Finite Group Databasebeta

← #15624519

Subgroups — #15624519

Order 2816.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic, complemented
2C2×D11×#121C211yesmaximal, characteristic, complemented
3#13079434C214yesmaximal, complemented
4#13079424C212yesmaximal, complemented
5#13079415C212yesmaximal, complemented
6#13079385C214yesmaximal, complemented
7#13079375C212yesmaximal, complemented
8#13079366C212yesmaximal, complemented
9#13078556C211yesmaximal, characteristic, complemented
10#13078542C212yesmaximal, complemented
11#13078236C212yesmaximal, complemented
12#13078233C212yesmaximal, complemented
13#13077870C211yesmaximal, characteristic, complemented
14#13077866C211yesmaximal, characteristic, complemented
15#13077845C212yesmaximal, complemented
16D11×#407C211yesmaximal, characteristic, complemented
17C11×#3094C211yesmaximal, characteristic, complemented
18C22×D4×D11—21no—
19C22×D4×D11C2211yescharacteristic, complemented
20C22×#4339C2211yescharacteristic, complemented
21C23×C4×D11C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic, complemented
24C2×#66992—21no—
25C2×#66991C2211yescharacteristic, complemented
26C2×#66985C2212yescomplemented
27C2×#66983C2211yescharacteristic
28C2×#66961C2212yescomplemented
29C2×M16×D11C2212yescomplemented
30D11×#121—21no—
31D11×#121—21no—
32D11×#121—21no—
33D11×#121—21no—
34D11×#121C2212yes—
35D11×#121C2212yes—
36D11×#121C2212yescomplemented
37D11×#121C2212yescomplemented
38#10623055—21no—
39#10623055—21no—
40#10623055—21no—
41#10623055—21no—
42#10623055C2212yes—
43#10623055C2212yescomplemented
44#10623055C2212yescomplemented
45#10623055C2212yescomplemented
46C2×#66950C2211yescharacteristic, complemented
47C2×#66950C2211yescharacteristic, complemented
48C2×#66948C2211yescharacteristic, complemented
49C2×#66948C2211yescharacteristic, complemented
50C2×#66948C2211yescharacteristic, complemented
51C2×C4⋊C4×D11C2211yescharacteristic, complemented
52C2×#66939—21no—
53C2×#66937—21no—
54C2×#66935—21no—
55C2×C22⋊C4×D11—21no—
56C2×C4×D44—21no—
57C2×C4×D44—21no—
58C11×#482C2214yescomplemented
59C11×#481C2212yescomplemented
60C11×#480C2212yescomplemented
61C11×#428C2212yescomplemented
62C11×#418C2212yescomplemented
63C11×#407C2211yescharacteristic, complemented
64#10622820C2211yescharacteristic, complemented
65#10622746C2212yescomplemented
66#10622739C2212yescomplemented
67#10622653C2212yescomplemented
68#10622650C2214yescomplemented
69#10622649C2212yescomplemented
70#10622616C2214yescomplemented
71#10622614C2212yescomplemented
72#10622608C2212yescomplemented
73#10622581C2212yescomplemented
74#10622580C2212yescomplemented
75#10622579C2212yescomplemented
76#10622499C2214yescomplemented
77#10622497C2214yescomplemented
78#10622496C2214yescomplemented
79#10622495C2214yescomplemented
80#10622478C2214yescomplemented
81#10622477C2214yescomplemented
82#10622476C2214yescomplemented
83#10622475C2214yescomplemented
84#10622395C2214yescomplemented
85#10622393C2214yescomplemented
86#10622391C2214yescomplemented
87#10622389C2214yescomplemented
88#10622389C2214yescomplemented
89#10622388C2214yescomplemented
90#10622386C2214yescomplemented
91#10622386C2214yescomplemented
92#10622351C2212yescomplemented
93#10622347C2214yescomplemented
94#10622345C2212yescomplemented
95#10622339C2212yescomplemented
96#10622339C2212yescomplemented
97D11×C22⋊C8C2212yescomplemented
98D11×C22⋊C8C2212yescomplemented
99C24×D11—21no—
100C24×D11D411yescharacteristic
101C22×D4×C11—21no—
102C22×D4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C22×C22⋊D11—21no—
105C22×C22⋊D11—21no—
106C22×C22⋊D11—21no—
107C22×C22⋊D11—21no—
108C23×Dic11D411yescharacteristic
109C2×D4×D11—22no—
110C2×D4×D11—22no—
111C2×D4×D11—22no—
112C2×D4×D11—22no—
113C2×D4×D11—21no—
114C2×D4×D11—21no—
115C2×D4×D11—44no—
116C2×D4×D11—48no—
117C2×D4×D11C2312yes—
118C2×D4×D11C2312yes—
119C2×#4339—21no—
120C2×#4339—21no—
121C2×#4339—44no—
122C2×#4339C2312yes—
123C2×#4339C2312yescomplemented
124C22×D44—21no—
125C22×D44—21no—
126C22×D44—21no—
127C22×D44C2311yescharacteristic
128C22×D44C2311yescharacteristic, complemented
129C22×C4×D11—21no—
130C22×C4×D11—21no—
131C22×C4×D11—44no—
132C22×C4×D11D411yescharacteristic
133C22×C4×D11D411yescharacteristic
134C22×C4×D11D411yescharacteristic
135C22×C4×D11D411yescharacteristic
136C22×C4×D11D411yescharacteristic
137C22×C4×D11D411yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×Dic22C2311yescharacteristic, complemented
145C2×C11×M16C2312yes—
146C11×#121—21no—
147C11×#121—21no—
148C11×#121C2312yes—
149C11×#121C2312yes—
150C11×#117—21no—
151C11×#117—21no—
152C11×#117C2312yes—
153C11×#117C2312yescomplemented
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic, complemented
156C2×C11×C4⋊C4C2311yescharacteristic, complemented
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—21no—
159C2×C42×C11—21no—
160C2×C22⋊Dic11—21no—
161#66992—22no—
162#66992—22no—
163#66992—22no—
164#66992—22no—
165#66991—21no—
166#66991—21no—
167#66991C2312yes—
168#66991C2312yes—
169C2×#4324C2314yescomplemented
170#66985—44no—
171C2×#4323C2314yescomplemented
172#66983—21no—
173#66983—21no—
174#66983C2312yes—
175#66983C2312yes—
176C2×(C2×D11)⋊C4—21no—
177C2×(C2×D11)⋊C4—21no—
178C2×(C2×D11)⋊C4—21no—
179C2×(C2×D11)⋊C4—21no—
180C2×(C2×D11)⋊C4—21no—
181C2×(C2×D11)⋊C4—21no—
182C2×C4⋊Dic11—21no—
183C2×C4⋊Dic11—21no—
184C2×C4⋊Dic11C2311yescharacteristic
185C2×Dic11⋊C4—21no—
186C2×#4318C2312yes—
187#66961—44no—
188M16×D11—44no—
189C2×D88C2314yescomplemented
190C2×#4314C2314yescomplemented
191C2×#4313C2314yescomplemented
192C2×C8×D11C2314yescomplemented
193#66950—21no—
194#66950—21no—
195#66950—21no—
196#66950—21no—
197#66950C2312yes—
198#66950C2312yes—
199#66950C2312yescomplemented
200#66950C2312yescomplemented
201#66948—21no—
202#66948—21no—
203#66948—21no—
204#66948—21no—
205#66948—21no—
206#66948—21no—
207#66948C2312yes—
208#66948C2312yes—
209#66948C2312yes—
210#66948C2312yes—
211#66948C2312yescomplemented
212#66948C2312yescomplemented
213C4⋊C4×D11—21no—
214C4⋊C4×D11—21no—
215C4⋊C4×D11C2312yes—
216C4⋊C4×D11C2312yes—
217#66939—22no—
218#66939—22no—
219#66939—22no—
220#66939—22no—
221#66937—22no—
222#66937—22no—
223#66937—22no—
224#66937—22no—
225#66935—22no—
226#66935—22no—
227#66935—22no—
228#66935—22no—
229C22⋊C4×D11—22no—
230C22⋊C4×D11—22no—
231C22⋊C4×D11—22no—
232C22⋊C4×D11—22no—
233C4×D44—22no—
234C4×D44—22no—
235C4×D44—22no—
236C4×D44—22no—
237C4×D44—22no—
238C4×D44—22no—
239C4×D44—22no—
240C4×D44—22no—
241C11×#107C2314yescomplemented
242C11×#106C2314yescomplemented
243C11×#102C2314yescomplemented
244C11×#102C2314yescomplemented
245C11×C22⋊C8C2312yescomplemented
246C11×C22⋊C8C2312yescomplemented
247C22⋊(C11⋊C8)C2312yescomplemented
248C22⋊(C11⋊C8)C2312yescomplemented
249#66885C2314yescomplemented
250(C2×D11)⋊C8C2314yes—
251(C2×D11)⋊C8C2314yes—
252#66880C2314yescomplemented
253#66874C2314yescomplemented
254#66873C2314yescomplemented
255#66873C2314yescomplemented
256#66873C2314yescomplemented
257#66872C2314yescomplemented
258#66871C2314yescomplemented
259#60750—111nomaximal, Sylow
260C24×C11—21no—
261C24×C11C2×D411yescharacteristic
262C23×D11—24no—
263C23×D11—21no—
264C23×D11—21no—
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11—44no—
270C23×D11—44no—
271C23×D11—44no—
272C23×D11C2×D411yescharacteristic
273C23×D11C2×D411yescharacteristic
274C23×D11C2×D411yescharacteristic
275C23×D11C2×D411yescharacteristic
276C23×D11C2×D411yescharacteristic
277C23×D11C2×D411yescharacteristic
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—21no—
281C2×D4×C11—24no—
282C2×D4×C11—44no—
283C2×D4×C11C2412yes—
284C22×C4×C11—24no—
285C22×C4×C11—21no—
286C22×C4×C11—21no—
287C22×C4×C11—21no—
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—44no—
303C2×C22⋊D11—44no—
304C2×C22⋊D11—44no—
305C2×C22⋊D11—44no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—42no—
309C22×Dic11C2×D411yescharacteristic
310C22×Dic11C2×D411yescharacteristic
311C22×Dic11C2×D411yescharacteristic
312C22×Dic11C2×D411yescharacteristic
313C22×Dic11C2×D411yescharacteristic
314C22×Dic11C2×D411yescharacteristic
315D4×D11—44no—
316D4×D11—44no—
317D4×D11—48no—
318D4×D11—48no—
319D4×D11—48no—
320D4×D11—44no—
321D4×D11—44no—
322D4×D11—48no—
323#4339—24no—
324#4339—24no—
325#4339—42no—
326#4339—42no—
327#4339—44no—
328#4339—44no—
329C2×D44—22no—
330C2×D44—22no—
331C2×D44—22no—
332C2×D44—22no—
333C2×D44—22no—
334C2×D44—22no—
335C2×D44—21no—
336C2×D44—21no—
337C2×D44—24no—
338C2×D44—42no—
339C2×D44—44no—
340C2×D44—44no—
341C2×D44—44no—
342C2×D44C2412yes—
343C2×D44C2412yes—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11—42no—
360C2×C4×D11—44no—
361C2×C4×D11—44no—
362C2×C4×D11C2×D411yescharacteristic
363C2×C4×D11C2×D411yescharacteristic
364C2×C4×D11C2×D411yescharacteristic
365C2×C4×D11C2×D411yescharacteristic
366C2×C4×D11C2×D411yescharacteristic
367C2×C4×D11C2×D411yescharacteristic
368C2×C4×D11C2×D411yescharacteristic
369C2×C4×D11C2×D411yescharacteristic
370C2×C4×D11C2×D411yescharacteristic
371C2×C4×D11C2×D411yescharacteristic
372C2×C4×D11C2×D411yescharacteristic
373C2×C4×D11C2×D411yescharacteristic
374C2×C4×D11C2411yescharacteristic
375C2×C4×D11C2411yescharacteristic
376C2×C4×D11C2411yescharacteristic
377C2×C4×D11C2411yescharacteristic
378C2×Dic22—21no—
379C2×Dic22—42no—
380C2×Dic22C2412yes—
381C11×M16—24no—
382C2×C8×C11C2414yes—
383C11×C4⋊C4—21no—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4C2412yes—
387C11×C4⋊C4C2412yes—
388C11×C4⋊C4C2412yes—
389C11×C22⋊C4—22no—
390C11×C22⋊C4—22no—
391C11×C22⋊C4—22no—
392C11×C22⋊C4—22no—
393C42×C11—22no—
394C42×C11—22no—
395C22⋊Dic11—22no—
396C22⋊Dic11—22no—
397#4324—44no—
398#4323—44no—
399(C2×D11)⋊C4—22no—
400(C2×D11)⋊C4—22no—
401(C2×D11)⋊C4—22no—
402(C2×D11)⋊C4—22no—
403(C2×D11)⋊C4—22no—
404(C2×D11)⋊C4—22no—
405(C2×D11)⋊C4—22no—
406(C2×D11)⋊C4—22no—
407(C2×D11)⋊C4—22no—
408(C2×D11)⋊C4—22no—
409(C2×D11)⋊C4—22no—
410(C2×D11)⋊C4—22no—
411C4⋊Dic11—22no—
412C4⋊Dic11—22no—
413C4⋊Dic11—22no—
414C4⋊Dic11—22no—
415C4⋊Dic11—21no—
416C4⋊Dic11C2412yes—
417Dic11⋊C4—22no—
418Dic11⋊C4—22no—
419#4318—24no—
420C2×C11⋊C8C2414yes—
421D88—44no—
422#4314—44no—
423#4313—44no—
424C8×D11—44no—
425C2×#525—111no—
426C22×#121—111no—
427#3194—114no—
428#3193—112no—
429#3192—112no—
430#3188—114no—
431#3187—112no—
432#3186—112no—
433#3094—111no—
434#3094D1111yescharacteristic, complemented
435#3092—112no—
436#3055—112no—
437#3055—112no—
438#3006—111no—
439#3006—111no—
440#3003—112no—
441C2×#407—111no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—41no—
446C23×C11—42no—
447C23×C11—42no—
448C23×C11—42no—
449C23×C11C22×D411yescharacteristic
450C23×C11C22×D411yescharacteristic
451C23×C11C22×D411yescharacteristic
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—416no—
472C22×D11—44no—
473C22×D11—44no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11—42no—
477C22×D11—42no—
478C22×D11—42no—
479C22×D11—42no—
480C22×D11—42no—
481C22×D11—42no—
482C22×D11—44no—
483C22×D11—44no—
484C22×D11—816no—
485C22×D11AGL(1,ℤ/8)14yescomplemented
486C22×D11C22×D411yescharacteristic
487C22×D11C22×D411yescharacteristic
488C22×D11C22×D411yescharacteristic
489C22×D11C22×D411yescharacteristic
490D4×C11—24no—
491D4×C11—44no—
492D4×C11—44no—
493D4×C11—42no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—42no—
503C2×C4×C11—42no—
504C2×C4×C11—42no—
505C2×C4×C11C22×D411yescharacteristic
506C2×C4×C11C22×D411yescharacteristic
507C2×C4×C11C22×D411yescharacteristic
508C2×C4×C11H(5,𝔽2)14yes—
509C2×C4×C11C2511yescharacteristic
510C22⋊D11—44no—
511C22⋊D11—44no—
512C22⋊D11—44no—
513C22⋊D11—44no—
514C22⋊D11—44no—
515C22⋊D11—44no—
516C22⋊D11—44no—
517C22⋊D11—44no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—42no—
527C2×Dic11—42no—
528C2×Dic11C22×D411yescharacteristic
529C2×Dic11C22×D411yescharacteristic
530C2×Dic11C22×D411yescharacteristic
531C2×Dic11C22×D411yescharacteristic
532D44—24no—
533D44—22no—
534D44—22no—
535D44—42no—
536D44—44no—
537D44—44no—
538D44—44no—
539D44—44no—
540D44—44no—
541D44—44no—
542D44—42no—
543C4×D11—22no—
544C4×D11—22no—
545C4×D11—22no—
546C4×D11—22no—
547C4×D11—22no—
548C4×D11—22no—
549C4×D11—22no—
550C4×D11—22no—
551C4×D11—41no—
552C4×D11—41no—
553C4×D11—41no—
554C4×D11—41no—
555C4×D11—41no—
556C4×D11—41no—
557C4×D11—41no—
558C4×D11—41no—
559C4×D11—44no—
560C4×D11—44no—
561C4×D11—44no—
562C4×D11—44no—
563Dic22—22no—
564Dic22—22no—
565Dic22—42no—
566C8×C11—24no—
567C11⋊C8—24no—
568C22×#41—111no—
569C23×D4—111no—
570C23×D4—221no—
571C24×C4—111no—
572C2×AGL(1,ℤ/8)—112no—
573C2×AGL(1,ℤ/8)—112no—
574C22×M16—112no—
575#525—112no—
576#525—112no—
577#525—112no—
578#525—112no—
579#525—221no—
580#525—221no—
581#525—221no—
582#525—221no—
583C2×#123—221no—
584C2×C22⋊Q8—111no—
585C2×C22⋊Q8—111no—
586C2×#121—111no—
587C2×#121—111no—
588C2×#121—112no—
589C2×#121—112no—
590C2×#121—112no—
591C2×#121—112no—
592C2×#121—111no—
593C2×#121—111no—
594C2×#121—111no—
595C2×#121—221no—
596C2×#121—221no—
597C2×#121—221no—
598C2×#121—221no—
599C2×#121—221no—
600C2×#121—221no—
601C2×#121C2×D1111yescharacteristic
602C2×#120—221no—
603C2×C4×D4—221no—
604C2×C4×D4—221no—
605C2×#117C2×D1111yescharacteristic, complemented
606C22×C4⋊C4—111no—
607C22×C22⋊C4—221no—
608#484—114no—
609#483—114no—
610#482—114no—
611#482C2×D1114yescomplemented
612#481—112no—
613#481—114no—
614#481C2×D1112yescomplemented
615#480—112no—
616#480—114no—
617#480C2×D1112yescomplemented
618#469—114no—
619#469—114no—
620#468—114no—
621#468—114no—
622#466—114no—
623#466—114no—
624#465—114no—
625#465—114no—
626#450—114no—
627#450—114no—
628#449—114no—
629#449—114no—
630#448—112no—
631#448—112no—
632#447—112no—
633#447—114no—
634#447—114no—
635#447—112no—
636#428—112no—
637#428C2×D1112yescomplemented
638#418—112no—
639#418C2×D1112yescomplemented
640#417—112no—
641#417—112no—
642#407—111no—
643#407—112no—
644#407—112no—
645#407—112no—
646#407C2×D1111yescharacteristic, complemented
647C2×C22⋊C8—112no—
648C2×C22⋊C8—112no—
649C22×C11—21no—
650C22×C11—21no—
651C22×C11—21no—
652C22×C11—21no—
653C22×C11—21no—
654C22×C11—21no—
655C22×C11—21no—
656C22×C11—44no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—84no—
661C22×C11#53412yes—
662C22×C11C2×AGL(1,ℤ/8)12yes—
663C22×C11C23×D411yescharacteristic
664C2×D11—28no—
665C2×D11—21no—
666C2×D11—21no—
667C2×D11—21no—
668C2×D11—21no—
669C2×D11—21no—
670C2×D11—21no—
671C2×D11—21no—
672C2×D11—21no—
673C2×D11—21no—
674C2×D11—44no—
675C2×D11—44no—
676C2×D11—44no—
677C2×D11—44no—
678C2×D11—44no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—88no—
686C2×D11—88no—
687C2×D11—84no—
688C2×D11—84no—
689C2×D11C2×AGL(1,ℤ/8)12yes—
690C2×D11C2×AGL(1,ℤ/8)12yes—
691C2×D11#57512yes—
692C4×C11—21no—
693C4×C11—21no—
694C4×C11—42no—
695C4×C11—42no—
696C4×C11—42no—
697C4×C11#53412yes—
698C4×C11C2×H(5,𝔽2)12yes—
699Dic11—21no—
700Dic11—21no—
701Dic11—21no—
702Dic11—21no—
703Dic11—42no—
704Dic11—42no—
705C25—111no—
706C25—221no—
707C2×#41—112no—
708C2×#41—112no—
709C2×#41—221no—
710C2×#41—221no—
711C2×#41—444no—
712C22×Q8—111no—
713C22×D4—21no—
714C22×D4—112no—
715C22×D4—112no—
716C22×D4—111no—
717C22×D4—111no—
718C22×D4—221no—
719C22×D4—221no—
720C22×D4—221no—
721C22×D4—221no—
722C22×D4—221no—
723C22×D4—221no—
724C22×D4—222no—
725C22×D4—222no—
726C22×D4—222no—
727C22×D4—222no—
728C22×D4—221no—
729C22×D4—221no—
730C22×D4—221no—
731C22×D4—444no—
732C22×D4—448no—
733C22×D4C22×D1111yescharacteristic
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—221no—
748C23×C4—221no—
749C23×C4—444no—
750C23×C4C22×D1111yescharacteristic
751AGL(1,ℤ/8)—444no—
752AGL(1,ℤ/8)—444no—
753C2×SD16—114no—
754C2×SD16—114no—
755C2×D8—114no—
756C2×D8—114no—
757C2×M16—112no—
758C2×M16—114no—
759C2×M16—444no—
760C2×M16C22×D1112yes—
761C22×C8—114no—
762#123—222no—
763#123—222no—
764#123—222no—
765#123—222no—
766C22⋊Q8—112no—
767C22⋊Q8—112no—
768C22⋊Q8—112no—
769C22⋊Q8—112no—
770C22⋊Q8—221no—
771C22⋊Q8—221no—
772C22⋊Q8—221no—
773C22⋊Q8—221no—
774#121—21no—
775#121—21no—
776#121—112no—
777#121—112no—
778#121—112no—
779#121—112no—
780#121—112no—
781#121—112no—
782#121—112no—
783#121—112no—
784#121—112no—
785#121—112no—
786#121—222no—
787#121—222no—
788#121—222no—
789#121—222no—
790#121—221no—
791#121—221no—
792#121—221no—
793#121—221no—
794#121—221no—
795#121—221no—
796#121—221no—
797#121—221no—
798#121—222no—
799#121—222no—
800#121—222no—
801#121—222no—
802#121—221no—
803#121—221no—
804#121C22×D1112yes—
805#121C22×D1112yes—
806#120—222no—
807#120—222no—
808#120—222no—
809#120—222no—
810C4×D4—222no—
811C4×D4—222no—
812C4×D4—222no—
813C4×D4—222no—
814C4×D4—222no—
815C4×D4—222no—
816C4×D4—222no—
817C4×D4—222no—
818#117—21no—
819#117—21no—
820#117C22×D1112yes—
821#117C22×D1112yescomplemented
822C2×C4⋊C4—111no—
823C2×C4⋊C4—112no—
824C2×C4⋊C4—112no—
825C2×C4⋊C4—221no—
826C2×C4⋊C4—221no—
827C2×C4⋊C4—221no—
828C2×C4⋊C4—221no—
829C2×C4⋊C4—221no—
830C2×C4⋊C4C22×D1111yescharacteristic
831C2×C4⋊C4C22×D1111yescharacteristic, complemented
832C2×C4⋊C4C22×D1111yescharacteristic, complemented
833C2×C22⋊C4—21no—
834C2×C22⋊C4—21no—
835C2×C22⋊C4—222no—
836C2×C22⋊C4—222no—
837C2×C22⋊C4—222no—
838C2×C22⋊C4—222no—
839C2×C22⋊C4—221no—
840C2×C22⋊C4—221no—
841C2×C22⋊C4—221no—
842C2×C22⋊C4—221no—
843C2×C22⋊C4—221no—
844C2×C22⋊C4—221no—
845C2×C22⋊C4—221no—
846C2×C42—21no—
847#107—114no—
848#107C22×D1114yescomplemented
849#106—114no—
850#106C22×D1114yescomplemented
851#103—114no—
852#103—114no—
853#102—114no—
854#102—114no—
855#102—114no—
856#102—114no—
857#102C22×D1114yescomplemented
858#102C22×D1114yescomplemented
859C22⋊C8—112no—
860C22⋊C8—112no—
861C22⋊C8—114no—
862C22⋊C8—114no—
863C22⋊C8C22×D1112yescomplemented
864C22⋊C8C22×D1112yescomplemented
865C2×C11—22no—
866C2×C11—22no—
867C2×C11—41no—
868C2×C11—82no—
869C2×C11C2×#53411yescharacteristic
870C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
871C2×C11C2×#57511yescharacteristic
872D11—22no—
873D11—22no—
874D11—22no—
875D11—41no—
876D11—82no—
877D11—82no—
878C24—21no—
879C24—111no—
880C24—111no—
881C24—111no—
882C24—111no—
883C24—111no—
884C24—111no—
885C24—224no—
886C24—222no—
887C24—222no—
888C24—221no—
889C24—221no—
890C24—442no—
891C24—442no—
892C24—444no—
893C24—444no—
894C24—444no—
895C24D4×D1111yescharacteristic
896#41—224no—
897#41—224no—
898#41—442no—
899#41—442no—
900#41—444no—
901#41—444no—
902C2×Q8—112no—
903C2×Q8—221no—
904C2×Q8—442no—
905C2×D4—22no—
906C2×D4—22no—
907C2×D4—21no—
908C2×D4—24no—
909C2×D4—44no—
910C2×D4—112no—
911C2×D4—112no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—222no—
915C2×D4—222no—
916C2×D4—222no—
917C2×D4—222no—
918C2×D4—222no—
919C2×D4—222no—
920C2×D4—222no—
921C2×D4—222no—
922C2×D4—222no—
923C2×D4—222no—
924C2×D4—222no—
925C2×D4—222no—
926C2×D4—221no—
927C2×D4—221no—
928C2×D4—224no—
929C2×D4—442no—
930C2×D4—444no—
931C2×D4—444no—
932C2×D4—444no—
933C2×D4—444no—
934C2×D4—444no—
935C2×D4—444no—
936C2×D4—444no—
937C2×D4—444no—
938C2×D4—448no—
939C2×D4—448no—
940C2×D4—448no—
941C2×D4—448no—
942C2×D4—444no—
943C2×D4—444no—
944C2×D4—444no—
945C2×D4C23×D1112yes—
946C22×C4—24no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—111no—
951C22×C4—111no—
952C22×C4—111no—
953C22×C4—111no—
954C22×C4—111no—
955C22×C4—111no—
956C22×C4—111no—
957C22×C4—111no—
958C22×C4—111no—
959C22×C4—111no—
960C22×C4—111no—
961C22×C4—111no—
962C22×C4—111no—
963C22×C4—111no—
964C22×C4—111no—
965C22×C4—111no—
966C22×C4—111no—
967C22×C4—111no—
968C22×C4—111no—
969C22×C4—111no—
970C22×C4—111no—
971C22×C4—111no—
972C22×C4—222no—
973C22×C4—222no—
974C22×C4—224no—
975C22×C4—224no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—222no—
979C22×C4—222no—
980C22×C4—442no—
981C22×C4—442no—
982C22×C4—442no—
983C22×C4—442no—
984C22×C4—442no—
985C22×C4—442no—
986C22×C4—442no—
987C22×C4—442no—
988C22×C4—442no—
989C22×C4—442no—
990C22×C4—444no—
991C22×C4—444no—
992C22×C4—442no—
993C22×C4D4×D1111yescharacteristic
994C22×C4D4×D1111yescharacteristic
995C22×C4D4×D1111yescharacteristic
996C22×C4C23×D1111yescharacteristic
997C22×C4C23×D1111yescharacteristic
998C22×C4C23×D1111yescharacteristic
999SD16—444no—
1000SD16—444no—
1001D8—444no—
1002D8—444no—
1003M16—24no—
1004M16—224no—
1005M16—444no—
1006C2×C8—114no—
1007C2×C8—444no—
1008C2×C8C23×D1114yes—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—112no—
1013C4⋊C4—222no—
1014C4⋊C4—222no—
1015C4⋊C4—222no—
1016C4⋊C4—222no—
1017C4⋊C4—222no—
1018C4⋊C4—222no—
1019C4⋊C4—221no—
1020C4⋊C4C23×D1112yes—
1021C4⋊C4C23×D1112yes—
1022C4⋊C4C23×D1112yes—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—222no—
1028C22⋊C4—222no—
1029C22⋊C4—222no—
1030C22⋊C4—222no—
1031C22⋊C4—222no—
1032C22⋊C4—222no—
1033C22⋊C4—222no—
1034C22⋊C4—222no—
1035C22⋊C4—222no—
1036C22⋊C4—222no—
1037C22⋊C4—222no—
1038C22⋊C4—222no—
1039C22⋊C4—222no—
1040C22⋊C4—222no—
1041C42—22no—
1042C42—22no—
1043C11#6075011yescharacteristic, complemented, Sylow
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—111no—
1052C23—111no—
1053C23—111no—
1054C23—114no—
1055C23—111no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23—441no—
1069C23—441no—
1070C23—441no—
1071C23—441no—
1072C23—441no—
1073C23—441no—
1074C23—441no—
1075C23—442no—
1076C23—442no—
1077C23—442no—
1078C23—442no—
1079C23—444no—
1080C23—444no—
1081C23—4416no—
1082C23—444no—
1083C23—444no—
1084C23—444no—
1085C23—444no—
1086C23—442no—
1087C23—442no—
1088C23—8816no—
1089C23C2×D4×D1111yescharacteristic
1090C23C2×D4×D1111yescharacteristic
1091C23C2×D4×D1111yescharacteristic
1092Q8—222no—
1093Q8—222no—
1094Q8—442no—
1095D4—24no—
1096D4—44no—
1097D4—44no—
1098D4—42no—
1099D4—222no—
1100D4—222no—
1101D4—224no—
1102D4—442no—
1103D4—444no—
1104D4—444no—
1105D4—444no—
1106D4—444no—
1107D4—444no—
1108D4—444no—
1109D4—444no—
1110D4—444no—
1111D4—444no—
1112D4—444no—
1113D4—444no—
1114D4—444no—
1115D4—444no—
1116D4—444no—
1117D4—442no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—111no—
1130C2×C4—111no—
1131C2×C4—111no—
1132C2×C4—111no—
1133C2×C4—222no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—222no—
1137C2×C4—222no—
1138C2×C4—222no—
1139C2×C4—222no—
1140C2×C4—222no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—441no—
1146C2×C4—441no—
1147C2×C4—441no—
1148C2×C4—441no—
1149C2×C4—441no—
1150C2×C4—441no—
1151C2×C4—441no—
1152C2×C4—441no—
1153C2×C4—444no—
1154C2×C4—444no—
1155C2×C4—444no—
1156C2×C4—441no—
1157C2×C4—441no—
1158C2×C4—441no—
1159C2×C4—441no—
1160C2×C4—442no—
1161C2×C4—442no—
1162C2×C4—444no—
1163C2×C4C2×D4×D1111yescharacteristic
1164C2×C4C2×D4×D1111yescharacteristic
1165C2×C4C2×D4×D1111yescharacteristic
1166C2×C4#6704214yes—
1167C2×C4C24×D1111yescharacteristic
1168C8—24no—
1169C8—224no—
1170C22—21no—
1171C22—21no—
1172C22—21no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—21no—
1177C22—44no—
1178C22—42no—
1179C22—42no—
1180C22—42no—
1181C22—84no—
1182C22—112no—
1183C22—112no—
1184C22—112no—
1185C22—228no—
1186C22—221no—
1187C22—221no—
1188C22—221no—
1189C22—221no—
1190C22—221no—
1191C22—221no—
1192C22—221no—
1193C22—221no—
1194C22—221no—
1195C22—444no—
1196C22—444no—
1197C22—444no—
1198C22—444no—
1199C22—444no—
1200C22—442no—
1201C22—442no—
1202C22—442no—
1203C22—442no—
1204C22—442no—
1205C22—442no—
1206C22—884no—
1207C22—884no—
1208C22—888no—
1209C22—888no—
1210C22#1062318412yes—
1211C22D11×AGL(1,ℤ/8)12yes—
1212C22C22×D4×D1111yescharacteristic
1213C4—21no—
1214C4—21no—
1215C4—42no—
1216C4—42no—
1217C4—42no—
1218C4—221no—
1219C4—221no—
1220C4—221no—
1221C4—221no—
1222C4—442no—
1223C4—442no—
1224C4#1062318412yes—
1225C4C2×#6704212yes—
1226C2—22no—
1227C2—22no—
1228C2—41no—
1229C2—82no—
1230C2—222no—
1231C2—222no—
1232C2—222no—
1233C2—441no—
1234C2—882no—
1235C2—882no—
1236C2C2×#1062318411yescharacteristic
1237C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1238C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3094C2
socleC22×C11C23×D4
hypercenter#3094D11
hypocenterC11#60750
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. C2×#10623055C2semidirect
2. C2×D11×#121C2semidirect
3. #13079434C2semidirect
4. #13079424C2semidirect
5. #13079415C2semidirect
6. #13079385C2semidirect
7. #13079375C2semidirect
8. #13079366C2semidirect
9. #13078556C2semidirect
10. #13078542C2semidirect
11. #13078236C2semidirect
12. #13078233C2semidirect
13. #13077870C2semidirect
14. #13077866C2semidirect
15. #13077845C2semidirect
16. D11×#407C2semidirect
17. C11×#3094C2semidirect
19. C22×D4×D11C22semidirect
20. C22×#4339C22semidirect
23. C2×C11×#117C22semidirect
25. C2×#66991C22semidirect
26. C2×#66985C22semidirect
28. C2×#66961C22semidirect
29. C2×M16×D11C22semidirect
36. D11×#121C22semidirect
37. D11×#121C22semidirect
43. #10623055C22semidirect
44. #10623055C22semidirect
45. #10623055C22semidirect
46. C2×#66950C22semidirect
47. C2×#66950C22semidirect
48. C2×#66948C22semidirect
49. C2×#66948C22semidirect
50. C2×#66948C22semidirect
51. C2×C4⋊C4×D11C22semidirect
58. C11×#482C22semidirect
59. C11×#481C22semidirect
60. C11×#480C22semidirect
61. C11×#428C22semidirect
62. C11×#418C22semidirect
63. C11×#407C22semidirect
64. #10622820C22semidirect
65. #10622746C22semidirect
66. #10622739C22semidirect
67. #10622653C22semidirect
68. #10622650C22semidirect
69. #10622649C22semidirect
70. #10622616C22semidirect
71. #10622614C22semidirect
72. #10622608C22semidirect
73. #10622581C22semidirect
74. #10622580C22semidirect
75. #10622579C22semidirect
76. #10622499C22semidirect
77. #10622497C22semidirect
78. #10622496C22semidirect
79. #10622495C22semidirect
80. #10622478C22semidirect
81. #10622477C22semidirect
82. #10622476C22semidirect
83. #10622475C22semidirect
84. #10622395C22semidirect
85. #10622393C22semidirect
86. #10622391C22semidirect
87. #10622389C22semidirect
88. #10622389C22semidirect
89. #10622388C22semidirect
90. #10622386C22semidirect
91. #10622386C22semidirect
92. #10622351C22semidirect
93. #10622347C22semidirect
94. #10622345C22semidirect
95. #10622339C22semidirect
96. #10622339C22semidirect
97. D11×C22⋊C8C22semidirect
98. D11×C22⋊C8C22semidirect
123. C2×#4339C23semidirect
128. C22×D44C23semidirect
144. C22×Dic22C23semidirect
153. C11×#117C23semidirect
155. C2×C11×C4⋊C4C23semidirect
156. C2×C11×C4⋊C4C23semidirect
169. C2×#4324C23semidirect
171. C2×#4323C23semidirect
189. C2×D88C23semidirect
190. C2×#4314C23semidirect
191. C2×#4313C23semidirect
192. C2×C8×D11C23semidirect
199. #66950C23semidirect
200. #66950C23semidirect
211. #66948C23semidirect
212. #66948C23semidirect
241. C11×#107C23semidirect
242. C11×#106C23semidirect
243. C11×#102C23semidirect
244. C11×#102C23semidirect
245. C11×C22⋊C8C23semidirect
246. C11×C22⋊C8C23semidirect
247. C22⋊(C11⋊C8)C23semidirect
248. C22⋊(C11⋊C8)C23semidirect
249. #66885C23semidirect
252. #66880C23semidirect
253. #66874C23semidirect
254. #66873C23semidirect
255. #66873C23semidirect
256. #66873C23semidirect
257. #66872C23semidirect
258. #66871C23semidirect
434. #3094D11semidirect
485. C22×D11AGL(1,ℤ/8)semidirect
605. C2×#117C2×D11semidirect
611. #482C2×D11semidirect
614. #481C2×D11semidirect
617. #480C2×D11semidirect
637. #428C2×D11semidirect
639. #418C2×D11semidirect
646. #407C2×D11semidirect
821. #117C22×D11semidirect
831. C2×C4⋊C4C22×D11semidirect
832. C2×C4⋊C4C22×D11semidirect
848. #107C22×D11semidirect
850. #106C22×D11semidirect
857. #102C22×D11semidirect
858. #102C22×D11semidirect
863. C22⋊C8C22×D11semidirect
864. C22⋊C8C22×D11semidirect
1043. C11#60750semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×D11×#1212
#130794342
#130794242
#130794152
#130793852
#130793752
#130793662
#130785562
#130785422
#130782362
#130782332
#130778702
#130778662
#130778452
D11×#4072
C11×#30942
#6075011