Finite Group Databasebeta

← C2×#13078890 #15622101

Subgroups — C2×#13078890 #15622101

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623213C211yesmaximal, characteristic, complemented
2C2×#10623077C211yesmaximal, characteristic, complemented
3#13078890C2116yesmaximal, direct product factor
4C2×#10622390C211yesmaximal, characteristic, complemented
5C2×#10622418C211yesmaximal, characteristic, complemented
6C2×#10622464C211yesmaximal, characteristic, complemented
7C2×#10622621C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622786C211yesmaximal, characteristic, complemented
10C2×#10622771C211yesmaximal, characteristic
11C2×#10622765C211yesmaximal, characteristic, complemented
12C2×#10622402C211yesmaximal, characteristic, complemented
13C2×#10622371C211yesmaximal, characteristic, complemented
14C2×SD16×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622453C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C2×C11×#124C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C2×#66991C2211yescharacteristic
26C2×D4×Dic11C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C2×C4×C22⋊D11—21no—
30C22×Dic11⋊C4—21no—
31#10623213—24no—
32#10623213C2218yescomplemented
33#10623077—24no—
34#10623077C2218yescomplemented
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×#66940C2211yescharacteristic
37C2×#66939—21no—
38C2×#66938—21no—
39C2×(C22⋊D11)⋊C4—21no—
40C2×#66932—21no—
41C2×#66931—21no—
42C2×#66930—21no—
43C2×#66925C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C11×#463C2218yescomplemented
47C2×C11×C4⋊C8C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622786C2218yescomplemented
55SD16×Dic11C2218yescomplemented
56#10622771C2218yes—
57#10622765C2218yescomplemented
58C2×(C2×D11)⋊C8C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66881C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66879C2211yescharacteristic
65C2×C8×Dic11C2211yescharacteristic
66#10622667C2218yescomplemented
67#10622621C2218yescomplemented
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×C4⋊(C11⋊C8)C2211yescharacteristic
71#10622464C2218yescomplemented
72#10622453C2218yescomplemented
73#10622418C2218yescomplemented
74#10622402C2218yescomplemented
75#10622390C2218yescomplemented
76#10622371C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C23×Dic11—21no—
84C23×Dic11—21no—
85C23×Dic11—21no—
86C2×#4341—24no—
87C2×#4341—22no—
88C2×#4341—24no—
89C2×#4341C2314yes—
90C22×C4×D11—21no—
91C22×C4×D11C2311yescharacteristic
92C22×Dic22—21no—
93C22×Dic22C2311yescharacteristic
94C2×C11×SD16—24no—
95C2×C11×SD16C2314yes—
96C2×C11×D8—24no—
97C2×C11×D8C2314yes—
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×#124—22no—
101C11×#124C2314yes—
102C4×D4×C11—22no—
103C4×D4×C11C2314yes—
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112#66999—22no—
113#66999C2314yes—
114Q8×Dic11—22no—
115Q8×Dic11C2314yes—
116C2×#4326—24no—
117C2×#4326C2314yes—
118#66991—22no—
119#66991C2314yes—
120D4×Dic11—22no—
121D4×Dic11—22no—
122D4×Dic11C2314yes—
123D4×Dic11C2314yes—
124C2×#4324—24no—
125C2×#4324C2314yes—
126C4×C22⋊D11—28no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4D411yescharacteristic
129C2×(C2×D11)⋊C4D411yescharacteristic
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—28no—
140C2×Dic11⋊C4D411yescharacteristic
141C2×Dic11⋊C4D411yescharacteristic
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×C4×Dic11C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148C4⋊C4×D11—22no—
149C4⋊C4×D11C2314yes—
150#66940—22no—
151#66940C2314yes—
152#66939—28no—
153#66938—28no—
154(C22⋊D11)⋊C4—28no—
155#66932—28no—
156#66931—28no—
157#66930—28no—
158#66925D414yes—
159#66925C2314yes—
160#66922—22no—
161#66922C2314yes—
162C4×Dic22—22no—
163C4×Dic22C2314yes—
164C11×C4⋊C8C2314yes—
165C11×#103C2314yes—
166C11×#102C2314yes—
167#66899C2314yes—
168#66896C2314yes—
169#66896C2314yes—
170#66896C2314yes—
171(C2×D11)⋊C8C2314yes—
172(C2×D11)⋊C8C2314yes—
173#66881C2314yes—
174#66881C2314yes—
175#66880C2314yes—
176#66880C2314yes—
177#66879C2314yes—
178C8×Dic11C2314yes—
179#66872C2314yes—
180#66872C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3125—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11—21no—
185C23×D11C2×D411yescharacteristic
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11#4114yes—
196C2×D4×C11C2412yes—
197C2×D4×C11C2412yes—
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—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—82no—
209C22×Dic11—28no—
210C22×Dic11—24no—
211C22×Dic11—24no—
212C22×Dic11—24no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—82no—
218C22×Dic11—82no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222#4341—216no—
223#4341—28no—
224#4341—28no—
225C2×C4×D11—24no—
226C2×C4×D11—22no—
227C2×C4×D11—22no—
228C2×C4×D11—82no—
229C2×C4×D11C2×D412yes—
230C2×C4×D11C2412yes—
231C2×Dic22—21no—
232C2×Dic22—24no—
233C2×Dic22—22no—
234C2×Dic22—82no—
235C2×Dic22#4114yes—
236C2×Dic22C2412yes—
237C11×SD16—28no—
238C11×D8—28no—
239C2×C8×C11—22no—
240C2×C8×C11—22no—
241C2×C8×C11C2412yes—
242C2×C8×C11C2412yes—
243C11×C4⋊C4—21no—
244C11×C4⋊C4C2412yes—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C42×C11C2×D412yes—
249C42×C11C2412yes—
250C22⋊Dic11—24no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253#4326—28no—
254#4324—28no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4C2×D414yes—
257(C2×D11)⋊C4C2×D414yes—
258C4⋊Dic11—24no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—24no—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4C2×D414yes—
271Dic11⋊C4C2×D414yes—
272C4×Dic11—24no—
273C4×Dic11—24no—
274C4×Dic11—24no—
275C4×Dic11C2×D412yes—
276C4×Dic11C2412yes—
277C2×C11⋊C8—22no—
278C2×C11⋊C8—22no—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281C2×#542—111no—
282C2×#520—111no—
283#3125—1116no—
284C2×#481—111no—
285C2×#483—111no—
286C2×#475—111no—
287C2×#476—111no—
288C2×#464—111no—
289C2×#463D1111yescharacteristic, complemented
290C2×#452—111no—
291C2×#449—111no—
292C2×#442—111no—
293C2×#441—111no—
294C2×C4×SD16—111no—
295C2×C4×SD16—111no—
296C2×#433—111no—
297C23×C11—24no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11C22×D412yes—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—42no—
313D4×C11—24no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—22no—
317D4×C11—42no—
318D4×C11C2×#4114yes—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—84no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4112yes—
330C2×C4×C11C2×#4112yes—
331C2×C4×C11C2511yescharacteristic
332C22⋊D11—216no—
333C22⋊D11—84no—
334C2×Dic11—216no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—84no—
347C2×Dic11—84no—
348C2×Dic11C22×D412yes—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351C4×D11—24no—
352C4×D11—22no—
353C4×D11—22no—
354C4×D11—84no—
355Dic22—24no—
356Dic22—22no—
357Dic22—84no—
358Dic22C2×#4114yes—
359C8×C11—22no—
360C8×C11—22no—
361C11⋊C8—22no—
362C11⋊C8—22no—
363C22×#41—111no—
364C22×Q16—111no—
365C22×SD16—111no—
366C22×SD16C2×D1111yescharacteristic
367C22×D8C2×D1111yescharacteristic
368#542—118no—
369#542—224no—
370C2×C4⋊Q8—111no—
371C2×#126—221no—
372C2×#124—221no—
373C2×#124C2×D1111yescharacteristic
374C2×#123—221no—
375C2×C22⋊Q8—111no—
376C2×C22⋊Q8—221no—
377C2×#121—111no—
378#520—118no—
379#520—224no—
380C2×C4×Q8—111no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—221no—
386C2×C4×D4—221no—
387C2×C4×D4C2×D1111yescharacteristic
388C2×#117—111no—
389C2×#117—221no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4—221no—
392#483—118no—
393#481—118no—
394#476—118no—
395#475—118no—
396#464—118no—
397#463C2×D1118yescomplemented
398#452—118no—
399#449—118no—
400#442—118no—
401#441—118no—
402C4×SD16—118no—
403C4×SD16—118no—
404#433—118no—
405C2×#106—111no—
406C2×#106—111no—
407C2×#106—111no—
408C2×#106—111no—
409C2×C4⋊C8—111no—
410C2×C4⋊C8C2×D1111yescharacteristic
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103C2×D1111yescharacteristic
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102C2×D1111yescharacteristic
419C2×C22⋊C8—111no—
420C2×C22⋊C8—111no—
421C2×#97—111no—
422C2×C4×C8—111no—
423C22×C11—24no—
424C22×C11—48no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—84no—
431C22×C11#52512yes—
432C22×C11#57712yes—
433C22×C11#57712yes—
434C22×C11C23×D411yescharacteristic
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—22no—
438C2×D11—44no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11#52512yes—
444C4×C11C22×#4111yescharacteristic
445C4×C11C22×#4111yescharacteristic
446Dic11—24no—
447Dic11—22no—
448Dic11—22no—
449Dic11—22no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453C2×#41—114no—
454C2×#41—222no—
455C2×#41—224no—
456C2×#41—224no—
457C22×Q8—111no—
458C22×Q8—221no—
459C22×Q8C22×D1111yescharacteristic
460C22×D4—221no—
461C22×D4—221no—
462C22×D4C22×D1111yescharacteristic
463C22×D4C22×D1111yescharacteristic
464C23×C4—21no—
465C23×C4—111no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C2×Q16—114no—
471C2×Q16—224no—
472C2×SD16—24no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16C22×D1114yes—
476C2×D8—24no—
477C2×D8C22×D1114yes—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C4⋊Q8—114no—
483C4⋊Q8—222no—
484#126—228no—
485#124—22no—
486#124—228no—
487#124C22×D1114yes—
488#123—228no—
489C22⋊Q8—114no—
490C22⋊Q8—228no—
491C22⋊Q8—222no—
492#121—114no—
493#121—222no—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—114no—
497C4×Q8—222no—
498C4×Q8—222no—
499C4×Q8—222no—
500C4×D4—22no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—222no—
504C4×D4—222no—
505C4×D4—228no—
506C4×D4—228no—
507C4×D4C22×D1114yes—
508#117—114no—
509#117—114no—
510#117—228no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—222no—
518C2×C4⋊C4—228no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4—111no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C42—111no—
536C2×C42—221no—
537C2×C42—221no—
538C2×C42—221no—
539C2×C42C22×D1111yescharacteristic
540#106—114no—
541#106—114no—
542#106—114no—
543#106—114no—
544C4⋊C8—114no—
545C4⋊C8C22×D1114yes—
546#103—114no—
547#103—114no—
548#103—114no—
549#103C22×D1114yes—
550#102—114no—
551#102—114no—
552#102—114no—
553#102C22×D1114yes—
554C22⋊C8—114no—
555C22⋊C8—114no—
556#97—114no—
557C4×C8—114no—
558C2×C11—44no—
559C2×C11—82no—
560C2×C11#312514yescomplemented
561C2×C11C2×#52511yescharacteristic
562C2×C11C2×#57711yescharacteristic
563C2×C11C2×#57711yescharacteristic
564D11—42no—
565C24—21no—
566C24—21no—
567C24—111no—
568#41—228no—
569#41—2216no—
570#41—228no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—114no—
575C2×Q8—112no—
576C2×Q8—221no—
577C2×Q8—224no—
578C2×Q8—222no—
579C2×Q8—882no—
580C2×Q8C23×D1112yes—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—224no—
587C2×D4—228no—
588C2×D4—224no—
589C2×D4—882no—
590C2×D4#434114yes—
591C2×D4C23×D1112yes—
592C2×D4C23×D1112yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—82no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—224no—
603C22×C4—224no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—228no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4—882no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619Q16—228no—
620SD16—28no—
621SD16—228no—
622D8—28no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8C23×D1112yes—
630C2×C8C23×D1112yes—
631C4⋊C4—21no—
632C4⋊C4—114no—
633C4⋊C4—114no—
634C4⋊C4—112no—
635C4⋊C4—112no—
636C4⋊C4—112no—
637C4⋊C4—224no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—224no—
645C4⋊C4—224no—
646C4⋊C4C23×D1112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—114no—
651C22⋊C4—114no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C42—112no—
657C42—112no—
658C42—224no—
659C42—224no—
660C42—224no—
661C42D4×D1112yes—
662C42C23×D1112yes—
663C11C2×#312511yescharacteristic, complemented, Sylow
664C23—24no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—112no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23C2×D4×D1111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—114no—
681Q8—224no—
682Q8—222no—
683Q8—884no—
684D4—24no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—42no—
689D4—2216no—
690D4—884no—
691D4C2×#434114yes—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—84no—
699C2×C4—112no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—2216no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—224no—
707C2×C4—222no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—884no—
718C2×C4—884no—
719C2×C4—884no—
720C2×C4C2×D4×D1112yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1111yescharacteristic
723C2×C4C2×#434112yes—
724C2×C4#41×D1112yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—222no—
729C8—222no—
730C22—24no—
731C22—48no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—222no—
739C22—222no—
740C22—222no—
741C22—444no—
742C22#1062313712yes—
743C22#1062330112yes—
744C22#1062330612yes—
745C22C22×D4×D1111yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—222no—
751C4—224no—
752C4—222no—
753C4—222no—
754C4—442no—
755C4—442no—
756C4—442no—
757C4#1062313712yes—
758C4C22×#434111yescharacteristic
759C4C2×#41×D1111yescharacteristic
760C2—44no—
761C2—82no—
762C2—442no—
763C2#1307889014yesdirect product factor
764C2C2×#1062313711yescharacteristic
765C2C2×#1062330111yescharacteristic
766C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC2×#10622771C2
hypercenterC2×#463D11
hypocenterC11C2×#3125
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#10623213C2semidirect
2. C2×#10623077C2semidirect
3. #13078890C2direct (N × H)
4. C2×#10622390C2semidirect
5. C2×#10622418C2semidirect
6. C2×#10622464C2semidirect
7. C2×#10622621C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622786C2semidirect
11. C2×#10622765C2semidirect
12. C2×#10622402C2semidirect
13. C2×#10622371C2semidirect
14. C2×SD16×Dic11C2semidirect
15. C2×#10622453C2semidirect
16. C2×C11×#463C2semidirect
32. #10623213C22semidirect
34. #10623077C22semidirect
46. C11×#463C22semidirect
54. #10622786C22semidirect
55. SD16×Dic11C22semidirect
57. #10622765C22semidirect
66. #10622667C22semidirect
67. #10622621C22semidirect
71. #10622464C22semidirect
72. #10622453C22semidirect
73. #10622418C22semidirect
74. #10622402C22semidirect
75. #10622390C22semidirect
76. #10622371C22semidirect
289. C2×#463D11semidirect
397. #463C2×D11semidirect
560. C2×C11#3125semidirect
663. C11C2×#3125semidirect
763. C2#13078890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232132
C2×#106230772
#130788902
C2×#106223902
C2×#106224182
C2×#106224642
C2×#106226212
C2×#106226672
C2×#106227862
C2×#106227712
C2×#106227652
C2×#106224022
C2×#106223712
C2×SD16×Dic112
C2×#106224532
C2×C11×#4632
C2×#312511