2×#447—111no—
295C2×#442—111no—
296C2×#440—111no—
297C2×C4×SD16—111no—
298C2×C4×D8—111no—
299C2×#433—111no—
300C23×C11—24no—
301C23×C11—22no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11C22×D411yescharacteristic
305C22×D11—22no—
306C22×D11—24no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—216no—
311C22×D11—22no—
312C22×D11—42no—
313C22×D11—42no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—84no—
318C22×D11—84no—
319C22×D11—816no—
320C22×D11C22×D412yes—
321Q8×C11—84no—
322D4×C11—24no—
323D4×C11—22no—
324D4×C11C2×#4114yes—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—84no—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4112yes—
338C2×C4×C11C2×#4112yes—
339C2×C4×C11C2511yescharacteristic
340C22⋊D11—216no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—84no—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352D44—24no—
353D44—22no—
354D44—22no—
355D44—22no—
356D44—42no—
357D44—84no—
358D44C2×#4114yes—
359C4×D11—24no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—84no—
363C4×D11—84no—
364C4×D11—84no—
365Dic22—22no—
366Dic22—22no—
367Dic22—42no—
368C8×C11—22no—
369C8×C11—22no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C23×D4—111no—
373C22×SD16—111no—
374C22×SD16—111no—
375C22×D8—111no—
376C22×D8—111no—
377#542—118no—
378#542—224no—
379C2×C4⋊Q8C2×D1111yescharacteristic, complemented
380C2×#126—221no—
381C2×#124—111no—
382C2×#124—221no—
383C2×#123—221no—
384C2×C22⋊Q8—111no—
385C2×C22⋊Q8—221no—
386C2×#121—111no—
387#518—118no—
388#518—224no—
389C2×C4×Q8—111no—
390C2×C4×D4—111no—
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×C4×D4—111no—
394C2×C4×D4—221no—
395C2×C4×D4—221no—
396C2×C4×D4C2×D1111yescharacteristic
397C2×#117—111no—
398C2×#117—111no—
399C22×C22⋊C4—221no—
400C22×C22⋊C4—221no—
401#485—118no—
402#482—118no—
403#476—118no—
404#474C2×D1118yescomplemented
405#463—118no—
406#463—118no—
407#450—118no—
408#447—118no—
409#442—118no—
410#440—118no—
411C4×SD16—118no—
412C4×D8—118no—
413#433—118no—
414C2×#107C2×D1111yescharacteristic, complemented
415C2×#107C2×D1111yescharacteristic, complemented
416C2×#106—111no—
417C2×#106—111no—
418C2×C4⋊C8—111no—
419C2×C4⋊C8C2×D1111yescharacteristic, complemented
420C2×#103—111no—
421C2×#103—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102C2×D1111yescharacteristic
427C2×#102C2×D1111yescharacteristic
428C2×C22⋊C8—111no—
429C2×C22⋊C8—111no—
430C2×#97—111no—
431C2×C4×C8—111no—
432C22×C11—24no—
433C22×C11—48no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11#52512yes—
437C22×C11#57612yes—
438C22×C11#57712yes—
439C22×C11C23×D411yescharacteristic
440C2×D11—22no—
441C2×D11—24no—
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—44no—
445C2×D11—48no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—816no—
452C2×D11—84no—
453C4×C11—22no—
454C4×C11—22no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11#52512yes—
459C4×C11C22×#4111yescharacteristic
460C4×C11C22×#4111yescharacteristic
461Dic11—22no—
462Dic11—22no—
463Dic11—22no—
464Dic11—42no—
465Dic11—42no—
466C25—221no—
467C22×Q8—21no—
468C22×Q8—111no—
469C22×D4—114no—
470C22×D4—111no—
471C22×D4—111no—
472C22×D4—221no—
473C22×D4—222no—
474C22×D4—221no—
475C22×D4—224no—
476C22×D4—224no—
477C22×D4C22×D1111yescharacteristic
478C23×C4—21no—
479C23×C4—111no—
480C23×C4—221no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4—221no—
484C2×SD16—114no—
485C2×SD16—114no—
486C2×SD16—224no—
487C2×SD16—224no—
488C2×D8—114no—
489C2×D8—114no—
490C2×D8—224no—
491C2×D8—224no—
492C22×C8—111no—
493C22×C8—111no—
494C22×C8C22×D1111yescharacteristic
495C22×C8C22×D1111yescharacteristic
496C4⋊Q8—22no—
497C4⋊Q8C22×D1114yescomplemented
498#126—228no—
499#124—114no—
500#124—228no—
501#124—222no—
502#123—228no—
503C22⋊Q8—114no—
504C22⋊Q8—222no—
505C22⋊Q8—228no—
506#121—114no—
507#121—222no—
508C4×Q8—114no—
509C4×Q8—222no—
510C4×D4—22no—
511C4×D4—114no—
512C4×D4—114no—
513C4×D4—114no—
514C4×D4—114no—
515C4×D4—222no—
516C4×D4—222no—
517C4×D4—222no—
518C4×D4—228no—
519C4×D4—228no—
520C4×D4—222no—
521C4×D4C22×D1114yes—
522#117—114no—
523#117—114no—
524#117—114no—
525#117—222no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—111no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—111no—
538C2×C22⋊C4—228no—
539C2×C22⋊C4—228no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C42—111no—
550C2×C42—221no—
551C2×C42—221no—
552C2×C42C22×D1111yescharacteristic
553#107C22×D1114yescomplemented
554#107C22×D1114yescomplemented
555#106—114no—
556#106—114no—
557C4⋊C8—114no—
558C4⋊C8C22×D1114yescomplemented
559#103—114no—
560#103—114no—
561#102—114no—
562#102—114no—
563#102—114no—
564#102—114no—
565#102C22×D1114yes—
566#102C22×D1114yes—
567C22⋊C8—114no—
568C22⋊C8—114no—
569#97—114no—
570C4×C8—114no—
571C2×C11—44no—
572C2×C11#311814yescomplemented
573C2×C11C2×#52511yescharacteristic
574C2×C11C2×#57611yescharacteristic
575C2×C11C2×#57711yescharacteristic
576D11—42no—
577D11—44no—
578D11—82no—
579C24—21no—
580C24—111no—
581C24—224no—
582C24—228no—
583C24—221no—
584C24—221no—
585C24—882no—
586C24—882no—
587C2×Q8—24no—
588C2×Q8—82no—
589C2×Q8—112no—
590C2×Q8—221no—
591C2×Q8—222no—
592C2×Q8—222no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—114no—
596C2×D4—112no—
597C2×D4—112no—
598C2×D4—224no—
599C2×D4—224no—
600C2×D4—228no—
601C2×D4—2216no—
602C2×D4—228no—
603C2×D4—228no—
604C2×D4—221no—
605C2×D4—221no—
606C2×D4—222no—
607C2×D4—222no—
608C2×D4—222no—
609C2×D4—882no—
610C2×D4#434314yes—
611C2×D4C23×D1112yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—82no—
617C22×C4—111no—
618C22×C4—111no—
619C22×C4—111no—
620C22×C4—112no—
621C22×C4—112no—
622C22×C4—224no—
623C22×C4—224no—
624C22×C4—224no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—224no—
630C22×C4—882no—
631C22×C4—882no—
632C22×C4—882no—
633C22×C4—882no—
634C22×C4D4×D1111yescharacteristic
635C22×C4D4×D1111yescharacteristic
636C22×C4C23×D1111yescharacteristic
637SD16—228no—
638SD16—228no—
639D8—228no—
640D8—228no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—112no—
644C2×C8—112no—
645C2×C8—222no—
646C2×C8—222no—
647C2×C8C23×D1112yes—
648C2×C8C23×D1112yes—
649C4⋊C4—24no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—114no—
654C4⋊C4—114no—
655C4⋊C4—112no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4—221no—
659C4⋊C4C23×D1112yes—
660C4⋊C4C23×D1112yes—
661C4⋊C4C23×D1112yes—
662C22⋊C4—24no—
663C22⋊C4—114no—
664C22⋊C4—114no—
665C22⋊C4—224no—
666C22⋊C4—224no—
667C22⋊C4—224no—
668C22⋊C4—224no—
669C22⋊C4—224no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C42—112no—
675C42—112no—
676C42—224no—
677C42—224no—
678C42D4×D1112yes—
679C42C23×D1112yes—
680C11C2×#311811yescharacteristic, complemented, Sylow
681C23—24no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—112no—
686C23—2216no—
687C23—222no—
688C23—222no—
689C23—222no—
690C23—224no—
691C23—222no—
692C23—222no—
693C23—442no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23—442no—
698C23—884no—
699C23—884no—
700C23—8816no—
701C23C2×D4×D1111yescharacteristic
702Q8—84no—
703Q8—222no—
704Q8—222no—
705Q8—442no—
706D4—24no—
707D4—22no—
708D4—114no—
709D4—2216no—
710D4—224no—
711D4—222no—
712D4—222no—
713D4—222no—
714D4—442no—
715D4—884no—
716D4C2×#434314yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—112no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—224no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—884no—
740C2×C4—884no—
741C2×C4—884no—
742C2×C4—884no—
743C2×C4C2×D4×D1112yes—
744C2×C4C2×D4×D1112yes—
745C2×C4C2×D4×D1111yescharacteristic
746C2×C4C2×#434312yes—
747C2×C4#41×D1112yes—
748C2×C4C24×D1111yescharacteristic
749C8—22no—
750C8—22no—
751C8—222no—
752C8—222no—
753C22—24no—
754C22—48no—
755C22—42no—
756C22—42no—
757C22—222no—
758C22—224no—
759C22—222no—
760C22—222no—
761C22—444no—
762C22—448no—
763C22—442no—
764C22—442no—
765C22—442no—
766C22—442no—
767C22—442no—
768C22—8816no—
769C22—884no—
770C22#1062315812yes—
771C22#1062328812yes—
772C22#1062330912yes—
773C22C22×D4×D1111yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—222no—
780C4—222no—
781C4—222no—
782C4—442no—
783C4—442no—
784C4#1062315812yes—
785C4C22×#434311yescharacteristic
786C4C2×#41×D1111yescharacteristic
787C2—44no—
788C2—442no—
789C2—444no—
790C2—882no—
791C2#1307880714yesdirect product factor
792C2C2×#1062315811yescharacteristic
793C2C2×#1062328811yescharacteristic
794C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC2×#10622386C2
hypercenterC2×#474D11
hypocenterC11C2×#3118
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623264C2semidirect
2. C2×#10623076C2semidirect
3. #13078807C2direct (N × H)
4. C2×#10622501C2semidirect
5. C2×#10622498C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622457C2semidirect
8. C2×#10622629C2semidirect
9. C2×#10622389C2semidirect
11. C2×#10622398C2semidirect
12. C2×#10622502C2semidirect
13. C2×#10622371C2semidirect
14. C2×#10622485C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#474C2semidirect
18. C2×C11×C4⋊Q8C22semidirect
30. #10623264C22semidirect
32. #10623076C22semidirect
38. C2×#66946C22semidirect
40. C2×#66940C22semidirect
43. C2×#66928C22semidirect
46. C11×#474C22semidirect
47. C2×C11×#107C22semidirect
48. C2×C11×#107C22semidirect
49. C2×C11×C4⋊C8C22semidirect
52. C2×#66885C22semidirect
55. C2×#66880C22semidirect
56. C2×#66879C22semidirect
57. C2×C8×Dic11C22semidirect
58. #10622697C22semidirect
59. #10622629C22semidirect
60. C2×#66874C22semidirect
63. C2×#66873C22semidirect
64. C2×#66872C22semidirect
65. C2×#66872C22semidirect
66. C2×C4⋊(C11⋊C8)C22semidirect
67. #10622502C22semidirect
68. #10622501C22semidirect
69. #10622498C22semidirect
70. #10622485C22semidirect
71. #10622457C22semidirect
72. #10622453C22semidirect
73. #10622398C22semidirect
74. #10622389C22semidirect
76. #10622371C22semidirect
98. C11×C4⋊Q8C23semidirect
151. #66946C23semidirect
155. #66940C23semidirect
159. #66928C23semidirect
164. C11×#107C23semidirect
165. C11×#107C23semidirect
166. C11×C4⋊C8C23semidirect
169. #66885C23semidirect
172. #66880C23semidirect
173. #66879C23semidirect
174. C8×Dic11C23semidirect
175. #66874C23semidirect
178. #66873C23semidirect
179. #66872C23semidirect
180. #66872C23semidirect
181. C4⋊(C11⋊C8)C23semidirect
290. C2×#474D11semidirect
379. C2×C4⋊Q8C2×D11semidirect
404. #474C2×D11semidirect
414. C2×#107C2×D11semidirect
415. C2×#107C2×D11semidirect
419. C2×C4⋊C8C2×D11semidirect
497. C4⋊Q8C22×D11semidirect
553. #107C22×D11semidirect
554. #107C22×D11semidirect
558. C4⋊C8C22×D11semidirect
572. C2×C11#3118semidirect
680. C11C2×#3118semidirect
791. C2#13078807direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232642
C2×#106230762
#130788072
C2×#106225012
C2×#106224982
C2×#106226972
C2×#106224572
C2×#106226292
C2×#106223892
C2×#106223862
C2×#106223982
C2×#106225022
C2×#106223712
C2×#106224852
C2×#106224532
C2×C11×#4742
C2×#311811