Finite Group Databasebeta

← C2×#13079204 #15623531

Subgroups — C2×#13079204 #15623531

Order 2816.

2266 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×#10623127C211yesmaximal, characteristic, complemented
2C2×#10623155C211yesmaximal, characteristic, complemented
3#13079204C2116yesmaximal, direct product factor
4C2×#10622489C211yesmaximal, characteristic, complemented
5C2×#10622789C211yesmaximal, characteristic, complemented
6C2×#10622377C211yesmaximal, characteristic, complemented
7C2×#10622408C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622652C211yesmaximal, characteristic, complemented
10C2×#10622662C211yesmaximal, characteristic, complemented
11C2×SD16×Dic11C211yesmaximal, characteristic, complemented
12C2×#10622401C211yesmaximal, characteristic, complemented
13C2×#10622485C211yesmaximal, characteristic, complemented
14C2×#10622369C211yesmaximal, characteristic, complemented
15C2×M16×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×SD16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×#67000C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×#66993C2211yescharacteristic
26C2×#66992—21no—
27C2×D4×Dic11C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C2×#66983C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C22×D88C2211yescharacteristic
34#10623155—24no—
35#10623155C2218yescomplemented
36#10623127—24no—
37#10623127C2218yescomplemented
38C2×#66951—21no—
39C2×#66946C2211yescharacteristic
40C2×#66946C2211yescharacteristic
41C2×#66945—21no—
42C2×#66943C2211yescharacteristic
43C2×#66941C2211yescharacteristic
44C2×#66939—21no—
45C2×#66938—21no—
46C2×(C22⋊D11)⋊C4—21no—
47C2×(C22⋊D11)⋊C4—21no—
48C11×#468C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622789C2218yescomplemented
55SD16×Dic11C2218yescomplemented
56#10622748C2218yescomplemented
57M16×Dic11C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66879C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×C8×Dic11C2211yescharacteristic
64C2×C8×Dic11C2211yescharacteristic
65#10622662C2218yescomplemented
66#10622652C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622489C2218yescomplemented
72#10622485C2218yescomplemented
73#10622408C2218yescomplemented
74#10622401C2218yescomplemented
75#10622377C2218yescomplemented
76#10622369C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C23×Dic11D411yescharacteristic
87C23×Dic11D411yescharacteristic
88C2×#4341—28no—
89C2×#4341—48no—
90C22×D44C2311yescharacteristic
91C22×D44C2311yescharacteristic
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×Dic22—21no—
95C2×C11×SD16—24no—
96C2×C11×SD16C2314yes—
97C2×C11×M16—24no—
98C2×C11×M16C2314yes—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×C22⋊Q8—22no—
102C11×C22⋊Q8C2314yes—
103C11×#121—22no—
104C11×#121C2314yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C22⋊Dic11—21no—
111#67000—22no—
112#67000C2314yes—
113Q8×Dic11—22no—
114Q8×Dic11C2314yes—
115C2×#4325—24no—
116C2×#4325C2314yes—
117#66993—22no—
118#66993C2314yes—
119#66992—28no—
120D4×Dic11—22no—
121D4×Dic11C2314yes—
122C2×#4323—24no—
123C2×#4323C2314yes—
124#66983—22no—
125#66983—22no—
126#66983C2314yes—
127#66983C2314yes—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×C4⋊Dic11—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11D411yescharacteristic
142C2×C4×Dic11D411yescharacteristic
143C2×C4×Dic11D414yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2311yescharacteristic
146C2×C4×Dic11C2311yescharacteristic
147C2×#4318—24no—
148C2×#4318C2314yes—
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C2×D88—24no—
152C2×D88C2314yes—
153#66951—28no—
154#66946—22no—
155#66946—22no—
156#66946C2314yes—
157#66946C2314yes—
158#66945—28no—
159#66943—22no—
160#66943C2314yes—
161#66941—22no—
162#66941C2314yes—
163#66939—28no—
164#66938—28no—
165(C22⋊D11)⋊C4—28no—
166(C22⋊D11)⋊C4—28no—
167C11×#107C2314yes—
168C11×#103C2314yes—
169C11×#102C2314yes—
170#66899C2314yes—
171#66896C2314yes—
172#66885C2314yes—
173#66885C2314yes—
174#66881C2314yes—
175#66879C2314yes—
176#66879C2314yes—
177C8×Dic11C2314yes—
178C8×Dic11C2314yes—
179#66873C2314yes—
180#66873C2314yes—
181#66872C2314yes—
182#66871C2314yes—
183C2×#3171—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11C2×D411yescharacteristic
186C23×D11—21no—
187C23×D11—21no—
188C2×Q8×C11—21no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11C2412yes—
192C2×D4×C11—24no—
193C2×D4×C11—21no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—44no—
197C2×D4×C11C2412yes—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2411yescharacteristic
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—44no—
215C22×Dic11—24no—
216C22×Dic11—24no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—42no—
220C22×Dic11—44no—
221C22×Dic11C2×D414yes—
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D414yes—
226C22×Dic11C2×D411yescharacteristic
227#4341—432no—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44—22no—
233C2×D44—22no—
234C2×D44C2412yes—
235C2×D44C2412yes—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—44no—
239C2×C4×D11—44no—
240C2×Dic22—24no—
241C2×Dic22—44no—
242C11×SD16—28no—
243C11×M16—28no—
244C2×C8×C11—22no—
245C2×C8×C11#4114yescomplemented
246C2×C8×C11C2412yes—
247C2×C8×C11C2412yes—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4C2412yes—
252C11×C4⋊C4C2412yes—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C22⋊Dic11—24no—
256#4325—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—
264C4⋊Dic11—24no—
265C4⋊Dic11—24no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11C2412yes—
269C4⋊Dic11C2412yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272C4×Dic11—24no—
273C4×Dic11C2×D414yes—
274C4×Dic11C2×D414yes—
275C4×Dic11C2×D412yes—
276C4×Dic11C2×D412yes—
277C4×Dic11C2412yes—
278C4×Dic11C2412yes—
279#4318—28no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8#4114yescomplemented
282C2×C11⋊C8C2412yes—
283C2×C11⋊C8C2412yes—
284D88—28no—
285C2×#532—111no—
286C2×#529—111no—
287#3171—1116no—
288C2×#501—111no—
289C2×#496—111no—
290C2×#490—111no—
291C2×#489—111no—
292C2×#469—111no—
293C2×#469—111no—
294C2×#468—111no—
295C2×#468D1111yescharacteristic, complemented
296C2×C4×SD16—111no—
297C2×C4×SD16—111no—
298C2×C4×D8—111no—
299C2×C4×D8—111no—
300C2×C4×M16—111no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11C22×D412yes—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—42no—
313C22×D11—42no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—42no—
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—42no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—48no—
324D4×C11—42no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4112yes—
338C2×C4×C11C2×#4112yes—
339C2×C4×C11C2511yescharacteristic
340C22⋊D11—48no—
341C22⋊D11—48no—
342C22⋊D11—48no—
343C22⋊D11—48no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—28no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—44no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—48no—
354C2×Dic11AGL(1,ℤ/8)14yes—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359D44—22no—
360D44—22no—
361D44—22no—
362D44—22no—
363D44—42no—
364D44—42no—
365C4×D11—48no—
366C4×D11—48no—
367Dic22—48no—
368C8×C11—22no—
369C8×C11C2×#4114yescomplemented
370C11⋊C8—22no—
371C11⋊C8C2×#4114yescomplemented
372C22×#41—221no—
373C22×SD16—111no—
374C22×SD16C2×D1111yescharacteristic
375C22×D8—111no—
376C22×D8—111no—
377C22×M16—111no—
378C22×M16C2×D1111yescharacteristic
379#532—118no—
380#532—224no—
381C2×C4⋊Q8—111no—
382C2×#127—111no—
383#529—118no—
384#529—224no—
385C2×#126—221no—
386C2×#125—111no—
387C2×#124—111no—
388C2×#124—221no—
389C2×#123—221no—
390C2×C22⋊Q8C2×D1111yescharacteristic
391C2×#121—111no—
392C2×#121—111no—
393C2×#121—221no—
394C2×#121C2×D1111yescharacteristic
395C2×C4×Q8—111no—
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4—111no—
399C2×C4×D4—221no—
400C2×C4×D4—221no—
401C2×#117—221no—
402C22×C42—111no—
403#501—118no—
404#496—118no—
405#490—118no—
406#489—118no—
407#469—118no—
408#469—118no—
409#468—118no—
410#468C2×D1118yescomplemented
411C4×SD16—118no—
412C4×SD16—118no—
413C4×D8—118no—
414C4×D8—118no—
415C2×#107—111no—
416C2×#107C2×D1111yescharacteristic
417C2×#106—111no—
418C2×#106—111no—
419C2×#103—111no—
420C2×#103C2×D1111yescharacteristic
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102C2×D1111yescharacteristic
427C4×M16—118no—
428C2×#97—111no—
429C2×#97—111no—
430C2×C4×C8—111no—
431C2×C4×C8—111no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—44no—
436C22×C11—42no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—84no—
440C22×C11#53212yes—
441C22×C11C2×AGL(1,ℤ/8)12yes—
442C22×C11#57512yes—
443C22×C11C23×D411yescharacteristic
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—84no—
451C2×D11—84no—
452C4×C11—22no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11#53212yes—
457C4×C11C22×#4111yescharacteristic
458C4×C11C22×#4111yescharacteristic
459Dic11—22no—
460Dic11—22no—
461Dic11—22no—
462Dic11—42no—
463Dic11—42no—
464Dic11C2×AGL(1,ℤ/8)14yes—
465C2×#41—228no—
466C2×#41—448no—
467C22×Q8—221no—
468C22×Q8C22×D1111yescharacteristic
469C22×D4—21no—
470C22×D4—111no—
471C22×D4—111no—
472C22×D4—221no—
473C22×D4—221no—
474C22×D4—221no—
475C22×D4—221no—
476C22×D4C22×D1111yescharacteristic
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—221no—
480C23×C4—221no—
481C23×C4—221no—
482C23×C4C22×D1111yescharacteristic
483C2×SD16—24no—
484C2×SD16—114no—
485C2×SD16—224no—
486C2×SD16C22×D1114yes—
487C2×D8—114no—
488C2×D8—114no—
489C2×D8—224no—
490C2×D8—224no—
491C2×M16—24no—
492C2×M16—114no—
493C2×M16—224no—
494C2×M16C22×D1114yes—
495C22×C8—111no—
496C22×C8—111no—
497C22×C8C22×D1111yescharacteristic
498C22×C8C22×D1111yescharacteristic
499C4⋊Q8—114no—
500C4⋊Q8—222no—
501#127—114no—
502#127—222no—
503#126—228no—
504#125—114no—
505#125—222no—
506#124—114no—
507#124—228no—
508#124—222no—
509#123—228no—
510C22⋊Q8—22no—
511C22⋊Q8C22×D1114yes—
512#121—22no—
513#121—114no—
514#121—114no—
515#121—228no—
516#121—222no—
517#121—222no—
518#121C22×D1114yes—
519C4×Q8—114no—
520C4×Q8—222no—
521C4×D4—114no—
522C4×D4—114no—
523C4×D4—114no—
524C4×D4—228no—
525C4×D4—222no—
526C4×D4—222no—
527C4×D4—222no—
528C4×D4—228no—
529#117—228no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—111no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
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—114no—
551C2×C42—111no—
552C2×C42—111no—
553C2×C42—114no—
554C2×C42—221no—
555#107—114no—
556#107C22×D1114yes—
557#106—114no—
558#106—114no—
559#103—114no—
560#103C22×D1114yes—
561#102—114no—
562#102—114no—
563#102—114no—
564#102—114no—
565#102—114no—
566#102C22×D1114yes—
567#97—114no—
568#97—114no—
569C4×C8—114no—
570C4×C8—114no—
571C2×C11—42no—
572C2×C11—82no—
573C2×C11#317114yescomplemented
574C2×C11C2×#53211yescharacteristic
575C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
576C2×C11C2×#57511yescharacteristic
577D11—82no—
578D11—82no—
579C24—21no—
580C24—221no—
581C24—221no—
582C24D4×D1111yescharacteristic
583#41—4432no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—224no—
588C2×Q8—444no—
589C2×Q8C23×D1112yes—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—44no—
595C2×D4—112no—
596C2×D4—112no—
597C2×D4—224no—
598C2×D4—224no—
599C2×D4—224no—
600C2×D4—224no—
601C2×D4—221no—
602C2×D4—221no—
603C2×D4—222no—
604C2×D4—222no—
605C2×D4—222no—
606C2×D4—222no—
607C2×D4—444no—
608C2×D4—444no—
609C2×D4—444no—
610C2×D4—444no—
611C2×D4C23×D1112yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—111no—
618C22×C4—114no—
619C22×C4—111no—
620C22×C4—111no—
621C22×C4—111no—
622C22×C4—114no—
623C22×C4—224no—
624C22×C4—224no—
625C22×C4—224no—
626C22×C4—224no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—444no—
630C22×C4—444no—
631C22×C4—444no—
632C22×C4—442no—
633C22×C4D4×D1112yes—
634C22×C4D4×D1111yescharacteristic
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637SD16—28no—
638SD16—228no—
639D8—228no—
640D8—228no—
641M16—28no—
642M16—228no—
643C2×C8—22no—
644C2×C8—114no—
645C2×C8—112no—
646C2×C8—112no—
647C2×C8—222no—
648C2×C8#434114yescomplemented
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⋊C4C23×D1112yes—
663C4⋊C4C23×D1112yes—
664C22⋊C4—24no—
665C22⋊C4—24no—
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—112no—
678C42—112no—
679C42—224no—
680C11C2×#317111yescharacteristic, complemented, Sylow
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—222no—
689C23—222no—
690C23—442no—
691C23—442no—
692C23—442no—
693C23—442no—
694C23—442no—
695C23—442no—
696C23C2×D4×D1112yes—
697C23C2×D4×D1111yescharacteristic
698Q8—22no—
699Q8—22no—
700Q8—42no—
701Q8—448no—
702D4—22no—
703D4—22no—
704D4—48no—
705D4—42no—
706D4—222no—
707D4—222no—
708D4—222no—
709D4—222no—
710D4—448no—
711D4—448no—
712D4—448no—
713D4—448no—
714D4—442no—
715D4—442no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—114no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—112no—
730C2×C4—112no—
731C2×C4—228no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—448no—
738C2×C4—448no—
739C2×C4—448no—
740C2×C4—444no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4C2×D4×D1112yes—
744C2×C4C2×D4×D1111yescharacteristic
745C2×C4C2×#434112yes—
746C2×C4#41×D1112yes—
747C2×C4C24×D1111yescharacteristic
748C8—22no—
749C8—114no—
750C8—222no—
751C8C2×#434114yescomplemented
752C22—22no—
753C22—22no—
754C22—22no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—84no—
760C22—442no—
761C22—442no—
762C22—442no—
763C22—442no—
764C22—442no—
765C22—442no—
766C22—884no—
767C22—884no—
768C22#1062312712yes—
769C22D11×AGL(1,ℤ/8)12yes—
770C22#1062330812yes—
771C22C22×D4×D1111yescharacteristic
772C4—22no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—114no—
777C4—222no—
778C4—222no—
779C4—222no—
780C4—442no—
781C4—442no—
782C4#1062312712yes—
783C4C22×#434111yescharacteristic
784C4C2×#41×D1111yescharacteristic
785C2—42no—
786C2—82no—
787C2—882no—
788C2—882no—
789C2#1307920414yesdirect product factor
790C2C2×#1062312711yescharacteristic
791C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
792C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
hypercenterC2×#468D11
hypocenterC11C2×#3171
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623127C2semidirect
2. C2×#10623155C2semidirect
3. #13079204C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622789C2semidirect
6. C2×#10622377C2semidirect
7. C2×#10622408C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622652C2semidirect
10. C2×#10622662C2semidirect
11. C2×SD16×Dic11C2semidirect
12. C2×#10622401C2semidirect
13. C2×#10622485C2semidirect
14. C2×#10622369C2semidirect
15. C2×M16×Dic11C2semidirect
16. C2×C11×#468C2semidirect
35. #10623155C22semidirect
37. #10623127C22semidirect
48. C11×#468C22semidirect
54. #10622789C22semidirect
55. SD16×Dic11C22semidirect
56. #10622748C22semidirect
57. M16×Dic11C22semidirect
65. #10622662C22semidirect
66. #10622652C22semidirect
71. #10622489C22semidirect
72. #10622485C22semidirect
73. #10622408C22semidirect
74. #10622401C22semidirect
75. #10622377C22semidirect
76. #10622369C22semidirect
245. C2×C8×C11#41semidirect
281. C2×C11⋊C8#41semidirect
295. C2×#468D11semidirect
369. C8×C11C2×#41semidirect
371. C11⋊C8C2×#41semidirect
410. #468C2×D11semidirect
573. C2×C11#3171semidirect
648. C2×C8#4341semidirect
680. C11C2×#3171semidirect
751. C8C2×#4341semidirect
789. C2#13079204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231272
C2×#106231552
#130792042
C2×#106224892
C2×#106227892
C2×#106223772
C2×#106224082
C2×#106227482
C2×#106226522
C2×#106226622
C2×SD16×Dic112
C2×#106224012
C2×#106224852
C2×#106223692
C2×M16×Dic112
C2×C11×#4682
C2×#317111