Finite Group Databasebeta

← C2×#13079576 #15624940

Subgroups — C2×#13079576 #15624940

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623211C211yesmaximal, characteristic, complemented
2C2×D11×#124C211yesmaximal, characteristic, complemented
3#13079576C2116yesmaximal, direct product factor
4C2×#10622672C211yesmaximal, characteristic, complemented
5C2×#10622310C211yesmaximal, characteristic, complemented
6C2×#10622669C211yesmaximal, characteristic, complemented
7C2×#10622798C211yesmaximal, characteristic, complemented
8C2×#10622779C211yesmaximal, characteristic, complemented
9C2×#10622778C211yesmaximal, characteristic, complemented
10C2×#10622766C211yesmaximal, characteristic, complemented
11C2×#10622799C211yesmaximal, characteristic, complemented
12C2×#10622783C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622769C211yesmaximal, characteristic
15C2×#10622298C211yesmaximal, characteristic, complemented
16C2×C11×#495C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic, complemented
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic, complemented
22C22×C11×D8C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic, complemented
25C2×#67000C2211yescharacteristic
26C2×#66999C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic, complemented
28C22×#4326C2211yescharacteristic, complemented
29C22×#4325C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66989C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic, complemented
33C22×#4324C2211yescharacteristic, complemented
34C22×#4323C2211yescharacteristic
35#10623211—24no—
36#10623211C2218yescomplemented
37D11×#124—24no—
38D11×#124C2218yescomplemented
39C2×#66938—21no—
40C2×#66938—21no—
41C2×#66936—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×C22⋊C4×D11—21no—
44C2×C22⋊C4×D11—21no—
45C2×#66932—21no—
46C2×#66930—21no—
47C2×#66928C2211yescharacteristic
48C2×C42×D11C2211yescharacteristic
49C2×#66923C2211yescharacteristic, complemented
50C11×#495C2218yescomplemented
51C2×C4×C8×C11C2211yescharacteristic, complemented
52C2×#66899C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56#10622799C2218yescomplemented
57#10622798C2218yescomplemented
58#10622783C2218yescomplemented
59#10622782C2218yescomplemented
60#10622779C2218yescomplemented
61#10622778C2218yescomplemented
62#10622769C2218yes—
63#10622766C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66885C2211yescharacteristic
66C2×(C2×D11)⋊C8C2211yescharacteristic
67C2×(C2×D11)⋊C8C2211yescharacteristic
68C2×#66880C2211yescharacteristic, complemented
69C2×#66880C2211yescharacteristic, complemented
70C2×Dic11⋊C8C2211yescharacteristic, complemented
71C2×Dic11⋊C8C2211yescharacteristic, complemented
72#10622672C2218yescomplemented
73#10622669C2218yescomplemented
74C2×C4×C11⋊C8C2211yescharacteristic, complemented
75#10622310C2218yescomplemented
76#10622298C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C2×Q8×D11—22no—
86C2×Q8×D11—42no—
87C2×Q8×D11—42no—
88C2×Q8×D11C2314yes—
89C2×D4×D11—22no—
90C2×D4×D11—42no—
91C2×D4×D11—42no—
92C2×D4×D11C2314yes—
93C22×D44C2311yescharacteristic
94C22×C4×D11—21no—
95C22×C4×D11D411yescharacteristic
96C22×C4×D11D411yescharacteristic
97C22×C4×D11C2311yescharacteristic
98C22×Dic22—21no—
99C22×Dic22C2311yescharacteristic
100C2×C11×Q16—42no—
101C2×C11×Q16C2314yescomplemented
102C2×C11×SD16—42no—
103C2×C11×SD16—42no—
104C2×C11×SD16C2314yes—
105C2×C11×SD16C2314yescomplemented
106C2×C11×D8—42no—
107C2×C11×D8C2314yes—
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C11×#124—22no—
111C11×#124—22no—
112C11×#124C2314yes—
113C11×#124C2314yescomplemented
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C42×C11C2311yescharacteristic
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123#67000—22no—
124#67000C2314yes—
125#66999—22no—
126#66999C2314yes—
127Q8×Dic11—22no—
128Q8×Dic11C2314yescomplemented
129C2×#4326—42no—
130C2×#4326C2314yescomplemented
131C2×#4325—42no—
132C2×#4325C2314yes—
133#66991—22no—
134#66991C2314yes—
135#66989—22no—
136#66989C2314yes—
137D4×Dic11—22no—
138D4×Dic11C2314yescomplemented
139C2×#4324—42no—
140C2×#4324C2314yescomplemented
141C2×#4323—42no—
142C2×#4323C2314yes—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×C4⋊Dic11—21no—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×C4×Dic11—21no—
155C2×C4×Dic11D411yescharacteristic
156C2×C4×Dic11D411yescharacteristic
157C2×C4×Dic11C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160#66938—28no—
161#66938—28no—
162#66936—28no—
163(C22⋊D11)⋊C4—28no—
164C22⋊C4×D11—28no—
165C22⋊C4×D11—28no—
166#66932—28no—
167#66930—28no—
168#66928—22no—
169#66928C2314yes—
170C42×D11D414yes—
171C42×D11C2314yes—
172#66923—22no—
173#66923C2314yescomplemented
174C4×C8×C11C2314yescomplemented
175#66899C2314yescomplemented
176#66899C2314yescomplemented
177#66896C2314yes—
178#66896C2314yes—
179#66885C2314yes—
180#66885C2314yes—
181(C2×D11)⋊C8C2314yes—
182(C2×D11)⋊C8C2314yes—
183#66880C2314yescomplemented
184#66880C2314yescomplemented
185Dic11⋊C8C2314yescomplemented
186Dic11⋊C8C2314yescomplemented
187C4×C11⋊C8C2314yescomplemented
188C2×#3211—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—44no—
194C23×D11—44no—
195C23×D11—44no—
196C23×D11C2×D411yescharacteristic
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11C2412yes—
204C2×Q8×C11C2412yes—
205C2×D4×C11—21no—
206C2×D4×C11—21no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11C2412yes—
212C2×D4×C11C2412yes—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C22×Dic11—24no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—44no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230Q8×D11—44no—
231Q8×D11—44no—
232Q8×D11—48no—
233D4×D11—44no—
234D4×D11—44no—
235D4×D11—48no—
236C2×D44—21no—
237C2×D44—22no—
238C2×D44—22no—
239C2×D44C2412yes—
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—42no—
245C2×C4×D11—44no—
246C2×C4×D11C2×D412yes—
247C2×C4×D11C2×D414yes—
248C2×C4×D11C2×D414yes—
249C2×C4×D11C2412yes—
250C2×Dic22—24no—
251C2×Dic22—21no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22—44no—
255C2×Dic22C2412yes—
256C11×Q16—44no—
257C11×SD16—44no—
258C11×SD16—44no—
259C11×D8—44no—
260C2×C8×C11—22no—
261C2×C8×C11—22no—
262C2×C8×C11C2412yes—
263C2×C8×C11C2412yes—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—24no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C42×C11C2×D412yes—
269C42×C11C2412yes—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272C22⋊Dic11—24no—
273C22⋊Dic11—24no—
274#4326—44no—
275#4325—44no—
276#4324—44no—
277#4323—44no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283C4⋊Dic11—24no—
284C4⋊Dic11—21no—
285C4⋊Dic11—21no—
286C4⋊Dic11C2412yes—
287C4⋊Dic11C2412yes—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291C4×Dic11—24no—
292C4×Dic11C2×D412yes—
293C4×Dic11C2×D414yes—
294C4×Dic11C2×D414yes—
295C4×Dic11C2412yes—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8C2412yes—
299C2×C11⋊C8C2412yes—
300C2×#529—111no—
301C22×#124—111no—
302#3211—1116no—
303C2×#495—111no—
304C2×#495D1111yescharacteristic, complemented
305C2×#488—111no—
306C2×#488—111no—
307C2×#464—111no—
308C2×#464—111no—
309C2×#463—111no—
310C2×#463—111no—
311C2×#451—111no—
312C2×#448—111no—
313C2×#450—111no—
314C2×#447—111no—
315C2×#431—111no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11C22×D411yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—48no—
329C22×D11—48no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—48no—
334C22×D11—816no—
335C22×D11#13514yes—
336C22×D11C22×D412yes—
337Q8×C11—22no—
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—22no—
341Q8×C11—42no—
342Q8×C11—42no—
343D4×C11—22no—
344D4×C11—22no—
345D4×C11—22no—
346D4×C11—22no—
347D4×C11—42no—
348D4×C11—42no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11C22×D412yes—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11H(5,𝔽2)12yes—
359C2×C4×C11H(5,𝔽2)12yes—
360C2×C4×C11C2511yescharacteristic
361C22⋊D11—48no—
362C22⋊D11—48no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—48no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11C22×D412yes—
374C2×Dic11C22×D412yes—
375C2×Dic11C22×D412yes—
376D44—22no—
377D44—22no—
378D44—42no—
379C4×D11—28no—
380C4×D11—24no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—44no—
384C4×D11—48no—
385Dic22—22no—
386Dic22—22no—
387Dic22—48no—
388Dic22—42no—
389C8×C11—22no—
390C8×C11—22no—
391C11⋊C8—22no—
392C11⋊C8—22no—
393C23×Q8—111no—
394C23×D4—111no—
395C22×Q16—111no—
396C22×Q16C2×D1111yescharacteristic, complemented
397C22×SD16—111no—
398C22×SD16—111no—
399C22×SD16C2×D1111yescharacteristic
400C22×SD16C2×D1111yescharacteristic, complemented
401C22×D8—111no—
402C22×D8C2×D1111yescharacteristic
403#529—118no—
404#529—224no—
405C2×#126—221no—
406C2×#125—111no—
407C2×#124—111no—
408C2×#124—111no—
409C2×#124—118no—
410C2×#124—111no—
411C2×#124—221no—
412C2×#124—221no—
413C2×#124—224no—
414C2×#124C2×D1111yescharacteristic
415C2×#124C2×D1111yescharacteristic, complemented
416C2×#123—221no—
417C2×C22⋊Q8—111no—
418C2×#121—111no—
419C2×C4×Q8—111no—
420C2×C4×D4—111no—
421C2×C4×D4—221no—
422C2×#117—221no—
423C22×C22⋊C4—221no—
424C22×C22⋊C4—221no—
425C22×C42—111no—
426#495—118no—
427#495C2×D1118yescomplemented
428#488—118no—
429#488—118no—
430#464—118no—
431#464—118no—
432#463—118no—
433#463—118no—
434#451—118no—
435#450—118no—
436#448—118no—
437#447—118no—
438#431—118no—
439C2×C4⋊C8—111no—
440C2×C4⋊C8—111no—
441C2×#103—111no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×C22⋊C8—111no—
450C2×C22⋊C8—111no—
451C2×C4×C8—111no—
452C2×C4×C8C2×D1111yescharacteristic, complemented
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—84no—
460C22×C11—84no—
461C22×C11#53512yes—
462C22×C11C2×#13512yes—
463C22×C11#57512yes—
464C22×C11C23×D411yescharacteristic
465C2×D11—22no—
466C2×D11—28no—
467C2×D11—22no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—816no—
472C2×D11—84no—
473C2×D11C2×#13514yes—
474C4×C11—22no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11#53512yes—
479C4×C11C2×H(5,𝔽2)11yescharacteristic
480C4×C11C2×H(5,𝔽2)11yescharacteristic
481Dic11—22no—
482Dic11—22no—
483Dic11—22no—
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C22×Q8—114no—
489C22×Q8—111no—
490C22×Q8—221no—
491C22×Q8—222no—
492C22×Q8—442no—
493C22×Q8—442no—
494C22×Q8C22×D1111yescharacteristic
495C22×Q8C22×D1111yescharacteristic
496C22×D4—114no—
497C22×D4—111no—
498C22×D4—222no—
499C22×D4—221no—
500C22×D4—221no—
501C22×D4—442no—
502C22×D4—442no—
503C22×D4C22×D1111yescharacteristic
504C22×D4C22×D1111yescharacteristic
505C23×C4—111no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4—221no—
509C23×C4—221no—
510C2×Q16—42no—
511C2×Q16—114no—
512C2×Q16—442no—
513C2×Q16C22×D1114yescomplemented
514C2×SD16—42no—
515C2×SD16—42no—
516C2×SD16—114no—
517C2×SD16—114no—
518C2×SD16—442no—
519C2×SD16—442no—
520C2×SD16C22×D1114yes—
521C2×SD16C22×D1114yescomplemented
522C2×D8—42no—
523C2×D8—114no—
524C2×D8—442no—
525C2×D8C22×D1114yes—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530#126—228no—
531#125—114no—
532#125—222no—
533#124—22no—
534#124—22no—
535#124—114no—
536#124—114no—
537#124—114no—
538#124—228no—
539#124—228no—
540#124—222no—
541#124—222no—
542#124—222no—
543#124C22×D1114yes—
544#124C22×D1114yescomplemented
545#123—228no—
546C22⋊Q8—114no—
547C22⋊Q8—222no—
548#121—114no—
549#121—222no—
550C4×Q8—114no—
551C4×Q8—222no—
552C4×D4—114no—
553C4×D4—222no—
554C4×D4—228no—
555#117—228no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—228no—
567C2×C22⋊C4—228no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C42—111no—
578C2×C42—111no—
579C2×C42—111no—
580C2×C42—114no—
581C2×C42—114no—
582C2×C42—221no—
583C2×C42C22×D1111yescharacteristic
584C4⋊C8—114no—
585C4⋊C8—114no—
586#103—114no—
587#103—114no—
588#103—114no—
589#103—114no—
590#102—114no—
591#102—114no—
592#102—114no—
593#102—114no—
594C22⋊C8—114no—
595C22⋊C8—114no—
596C4×C8—114no—
597C4×C8C22×D1114yescomplemented
598C2×C11—82no—
599C2×C11—82no—
600C2×C11#321114yescomplemented
601C2×C11C2×#53511yescharacteristic
602C2×C11C22×#13511yescharacteristic
603C2×C11C2×#57511yescharacteristic
604D11—24no—
605D11—82no—
606C24—21no—
607C24—21no—
608C24—111no—
609C24—224no—
610C24—221no—
611C24—444no—
612C24—444no—
613C24—444no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8—112no—
621C2×Q8—224no—
622C2×Q8—221no—
623C2×Q8—222no—
624C2×Q8—222no—
625C2×Q8—444no—
626C2×Q8—444no—
627C2×Q8—444no—
628C2×Q8—448no—
629C2×Q8C23×D1112yes—
630C2×Q8C23×D1112yes—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—112no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—221no—
641C2×D4—222no—
642C2×D4—222no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—448no—
646C2×D4—444no—
647C2×D4—444no—
648C2×D4C23×D1112yes—
649C2×D4C23×D1112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—111no—
653C22×C4—111no—
654C22×C4—111no—
655C22×C4—114no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—114no—
659C22×C4—224no—
660C22×C4—224no—
661C22×C4—224no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—442no—
668C22×C4—444no—
669C22×C4—444no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673Q16—44no—
674Q16—444no—
675SD16—44no—
676SD16—44no—
677SD16—444no—
678SD16—444no—
679D8—44no—
680D8—444no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—112no—
684C2×C8—112no—
685C2×C8—222no—
686C2×C8—222no—
687C2×C8C23×D1112yes—
688C2×C8C23×D1112yes—
689C4⋊C4—112no—
690C4⋊C4—112no—
691C4⋊C4—224no—
692C4⋊C4—224no—
693C4⋊C4—221no—
694C4⋊C4—221no—
695C4⋊C4—224no—
696C4⋊C4—224no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C22⋊C4—224no—
710C42—114no—
711C42—112no—
712C42—114no—
713C42—112no—
714C42—224no—
715C42D4×D1112yes—
716C42C23×D1112yes—
717C11C2×#321111yescharacteristic, complemented, Sylow
718C23—22no—
719C23—22no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—114no—
727C23—112no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—448no—
732C23—448no—
733C23—448no—
734C23—442no—
735C23—442no—
736C23—442no—
737C23—8816no—
738C23C2×D4×D1111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—42no—
744Q8—42no—
745Q8—222no—
746Q8—222no—
747Q8—448no—
748Q8—442no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—42no—
754D4—42no—
755D4—222no—
756D4—222no—
757D4—448no—
758D4—448no—
759D4—442no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—112no—
767C2×C4—112no—
768C2×C4—112no—
769C2×C4—228no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—224no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—444no—
780C2×C4—448no—
781C2×C4—448no—
782C2×C4—442no—
783C2×C4—442no—
784C2×C4—442no—
785C2×C4C2×D4×D1112yes—
786C2×C4C2×D4×D1112yes—
787C2×C4C2×D4×D1111yescharacteristic
788C2×C4#6703712yes—
789C2×C4#6703712yes—
790C2×C4C24×D1111yescharacteristic
791C8—22no—
792C8—22no—
793C8—222no—
794C8—222no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—84no—
802C22—84no—
803C22—114no—
804C22—228no—
805C22—222no—
806C22—222no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—8816no—
811C22—884no—
812C22#1062324612yes—
813C22D11×#13512yes—
814C22#1062329912yes—
815C22C22×D4×D1111yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—222no—
821C4—222no—
822C4—222no—
823C4—442no—
824C4—442no—
825C4—442no—
826C4#1062324612yes—
827C4C2×#6703711yescharacteristic
828C4C2×#6703711yescharacteristic
829C2—82no—
830C2—82no—
831C2—224no—
832C2—882no—
833C2#1307957614yesdirect product factor
834C2C2×#1062324611yescharacteristic
835C2C2×D11×#13511yescharacteristic
836C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#495C2
socleC23×C11C22×D4
prime radicalC2×#10622769C2
hypercenterC2×#495D11
hypocenterC11C2×#3211
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. C2×#10623211C2semidirect
2. C2×D11×#124C2semidirect
3. #13079576C2direct (N × H)
4. C2×#10622672C2semidirect
5. C2×#10622310C2semidirect
6. C2×#10622669C2semidirect
7. C2×#10622798C2semidirect
8. C2×#10622779C2semidirect
9. C2×#10622778C2semidirect
10. C2×#10622766C2semidirect
11. C2×#10622799C2semidirect
12. C2×#10622783C2semidirect
13. C2×#10622782C2semidirect
15. C2×#10622298C2semidirect
16. C2×C11×#495C2semidirect
19. C22×C11×Q16C22semidirect
21. C22×C11×SD16C22semidirect
24. C2×C11×#124C22semidirect
27. C2×Q8×Dic11C22semidirect
28. C22×#4326C22semidirect
32. C2×D4×Dic11C22semidirect
33. C22×#4324C22semidirect
36. #10623211C22semidirect
38. D11×#124C22semidirect
49. C2×#66923C22semidirect
50. C11×#495C22semidirect
51. C2×C4×C8×C11C22semidirect
52. C2×#66899C22semidirect
53. C2×#66899C22semidirect
56. #10622799C22semidirect
57. #10622798C22semidirect
58. #10622783C22semidirect
59. #10622782C22semidirect
60. #10622779C22semidirect
61. #10622778C22semidirect
63. #10622766C22semidirect
68. C2×#66880C22semidirect
69. C2×#66880C22semidirect
70. C2×Dic11⋊C8C22semidirect
71. C2×Dic11⋊C8C22semidirect
72. #10622672C22semidirect
73. #10622669C22semidirect
74. C2×C4×C11⋊C8C22semidirect
75. #10622310C22semidirect
76. #10622298C22semidirect
101. C2×C11×Q16C23semidirect
105. C2×C11×SD16C23semidirect
113. C11×#124C23semidirect
128. Q8×Dic11C23semidirect
130. C2×#4326C23semidirect
138. D4×Dic11C23semidirect
140. C2×#4324C23semidirect
173. #66923C23semidirect
174. C4×C8×C11C23semidirect
175. #66899C23semidirect
176. #66899C23semidirect
183. #66880C23semidirect
184. #66880C23semidirect
185. Dic11⋊C8C23semidirect
186. Dic11⋊C8C23semidirect
187. C4×C11⋊C8C23semidirect
304. C2×#495D11semidirect
396. C22×Q16C2×D11semidirect
400. C22×SD16C2×D11semidirect
415. C2×#124C2×D11semidirect
427. #495C2×D11semidirect
452. C2×C4×C8C2×D11semidirect
513. C2×Q16C22×D11semidirect
521. C2×SD16C22×D11semidirect
544. #124C22×D11semidirect
597. C4×C8C22×D11semidirect
600. C2×C11#3211semidirect
717. C11C2×#3211semidirect
833. C2#13079576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232112
C2×D11×#1242
#130795762
C2×#106226722
C2×#106223102
C2×#106226692
C2×#106227982
C2×#106227792
C2×#106227782
C2×#106227662
C2×#106227992
C2×#106227832
C2×#106227822
C2×#106227692
C2×#106222982
C2×C11×#4952
C2×#321111