Finite Group Databasebeta

← #14769248

Subgroups — #14769248

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×#10623143C211yesmaximal, characteristic
2C2×#10622740C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic, complemented
4C2×D11×#102C211yesmaximal, characteristic, complemented
5#13071512C211yesmaximal, characteristic, complemented
6#13069547C211yesmaximal, characteristic, complemented
7#13069431C211yesmaximal, characteristic, complemented
8#13069038C211yesmaximal, characteristic, complemented
9#13068934C211yesmaximal, characteristic, complemented
10#13068922C211yesmaximal, characteristic, complemented
11#13068615C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068440C211yesmaximal, characteristic, complemented
15C11×#1895C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C2×C11×#121C2211yescharacteristic
20C2×#66991—21no—
21C2×#66990—21no—
22C2×#66989C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic, complemented
25C22×C8×D11C2211yescharacteristic
26#10623143—24no—
27#10623143C418yescomplemented
28C2×#66950C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×#66936—21no—
32C2×(C22⋊D11)⋊C4—21no—
33C2×C22⋊C4×D11—21no—
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C11×#380C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
40#10622746—24no—
41#10622740—24no—
42C2×#66885C2211yescharacteristic
43C2×#66885C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×#66880C2211yescharacteristic, complemented
46C2×#66880C2211yescharacteristic, complemented
47C2×#66879C2211yescharacteristic, complemented
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49#10622600C2211yescharacteristic
50#10622589C2211yescharacteristic, complemented
51C4⋊C4×Dic11C2211yescharacteristic, complemented
52C2×#66874C2211yescharacteristic, complemented
53C2×#66874C2211yescharacteristic, complemented
54C2×#66873C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56#10622559—21no—
57D11×#102—24no—
58#10622281—21no—
59#10622260—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C22×C22⋊D11D411yescharacteristic
71C23×Dic11—21no—
72C2×D4×D11—22no—
73C2×D4×D11—22no—
74C2×D4×D11—22no—
75C2×D4×D11—41no—
76C2×D4×D11—41no—
77C2×D4×D11C2×C414yescomplemented
78C2×#4339—22no—
79C2×#4339—22no—
80C2×#4339—22no—
81C2×#4339—41no—
82C2×#4339—41no—
83C2×#4339C2×C414yescomplemented
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×Dic22C2311yescharacteristic
90C2×C11×M16—22no—
91C2×C11×M16—22no—
92C2×C11×M16—41no—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×#121—22no—
96C11×#121C2×C414yescomplemented
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11D411yescharacteristic
105#66991—28no—
106#66990—28no—
107#66989—22no—
108#66989C2×C414yescomplemented
109C4×C22⋊D11C2×C414yes—
110C4×C22⋊D11D414yes—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4D411yescharacteristic
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—41no—
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4D411yescharacteristic
125C2×C4×Dic11—21no—
126C2×C4×Dic11C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C2×C8×D11—22no—
130C2×C8×D11—22no—
131C2×C8×D11—41no—
132#66950—22no—
133#66950C2×C414yescomplemented
134#66946—22no—
135#66946C2×C414yescomplemented
136C4⋊C4×D11—22no—
137C4⋊C4×D11—41no—
138#66936—28no—
139(C22⋊D11)⋊C4—44no—
140C22⋊C4×D11—28no—
141C11×#102—22no—
142C11×#102—41no—
143C11×#95—21no—
144#66896—22no—
145#66896—41no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—22no—
149#66885—22no—
150#66885D414yescomplemented
151(C2×D11)⋊C8—22no—
152#66880—22no—
153#66880—22no—
154#66879—22no—
155Dic11⋊C8—22no—
156#66874—41no—
157#66874—41no—
158#66873—22no—
159#66873—22no—
160#22419—111nomaximal, Sylow
161C24×C11—21no—
162C24×C11C2×D411yescharacteristic
163C23×D11—21no—
164C23×D11—24no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—81no—
170C23×D11—81no—
171C23×D11C2×D411yescharacteristic
172C2×D4×C11—24no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—81no—
179C2×D4×C11—81no—
180C2×D4×C11C22×C412yes—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—24no—
193C2×C22⋊D11—24no—
194C2×C22⋊D11—22no—
195C2×C22⋊D11—22no—
196C2×C22⋊D11—42no—
197C2×C22⋊D11—42no—
198C2×C22⋊D11—42no—
199C2×C22⋊D11—42no—
200C2×C22⋊D11C22⋊C414yes—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—42no—
205C22×Dic11—42no—
206C22×Dic11—81no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210D4×D11—28no—
211D4×D11—44no—
212D4×D11—44no—
213D4×D11—44no—
214#4339—28no—
215#4339—44no—
216#4339—44no—
217#4339—44no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44C22×C412yes—
222C2×D44C2×D412yes—
223C2×D44#4112yes—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—42no—
231C2×C4×D11—42no—
232C2×C4×D11—42no—
233C2×C4×D11—42no—
234C2×C4×D11—81no—
235C2×C4×D11—81no—
236C2×C4×D11—81no—
237C2×C4×D11C22×C412yes—
238C2×C4×D11C2×D412yes—
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×C11C2×D412yes—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4C22×C412yes—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—42no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11C22⋊C414yes—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—42no—
266(C2×D11)⋊C4C22⋊C414yes—
267C4⋊Dic11—24no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—42no—
272C4⋊Dic11C2×D412yes—
273Dic11⋊C4—42no—
274Dic11⋊C4—42no—
275Dic11⋊C4—81no—
276Dic11⋊C4C22⋊C414yes—
277C4×Dic11—42no—
278C4×Dic11C22×C412yes—
279C4×Dic11C2×D412yes—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286C8×D11—44no—
287C2×#546—111no—
288C2×#435—111no—
289C2×#417—111no—
290C22×#102—111no—
291D4×C4⋊C4—111no—
292#1983—111no—
293#1959—111no—
294#1895D1111yescharacteristic, complemented
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—22no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11C2×C22⋊C412yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—21no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—48no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—48no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11—84no—
333C22×D11—84no—
334C22×D11—84no—
335C22×D11C2×C22⋊C412yes—
336C22×D11AGL(1,ℤ/8)12yes—
337C22×D11#13712yes—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—41no—
341D4×C11—41no—
342D4×C11—84no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
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—28no—
366C22⋊D11—48no—
367C22⋊D11—48no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—84no—
384C2×Dic11C2×C22⋊C412yes—
385C2×Dic11C2×C22⋊C412yes—
386C2×Dic11C2×C22⋊C412yes—
387D44—22no—
388D44—22no—
389D44—22no—
390D44C4×D414yescomplemented
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—48no—
396C4×D11—84no—
397C4×D11—84no—
398Dic22—22no—
399Dic22—22no—
400Dic22—41no—
401Dic22—41no—
402C8×C11—22no—
403C8×C11—41no—
404C11⋊C8—41no—
405C11⋊C8—41no—
406C22×#41—111no—
407C23×D4—111no—
408C22×M16C2×D1111yescharacteristic, complemented
409C23×C8—111no—
410#546—118no—
411#546—224no—
412C2×#124—111no—
413C2×#123—221no—
414C2×C22⋊Q8—111no—
415C2×#121—221no—
416C2×#121C2×D1111yescharacteristic
417C2×#120—221no—
418C2×C4×D4—111no—
419C2×C4×D4—111no—
420C2×C4×D4—221no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—111no—
423C22×C22⋊C4—221no—
424#435—224no—
425C2×C4⋊C8—111no—
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—224no—
438C2×#102C2×D1111yescharacteristic
439C2×#102C2×D1111yescharacteristic
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×#97—111no—
443#389—221no—
444#385—221no—
445#385—221no—
446#384—111no—
447#380—111no—
448#380C2×D1111yescharacteristic, complemented
449C4×C4⋊C4—111no—
450#340—111no—
451#340—111no—
452#340C2×D1111yescharacteristic, complemented
453#340C2×D1111yescharacteristic, complemented
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
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—22no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—24no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—816no—
489C2×D11#41714yescomplemented
490C4×C11—22no—
491C4×C11—42no—
492C4×C11—81no—
493C4×C11—81no—
494C4×C11C2×C4×D411yescharacteristic
495C4×C11#51811yescharacteristic
496C4×C11D4211yescharacteristic
497C4×C11#54611yescharacteristic
498Dic11—22no—
499Dic11—22no—
500Dic11—22no—
501Dic11—42no—
502Dic11—42no—
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—21no—
513C22×D4—111no—
514C22×D4—114no—
515C22×D4—111no—
516C22×D4—222no—
517C22×D4—221no—
518C22×D4—222no—
519C22×D4—222no—
520C22×D4—221no—
521C22×D4—441no—
522C22×D4—441no—
523C22×D4C22×D1111yescharacteristic
524C23×C4—111no—
525C23×C4—221no—
526C23×C4—221no—
527C23×C4—221no—
528C23×C4—221no—
529C23×C4C22×D1111yescharacteristic
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—41no—
533C22×C8—111no—
534C22×C8—111no—
535C22×C8—222no—
536C22×C8—222no—
537C22×C8—441no—
538C22×C8C22×D1111yescharacteristic
539C22×C8C22×D1111yescharacteristic
540#124—114no—
541#124—222no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—222no—
545#121—22no—
546#121—228no—
547#121C4×D1114yescomplemented
548#120—228no—
549C4×D4—114no—
550C4×D4—114no—
551C4×D4—114no—
552C4×D4—222no—
553C4×D4—444no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—222no—
558C2×C4⋊C4—222no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—441no—
565C2×C4⋊C4—441no—
566C2×C4⋊C4C22×D1111yescharacteristic
567C2×C4⋊C4C22×D1111yescharacteristic
568C2×C4⋊C4C22×D1111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—111no—
572C2×C22⋊C4—111no—
573C2×C22⋊C4—228no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C42—111no—
580C2×C42—221no—
581C4⋊C8—222no—
582#103—222no—
583#103—222no—
584#103—441no—
585#103—441no—
586#102—22no—
587#102—41no—
588#102—114no—
589#102—222no—
590#102—222no—
591#102—222no—
592#102—222no—
593#102—441no—
594C22⋊C8—222no—
595C22⋊C8—222no—
596#97—222no—
597#95—21no—
598#95—221no—
599#95—221no—
600C2×C11—42no—
601C2×C11—82no—
602C2×C11D4×C22⋊C411yescharacteristic
603C2×C11C2×#41711yescharacteristic
604C2×C11#289711yescharacteristic
605C2×C11#326411yescharacteristic
606C2×C11#326611yescharacteristic
607C2×C11#330611yescharacteristic
608C2×C11#331411yescharacteristic
609D11—24no—
610D11—44no—
611C24—21no—
612C24—111no—
613C24—224no—
614C24—221no—
615C24—442no—
616C24—442no—
617C24—442no—
618C24—442no—
619C24—881no—
620C24—881no—
621C24D4×D1111yescharacteristic
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—24no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4—114no—
641C2×D4—112no—
642C2×D4—112no—
643C2×D4—112no—
644C2×D4—224no—
645C2×D4—228no—
646C2×D4—222no—
647C2×D4—222no—
648C2×D4—224no—
649C2×D4—221no—
650C2×D4—221no—
651C2×D4—221no—
652C2×D4—444no—
653C2×D4—444no—
654C2×D4—444no—
655C2×D4—442no—
656C2×D4—442no—
657C2×D4—442no—
658C2×D4—442no—
659C2×D4C2×C4×D1112yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—111no—
668C22×C4—111no—
669C22×C4—111no—
670C22×C4—112no—
671C22×C4—112no—
672C22×C4—224no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—224no—
680C22×C4—221no—
681C22×C4—442no—
682C22×C4—442no—
683C22×C4—442no—
684C22×C4—442no—
685C22×C4—442no—
686C22×C4—442no—
687C22×C4—881no—
688C22×C4—881no—
689C22×C4—881no—
690C22×C4—881no—
691C22×C4C2×C4×D1112yes—
692C22×C4D4×D1111yescharacteristic
693C22×C4D4×D1112yes—
694C22×C4C23×D1111yescharacteristic
695M16—44no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—221no—
702C2×C8—221no—
703C2×C8—221no—
704C2×C8—221no—
705C2×C8—221no—
706C2×C8—221no—
707C2×C8—444no—
708C2×C8D4×D1112yes—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—114no—
715C4⋊C4—112no—
716C4⋊C4—224no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—442no—
721C4⋊C4—442no—
722C4⋊C4—442no—
723C4⋊C4—881no—
724C4⋊C4C2×C4×D1112yes—
725C22⋊C4—24no—
726C22⋊C4—42no—
727C22⋊C4—114no—
728C22⋊C4—114no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—442no—
734C42—112no—
735C42—112no—
736C42—442no—
737C11#2241911yescharacteristic, complemented, Sylow
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—112no—
752C23—112no—
753C23—112no—
754C23—221no—
755C23—221no—
756C23—221no—
757C23—221no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—448no—
762C23—448no—
763C23—441no—
764C23—441no—
765C23—441no—
766C23—441no—
767C23—884no—
768C23—884no—
769C23—884no—
770C23—884no—
771C23—884no—
772C23C22⋊C4×D1112yes—
773C23C2×D4×D1111yescharacteristic
774Q8—222no—
775Q8—222no—
776Q8—441no—
777Q8—441no—
778D4—22no—
779D4—22no—
780D4—41no—
781D4—41no—
782D4—84no—
783D4—114no—
784D4—228no—
785D4—222no—
786D4—222no—
787D4—222no—
788D4—448no—
789D4—448no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—112no—
806C2×C4—112no—
807C2×C4—112no—
808C2×C4—221no—
809C2×C4—221no—
810C2×C4—221no—
811C2×C4—221no—
812C2×C4—221no—
813C2×C4—221no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—448no—
821C2×C4—441no—
822C2×C4—441no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—884no—
829C2×C4—884no—
830C2×C4—884no—
831C2×C4C22⋊C4×D1112yes—
832C2×C4C22×C4×D1111yescharacteristic
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4#6703711yescharacteristic
836C2×C4#41×D1111yescharacteristic
837C2×C4#6704211yescharacteristic
838C8—22no—
839C8—41no—
840C8—441no—
841C8—441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—114no—
857C22—222no—
858C22—222no—
859C22—222no—
860C22—222no—
861C22—222no—
862C22—222no—
863C22—224no—
864C22—442no—
865C22—442no—
866C22—442no—
867C22—442no—
868C22—442no—
869C22—442no—
870C22—8816no—
871C22C2×C22⋊C4×D1111yescharacteristic
872C22#1062314011yescharacteristic
873C22#1062314111yescharacteristic
874C22D11×AGL(1,ℤ/8)11yescharacteristic
875C22#1062330511yescharacteristic
876C22#1062330611yescharacteristic
877C22D11×#13711yescharacteristic
878C4—22no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—222no—
883C4—222no—
884C4—222no—
885C4—442no—
886C4—442no—
887C4—881no—
888C4C4×D4×D1111yescharacteristic
889C4#1062307611yescharacteristic
890C4#1062312111yescharacteristic
891C4#1062318511yescharacteristic
892C2—42no—
893C2—82no—
894C2—224no—
895C2—444no—
896C2#1307143411yescharacteristic
897C2D11×#41711yescharacteristic
898C2#1307714111yescharacteristic
899C2#1308010311yescharacteristic
900C2#1308013311yescharacteristic
901C2#1308057211yescharacteristic
902C2#1308069211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×#10623143C2
cosocleC22×C4×C11C24
hypercenter#1895D11
hypocenterC11#22419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#10622740C2semidirect
3. C2×#10622746C2semidirect
4. C2×D11×#102C2semidirect
5. #13071512C2semidirect
6. #13069547C2semidirect
7. #13069431C2semidirect
8. #13069038C2semidirect
9. #13068934C2semidirect
10. #13068922C2semidirect
11. #13068615C2semidirect
12. #13068554C2semidirect
13. #13068545C2semidirect
14. #13068440C2semidirect
15. C11×#1895C2semidirect
18. C22×C11×M16C22semidirect
24. C22×C4⋊Dic11C22semidirect
27. #10623143C4semidirect
36. C11×#380C22semidirect
39. C2×C22⋊(C11⋊C8)C22semidirect
45. C2×#66880C22semidirect
46. C2×#66880C22semidirect
47. C2×#66879C22semidirect
48. C2×Dic11⋊C8C22semidirect
50. #10622589C22semidirect
51. C4⋊C4×Dic11C22semidirect
52. C2×#66874C22semidirect
53. C2×#66874C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
77. C2×D4×D11C2×C4semidirect
83. C2×#4339C2×C4semidirect
96. C11×#121C2×C4semidirect
108. #66989C2×C4semidirect
133. #66950C2×C4semidirect
135. #66946C2×C4semidirect
150. #66885D4semidirect
294. #1895D11semidirect
390. D44C4×D4semidirect
408. C22×M16C2×D11semidirect
448. #380C2×D11semidirect
452. #340C2×D11semidirect
453. #340C2×D11semidirect
489. C2×D11#417semidirect
547. #121C4×D11semidirect
737. C11#22419semidirect

Maximal subgroups

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

subgroupindex
C2×#106231432
C2×#106227402
C2×#106227462
C2×D11×#1022
#130715122
#130695472
#130694312
#130690382
#130689342
#130689222
#130686152
#130685542
#130685452
#130684402
C11×#18952
#2241911