Finite Group Databasebeta

← #15624518

Subgroups — #15624518

Order 2816.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic, complemented
3#13079432C214yesmaximal, complemented
4#13079423C212yesmaximal, complemented
5#13079416C212yesmaximal, complemented
6#13079383C214yesmaximal, complemented
7#13079374C212yesmaximal, complemented
8#13079367C212yesmaximal, complemented
9#13078557C212yesmaximal, complemented
10#13078541C212yesmaximal, complemented
11#13078235C214yesmaximal, complemented
12#13077870C212yesmaximal, complemented
13#13077846C212yesmaximal, complemented
14C2×C11×#407C211yesmaximal, characteristic, complemented
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11—21no—
17C22×#4339C2211yescharacteristic, complemented
18C23×D44C2211yescharacteristic, complemented
19C22×C11×M16C2212yescomplemented
20C2×#67006—21no—
21#10623322—21no—
22#10623322—21no—
23#10623322—21no—
24#10623322—21no—
25#10623322C2212yes—
26#10623322C2212yescomplemented
27#10623322C2212yescomplemented
28#10623322C2212yescomplemented
29C2×#66983—21no—
30C2×#66983—21no—
31C2×#66983—21no—
32C2×#66983—21no—
33C2×#66983—21no—
34C2×#66983—21no—
35C2×#66983C2212yes—
36C2×#66983C2212yes—
37C2×#66983C2212yes—
38C2×#66983C2212yescomplemented
39C2×#66983C2212yescomplemented
40C2×#66983C2212yescomplemented
41C2×#66983C2211yescharacteristic, complemented
42C2×#66983C2211yescharacteristic, complemented
43C2×#66982—21no—
44C2×C4×C22⋊D11—21no—
45C2×C4×C22⋊D11—21no—
46C22×(C2×D11)⋊C4—21no—
47C2×#66979C2211yescharacteristic, complemented
48C22×C4⋊Dic11C2211yescharacteristic, complemented
49C2×#66977C2211yescharacteristic, complemented
50C2×#66977C2211yescharacteristic, complemented
51C2×#66961C2214yescomplemented
52C11×#407C2212yescomplemented
53C11×#407C2212yescomplemented
54C11×#407C2212yescomplemented
55C11×#407C2212yescomplemented
56C2×C11×C22⋊C8C2212yescomplemented
57C2×C11×C22⋊C8C2212yescomplemented
58#10622748C2218yescomplemented
59#10622747C2218yescomplemented
60#10622746C2214yescomplemented
61#10622744C2214yescomplemented
62#10622734C2214yescomplemented
63#10622728C2218yescomplemented
64#10622727C2218yescomplemented
65#10622351C2214yescomplemented
66#10622350C2218yescomplemented
67#10622349C2214yescomplemented
68#10622349C2214yescomplemented
69#10622348C2214yescomplemented
70#10622348C2214yescomplemented
71#10622347C2218yescomplemented
72#10622345C2214yescomplemented
73#10622345C2214yescomplemented
74#10622345C2214yescomplemented
75#10622344C2214yescomplemented
76#10622344C2214yescomplemented
77#10622335C2214yescomplemented
78#10622334C2214yescomplemented
79C25×C11D411yescharacteristic
80C24×D11—21no—
81C23×C4×C11—44no—
82C23×C4×C11D411yescharacteristic
83C23×C4×C11D411yescharacteristic
84C23×C4×C11D411yescharacteristic
85C23×C4×C11D411yescharacteristic
86C23×C4×C11D411yescharacteristic
87C23×C4×C11D411yescharacteristic
88C23×C4×C11D411yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11—22no—
100C22×C22⋊D11—22no—
101C22×C22⋊D11—22no—
102C22×C22⋊D11—22no—
103C22×C22⋊D11—22no—
104C22×C22⋊D11—22no—
105C22×C22⋊D11—48no—
106C23×Dic11—21no—
107C2×#4339—21no—
108C2×#4339—21no—
109C2×#4339—44no—
110C2×#4339C2312yes—
111C2×#4339C2312yescomplemented
112C22×D44—21no—
113C22×D44—21no—
114C22×D44—21no—
115C22×D44—44no—
116C22×D44C2312yes—
117C22×D44C2312yes—
118C22×D44C2312yes—
119C22×D44C2311yescharacteristic, complemented
120C22×C4×D11—21no—
121C22×Dic22C2311yescharacteristic, complemented
122C2×C11×M16—44no—
123C2×C11×M16C2314yes—
124C2×C11×M16C2314yescomplemented
125C22×C8×C11C2314yescomplemented
126#67006—22no—
127#67006—22no—
128#67006—22no—
129#67006—22no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11—21no—
133#66983—22no—
134#66983—22no—
135#66983—22no—
136#66983—22no—
137#66983—22no—
138#66983—22no—
139#66983—22no—
140#66983—22no—
141#66983—22no—
142#66983—22no—
143#66983—22no—
144#66983—22no—
145#66983—21no—
146#66983—21no—
147#66983—21no—
148#66983—21no—
149#66983C2314yes—
150#66983C2314yes—
151#66983C2314yes—
152#66983C2314yes—
153#66983C2312yes—
154#66983C2312yes—
155#66983C2312yescomplemented
156#66983C2312yescomplemented
157#66982—22no—
158#66982—22no—
159#66982—22no—
160#66982—22no—
161C4×C22⋊D11—22no—
162C4×C22⋊D11—22no—
163C4×C22⋊D11—22no—
164C4×C22⋊D11—22no—
165C4×C22⋊D11—22no—
166C4×C22⋊D11—22no—
167C4×C22⋊D11—22no—
168C4×C22⋊D11—22no—
169C2×(C2×D11)⋊C4—22no—
170C2×(C2×D11)⋊C4—22no—
171C2×(C2×D11)⋊C4—22no—
172C2×(C2×D11)⋊C4—22no—
173C2×(C2×D11)⋊C4—22no—
174C2×(C2×D11)⋊C4—22no—
175C2×(C2×D11)⋊C4—21no—
176C2×(C2×D11)⋊C4—21no—
177#66979—21no—
178#66979—21no—
179#66979C2312yes—
180#66979C2312yescomplemented
181C2×C4⋊Dic11—21no—
182C2×C4⋊Dic11—21no—
183C2×C4⋊Dic11—21no—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2312yes—
186C2×C4⋊Dic11C2312yes—
187C2×C4⋊Dic11C2311yescharacteristic, complemented
188C2×C4⋊Dic11C2311yescharacteristic, complemented
189#66977—21no—
190#66977—21no—
191#66977—21no—
192#66977—21no—
193#66977C2312yes—
194#66977C2312yes—
195#66977C2312yescomplemented
196#66977C2312yescomplemented
197C2×Dic11⋊C4—21no—
198C2×Dic11⋊C4—21no—
199C2×C4×Dic11—21no—
200#66961—48no—
201C2×D88C2318yescomplemented
202C2×#4314C2318yescomplemented
203C11×C22⋊C8C2314yes—
204C11×C22⋊C8C2314yes—
205C11×C22⋊C8C2314yescomplemented
206C11×C22⋊C8C2314yescomplemented
207#66885C2318yescomplemented
208#66885C2318yescomplemented
209#66885C2318yescomplemented
210#66882C2318yescomplemented
211#66881C2318yescomplemented
212#66880C2318yescomplemented
213#60750—111nomaximal, Sylow
214C24×C11—24no—
215C24×C11—42no—
216C24×C11—42no—
217C24×C11C2×D411yescharacteristic
218C24×C11C2×D411yescharacteristic
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C24×C11C2×D411yescharacteristic
222C24×C11C2×D411yescharacteristic
223C24×C11C2×D411yescharacteristic
224C23×D11—21no—
225C23×D11—22no—
226C23×D11—22no—
227C23×D11—22no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—44no—
231C22×C4×C11—24no—
232C22×C4×C11—24no—
233C22×C4×C11—24no—
234C22×C4×C11—42no—
235C22×C4×C11—42no—
236C22×C4×C11—42no—
237C22×C4×C11—42no—
238C22×C4×C11—42no—
239C22×C4×C11—42no—
240C22×C4×C11—42no—
241C22×C4×C11—42no—
242C22×C4×C11—42no—
243C22×C4×C11—42no—
244C22×C4×C11—42no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D411yescharacteristic
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2411yescharacteristic
273C2×C22⋊D11—22no—
274C2×C22⋊D11—22no—
275C2×C22⋊D11—22no—
276C2×C22⋊D11—22no—
277C2×C22⋊D11—22no—
278C2×C22⋊D11—22no—
279C2×C22⋊D11—24no—
280C2×C22⋊D11—24no—
281C2×C22⋊D11—24no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—44no—
284C2×C22⋊D11—44no—
285C2×C22⋊D11—48no—
286C2×C22⋊D11—48no—
287C2×C22⋊D11—48no—
288C2×C22⋊D11—48no—
289C2×C22⋊D11—48no—
290C2×C22⋊D11—44no—
291C2×C22⋊D11—48no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—44no—
299#4339—28no—
300#4339—44no—
301#4339—44no—
302#4339—44no—
303C2×D44—22no—
304C2×D44—22no—
305C2×D44—22no—
306C2×D44—21no—
307C2×D44—28no—
308C2×D44—44no—
309C2×D44—44no—
310C2×D44—42no—
311C2×D44—44no—
312C2×D44—44no—
313C2×D44—44no—
314C2×D44C2414yes—
315C2×D44C2412yes—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—44no—
319C2×Dic22—21no—
320C2×Dic22—42no—
321C2×Dic22C2412yes—
322C11×M16—28no—
323C11×M16—44no—
324C2×C8×C11—44no—
325C2×C8×C11C2418yes—
326C22⋊Dic11—22no—
327C22⋊Dic11—22no—
328C22⋊Dic11—22no—
329C22⋊Dic11—22no—
330C22⋊Dic11—22no—
331C22⋊Dic11—22no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—24no—
335(C2×D11)⋊C4—24no—
336(C2×D11)⋊C4—22no—
337(C2×D11)⋊C4—22no—
338(C2×D11)⋊C4—22no—
339(C2×D11)⋊C4—22no—
340C4⋊Dic11—21no—
341C4⋊Dic11—21no—
342C4⋊Dic11—22no—
343C4⋊Dic11—22no—
344C4⋊Dic11—22no—
345C4⋊Dic11C2414yes—
346C4⋊Dic11C2412yes—
347C4⋊Dic11C2412yes—
348Dic11⋊C4—22no—
349Dic11⋊C4—22no—
350Dic11⋊C4—22no—
351Dic11⋊C4—22no—
352C4×Dic11—22no—
353C4×Dic11—22no—
354D88—48no—
355#4314—48no—
356C2×#525—111no—
357C22×#121—111no—
358#3194—114no—
359#3193—112no—
360#3192—112no—
361#3188—114no—
362#3187—112no—
363#3186—112no—
364#3094—112no—
365#3092—112no—
366#3055—114no—
367#3006—112no—
368#3003—112no—
369C2×#407D1111yescharacteristic, complemented
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—416no—
391C23×C11AGL(1,ℤ/8)14yescomplemented
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394C23×C11C22×D411yescharacteristic
395C23×C11C22×D411yescharacteristic
396C23×C11C22×D411yescharacteristic
397C23×C11C22×D411yescharacteristic
398C23×C11C22×D411yescharacteristic
399C22×D11—22no—
400C22×D11—24no—
401C22×D11—42no—
402C22×D11—44no—
403C22×D11—44no—
404C22×D11—44no—
405C22×D11—44no—
406C22×D11—42no—
407C22×D11—44no—
408C22×D11—44no—
409C22×D11—44no—
410C22×D11—44no—
411C22×D11—42no—
412C22×D11—44no—
413C22×D11—816no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11C22×D411yescharacteristic
442C2×C4×C11C22×D411yescharacteristic
443C2×C4×C11C22×D411yescharacteristic
444C2×C4×C11C22×D411yescharacteristic
445C2×C4×C11C22×D411yescharacteristic
446C2×C4×C11C22×D411yescharacteristic
447C2×C4×C11C22×D411yescharacteristic
448C2×C4×C11H(5,𝔽2)14yes—
449C2×C4×C11C2511yescharacteristic
450C22⋊D11—44no—
451C22⋊D11—44no—
452C22⋊D11—48no—
453C22⋊D11—48no—
454C22⋊D11—44no—
455C22⋊D11—44no—
456C22⋊D11—44no—
457C22⋊D11—48no—
458C22⋊D11—48no—
459C22⋊D11—44no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—24no—
464C2×Dic11—42no—
465C2×Dic11—44no—
466C2×Dic11—44no—
467C2×Dic11—42no—
468C2×Dic11—44no—
469C2×Dic11—42no—
470D44—28no—
471D44—24no—
472D44—44no—
473D44—44no—
474D44—42no—
475D44—44no—
476C4×D11—44no—
477C4×D11—44no—
478Dic22—24no—
479Dic22—42no—
480C8×C11—28no—
481C22×#41—111no—
482C23×D4—111no—
483C23×D4—221no—
484C24×C4C2×D1111yescharacteristic
485C2×AGL(1,ℤ/8)—114no—
486C22×M16C2×D1112yescomplemented
487#525—112no—
488#525—112no—
489#525—112no—
490#525—112no—
491#525—221no—
492#525—221no—
493#525—221no—
494#525—221no—
495C2×#123—221no—
496C2×C22⋊Q8—111no—
497C2×C22⋊Q8—111no—
498C2×#121—112no—
499C2×#121—112no—
500C2×#121—112no—
501C2×#121—112no—
502C2×#121—112no—
503C2×#121—112no—
504C2×#121—111no—
505C2×#121—111no—
506C2×#121—221no—
507C2×#121—221no—
508C2×#121—221no—
509C2×#121—221no—
510C2×#121—221no—
511C2×#121—221no—
512C2×#120—221no—
513C2×C4×D4—221no—
514C2×C4×D4—221no—
515C2×#117—111no—
516C22×C4⋊C4—111no—
517C22×C22⋊C4—221no—
518#484—114no—
519#483—114no—
520#482—118no—
521#481—114no—
522#481—114no—
523#480—114no—
524#480—114no—
525#469—118no—
526#468—118no—
527#466—118no—
528#465—118no—
529#450—114no—
530#450—114no—
531#449—118no—
532#448—114no—
533#447—114no—
534#447—114no—
535#447—114no—
536#428—114no—
537#418—114no—
538#417—114no—
539#407C2×D1112yescomplemented
540#407C2×D1112yescomplemented
541#407C2×D1112yescomplemented
542#407C2×D1112yescomplemented
543C2×C22⋊C8C2×D1112yescomplemented
544C2×C22⋊C8C2×D1112yescomplemented
545C22×C11—28no—
546C22×C11—21no—
547C22×C11—21no—
548C22×C11—21no—
549C22×C11—21no—
550C22×C11—21no—
551C22×C11—21no—
552C22×C11—21no—
553C22×C11—21no—
554C22×C11—21no—
555C22×C11—21no—
556C22×C11—21no—
557C22×C11—21no—
558C22×C11—21no—
559C22×C11—21no—
560C22×C11—21no—
561C22×C11—21no—
562C22×C11—44no—
563C22×C11—44no—
564C22×C11—44no—
565C22×C11—44no—
566C22×C11—44no—
567C22×C11—44no—
568C22×C11#53412yes—
569C22×C11C2×AGL(1,ℤ/8)12yes—
570C22×C11C2×AGL(1,ℤ/8)12yes—
571C22×C11C2×AGL(1,ℤ/8)12yes—
572C22×C11#57512yes—
573C22×C11C23×D411yescharacteristic
574C2×D11—44no—
575C2×D11—42no—
576C2×D11—44no—
577C2×D11—42no—
578C2×D11—44no—
579C2×D11—42no—
580C2×D11—84no—
581C2×D11—88no—
582C2×D11—88no—
583C2×D11—88no—
584C4×C11—21no—
585C4×C11—21no—
586C4×C11—21no—
587C4×C11—21no—
588C4×C11—21no—
589C4×C11—21no—
590C4×C11#53412yes—
591C4×C11C2×H(5,𝔽2)12yes—
592Dic11—42no—
593Dic11—44no—
594Dic11—42no—
595Dic11—42no—
596C25—221no—
597C25D4411yescharacteristic
598C2×#41—112no—
599C2×#41—112no—
600C2×#41—221no—
601C2×#41—221no—
602C2×#41—444no—
603C22×Q8—111no—
604C22×D4—112no—
605C22×D4—112no—
606C22×D4—112no—
607C22×D4—111no—
608C22×D4—221no—
609C22×D4—221no—
610C22×D4—221no—
611C22×D4—222no—
612C22×D4—222no—
613C22×D4—222no—
614C22×D4—222no—
615C22×D4—222no—
616C22×D4—222no—
617C22×D4—221no—
618C22×D4—221no—
619C22×D4—221no—
620C22×D4—444no—
621C22×D4—448no—
622C23×C4—44no—
623C23×C4—221no—
624C23×C4—221no—
625C23×C4D4411yescharacteristic
626C23×C4D4411yescharacteristic
627C23×C4D4411yescharacteristic
628C23×C4D4411yescharacteristic
629C23×C4D4411yescharacteristic
630C23×C4D4411yescharacteristic
631C23×C4D4411yescharacteristic
632C23×C4C22×D1111yescharacteristic
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1111yescharacteristic
637C23×C4C22×D1111yescharacteristic
638C23×C4C22×D1111yescharacteristic
639AGL(1,ℤ/8)—448no—
640C2×SD16—118no—
641C2×D8—118no—
642C2×M16—44no—
643C2×M16C22×D1114yes—
644C2×M16C22×D1114yescomplemented
645C22×C8C22×D1114yescomplemented
646#123—222no—
647#123—222no—
648#123—222no—
649#123—222no—
650C22⋊Q8—112no—
651C22⋊Q8—112no—
652C22⋊Q8—112no—
653C22⋊Q8—112no—
654C22⋊Q8—221no—
655C22⋊Q8—221no—
656C22⋊Q8—221no—
657C22⋊Q8—221no—
658#121—114no—
659#121—114no—
660#121—114no—
661#121—114no—
662#121—112no—
663#121—112no—
664#121—112no—
665#121—112no—
666#121—222no—
667#121—222no—
668#121—222no—
669#121—222no—
670#121—222no—
671#121—222no—
672#121—222no—
673#121—222no—
674#121—222no—
675#121—222no—
676#121—222no—
677#121—222no—
678#121—221no—
679#121—221no—
680#121—221no—
681#121—221no—
682#120—222no—
683#120—222no—
684#120—222no—
685#120—222no—
686C4×D4—222no—
687C4×D4—222no—
688C4×D4—222no—
689C4×D4—222no—
690C4×D4—222no—
691C4×D4—222no—
692C4×D4—222no—
693C4×D4—222no—
694#117—112no—
695#117—112no—
696#117—221no—
697#117—221no—
698C2×C4⋊C4—112no—
699C2×C4⋊C4—112no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—111no—
702C2×C4⋊C4—111no—
703C2×C4⋊C4—221no—
704C2×C4⋊C4—221no—
705C2×C4⋊C4—221no—
706C2×C4⋊C4—221no—
707C2×C4⋊C4—221no—
708C2×C22⋊C4—221no—
709C2×C22⋊C4—221no—
710C2×C22⋊C4—221no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—221no—
718C2×C22⋊C4—221no—
719C2×C42—221no—
720#107—118no—
721#106—118no—
722#103—118no—
723#102—118no—
724#102—118no—
725#102—118no—
726C22⋊C8C22×D1114yes—
727C22⋊C8C22×D1114yes—
728C22⋊C8C22×D1114yescomplemented
729C22⋊C8C22×D1114yescomplemented
730C2×C11—22no—
731C2×C11—22no—
732C2×C11—22no—
733C2×C11—22no—
734C2×C11—22no—
735C2×C11—41no—
736C2×C11—41no—
737C2×C11C2×#53411yescharacteristic
738C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
739C2×C11C2×#57511yescharacteristic
740D11—82no—
741D11—84no—
742C24—24no—
743C24—42no—
744C24—42no—
745C24—221no—
746C24—222no—
747C24—222no—
748C24—222no—
749C24—444no—
750C24—444no—
751C24—444no—
752C24C2×D4411yescharacteristic
753C24C2×D4411yescharacteristic
754C24C2×D4411yescharacteristic
755C24C2×D4411yescharacteristic
756C24C2×D4411yescharacteristic
757C24C2×D4411yescharacteristic
758C24C2×D4411yescharacteristic
759#41—228no—
760#41—444no—
761#41—444no—
762#41—444no—
763C2×Q8—112no—
764C2×Q8—221no—
765C2×Q8—442no—
766C2×D4—112no—
767C2×D4—114no—
768C2×D4—222no—
769C2×D4—222no—
770C2×D4—222no—
771C2×D4—222no—
772C2×D4—222no—
773C2×D4—222no—
774C2×D4—224no—
775C2×D4—224no—
776C2×D4—224no—
777C2×D4—224no—
778C2×D4—222no—
779C2×D4—222no—
780C2×D4—222no—
781C2×D4—221no—
782C2×D4—228no—
783C2×D4—444no—
784C2×D4—444no—
785C2×D4—442no—
786C2×D4—444no—
787C2×D4—444no—
788C2×D4—444no—
789C2×D4—448no—
790C2×D4—448no—
791C2×D4—448no—
792C2×D4—448no—
793C2×D4—448no—
794C2×D4—444no—
795C2×D4—444no—
796C2×D4—448no—
797C2×D4—444no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—222no—
815C22×C4—222no—
816C22×C4—222no—
817C22×C4—221no—
818C22×C4—222no—
819C22×C4—222no—
820C22×C4—444no—
821C22×C4—444no—
822C22×C4C2×D4411yescharacteristic
823C22×C4C2×D4411yescharacteristic
824C22×C4C2×D4411yescharacteristic
825C22×C4C2×D4411yescharacteristic
826C22×C4C2×D4411yescharacteristic
827C22×C4C2×D4411yescharacteristic
828C22×C4C2×D4411yescharacteristic
829C22×C4C2×D4411yescharacteristic
830C22×C4C2×D4411yescharacteristic
831C22×C4C2×D4411yescharacteristic
832C22×C4C2×D4411yescharacteristic
833C22×C4C2×D4411yescharacteristic
834C22×C4C2×D4411yescharacteristic
835C22×C4C2×D4411yescharacteristic
836C22×C4C2×D4411yescharacteristic
837C22×C4C2×D4411yescharacteristic
838C22×C4C2×D4411yescharacteristic
839C22×C4C2×D4411yescharacteristic
840C22×C4C2×D4411yescharacteristic
841C22×C4C2×D4411yescharacteristic
842C22×C4C2×D4411yescharacteristic
843C22×C4C23×D1111yescharacteristic
844C22×C4C23×D1111yescharacteristic
845C22×C4C23×D1111yescharacteristic
846C22×C4C23×D1111yescharacteristic
847C22×C4C23×D1111yescharacteristic
848C22×C4C23×D1111yescharacteristic
849C22×C4C23×D1111yescharacteristic
850SD16—448no—
851D8—448no—
852M16—28no—
853M16—44no—
854C2×C8—44no—
855C2×C8C23×D1118yes—
856C4⋊C4—112no—
857C4⋊C4—112no—
858C4⋊C4—114no—
859C4⋊C4—222no—
860C4⋊C4—222no—
861C4⋊C4—222no—
862C4⋊C4—221no—
863C4⋊C4—221no—
864C4⋊C4—222no—
865C4⋊C4—222no—
866C4⋊C4—222no—
867C4⋊C4—222no—
868C22⋊C4—222no—
869C22⋊C4—222no—
870C22⋊C4—222no—
871C22⋊C4—222no—
872C22⋊C4—222no—
873C22⋊C4—222no—
874C22⋊C4—224no—
875C22⋊C4—224no—
876C22⋊C4—224no—
877C22⋊C4—224no—
878C22⋊C4—222no—
879C22⋊C4—222no—
880C22⋊C4—222no—
881C22⋊C4—222no—
882C42—222no—
883C42—222no—
884C11#6075011yescharacteristic, complemented, Sylow
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—416no—
906C23—222no—
907C23—224no—
908C23—442no—
909C23—444no—
910C23—444no—
911C23—444no—
912C23—444no—
913C23—442no—
914C23—444no—
915C23—444no—
916C23—444no—
917C23—442no—
918C23—444no—
919C23—444no—
920C23—8816no—
921C23#6696114yescomplemented
922C23C22×D4411yescharacteristic
923C23C22×D4411yescharacteristic
924C23C22×D4411yescharacteristic
925C23C22×D4411yescharacteristic
926C23C22×D4411yescharacteristic
927C23C22×D4411yescharacteristic
928C23C22×D4411yescharacteristic
929Q8—224no—
930Q8—442no—
931D4—224no—
932D4—228no—
933D4—444no—
934D4—444no—
935D4—442no—
936D4—448no—
937D4—448no—
938D4—444no—
939D4—444no—
940D4—448no—
941D4—448no—
942D4—444no—
943D4—444no—
944D4—444no—
945D4—444no—
946D4—444no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—222no—
975C2×C4—222no—
976C2×C4—224no—
977C2×C4—222no—
978C2×C4—444no—
979C2×C4—444no—
980C2×C4—444no—
981C2×C4—442no—
982C2×C4—442no—
983C2×C4—444no—
984C2×C4—442no—
985C2×C4—444no—
986C2×C4C22×D4411yescharacteristic
987C2×C4C22×D4411yescharacteristic
988C2×C4C22×D4411yescharacteristic
989C2×C4C22×D4411yescharacteristic
990C2×C4C22×D4411yescharacteristic
991C2×C4C22×D4411yescharacteristic
992C2×C4C22×D4411yescharacteristic
993C2×C4#6703714yes—
994C2×C4C24×D1111yescharacteristic
995C8—28no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—442no—
1020C22—444no—
1021C22—444no—
1022C22—442no—
1023C22—442no—
1024C22—444no—
1025C22—888no—
1026C22—888no—
1027C22—888no—
1028C22—884no—
1029C22#1062302412yes—
1030C22C2×#6696112yes—
1031C22C2×#6696112yes—
1032C22C2×#6696112yes—
1033C22#1062327912yes—
1034C22C23×D4411yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—442no—
1042C4—444no—
1043C4—442no—
1044C4—442no—
1045C4#1062302412yes—
1046C4C2×#6703712yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—884no—
1055C2—882no—
1056C2C2×#1062302411yescharacteristic
1057C2C22×#6696111yescharacteristic
1058C2C2×#1062327911yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#407C2
socleC22×C11C23×D4
hypercenterC2×#407D11
hypocenterC11#60750
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. C22×#66983C2semidirect
3. #13079432C2semidirect
4. #13079423C2semidirect
5. #13079416C2semidirect
6. #13079383C2semidirect
7. #13079374C2semidirect
8. #13079367C2semidirect
9. #13078557C2semidirect
10. #13078541C2semidirect
11. #13078235C2semidirect
12. #13077870C2semidirect
13. #13077846C2semidirect
14. C2×C11×#407C2semidirect
17. C22×#4339C22semidirect
18. C23×D44C22semidirect
19. C22×C11×M16C22semidirect
26. #10623322C22semidirect
27. #10623322C22semidirect
28. #10623322C22semidirect
38. C2×#66983C22semidirect
39. C2×#66983C22semidirect
40. C2×#66983C22semidirect
41. C2×#66983C22semidirect
42. C2×#66983C22semidirect
47. C2×#66979C22semidirect
48. C22×C4⋊Dic11C22semidirect
49. C2×#66977C22semidirect
50. C2×#66977C22semidirect
51. C2×#66961C22semidirect
52. C11×#407C22semidirect
53. C11×#407C22semidirect
54. C11×#407C22semidirect
55. C11×#407C22semidirect
56. C2×C11×C22⋊C8C22semidirect
57. C2×C11×C22⋊C8C22semidirect
58. #10622748C22semidirect
59. #10622747C22semidirect
60. #10622746C22semidirect
61. #10622744C22semidirect
62. #10622734C22semidirect
63. #10622728C22semidirect
64. #10622727C22semidirect
65. #10622351C22semidirect
66. #10622350C22semidirect
67. #10622349C22semidirect
68. #10622349C22semidirect
69. #10622348C22semidirect
70. #10622348C22semidirect
71. #10622347C22semidirect
72. #10622345C22semidirect
73. #10622345C22semidirect
74. #10622345C22semidirect
75. #10622344C22semidirect
76. #10622344C22semidirect
77. #10622335C22semidirect
78. #10622334C22semidirect
111. C2×#4339C23semidirect
119. C22×D44C23semidirect
121. C22×Dic22C23semidirect
124. C2×C11×M16C23semidirect
125. C22×C8×C11C23semidirect
155. #66983C23semidirect
156. #66983C23semidirect
180. #66979C23semidirect
187. C2×C4⋊Dic11C23semidirect
188. C2×C4⋊Dic11C23semidirect
195. #66977C23semidirect
196. #66977C23semidirect
201. C2×D88C23semidirect
202. C2×#4314C23semidirect
205. C11×C22⋊C8C23semidirect
206. C11×C22⋊C8C23semidirect
207. #66885C23semidirect
208. #66885C23semidirect
209. #66885C23semidirect
210. #66882C23semidirect
211. #66881C23semidirect
212. #66880C23semidirect
369. C2×#407D11semidirect
391. C23×C11AGL(1,ℤ/8)semidirect
486. C22×M16C2×D11semidirect
539. #407C2×D11semidirect
540. #407C2×D11semidirect
541. #407C2×D11semidirect
542. #407C2×D11semidirect
543. C2×C22⋊C8C2×D11semidirect
544. C2×C22⋊C8C2×D11semidirect
644. C2×M16C22×D11semidirect
645. C22×C8C22×D11semidirect
728. C22⋊C8C22×D11semidirect
729. C22⋊C8C22×D11semidirect
884. C11#60750semidirect
921. C23#66961semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C22×#669832
#130794322
#130794232
#130794162
#130793832
#130793742
#130793672
#130785572
#130785412
#130782352
#130778702
#130778462
C2×C11×#4072
#6075011