Finite Group Databasebeta

← #14914039

Subgroups — #14914039

Order 2816.

3190 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#123C211yesmaximal, characteristic
2C2×#10623076C211yesmaximal, characteristic
3C22×#66945C211yesmaximal, characteristic, complemented
4#13071615C212yesmaximal, complemented
5#13071611C212yesmaximal, complemented
6#13071607C212yesmaximal, complemented
7#13071603C212yesmaximal, complemented
8#13071484C212yesmaximal, complemented
9#13071482C212yesmaximal, complemented
10#13071464C212yesmaximal, complemented
11#13071463C212yesmaximal, complemented
12#13071288C211yesmaximal, characteristic, complemented
13#13071285C211yesmaximal, characteristic, complemented
14#13071282C211yesmaximal, characteristic, complemented
15#13071227C211yesmaximal, characteristic, complemented
16#13071190C211yesmaximal, characteristic
17#13071141C211yesmaximal, characteristic, complemented
18C4×#66939C211yesmaximal, characteristic, complemented
19#13071135C211yesmaximal, characteristic, complemented
20C4×#66988C211yesmaximal, characteristic, complemented
21D11×#381C211yesmaximal, characteristic, complemented
22#13070968C211yesmaximal, characteristic, complemented
23C11×#2322C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#123C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic, complemented
29C2×#66988C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C2×#66982C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic, complemented
38C22×C4×Dic11C2211yescharacteristic, complemented
39C22×C4×Dic11C2211yescharacteristic, complemented
40D11×#123C4116yescomplemented
41#10623076—28no—
42C2×#66947C2212yes—
43C2×#66946C2211yescharacteristic
44C2×#66945—28no—
45C2×#66945C2212yes—
46C2×#66945C2212yes—
47C2×#66945C2211yescharacteristic
48C2×#66945C2212yescomplemented
49C2×#66945C2212yescomplemented
50C2×C4⋊C4×D11C2212yes—
51C2×#66939C2211yescharacteristic
52C2×#66936C2212yes—
53C2×(C22⋊D11)⋊C4C2211yescharacteristic
54C2×(C22⋊D11)⋊C4C2211yescharacteristic
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C22⋊C4×D11C2211yescharacteristic
58C2×C22⋊C4×D11C2212yes—
59C2×C22⋊C4×D11C2211yescharacteristic
60C2×C4×D44C2211yescharacteristic
61C2×#66925C2211yescharacteristic
62C11×#389C2212yescomplemented
63C11×#388C2212yescomplemented
64C11×#387C2212yescomplemented
65C11×#386C2211yescharacteristic
66C11×#385C2211yescharacteristic, complemented
67C11×#385C2212yescomplemented
68C11×#381C2211yescharacteristic, complemented
69C4×C11×C22⋊C4C2211yescharacteristic, complemented
70#10622833C2211yescharacteristic
71#10622826C2211yescharacteristic
72#10622824C2211yescharacteristic, complemented
73#10622823C2211yescharacteristic, complemented
74C4×C22⋊Dic11C2212yescomplemented
75C4×C22⋊Dic11C2211yescharacteristic, complemented
76#10622603C2212yescomplemented
77#10622603C2212yescomplemented
78#10622602C2212yescomplemented
79#10622602C2212yescomplemented
80#10622600C2212yes—
81#10622598C2212yescomplemented
82#10622594C2212yescomplemented
83#10622591C2212yescomplemented
84#10622591C2212yescomplemented
85C4⋊C4×Dic11C2212yescomplemented
86#10622585C2212yescomplemented
87#10622571C2211yescharacteristic
88#10622569C2212yes—
89#10622568C2212yes—
90#10622564C2212yescomplemented
91#10622563C2211yescharacteristic, complemented
92#10622563C2212yescomplemented
93#10622559C2211yescharacteristic, complemented
94#10622558C2212yescomplemented
95#10622557C2212yescomplemented
96#10622556C2211yescharacteristic, complemented
97#10622556C2211yescharacteristic, complemented
98C22⋊C4×Dic11C2211yescharacteristic, complemented
99C22⋊C4×Dic11C2212yescomplemented
100C22⋊C4×Dic11C2211yescharacteristic, complemented
101C4×(C2×D11)⋊C4C2212yes—
102C4×(C2×D11)⋊C4C2212yescomplemented
103C4×(C2×D11)⋊C4C2212yescomplemented
104C4×C4⋊Dic11C2212yescomplemented
105C4×Dic11⋊C4C2212yescomplemented
106#10622283C2212yescomplemented
107#10622283C2212yescomplemented
108#10622281C2212yescomplemented
109#10622281C2212yescomplemented
110#10622280C2212yes—
111#10622279C2212yes—
112#10622279C2212yescomplemented
113#10622279C2212yescomplemented
114#10622278C2212yes—
115#10622277C2212yes—
116#10622277C2212yes—
117#10622277C2212yes—
118D11×#95C2212yescomplemented
119D11×#95C2212yescomplemented
120#10622268C2212yescomplemented
121#10622268C2212yescomplemented
122#10622267C2212yescomplemented
123#10622266C2212yescomplemented
124#10622262C2212yescomplemented
125#10622260C2212yescomplemented
126C24×D11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11C2×C418yes—
142C22×D44C2311yescharacteristic
143C22×C4×D11—24no—
144C22×C4×D11—24no—
145C22×C4×D11C2×C418yescomplemented
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C11×#123C2×C418yescomplemented
156C4×D4×C11—24no—
157C2×C11×C4⋊C4—24no—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2312yes—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2311yescharacteristic
177#66988C2×C418yescomplemented
178D4×Dic11—24no—
179#66982C2×C418yescomplemented
180C4×C22⋊D11—24no—
181C4×C22⋊D11—24no—
182C2×(C2×D11)⋊C4—24no—
183C2×(C2×D11)⋊C4—24no—
184C2×(C2×D11)⋊C4D418yes—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×C4⋊Dic11—24no—
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2312yes—
205C2×C4⋊Dic11C2312yes—
206C2×C4⋊Dic11C2312yes—
207C2×Dic11⋊C4C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×C4×Dic11—24no—
214C2×C4×Dic11—24no—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225#66947C2×C4116yescomplemented
226#66946—24no—
227#66945—28no—
228#66945—28no—
229#66945—28no—
230#66945—28no—
231#66945—24no—
232C4⋊C4×D11C2×C4116yescomplemented
233#66939C2×C418yescomplemented
234#66936C2×C4116yescomplemented
235(C22⋊D11)⋊C4—24no—
236(C22⋊D11)⋊C4—24no—
237C22⋊C4×D11—24no—
238C22⋊C4×D11—24no—
239C22⋊C4×D11—24no—
240C22⋊C4×D11C2×C418yescomplemented
241C22⋊C4×D11C2×C4116yescomplemented
242C4×D44—24no—
243#66925—24no—
244C11×#95C2312yes—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34199—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C24×C11C2411yescharacteristic
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—42no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11—42no—
273C23×D11C22×C414yes—
274C23×D11C22×C414yes—
275C23×D11C2×D414yes—
276C23×D11#4114yes—
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C23×D11C2411yescharacteristic
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11C22×C414yes—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—22no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11C22×C414yes—
291C22×C4×C11C2×D414yes—
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11C22×C414yes—
306C2×C22⋊D11C22×C414yes—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—22no—
310C22×Dic11—22no—
311C22×Dic11—42no—
312C22×Dic11—42no—
313C22×Dic11—42no—
314C22×Dic11C22×C414yes—
315C22×Dic11C2×D414yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2412yes—
320C22×Dic11C2412yes—
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325D4×D11—232no—
326C2×D44—22no—
327C2×D44—22no—
328C2×D44C22×C414yes—
329C2×C4×D11—22no—
330C2×C4×D11—232no—
331C2×C4×D11—22no—
332C2×C4×D11—24no—
333C2×C4×D11—24no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—24no—
340C2×C4×D11—22no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11C22×C418yes—
350C2×C4×D11C22×C418yes—
351C2×C4×D11C22×C414yes—
352C2×C4×D11C22×C418yes—
353C11×C4⋊C4—24no—
354C11×C4⋊C4—24no—
355C11×C4⋊C4—22no—
356C11×C4⋊C4—42no—
357C11×C4⋊C4C22×C418yes—
358C11×C22⋊C4—22no—
359C11×C22⋊C4—22no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—42no—
362C11×C22⋊C4C22×C418yes—
363C11×C22⋊C4C22×C414yes—
364C42×C11—22no—
365C42×C11—42no—
366C22⋊Dic11—22no—
367C22⋊Dic11—22no—
368C22⋊Dic11—22no—
369C22⋊Dic11—42no—
370C22⋊Dic11C22×C418yes—
371C22⋊Dic11C22×C414yes—
372(C2×D11)⋊C4—22no—
373(C2×D11)⋊C4—22no—
374(C2×D11)⋊C4—22no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—42no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4C22×C418yes—
382(C2×D11)⋊C4C22×C418yes—
383(C2×D11)⋊C4C22×C418yes—
384(C2×D11)⋊C4C2×D414yes—
385(C2×D11)⋊C4C2×D414yes—
386(C2×D11)⋊C4C2×D414yes—
387(C2×D11)⋊C4C2×D414yes—
388C4⋊Dic11—22no—
389C4⋊Dic11—24no—
390C4⋊Dic11—24no—
391C4⋊Dic11—42no—
392C4⋊Dic11C22×C418yes—
393Dic11⋊C4—22no—
394Dic11⋊C4—22no—
395Dic11⋊C4—42no—
396Dic11⋊C4—42no—
397Dic11⋊C4C22×C418yes—
398Dic11⋊C4C22×C418yes—
399C4×Dic11—22no—
400C4×Dic11—22no—
401C4×Dic11—24no—
402C4×Dic11—24no—
403C4×Dic11—22no—
404C4×Dic11—24no—
405C4×Dic11—24no—
406C4×Dic11—42no—
407C4×Dic11—42no—
408C4×Dic11—42no—
409C22×#123—111no—
410C2×#518—111no—
411C22×#117—111no—
412#2359—112no—
413#2359—112no—
414#2359—112no—
415#2359—112no—
416#2344—112no—
417#2344—112no—
418#2342—112no—
419#2342—112no—
420#2322—111no—
421#2322—111no—
422#2322—111no—
423#2322D1111yescharacteristic, complemented
424#2315—111no—
425#2308—111no—
426C4×#123—111no—
427C4×#123—111no—
428C4×#123—111no—
429C4×#123—111no—
430C2×#381—111no—
431#2273—111no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—21no—
435C23×C11—21no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11C23×C412yes—
439C23×C11C23×C412yes—
440C23×C11C22×D412yes—
441C23×C11C2×#4112yes—
442C23×C11C2511yescharacteristic
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—28no—
452C22×D11—48no—
453C22×D11—44no—
454C22×D11—44no—
455C22×D11—48no—
456C22×D11—48no—
457C22×D11—82no—
458C22×D11—82no—
459C22×D11—84no—
460C22×D11C4×D4116yes—
461C22×D11C23×C412yes—
462C22×D11C23×C412yes—
463C22×D11C23×C412yes—
464C22×D11C22×D412yes—
465C22×D11C22×D412yes—
466C22×D11C2×#4112yes—
467C22×D11C2×#4112yes—
468D4×C11—28no—
469C2×C4×C11—28no—
470C2×C4×C11—21no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—21no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—44no—
489C2×C4×C11—44no—
490C2×C4×C11—82no—
491C2×C4×C11C23×C412yes—
492C2×C4×C11C23×C414yes—
493C2×C4×C11C23×C414yes—
494C2×C4×C11C22×D412yes—
495C2×C4×C11C22×D412yes—
496C22⋊D11—28no—
497C22⋊D11—28no—
498C2×Dic11—28no—
499C2×Dic11—22no—
500C2×Dic11—21no—
501C2×Dic11—22no—
502C2×Dic11—21no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—44no—
518C2×Dic11—44no—
519C2×Dic11—82no—
520C2×Dic11C23×C412yes—
521C2×Dic11C23×C414yes—
522C2×Dic11C23×C414yes—
523C2×Dic11C22×D412yes—
524C2×Dic11C22×D412yes—
525D44—28no—
526C4×D11—216no—
527C4×D11—216no—
528C4×D11—28no—
529C4×D11—48no—
530C4×D11—82no—
531C4×D11—82no—
532C4×D11—82no—
533C4×D11—82no—
534C4×D11—84no—
535C23×D4—111no—
536C24×C4—111no—
537C2×#123—111no—
538C2×#123—111no—
539C2×#123—1116no—
540C2×#123—112no—
541C2×#123—112no—
542C2×#123—111no—
543C2×#123C2×D1111yescharacteristic
544#518—228no—
545C2×C4×D4—111no—
546C2×C4×D4—111no—
547C2×C4×D4—111no—
548C2×C4×D4—111no—
549C2×C4×D4—111no—
550C2×C4×D4—111no—
551C2×C4×D4—111no—
552C2×C4×D4C2×D1111yescharacteristic
553C2×#117—112no—
554C2×#117—112no—
555C2×#117—111no—
556C2×#117—112no—
557C2×#117—112no—
558C2×#117—111no—
559C2×#117—228no—
560C22×C4⋊C4—112no—
561C22×C4⋊C4—111no—
562C22×C4⋊C4C2×D1111yescharacteristic, complemented
563C22×C22⋊C4—111no—
564C22×C22⋊C4—111no—
565C22×C22⋊C4—112no—
566C22×C22⋊C4—111no—
567C22×C22⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C42—111no—
572C22×C42—111no—
573#389—112no—
574#389—112no—
575#389—112no—
576#389C2×D1112yescomplemented
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388C2×D1112yescomplemented
585#387—112no—
586#387—112no—
587#387—112no—
588#387—112no—
589#387—112no—
590#387—112no—
591#387—112no—
592#387C2×D1112yescomplemented
593#386—111no—
594#386—111no—
595#386—111no—
596#386—112no—
597#386—112no—
598#386C2×D1111yescharacteristic
599#385—111no—
600#385—112no—
601#385—112no—
602#385—111no—
603#385—111no—
604#385—112no—
605#385—112no—
606#385—112no—
607#385C2×D1111yescharacteristic, complemented
608#385C2×D1112yescomplemented
609#381—111no—
610#381—111no—
611#381—111no—
612#381—112no—
613#381—112no—
614#381—112no—
615#381C2×D1111yescharacteristic, complemented
616#380—112no—
617#380—112no—
618#379—112no—
619C4×C4⋊C4—112no—
620C4×C4⋊C4—112no—
621C4×C4⋊C4—112no—
622C4×C4⋊C4—112no—
623C4×C22⋊C4—111no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—111no—
626C4×C22⋊C4—111no—
627C4×C22⋊C4—112no—
628C4×C22⋊C4—112no—
629C4×C22⋊C4—112no—
630C4×C22⋊C4—112no—
631C4×C22⋊C4—112no—
632C4×C22⋊C4—112no—
633C4×C22⋊C4—112no—
634C4×C22⋊C4C2×D1111yescharacteristic, complemented
635C2×#95—112no—
636C2×#95—112no—
637C22×C11—24no—
638C22×C11—22no—
639C22×C11—22no—
640C22×C11—24no—
641C22×C11—22no—
642C22×C11—24no—
643C22×C11—41no—
644C22×C11—41no—
645C22×C11—42no—
646C22×C11C2×C4×D414yes—
647C22×C11C24×C411yescharacteristic
648C22×C11C23×D411yescharacteristic
649C22×C11C22×#4111yescharacteristic
650C22×C11#58512yes—
651C22×C11#58512yes—
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—22no—
657C2×D11—22no—
658C2×D11—24no—
659C2×D11—24no—
660C2×D11—22no—
661C2×D11—24no—
662C2×D11—416no—
663C2×D11—41no—
664C2×D11—41no—
665C2×D11—42no—
666C2×D11—88no—
667C2×D11C2×C4×D414yes—
668C2×D11C2×C4×D414yes—
669C4×C11—24no—
670C4×C11—22no—
671C4×C11—24no—
672C4×C11—22no—
673C4×C11—22no—
674C4×C11—42no—
675C4×C11—41no—
676C4×C11—41no—
677C4×C11—42no—
678Dic11—24no—
679Dic11—22no—
680Dic11—24no—
681Dic11—22no—
682Dic11—22no—
683Dic11—41no—
684Dic11—41no—
685Dic11—42no—
686Dic11—42no—
687C25—111no—
688C25—111no—
689C22×D4—111no—
690C22×D4—111no—
691C22×D4—118no—
692C22×D4—111no—
693C22×D4—224no—
694C22×D4—224no—
695C22×D4C22×D1111yescharacteristic
696C23×C4—111no—
697C23×C4—111no—
698C23×C4—118no—
699C23×C4—112no—
700C23×C4—111no—
701C23×C4—112no—
702C23×C4—112no—
703C23×C4—111no—
704C23×C4—111no—
705C23×C4—111no—
706C23×C4—111no—
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—112no—
710C23×C4—224no—
711C23×C4—224no—
712C23×C4C22×D1111yescharacteristic
713C23×C4C22×D1111yescharacteristic
714C23×C4C22×D1111yescharacteristic
715C23×C4C22×D1111yescharacteristic
716#123—118no—
717#123—118no—
718#123—1116no—
719#123—1116no—
720#123—118no—
721#123C4×D1118yescomplemented
722C4×D4—24no—
723C4×D4—224no—
724C4×D4—224no—
725C4×D4—224no—
726C4×D4—224no—
727C4×D4—224no—
728C4×D4—224no—
729C4×D4—224no—
730#117—224no—
731#117—228no—
732#117—228no—
733#117—228no—
734#117—228no—
735#117—224no—
736C2×C4⋊C4—24no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—1116no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—111no—
744C2×C4⋊C4—111no—
745C2×C4⋊C4—111no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—112no—
749C2×C4⋊C4—224no—
750C2×C4⋊C4C22×D1112yes—
751C2×C4⋊C4C22×D1112yes—
752C2×C4⋊C4C22×D1111yescharacteristic
753C2×C4⋊C4C22×D1112yes—
754C2×C4⋊C4C22×D1112yes—
755C2×C22⋊C4—111no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—118no—
758C2×C22⋊C4—111no—
759C2×C22⋊C4—111no—
760C2×C22⋊C4—111no—
761C2×C22⋊C4—111no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—1116no—
766C2×C22⋊C4—118no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—111no—
771C2×C22⋊C4—111no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—111no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—224no—
781C2×C22⋊C4—224no—
782C2×C22⋊C4—224no—
783C2×C22⋊C4—224no—
784C2×C22⋊C4—224no—
785C2×C22⋊C4C22×D1111yescharacteristic
786C2×C22⋊C4C22×D1111yescharacteristic
787C2×C22⋊C4C22×D1111yescharacteristic
788C2×C22⋊C4C22×D1112yes—
789C2×C22⋊C4C22×D1111yescharacteristic
790C2×C22⋊C4C22×D1112yes—
791C2×C42—112no—
792C2×C42—112no—
793C2×C42—112no—
794C2×C42—112no—
795C2×C42—111no—
796C2×C42—111no—
797C2×C42—111no—
798C2×C42—112no—
799C2×C42—112no—
800C2×C42—112no—
801C2×C42—224no—
802C2×C42—224no—
803C2×C42C22×D1111yescharacteristic
804C2×C42C22×D1112yes—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—112no—
812#95—112no—
813#95—112no—
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95C22×D1112yes—
821#95C22×D1112yes—
822#95C22×D1112yes—
823#95C22×D1112yes—
824#95C22×D1112yes—
825C2×C11—24no—
826C2×C11—42no—
827C2×C11C22×C4×D411yescharacteristic
828C2×C11#342812yes—
829C2×C11#348511yescharacteristic
830C2×C11#348511yescharacteristic
831C2×C11#349112yes—
832D11—24no—
833D11—24no—
834D11—42no—
835C24—111no—
836C24—111no—
837C24—114no—
838C24—114no—
839C24—114no—
840C24—111no—
841C24—114no—
842C24—222no—
843C24—222no—
844C24—442no—
845C24—442no—
846C24—442no—
847C24—442no—
848C24C23×D1111yescharacteristic
849C24C23×D1111yescharacteristic
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—114no—
853C2×D4—114no—
854C2×D4—114no—
855C2×D4—222no—
856C2×D4—222no—
857C2×D4—2232no—
858C2×D4—222no—
859C2×D4—222no—
860C2×D4—222no—
861C2×D4—222no—
862C2×D4C2×C4×D1114yes—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—114no—
871C22×C4—112no—
872C22×C4—112no—
873C22×C4—111no—
874C22×C4—111no—
875C22×C4—111no—
876C22×C4—114no—
877C22×C4—118no—
878C22×C4—114no—
879C22×C4—118no—
880C22×C4—118no—
881C22×C4—112no—
882C22×C4—111no—
883C22×C4—111no—
884C22×C4—112no—
885C22×C4—222no—
886C22×C4—224no—
887C22×C4—224no—
888C22×C4—222no—
889C22×C4—2232no—
890C22×C4—224no—
891C22×C4—224no—
892C22×C4—222no—
893C22×C4—222no—
894C22×C4—222no—
895C22×C4—224no—
896C22×C4—222no—
897C22×C4—222no—
898C22×C4—222no—
899C22×C4—222no—
900C22×C4—222no—
901C22×C4—442no—
902C22×C4—442no—
903C22×C4—442no—
904C22×C4—442no—
905C22×C4—442no—
906C22×C4—442no—
907C22×C4—442no—
908C22×C4—442no—
909C22×C4—442no—
910C22×C4—442no—
911C22×C4—442no—
912C22×C4C2×C4×D1114yes—
913C22×C4D4×D1114yes—
914C22×C4C23×D1112yes—
915C22×C4C23×D1111yescharacteristic
916C22×C4C23×D1111yescharacteristic
917C22×C4C23×D1112yes—
918C22×C4C23×D1112yes—
919C22×C4C23×D1111yescharacteristic
920C22×C4C23×D1112yes—
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—22no—
926C4⋊C4—42no—
927C4⋊C4—118no—
928C4⋊C4—118no—
929C4⋊C4—118no—
930C4⋊C4—224no—
931C4⋊C4—224no—
932C4⋊C4—222no—
933C4⋊C4—222no—
934C4⋊C4—222no—
935C4⋊C4—442no—
936C4⋊C4—442no—
937C4⋊C4—442no—
938C4⋊C4C2×C4×D1118yes—
939C22⋊C4—22no—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—42no—
943C22⋊C4—114no—
944C22⋊C4—118no—
945C22⋊C4—118no—
946C22⋊C4—118no—
947C22⋊C4—118no—
948C22⋊C4—114no—
949C22⋊C4—114no—
950C22⋊C4—114no—
951C22⋊C4—114no—
952C22⋊C4—222no—
953C22⋊C4—222no—
954C22⋊C4—222no—
955C22⋊C4—224no—
956C22⋊C4—224no—
957C22⋊C4—224no—
958C22⋊C4—222no—
959C22⋊C4—222no—
960C22⋊C4—222no—
961C22⋊C4—222no—
962C22⋊C4—442no—
963C22⋊C4—442no—
964C22⋊C4—442no—
965C22⋊C4C2×C4×D1114yes—
966C22⋊C4C2×C4×D1118yes—
967C42—22no—
968C42—42no—
969C42—224no—
970C42—224no—
971C42—222no—
972C42—222no—
973C42—224no—
974C42—224no—
975C42—222no—
976C42—442no—
977C42—442no—
978C42—442no—
979C11#3419911yescharacteristic, complemented, Sylow
980C23—22no—
981C23—22no—
982C23—21no—
983C23—21no—
984C23—22no—
985C23—22no—
986C23—112no—
987C23—112no—
988C23—112no—
989C23—112no—
990C23—112no—
991C23—112no—
992C23—1116no—
993C23—112no—
994C23—228no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—221no—
1000C23—221no—
1001C23—222no—
1002C23—222no—
1003C23—444no—
1004C23—444no—
1005C23—448no—
1006C23—448no—
1007C23—448no—
1008C23—882no—
1009C23—882no—
1010C23—884no—
1011C23C22×C4×D1112yes—
1012C23C22×C4×D1112yes—
1013C23C2×D4×D1112yes—
1014C23#41×D1112yes—
1015C23C24×D1111yescharacteristic
1016D4—28no—
1017D4—228no—
1018D4—228no—
1019D4—228no—
1020C2×C4—28no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—44no—
1040C2×C4—44no—
1041C2×C4—82no—
1042C2×C4—114no—
1043C2×C4—114no—
1044C2×C4—112no—
1045C2×C4—112no—
1046C2×C4—112no—
1047C2×C4—2216no—
1048C2×C4—2216no—
1049C2×C4—228no—
1050C2×C4—228no—
1051C2×C4—222no—
1052C2×C4—221no—
1053C2×C4—222no—
1054C2×C4—221no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—221no—
1061C2×C4—221no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—448no—
1070C2×C4—444no—
1071C2×C4—444no—
1072C2×C4—882no—
1073C2×C4—882no—
1074C2×C4—882no—
1075C2×C4—882no—
1076C2×C4—884no—
1077C2×C4—882no—
1078C2×C4C22×C4×D1114yes—
1079C2×C4C22×C4×D1114yes—
1080C2×C4C22×C4×D1112yes—
1081C2×C4C2×D4×D1112yes—
1082C2×C4C2×D4×D1112yes—
1083C22—22no—
1084C22—22no—
1085C22—24no—
1086C22—24no—
1087C22—22no—
1088C22—24no—
1089C22—41no—
1090C22—41no—
1091C22—42no—
1092C22—114no—
1093C22—114no—
1094C22—222no—
1095C22—222no—
1096C22—222no—
1097C22—222no—
1098C22—224no—
1099C22—224no—
1100C22—224no—
1101C22—224no—
1102C22—222no—
1103C22—224no—
1104C22—4416no—
1105C22—441no—
1106C22—441no—
1107C22—442no—
1108C22—888no—
1109C22C4×D4×D1114yes—
1110C22C23×C4×D1111yescharacteristic
1111C22C22×D4×D1111yescharacteristic
1112C22C2×#41×D1111yescharacteristic
1113C22#1062345512yes—
1114C22#1062345712yes—
1115C4—22no—
1116C4—22no—
1117C4—24no—
1118C4—22no—
1119C4—24no—
1120C4—42no—
1121C4—41no—
1122C4—41no—
1123C4—42no—
1124C4—222no—
1125C4—222no—
1126C4—224no—
1127C4—222no—
1128C4—224no—
1129C4—441no—
1130C4—442no—
1131C4—441no—
1132C4—442no—
1133C2—24no—
1134C2—42no—
1135C2—224no—
1136C2—224no—
1137C2—442no—
1138C2C2×C4×D4×D1111yescharacteristic
1139C2#1308181612yes—
1140C2#1308225711yescharacteristic
1141C2#1308225911yescharacteristic
1142C2#1308231012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2322C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenter#2322D11
hypocenterC11#34199
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2322

Complements

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

NH ≅ G/Ntype
3. C22×#66945C2semidirect
4. #13071615C2semidirect
5. #13071611C2semidirect
6. #13071607C2semidirect
7. #13071603C2semidirect
8. #13071484C2semidirect
9. #13071482C2semidirect
10. #13071464C2semidirect
11. #13071463C2semidirect
12. #13071288C2semidirect
13. #13071285C2semidirect
14. #13071282C2semidirect
15. #13071227C2semidirect
17. #13071141C2semidirect
18. C4×#66939C2semidirect
19. #13071135C2semidirect
20. C4×#66988C2semidirect
21. D11×#381C2semidirect
22. #13070968C2semidirect
23. C11×#2322C2semidirect
28. C22×C11×C4⋊C4C22semidirect
37. C22×C4⋊Dic11C22semidirect
38. C22×C4×Dic11C22semidirect
39. C22×C4×Dic11C22semidirect
40. D11×#123C4semidirect
48. C2×#66945C22semidirect
49. C2×#66945C22semidirect
62. C11×#389C22semidirect
63. C11×#388C22semidirect
64. C11×#387C22semidirect
66. C11×#385C22semidirect
67. C11×#385C22semidirect
68. C11×#381C22semidirect
69. C4×C11×C22⋊C4C22semidirect
72. #10622824C22semidirect
73. #10622823C22semidirect
74. C4×C22⋊Dic11C22semidirect
75. C4×C22⋊Dic11C22semidirect
76. #10622603C22semidirect
77. #10622603C22semidirect
78. #10622602C22semidirect
79. #10622602C22semidirect
81. #10622598C22semidirect
82. #10622594C22semidirect
83. #10622591C22semidirect
84. #10622591C22semidirect
85. C4⋊C4×Dic11C22semidirect
86. #10622585C22semidirect
90. #10622564C22semidirect
91. #10622563C22semidirect
92. #10622563C22semidirect
93. #10622559C22semidirect
94. #10622558C22semidirect
95. #10622557C22semidirect
96. #10622556C22semidirect
97. #10622556C22semidirect
98. C22⋊C4×Dic11C22semidirect
99. C22⋊C4×Dic11C22semidirect
100. C22⋊C4×Dic11C22semidirect
102. C4×(C2×D11)⋊C4C22semidirect
103. C4×(C2×D11)⋊C4C22semidirect
104. C4×C4⋊Dic11C22semidirect
105. C4×Dic11⋊C4C22semidirect
106. #10622283C22semidirect
107. #10622283C22semidirect
108. #10622281C22semidirect
109. #10622281C22semidirect
112. #10622279C22semidirect
113. #10622279C22semidirect
118. D11×#95C22semidirect
119. D11×#95C22semidirect
120. #10622268C22semidirect
121. #10622268C22semidirect
122. #10622267C22semidirect
123. #10622266C22semidirect
124. #10622262C22semidirect
125. #10622260C22semidirect
145. C22×C4×D11C2×C4semidirect
155. C11×#123C2×C4semidirect
177. #66988C2×C4semidirect
179. #66982C2×C4semidirect
225. #66947C2×C4semidirect
232. C4⋊C4×D11C2×C4semidirect
233. #66939C2×C4semidirect
234. #66936C2×C4semidirect
240. C22⋊C4×D11C2×C4semidirect
241. C22⋊C4×D11C2×C4semidirect
423. #2322D11semidirect
562. C22×C4⋊C4C2×D11semidirect
576. #389C2×D11semidirect
584. #388C2×D11semidirect
592. #387C2×D11semidirect
607. #385C2×D11semidirect
608. #385C2×D11semidirect
615. #381C2×D11semidirect
634. C4×C22⋊C4C2×D11semidirect
721. #123C4×D11semidirect
979. C11#34199semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1232
C2×#106230762
C22×#669452
#130716152
#130716112
#130716072
#130716032
#130714842
#130714822
#130714642
#130714632
#130712882
#130712852
#130712822
#130712272
#130711902
#130711412
C4×#669392
#130711352
C4×#669882
D11×#3812
#130709682
C11×#23222
#3419911