Finite Group Databasebeta

← #14769255

Subgroups — #14769255

Order 2816.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2C2×#10622746C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13069546C211yesmaximal, characteristic, complemented
6#13069432C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069039C211yesmaximal, characteristic, complemented
9#13068931C211yesmaximal, characteristic, complemented
10#13068921C211yesmaximal, characteristic, complemented
11#13068617C211yesmaximal, characteristic, complemented
12#13068557C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14#13068442C211yesmaximal, characteristic, complemented
15C2×C11×#435C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66990—21no—
22C2×D4×Dic11—21no—
23C2×#66983C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic, complemented
26C2×#66977C2211yescharacteristic
27#10623081—24no—
28#10623081C418yescomplemented
29C2×#66947—21no—
30C2×#66937—21no—
31C2×C22⋊C4×D11—21no—
32C2×#66928C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C11×#435—24no—
35C2×C11×C4⋊C8C2211yescharacteristic, complemented
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic, complemented
38C2×C11×#97C2211yescharacteristic, complemented
39#10622825C2211yescharacteristic
40#10622825C2211yescharacteristic, complemented
41#10622746—24no—
42C2×#66885—24no—
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×#66885C2211yescharacteristic
48C2×#66885C2211yescharacteristic
49C2×#66885C2211yescharacteristic
50C2×#66885C2211yescharacteristic
51C2×#66880C2211yescharacteristic, complemented
52C2×#66880C2211yescharacteristic, complemented
53C2×#66880C2211yescharacteristic, complemented
54C2×#66880C2211yescharacteristic, complemented
55#10622598—21no—
56#10622563—21no—
57#10622563—21no—
58#10622548C2211yescharacteristic, complemented
59C4×C4⋊Dic11C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63#10622189C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11D411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C23×Dic11—21no—
71C23×Dic11—21no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—41no—
76C2×#4339—41no—
77C2×#4339C2×C414yescomplemented
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—21no—
81C22×D44—22no—
82C22×D44—41no—
83C22×D44—41no—
84C22×D44C2×C414yescomplemented
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×Dic22C2311yescharacteristic
90C2×C11×M16—22no—
91C2×C11×M16—22no—
92C2×C11×M16—41no—
93C22×C8×C11—22no—
94C22×C8×C11—22no—
95C22×C8×C11—41no—
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C4×D4×C11C2×C414yes—
101C4×D4×C11D414yes—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109#66990—28no—
110D4×Dic11—44no—
111#66983—22no—
112#66983C2×C414yescomplemented
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×C4⋊Dic11—22no—
118C2×C4⋊Dic11—22no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—41no—
124C2×C4⋊Dic11—41no—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130#66977—22no—
131#66977C2×C414yescomplemented
132C2×Dic11⋊C4—21no—
133C2×C4×Dic11—21no—
134#66947—28no—
135#66937—28no—
136C22⋊C4×D11—28no—
137#66928—22no—
138#66928C2×C414yescomplemented
139C4×D44—22no—
140C4×D44C2×C414yescomplemented
141C11×C4⋊C8—22no—
142C11×C22⋊C8—22no—
143C11×C22⋊C8—22no—
144C11×#97—22no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148#66885—22no—
149#66885—22no—
150#66885—22no—
151#66885—22no—
152#66885—22no—
153#66885—41no—
154#66885—41no—
155#66885D414yescomplemented
156#66880—22no—
157#66880—22no—
158#66880—41no—
159#66880—41no—
160#22419—111nomaximal, Sylow
161C24×C11C2×D411yescharacteristic
162C24×C11C2×D411yescharacteristic
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—24no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—42no—
170C23×D11—81no—
171C23×D11—81no—
172C2×D4×C11—22no—
173C2×D4×C11—22no—
174C2×D4×C11C22⋊C414yes—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11C22×C412yes—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—24no—
193C2×C22⋊D11—24no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—42no—
196C2×C22⋊D11—81no—
197C2×C22⋊D11—81no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—42no—
205C22×Dic11—42no—
206C22×Dic11—42no—
207C22×Dic11—42no—
208C22×Dic11—81no—
209C22×Dic11—81no—
210#4339—28no—
211#4339—44no—
212#4339—44no—
213#4339—44no—
214C2×D44—28no—
215C2×D44—24no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—42no—
225C2×D44—42no—
226C2×D44—44no—
227C2×D44—44no—
228C2×D44—44no—
229C2×D44C22×C412yes—
230C2×D44C22×C412yes—
231C2×D44C2×D412yes—
232C2×D44#4112yes—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—42no—
236C2×C4×D11—42no—
237C2×C4×D11—81no—
238C2×C4×D11—81no—
239C2×Dic22—21no—
240C2×Dic22—21no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—21no—
244C2×Dic22C22×C412yes—
245C11×M16—44no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11—21no—
255C2×C8×C11—21no—
256C2×C8×C11—21no—
257C2×C8×C11—44no—
258C2×C8×C11C2×D412yes—
259C11×C4⋊C4C22⋊C414yes—
260C11×C22⋊C4C22⋊C414yes—
261C11×C22⋊C4C22⋊C414yes—
262C42×C11C22×C412yes—
263C42×C11C2×D412yes—
264C22⋊Dic11—24no—
265C22⋊Dic11—42no—
266C22⋊Dic11—42no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11—21no—
279C4⋊Dic11—42no—
280C4⋊Dic11—42no—
281C4⋊Dic11—42no—
282C4⋊Dic11—81no—
283C4⋊Dic11C22×C412yes—
284C4⋊Dic11C2×D412yes—
285Dic11⋊C4—24no—
286C4×Dic11—42no—
287C2×#546—111no—
288C2×#435D1111yescharacteristic, complemented
289C2×#417—111no—
290C22×#102—111no—
291D4×C4⋊C4—111no—
292#1983—111no—
293#1959—111no—
294#1895—111no—
295#1892—111no—
296#1874—111no—
297#1872—111no—
298#1802—111no—
299#1788—111no—
300#1786—111no—
301#1762—111no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11C2×C22⋊C412yes—
313C23×C11C2×C22⋊C412yes—
314C23×C11AGL(1,ℤ/8)12yes—
315C23×C11#13712yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—48no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—48no—
333C22×D11—84no—
334C22×D11—84no—
335C22×D11—84no—
336C22×D11—84no—
337C22×D11—84no—
338D4×C11—28no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11C2×C22⋊C412yes—
356C2×C4×C11C2×C22⋊C412yes—
357C2×C4×C11C2×C22⋊C412yes—
358C2×C4×C11C2×C22⋊C412yes—
359C2×C4×C11C23×C411yescharacteristic
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C2×#4111yescharacteristic
363C2×C4×C11H(5,𝔽2)11yescharacteristic
364C2×C4×C11H(5,𝔽2)11yescharacteristic
365C22⋊D11—48no—
366C22⋊D11—84no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—84no—
386C2×Dic11—84no—
387D44—22no—
388D44—22no—
389D44—22no—
390D44—22no—
391D44—22no—
392D44—48no—
393D44—41no—
394D44—41no—
395D44C4×D414yescomplemented
396C4×D11—48no—
397C4×D11—84no—
398Dic22—22no—
399Dic22—22no—
400Dic22—41no—
401Dic22—41no—
402C8×C11—22no—
403C8×C11—41no—
404C8×C11—41no—
405C8×C11—41no—
406C22×#41—111no—
407C23×D4—111no—
408C22×M16C2×D1111yescharacteristic, complemented
409C23×C8C2×D1111yescharacteristic
410#546—118no—
411#546—224no—
412C2×#124—111no—
413C2×#123—221no—
414C2×C22⋊Q8—111no—
415C2×#121—111no—
416C2×#121—221no—
417C2×#120—221no—
418C2×C4×D4—111no—
419C2×C4×D4—221no—
420C2×C4×D4C2×D1111yescharacteristic
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C22⋊C4—221no—
424#435—24no—
425C2×C4⋊C8C2×D1111yescharacteristic, complemented
426#417—224no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—224no—
440C2×C22⋊C8C2×D1111yescharacteristic
441C2×C22⋊C8C2×D1111yescharacteristic, complemented
442C2×#97C2×D1111yescharacteristic, complemented
443#389—221no—
444#385—221no—
445#385—221no—
446#384—111no—
447#380—111no—
448#380—111no—
449C4×C4⋊C4—111no—
450#340—111no—
451#340—111no—
452#340—111no—
453#340—111no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—41no—
467C22×C11#41714yescomplemented
468C22×C11C22×C22⋊C411yescharacteristic
469C22×C11D4211yescharacteristic
470C22×C11#54611yescharacteristic
471C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
472C22×C11C2×#13711yescharacteristic
473C22×C11#57611yescharacteristic
474C22×C11#57711yescharacteristic
475C2×D11—24no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—816no—
486C2×D11—81no—
487C2×D11—81no—
488C2×D11—81no—
489C2×D11—81no—
490C4×C11—22no—
491C4×C11—22no—
492C4×C11—22no—
493C4×C11—22no—
494C4×C11C2×C4×D411yescharacteristic
495C4×C11#51811yescharacteristic
496C4×C11D4211yescharacteristic
497C4×C11#54611yescharacteristic
498Dic11—42no—
499Dic11—42no—
500Dic11—42no—
501Dic11—81no—
502Dic11—81no—
503Dic11—81no—
504C25—221no—
505C2×#41—114no—
506C2×#41—222no—
507C2×#41—222no—
508C2×#41—222no—
509C2×#41—441no—
510C2×#41—441no—
511C22×Q8—111no—
512C22×D4—114no—
513C22×D4—111no—
514C22×D4—111no—
515C22×D4—222no—
516C22×D4—222no—
517C22×D4—221no—
518C22×D4—221no—
519C22×D4—221no—
520C22×D4—222no—
521C22×D4—441no—
522C22×D4—441no—
523C22×D4D4411yescharacteristic
524C23×C4—221no—
525C23×C4—221no—
526C23×C4—221no—
527C23×C4—221no—
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—41no—
533C22×C8—22no—
534C22×C8—22no—
535C22×C8—41no—
536C22×C8C22×D1111yescharacteristic
537C22×C8C22×D1111yescharacteristic
538C22×C8C22×D1111yescharacteristic
539C22×C8C22×D1111yescharacteristic
540#124—114no—
541#124—222no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—222no—
545#121—114no—
546#121—222no—
547#121—228no—
548#120—228no—
549C4×D4—114no—
550C4×D4—222no—
551C4×D4—444no—
552C4×D4C4×D1114yes—
553C4×D4C22⋊D1114yes—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4—222no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4—221no—
566C2×C4⋊C4—441no—
567C2×C4⋊C4—441no—
568C2×C4⋊C4D4411yescharacteristic
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—228no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4D4411yescharacteristic
578C2×C22⋊C4D4411yescharacteristic
579C2×C42—221no—
580C2×C42C22×D1111yescharacteristic
581C4⋊C8—22no—
582#103—222no—
583#103—222no—
584#103—441no—
585#103—441no—
586#102—114no—
587#102—222no—
588#102—222no—
589#102—222no—
590#102—222no—
591#102—222no—
592#102—441no—
593#102—441no—
594C22⋊C8—22no—
595C22⋊C8—22no—
596#97—22no—
597#95—221no—
598#95—221no—
599#95—221no—
600C2×C11—24no—
601C2×C11—42no—
602C2×C11D4×C22⋊C411yescharacteristic
603C2×C11C2×#41711yescharacteristic
604C2×C11#289711yescharacteristic
605C2×C11#326411yescharacteristic
606C2×C11#326611yescharacteristic
607C2×C11#330611yescharacteristic
608C2×C11#331411yescharacteristic
609D11—44no—
610D11—82no—
611C24—221no—
612C24—221no—
613C24—224no—
614C24—442no—
615C24—442no—
616C24—442no—
617C24—442no—
618C24—881no—
619C24—881no—
620C24C2×D4411yescharacteristic
621C24C2×D4411yescharacteristic
622#41—228no—
623#41—444no—
624#41—444no—
625#41—444no—
626C2×Q8—112no—
627C2×Q8—221no—
628C2×Q8—221no—
629C2×Q8—221no—
630C2×Q8—221no—
631C2×Q8—221no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—112no—
635C2×D4—112no—
636C2×D4—112no—
637C2×D4—112no—
638C2×D4—228no—
639C2×D4—224no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—221no—
643C2×D4—221no—
644C2×D4—221no—
645C2×D4—221no—
646C2×D4—221no—
647C2×D4—221no—
648C2×D4—221no—
649C2×D4—221no—
650C2×D4—444no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—442no—
654C2×D4—442no—
655C2×D4—442no—
656C2×D4—442no—
657C2×D4—881no—
658C2×D4—881no—
659C2×D4(C2×D11)⋊C414yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—224no—
672C22×C4—224no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—442no—
677C22×C4—442no—
678C22×C4—442no—
679C22×C4—442no—
680C22×C4—442no—
681C22×C4—442no—
682C22×C4—881no—
683C22×C4—881no—
684C22×C4—881no—
685C22×C4—881no—
686C22×C4C2×C4×D1112yes—
687C22×C4C2×C4×D1112yes—
688C22×C4C2×D4411yescharacteristic
689C22×C4C2×D4411yescharacteristic
690C22×C4C2×D4411yescharacteristic
691C22×C4C2×D4411yescharacteristic
692C22×C4C2×C22⋊D1112yes—
693C22×C4C2×C22⋊D1112yes—
694C22×C4C23×D1111yescharacteristic
695M16—44no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—44no—
708C2×C8D4×D1112yes—
709C4⋊C4—112no—
710C4⋊C4—112no—
711C4⋊C4—224no—
712C4⋊C4—221no—
713C4⋊C4—221no—
714C4⋊C4—221no—
715C4⋊C4—221no—
716C4⋊C4—221no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—442no—
721C4⋊C4—442no—
722C4⋊C4—442no—
723C4⋊C4—881no—
724C4⋊C4(C2×D11)⋊C414yes—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C22⋊C4—224no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—442no—
731C22⋊C4—442no—
732C22⋊C4(C2×D11)⋊C414yes—
733C22⋊C4(C2×D11)⋊C414yes—
734C42—442no—
735C42C2×C4×D1112yes—
736C42C2×C22⋊D1112yes—
737C11#2241911yescharacteristic, complemented, Sylow
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—448no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—448no—
758C23—441no—
759C23—441no—
760C23—441no—
761C23—441no—
762C23—441no—
763C23—441no—
764C23—884no—
765C23—884no—
766C23—884no—
767C23—884no—
768C23—884no—
769C23#6696112yes—
770C23#6696212yes—
771C23C2×(C2×D11)⋊C412yes—
772C23C2×(C2×D11)⋊C412yes—
773C23C22×D4411yescharacteristic
774Q8—222no—
775Q8—222no—
776Q8—441no—
777Q8—441no—
778D4—28no—
779D4—114no—
780D4—222no—
781D4—222no—
782D4—222no—
783D4—222no—
784D4—222no—
785D4—448no—
786D4—448no—
787D4—441no—
788D4—441no—
789D4—884no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—448no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—441no—
820C2×C4—441no—
821C2×C4—441no—
822C2×C4—441no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—884no—
826C2×C4—884no—
827C2×C4—884no—
828C2×C4C2×(C2×D11)⋊C412yes—
829C2×C4C2×(C2×D11)⋊C412yes—
830C2×C4C2×(C2×D11)⋊C412yes—
831C2×C4C2×(C2×D11)⋊C412yes—
832C2×C4C22×C4×D1111yescharacteristic
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4#6703711yescharacteristic
835C2×C4#41×D1111yescharacteristic
836C2×C4#6704211yescharacteristic
837C2×C4C22×C22⋊D1111yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—224no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—8816no—
866C22—881no—
867C22—881no—
868C22—881no—
869C22—881no—
870C22#1062274614yescomplemented
871C22D4×D4411yescharacteristic
872C22#1062308511yescharacteristic
873C22C2×#6696111yescharacteristic
874C22C2×#6696211yescharacteristic
875C22#1062328211yescharacteristic
876C22#1062328311yescharacteristic
877C22C22×(C2×D11)⋊C411yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—442no—
883C4—442no—
884C4—442no—
885C4—881no—
886C4—881no—
887C4—881no—
888C4C4×D4×D1111yescharacteristic
889C4#1062307611yescharacteristic
890C4D4×C22⋊D1111yescharacteristic
891C4#1062336011yescharacteristic
892C2—24no—
893C2—42no—
894C2—444no—
895C2—882no—
896C2D4×(C2×D11)⋊C411yescharacteristic
897C2C2×#1062274611yescharacteristic
898C2#1307714311yescharacteristic
899C2#1308010111yescharacteristic
900C2#1308013111yescharacteristic
901C2#1308057911yescharacteristic
902C2#1308069911yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
cosocleC22×C4×C11C24
hypercenterC2×#435D11
hypocenterC11#22419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#10622746C2semidirect
3. C22×#66885C2semidirect
4. D4×C4⋊Dic11C2semidirect
5. #13069546C2semidirect
6. #13069432C2semidirect
7. #13069054C2semidirect
8. #13069039C2semidirect
9. #13068931C2semidirect
10. #13068921C2semidirect
11. #13068617C2semidirect
12. #13068557C2semidirect
13. #13068548C2semidirect
14. #13068442C2semidirect
15. C2×C11×#435C2semidirect
18. C22×C11×M16C22semidirect
25. C22×C4⋊Dic11C22semidirect
28. #10623081C4semidirect
35. C2×C11×C4⋊C8C22semidirect
37. C2×C11×C22⋊C8C22semidirect
38. C2×C11×#97C22semidirect
40. #10622825C22semidirect
51. C2×#66880C22semidirect
52. C2×#66880C22semidirect
53. C2×#66880C22semidirect
54. C2×#66880C22semidirect
58. #10622548C22semidirect
59. C4×C4⋊Dic11C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622189C22semidirect
63. #10622189C22semidirect
77. C2×#4339C2×C4semidirect
84. C22×D44C2×C4semidirect
112. #66983C2×C4semidirect
131. #66977C2×C4semidirect
138. #66928C2×C4semidirect
140. C4×D44C2×C4semidirect
155. #66885D4semidirect
288. C2×#435D11semidirect
395. D44C4×D4semidirect
408. C22×M16C2×D11semidirect
425. C2×C4⋊C8C2×D11semidirect
441. C2×C22⋊C8C2×D11semidirect
442. C2×#97C2×D11semidirect
467. C22×C11#417semidirect
737. C11#22419semidirect
870. C22#10622746semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
C2×#106227462
C22×#668852
D4×C4⋊Dic112
#130695462
#130694322
#130690542
#130690392
#130689312
#130689212
#130686172
#130685572
#130685482
#130684422
C2×C11×#4352
#2241911