Finite Group Databasebeta

← #14769127

Subgroups — #14769127

Order 2816.

1544 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2D4×#4318C211yesmaximal, characteristic, complemented
3C2×#10622745C211yesmaximal, characteristic, complemented
4C22×#66887C211yesmaximal, characteristic, complemented
5#13069465C211yesmaximal, characteristic, complemented
6#13069463C211yesmaximal, characteristic, complemented
7#13069084C211yesmaximal, characteristic, complemented
8#13069082C211yesmaximal, characteristic, complemented
9#13069079C211yesmaximal, characteristic, complemented
10#13069077C211yesmaximal, characteristic, complemented
11#13068605C211yesmaximal, characteristic, complemented
12#13068542C211yesmaximal, characteristic, complemented
13#13068536C211yesmaximal, characteristic, complemented
14C4×#66887C211yesmaximal, characteristic, complemented
15D4×C11×M16C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66990C412yes—
22C2×#66983C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic, complemented
26#10623081—21no—
27#10623081—21no—
28#10623081—21no—
29#10623081—21no—
30#10623081—21no—
31#10623081—21no—
32#10623081—21no—
33#10623081—21no—
34C2×#66947C412yes—
35C2×#66937C412yes—
36C2×C22⋊C4×D11C412yes—
37C2×#66928C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C11×#436—21no—
40C11×#435—21no—
41C11×#435—21no—
42C8×D4×C11—21no—
43C11×#423C2211yescharacteristic, complemented
44C11×#407C2211yescharacteristic
45C11×#407C2211yescharacteristic, complemented
46C4×C11×M16C2211yescharacteristic, complemented
47#10622820C2211yescharacteristic
48#10622820C2211yescharacteristic, complemented
49C2×#66888C2211yescharacteristic, complemented
50C2×#66888C2211yescharacteristic, complemented
51C2×#66888C2211yescharacteristic, complemented
52C2×#66888C2211yescharacteristic, complemented
53#10622745—24no—
54C2×#66887—24no—
55C2×#66887C2211yescharacteristic
56C2×#66887C2211yescharacteristic
57C2×#66887C2211yescharacteristic
58C2×#66887C2211yescharacteristic
59C2×#66887C2211yescharacteristic
60C2×#66887C2211yescharacteristic
61C2×#66887C2211yescharacteristic
62C2×#66887C2211yescharacteristic
63#10622625—21no—
64#10622624—21no—
65#10622624—21no—
66D4×C11⋊C8—21no—
67#10622537C2211yescharacteristic, complemented
68C4×#4318C2211yescharacteristic, complemented
69#10622192C2211yescharacteristic, complemented
70#10622192C2211yescharacteristic, complemented
71#10622192C2211yescharacteristic, complemented
72#10622192C2211yescharacteristic, complemented
73C24×D11C2×C412yes—
74C22×D4×C11C2×C411yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11C2×C412yes—
78C22×C22⋊D11C2×C412yes—
79C2×#4339—21no—
80C2×#4339—21no—
81C2×#4339—21no—
82C2×#4339—21no—
83C2×#4339—22no—
84C2×#4339—22no—
85C2×#4339—41no—
86C2×#4339—41no—
87C22×D44—21no—
88C22×D44—21no—
89C22×D44—21no—
90C22×D44—21no—
91C22×D44—22no—
92C22×D44—22no—
93C22×D44—41no—
94C22×D44—41no—
95C22×D44C2×C412yes—
96C22×D44C2311yescharacteristic
97C22×D44C2311yescharacteristic
98C22×C4×D11C2×C412yes—
99C22×C4×D11C2×C412yes—
100C22×Dic22C2311yescharacteristic
101C2×C11×M16—21no—
102C2×C11×M16—21no—
103C2×C11×M16—22no—
104C2×C11×M16—22no—
105C2×C11×M16—41no—
106C2×C11×M16—41no—
107C2×C11×M16C2311yescharacteristic
108C2×C11×M16C2311yescharacteristic
109C2×C11×M16C2311yescharacteristic
110C2×C11×M16C2311yescharacteristic
111C22×C8×C11—21no—
112C22×C8×C11—21no—
113C4×D4×C11D411yescharacteristic
114C4×D4×C11D411yescharacteristic
115C4×D4×C11D411yescharacteristic
116C4×D4×C11D411yescharacteristic
117C4×D4×C11D411yescharacteristic
118C4×D4×C11D411yescharacteristic
119C4×D4×C11D411yescharacteristic
120C4×D4×C11D411yescharacteristic
121C2×C11×C4⋊C4C2×C411yescharacteristic
122C2×C11×C22⋊C4C2×C411yescharacteristic
123C2×C11×C22⋊C4C2×C411yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C2×C22⋊Dic11C2×C412yes—
126#66990—22no—
127#66990—22no—
128#66990—22no—
129#66990—22no—
130#66983—21no—
131#66983—21no—
132#66983—21no—
133#66983—21no—
134C2×(C2×D11)⋊C4C2×C412yes—
135C2×(C2×D11)⋊C4C2×C412yes—
136C2×(C2×D11)⋊C4C2×C412yes—
137C2×(C2×D11)⋊C4C2×C412yes—
138C2×C4⋊Dic11C2311yescharacteristic
139#66977—21no—
140#66977—21no—
141#66977—21no—
142#66977—21no—
143C2×Dic11⋊C4C2×C412yes—
144C2×#4318—21no—
145C2×#4318—21no—
146C2×#4318—22no—
147C2×#4318—22no—
148C2×#4318—41no—
149C2×#4318—41no—
150C2×#4318C2311yescharacteristic
151C2×#4318C2311yescharacteristic
152C2×#4318C2311yescharacteristic
153C2×#4318C2311yescharacteristic
154C22×C11⋊C8—21no—
155C22×C11⋊C8—21no—
156#66947—22no—
157#66947—22no—
158#66947—22no—
159#66947—22no—
160#66937—22no—
161#66937—22no—
162#66937—22no—
163#66937—22no—
164C22⋊C4×D11—22no—
165C22⋊C4×D11—22no—
166C22⋊C4×D11—22no—
167C22⋊C4×D11—22no—
168#66928—21no—
169#66928—21no—
170#66928—21no—
171#66928—21no—
172C4×D44—21no—
173C4×D44—21no—
174C4×D44—21no—
175C4×D44—21no—
176C11×C4⋊C8—21no—
177C11×C4⋊C8—21no—
178C11×C22⋊C8—21no—
179C11×C22⋊C8—21no—
180C11×C22⋊C8—21no—
181C11×C22⋊C8—21no—
182C11×#97—21no—
183C4×C8×C11—21no—
184C22⋊(C11⋊C8)—21no—
185C22⋊(C11⋊C8)—21no—
186C22⋊(C11⋊C8)—21no—
187C22⋊(C11⋊C8)—21no—
188#66888—22no—
189#66888—22no—
190#66888—41no—
191#66888—41no—
192#66887—22no—
193#66887—22no—
194#66887—22no—
195#66887—22no—
196#66887—22no—
197#66887—41no—
198#66887—41no—
199#66887D414yescomplemented
200C4⋊(C11⋊C8)—21no—
201C4⋊(C11⋊C8)—21no—
202#66867—21no—
203C4×C11⋊C8—21no—
204#22408—111nomaximal, Sylow
205C24×C11C22×C411yescharacteristic
206C24×C11C22×C411yescharacteristic
207C23×D11—22no—
208C23×D11—22no—
209C23×D11—24no—
210C23×D11—42no—
211C23×D11—44no—
212C23×D11—82no—
213C23×D11C22×C412yes—
214C23×D11C22×C412yes—
215C2×D4×C11—42no—
216C2×D4×C11C22⋊C411yescharacteristic
217C2×D4×C11C22⋊C411yescharacteristic
218C2×D4×C11C22⋊C411yescharacteristic
219C2×D4×C11C22⋊C411yescharacteristic
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11C22×C411yescharacteristic
229C22×C4×C11C22×C411yescharacteristic
230C22×C4×C11C22×C411yescharacteristic
231C22×C4×C11C22×C411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C2×C22⋊D11—22no—
242C2×C22⋊D11—22no—
243C2×C22⋊D11—22no—
244C2×C22⋊D11—22no—
245C2×C22⋊D11—24no—
246C2×C22⋊D11—42no—
247C2×C22⋊D11—82no—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250#4339—42no—
251#4339—42no—
252#4339—42no—
253#4339—42no—
254#4339—42no—
255#4339—42no—
256#4339—42no—
257#4339—42no—
258C2×D44—24no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44—21no—
262C2×D44—21no—
263C2×D44—21no—
264C2×D44—21no—
265C2×D44—21no—
266C2×D44—21no—
267C2×D44—21no—
268C2×D44—21no—
269C2×D44—21no—
270C2×D44—21no—
271C2×D44—42no—
272C2×D44—42no—
273C2×D44—42no—
274C2×D44—42no—
275C2×D44—42no—
276C2×D44—42no—
277C2×D44—42no—
278C2×D44—42no—
279C2×D44—42no—
280C2×D44C2×D412yes—
281C2×D44#4112yes—
282C2×C4×D11—24no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—22no—
287C2×C4×D11—42no—
288C2×C4×D11—82no—
289C2×Dic22—21no—
290C2×Dic22—21no—
291C2×Dic22—21no—
292C2×Dic22—21no—
293C2×Dic22—21no—
294C2×Dic22—21no—
295C11×M16—21no—
296C11×M16—21no—
297C11×M16—21no—
298C11×M16—21no—
299C11×M16—21no—
300C11×M16—21no—
301C11×M16—21no—
302C11×M16—42no—
303C11×M16—42no—
304C11×M16C2×D412yes—
305C2×C8×C11—21no—
306C2×C8×C11—21no—
307C2×C8×C11—21no—
308C2×C8×C11—21no—
309C2×C8×C11—42no—
310C2×C8×C11—42no—
311C11×C4⋊C4C22⋊C411yescharacteristic
312C11×C4⋊C4C22⋊C411yescharacteristic
313C11×C4⋊C4C22⋊C411yescharacteristic
314C11×C4⋊C4C22⋊C411yescharacteristic
315C11×C22⋊C4C22⋊C411yescharacteristic
316C11×C22⋊C4C22⋊C411yescharacteristic
317C11×C22⋊C4C22⋊C411yescharacteristic
318C11×C22⋊C4C22⋊C411yescharacteristic
319C11×C22⋊C4C22⋊C411yescharacteristic
320C11×C22⋊C4C22⋊C411yescharacteristic
321C11×C22⋊C4C22⋊C411yescharacteristic
322C11×C22⋊C4C22⋊C411yescharacteristic
323C42×C11C2×D411yescharacteristic
324C42×C11C2×D411yescharacteristic
325C42×C11C2×D411yescharacteristic
326C42×C11C2×D411yescharacteristic
327C22⋊Dic11—22no—
328C22⋊Dic11—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4—22no—
334(C2×D11)⋊C4—22no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4—22no—
337C4⋊Dic11—21no—
338C4⋊Dic11—21no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341#4318—21no—
342#4318—21no—
343#4318—21no—
344#4318—21no—
345#4318—21no—
346#4318—21no—
347#4318—21no—
348#4318—42no—
349#4318—42no—
350#4318C2×D412yes—
351C2×C11⋊C8—21no—
352C2×C11⋊C8—21no—
353C2×C11⋊C8—21no—
354C2×C11⋊C8—21no—
355C2×C11⋊C8—42no—
356C2×C11⋊C8—42no—
357C2×#546—111no—
358D4×M16—111no—
359D4×M16D1111yescharacteristic, complemented
360C2×#413—111no—
361C22×#100—111no—
362#1967—111no—
363#1967—111no—
364#1901—111no—
365#1901—111no—
366#1900—111no—
367#1900—111no—
368#1800—111no—
369#1785—111no—
370#1783—111no—
371C4×#100—111no—
372C23×C11—21no—
373C23×C11—21no—
374C23×C11—22no—
375C23×C11—21no—
376C23×C11—21no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11C2×C22⋊C411yescharacteristic
381C23×C11C2×C22⋊C411yescharacteristic
382C23×C11C2×C22⋊C411yescharacteristic
383C23×C11C2×C22⋊C411yescharacteristic
384C23×C11C23×C411yescharacteristic
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—44no—
391C22×D11—44no—
392C22×D11—42no—
393C22×D11—42no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11—42no—
397C22×D11—42no—
398C22×D11—82no—
399C22×D11—82no—
400C22×D11—88no—
401C22×D11—88no—
402C22×D11C4×D414yes—
403D4×C11—22no—
404D4×C11—22no—
405D4×C11—41no—
406D4×C11—41no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11C2×C22⋊C411yescharacteristic
430C2×C4×C11C2×C22⋊C411yescharacteristic
431C2×C4×C11C2×C22⋊C411yescharacteristic
432C2×C4×C11C2×C22⋊C411yescharacteristic
433C2×C4×C11C2×C22⋊C411yescharacteristic
434C2×C4×C11C2×C22⋊C411yescharacteristic
435C2×C4×C11C2×C22⋊C411yescharacteristic
436C2×C4×C11C2×C22⋊C411yescharacteristic
437C2×C4×C11C22×D411yescharacteristic
438C2×C4×C11C22×D411yescharacteristic
439C2×C4×C11C22×D411yescharacteristic
440C2×C4×C11C2×#4111yescharacteristic
441C2×C4×C11H(5,𝔽2)11yescharacteristic
442C2×C4×C11H(5,𝔽2)11yescharacteristic
443C22⋊D11—44no—
444C22⋊D11—44no—
445C22⋊D11—82no—
446C22⋊D11—82no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—42no—
452D44—22no—
453D44—22no—
454D44—22no—
455D44—22no—
456D44—44no—
457D44—44no—
458D44—41no—
459D44—41no—
460D44—41no—
461D44—41no—
462C4×D11—44no—
463C4×D11—44no—
464C4×D11—82no—
465C4×D11—82no—
466Dic22—41no—
467Dic22—41no—
468Dic22—41no—
469Dic22—41no—
470C8×C11—22no—
471C8×C11—41no—
472C8×C11—41no—
473C8×C11—41no—
474C11⋊C8—22no—
475C11⋊C8—41no—
476C11⋊C8—41no—
477C11⋊C8—41no—
478C22×#41—111no—
479C23×D4—111no—
480C22×M16—111no—
481C22×M16—111no—
482C22×M16C2×D1111yescharacteristic
483C22×M16C2×D1111yescharacteristic, complemented
484#546—221no—
485#546—221no—
486#546—221no—
487#546—221no—
488#546—221no—
489#546—221no—
490#546—221no—
491#546—221no—
492C2×#124—111no—
493C2×#123—112no—
494C2×C22⋊Q8—111no—
495C2×#121—111no—
496C2×#121—112no—
497C2×#120—112no—
498C2×C4×D4—111no—
499C2×C4×D4C2×D1111yescharacteristic
500C22×C22⋊C4—112no—
501#436—21no—
502#436—221no—
503#435—21no—
504#435—21no—
505#435—221no—
506#435—221no—
507C8×D4—21no—
508C8×D4—221no—
509#423—111no—
510#423C2×D1111yescharacteristic, complemented
511#413—224no—
512C2×#101—111no—
513C2×#101—111no—
514C2×#101—111no—
515C2×#101—111no—
516C2×#100—111no—
517C2×#100—111no—
518C2×#100—111no—
519C2×#100—111no—
520C2×#100—111no—
521C2×#100—111no—
522C2×#100—111no—
523C2×#100—111no—
524C2×#100—224no—
525#407—111no—
526#407—111no—
527#407C2×D1111yescharacteristic
528#407C2×D1111yescharacteristic, complemented
529C4×M16—111no—
530C4×M16C2×D1111yescharacteristic, complemented
531#343—111no—
532#343—111no—
533#343—111no—
534#343—111no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—21no—
540C22×C11—21no—
541C22×C11—21no—
542C22×C11—21no—
543C22×C11—21no—
544C22×C11—21no—
545C22×C11—21no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—81no—
551C22×C11—81no—
552C22×C11#41312yescomplemented
553C22×C11C22×C22⋊C411yescharacteristic
554C22×C11C2×C4×D411yescharacteristic
555C22×C11#51811yescharacteristic
556C2×D11—24no—
557C2×D11—44no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—44no—
561C2×D11—42no—
562C2×D11—42no—
563C2×D11—42no—
564C2×D11—88no—
565C2×D11—88no—
566C2×D11—82no—
567C2×D11—82no—
568C4×C11—21no—
569C4×C11—21no—
570C4×C11—21no—
571C4×C11—21no—
572C4×C11—21no—
573C4×C11—21no—
574C4×C11—21no—
575C4×C11—21no—
576C4×C11D4211yescharacteristic
577C4×C11D4211yescharacteristic
578C4×C11#54611yescharacteristic
579C4×C11#54611yescharacteristic
580Dic11—42no—
581Dic11—42no—
582C25—112no—
583C2×#41—222no—
584C2×#41—222no—
585C2×#41—221no—
586C2×#41—221no—
587C2×#41—221no—
588C2×#41—221no—
589C2×#41—441no—
590C2×#41—441no—
591C22×Q8—111no—
592C22×D4—112no—
593C22×D4—112no—
594C22×D4—112no—
595C22×D4—111no—
596C22×D4—111no—
597C22×D4—222no—
598C22×D4—222no—
599C22×D4—221no—
600C22×D4—221no—
601C22×D4—221no—
602C22×D4—221no—
603C22×D4—441no—
604C22×D4—441no—
605C22×D4C4×D1111yescharacteristic
606C23×C4—112no—
607C23×C4—112no—
608C23×C4C22×D1111yescharacteristic
609C23×C4C22×D1111yescharacteristic
610C2×M16—21no—
611C2×M16—21no—
612C2×M16—22no—
613C2×M16—22no—
614C2×M16—41no—
615C2×M16—41no—
616C2×M16—111no—
617C2×M16—111no—
618C2×M16—111no—
619C2×M16—111no—
620C2×M16—221no—
621C2×M16—221no—
622C2×M16—222no—
623C2×M16—222no—
624C2×M16—441no—
625C2×M16—441no—
626C2×M16C22×D1111yescharacteristic
627C2×M16C22×D1111yescharacteristic
628C2×M16C22×D1111yescharacteristic
629C2×M16C22×D1111yescharacteristic
630C22×C8—21no—
631C22×C8—21no—
632C22×C8—221no—
633C22×C8—221no—
634#124—221no—
635#124—221no—
636#124—221no—
637#124—221no—
638#123—222no—
639#123—222no—
640#123—222no—
641#123—222no—
642C22⋊Q8—221no—
643C22⋊Q8—221no—
644C22⋊Q8—221no—
645C22⋊Q8—221no—
646#121—221no—
647#121—221no—
648#121—221no—
649#121—221no—
650#121—222no—
651#121—222no—
652#121—222no—
653#121—222no—
654#120—222no—
655#120—222no—
656#120—222no—
657#120—222no—
658C4×D4—221no—
659C4×D4—221no—
660C4×D4—221no—
661C4×D4—221no—
662C4×D4D4411yescharacteristic
663C4×D4D4411yescharacteristic
664C4×D4D4411yescharacteristic
665C4×D4D4411yescharacteristic
666C4×D4C22⋊D1111yescharacteristic
667C4×D4C22⋊D1111yescharacteristic
668C4×D4C22⋊D1111yescharacteristic
669C4×D4C22⋊D1111yescharacteristic
670C2×C4⋊C4—112no—
671C2×C4⋊C4—111no—
672C2×C4⋊C4C4×D1111yescharacteristic
673C2×C22⋊C4—112no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4—112no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4C4×D1111yescharacteristic
683C2×C22⋊C4C4×D1111yescharacteristic
684C2×C42C22×D1111yescharacteristic
685C4⋊C8—21no—
686C4⋊C8—21no—
687C4⋊C8—221no—
688C4⋊C8—221no—
689#101—222no—
690#101—222no—
691#101—441no—
692#101—441no—
693#100—114no—
694#100—222no—
695#100—222no—
696#100—222no—
697#100—222no—
698#100—222no—
699#100—441no—
700#100—441no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704C22⋊C8—21no—
705C22⋊C8—221no—
706C22⋊C8—221no—
707C22⋊C8—221no—
708C22⋊C8—221no—
709#97—21no—
710#97—221no—
711C4×C8—21no—
712C4×C8—221no—
713C2×C11—21no—
714C2×C11—21no—
715C2×C11—22no—
716C2×C11—41no—
717C2×C11—41no—
718C2×C11—41no—
719C2×C11D4×C22⋊C411yescharacteristic
720C2×C11C2×#41311yescharacteristic
721C2×C11#288811yescharacteristic
722D11—44no—
723D11—82no—
724C24—112no—
725C24—112no—
726C24—224no—
727C24—222no—
728C24—222no—
729C24—442no—
730C24—444no—
731C24—882no—
732C24C2×C4×D1111yescharacteristic
733C24C2×C4×D1111yescharacteristic
734#41—442no—
735#41—442no—
736#41—442no—
737#41—442no—
738#41—442no—
739#41—442no—
740#41—442no—
741#41—442no—
742C2×Q8—221no—
743C2×Q8—221no—
744C2×Q8—221no—
745C2×Q8—221no—
746C2×Q8—221no—
747C2×Q8—221no—
748C2×D4—42no—
749C2×D4—112no—
750C2×D4—112no—
751C2×D4—224no—
752C2×D4—224no—
753C2×D4—222no—
754C2×D4—222no—
755C2×D4—222no—
756C2×D4—222no—
757C2×D4—222no—
758C2×D4—222no—
759C2×D4—221no—
760C2×D4—221no—
761C2×D4—221no—
762C2×D4—221no—
763C2×D4—221no—
764C2×D4—221no—
765C2×D4—221no—
766C2×D4—221no—
767C2×D4—221no—
768C2×D4—221no—
769C2×D4—442no—
770C2×D4—442no—
771C2×D4—442no—
772C2×D4—442no—
773C2×D4—442no—
774C2×D4—442no—
775C2×D4—442no—
776C2×D4—442no—
777C2×D4—442no—
778C2×D4—442no—
779C2×D4—882no—
780C2×D4(C2×D11)⋊C411yescharacteristic
781C2×D4(C2×D11)⋊C411yescharacteristic
782C2×D4(C2×D11)⋊C411yescharacteristic
783C2×D4(C2×D11)⋊C411yescharacteristic
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—112no—
793C22×C4—112no—
794C22×C4—224no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—222no—
798C22×C4—222no—
799C22×C4—442no—
800C22×C4—882no—
801C22×C4C2×C4×D1111yescharacteristic
802C22×C4C2×C4×D1111yescharacteristic
803C22×C4C2×C4×D1111yescharacteristic
804C22×C4C2×C4×D1111yescharacteristic
805C22×C4C2×D4411yescharacteristic
806C22×C4C2×D4411yescharacteristic
807C22×C4C2×D4411yescharacteristic
808C22×C4C2×D4411yescharacteristic
809C22×C4C2×C22⋊D1111yescharacteristic
810C22×C4C2×C22⋊D1111yescharacteristic
811C22×C4C2×C22⋊D1111yescharacteristic
812C22×C4C2×C22⋊D1111yescharacteristic
813C22×C4C23×D1111yescharacteristic
814M16—21no—
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16—21no—
821M16—42no—
822M16—42no—
823M16—112no—
824M16—221no—
825M16—221no—
826M16—221no—
827M16—221no—
828M16—221no—
829M16—221no—
830M16—221no—
831M16—442no—
832M16—442no—
833M16D4×D1112yes—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—42no—
839C2×C8—42no—
840C2×C8—221no—
841C2×C8—221no—
842C2×C8—221no—
843C2×C8—221no—
844C2×C8—442no—
845C2×C8—442no—
846C4⋊C4—222no—
847C4⋊C4—222no—
848C4⋊C4—221no—
849C4⋊C4—221no—
850C4⋊C4(C2×D11)⋊C411yescharacteristic
851C4⋊C4(C2×D11)⋊C411yescharacteristic
852C4⋊C4(C2×D11)⋊C411yescharacteristic
853C4⋊C4(C2×D11)⋊C411yescharacteristic
854C22⋊C4—222no—
855C22⋊C4—222no—
856C22⋊C4—222no—
857C22⋊C4—222no—
858C22⋊C4—222no—
859C22⋊C4—222no—
860C22⋊C4—222no—
861C22⋊C4—222no—
862C22⋊C4—222no—
863C22⋊C4—222no—
864C22⋊C4(C2×D11)⋊C411yescharacteristic
865C22⋊C4(C2×D11)⋊C411yescharacteristic
866C22⋊C4(C2×D11)⋊C411yescharacteristic
867C22⋊C4(C2×D11)⋊C411yescharacteristic
868C22⋊C4(C2×D11)⋊C411yescharacteristic
869C22⋊C4(C2×D11)⋊C411yescharacteristic
870C22⋊C4(C2×D11)⋊C411yescharacteristic
871C22⋊C4(C2×D11)⋊C411yescharacteristic
872C42C2×D4411yescharacteristic
873C42C2×D4411yescharacteristic
874C42C2×C22⋊D1111yescharacteristic
875C42C2×C22⋊D1111yescharacteristic
876C11#2240811yescharacteristic, complemented, Sylow
877C23—22no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—114no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—444no—
892C23—444no—
893C23—442no—
894C23—442no—
895C23—444no—
896C23—442no—
897C23—442no—
898C23—444no—
899C23—882no—
900C23—882no—
901C23—888no—
902C23—888no—
903C23C2×(C2×D11)⋊C411yescharacteristic
904C23C2×(C2×D11)⋊C411yescharacteristic
905C23C2×(C2×D11)⋊C411yescharacteristic
906C23C2×(C2×D11)⋊C411yescharacteristic
907C23C22×C4×D1111yescharacteristic
908Q8—441no—
909Q8—441no—
910Q8—441no—
911Q8—441no—
912D4—22no—
913D4—22no—
914D4—41no—
915D4—41no—
916D4—222no—
917D4—222no—
918D4—222no—
919D4—222no—
920D4—444no—
921D4—444no—
922D4—444no—
923D4—444no—
924D4—441no—
925D4—441no—
926D4—441no—
927D4—441no—
928D4—882no—
929D4—882no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—444no—
957C2×C4—444no—
958C2×C4—442no—
959C2×C4—882no—
960C2×C4—882no—
961C2×C4C2×(C2×D11)⋊C411yescharacteristic
962C2×C4C2×(C2×D11)⋊C411yescharacteristic
963C2×C4C2×(C2×D11)⋊C411yescharacteristic
964C2×C4C2×(C2×D11)⋊C411yescharacteristic
965C2×C4C2×(C2×D11)⋊C411yescharacteristic
966C2×C4C2×(C2×D11)⋊C411yescharacteristic
967C2×C4C2×(C2×D11)⋊C411yescharacteristic
968C2×C4C2×(C2×D11)⋊C411yescharacteristic
969C2×C4C22×D4411yescharacteristic
970C2×C4C2×D4×D1111yescharacteristic
971C2×C4#6703711yescharacteristic
972C2×C4#41×D1111yescharacteristic
973C2×C4#6704211yescharacteristic
974C2×C4C22×C22⋊D1111yescharacteristic
975C8—22no—
976C8—41no—
977C8—41no—
978C8—41no—
979C8—222no—
980C8—441no—
981C8—441no—
982C8—441no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—42no—
997C22—42no—
998C22—81no—
999C22—81no—
1000C22—224no—
1001C22—444no—
1002C22—444no—
1003C22—442no—
1004C22—442no—
1005C22—442no—
1006C22—442no—
1007C22—442no—
1008C22—888no—
1009C22—882no—
1010C22—882no—
1011C22—888no—
1012C22#1062274512yescomplemented
1013C22C4×D4×D1111yescharacteristic
1014C22#1062307611yescharacteristic
1015C22C22×(C2×D11)⋊C411yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—442no—
1025C4—442no—
1026C4D4×D4411yescharacteristic
1027C4#1062308511yescharacteristic
1028C4D4×C22⋊D1111yescharacteristic
1029C4#1062336011yescharacteristic
1030C2—21no—
1031C2—21no—
1032C2—22no—
1033C2—41no—
1034C2—41no—
1035C2—41no—
1036C2—444no—
1037C2—882no—
1038C2D4×(C2×D11)⋊C411yescharacteristic
1039C2C2×#1062274511yescharacteristic
1040C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×M16C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623081C2
cosocleC22×C4×C11C24
hypercenterD4×M16D11
hypocenterC11#22408
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. D4×#4318C2semidirect
3. C2×#10622745C2semidirect
4. C22×#66887C2semidirect
5. #13069465C2semidirect
6. #13069463C2semidirect
7. #13069084C2semidirect
8. #13069082C2semidirect
9. #13069079C2semidirect
10. #13069077C2semidirect
11. #13068605C2semidirect
12. #13068542C2semidirect
13. #13068536C2semidirect
14. C4×#66887C2semidirect
15. D4×C11×M16C2semidirect
19. C22×C11×M16C22semidirect
25. C22×#4318C22semidirect
43. C11×#423C22semidirect
45. C11×#407C22semidirect
46. C4×C11×M16C22semidirect
48. #10622820C22semidirect
49. C2×#66888C22semidirect
50. C2×#66888C22semidirect
51. C2×#66888C22semidirect
52. C2×#66888C22semidirect
67. #10622537C22semidirect
68. C4×#4318C22semidirect
69. #10622192C22semidirect
70. #10622192C22semidirect
71. #10622192C22semidirect
72. #10622192C22semidirect
199. #66887D4semidirect
359. D4×M16D11semidirect
483. C22×M16C2×D11semidirect
510. #423C2×D11semidirect
528. #407C2×D11semidirect
530. C4×M16C2×D11semidirect
552. C22×C11#413semidirect
876. C11#22408semidirect
1012. C22#10622745semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
D4×#43182
C2×#106227452
C22×#668872
#130694652
#130694632
#130690842
#130690822
#130690792
#130690772
#130686052
#130685422
#130685362
C4×#668872
D4×C11×M162
#2240811