Finite Group Databasebeta

← C2×#13078736 #15621965

Subgroups — C2×#13078736 #15621965

Order 2816.

2398 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic
2C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
3#13078736C2116yesmaximal, direct product factor
4C2×#10622495C211yesmaximal, characteristic, complemented
5C2×#10622387C211yesmaximal, characteristic, complemented
6C2×#10622488C211yesmaximal, characteristic, complemented
7C2×#10622407C211yesmaximal, characteristic, complemented
8C2×#10622375C211yesmaximal, characteristic, complemented
9C2×#10622776C211yesmaximal, characteristic, complemented
10C2×#10622419C211yesmaximal, characteristic, complemented
11C2×#10622783C211yesmaximal, characteristic, complemented
12C2×#10622323C211yesmaximal, characteristic, complemented
13C2×#10622631C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×#10622318C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4339—21no—
19C22×C11×SD16C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66993C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C22×#4324C2211yescharacteristic
27C2×C4×C22⋊D11—21no—
28C22×#4314C2211yescharacteristic
29C4×Q8×D11—24no—
30C4×Q8×D11C2218yescomplemented
31#10623079—24no—
32#10623079C2218yes—
33C2×#66948C2211yescharacteristic
34C2×C4⋊C4×D11—21no—
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×#66941C2211yescharacteristic
37C2×#66940—21no—
38C2×#66940C2211yescharacteristic
39C2×#66938—21no—
40C2×#66937—21no—
41C2×C4×D44C2211yescharacteristic
42C2×C42×D11—21no—
43C2×C42×D11C2211yescharacteristic
44C2×C4×Dic22—21no—
45C2×C4×Dic22C2211yescharacteristic
46C11×#440C2218yescomplemented
47C2×C11×#107C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53#10622783C2218yescomplemented
54#10622776C2218yescomplemented
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62#10622639C2218yescomplemented
63#10622631C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66867C2211yescharacteristic
69#10622495C2218yescomplemented
70#10622488C2218yescomplemented
71#10622419C2218yescomplemented
72#10622407C2218yescomplemented
73#10622387C2218yescomplemented
74#10622375C2218yescomplemented
75#10622323C2218yescomplemented
76#10622318C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×Q8×D11—24no—
84C2×Q8×D11—22no—
85C2×Q8×D11—24no—
86C2×Q8×D11C2314yes—
87C2×#4339—28no—
88C2×#4339—48no—
89C22×D44—21no—
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11D411yescharacteristic
95C22×C4×D11D411yescharacteristic
96C22×C4×D11C2311yescharacteristic
97C22×Dic22—21no—
98C22×Dic22—21no—
99C22×Dic22C2311yescharacteristic
100C2×C11×SD16—24no—
101C2×C11×SD16C2314yes—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C4×Q8×C11—22no—
105C4×Q8×C11C2314yes—
106C4×D4×C11—22no—
107C4×D4×C11C2314yes—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—21no—
115Q8×Dic11—22no—
116Q8×Dic11C2314yes—
117C2×#4325—24no—
118C2×#4325C2314yes—
119#66993—22no—
120#66993C2314yes—
121#66991—22no—
122#66991C2314yes—
123C2×#4324—24no—
124C2×#4324C2314yes—
125C4×C22⋊D11—28no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11D411yescharacteristic
139C2×C4×Dic11D411yescharacteristic
140C2×C4×Dic11C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C2×#4314—24no—
144C2×#4314C2314yes—
145#66948—22no—
146#66948C2314yes—
147C4⋊C4×D11—28no—
148C4⋊C4×D11—22no—
149C4⋊C4×D11C2314yes—
150#66941—22no—
151#66941C2314yes—
152#66940—28no—
153#66940—22no—
154#66940C2314yes—
155#66938—28no—
156#66937—28no—
157C4×D44—22no—
158C4×D44C2314yes—
159C42×D11—28no—
160C42×D11D414yes—
161C42×D11C2314yes—
162C4×Dic22—22no—
163C4×Dic22—28no—
164C4×Dic22C2314yes—
165C11×#107C2314yes—
166C11×#103C2314yes—
167C11×#102C2314yes—
168C11×#97C2314yes—
169#66899C2314yes—
170#66896C2314yes—
171#66885C2314yes—
172(C2×D11)⋊C8C2314yes—
173(C2×D11)⋊C8C2314yes—
174#66882C2314yes—
175#66880C2314yes—
176Dic11⋊C8C2314yes—
177Dic11⋊C8C2314yes—
178#66874C2314yes—
179#66873C2314yes—
180#66871C2314yes—
181#66871C2314yes—
182#66867C2314yes—
183C2×#3112—111nomaximal, Sylow
184C24×C11—21no—
185C23×D11—21no—
186C23×D11C2×D411yescharacteristic
187C2×Q8×C11—21no—
188C2×Q8×C11—22no—
189C2×Q8×C11#4114yescomplemented
190C2×Q8×C11C2412yes—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11C2412yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—24no—
199C22×C4×C11—44no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11—44no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215Q8×D11—216no—
216Q8×D11—28no—
217Q8×D11—28no—
218#4339—432no—
219C2×D44—24no—
220C2×D44—21no—
221C2×D44—22no—
222C2×D44—22no—
223C2×D44—44no—
224C2×D44C2412yes—
225C2×C4×D11—28no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—22no—
232C2×C4×D11—22no—
233C2×C4×D11—44no—
234C2×C4×D11—44no—
235C2×C4×D11C2×D414yes—
236C2×C4×D11C2×D412yes—
237C2×C4×D11C2×D414yes—
238C2×C4×D11C2412yes—
239C2×Dic22—28no—
240C2×Dic22—24no—
241C2×Dic22—24no—
242C2×Dic22—21no—
243C2×Dic22—22no—
244C2×Dic22—44no—
245C2×Dic22#4114yescomplemented
246C2×Dic22C2412yes—
247C11×SD16—28no—
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C2×C8×C11C2412yes—
251C2×C8×C11C2412yes—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C22⋊C4—24no—
258C42×C11—24no—
259C42×C11C2×D412yes—
260C42×C11C2412yes—
261C22⋊Dic11—24no—
262#4325—28no—
263#4324—28no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266C4⋊Dic11—24no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11C2412yes—
270C4⋊Dic11C2412yes—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275C4×Dic11—24no—
276C4×Dic11—24no—
277C4×Dic11—24no—
278C4×Dic11C2×D414yes—
279C4×Dic11C2×D412yes—
280C4×Dic11C2×D414yes—
281C4×Dic11C2412yes—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8C2412yes—
285C2×C11⋊C8C2412yes—
286#4314—28no—
287C2×#532—111no—
288C22×C4×Q8—111no—
289#3112—1116no—
290C2×#480—111no—
291C2×#480—111no—
292C2×#477—111no—
293C2×#477—111no—
294C2×#460—111no—
295C2×#460—111no—
296C2×#448—111no—
297C2×#448—111no—
298C2×#440—111no—
299C2×#440—111no—
300C2×#440—111no—
301C2×#440D1111yescharacteristic, complemented
302C2×#432—111no—
303C23×C11—22no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11C22×D411yescharacteristic
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11—42no—
314C22×D11AGL(1,ℤ/8)14yes—
315C22×D11C22×D412yes—
316Q8×C11—24no—
317Q8×C11—22no—
318Q8×C11C2×#4114yescomplemented
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—42no—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—48no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C2×#4112yes—
335C2×C4×C11C2×#4112yes—
336C2×C4×C11C2511yescharacteristic
337C22⋊D11—48no—
338C22⋊D11—48no—
339C22⋊D11—48no—
340C2×Dic11—22no—
341C2×Dic11—24no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11#13714yes—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352D44—22no—
353D44—22no—
354D44—48no—
355D44—42no—
356C4×D11—216no—
357C4×D11—28no—
358C4×D11—24no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—28no—
362C4×D11—48no—
363C4×D11—48no—
364Dic22—216no—
365Dic22—24no—
366Dic22—22no—
367Dic22—48no—
368Dic22C2×#4114yescomplemented
369C8×C11—22no—
370C8×C11—22no—
371C11⋊C8—22no—
372C11⋊C8—22no—
373C22×#41—221no—
374C23×Q8—111no—
375C22×SD16—111no—
376C22×SD16—111no—
377C22×SD16—111no—
378C22×SD16C2×D1111yescharacteristic
379#532—118no—
380#532—224no—
381C2×C4⋊Q8—111no—
382C2×#127—111no—
383C2×#124—221no—
384C2×#121—111no—
385C2×#121—111no—
386C2×#121—221no—
387C2×C4×Q8—111no—
388C2×C4×Q8—118no—
389C2×C4×Q8—111no—
390C2×C4×Q8—111no—
391C2×C4×Q8—221no—
392C2×C4×Q8—221no—
393C2×C4×Q8—224no—
394C2×C4×Q8C2×D1111yescharacteristic
395C2×C4×D4—111no—
396C2×C4×D4—221no—
397C2×C4×D4C2×D1111yescharacteristic
398C22×C4⋊C4—111no—
399C22×C4⋊C4—221no—
400C22×C42—111no—
401C22×C42—221no—
402#480—118no—
403#480—118no—
404#477—118no—
405#477—118no—
406#460—118no—
407#460—118no—
408#448—118no—
409#448—118no—
410#440—118no—
411#440—118no—
412#440—118no—
413#440C2×D1118yescomplemented
414#432—118no—
415C2×#107—111no—
416C2×#107—111no—
417C2×#107—111no—
418C2×#107C2×D1111yescharacteristic
419C2×C4⋊C8—111no—
420C2×C4⋊C8—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103C2×D1111yescharacteristic
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102C2×D1111yescharacteristic
429C2×C22⋊C8—111no—
430C2×C22⋊C8—111no—
431C2×#97—111no—
432C2×#97C2×D1111yescharacteristic
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—42no—
436C22×C11—84no—
437C22×C11#52512yes—
438C22×C11C2×AGL(1,ℤ/8)12yes—
439C22×C11C2×#13712yes—
440C22×C11C23×D411yescharacteristic
441C2×D11—28no—
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—84no—
448C2×D11C2×AGL(1,ℤ/8)14yes—
449C4×C11—24no—
450C4×C11—22no—
451C4×C11—22no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11#52512yes—
455C4×C11C22×#4111yescharacteristic
456C4×C11C22×#4111yescharacteristic
457Dic11—22no—
458Dic11—24no—
459Dic11—22no—
460Dic11—42no—
461Dic11—42no—
462Dic11C2×#13714yes—
463C2×#41—228no—
464C2×#41—448no—
465C22×Q8—114no—
466C22×Q8—111no—
467C22×Q8—221no—
468C22×Q8—221no—
469C22×Q8—222no—
470C22×Q8—224no—
471C22×Q8—224no—
472C22×Q8C22×D1111yescharacteristic
473C22×D4—111no—
474C22×D4—221no—
475C22×D4—221no—
476C22×D4—221no—
477C22×D4—221no—
478C22×D4C22×D1111yescharacteristic
479C23×C4—21no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4—221no—
484C23×C4—221no—
485C23×C4—221no—
486C2×SD16—24no—
487C2×SD16—114no—
488C2×SD16—114no—
489C2×SD16—114no—
490C2×SD16—224no—
491C2×SD16—224no—
492C2×SD16—224no—
493C2×SD16C22×D1114yes—
494C22×C8—111no—
495C22×C8—111no—
496C22×C8C22×D1111yescharacteristic
497C22×C8C22×D1111yescharacteristic
498C4⋊Q8—114no—
499C4⋊Q8—222no—
500#127—114no—
501#127—222no—
502#124—228no—
503#121—114no—
504#121—114no—
505#121—228no—
506#121—222no—
507#121—222no—
508C4×Q8—22no—
509C4×Q8—114no—
510C4×Q8—114no—
511C4×Q8—114no—
512C4×Q8—228no—
513C4×Q8—228no—
514C4×Q8—222no—
515C4×Q8—222no—
516C4×Q8—222no—
517C4×Q8C22×D1114yes—
518C4×D4—22no—
519C4×D4—114no—
520C4×D4—228no—
521C4×D4—222no—
522C4×D4C22×D1114yes—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—222no—
528C2×C4⋊C4—228no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C42—21no—
541C2×C42—111no—
542C2×C42—111no—
543C2×C42—111no—
544C2×C42—114no—
545C2×C42—114no—
546C2×C42—228no—
547C2×C42—221no—
548C2×C42—221no—
549C2×C42—221no—
550C2×C42C22×D1111yescharacteristic
551#107—114no—
552#107—114no—
553#107—114no—
554#107C22×D1114yes—
555C4⋊C8—114no—
556C4⋊C8—114no—
557#103—114no—
558#103—114no—
559#103—114no—
560#103C22×D1114yes—
561#102—114no—
562#102—114no—
563#102—114no—
564#102C22×D1114yes—
565C22⋊C8—114no—
566C22⋊C8—114no—
567#97—114no—
568#97C22×D1114yes—
569C2×C11—82no—
570C2×C11#311214yescomplemented
571C2×C11C2×#52511yescharacteristic
572C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
573C2×C11C22×#13711yescharacteristic
574D11—24no—
575D11—82no—
576C24—21no—
577C24—111no—
578C24—221no—
579#41—4432no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—114no—
583C2×Q8—112no—
584C2×Q8—224no—
585C2×Q8—224no—
586C2×Q8—228no—
587C2×Q8—228no—
588C2×Q8—2216no—
589C2×Q8—228no—
590C2×Q8—222no—
591C2×Q8—221no—
592C2×Q8—444no—
593C2×Q8#433914yescomplemented
594C2×Q8C23×D1112yes—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—112no—
599C2×D4—224no—
600C2×D4—224no—
601C2×D4—224no—
602C2×D4—224no—
603C2×D4—222no—
604C2×D4—221no—
605C2×D4—222no—
606C2×D4—444no—
607C2×D4—444no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4C23×D1112yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—24no—
615C22×C4—44no—
616C22×C4—111no—
617C22×C4—111no—
618C22×C4—111no—
619C22×C4—114no—
620C22×C4—114no—
621C22×C4—112no—
622C22×C4—112no—
623C22×C4—224no—
624C22×C4—224no—
625C22×C4—224no—
626C22×C4—228no—
627C22×C4—224no—
628C22×C4—221no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4—224no—
634C22×C4—444no—
635C22×C4—444no—
636C22×C4D4×D1111yescharacteristic
637C22×C4D4×D1111yescharacteristic
638C22×C4C23×D1111yescharacteristic
639SD16—28no—
640SD16—228no—
641SD16—228no—
642SD16—228no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—112no—
646C2×C8—112no—
647C2×C8—222no—
648C2×C8—222no—
649C2×C8C23×D1112yes—
650C2×C8C23×D1112yes—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—112no—
655C4⋊C4—112no—
656C4⋊C4—224no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—221no—
661C4⋊C4—221no—
662C4⋊C4—224no—
663C4⋊C4C23×D1112yes—
664C4⋊C4C23×D1112yes—
665C22⋊C4—24no—
666C22⋊C4—224no—
667C22⋊C4—224no—
668C22⋊C4—224no—
669C42—24no—
670C42—114no—
671C42—114no—
672C42—112no—
673C42—112no—
674C42—224no—
675C42—224no—
676C42—224no—
677C42D4×D1112yes—
678C42C23×D1112yes—
679C11C2×#311211yescharacteristic, complemented, Sylow
680C23—22no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—114no—
685C23—112no—
686C23—222no—
687C23—222no—
688C23—222no—
689C23—442no—
690C23—442no—
691C23—442no—
692C23C2×D4×D1111yescharacteristic
693Q8—24no—
694Q8—22no—
695Q8—114no—
696Q8—2216no—
697Q8—224no—
698Q8—222no—
699Q8—448no—
700Q8C2×#433914yescomplemented
701D4—22no—
702D4—22no—
703D4—42no—
704D4—222no—
705D4—222no—
706D4—448no—
707D4—448no—
708D4—448no—
709D4—448no—
710D4—442no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—114no—
721C2×C4—112no—
722C2×C4—112no—
723C2×C4—112no—
724C2×C4—228no—
725C2×C4—228no—
726C2×C4—2216no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—224no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—448no—
737C2×C4—448no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4C2×#433912yes—
741C2×C4C2×D4×D1112yes—
742C2×C4C2×D4×D1112yes—
743C2×C4C2×D4×D1111yescharacteristic
744C2×C4#41×D1112yes—
745C2×C4C24×D1111yescharacteristic
746C8—22no—
747C8—22no—
748C8—222no—
749C8—222no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22—114no—
755C22—222no—
756C22—228no—
757C22—222no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—884no—
762C22#1062307812yes—
763C22D11×AGL(1,ℤ/8)12yes—
764C22D11×#13712yes—
765C22C22×D4×D1111yescharacteristic
766C4—24no—
767C4—22no—
768C4—22no—
769C4—42no—
770C4—42no—
771C4—114no—
772C4—222no—
773C4—224no—
774C4—222no—
775C4—442no—
776C4—442no—
777C4#1062307812yes—
778C4C22×#433911yescharacteristic
779C4C2×#41×D1111yescharacteristic
780C2—82no—
781C2—224no—
782C2—882no—
783C2#1307873614yesdirect product factor
784C2C2×#1062307811yescharacteristic
785C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
786C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC2×#10623079C2
hypercenterC2×#440D11
hypocenterC11C2×#3112
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D11C2semidirect
3. #13078736C2direct (N × H)
4. C2×#10622495C2semidirect
5. C2×#10622387C2semidirect
6. C2×#10622488C2semidirect
7. C2×#10622407C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622776C2semidirect
10. C2×#10622419C2semidirect
11. C2×#10622783C2semidirect
12. C2×#10622323C2semidirect
13. C2×#10622631C2semidirect
14. C2×#10622639C2semidirect
15. C2×#10622318C2semidirect
16. C2×C11×#440C2semidirect
30. C4×Q8×D11C22semidirect
46. C11×#440C22semidirect
53. #10622783C22semidirect
54. #10622776C22semidirect
62. #10622639C22semidirect
63. #10622631C22semidirect
69. #10622495C22semidirect
70. #10622488C22semidirect
71. #10622419C22semidirect
72. #10622407C22semidirect
73. #10622387C22semidirect
74. #10622375C22semidirect
75. #10622323C22semidirect
76. #10622318C22semidirect
189. C2×Q8×C11#41semidirect
245. C2×Dic22#41semidirect
301. C2×#440D11semidirect
318. Q8×C11C2×#41semidirect
368. Dic22C2×#41semidirect
413. #440C2×D11semidirect
570. C2×C11#3112semidirect
593. C2×Q8#4339semidirect
679. C11C2×#3112semidirect
700. Q8C2×#4339semidirect
783. C2#13078736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×C4×Q8×D112
#130787362
C2×#106224952
C2×#106223872
C2×#106224882
C2×#106224072
C2×#106223752
C2×#106227762
C2×#106224192
C2×#106227832
C2×#106223232
C2×#106226312
C2×#106226392
C2×#106223182
C2×C11×#4402
C2×#311211