Finite Group Databasebeta

← #14921950

Subgroups — #14921950

Order 2816.

2992 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623131C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13072855C212yesmaximal, complemented
4#13072679C212yesmaximal, complemented
5#13072520C212yesmaximal, complemented
6#13072489C211yesmaximal, characteristic, complemented
7#13072397C211yesmaximal, characteristic, complemented
8#13072343C211yesmaximal, characteristic, complemented
9#13072266C211yesmaximal, characteristic, complemented
10#13072193C211yesmaximal, characteristic, complemented
11#13072071C212yesmaximal, complemented
12#13072069C211yesmaximal, characteristic, complemented
13#13071968C211yesmaximal, characteristic
14#13071874C212yesmaximal, complemented
15#13071859C212yesmaximal, complemented
16#13071155C211yesmaximal, characteristic, complemented
17#13071146C211yesmaximal, characteristic, complemented
18#13071122C211yesmaximal, characteristic, complemented
19#13071121C212yesmaximal, complemented
20#13071078C211yesmaximal, characteristic, complemented
21#13070996C212yesmaximal, complemented
22C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
23C11×#2420C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2212yes—
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×#66990C2212yes—
29C2×#66989C2211yescharacteristic
30C2×#66988C2212yescomplemented
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2212yescomplemented
33C2×#66983C2211yescharacteristic
34C2×C4×C22⋊D11C2212yes—
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×#66977C2211yescharacteristic, complemented
37C22×C4×Dic11C2211yescharacteristic, complemented
38#10623131—28no—
39C4×D4×D11—28no—
40C2×#66950C2211yescharacteristic
41C2×#66946C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×#66943C2211yescharacteristic, complemented
44C2×#66940C2211yescharacteristic, complemented
45C2×(C22⋊D11)⋊C4C2212yes—
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×(C22⋊D11)⋊C4C2212yescomplemented
49C2×C22⋊C4×D11C2212yes—
50C2×#66932C2212yescomplemented
51C2×#66930C2212yescomplemented
52C2×#66930C2212yescomplemented
53C2×#66928C2211yescharacteristic
54C2×C4×D44C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56C11×#397C2212yescomplemented
57C11×#394C2212yescomplemented
58C11×#390C2211yescharacteristic
59C11×#389C2211yescharacteristic, complemented
60C11×#386C2212yescomplemented
61C11×#382C2211yescharacteristic, complemented
62C11×#381C2212yescomplemented
63C11×#380C2211yescharacteristic, complemented
64C4×C11×C22⋊C4C2211yescharacteristic, complemented
65#10622836C2212yes—
66#10622834C2211yescharacteristic
67#10622824C2212yescomplemented
68#10622823C2212yescomplemented
69#10622607C2212yescomplemented
70#10622605C2212yescomplemented
71#10622602C2212yes—
72#10622601C2211yescharacteristic
73#10622601C2211yescharacteristic
74#10622600C2211yescharacteristic
75C4⋊C4×Dic11C2212yescomplemented
76C4⋊C4×Dic11C2211yescharacteristic, complemented
77#10622587C2211yescharacteristic, complemented
78#10622586C2211yescharacteristic, complemented
79#10622586C2211yescharacteristic, complemented
80#10622574C2212yes—
81#10622574C2212yes—
82#10622572C2212yes—
83#10622572C2212yescomplemented
84#10622571C2212yescomplemented
85#10622569C2212yes—
86#10622569C2212yescomplemented
87#10622568C2212yes—
88#10622568C2212yes—
89#10622568C2212yes—
90#10622565C2212yescomplemented
91#10622565C2212yescomplemented
92#10622561C2212yescomplemented
93#10622558C2212yescomplemented
94#10622557C2212yescomplemented
95C22⋊C4×Dic11C2212yescomplemented
96C22⋊C4×Dic11C2211yescharacteristic, complemented
97C22⋊C4×Dic11C2211yescharacteristic, complemented
98C4×(C2×D11)⋊C4C2211yescharacteristic
99C4×Dic11⋊C4C2211yescharacteristic, complemented
100C42×Dic11C2211yescharacteristic, complemented
101#10622542C2211yescharacteristic, complemented
102#10622541C2211yescharacteristic, complemented
103#10622288C2212yescomplemented
104#10622282C2212yescomplemented
105#10622282C2212yescomplemented
106#10622282C2212yescomplemented
107#10622281C2212yes—
108#10622281C2212yescomplemented
109#10622280C2212yes—
110#10622280C2212yes—
111#10622280C2212yescomplemented
112#10622280C2212yescomplemented
113#10622279C2212yes—
114#10622279C2211yescharacteristic
115#10622279C2211yescharacteristic
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622279C2212yescomplemented
119#10622271C2212yescomplemented
120#10622270C2212yescomplemented
121#10622270C2212yescomplemented
122#10622267C2212yescomplemented
123#10622262C2211yescharacteristic, complemented
124#10622262C2211yescharacteristic, complemented
125C24×D11C2312yes—
126C22×D4×C11C2312yes—
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2312yes—
136C2×D4×D11—24no—
137C2×D4×D11—24no—
138C2×D4×D11—24no—
139C22×D44C2311yescharacteristic
140C22×C4×D11—28no—
141C22×C4×D11—28no—
142C22×C4×D11—44no—
143C22×C4×D11C2312yes—
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2311yescharacteristic
150C11×#121—24no—
151C4×D4×C11—24no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172#66990—28no—
173#66989—24no—
174#66988—28no—
175D4×Dic11—28no—
176D4×Dic11D418yescomplemented
177#66983—24no—
178C4×C22⋊D11—24no—
179C4×C22⋊D11—28no—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×C4⋊Dic11C2312yes—
195C2×C4⋊Dic11C2312yes—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198#66977—24no—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2311yescharacteristic
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×C4×Dic11—24no—
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223#66950—24no—
224#66946—24no—
225C4⋊C4×D11—24no—
226#66943—24no—
227#66940—24no—
228(C22⋊D11)⋊C4—24no—
229(C22⋊D11)⋊C4—28no—
230(C22⋊D11)⋊C4—24no—
231(C22⋊D11)⋊C4—44no—
232C22⋊C4×D11—28no—
233#66932—28no—
234#66930—28no—
235#66930—44no—
236#66928—24no—
237C4×D44—24no—
238C42×D11—24no—
239C11×#95C2311yescharacteristic
240C11×#95C2311yescharacteristic
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#34700—111nomaximal, Sylow
259C24×C11C2412yes—
260C24×C11C2411yescharacteristic
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—24no—
265C23×D11—24no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11C2412yes—
269C23×D11C2411yescharacteristic
270C2×D4×C11—24no—
271C2×D4×C11—24no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—42no—
275C2×D4×C11C2×D414yes—
276C22×C4×C11—24no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—24no—
281C22×C4×C11—42no—
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C2×C22⋊D11—24no—
292C2×C22⋊D11—24no—
293C2×C22⋊D11—24no—
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—42no—
299C2×C22⋊D11#4114yes—
300C22×Dic11—24no—
301C22×Dic11—24no—
302C22×Dic11—22no—
303C22×Dic11—22no—
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—41no—
308C22×Dic11C2×D418yes—
309C22×Dic11C2412yes—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319D4×D11—232no—
320C2×D44—22no—
321C2×D44—22no—
322C2×D44#4114yes—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—22no—
326C2×C4×D11—24no—
327C2×C4×D11—24no—
328C2×C4×D11—24no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—22no—
332C2×C4×D11—24no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—24no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
338C2×C4×D11—41no—
339C2×C4×D11—432no—
340C2×C4×D11#4114yes—
341C2×C4×D11#4114yes—
342C2×Dic22—22no—
343C2×Dic22—22no—
344C2×Dic22—22no—
345C11×C4⋊C4—22no—
346C11×C4⋊C4—22no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—42no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—24no—
351C11×C22⋊C4—22no—
352C11×C22⋊C4—22no—
353C11×C22⋊C4—42no—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C42×C11—22no—
357C42×C11—22no—
358C22⋊Dic11—24no—
359C22⋊Dic11—22no—
360C22⋊Dic11—24no—
361C22⋊Dic11—24no—
362C22⋊Dic11—24no—
363C22⋊Dic11—42no—
364C22⋊Dic11C2×D418yes—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—24no—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—22no—
372(C2×D11)⋊C4—24no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—24no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4—42no—
379C4⋊Dic11—24no—
380C4⋊Dic11—24no—
381C4⋊Dic11—22no—
382C4⋊Dic11C2×D414yes—
383Dic11⋊C4—24no—
384Dic11⋊C4—24no—
385Dic11⋊C4—24no—
386Dic11⋊C4—24no—
387Dic11⋊C4—22no—
388Dic11⋊C4—22no—
389Dic11⋊C4—22no—
390Dic11⋊C4—42no—
391Dic11⋊C4—42no—
392Dic11⋊C4—42no—
393C4×Dic11—22no—
394C4×Dic11—22no—
395C4×Dic11—22no—
396C4×Dic11—24no—
397C4×Dic11—22no—
398C4×Dic11—22no—
399C4×Dic11—22no—
400C4×Dic11—22no—
401C4×Dic11—24no—
402C4×Dic11—22no—
403C4×Dic11—22no—
404C4×Dic11—41no—
405C4×Dic11C2×D414yes—
406C2×#529—111no—
407C22×C4×D4—111no—
408#2480—112no—
409#2468—112no—
410#2457—112no—
411#2454—111no—
412#2447—111no—
413#2442—111no—
414#2435—111no—
415#2427—111no—
416#2420D1111yescharacteristic, complemented
417#2418—112no—
418#2417—111no—
419#2408—111no—
420#2395—112no—
421#2392—112no—
422C4×#124—111no—
423C4×C22⋊Q8—111no—
424C4×#121—111no—
425C4×#120—112no—
426#2293—111no—
427#2280—112no—
428C42×D4—111no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—22no—
432C23×C11—21no—
433C23×C11—22no—
434C23×C11—21no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—21no—
441C23×C11C22×D414yes—
442C23×C11C2×#4112yes—
443C23×C11C2511yescharacteristic
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—216no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—48no—
456C22×D11—48no—
457C22×D11—48no—
458C22×D11—48no—
459C22×D11—48no—
460C22×D11—48no—
461C22×D11C2×#4114yes—
462C22×D11C2×#4112yes—
463C22×D11C2×#4112yes—
464C22×D11C2×#4112yes—
465D4×C11—28no—
466D4×C11—48no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—48no—
491C2×C4×C11—44no—
492C2×C4×C11C22×D412yes—
493C2×C4×C11C2×#4112yes—
494C2×C4×C11C2×#4112yes—
495C2×C4×C11C2×#4112yes—
496C22⋊D11—216no—
497C22⋊D11—28no—
498C22⋊D11—48no—
499C2×Dic11—21no—
500C2×Dic11—21no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—22no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—21no—
507C2×Dic11—216no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—44no—
524C2×Dic11—44no—
525C2×Dic11C22×D412yes—
526C2×Dic11C22×D414yes—
527C2×Dic11C22×D412yes—
528C2×Dic11C2×#4112yes—
529C2×Dic11C2×#4112yes—
530C2×Dic11C2×#4112yes—
531C2×Dic11H(5,𝔽2)12yes—
532D44—28no—
533C4×D11—28no—
534C4×D11—28no—
535C4×D11—48no—
536C4×D11—44no—
537C4×D11—48no—
538C4×D11—48no—
539Dic22—44no—
540C23×D4—111no—
541C24×C4—112no—
542#529—228no—
543C2×#126—112no—
544C2×#125—111no—
545C2×#124—111no—
546C2×#124—111no—
547C2×#123—112no—
548C2×C22⋊Q8—111no—
549C2×C22⋊Q8—111no—
550C2×#121—111no—
551C2×#121C2×D1111yescharacteristic
552C2×#120—112no—
553C2×C4×Q8—111no—
554C2×C4×D4—111no—
555C2×C4×D4—112no—
556C2×C4×D4—112no—
557C2×C4×D4—111no—
558C2×C4×D4—111no—
559C2×C4×D4—112no—
560C2×C4×D4—111no—
561C2×C4×D4—111no—
562C2×C4×D4—112no—
563C2×C4×D4—111no—
564C2×C4×D4—228no—
565C2×C4×D4C2×D1111yescharacteristic
566C2×#117—112no—
567C2×#117—112no—
568C22×C4⋊C4—111no—
569C22×C22⋊C4—112no—
570C22×C42—111no—
571C22×C42—111no—
572#400—112no—
573#399—112no—
574#398—112no—
575#398—112no—
576#397—112no—
577#397—112no—
578#397—112no—
579#397C2×D1112yescomplemented
580#396—112no—
581#396—112no—
582#394—112no—
583#394—112no—
584#394—112no—
585#394—112no—
586#394C2×D1112yescomplemented
587#392—112no—
588#391—111no—
589#391—111no—
590#390—111no—
591#390—111no—
592#390—111no—
593#390C2×D1111yescharacteristic
594#389—111no—
595#389—111no—
596#389—111no—
597#389C2×D1111yescharacteristic, complemented
598#388—112no—
599#388—112no—
600#388—112no—
601#388—112no—
602#388—112no—
603#387—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#386C2×D1112yescomplemented
608#385—112no—
609#385—112no—
610#385—112no—
611#385—112no—
612#382C2×D1111yescharacteristic, complemented
613#381—112no—
614#381C2×D1112yescomplemented
615#380—111no—
616#380—112no—
617#380—112no—
618#380—112no—
619#380—112no—
620#380C2×D1111yescharacteristic, complemented
621#379—112no—
622#379—112no—
623#379—112no—
624C4×C4⋊C4—112no—
625C4×C4⋊C4—111no—
626C4×C4⋊C4—111no—
627C4×C4⋊C4—111no—
628C4×C4⋊C4—111no—
629C4×C22⋊C4—111no—
630C4×C22⋊C4—112no—
631C4×C22⋊C4—111no—
632C4×C22⋊C4—111no—
633C4×C22⋊C4—111no—
634C4×C22⋊C4—111no—
635C4×C22⋊C4—112no—
636C4×C22⋊C4—112no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4C2×D1111yescharacteristic, complemented
640C43—111no—
641C22×C11—24no—
642C22×C11—22no—
643C22×C11—24no—
644C22×C11—22no—
645C22×C11—24no—
646C22×C11—22no—
647C22×C11—41no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—41no—
651C22×C11—41no—
652C22×C11—42no—
653C22×C11—41no—
654C22×C11—42no—
655C22×C11C23×D411yescharacteristic
656C22×C11C22×#4111yescharacteristic
657C22×C11C22×#4111yescharacteristic
658C22×C11C22×#4111yescharacteristic
659C22×C11C22×#4111yescharacteristic
660C22×C11C2×H(5,𝔽2)11yescharacteristic
661C22×C11#58511yescharacteristic
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—24no—
669C2×D11—24no—
670C2×D11—24no—
671C2×D11—432no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11#52914yescomplemented
677C4×C11—22no—
678C4×C11—41no—
679C4×C11—42no—
680C4×C11—42no—
681C4×C11—42no—
682C4×C11—41no—
683C4×C11—41no—
684C4×C11—41no—
685C4×C11#52514yes—
686Dic11—22no—
687Dic11—22no—
688Dic11—24no—
689Dic11—22no—
690Dic11—42no—
691Dic11—41no—
692Dic11—41no—
693Dic11—41no—
694Dic11—42no—
695Dic11#54614yes—
696C25—112no—
697C22×Q8—111no—
698C22×D4—111no—
699C22×D4—112no—
700C22×D4—112no—
701C22×D4—111no—
702C22×D4—224no—
703C22×D4—224no—
704C22×D4—224no—
705C22×D4C22×D1112yes—
706C22×D4C22×D1111yescharacteristic
707C23×C4—112no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—111no—
712C23×C4—112no—
713C23×C4—111no—
714C23×C4—112no—
715C23×C4—112no—
716C23×C4—228no—
717C23×C4—228no—
718C23×C4—444no—
719C23×C4C22×D1111yescharacteristic
720C23×C4C22×D1112yes—
721#126—228no—
722#125—224no—
723#124—224no—
724#124—224no—
725#123—228no—
726C22⋊Q8—224no—
727C22⋊Q8—224no—
728#121—24no—
729#121—224no—
730#120—228no—
731C4×Q8—224no—
732C4×D4—24no—
733C4×D4—118no—
734C4×D4—224no—
735C4×D4—224no—
736C4×D4—228no—
737C4×D4—224no—
738C4×D4—224no—
739C4×D4—228no—
740C4×D4—224no—
741C4×D4—228no—
742C4×D4—444no—
743#117—228no—
744#117—444no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—112no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—111no—
751C2×C4⋊C4—111no—
752C2×C4⋊C4—111no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—224no—
760C2×C4⋊C4C22×D1111yescharacteristic
761C2×C4⋊C4C22×D1111yescharacteristic
762C2×C4⋊C4C22×D1111yescharacteristic
763C2×C4⋊C4C22×D1112yes—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—111no—
774C2×C22⋊C4—111no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—228no—
786C2×C22⋊C4C22×D1112yes—
787C2×C22⋊C4C22×D1112yes—
788C2×C22⋊C4C22×D1111yescharacteristic
789C2×C22⋊C4C22×D1111yescharacteristic
790C2×C22⋊C4C22×D1112yes—
791C2×C22⋊C4C22×D1112yes—
792C2×C22⋊C4C22×D1112yes—
793C2×C42—111no—
794C2×C42—111no—
795C2×C42—111no—
796C2×C42—112no—
797C2×C42—112no—
798C2×C42—111no—
799C2×C42—111no—
800C2×C42—111no—
801C2×C42—111no—
802C2×C42—111no—
803C2×C42—111no—
804C2×C42—111no—
805C2×C42—111no—
806C2×C42—224no—
807C2×C42—224no—
808C2×C42C22×D1111yescharacteristic
809C2×C42C22×D1111yescharacteristic
810#95—111no—
811#95—111no—
812#95—111no—
813#95—111no—
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—112no—
823#95C22×D1111yescharacteristic
824#95C22×D1111yescharacteristic
825#95C22×D1112yes—
826#95C22×D1112yes—
827#95C22×D1112yes—
828#95C22×D1112yes—
829C2×C11—44no—
830C2×C11—42no—
831C2×C11C2×#52511yescharacteristic
832C2×C11C2×#52911yescharacteristic
833C2×C11#346011yescharacteristic
834C2×C11C2×#54611yescharacteristic
835C2×C11D4×#4111yescharacteristic
836C2×C11#347511yescharacteristic
837C2×C11#348111yescharacteristic
838D11—24no—
839D11—44no—
840C24—111no—
841C24—112no—
842C24—224no—
843C24—224no—
844C24—224no—
845C24—224no—
846C24—224no—
847C24—442no—
848C24—442no—
849C24C23×D1112yes—
850C24C23×D1111yescharacteristic
851C2×Q8—222no—
852C2×Q8—222no—
853C2×Q8—222no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—42no—
859C2×D4—114no—
860C2×D4—114no—
861C2×D4—224no—
862C2×D4—2232no—
863C2×D4—222no—
864C2×D4—222no—
865C2×D4—224no—
866C2×D4—224no—
867C2×D4—224no—
868C2×D4—224no—
869C2×D4—222no—
870C2×D4—222no—
871C2×D4—442no—
872C2×D4D4×D1114yes—
873C22×C4—24no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—24no—
878C22×C4—42no—
879C22×C4—111no—
880C22×C4—118no—
881C22×C4—111no—
882C22×C4—111no—
883C22×C4—111no—
884C22×C4—112no—
885C22×C4—114no—
886C22×C4—114no—
887C22×C4—112no—
888C22×C4—111no—
889C22×C4—111no—
890C22×C4—112no—
891C22×C4—111no—
892C22×C4—222no—
893C22×C4—222no—
894C22×C4—222no—
895C22×C4—224no—
896C22×C4—224no—
897C22×C4—224no—
898C22×C4—224no—
899C22×C4—224no—
900C22×C4—222no—
901C22×C4—224no—
902C22×C4—224no—
903C22×C4—224no—
904C22×C4—222no—
905C22×C4—222no—
906C22×C4—222no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—224no—
912C22×C4—442no—
913C22×C4—442no—
914C22×C4—441no—
915C22×C4—4432no—
916C22×C4—441no—
917C22×C4C23×D1111yescharacteristic
918C22×C4C23×D1112yes—
919C22×C4C23×D1111yescharacteristic
920C22×C4C23×D1112yes—
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1112yes—
923C22×C4C23×D1111yescharacteristic
924C22×C4C23×D1111yescharacteristic
925C22×C4C23×D1111yescharacteristic
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—42no—
930C4⋊C4—114no—
931C4⋊C4—224no—
932C4⋊C4—224no—
933C4⋊C4—224no—
934C4⋊C4—224no—
935C4⋊C4—222no—
936C4⋊C4—222no—
937C4⋊C4—224no—
938C4⋊C4—224no—
939C4⋊C4—222no—
940C4⋊C4—222no—
941C4⋊C4—442no—
942C4⋊C4—442no—
943C4⋊C4—442no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—118no—
952C22⋊C4—224no—
953C22⋊C4—224no—
954C22⋊C4—224no—
955C22⋊C4—222no—
956C22⋊C4—222no—
957C22⋊C4—222no—
958C22⋊C4—224no—
959C22⋊C4—224no—
960C22⋊C4—224no—
961C22⋊C4—224no—
962C22⋊C4—224no—
963C22⋊C4—224no—
964C22⋊C4—222no—
965C22⋊C4—224no—
966C22⋊C4—224no—
967C22⋊C4—224no—
968C22⋊C4—442no—
969C22⋊C4—442no—
970C22⋊C4—442no—
971C22⋊C4—442no—
972C42—22no—
973C42—22no—
974C42—114no—
975C42—222no—
976C42—222no—
977C42—222no—
978C42—222no—
979C42—224no—
980C42—222no—
981C42—224no—
982C42—222no—
983C42—222no—
984C42—222no—
985C42—222no—
986C42—441no—
987C11#3470011yescharacteristic, complemented, Sylow
988C23—21no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—21no—
994C23—22no—
995C23—22no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—21no—
1000C23—112no—
1001C23—112no—
1002C23—112no—
1003C23—114no—
1004C23—2216no—
1005C23—221no—
1006C23—221no—
1007C23—221no—
1008C23—221no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—222no—
1015C23—448no—
1016C23—448no—
1017C23—448no—
1018C23—448no—
1019C23—448no—
1020C23—448no—
1021C23C2×D4×D1114yes—
1022C23#41×D1112yes—
1023C23C24×D1111yescharacteristic
1024Q8—444no—
1025D4—28no—
1026D4—48no—
1027D4—228no—
1028D4—2216no—
1029D4—228no—
1030D4—448no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—48no—
1055C2×C4—44no—
1056C2×C4—112no—
1057C2×C4—112no—
1058C2×C4—112no—
1059C2×C4—112no—
1060C2×C4—114no—
1061C2×C4—112no—
1062C2×C4—112no—
1063C2×C4—228no—
1064C2×C4—2216no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—221no—
1068C2×C4—221no—
1069C2×C4—222no—
1070C2×C4—221no—
1071C2×C4—222no—
1072C2×C4—221no—
1073C2×C4—228no—
1074C2×C4—221no—
1075C2×C4—221no—
1076C2×C4—222no—
1077C2×C4—221no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—221no—
1085C2×C4—222no—
1086C2×C4—221no—
1087C2×C4—221no—
1088C2×C4—221no—
1089C2×C4—448no—
1090C2×C4—448no—
1091C2×C4—448no—
1092C2×C4—444no—
1093C2×C4—444no—
1094C2×C4—444no—
1095C2×C4C2×D4×D1112yes—
1096C2×C4#41×D1112yes—
1097C2×C4#41×D1112yes—
1098C2×C4#41×D1112yes—
1099C22—22no—
1100C22—22no—
1101C22—24no—
1102C22—22no—
1103C22—24no—
1104C22—24no—
1105C22—42no—
1106C22—42no—
1107C22—41no—
1108C22—42no—
1109C22—42no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—114no—
1114C22—222no—
1115C22—222no—
1116C22—222no—
1117C22—222no—
1118C22—222no—
1119C22—222no—
1120C22—224no—
1121C22—224no—
1122C22—224no—
1123C22—4432no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22C22×D4×D1111yescharacteristic
1129C22C2×#41×D1111yescharacteristic
1130C22C2×#41×D1111yescharacteristic
1131C22C2×#41×D1111yescharacteristic
1132C22C2×#41×D1111yescharacteristic
1133C22D11×H(5,𝔽2)11yescharacteristic
1134C22#1062345511yescharacteristic
1135C4—22no—
1136C4—41no—
1137C4—41no—
1138C4—42no—
1139C4—42no—
1140C4—41no—
1141C4—42no—
1142C4—41no—
1143C4—114no—
1144C4—222no—
1145C4—224no—
1146C4—222no—
1147C4—222no—
1148C4—442no—
1149C4—441no—
1150C4—441no—
1151C4—441no—
1152C4—442no—
1153C4#1062318714yes—
1154C2—44no—
1155C2—42no—
1156C2—224no—
1157C2—444no—
1158C2C2×#1062318711yescharacteristic
1159C2D11×#52911yescharacteristic
1160C2#1308203111yescharacteristic
1161C2D11×#54611yescharacteristic
1162C2#1308210011yescharacteristic
1163C2#1308217311yescharacteristic
1164C2#1308222311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2420C2
prime radical#13071968C2
hypercenter#2420D11
hypocenterC11#34700
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2420

Complements

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

NH ≅ G/Ntype
1. C2×#10623131C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13072855C2semidirect
4. #13072679C2semidirect
5. #13072520C2semidirect
6. #13072489C2semidirect
7. #13072397C2semidirect
8. #13072343C2semidirect
9. #13072266C2semidirect
10. #13072193C2semidirect
11. #13072071C2semidirect
12. #13072069C2semidirect
14. #13071874C2semidirect
15. #13071859C2semidirect
16. #13071155C2semidirect
17. #13071146C2semidirect
18. #13071122C2semidirect
19. #13071121C2semidirect
20. #13071078C2semidirect
21. #13070996C2semidirect
22. C4×(C22⋊D11)⋊C4C2semidirect
23. C11×#2420C2semidirect
30. C2×#66988C22semidirect
32. C2×D4×Dic11C22semidirect
36. C2×#66977C22semidirect
37. C22×C4×Dic11C22semidirect
43. C2×#66943C22semidirect
44. C2×#66940C22semidirect
48. C2×(C22⋊D11)⋊C4C22semidirect
50. C2×#66932C22semidirect
51. C2×#66930C22semidirect
52. C2×#66930C22semidirect
56. C11×#397C22semidirect
57. C11×#394C22semidirect
59. C11×#389C22semidirect
60. C11×#386C22semidirect
61. C11×#382C22semidirect
62. C11×#381C22semidirect
63. C11×#380C22semidirect
64. C4×C11×C22⋊C4C22semidirect
67. #10622824C22semidirect
68. #10622823C22semidirect
69. #10622607C22semidirect
70. #10622605C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. C4⋊C4×Dic11C22semidirect
77. #10622587C22semidirect
78. #10622586C22semidirect
79. #10622586C22semidirect
83. #10622572C22semidirect
84. #10622571C22semidirect
86. #10622569C22semidirect
90. #10622565C22semidirect
91. #10622565C22semidirect
92. #10622561C22semidirect
93. #10622558C22semidirect
94. #10622557C22semidirect
95. C22⋊C4×Dic11C22semidirect
96. C22⋊C4×Dic11C22semidirect
97. C22⋊C4×Dic11C22semidirect
99. C4×Dic11⋊C4C22semidirect
100. C42×Dic11C22semidirect
101. #10622542C22semidirect
102. #10622541C22semidirect
103. #10622288C22semidirect
104. #10622282C22semidirect
105. #10622282C22semidirect
106. #10622282C22semidirect
108. #10622281C22semidirect
111. #10622280C22semidirect
112. #10622280C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
118. #10622279C22semidirect
119. #10622271C22semidirect
120. #10622270C22semidirect
121. #10622270C22semidirect
122. #10622267C22semidirect
123. #10622262C22semidirect
124. #10622262C22semidirect
176. D4×Dic11D4semidirect
416. #2420D11semidirect
579. #397C2×D11semidirect
586. #394C2×D11semidirect
597. #389C2×D11semidirect
607. #386C2×D11semidirect
612. #382C2×D11semidirect
614. #381C2×D11semidirect
620. #380C2×D11semidirect
639. C4×C22⋊C4C2×D11semidirect
676. C2×D11#529semidirect
987. C11#34700semidirect

Maximal subgroups

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

subgroupindex
C2×#106231312
C2×C4×D4×D112
#130728552
#130726792
#130725202
#130724892
#130723972
#130723432
#130722662
#130721932
#130720712
#130720692
#130719682
#130718742
#130718592
#130711552
#130711462
#130711222
#130711212
#130710782
#130709962
C4×(C22⋊D11)⋊C42
C11×#24202
#3470011