Finite Group Databasebeta

← C2×#13080251 #15628907

Subgroups — C2×#13080251 #15628907

Order 2816.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66968C211yesmaximal, characteristic, complemented
2C22×#66985C211yesmaximal, characteristic, complemented
3C2×#10623164C211yesmaximal, characteristic, complemented
4C2×#10623337C211yesmaximal, characteristic, complemented
5#13080251C2116yesmaximal, direct product factor
6C2×#10622781C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622380C211yesmaximal, characteristic, complemented
10C2×#10622778C211yesmaximal, characteristic, complemented
11C2×#10622346C211yesmaximal, characteristic, complemented
12C2×#10622394C211yesmaximal, characteristic, complemented
13C2×#10622783C211yesmaximal, characteristic, complemented
14C2×#10622371C211yesmaximal, characteristic, complemented
15C2×#10622342C211yesmaximal, characteristic, complemented
16C2×C11×#450C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic, complemented
19C22×#4341C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×#67006—21no—
25C22×C22⋊Dic11—21no—
26C2×#67000C2211yescharacteristic, complemented
27C22×#4326C2211yescharacteristic, complemented
28#10623337—24no—
29#10623337C2218yescomplemented
30C2×#66992—21no—
31C2×#66991C2211yescharacteristic
32C2×#66989C2211yescharacteristic
33C2×#66988—21no—
34C2×D4×Dic11C2211yescharacteristic
35C22×#4324C2211yescharacteristic
36C22×#4324C2211yescharacteristic
37C2×#66985—28no—
38C2×#66985C2218yescomplemented
39C22×#4323C2211yescharacteristic
40C22×#4323C2211yescharacteristic
41C2×C4×C22⋊D11C2211yescharacteristic
42C2×#66977C2211yescharacteristic
43C22×#4318C2211yescharacteristic
44C2×#66968—28no—
45C2×#66968C2218yescomplemented
46C22×Dic44C2211yescharacteristic, complemented
47C22×#4314C2211yescharacteristic, complemented
48C22×#4313C2211yescharacteristic, complemented
49#10623164—24no—
50#10623164C2218yescomplemented
51C2×#66949—21no—
52C2×#66948C2211yescharacteristic, complemented
53C2×#66946—21no—
54C2×#66940C2211yescharacteristic, complemented
55C2×#66938—21no—
56C2×#66937—21no—
57C11×#450C2218yescomplemented
58C2×C11×#102C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C2×#66899C2211yescharacteristic, complemented
62#10622783C2218yescomplemented
63#10622781C2218yescomplemented
64#10622778C2218yescomplemented
65C2×#66885C2211yescharacteristic, complemented
66C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68C2×Dic11⋊C8C2211yescharacteristic, complemented
69C2×C8×Dic11C2211yescharacteristic, complemented
70#10622665C2218yescomplemented
71C2×#66874C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73#10622395C2218yescomplemented
74#10622394C2218yescomplemented
75#10622380C2218yescomplemented
76#10622371C2218yescomplemented
77#10622346C2218yescomplemented
78#10622342C2218yescomplemented
79C25×C11—21no—
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—24no—
82C22×D4×C11—21no—
83C22×D4×C11—22no—
84C22×D4×C11—42no—
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2314yes—
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11D411yescharacteristic
93C23×Dic11—21no—
94C23×Dic11—21no—
95C2×Q8×D11—22no—
96C2×Q8×D11—24no—
97C2×Q8×D11—42no—
98C2×Q8×D11C2314yescomplemented
99C2×#4341—24no—
100C2×#4341—22no—
101C2×#4341—42no—
102C2×#4341C2314yes—
103C2×#4339—22no—
104C2×#4339—24no—
105C2×#4339—42no—
106C2×#4339C2314yes—
107C22×D44—21no—
108C22×D44C2311yescharacteristic
109C22×C4×D11—21no—
110C22×C4×D11—21no—
111C22×C4×D11C2311yescharacteristic
112C22×Dic22—21no—
113C22×Dic22C2311yescharacteristic
114C22×Dic22C2311yescharacteristic
115C2×C11×SD16—24no—
116C2×C11×SD16—42no—
117C2×C11×SD16C2314yes—
118C2×C11×SD16C2314yes—
119C22×C8×C11C2311yescharacteristic
120C22×C8×C11C2311yescharacteristic
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8C2314yes—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C22⋊C4—21no—
126#67006—28no—
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11—28no—
133C2×C22⋊Dic11D411yescharacteristic
134#67000—22no—
135#67000C2314yescomplemented
136C2×#4326—24no—
137C2×#4326C2314yescomplemented
138#66992—28no—
139#66991—22no—
140#66991C2314yes—
141#66989—22no—
142#66989C2314yes—
143#66988—28no—
144D4×Dic11—22no—
145D4×Dic11C2314yes—
146C2×#4324—24no—
147C2×#4324D418yescomplemented
148C2×#4324C2314yes—
149C2×#4324C2314yes—
150#66985—232no—
151C2×#4323—24no—
152C2×#4323—24no—
153C2×#4323C2314yes—
154C2×#4323C2314yes—
155C4×C22⋊D11D414yes—
156C4×C22⋊D11C2314yes—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4—21no—
159C2×(C2×D11)⋊C4—21no—
160C2×(C2×D11)⋊C4D411yescharacteristic
161C2×C4⋊Dic11C2311yescharacteristic
162#66977—22no—
163#66977C2314yes—
164C2×Dic11⋊C4—21no—
165C2×Dic11⋊C4—21no—
166C2×Dic11⋊C4D411yescharacteristic
167C2×C4×Dic11—21no—
168C2×C4×Dic11C2311yescharacteristic
169C2×#4318—24no—
170C2×#4318C2314yes—
171C22×C11⋊C8C2311yescharacteristic
172C22×C11⋊C8C2311yescharacteristic
173#66968—232no—
174C2×Dic44—24no—
175C2×Dic44C2314yescomplemented
176C2×#4314—42no—
177C2×#4314C2314yescomplemented
178C2×#4313—24no—
179C2×#4313C2314yescomplemented
180#66949—28no—
181#66948—22no—
182#66948C2314yescomplemented
183#66946—28no—
184#66940—22no—
185#66940C2314yescomplemented
186#66938—28no—
187#66937—28no—
188C11×#102C2314yes—
189C11×#102C2314yes—
190C11×C22⋊C8C2314yes—
191#66899C2314yescomplemented
192#66885C2314yescomplemented
193(C2×D11)⋊C8C2314yescomplemented
194#66880C2314yescomplemented
195Dic11⋊C8C2314yescomplemented
196C8×Dic11C2314yescomplemented
197#66874C2314yescomplemented
198#66872C2314yescomplemented
199C2×#3275—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—24no—
203C24×C11—44no—
204C24×C11—44no—
205C24×C11—82no—
206C24×C11C2×D411yescharacteristic
207C23×D11—21no—
208C23×D11C2×D411yescharacteristic
209C2×Q8×C11—21no—
210C2×Q8×C11—22no—
211C2×Q8×C11—22no—
212C2×Q8×C11C2412yes—
213C2×D4×C11—28no—
214C2×D4×C11—21no—
215C2×D4×C11—22no—
216C2×D4×C11—24no—
217C2×D4×C11—21no—
218C2×D4×C11—22no—
219C2×D4×C11—22no—
220C2×D4×C11—44no—
221C2×D4×C11—48no—
222C2×D4×C11—44no—
223C2×D4×C11C2×D414yes—
224C2×D4×C11C2412yes—
225C2×D4×C11C2412yes—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2411yescharacteristic
234C2×C22⋊D11—24no—
235C2×C22⋊D11—24no—
236C2×C22⋊D11—24no—
237C2×C22⋊D11—42no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—82no—
241C2×C22⋊D11C2×D414yes—
242C22×Dic11—24no—
243C22×Dic11—24no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—44no—
248C22×Dic11—82no—
249C22×Dic11C2×D411yescharacteristic
250C22×Dic11C2×D411yescharacteristic
251C22×Dic11C2×D411yescharacteristic
252Q8×D11—28no—
253Q8×D11—44no—
254Q8×D11—48no—
255#4341—28no—
256#4341—44no—
257#4341—48no—
258#4339—28no—
259#4339—44no—
260#4339—48no—
261C2×D44—24no—
262C2×D44—21no—
263C2×D44—22no—
264C2×D44—22no—
265C2×D44—44no—
266C2×D44C2412yes—
267C2×C4×D11—24no—
268C2×C4×D11—22no—
269C2×C4×D11—24no—
270C2×C4×D11—22no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11C2×D412yes—
274C2×C4×D11C2412yes—
275C2×Dic22—24no—
276C2×Dic22—21no—
277C2×Dic22—22no—
278C2×Dic22—21no—
279C2×Dic22—22no—
280C2×Dic22—22no—
281C2×Dic22—44no—
282C2×Dic22C2×D414yes—
283C2×Dic22C2412yes—
284C2×Dic22C2412yes—
285C11×SD16—28no—
286C11×SD16—44no—
287C2×C8×C11—22no—
288C2×C8×C11—22no—
289C2×C8×C11C2412yes—
290C2×C8×C11C2412yes—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—24no—
293C11×C4⋊C4C2412yes—
294C11×C22⋊C4—24no—
295C22⋊Dic11—24no—
296C22⋊Dic11—24no—
297C22⋊Dic11—24no—
298C22⋊Dic11—24no—
299C22⋊Dic11—24no—
300C22⋊Dic11C2×D414yes—
301#4326—28no—
302#4324—28no—
303#4324C2×D4116yescomplemented
304#4323—28no—
305#4323—28no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4C2×D414yes—
310C4⋊Dic11—21no—
311C4⋊Dic11C2412yes—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314Dic11⋊C4C2×D414yes—
315C4×Dic11—24no—
316C4×Dic11C2×D412yes—
317C4×Dic11C2412yes—
318#4318—28no—
319C2×C11⋊C8—22no—
320C2×C11⋊C8C2×D414yes—
321C2×C11⋊C8C2412yes—
322C2×C11⋊C8C2412yes—
323Dic44—28no—
324#4314—44no—
325#4313—28no—
326C22×#137—111no—
327C22×AGL(1,ℤ/8)—111no—
328C2×#548—111no—
329C2×#546—111no—
330#3275—1116no—
331C2×#495—111no—
332C2×#470—111no—
333C2×#469—111no—
334C2×#464—111no—
335C2×#463—111no—
336C2×#452—111no—
337C2×#449—111no—
338C2×#448—111no—
339C2×#450D1111yescharacteristic, complemented
340C2×C4×SD16—111no—
341C2×#436—111no—
342C23×C11—24no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—48no—
349C23×C11—48no—
350C23×C11—42no—
351C23×C11—42no—
352C23×C11—42no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11—84no—
356C23×C11—816no—
357C23×C11C22×D412yes—
358C23×C11C22×D411yescharacteristic
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—42no—
364C22×D11—42no—
365C22×D11—42no—
366C22×D11C22×D412yes—
367Q8×C11—22no—
368Q8×C11—22no—
369Q8×C11—42no—
370D4×C11—24no—
371D4×C11—22no—
372D4×C11—22no—
373D4×C11—22no—
374D4×C11—48no—
375D4×C11—42no—
376D4×C11C22×D414yes—
377C2×C4×C11—22no—
378C2×C4×C11—24no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—42no—
384C2×C4×C11—42no—
385C2×C4×C11C22×D412yes—
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D412yes—
388C2×C4×C11H(5,𝔽2)12yes—
389C2×C4×C11C2511yescharacteristic
390C22⋊D11—44no—
391C22⋊D11—48no—
392C22⋊D11—48no—
393C22⋊D11—84no—
394C2×Dic11—24no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—48no—
402C2×Dic11—42no—
403C2×Dic11—42no—
404C2×Dic11—84no—
405C2×Dic11C22×D412yes—
406C2×Dic11C22×D412yes—
407C2×Dic11C22×D412yes—
408D44—22no—
409D44—22no—
410D44—48no—
411D44—42no—
412C4×D11—24no—
413C4×D11—22no—
414C4×D11—22no—
415C4×D11—48no—
416C4×D11—48no—
417Dic22—24no—
418Dic22—22no—
419Dic22—22no—
420Dic22—22no—
421Dic22—48no—
422Dic22—42no—
423Dic22C22×D414yes—
424C8×C11—22no—
425C8×C11—22no—
426C11⋊C8—22no—
427C11⋊C8C22×D414yes—
428C22×#41—111no—
429C22×#41—111no—
430C23×Q8—111no—
431C23×D4C2×D1111yescharacteristic
432C2×#137—118no—
433C2×#137—228no—
434C2×AGL(1,ℤ/8)—118no—
435C2×AGL(1,ℤ/8)—228no—
436C22×Q16—111no—
437C22×Q16—111no—
438C22×SD16—111no—
439C22×SD16—111no—
440C22×SD16—111no—
441C22×SD16C2×D1111yescharacteristic
442C22×SD16C2×D1111yescharacteristic
443C22×D8—111no—
444C22×D8—111no—
445C22×M16—111no—
446C22×M16—111no—
447#548—118no—
448#548—224no—
449#546—118no—
450#546—224no—
451C2×#124—111no—
452C2×#124—111no—
453C2×#124—221no—
454C2×#123—221no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—221no—
457C2×C22⋊Q8C2×D1111yescharacteristic
458C2×#121—111no—
459C2×#121—111no—
460C2×#121—221no—
461C2×#121—221no—
462C2×#120—221no—
463C2×C4×Q8—111no—
464C2×C4×D4—111no—
465C2×C4×D4—111no—
466C2×C4×D4—221no—
467C22×C22⋊C4—221no—
468#495—118no—
469#470—118no—
470#469—118no—
471#464—118no—
472#463—118no—
473#452—118no—
474#450C2×D1118yescomplemented
475#449—118no—
476#448—118no—
477C4×SD16—118no—
478#436—118no—
479C2×#106—111no—
480C2×C4⋊C8—111no—
481C2×#103—111no—
482C2×#103—111no—
483C2×#103—111no—
484C2×#102—111no—
485C2×#102C2×D1111yescharacteristic
486C2×#102C2×D1111yescharacteristic
487C2×C22⋊C8—111no—
488C2×C22⋊C8C2×D1111yescharacteristic
489C2×C4×C8—111no—
490C22×C11—22no—
491C22×C11—24no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—44no—
495C22×C11—48no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—42no—
501C22×C11—816no—
502C22×C11—84no—
503C22×C11D4212yes—
504C22×C11#57512yes—
505C22×C11#57712yes—
506C22×C11C23×D411yescharacteristic
507C2×D11—22no—
508C2×D11—22no—
509C2×D11—22no—
510C2×D11—44no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—84no—
515C4×C11—22no—
516C4×C11—42no—
517C4×C11—42no—
518C4×C11D4212yes—
519C4×C11C23×D411yescharacteristic
520C4×C11C2×H(5,𝔽2)11yescharacteristic
521Dic11—24no—
522Dic11—22no—
523Dic11—22no—
524Dic11—22no—
525Dic11—42no—
526Dic11—42no—
527C25—21no—
528C2×#41—114no—
529C2×#41—114no—
530C2×#41—224no—
531C2×#41—222no—
532C2×#41—222no—
533C2×#41—224no—
534C2×#41—442no—
535C2×#41—442no—
536C22×Q8—114no—
537C22×Q8—111no—
538C22×Q8—111no—
539C22×Q8—221no—
540C22×Q8—222no—
541C22×Q8—224no—
542C22×Q8—442no—
543C22×Q8C22×D1111yescharacteristic
544C22×D4—24no—
545C22×D4—21no—
546C22×D4—22no—
547C22×D4—42no—
548C22×D4—111no—
549C22×D4—111no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—221no—
553C22×D4—221no—
554C22×D4C22×D1111yescharacteristic
555C22×D4C22×D1114yes—
556C22×D4C22×D1111yescharacteristic
557C23×C4—111no—
558C23×C4—221no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4—221no—
562C23×C4C22×D1111yescharacteristic
563#137—2232no—
564AGL(1,ℤ/8)—2232no—
565C2×Q16—114no—
566C2×Q16—114no—
567C2×Q16—224no—
568C2×Q16—224no—
569C2×SD16—24no—
570C2×SD16—42no—
571C2×SD16—118no—
572C2×SD16—114no—
573C2×SD16—114no—
574C2×SD16—114no—
575C2×SD16—224no—
576C2×SD16—442no—
577C2×SD16C22×D1114yes—
578C2×SD16C22×D1114yes—
579C2×D8—114no—
580C2×D8—114no—
581C2×D8—224no—
582C2×D8—224no—
583C2×M16—114no—
584C2×M16—114no—
585C2×M16—224no—
586C2×M16—224no—
587C22×C8—111no—
588C22×C8—111no—
589C22×C8C22×D1111yescharacteristic
590C22×C8C22×D1111yescharacteristic
591#124—114no—
592#124—114no—
593#124—222no—
594#124—222no—
595#124—228no—
596#123—228no—
597C22⋊Q8—22no—
598C22⋊Q8—114no—
599C22⋊Q8—228no—
600C22⋊Q8—222no—
601C22⋊Q8C22×D1114yes—
602#121—114no—
603#121—114no—
604#121—228no—
605#121—228no—
606#121—222no—
607#121—222no—
608#120—228no—
609C4×Q8—114no—
610C4×Q8—222no—
611C4×D4—114no—
612C4×D4—114no—
613C4×D4—114no—
614C4×D4—222no—
615C4×D4—228no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4C22×D1111yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—111no—
624C2×C22⋊C4—111no—
625C2×C22⋊C4—228no—
626C2×C22⋊C4—221no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C22⋊C4—221no—
633C2×C22⋊C4—221no—
634C2×C42—111no—
635C2×C42—221no—
636#106—114no—
637C4⋊C8—114no—
638#103—114no—
639#103—114no—
640#103—114no—
641#102—114no—
642#102C22×D1114yes—
643#102C22×D1114yes—
644C22⋊C8—114no—
645C22⋊C8C22×D1114yes—
646C4×C8—114no—
647C2×C11—42no—
648C2×C11—44no—
649C2×C11—82no—
650C2×C11#327514yescomplemented
651C2×C11C2×D4211yescharacteristic
652C2×C11C2×#57511yescharacteristic
653C2×C11C2×#57711yescharacteristic
654D11—42no—
655D11—82no—
656C24—21no—
657C24—21no—
658C24—24no—
659C24—44no—
660C24—44no—
661C24—82no—
662C24—111no—
663C24—221no—
664C24D4×D1111yescharacteristic
665#41—228no—
666#41—228no—
667#41—444no—
668#41—448no—
669#41—444no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—22no—
673C2×Q8—22no—
674C2×Q8—114no—
675C2×Q8—112no—
676C2×Q8—112no—
677C2×Q8—224no—
678C2×Q8—221no—
679C2×Q8—221no—
680C2×Q8—222no—
681C2×Q8—228no—
682C2×Q8—222no—
683C2×Q8—222no—
684C2×Q8—444no—
685C2×Q8—444no—
686C2×Q8—448no—
687C2×Q8C23×D1112yes—
688C2×D4—28no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—24no—
692C2×D4—21no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—44no—
696C2×D4—48no—
697C2×D4—44no—
698C2×D4—114no—
699C2×D4—112no—
700C2×D4—224no—
701C2×D4—224no—
702C2×D4—224no—
703C2×D4—224no—
704C2×D4—222no—
705C2×D4—221no—
706C2×D4—222no—
707C2×D4—444no—
708C2×D4—442no—
709C2×D4—444no—
710C2×D4—444no—
711C2×D4—882no—
712C2×D4D4×D1114yes—
713C2×D4C23×D1112yes—
714C2×D4C23×D1112yes—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—111no—
720C22×C4—111no—
721C22×C4—111no—
722C22×C4—112no—
723C22×C4—112no—
724C22×C4—224no—
725C22×C4—224no—
726C22×C4—224no—
727C22×C4—221no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—224no—
733C22×C4—444no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—882no—
737C22×C4D4×D1112yes—
738C22×C4D4×D1111yescharacteristic
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—228no—
742Q16—228no—
743SD16—28no—
744SD16—44no—
745SD16—1116no—
746SD16—228no—
747SD16—444no—
748D8—228no—
749D8—228no—
750M16—228no—
751M16—228no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—114no—
755C2×C8—112no—
756C2×C8—112no—
757C2×C8—222no—
758C2×C8C23×D1112yes—
759C2×C8C23×D1112yes—
760C4⋊C4—24no—
761C4⋊C4—21no—
762C4⋊C4—114no—
763C4⋊C4—112no—
764C4⋊C4—224no—
765C4⋊C4—221no—
766C4⋊C4—224no—
767C4⋊C4C23×D1112yes—
768C22⋊C4—24no—
769C22⋊C4—114no—
770C22⋊C4—114no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C22⋊C4—224no—
778C22⋊C4—224no—
779C42—112no—
780C42—112no—
781C42—224no—
782C11C2×#327511yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—22no—
786C23—24no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—84no—
797C23—816no—
798C23—112no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—442no—
804C23—442no—
805C23—442no—
806C23C2×D4×D1112yes—
807C23C2×D4×D1111yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—42no—
811Q8—114no—
812Q8—224no—
813Q8—222no—
814Q8—222no—
815Q8—222no—
816Q8—448no—
817Q8—442no—
818D4—24no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—48no—
823D4—42no—
824D4—222no—
825D4—222no—
826D4—448no—
827D4—444no—
828D4—448no—
829D4—448no—
830D4—442no—
831D4—884no—
832D4C2×D4×D1114yes—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—112no—
842C2×C4—112no—
843C2×C4—112no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—224no—
848C2×C4—222no—
849C2×C4—224no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—448no—
855C2×C4—448no—
856C2×C4—448no—
857C2×C4—442no—
858C2×C4—442no—
859C2×C4—884no—
860C2×C4C2×D4×D1112yes—
861C2×C4C2×D4×D1111yescharacteristic
862C2×C4C2×D4×D1112yes—
863C2×C4#6703712yes—
864C2×C4C24×D1111yescharacteristic
865C8—22no—
866C8—22no—
867C8—114no—
868C8—222no—
869C22—22no—
870C22—24no—
871C22—22no—
872C22—22no—
873C22—44no—
874C22—48no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—816no—
881C22—84no—
882C22—222no—
883C22—222no—
884C22—222no—
885C22—444no—
886C22—442no—
887C22—442no—
888C22—442no—
889C22—884no—
890C22#1062312112yes—
891C22#1062329312yes—
892C22#1062330412yes—
893C22C22×D4×D1111yescharacteristic
894C4—22no—
895C4—42no—
896C4—42no—
897C4—222no—
898C4—224no—
899C4—222no—
900C4—222no—
901C4—442no—
902C4—442no—
903C4#1062312112yes—
904C4C22×D4×D1111yescharacteristic
905C4C2×#6703711yescharacteristic
906C2—42no—
907C2—44no—
908C2—82no—
909C2—442no—
910C2—882no—
911C2#1308025114yesdirect product factor
912C2C2×#1062312111yescharacteristic
913C2C2×#1062330411yescharacteristic
914C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
hypercenterC2×#450D11
hypocenterC11C2×#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C22×#66968C2semidirect
2. C22×#66985C2semidirect
3. C2×#10623164C2semidirect
4. C2×#10623337C2semidirect
5. #13080251C2direct (N × H)
6. C2×#10622781C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622380C2semidirect
10. C2×#10622778C2semidirect
11. C2×#10622346C2semidirect
12. C2×#10622394C2semidirect
13. C2×#10622783C2semidirect
14. C2×#10622371C2semidirect
15. C2×#10622342C2semidirect
16. C2×C11×#450C2semidirect
18. C22×Q8×D11C22semidirect
26. C2×#67000C22semidirect
27. C22×#4326C22semidirect
29. #10623337C22semidirect
38. C2×#66985C22semidirect
45. C2×#66968C22semidirect
46. C22×Dic44C22semidirect
47. C22×#4314C22semidirect
48. C22×#4313C22semidirect
50. #10623164C22semidirect
52. C2×#66948C22semidirect
54. C2×#66940C22semidirect
57. C11×#450C22semidirect
61. C2×#66899C22semidirect
62. #10622783C22semidirect
63. #10622781C22semidirect
64. #10622778C22semidirect
65. C2×#66885C22semidirect
66. C2×(C2×D11)⋊C8C22semidirect
67. C2×#66880C22semidirect
68. C2×Dic11⋊C8C22semidirect
69. C2×C8×Dic11C22semidirect
70. #10622665C22semidirect
71. C2×#66874C22semidirect
72. C2×#66872C22semidirect
73. #10622395C22semidirect
74. #10622394C22semidirect
75. #10622380C22semidirect
76. #10622371C22semidirect
77. #10622346C22semidirect
78. #10622342C22semidirect
98. C2×Q8×D11C23semidirect
135. #67000C23semidirect
137. C2×#4326C23semidirect
147. C2×#4324D4semidirect
175. C2×Dic44C23semidirect
177. C2×#4314C23semidirect
179. C2×#4313C23semidirect
182. #66948C23semidirect
185. #66940C23semidirect
191. #66899C23semidirect
192. #66885C23semidirect
193. (C2×D11)⋊C8C23semidirect
194. #66880C23semidirect
195. Dic11⋊C8C23semidirect
196. C8×Dic11C23semidirect
197. #66874C23semidirect
198. #66872C23semidirect
303. #4324C2×D4semidirect
339. C2×#450D11semidirect
474. #450C2×D11semidirect
650. C2×C11#3275semidirect
782. C11C2×#3275semidirect
911. C2#13080251direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C22×#669852
C2×#106231642
C2×#106233372
#130802512
C2×#106227812
C2×#106226652
C2×#106223952
C2×#106223802
C2×#106227782
C2×#106223462
C2×#106223942
C2×#106227832
C2×#106223712
C2×#106223422
C2×C11×#4502
C2×#327511