Finite Group Databasebeta

← C2×#13079941 #15626565

Subgroups — C2×#13079941 #15626565

Order 2816.

2210 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic, complemented
2C2×#10623222C211yesmaximal, characteristic, complemented
3#13079941C2116yesmaximal, direct product factor
4C2×#10622488C211yesmaximal, characteristic, complemented
5C2×#10622679C211yesmaximal, characteristic, complemented
6C2×#10622483C211yesmaximal, characteristic, complemented
7C2×#10622496C211yesmaximal, characteristic, complemented
8C2×#10622388C211yesmaximal, characteristic, complemented
9C2×#10622477C211yesmaximal, characteristic, complemented
10C2×#10622391C211yesmaximal, characteristic, complemented
11C2×#10622375C211yesmaximal, characteristic, complemented
12C2×#10622457C211yesmaximal, characteristic, complemented
13C2×#10622629C211yesmaximal, characteristic, complemented
14C2×#10622399C211yesmaximal, characteristic, complemented
15C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#478C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×C4×C22⋊D11—21no—
25C22×D88C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623222—24no—
30#10623222C2218yescomplemented
31#10623079—24no—
32#10623079C2218yescomplemented
33C2×#66951—21no—
34C2×#66950C2211yescharacteristic
35C2×#66948C2211yescharacteristic
36C2×#66948C2211yescharacteristic
37C2×#66947—21no—
38C2×#66946—21no—
39C2×#66946C2211yescharacteristic
40C2×#66945—21no—
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66938—21no—
44C2×#66937—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×C42×D11C2211yescharacteristic
48C11×#478C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#106C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58#10622679C2218yescomplemented
59#10622629C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622496C2218yescomplemented
68#10622488C2218yescomplemented
69#10622483C2218yescomplemented
70#10622477C2218yescomplemented
71#10622457C2218yescomplemented
72D11×C4⋊C8C2218yescomplemented
73#10622399C2218yescomplemented
74#10622391C2218yescomplemented
75#10622388C2218yescomplemented
76#10622375C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C2×#4339—28no—
83C2×#4339—48no—
84C22×D44—21no—
85C22×D44—21no—
86C22×D44C2311yescharacteristic
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11D411yescharacteristic
91C22×C4×D11D411yescharacteristic
92C22×C4×D11C2311yescharacteristic
93C22×Dic22—21no—
94C22×Dic22C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C11×#125—22no—
98C11×#125C2314yes—
99C4×D4×C11—22no—
100C4×D4×C11C2314yes—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109#66993—22no—
110#66993C2314yes—
111#66991—22no—
112#66991C2314yes—
113C2×#4324—42no—
114C2×#4324C2314yes—
115C2×#4323—42no—
116C2×#4323C2314yes—
117C4×C22⋊D11—28no—
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×C4⋊Dic11—21no—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11D411yescharacteristic
131C2×C4×Dic11D411yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×D88—42no—
136C2×D88C2314yes—
137C2×#4314—42no—
138C2×#4314C2314yes—
139C2×C8×D11—42no—
140C2×C8×D11—42no—
141C2×C8×D11C2314yes—
142C2×C8×D11C2314yes—
143#66951—28no—
144#66950—22no—
145#66950C2314yes—
146#66948—22no—
147#66948—22no—
148#66948C2314yes—
149#66948C2314yes—
150#66947—28no—
151#66946—28no—
152#66946—22no—
153#66946C2314yes—
154#66945—28no—
155#66941—22no—
156#66941C2314yes—
157#66940—22no—
158#66940C2314yes—
159#66938—28no—
160#66937—28no—
161#66928—22no—
162#66928C2314yes—
163C4×D44—22no—
164C4×D44C2314yes—
165C42×D11D414yes—
166C42×D11C2314yes—
167C11×#107C2314yes—
168C11×#106C2314yes—
169C11×C4⋊C8C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yes—
172#66885C2314yes—
173#66880C2314yes—
174Dic11⋊C8C2314yes—
175Dic11⋊C8C2314yes—
176#66874C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C4⋊(C11⋊C8)C2314yes—
183C2×#3247—111nomaximal, Sylow
184C24×C11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11C2×D411yescharacteristic
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11C2412yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—24no—
196C22×C4×C11—44no—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11—44no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C22×Dic11C2×D411yescharacteristic
211#4339—432no—
212C2×D44—24no—
213C2×D44—24no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44—44no—
221C2×D44—44no—
222C2×D44C2412yes—
223C2×D44C2412yes—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—44no—
231C2×C4×D11—44no—
232C2×C4×D11C2×D412yes—
233C2×C4×D11C2×D414yes—
234C2×C4×D11C2×D414yes—
235C2×C4×D11C2412yes—
236C2×Dic22—24no—
237C2×Dic22—21no—
238C2×Dic22—22no—
239C2×Dic22—22no—
240C2×Dic22—44no—
241C2×Dic22C2412yes—
242C2×C8×C11—22no—
243C2×C8×C11—22no—
244C2×C8×C11C2412yes—
245C2×C8×C11C2412yes—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4C2412yes—
252C11×C4⋊C4C2412yes—
253C11×C4⋊C4C2412yes—
254C11×C22⋊C4—24no—
255C42×C11C2×D412yes—
256C42×C11C2412yes—
257C22⋊Dic11—24no—
258#4324—44no—
259#4323—44no—
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)⋊C4—24no—
267C4⋊Dic11—24no—
268C4⋊Dic11—21no—
269C4⋊Dic11C2412yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D412yes—
274C4×Dic11C2×D414yes—
275C4×Dic11C2×D414yes—
276C4×Dic11C2412yes—
277C2×C11⋊C8—22no—
278C2×C11⋊C8—22no—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281D88—44no—
282#4314—44no—
283C8×D11—44no—
284C8×D11—44no—
285C2×#532—111no—
286C2×#529—111no—
287#3247—1116no—
288C2×#477—111no—
289C2×#478—111no—
290C2×#478D1111yescharacteristic, complemented
291C2×#476—111no—
292C2×#466—111no—
293C2×#466—111no—
294C2×#465—111no—
295C2×#465—111no—
296C2×#460—111no—
297C2×#463—111no—
298C2×#463—111no—
299C2×#459—111no—
300C22×C4⋊C8—111no—
301C23×C11—22no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11—42no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11AGL(1,ℤ/8)14yes—
317C22×D11C22×D412yes—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—42no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—48no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11C22×D412yes—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11H(5,𝔽2)12yes—
334C2×C4×C112−1+412yes—
335C2×C4×C11C2511yescharacteristic
336C22⋊D11—48no—
337C22⋊D11—48no—
338C22⋊D11—48no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11#13514yes—
346C2×Dic11C22×D412yes—
347C2×Dic11C22×D412yes—
348C2×Dic11C22×D412yes—
349D44—22no—
350D44—22no—
351D44—22no—
352D44—22no—
353D44—48no—
354D44—48no—
355D44—42no—
356D44—42no—
357C4×D11—28no—
358C4×D11—24no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—28no—
362C4×D11—48no—
363C4×D11—48no—
364Dic22—22no—
365Dic22—22no—
366Dic22—48no—
367Dic22—42no—
368C8×C11—22no—
369C8×C11—22no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C22×#41—221no—
373C22×SD16—111no—
374C22×SD16—111no—
375C22×D8—111no—
376C22×D8—111no—
377C23×C8—111no—
378C23×C8—111no—
379#532—118no—
380#532—224no—
381C2×C4⋊Q8—111no—
382C2×#127—111no—
383#529—118no—
384#529—224no—
385C2×#126—221no—
386C2×#125C2×D1111yescharacteristic
387C2×#124—111no—
388C2×#124—221no—
389C2×#123—221no—
390C2×C22⋊Q8—111no—
391C2×#121—111no—
392C2×#121—111no—
393C2×#121—111no—
394C2×#121—221no—
395C2×C4×Q8—111no—
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4—221no—
399C2×C4×D4—221no—
400C2×C4×D4C2×D1111yescharacteristic
401C2×#117—221no—
402C22×C42—111no—
403#478—118no—
404#478C2×D1118yescomplemented
405#477—118no—
406#476—118no—
407#466—118no—
408#466—118no—
409#465—118no—
410#465—118no—
411#463—118no—
412#463—118no—
413#460—118no—
414#459—118no—
415C2×#107—111no—
416C2×#107C2×D1111yescharacteristic
417C2×#106—111no—
418C2×#106C2×D1111yescharacteristic
419C2×C4⋊C8—111no—
420C2×C4⋊C8—111no—
421C2×C4⋊C8—111no—
422C2×C4⋊C8—118no—
423C2×C4⋊C8C2×D1111yescharacteristic
424C2×#103—111no—
425C2×#103—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102C2×D1111yescharacteristic
431C2×#102C2×D1111yescharacteristic
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—42no—
435C22×C11—84no—
436C22×C11#53712yes—
437C22×C11C2×#13512yes—
438C22×C11C2×AGL(1,ℤ/8)12yes—
439C22×C11C23×D411yescharacteristic
440C2×D11—22no—
441C2×D11—28no—
442C2×D11—22no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—84no—
450C2×D11—84no—
451C2×D11C2×AGL(1,ℤ/8)14yes—
452C4×C11—22no—
453C4×C11—22no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11#53712yes—
458C4×C11C2×H(5,𝔽2)11yescharacteristic
459C4×C11C2×2−1+411yescharacteristic
460Dic11—22no—
461Dic11—22no—
462Dic11—42no—
463Dic11—42no—
464Dic11C2×#13514yes—
465C2×#41—228no—
466C2×#41—448no—
467C22×Q8—111no—
468C22×Q8—221no—
469C22×D4—111no—
470C22×D4—111no—
471C22×D4—221no—
472C22×D4—221no—
473C22×D4—221no—
474C22×D4—221no—
475C22×D4—221no—
476C22×D4C22×D1111yescharacteristic
477C23×C4—21no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—221no—
482C23×C4—221no—
483C2×SD16—114no—
484C2×SD16—114no—
485C2×SD16—442no—
486C2×SD16—442no—
487C2×D8—114no—
488C2×D8—114no—
489C2×D8—442no—
490C2×D8—442no—
491C22×C8—111no—
492C22×C8—111no—
493C22×C8—114no—
494C22×C8—114no—
495C22×C8—442no—
496C22×C8—442no—
497C22×C8C22×D1111yescharacteristic
498C22×C8C22×D1111yescharacteristic
499C4⋊Q8—114no—
500C4⋊Q8—222no—
501#127—114no—
502#127—222no—
503#126—228no—
504#125—22no—
505#125C22×D1114yes—
506#124—114no—
507#124—228no—
508#124—222no—
509#123—228no—
510C22⋊Q8—114no—
511C22⋊Q8—222no—
512#121—114no—
513#121—114no—
514#121—114no—
515#121—228no—
516#121—222no—
517#121—222no—
518#121—222no—
519C4×Q8—114no—
520C4×Q8—222no—
521C4×D4—22no—
522C4×D4—114no—
523C4×D4—114no—
524C4×D4—222no—
525C4×D4—228no—
526C4×D4—228no—
527C4×D4—222no—
528C4×D4C22×D1114yes—
529#117—228no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C22⋊C4—21no—
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×C42—111no—
549C2×C42—111no—
550C2×C42—111no—
551C2×C42—114no—
552C2×C42—114no—
553C2×C42—221no—
554C2×C42C22×D1111yescharacteristic
555#107—114no—
556#107C22×D1114yes—
557#106—114no—
558#106C22×D1114yes—
559C4⋊C8—114no—
560C4⋊C8—114no—
561C4⋊C8—114no—
562C4⋊C8C22×D1114yes—
563#103—114no—
564#103—114no—
565#102—114no—
566#102—114no—
567#102—114no—
568#102—114no—
569#102C22×D1114yes—
570#102C22×D1114yes—
571C2×C11—82no—
572C2×C11#324714yescomplemented
573C2×C11C2×#53711yescharacteristic
574C2×C11C22×#13511yescharacteristic
575C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
576D11—24no—
577D11—82no—
578D11—82no—
579C24—21no—
580C24—111no—
581C24—221no—
582C24—221no—
583#41—4432no—
584C2×Q8—112no—
585C2×Q8—224no—
586C2×Q8—221no—
587C2×Q8—222no—
588C2×Q8—222no—
589C2×Q8—444no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—112no—
594C2×D4—112no—
595C2×D4—224no—
596C2×D4—224no—
597C2×D4—224no—
598C2×D4—224no—
599C2×D4—224no—
600C2×D4—221no—
601C2×D4—221no—
602C2×D4—222no—
603C2×D4—222no—
604C2×D4—222no—
605C2×D4—222no—
606C2×D4—444no—
607C2×D4—444no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4—444no—
611C2×D4C23×D1112yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—111no—
618C22×C4—111no—
619C22×C4—111no—
620C22×C4—114no—
621C22×C4—112no—
622C22×C4—114no—
623C22×C4—112no—
624C22×C4—224no—
625C22×C4—224no—
626C22×C4—224no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—224no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4D4×D1111yescharacteristic
635C22×C4D4×D1111yescharacteristic
636C22×C4C23×D1111yescharacteristic
637SD16—444no—
638SD16—444no—
639D8—444no—
640D8—444no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—112no—
644C2×C8—112no—
645C2×C8—222no—
646C2×C8—222no—
647C2×C8—444no—
648C2×C8—444no—
649C2×C8C23×D1112yes—
650C2×C8C23×D1112yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—112no—
657C4⋊C4—224no—
658C4⋊C4—224no—
659C4⋊C4—224no—
660C4⋊C4—221no—
661C4⋊C4C23×D1112yes—
662C4⋊C4C23×D1112yes—
663C4⋊C4C23×D1112yes—
664C22⋊C4—24no—
665C22⋊C4—224no—
666C22⋊C4—224no—
667C22⋊C4—224no—
668C22⋊C4—224no—
669C22⋊C4—224no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C42—114no—
674C42—112no—
675C42—114no—
676C42—112no—
677C42—224no—
678C42D4×D1112yes—
679C42C23×D1112yes—
680C11C2×#324711yescharacteristic, complemented, Sylow
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—114no—
686C23—112no—
687C23—222no—
688C23—222no—
689C23—222no—
690C23—222no—
691C23—442no—
692C23—442no—
693C23—442no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23C2×D4×D1111yescharacteristic
698Q8—222no—
699Q8—222no—
700Q8—448no—
701Q8—442no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—222no—
706D4—222no—
707D4—222no—
708D4—222no—
709D4—448no—
710D4—448no—
711D4—448no—
712D4—448no—
713D4—448no—
714D4—442no—
715D4—442no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—114no—
726C2×C4—112no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—228no—
730C2×C4—228no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—224no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—448no—
739C2×C4—448no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4C2×D4×D1112yes—
743C2×C4C2×D4×D1112yes—
744C2×C4C2×D4×D1111yescharacteristic
745C2×C4#6704012yes—
746C2×C4#6704212yes—
747C2×C4C24×D1111yescharacteristic
748C8—22no—
749C8—22no—
750C8—222no—
751C8—222no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22—114no—
757C22—222no—
758C22—228no—
759C22—222no—
760C22—442no—
761C22—442no—
762C22—442no—
763C22—442no—
764C22—442no—
765C22—442no—
766C22—884no—
767C22—884no—
768C22#1062316012yes—
769C22D11×#13512yes—
770C22D11×AGL(1,ℤ/8)12yes—
771C22C22×D4×D1111yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—114no—
778C4—222no—
779C4—222no—
780C4—442no—
781C4—442no—
782C4#1062316012yes—
783C4C2×#6704011yescharacteristic
784C4C2×#6704211yescharacteristic
785C2—82no—
786C2—224no—
787C2—882no—
788C2—882no—
789C2#1307994114yesdirect product factor
790C2C2×#1062316011yescharacteristic
791C2C2×D11×#13511yescharacteristic
792C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
hypercenterC2×#478D11
hypocenterC11C2×#3247
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#10623079C2semidirect
2. C2×#10623222C2semidirect
3. #13079941C2direct (N × H)
4. C2×#10622488C2semidirect
5. C2×#10622679C2semidirect
6. C2×#10622483C2semidirect
7. C2×#10622496C2semidirect
8. C2×#10622388C2semidirect
9. C2×#10622477C2semidirect
10. C2×#10622391C2semidirect
11. C2×#10622375C2semidirect
12. C2×#10622457C2semidirect
13. C2×#10622629C2semidirect
14. C2×#10622399C2semidirect
15. C2×D11×C4⋊C8C2semidirect
16. C2×C11×#478C2semidirect
30. #10623222C22semidirect
32. #10623079C22semidirect
48. C11×#478C22semidirect
58. #10622679C22semidirect
59. #10622629C22semidirect
67. #10622496C22semidirect
68. #10622488C22semidirect
69. #10622483C22semidirect
70. #10622477C22semidirect
71. #10622457C22semidirect
72. D11×C4⋊C8C22semidirect
73. #10622399C22semidirect
74. #10622391C22semidirect
75. #10622388C22semidirect
76. #10622375C22semidirect
290. C2×#478D11semidirect
404. #478C2×D11semidirect
572. C2×C11#3247semidirect
680. C11C2×#3247semidirect
789. C2#13079941direct (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×#106232222
#130799412
C2×#106224882
C2×#106226792
C2×#106224832
C2×#106224962
C2×#106223882
C2×#106224772
C2×#106223912
C2×#106223752
C2×#106224572
C2×#106226292
C2×#106223992
C2×D11×C4⋊C82
C2×C11×#4782
C2×#324711