Finite Group Databasebeta

← C2×#13081703 #15634802

Subgroups — C2×#13081703 #15634802

Order 2816.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2C2×#10623212C211yesmaximal, characteristic, complemented
3#13081703C2116yesmaximal, direct product factor
4C2×#10622671C211yesmaximal, characteristic, complemented
5C2×#10622789C211yesmaximal, characteristic, complemented
6C2×#10622804C211yesmaximal, characteristic, complemented
7C2×#10622798C211yesmaximal, characteristic, complemented
8C2×#10622432C211yesmaximal, characteristic, complemented
9C2×#10622778C211yesmaximal, characteristic, complemented
10C2×#10622456C211yesmaximal, characteristic, complemented
11C2×#10622399C211yesmaximal, characteristic, complemented
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622430C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×#10622369C211yesmaximal, characteristic, complemented
16C2×C11×#464C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×#67000C2211yescharacteristic
23C2×#67000C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C22×#4325C2211yescharacteristic
26C22×#4325C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C2×#66993C2211yescharacteristic
29C2×D4×Dic11C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C22×D88C2211yescharacteristic
33C22×D88C2211yescharacteristic
34#10623212—24no—
35#10623212C2218yescomplemented
36#10623116—24no—
37#10623116C2218yescomplemented
38C2×#66947—21no—
39C2×#66947—21no—
40C2×#66946C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×#66939—21no—
43C2×#66938—21no—
44C2×#66936—21no—
45C2×(C22⋊D11)⋊C4—21no—
46C2×#66928—21no—
47C2×#66927C2211yescharacteristic
48C2×C4×D44—21no—
49C2×C4×D44C2211yescharacteristic
50C2×C4×Dic22C2211yescharacteristic
51C11×#464C2218yescomplemented
52C2×C11×C4⋊C8C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×C11×#102C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56#10622804C2218yescomplemented
57#10622798C2218yescomplemented
58#10622789C2218yescomplemented
59#10622778C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×#66879C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622671C2218yescomplemented
67#10622639C2218yescomplemented
68C2×#66873C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66867C2211yescharacteristic
71#10622456C2218yescomplemented
72#10622441C2218yescomplemented
73#10622432C2218yescomplemented
74#10622430C2218yescomplemented
75#10622399C2218yescomplemented
76#10622369C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C23×Dic11—21no—
83C22×D44—21no—
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×Dic22D411yescharacteristic
92C2×C11×Q16—42no—
93C2×C11×Q16C2314yes—
94C2×C11×SD16—42no—
95C2×C11×SD16C2314yes—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×#124—22no—
99C11×#124C2314yes—
100C4×Q8×C11—22no—
101C4×Q8×C11C2314yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109#67000—22no—
110#67000—22no—
111#67000—22no—
112#67000C2314yes—
113#67000C2314yes—
114#67000C2314yes—
115Q8×Dic11—22no—
116Q8×Dic11C2314yes—
117C2×#4325—24no—
118C2×#4325—24no—
119C2×#4325—42no—
120C2×#4325C2314yes—
121C2×#4325C2314yes—
122C2×#4325C2314yes—
123#66993—22no—
124#66993C2314yes—
125D4×Dic11—22no—
126D4×Dic11C2314yes—
127C2×#4323—24no—
128C2×#4323—42no—
129C2×#4323C2314yes—
130C2×#4323C2314yes—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11D411yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×Dic11⋊C4D411yescharacteristic
144C2×Dic11⋊C4D411yescharacteristic
145C2×C4×Dic11—21no—
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C2×D88—42no—
151C2×D88—42no—
152C2×D88C2314yes—
153C2×D88C2314yes—
154#66947—28no—
155#66947—28no—
156#66946—22no—
157#66946—22no—
158#66946C2314yes—
159#66946C2314yes—
160#66939—28no—
161#66938—28no—
162#66936—28no—
163(C22⋊D11)⋊C4—28no—
164#66928—28no—
165#66927—22no—
166#66927C2314yes—
167C4×D44—22no—
168C4×D44—28no—
169C4×D44C2314yes—
170C4×Dic22D414yes—
171C4×Dic22C2314yes—
172C11×C4⋊C8C2314yes—
173C11×#103C2314yes—
174C11×#102C2314yes—
175#66899C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178#66879C2314yes—
179Dic11⋊C8C2314yes—
180Dic11⋊C8C2314yes—
181C8×Dic11C2314yes—
182#66873C2314yes—
183#66871C2314yes—
184#66867C2314yes—
185C2×#3403—111nomaximal, Sylow
186C24×C11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11C2412yes—
197C2×Q8×C11C2412yes—
198C2×D4×C11—21no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11C2412yes—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—82no—
212C22×Dic11—24no—
213C22×Dic11—21no—
214C22×Dic11—82no—
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C2×D44—24no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—24no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44—22no—
228C2×D44—22no—
229C2×D44—22no—
230C2×D44—44no—
231C2×D44—82no—
232C2×D44C2412yes—
233C2×D44C2412yes—
234C2×D44C2412yes—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—82no—
239C2×C4×D11—82no—
240C2×C4×D11—82no—
241C2×Dic22—42no—
242C2×Dic22C2×D414yes—
243C11×Q16—44no—
244C11×SD16—44no—
245C2×C8×C11—22no—
246C2×C8×C11—22no—
247C2×C8×C11C2412yes—
248C2×C8×C11C2412yes—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4C2412yes—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C42×C11—24no—
255C42×C11C2×D412yes—
256C42×C11C2412yes—
257C22⋊Dic11—24no—
258#4325—28no—
259#4325—28no—
260#4325—44no—
261#4323—28no—
262#4323—44no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
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—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272C4⋊Dic11—24no—
273C4⋊Dic11—21no—
274C4⋊Dic11C2×D414yes—
275C4⋊Dic11C2412yes—
276Dic11⋊C4C2×D414yes—
277Dic11⋊C4C2×D414yes—
278C4×Dic11—24no—
279C4×Dic11C2×D412yes—
280C4×Dic11C2×D412yes—
281C4×Dic11C2412yes—
282C4×Dic11C2412yes—
283C2×C11⋊C8—22no—
284C2×C11⋊C8#4114yes—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287D88—44no—
288D88—44no—
289C2×#559—111no—
290C2×#559—111no—
291#3403—1116no—
292C2×#496—111no—
293C2×#496—111no—
294C2×#495—111no—
295C2×#464—111no—
296C2×#464D1111yescharacteristic, complemented
297C2×#463—111no—
298C2×#463—111no—
299C2×#459—111no—
300C2×#459—111no—
301C2×#446—111no—
302C2×#440—111no—
303C2×#440—111no—
304C2×C4×D8—111no—
305C23×C11—22no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—42no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11—42no—
322Q8×C11—22no—
323Q8×C11—22no—
324Q8×C11—22no—
325Q8×C11—22no—
326Q8×C11—42no—
327Q8×C11—42no—
328D4×C11—22no—
329D4×C11—22no—
330D4×C11—42no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4112yes—
343C2×C4×C11H(5,𝔽2)12yes—
344C2×C4×C11C2511yescharacteristic
345C22⋊D11—48no—
346C22⋊D11—84no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—42no—
353C2×Dic11—84no—
354C2×Dic11C22×D412yes—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358D44—22no—
359D44—22no—
360D44—22no—
361D44—22no—
362D44—22no—
363D44—22no—
364D44—48no—
365D44—42no—
366D44—42no—
367D44—42no—
368D44—84no—
369C4×D11—84no—
370C4×D11—84no—
371C4×D11—84no—
372Dic22—44no—
373C8×C11—22no—
374C8×C11—22no—
375C11⋊C8—22no—
376C11⋊C8C2×#4114yes—
377C22×Q16C2×D1111yescharacteristic
378C22×SD16—111no—
379C22×SD16—111no—
380C22×SD16—111no—
381C22×SD16C2×D1111yescharacteristic
382C22×D8—111no—
383C22×D8—111no—
384C22×D8—111no—
385C22×D8—111no—
386#559—118no—
387#559—118no—
388#559—224no—
389#559—224no—
390C2×#127—111no—
391C2×#127—111no—
392C2×#124—111no—
393C2×#124—111no—
394C2×#124—111no—
395C2×#124—221no—
396C2×#124—221no—
397C2×#124C2×D1111yescharacteristic
398C2×#123—221no—
399C2×#123—221no—
400C2×#123—221no—
401C2×#123—221no—
402C2×C4×Q8—111no—
403C2×C4×Q8—111no—
404C2×C4×Q8C2×D1111yescharacteristic
405C2×C4×D4—111no—
406C2×C4×D4—111no—
407C2×C4×D4—111no—
408C2×C4×D4—111no—
409C2×C4×D4—221no—
410C2×C4×D4—221no—
411#496—118no—
412#496—118no—
413#495—118no—
414#464—118no—
415#464C2×D1118yescomplemented
416#463—118no—
417#463—118no—
418#459—118no—
419#459—118no—
420#446—118no—
421#440—118no—
422#440—118no—
423C4×D8—118no—
424C2×#107—111no—
425C2×C4⋊C8—111no—
426C2×C4⋊C8—111no—
427C2×C4⋊C8C2×D1111yescharacteristic
428C2×#103—111no—
429C2×#103C2×D1111yescharacteristic
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102C2×D1111yescharacteristic
434C2×#97—111no—
435C2×#97—111no—
436C2×C4×C8—111no—
437C22×C11—42no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—84no—
441C22×C11#55012yes—
442C22×C11#57512yes—
443C22×C11#57612yes—
444C22×C11C23×D411yescharacteristic
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—84no—
455C2×D11—84no—
456C2×D11—84no—
457C4×C11—22no—
458C4×C11—22no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11—42no—
462C4×C11#55012yes—
463C4×C11C22×#4111yescharacteristic
464C4×C11C2×H(5,𝔽2)11yescharacteristic
465Dic11—22no—
466Dic11—22no—
467Dic11—22no—
468Dic11—22no—
469Dic11—42no—
470C22×Q8—111no—
471C22×Q8C22×D1111yescharacteristic
472C22×Q8C22×D1111yescharacteristic
473C22×D4—111no—
474C22×D4—111no—
475C22×D4—111no—
476C22×D4—221no—
477C22×D4—221no—
478C22×D4—221no—
479C22×D4—221no—
480C22×D4C22×D1111yescharacteristic
481C23×C4—221no—
482C23×C4—221no—
483C23×C4—221no—
484C23×C4—221no—
485C2×Q16—42no—
486C2×Q16C22×D1114yes—
487C2×SD16—42no—
488C2×SD16—114no—
489C2×SD16—114no—
490C2×SD16—114no—
491C2×SD16—224no—
492C2×SD16—224no—
493C2×SD16—442no—
494C2×SD16C22×D1114yes—
495C2×D8—114no—
496C2×D8—114no—
497C2×D8—114no—
498C2×D8—114no—
499C2×D8—224no—
500C2×D8—442no—
501C2×D8—442no—
502C2×D8—442no—
503C22×C8—111no—
504C22×C8—111no—
505C22×C8C22×D1111yescharacteristic
506C22×C8C22×D1111yescharacteristic
507#127—114no—
508#127—114no—
509#127—222no—
510#127—222no—
511#124—22no—
512#124—114no—
513#124—114no—
514#124—114no—
515#124—228no—
516#124—222no—
517#124—222no—
518#124—222no—
519#124—228no—
520#124C22×D1114yes—
521#123—228no—
522#123—228no—
523#123—228no—
524#123—228no—
525C4×Q8—22no—
526C4×Q8—114no—
527C4×Q8—114no—
528C4×Q8—114no—
529C4×Q8—222no—
530C4×Q8C22×D1114yes—
531C4×D4—114no—
532C4×D4—114no—
533C4×D4—114no—
534C4×D4—114no—
535C4×D4—228no—
536C4×D4—222no—
537C4×D4—222no—
538C4×D4—222no—
539C4×D4—228no—
540C4×D4—222no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4C22×D1111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C42—21no—
561C2×C42—111no—
562C2×C42—111no—
563C2×C42—221no—
564C2×C42C22×D1111yescharacteristic
565#107—114no—
566C4⋊C8—114no—
567C4⋊C8—114no—
568C4⋊C8C22×D1114yes—
569#103—114no—
570#103C22×D1114yes—
571#102—114no—
572#102—114no—
573#102—114no—
574#102C22×D1114yes—
575#97—114no—
576#97—114no—
577C4×C8—114no—
578C2×C11—82no—
579C2×C11#340314yescomplemented
580C2×C11C2×#55011yescharacteristic
581C2×C11C2×#57511yescharacteristic
582C2×C11C2×#57611yescharacteristic
583D11—82no—
584D11—82no—
585D11—82no—
586C24—21no—
587C24—221no—
588C24—221no—
589C24—221no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—114no—
597C2×Q8—442no—
598C2×Q8C23×D1112yes—
599C2×Q8C23×D1112yes—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—112no—
604C2×D4—112no—
605C2×D4—112no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—221no—
610C2×D4—221no—
611C2×D4—221no—
612C2×D4—224no—
613C2×D4—222no—
614C2×D4—222no—
615C2×D4—222no—
616C2×D4—222no—
617C2×D4—222no—
618C2×D4—222no—
619C2×D4—444no—
620C2×D4—444no—
621C2×D4—882no—
622C2×D4—882no—
623C2×D4C23×D1112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—111no—
628C22×C4—111no—
629C22×C4—111no—
630C22×C4—111no—
631C22×C4—224no—
632C22×C4—224no—
633C22×C4—224no—
634C22×C4—221no—
635C22×C4—224no—
636C22×C4—882no—
637C22×C4—882no—
638C22×C4—882no—
639C22×C4—882no—
640C22×C4D4×D1111yescharacteristic
641C22×C4D4×D1111yescharacteristic
642C22×C4C23×D1111yescharacteristic
643Q16—44no—
644SD16—44no—
645SD16—228no—
646SD16—228no—
647SD16—444no—
648D8—228no—
649D8—444no—
650D8—444no—
651D8—444no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—114no—
655C2×C8—112no—
656C2×C8—112no—
657C2×C8—222no—
658C2×C8C23×D1112yes—
659C2×C8C23×D1112yes—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—114no—
663C4⋊C4—114no—
664C4⋊C4—114no—
665C4⋊C4—112no—
666C4⋊C4—224no—
667C4⋊C4—221no—
668C4⋊C4C23×D1112yes—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C42—24no—
682C42—112no—
683C42—112no—
684C42—112no—
685C42—112no—
686C42—224no—
687C42D4×D1112yes—
688C42C23×D1112yes—
689C11C2×#340311yescharacteristic, complemented, Sylow
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—442no—
698C23—442no—
699C23—442no—
700C23—442no—
701C23—442no—
702C23—442no—
703C23—442no—
704C23—442no—
705C23—442no—
706C23C2×D4×D1111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—42no—
712Q8—42no—
713Q8—444no—
714D4—22no—
715D4—22no—
716D4—42no—
717D4—222no—
718D4—222no—
719D4—222no—
720D4—222no—
721D4—222no—
722D4—222no—
723D4—448no—
724D4—448no—
725D4—442no—
726D4—442no—
727D4—442no—
728D4—884no—
729D4—884no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—112no—
739C2×C4—112no—
740C2×C4—112no—
741C2×C4—112no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—442no—
748C2×C4—884no—
749C2×C4—884no—
750C2×C4—884no—
751C2×C4—884no—
752C2×C4C2×D4×D1112yes—
753C2×C4C2×D4×D1112yes—
754C2×C4C2×D4×D1111yescharacteristic
755C2×C4#6703712yes—
756C2×C4#41×D1112yes—
757C2×C4C24×D1111yescharacteristic
758C8—22no—
759C8—22no—
760C8—114no—
761C8—222no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—442no—
767C22—442no—
768C22—442no—
769C22—442no—
770C22—442no—
771C22—442no—
772C22—442no—
773C22—442no—
774C22—442no—
775C22—884no—
776C22—884no—
777C22—884no—
778C22#1062313012yes—
779C22#1062330012yes—
780C22#1062330812yes—
781C22C22×D4×D1111yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—222no—
788C4—222no—
789C4—222no—
790C4—222no—
791C4—442no—
792C4#1062313012yes—
793C4C2×#6703711yescharacteristic
794C4C2×#41×D1111yescharacteristic
795C2—82no—
796C2—882no—
797C2—882no—
798C2—882no—
799C2#1308170314yesdirect product factor
800C2C2×#1062313011yescharacteristic
801C2C2×#1062330811yescharacteristic
802C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
hypercenterC2×#464D11
hypocenterC11C2×#3403
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. C2×#10623212C2semidirect
3. #13081703C2direct (N × H)
4. C2×#10622671C2semidirect
5. C2×#10622789C2semidirect
6. C2×#10622804C2semidirect
7. C2×#10622798C2semidirect
8. C2×#10622432C2semidirect
9. C2×#10622778C2semidirect
10. C2×#10622456C2semidirect
11. C2×#10622399C2semidirect
12. C2×#10622441C2semidirect
13. C2×#10622430C2semidirect
14. C2×#10622639C2semidirect
15. C2×#10622369C2semidirect
16. C2×C11×#464C2semidirect
35. #10623212C22semidirect
37. #10623116C22semidirect
51. C11×#464C22semidirect
56. #10622804C22semidirect
57. #10622798C22semidirect
58. #10622789C22semidirect
59. #10622778C22semidirect
66. #10622671C22semidirect
67. #10622639C22semidirect
71. #10622456C22semidirect
72. #10622441C22semidirect
73. #10622432C22semidirect
74. #10622430C22semidirect
75. #10622399C22semidirect
76. #10622369C22semidirect
296. C2×#464D11semidirect
415. #464C2×D11semidirect
579. C2×C11#3403semidirect
689. C11C2×#3403semidirect
799. C2#13081703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106232122
#130817032
C2×#106226712
C2×#106227892
C2×#106228042
C2×#106227982
C2×#106224322
C2×#106227782
C2×#106224562
C2×#106223992
C2×#106224412
C2×#106224302
C2×#106226392
C2×#106223692
C2×C11×#4642
C2×#340311