Finite Group Databasebeta

← C2×#13080125 #15628753

Subgroups — C2×#13080125 #15628753

Order 2816.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C211yesmaximal, characteristic, complemented
2C22×SD16×D11C211yesmaximal, characteristic, complemented
3C2×#10623258C211yesmaximal, characteristic, complemented
4C2×#10623207C211yesmaximal, characteristic
5#13080125C2116yesmaximal, direct product factor
6C2×#10622787C211yesmaximal, characteristic, complemented
7C2×#10622801C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622696C211yesmaximal, characteristic, complemented
10C2×#10622800C211yesmaximal, characteristic, complemented
11C2×#10622799C211yesmaximal, characteristic, complemented
12C2×#10622783C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622323C211yesmaximal, characteristic, complemented
15C2×#10622319C211yesmaximal, characteristic, complemented
16C2×C11×#497C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×Q8×D11C2211yescharacteristic, complemented
20C22×D4×D11C2211yescharacteristic
21C22×C11×Q16C2211yescharacteristic, complemented
22C22×C11×Q16C2211yescharacteristic, complemented
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic, complemented
26C2×C11×#124C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C2×#66999C2211yescharacteristic
29C2×#66999C2211yescharacteristic, complemented
30C22×#4326C2211yescharacteristic, complemented
31C22×#4325C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C2×#66991C2211yescharacteristic
34C22×#4324C2211yescharacteristic
35C2×#66971—28no—
36C2×#66971C2218yescomplemented
37C2×SD16×D11—28no—
38C2×SD16×D11C2218yescomplemented
39C22×#4314C2211yescharacteristic
40C22×#4313C2211yescharacteristic, complemented
41C22×C8×D11C2211yescharacteristic
42#10623258—24no—
43#10623258C2218yescomplemented
44#10623207—24no—
45#10623207C2218yes—
46C2×#66949—21no—
47C2×#66949—21no—
48C2×#66946—21no—
49C2×#66941—21no—
50C2×#66937—21no—
51C2×#66936—21no—
52C2×#66935—21no—
53C2×C22⋊C4×D11—21no—
54C2×C4×D44C2211yescharacteristic
55C2×C4×D44C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic, complemented
57C11×#497C2218yescomplemented
58C2×C11×#97C2211yescharacteristic, complemented
59C2×#66899C2211yescharacteristic, complemented
60C2×#66899C2211yescharacteristic, complemented
61C2×#66899C2211yescharacteristic, complemented
62C2×#66896C2211yescharacteristic
63#10622801C2218yescomplemented
64#10622800C2218yescomplemented
65#10622799C2218yescomplemented
66#10622787C2218yescomplemented
67#10622783C2218yescomplemented
68#10622782C2218yescomplemented
69C2×#66885C2211yescharacteristic
70C2×(C2×D11)⋊C8C2211yescharacteristic
71C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
72C2×#66882C2211yescharacteristic, complemented
73C2×#66880C2211yescharacteristic, complemented
74#10622696C2218yescomplemented
75#10622667C2218yescomplemented
76C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
77#10622323C2218yescomplemented
78#10622319C2218yescomplemented
79C24×D11—21no—
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C2×#4343—22no—
87C2×#4343—24no—
88C2×#4343—42no—
89C2×#4343C2314yes—
90C2×Q8×D11—22no—
91C2×Q8×D11—22no—
92C2×Q8×D11—24no—
93C2×Q8×D11—24no—
94C2×Q8×D11—42no—
95C2×Q8×D11—42no—
96C2×Q8×D11C2314yes—
97C2×Q8×D11C2314yescomplemented
98C2×D4×D11—24no—
99C2×D4×D11—22no—
100C2×D4×D11—42no—
101C2×D4×D11C2314yes—
102C22×D44—21no—
103C22×D44D411yescharacteristic
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×C4×D11—21no—
109C22×C4×D11C2311yescharacteristic
110C22×C4×D11C2311yescharacteristic
111C22×Dic22—21no—
112C22×Dic22—21no—
113C22×Dic22C2311yescharacteristic
114C2×C11×Q16—24no—
115C2×C11×Q16—42no—
116C2×C11×Q16C2314yescomplemented
117C2×C11×Q16C2314yescomplemented
118C2×C11×SD16—24no—
119C2×C11×SD16—42no—
120C2×C11×SD16C2314yes—
121C2×C11×SD16C2314yes—
122C22×C8×C11C2311yescharacteristic
123C22×C8×C11C2311yescharacteristic
124C11×C4⋊Q8—22no—
125C11×C4⋊Q8C2314yescomplemented
126C11×#124—22no—
127C11×#124C2314yes—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C42×C11C2311yescharacteristic
133C2×C22⋊Dic11—21no—
134#66999—22no—
135#66999—22no—
136#66999—22no—
137#66999C2314yes—
138#66999C2314yes—
139#66999C2314yescomplemented
140C2×#4326—24no—
141C2×#4326C2314yescomplemented
142C2×#4325—24no—
143C2×#4325—24no—
144C2×#4325C2314yes—
145C2×#4325C2314yes—
146#66991—22no—
147#66991C2314yes—
148C2×#4324—24no—
149C2×#4324C2314yes—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153C2×(C2×D11)⋊C4—21no—
154C2×(C2×D11)⋊C4D411yescharacteristic
155C2×(C2×D11)⋊C4D411yescharacteristic
156C2×C4⋊Dic11D411yescharacteristic
157C2×C4⋊Dic11C2311yescharacteristic
158C2×C4⋊Dic11C2311yescharacteristic
159C2×Dic11⋊C4—21no—
160C2×Dic11⋊C4—21no—
161C2×Dic11⋊C4—21no—
162C2×Dic11⋊C4—21no—
163C2×C4×Dic11—21no—
164C22×C11⋊C8C2311yescharacteristic
165C22×C11⋊C8C2311yescharacteristic
166#66971—232no—
167SD16×D11—232no—
168C2×#4314D418yescomplemented
169C2×#4314C2314yes—
170C2×#4313—24no—
171C2×#4313C2314yescomplemented
172C2×C8×D11—24no—
173C2×C8×D11C2314yes—
174#66949—28no—
175#66949—28no—
176#66946—28no—
177#66941—28no—
178#66937—28no—
179#66936—28no—
180#66935—28no—
181C22⋊C4×D11—28no—
182C4×D44—22no—
183C4×D44D414yes—
184C4×D44C2314yes—
185C4×D44C2314yes—
186C4×Dic22—22no—
187C4×Dic22C2314yescomplemented
188C11×#97C2314yescomplemented
189#66899C2314yescomplemented
190#66899C2314yescomplemented
191#66899C2314yescomplemented
192#66896C2314yes—
193#66885C2314yes—
194(C2×D11)⋊C8C2314yes—
195(C2×D11)⋊C8C2314yescomplemented
196#66882C2314yescomplemented
197#66880C2314yescomplemented
198C4⋊(C11⋊C8)C2314yescomplemented
199C2×#3266—111nomaximal, Sylow
200C24×C11—21no—
201C23×D11—21no—
202C23×D11—24no—
203C23×D11—44no—
204C23×D11—44no—
205C23×D11—82no—
206C23×D11C2×D411yescharacteristic
207C23×D11C2×D411yescharacteristic
208C2×Q8×C11—21no—
209C2×Q8×C11—21no—
210C2×Q8×C11—21no—
211C2×Q8×C11—22no—
212C2×Q8×C11—22no—
213C2×Q8×C11—22no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11—22no—
217C2×Q8×C11C2412yes—
218C2×Q8×C11C2412yes—
219C2×Q8×C11C2412yes—
220C2×D4×C11—22no—
221C2×D4×C11—21no—
222C2×D4×C11—22no—
223C2×D4×C11C2412yes—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2411yescharacteristic
230C2×C22⋊D11—24no—
231C2×C22⋊D11—24no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—82no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11C2×D411yescharacteristic
238C22×Dic11C2×D411yescharacteristic
239#4343—28no—
240#4343—44no—
241#4343—48no—
242Q8×D11—28no—
243Q8×D11—28no—
244Q8×D11—44no—
245Q8×D11—44no—
246Q8×D11—48no—
247Q8×D11—48no—
248D4×D11—28no—
249D4×D11—44no—
250D4×D11—48no—
251C2×D44—24no—
252C2×D44—24no—
253C2×D44—21no—
254C2×D44—22no—
255C2×D44—44no—
256C2×D44C2×D414yes—
257C2×D44C2×D414yes—
258C2×D44C2412yes—
259C2×C4×D11—24no—
260C2×C4×D11—24no—
261C2×C4×D11—24no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—24no—
265C2×C4×D11—22no—
266C2×C4×D11—22no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—82no—
271C2×C4×D11C2×D412yes—
272C2×C4×D11C2×D412yes—
273C2×C4×D11C2412yes—
274C2×C4×D11C2412yes—
275C2×Dic22—24no—
276C2×Dic22—24no—
277C2×Dic22—21no—
278C2×Dic22—22no—
279C2×Dic22—44no—
280C2×Dic22—44no—
281C2×Dic22C2×D414yes—
282C2×Dic22C2412yes—
283C11×Q16—28no—
284C11×Q16—44no—
285C11×SD16—28no—
286C11×SD16—44no—
287C2×C8×C11—22no—
288C2×C8×C11C2×D414yes—
289C2×C8×C11C2412yes—
290C2×C8×C11C2412yes—
291C11×C4⋊C4—24no—
292C11×C4⋊C4—24no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—24no—
295C42×C11C2×D412yes—
296C42×C11C2412yes—
297C22⋊Dic11—24no—
298#4326—28no—
299#4325—28no—
300#4325—28no—
301#4324—28no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4C2×D414yes—
307(C2×D11)⋊C4C2×D414yes—
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11C2×D414yes—
311C4⋊Dic11C2412yes—
312C4⋊Dic11C2412yes—
313Dic11⋊C4—24no—
314Dic11⋊C4—24no—
315Dic11⋊C4—24no—
316Dic11⋊C4—24no—
317C4×Dic11—24no—
318C2×C11⋊C8—22no—
319C2×C11⋊C8—22no—
320C2×C11⋊C8C2412yes—
321C2×C11⋊C8C2412yes—
322#4314C2×D4116yescomplemented
323#4313—28no—
324C8×D11—28no—
325C22×#137—111no—
326C23×SD16—111no—
327C2×D4×Q8—111no—
328C2×#546—111no—
329#3266—1116no—
330C2×#497D1111yescharacteristic, complemented
331C2×#468—111no—
332C2×#467—111no—
333C2×#464—111no—
334C2×#461—111no—
335C2×#452—111no—
336C2×#451—111no—
337C2×#448—111no—
338C2×#450—111no—
339C2×#440—111no—
340C2×#435—111no—
341C23×C11—22no—
342C23×C11—42no—
343C23×C11—42no—
344C23×C11—42no—
345C23×C11C22×D411yescharacteristic
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—24no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—48no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—48no—
357C22×D11—84no—
358C22×D11—816no—
359C22×D11#13714yescomplemented
360C22×D11C22×D412yes—
361C22×D11C22×D412yes—
362Q8×C11—22no—
363Q8×C11—22no—
364Q8×C11—22no—
365Q8×C11—22no—
366Q8×C11—22no—
367Q8×C11—22no—
368Q8×C11—42no—
369Q8×C11—42no—
370Q8×C11—42no—
371D4×C11—22no—
372D4×C11—22no—
373D4×C11—42no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—42no—
380C2×C4×C11—42no—
381C2×C4×C11—42no—
382C2×C4×C11C22×D412yes—
383C2×C4×C11C22×D412yes—
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D412yes—
386C2×C4×C11H(5,𝔽2)12yes—
387C2×C4×C11C2511yescharacteristic
388C22⋊D11—48no—
389C22⋊D11—84no—
390C2×Dic11—24no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11C22×D412yes—
399C2×Dic11C22×D412yes—
400D44—28no—
401D44—24no—
402D44—22no—
403D44—48no—
404D44C22×D414yes—
405C4×D11—24no—
406C4×D11—24no—
407C4×D11—22no—
408C4×D11—22no—
409C4×D11—22no—
410C4×D11—22no—
411C4×D11—48no—
412C4×D11—48no—
413C4×D11—48no—
414C4×D11—84no—
415Dic22—24no—
416Dic22—22no—
417Dic22—48no—
418Dic22—48no—
419Dic22C22×D414yes—
420C8×C11—22no—
421C8×C11C22×D414yes—
422C11⋊C8—22no—
423C11⋊C8—22no—
424C22×#41—111no—
425C23×Q8—111no—
426C23×Q8—111no—
427C23×D4—111no—
428C2×#137—118no—
429C2×#137—228no—
430C22×Q16—111no—
431C22×Q16C2×D1111yescharacteristic, complemented
432C22×Q16C2×D1111yescharacteristic, complemented
433C22×SD16—111no—
434C22×SD16—111no—
435C22×SD16—111no—
436C22×SD16—118no—
437C22×SD16—111no—
438C22×SD16—228no—
439C22×SD16C2×D1111yescharacteristic
440C22×SD16C2×D1111yescharacteristic
441C22×M16—111no—
442C23×C8—111no—
443D4×Q8—118no—
444D4×Q8—224no—
445#546—118no—
446#546—224no—
447C2×C4⋊Q8—221no—
448C2×C4⋊Q8C2×D1111yescharacteristic, complemented
449C2×#124C2×D1111yescharacteristic
450C2×#123—221no—
451C2×C22⋊Q8—111no—
452C2×C22⋊Q8—111no—
453C2×C22⋊Q8—111no—
454C2×C22⋊Q8—221no—
455C2×C22⋊Q8—221no—
456C2×#121—111no—
457C2×#121—221no—
458C2×#120—221no—
459C2×C4×Q8—111no—
460C2×C4×D4—111no—
461C2×C4×D4—111no—
462C2×C4×D4—221no—
463C22×C22⋊C4—221no—
464#497C2×D1118yescomplemented
465#468—118no—
466#467—118no—
467#464—118no—
468#461—118no—
469#452—118no—
470#451—118no—
471#450—118no—
472#448—118no—
473#440—118no—
474#435—118no—
475C2×#107—111no—
476C2×C4⋊C8—111no—
477C2×#103—111no—
478C2×#103—111no—
479C2×#103—111no—
480C2×#103—111no—
481C2×#102—111no—
482C2×#102—111no—
483C2×C22⋊C8—111no—
484C2×C22⋊C8—111no—
485C2×#97C2×D1111yescharacteristic, complemented
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—84no—
490C22×C11D4212yes—
491C22×C11C2×#13712yes—
492C22×C11#57712yes—
493C22×C11C23×D411yescharacteristic
494C2×D11—22no—
495C2×D11—28no—
496C2×D11—22no—
497C2×D11—24no—
498C2×D11—22no—
499C2×D11—22no—
500C2×D11—22no—
501C2×D11—44no—
502C2×D11—48no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—816no—
506C2×D11C2×#13714yescomplemented
507C4×C11—22no—
508C4×C11—22no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11D4212yes—
513C4×C11C23×D411yescharacteristic
514C4×C11C2×H(5,𝔽2)11yescharacteristic
515Dic11—24no—
516Dic11—22no—
517Dic11—22no—
518Dic11—42no—
519Dic11—42no—
520C25—221no—
521C2×#41—114no—
522C2×#41—222no—
523C2×#41—224no—
524C2×#41—442no—
525C22×Q8—114no—
526C22×Q8—114no—
527C22×Q8—111no—
528C22×Q8—221no—
529C22×Q8—221no—
530C22×Q8—222no—
531C22×Q8—222no—
532C22×Q8—224no—
533C22×Q8—224no—
534C22×Q8—442no—
535C22×Q8—442no—
536C22×Q8C22×D1111yescharacteristic
537C22×Q8C22×D1111yescharacteristic
538C22×Q8C22×D1111yescharacteristic
539C22×D4—114no—
540C22×D4—111no—
541C22×D4—111no—
542C22×D4—221no—
543C22×D4—222no—
544C22×D4—221no—
545C22×D4—224no—
546C22×D4—221no—
547C22×D4—442no—
548C22×D4C22×D1111yescharacteristic
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—221no—
552C23×C4—221no—
553C23×C4—221no—
554C23×C4—221no—
555#137—2232no—
556C2×Q16—24no—
557C2×Q16—42no—
558C2×Q16—114no—
559C2×Q16—224no—
560C2×Q16C22×D1114yescomplemented
561C2×Q16C22×D1114yescomplemented
562C2×SD16—24no—
563C2×SD16—42no—
564C2×SD16—114no—
565C2×SD16—114no—
566C2×SD16—114no—
567C2×SD16—118no—
568C2×SD16—114no—
569C2×SD16—2232no—
570C2×SD16—224no—
571C2×SD16—224no—
572C2×SD16—224no—
573C2×SD16C22×D1114yes—
574C2×SD16C22×D1114yes—
575C2×M16—114no—
576C2×M16—224no—
577C22×C8—111no—
578C22×C8—111no—
579C22×C8—114no—
580C22×C8—224no—
581C22×C8C22×D1111yescharacteristic
582C22×C8C22×D1111yescharacteristic
583C4⋊Q8—22no—
584C4⋊Q8—228no—
585C4⋊Q8C22×D1114yescomplemented
586#124—22no—
587#124C22×D1114yes—
588#123—228no—
589C22⋊Q8—114no—
590C22⋊Q8—114no—
591C22⋊Q8—114no—
592C22⋊Q8—228no—
593C22⋊Q8—228no—
594C22⋊Q8—222no—
595C22⋊Q8—222no—
596C22⋊Q8—222no—
597#121—114no—
598#121—228no—
599#121—222no—
600#120—228no—
601C4×Q8—114no—
602C4×Q8—222no—
603C4×D4—114no—
604C4×D4—114no—
605C4×D4—114no—
606C4×D4—228no—
607C4×D4—222no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—111no—
613C2×C4⋊C4—221no—
614C2×C4⋊C4—221no—
615C2×C4⋊C4—221no—
616C2×C4⋊C4—221no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—111no—
620C2×C22⋊C4—111no—
621C2×C22⋊C4—228no—
622C2×C22⋊C4—221no—
623C2×C22⋊C4—221no—
624C2×C22⋊C4—221no—
625C2×C22⋊C4—221no—
626C2×C22⋊C4—221no—
627C2×C42—221no—
628C2×C42C22×D1111yescharacteristic
629#107—114no—
630C4⋊C8—114no—
631#103—114no—
632#103—114no—
633#103—114no—
634#103—114no—
635#102—114no—
636#102—114no—
637C22⋊C8—114no—
638C22⋊C8—114no—
639#97C22×D1114yescomplemented
640C2×C11—82no—
641C2×C11#326614yescomplemented
642C2×C11C2×D4211yescharacteristic
643C2×C11C22×#13711yescharacteristic
644C2×C11C2×#57711yescharacteristic
645D11—24no—
646D11—42no—
647D11—44no—
648C24—21no—
649C24—111no—
650C24—111no—
651C24—224no—
652C24—221no—
653C24—444no—
654C24—444no—
655C24—882no—
656#41—228no—
657#41—444no—
658#41—448no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—114no—
669C2×Q8—112no—
670C2×Q8—224no—
671C2×Q8—224no—
672C2×Q8—221no—
673C2×Q8—222no—
674C2×Q8—228no—
675C2×Q8—228no—
676C2×Q8—444no—
677C2×Q8—444no—
678C2×Q8—444no—
679C2×Q8—444no—
680C2×Q8—448no—
681C2×Q8—448no—
682C2×Q8C23×D1112yes—
683C2×Q8C23×D1112yes—
684C2×Q8C23×D1112yes—
685C2×D4—22no—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—114no—
689C2×D4—114no—
690C2×D4—112no—
691C2×D4—224no—
692C2×D4—224no—
693C2×D4—224no—
694C2×D4—228no—
695C2×D4—224no—
696C2×D4—221no—
697C2×D4—222no—
698C2×D4—444no—
699C2×D4—444no—
700C2×D4—448no—
701C2×D4—444no—
702C2×D4—882no—
703C2×D4C23×D1112yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—111no—
708C22×C4—111no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—224no—
714C22×C4—224no—
715C22×C4—224no—
716C22×C4—221no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4—222no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—224no—
724C22×C4—444no—
725C22×C4—444no—
726C22×C4—444no—
727C22×C4—882no—
728C22×C4D4×D1111yescharacteristic
729C22×C4D4×D1111yescharacteristic
730C22×C4C23×D1111yescharacteristic
731Q16—28no—
732Q16—44no—
733Q16—228no—
734SD16—28no—
735SD16—44no—
736SD16—1116no—
737SD16—228no—
738SD16—228no—
739SD16—228no—
740M16—228no—
741C2×C8—22no—
742C2×C8—112no—
743C2×C8—112no—
744C2×C8—222no—
745C2×C8—222no—
746C2×C8—228no—
747C2×C8D4×D1114yes—
748C2×C8C23×D1112yes—
749C2×C8C23×D1112yes—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4—114no—
753C4⋊C4—112no—
754C4⋊C4—112no—
755C4⋊C4—224no—
756C4⋊C4—224no—
757C4⋊C4—224no—
758C4⋊C4—221no—
759C4⋊C4—221no—
760C4⋊C4—224no—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—114no—
764C22⋊C4—114no—
765C22⋊C4—224no—
766C22⋊C4—224no—
767C22⋊C4—224no—
768C22⋊C4—224no—
769C22⋊C4—224no—
770C42—224no—
771C42D4×D1112yes—
772C42C23×D1112yes—
773C11C2×#326611yescharacteristic, complemented, Sylow
774C23—22no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—114no—
779C23—112no—
780C23—112no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—224no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—448no—
789C23—448no—
790C23—442no—
791C23—442no—
792C23—884no—
793C23—8816no—
794C23C2×D4×D1111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—22no—
798Q8—22no—
799Q8—22no—
800Q8—22no—
801Q8—42no—
802Q8—42no—
803Q8—42no—
804Q8—114no—
805Q8—224no—
806Q8—222no—
807Q8—448no—
808Q8—448no—
809D4—22no—
810D4—22no—
811D4—42no—
812D4—114no—
813D4—228no—
814D4—224no—
815D4—222no—
816D4—448no—
817D4—448no—
818D4—884no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—112no—
828C2×C4—112no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—224no—
832C2×C4—222no—
833C2×C4—224no—
834C2×C4—224no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—448no—
842C2×C4—448no—
843C2×C4—448no—
844C2×C4—442no—
845C2×C4—442no—
846C2×C4—884no—
847C2×C4C2×D4×D1112yes—
848C2×C4C2×D4×D1112yes—
849C2×C4C2×D4×D1111yescharacteristic
850C2×C4C2×D4×D1112yes—
851C2×C4#6703712yes—
852C2×C4C24×D1111yescharacteristic
853C8—22no—
854C8—222no—
855C8—222no—
856C8C2×D4×D1114yes—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—84no—
861C22—114no—
862C22—228no—
863C22—222no—
864C22—222no—
865C22—222no—
866C22—224no—
867C22—222no—
868C22—222no—
869C22—444no—
870C22—448no—
871C22—442no—
872C22—442no—
873C22—8816no—
874C22#1062324812yes—
875C22D11×#13712yes—
876C22#1062330912yes—
877C22C22×D4×D1111yescharacteristic
878C4—22no—
879C4—22no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—222no—
884C4—222no—
885C4—224no—
886C4—442no—
887C4—442no—
888C4#1062324812yes—
889C4C22×D4×D1111yescharacteristic
890C4C2×#6703711yescharacteristic
891C2—82no—
892C2—224no—
893C2—442no—
894C2—444no—
895C2#1308012514yesdirect product factor
896C2C2×#1062324811yescharacteristic
897C2C2×D11×#13711yescharacteristic
898C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#497C2
socleC23×C11C22×D4
prime radicalC2×#10623207C2
hypercenterC2×#497D11
hypocenterC11C2×#3266
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
2. C22×SD16×D11C2semidirect
3. C2×#10623258C2semidirect
5. #13080125C2direct (N × H)
6. C2×#10622787C2semidirect
7. C2×#10622801C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622696C2semidirect
10. C2×#10622800C2semidirect
11. C2×#10622799C2semidirect
12. C2×#10622783C2semidirect
13. C2×#10622782C2semidirect
14. C2×#10622323C2semidirect
15. C2×#10622319C2semidirect
16. C2×C11×#497C2semidirect
19. C22×Q8×D11C22semidirect
21. C22×C11×Q16C22semidirect
22. C22×C11×Q16C22semidirect
25. C2×C11×C4⋊Q8C22semidirect
29. C2×#66999C22semidirect
30. C22×#4326C22semidirect
36. C2×#66971C22semidirect
38. C2×SD16×D11C22semidirect
40. C22×#4313C22semidirect
43. #10623258C22semidirect
56. C2×C4×Dic22C22semidirect
57. C11×#497C22semidirect
58. C2×C11×#97C22semidirect
59. C2×#66899C22semidirect
60. C2×#66899C22semidirect
61. C2×#66899C22semidirect
63. #10622801C22semidirect
64. #10622800C22semidirect
65. #10622799C22semidirect
66. #10622787C22semidirect
67. #10622783C22semidirect
68. #10622782C22semidirect
71. C2×(C2×D11)⋊C8C22semidirect
72. C2×#66882C22semidirect
73. C2×#66880C22semidirect
74. #10622696C22semidirect
75. #10622667C22semidirect
76. C2×C4⋊(C11⋊C8)C22semidirect
77. #10622323C22semidirect
78. #10622319C22semidirect
97. C2×Q8×D11C23semidirect
116. C2×C11×Q16C23semidirect
117. C2×C11×Q16C23semidirect
125. C11×C4⋊Q8C23semidirect
139. #66999C23semidirect
141. C2×#4326C23semidirect
168. C2×#4314D4semidirect
171. C2×#4313C23semidirect
187. C4×Dic22C23semidirect
188. C11×#97C23semidirect
189. #66899C23semidirect
190. #66899C23semidirect
191. #66899C23semidirect
195. (C2×D11)⋊C8C23semidirect
196. #66882C23semidirect
197. #66880C23semidirect
198. C4⋊(C11⋊C8)C23semidirect
322. #4314C2×D4semidirect
330. C2×#497D11semidirect
359. C22×D11#137semidirect
431. C22×Q16C2×D11semidirect
432. C22×Q16C2×D11semidirect
448. C2×C4⋊Q8C2×D11semidirect
464. #497C2×D11semidirect
485. C2×#97C2×D11semidirect
506. C2×D11C2×#137semidirect
560. C2×Q16C22×D11semidirect
561. C2×Q16C22×D11semidirect
585. C4⋊Q8C22×D11semidirect
639. #97C22×D11semidirect
641. C2×C11#3266semidirect
773. C11C2×#3266semidirect
895. C2#13080125direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C22×SD16×D112
C2×#106232582
C2×#106232072
#130801252
C2×#106227872
C2×#106228012
C2×#106226672
C2×#106226962
C2×#106228002
C2×#106227992
C2×#106227832
C2×#106227822
C2×#106223232
C2×#106223192
C2×C11×#4972
C2×#326611