Finite Group Databasebeta

← #14913340

Subgroups — #14913340

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic
2C2×C4×#4341C211yesmaximal, characteristic, complemented
3C22×#66945C211yesmaximal, characteristic, complemented
4#13071659C211yesmaximal, characteristic, complemented
5#13071650C211yesmaximal, characteristic, complemented
6#13071645C211yesmaximal, characteristic, complemented
7#13071642C211yesmaximal, characteristic, complemented
8#13071636C211yesmaximal, characteristic, complemented
9#13071621C211yesmaximal, characteristic, complemented
10#13071619C211yesmaximal, characteristic, complemented
11#13071611C212yesmaximal, complemented
12#13071607C212yesmaximal, complemented
13#13071596C212yesmaximal, complemented
14#13071593C212yesmaximal, complemented
15#13071103C211yesmaximal, characteristic, complemented
16#13071097C211yesmaximal, characteristic, complemented
17#13071076C212yesmaximal, complemented
18#13071056C212yesmaximal, complemented
19#13071052C212yesmaximal, complemented
20C4×D4×Dic11C212yesmaximal, complemented
21C4×#66945C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2361C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66990C2212yes—
32C2×D4×Dic11C2212yes—
33C2×D4×Dic11C2212yes—
34C2×D4×Dic11C2211yescharacteristic, complemented
35C2×C4×C22⋊D11C2212yes—
36C22×(C2×D11)⋊C4C2212yes—
37C22×C4⋊Dic11C2211yescharacteristic
38C2×#66977C2211yescharacteristic
39C22×C4×Dic11C2212yes—
40C22×C4×Dic11C2212yescomplemented
41#10623137C4116yescomplemented
42C4×#4341—28no—
43C2×#66950C2211yescharacteristic
44C2×#66945—28no—
45C2×#66945C2211yescharacteristic
46C2×#66945C2211yescharacteristic
47C2×#66945C2212yes—
48C2×#66945C2212yes—
49C2×#66945C2211yescharacteristic
50C2×#66945C2211yescharacteristic
51C2×#66945C2211yescharacteristic
52C2×#66940C2211yescharacteristic, complemented
53C2×#66936C2212yes—
54C2×(C22⋊D11)⋊C4C2212yes—
55C2×(C22⋊D11)⋊C4C2212yes—
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C22⋊C4×D11C2211yescharacteristic
58C2×#66930C2212yescomplemented
59C2×C42×D11C2211yescharacteristic
60C2×C42×D11C2211yescharacteristic
61C2×C4×Dic22C2211yescharacteristic, complemented
62C11×#390C2211yescharacteristic, complemented
63C11×#389C2211yescharacteristic, complemented
64C11×#388C2212yescomplemented
65C11×#386C2212yes—
66C11×#385C2212yescomplemented
67C4×C11×C4⋊C4C2211yescharacteristic, complemented
68C4×C11×C22⋊C4C2211yescharacteristic
69#10622834C2211yescharacteristic, complemented
70#10622833C2212yes—
71#10622826C2212yes—
72#10622823C2212yes—
73C4×C22⋊Dic11C2211yescharacteristic
74C4×C22⋊Dic11C2212yes—
75C4×C22⋊Dic11C2212yescomplemented
76#10622603C2212yes—
77#10622602C2212yes—
78#10622598C2211yescharacteristic, complemented
79#10622591C2212yescomplemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81C4⋊C4×Dic11C2211yescharacteristic, complemented
82C4⋊C4×Dic11C2212yescomplemented
83C4⋊C4×Dic11C2212yescomplemented
84#10622587C2211yescharacteristic, complemented
85#10622586C2211yescharacteristic, complemented
86#10622585C2212yescomplemented
87#10622571C2212yes—
88#10622570C2212yes—
89#10622570C2212yes—
90#10622569C2212yes—
91#10622569C2212yes—
92#10622564C2212yescomplemented
93#10622563C2212yescomplemented
94#10622559C2212yes—
95#10622558C2212yescomplemented
96#10622557C2212yescomplemented
97C22⋊C4×Dic11C2212yes—
98C22⋊C4×Dic11C2211yescharacteristic
99C22⋊C4×Dic11C2211yescharacteristic
100C22⋊C4×Dic11C2212yescomplemented
101C22⋊C4×Dic11C2212yescomplemented
102C22⋊C4×Dic11C2212yescomplemented
103#10622553C2212yes—
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2212yes—
107C4×C4⋊Dic11C2211yescharacteristic, complemented
108C4×C4⋊Dic11C2212yescomplemented
109C42×Dic11C2212yescomplemented
110#10622542C2211yescharacteristic, complemented
111#10622541C2211yescharacteristic, complemented
112#10622283C2212yes—
113#10622282C2212yes—
114#10622281C2212yes—
115#10622279C2211yescharacteristic
116#10622279C2211yescharacteristic
117#10622279C2212yes—
118D11×#95C2211yescharacteristic
119D11×#95C2211yescharacteristic
120#10622268C2212yescomplemented
121#10622267C2212yescomplemented
122#10622266C2212yescomplemented
123#10622262C2212yescomplemented
124#10622261C2212yescomplemented
125#10622260C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2312yes—
135C23×Dic11C2312yes—
136C23×Dic11C2312yes—
137C23×Dic11C2311yescharacteristic
138C2×#4341—24no—
139C2×#4341—24no—
140C2×#4341C2×C418yescomplemented
141C22×C4×D11—24no—
142C22×C4×D11—24no—
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×Dic22C2311yescharacteristic
153C11×#121C2×C418yescomplemented
154C4×D4×C11—24no—
155C4×D4×C11—28no—
156C2×C11×C4⋊C4—24no—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178#66991C2×C418yescomplemented
179#66990C2×C4116yescomplemented
180D4×Dic11—28no—
181D4×Dic11—24no—
182D4×Dic11C2×C4116yescomplemented
183C4×C22⋊D11—28no—
184C2×(C2×D11)⋊C4—28no—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×C4⋊Dic11—24no—
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202#66977C2×C418yescomplemented
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×C4×Dic11—28no—
209C2×C4×Dic11—28no—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226#66950C2×C418yescomplemented
227#66945—24no—
228#66945—24no—
229#66945—28no—
230#66945—24no—
231#66945—28no—
232#66945C2×C418yescomplemented
233#66945D418yescomplemented
234#66940—24no—
235#66936C2×C4116yescomplemented
236(C22⋊D11)⋊C4—28no—
237(C22⋊D11)⋊C4C2×C4116yescomplemented
238C22⋊C4×D11—24no—
239C22⋊C4×D11—24no—
240#66930—28no—
241C42×D11—24no—
242C42×D11—24no—
243C4×Dic22—24no—
244C11×#95C2311yescharacteristic
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2311yescharacteristic
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2311yescharacteristic
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34136—111nomaximal, Sylow
265C24×C11C2412yes—
266C24×C11C2411yescharacteristic
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—41no—
272C23×D11—41no—
273C23×D11C22×C414yes—
274C23×D11C2411yescharacteristic
275C23×D11C2411yescharacteristic
276C2×D4×C11—24no—
277C2×D4×C11—24no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11C22×C418yes—
281C2×D4×C11C22×C414yes—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11—24no—
286C22×C4×C11—24no—
287C22×C4×C11—24no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11C22×C414yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11C22×C418yes—
305C2×C22⋊D11C22×C418yes—
306C22×Dic11—24no—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—24no—
310C22×Dic11—24no—
311C22×Dic11—24no—
312C22×Dic11—24no—
313C22×Dic11—24no—
314C22×Dic11—42no—
315C22×Dic11—42no—
316C22×Dic11C22×C418yes—
317C22×Dic11C22×C414yes—
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2412yes—
323C22×Dic11C2412yes—
324C22×Dic11C2412yes—
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328#4341—232no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—232no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—41no—
347C2×C4×D11—41no—
348C2×C4×D11C22×C414yes—
349C2×C4×D11C22×C414yes—
350C2×C4×D11C22×C414yes—
351C2×C4×D11C22×C414yes—
352C2×C4×D11C2×D414yes—
353C2×C4×D11#4114yes—
354C2×Dic22—22no—
355C2×Dic22—22no—
356C2×Dic22C22×C414yes—
357C11×C4⋊C4—24no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—24no—
360C11×C4⋊C4C22×C414yes—
361C11×C4⋊C4C2×D414yes—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4C22×C418yes—
367C11×C22⋊C4#4114yescomplemented
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—24no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—22no—
374C22⋊Dic11—42no—
375C22⋊Dic11C22×C418yes—
376C22⋊Dic11C22×C418yes—
377C22⋊Dic11#4114yescomplemented
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4C22×C418yes—
386(C2×D11)⋊C4C22×C418yes—
387(C2×D11)⋊C4C2×D418yes—
388C4⋊Dic11—24no—
389C4⋊Dic11—24no—
390C4⋊Dic11—22no—
391C4⋊Dic11C22×C418yes—
392C4⋊Dic11C22×C414yes—
393C4⋊Dic11C2×D414yes—
394Dic11⋊C4—24no—
395Dic11⋊C4—24no—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398Dic11⋊C4C22×C418yes—
399C4×Dic11—24no—
400C4×Dic11—22no—
401C4×Dic11—22no—
402C4×Dic11—24no—
403C4×Dic11—24no—
404C4×Dic11—22no—
405C4×Dic11—22no—
406C4×Dic11—24no—
407C4×Dic11—22no—
408C4×Dic11—24no—
409C4×Dic11—24no—
410C4×Dic11—22no—
411C4×Dic11—42no—
412C4×Dic11—42no—
413C4×Dic11C22×C418yes—
414C4×Dic11C2×D418yes—
415C2×#525—111no—
416C2×C4×#41—111no—
417C22×#117—111no—
418#2363—111no—
419#2363—111no—
420#2362—111no—
421#2362—111no—
422#2361—111no—
423#2361D1111yescharacteristic, complemented
424#2360—111no—
425#2360—111no—
426#2359—112no—
427#2359—112no—
428#2358—112no—
429#2358—112no—
430#2297—111no—
431#2296—111no—
432#2293—112no—
433#2290—112no—
434#2290—112no—
435C42×D4—112no—
436C4×#117—111no—
437C2×C4×C22⋊C4—111no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11C23×C414yes—
449C23×C11C23×C412yes—
450C23×C11C2×#4112yes—
451C23×C11C2×#4112yes—
452C23×C11C2511yescharacteristic
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—28no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—28no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11C23×C412yes—
471C22×D11C23×C412yes—
472C22×D11C22×D412yes—
473C22×D11C2×#4112yes—
474D4×C11—216no—
475D4×C11—28no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—28no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—48no—
497C2×C4×C11—48no—
498C2×C4×C11C23×C414yes—
499C2×C4×C11C23×C412yes—
500C2×C4×C11C23×C412yes—
501C2×C4×C11C22×D414yes—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C2×#4112yes—
504C2×C4×C11C2×#4112yes—
505C2×C4×C11C2×#4112yes—
506C22⋊D11—216no—
507C22⋊D11—48no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—21no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—21no—
520C2×Dic11—28no—
521C2×Dic11—216no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—21no—
531C2×Dic11—48no—
532C2×Dic11—48no—
533C2×Dic11C23×C414yes—
534C2×Dic11C23×C414yes—
535C2×Dic11C23×C412yes—
536C2×Dic11C23×C412yes—
537C2×Dic11C22×D414yes—
538C2×Dic11C22×D412yes—
539C2×Dic11C2×#4112yes—
540C2×Dic11C2×#4112yes—
541C2×Dic11C2×#4112yes—
542C4×D11—28no—
543C4×D11—28no—
544C4×D11—28no—
545C4×D11—44no—
546C4×D11—44no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11C4×D4116yescomplemented
550Dic22—28no—
551C22×#41—111no—
552C24×C4—111no—
553#525—1116no—
554C2×#123—112no—
555C2×C22⋊Q8—111no—
556C2×C22⋊Q8—111no—
557C2×#121—111no—
558C2×#121C2×D1111yescharacteristic
559C2×#120—112no—
560C4×#41—228no—
561C2×C4×Q8—111no—
562C2×C4×Q8—111no—
563C2×C4×D4—112no—
564C2×C4×D4—112no—
565C2×C4×D4—111no—
566C2×C4×D4—112no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4C2×D1112yes—
570C2×C4×D4C2×D1111yescharacteristic, complemented
571C2×#117—111no—
572C2×#117—111no—
573C2×#117—112no—
574C2×#117—111no—
575C2×#117—111no—
576C2×#117—112no—
577C2×#117—111no—
578C2×#117—112no—
579C2×#117—228no—
580C22×C4⋊C4—111no—
581C22×C4⋊C4C2×D1111yescharacteristic
582C22×C22⋊C4—112no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C42—112no—
586C22×C42—112no—
587C22×C42—111no—
588C22×C42—111no—
589#391—111no—
590#391—111no—
591#390—111no—
592#390—112no—
593#390—112no—
594#390C2×D1111yescharacteristic, complemented
595#389—112no—
596#389—111no—
597#389—111no—
598#389—111no—
599#389—112no—
600#389C2×D1111yescharacteristic, complemented
601#388—112no—
602#388—112no—
603#388—112no—
604#388—112no—
605#388—112no—
606#388—112no—
607#388—112no—
608#388C2×D1112yescomplemented
609#387—112no—
610#387—112no—
611#387—112no—
612#387—112no—
613#386—112no—
614#386—112no—
615#386—112no—
616#386—112no—
617#386—112no—
618#386C2×D1112yes—
619#385—112no—
620#385—112no—
621#385—112no—
622#385—112no—
623#385—112no—
624#385C2×D1112yescomplemented
625C4×C4⋊C4—112no—
626C4×C4⋊C4—111no—
627C4×C4⋊C4—111no—
628C4×C4⋊C4—112no—
629C4×C4⋊C4—112no—
630C4×C4⋊C4—111no—
631C4×C4⋊C4—112no—
632C4×C4⋊C4C2×D1111yescharacteristic, complemented
633C4×C22⋊C4—112no—
634C4×C22⋊C4—112no—
635C4×C22⋊C4—111no—
636C4×C22⋊C4—112no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—111no—
639C4×C22⋊C4—111no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4C2×D1111yescharacteristic
649#376—112no—
650C2×#95—111no—
651C2×#95—111no—
652C43—112no—
653C22×C11—22no—
654C22×C11—22no—
655C22×C11—22no—
656C22×C11—22no—
657C22×C11—22no—
658C22×C11—22no—
659C22×C11—24no—
660C22×C11—24no—
661C22×C11—24no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11C4×#4114yescomplemented
667C22×C11C24×C411yescharacteristic
668C22×C11C23×D411yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C22×#4111yescharacteristic
671C22×C11C22×#4111yescharacteristic
672C22×C11#58511yescharacteristic
673C22×C11#58511yescharacteristic
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—416no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—41no—
687C2×D11—41no—
688C2×D11C2×C4×D414yes—
689C4×C11—22no—
690C4×C11—24no—
691C4×C11—24no—
692C4×C11—22no—
693C4×C11—22no—
694C4×C11—42no—
695C4×C11—41no—
696C4×C11—41no—
697C4×C11C2×C4×D414yes—
698Dic11—24no—
699Dic11—22no—
700Dic11—24no—
701Dic11—22no—
702Dic11—24no—
703Dic11—22no—
704Dic11—41no—
705Dic11—42no—
706Dic11—41no—
707Dic11C2×C4×D414yes—
708C25—111no—
709C2×#41—118no—
710C2×#41—224no—
711C2×#41—224no—
712C22×Q8—111no—
713C22×D4—112no—
714C22×D4—112no—
715C22×D4C22×D1112yes—
716C22×D4C22×D1111yescharacteristic
717C23×C4—111no—
718C23×C4—112no—
719C23×C4—111no—
720C23×C4—118no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—112no—
725C23×C4—112no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—224no—
731C23×C4—224no—
732C23×C4C22×D1112yes—
733C23×C4C22×D1112yes—
734C23×C4C22×D1111yescharacteristic
735#123—1116no—
736C22⋊Q8—118no—
737C22⋊Q8—118no—
738#121—118no—
739#121C4×D1118yescomplemented
740#120—1116no—
741C4×Q8—224no—
742C4×Q8—224no—
743C4×D4—24no—
744C4×D4—28no—
745C4×D4—1116no—
746C4×D4—1116no—
747C4×D4—228no—
748C4×D4—228no—
749C4×D4—228no—
750C4×D4—224no—
751#117—118no—
752#117—118no—
753#117—228no—
754#117—228no—
755#117—228no—
756#117—224no—
757#117—224no—
758#117—224no—
759C2×C4⋊C4—24no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—224no—
772C2×C4⋊C4C22×D1112yes—
773C2×C4⋊C4C22×D1111yescharacteristic
774C2×C4⋊C4C22×D1112yes—
775C2×C4⋊C4C22×D1111yescharacteristic
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4—111no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—224no—
795C2×C22⋊C4—228no—
796C2×C22⋊C4—224no—
797C2×C22⋊C4C22×D1111yescharacteristic
798C2×C22⋊C4C22×D1112yes—
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C22⋊C4C22×D1111yescharacteristic
803C2×C42—112no—
804C2×C42—112no—
805C2×C42—112no—
806C2×C42—111no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—111no—
810C2×C42—112no—
811C2×C42—112no—
812C2×C42—112no—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—112no—
818C2×C42—112no—
819C2×C42—224no—
820C2×C42—224no—
821C2×C42—228no—
822C2×C42—228no—
823C2×C42C22×D1112yes—
824C2×C42C22×D1111yescharacteristic
825C2×C42C22×D1111yescharacteristic
826#95—111no—
827#95—111no—
828#95—111no—
829#95—111no—
830#95—111no—
831#95—111no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95C22×D1111yescharacteristic
843#95C22×D1111yescharacteristic
844#95C22×D1112yes—
845#95C22×D1112yes—
846C2×C11—24no—
847C2×C11—44no—
848C2×C11C22×C4×D411yescharacteristic
849C2×C11C2×C4×#4111yescharacteristic
850C2×C11#342811yescharacteristic
851C2×C11D4×#4111yescharacteristic
852C2×C11D4×#4111yescharacteristic
853C2×C11#347511yescharacteristic
854C2×C11#347511yescharacteristic
855D11—24no—
856D11—42no—
857C24—111no—
858C24—111no—
859C24—114no—
860C24—222no—
861C24—222no—
862C24—222no—
863C24—222no—
864C24—441no—
865C24—441no—
866C24C23×D1112yes—
867C24C23×D1111yescharacteristic
868#41—2232no—
869C2×Q8—114no—
870C2×Q8—222no—
871C2×Q8—222no—
872C2×D4—24no—
873C2×D4—24no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—118no—
877C2×D4—118no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—442no—
881C2×D4—442no—
882C2×D4C2×C4×D1118yes—
883C2×D4C2×C4×D1114yes—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—111no—
893C22×C4—114no—
894C22×C4—114no—
895C22×C4—114no—
896C22×C4—114no—
897C22×C4—118no—
898C22×C4—111no—
899C22×C4—111no—
900C22×C4—111no—
901C22×C4—112no—
902C22×C4—112no—
903C22×C4—112no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—112no—
910C22×C4—222no—
911C22×C4—222no—
912C22×C4—2232no—
913C22×C4—222no—
914C22×C4—222no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—224no—
923C22×C4—222no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—224no—
928C22×C4—222no—
929C22×C4—222no—
930C22×C4—224no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—441no—
934C22×C4—441no—
935C22×C4—441no—
936C22×C4—441no—
937C22×C4—442no—
938C22×C4—442no—
939C22×C4C2×C4×D1114yes—
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1112yes—
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1112yes—
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1112yes—
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1111yescharacteristic
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—24no—
952C4⋊C4—114no—
953C4⋊C4—118no—
954C4⋊C4—118no—
955C4⋊C4—114no—
956C4⋊C4—224no—
957C4⋊C4—224no—
958C4⋊C4—224no—
959C4⋊C4—222no—
960C4⋊C4—224no—
961C4⋊C4—442no—
962C4⋊C4—442no—
963C4⋊C4C2×C4×D1114yes—
964C4⋊C4D4×D1114yes—
965C22⋊C4—22no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—42no—
969C22⋊C4—118no—
970C22⋊C4—118no—
971C22⋊C4—114no—
972C22⋊C4—118no—
973C22⋊C4—118no—
974C22⋊C4—118no—
975C22⋊C4—224no—
976C22⋊C4—222no—
977C22⋊C4—222no—
978C22⋊C4—224no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—222no—
982C22⋊C4—224no—
983C22⋊C4—222no—
984C22⋊C4—222no—
985C22⋊C4—442no—
986C22⋊C4C2×C4×D1118yes—
987C22⋊C4#434114yescomplemented
988C42—22no—
989C42—24no—
990C42—22no—
991C42—118no—
992C42—118no—
993C42—222no—
994C42—222no—
995C42—224no—
996C42—224no—
997C42—224no—
998C42—222no—
999C42—222no—
1000C42—224no—
1001C42—224no—
1002C42—224no—
1003C42—222no—
1004C42—222no—
1005C42—442no—
1006C42—442no—
1007C11#3413611yescharacteristic, complemented, Sylow
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—112no—
1019C23—112no—
1020C23—112no—
1021C23—112no—
1022C23—228no—
1023C23—221no—
1024C23—221no—
1025C23—221no—
1026C23—221no—
1027C23—228no—
1028C23—221no—
1029C23—221no—
1030C23—221no—
1031C23—221no—
1032C23—221no—
1033C23—221no—
1034C23—444no—
1035C23—444no—
1036C23—444no—
1037C23—444no—
1038C23—444no—
1039C23C22×C4×D1114yes—
1040C23C22×C4×D1112yes—
1041C23C2×#434112yes—
1042C23#41×D1112yes—
1043C23C24×D1111yescharacteristic
1044Q8—228no—
1045D4—216no—
1046D4—28no—
1047D4—2216no—
1048D4—448no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—28no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—48no—
1070C2×C4—48no—
1071C2×C4—112no—
1072C2×C4—112no—
1073C2×C4—112no—
1074C2×C4—1116no—
1075C2×C4—114no—
1076C2×C4—112no—
1077C2×C4—114no—
1078C2×C4—114no—
1079C2×C4—112no—
1080C2×C4—112no—
1081C2×C4—228no—
1082C2×C4—228no—
1083C2×C4—228no—
1084C2×C4—2216no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—222no—
1088C2×C4—221no—
1089C2×C4—222no—
1090C2×C4—221no—
1091C2×C4—222no—
1092C2×C4—221no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—221no—
1097C2×C4—228no—
1098C2×C4—221no—
1099C2×C4—222no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—222no—
1107C2×C4—444no—
1108C2×C4—444no—
1109C2×C4—444no—
1110C2×C4—444no—
1111C2×C4—448no—
1112C2×C4—448no—
1113C2×C4C22×C4×D1114yes—
1114C2×C4C22×C4×D1112yes—
1115C2×C4C22×C4×D1112yes—
1116C2×C4C2×D4×D1114yes—
1117C2×C4C2×D4×D1112yes—
1118C2×C4C2×#434112yes—
1119C2×C4C2×#434112yes—
1120C2×C4#41×D1112yes—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—22no—
1127C22—24no—
1128C22—24no—
1129C22—24no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—114no—
1135C22—222no—
1136C22—222no—
1137C22—222no—
1138C22—222no—
1139C22—222no—
1140C22—222no—
1141C22—222no—
1142C22—222no—
1143C22—222no—
1144C22—4416no—
1145C22—441no—
1146C22—441no—
1147C22—441no—
1148C22—441no—
1149C22C4×#434114yescomplemented
1150C22C23×C4×D1111yescharacteristic
1151C22C22×D4×D1111yescharacteristic
1152C22C22×#434111yescharacteristic
1153C22C2×#41×D1111yescharacteristic
1154C22C2×#41×D1111yescharacteristic
1155C22#1062345511yescharacteristic
1156C22#1062345711yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—24no—
1160C4—22no—
1161C4—24no—
1162C4—41no—
1163C4—42no—
1164C4—41no—
1165C4—114no—
1166C4—222no—
1167C4—222no—
1168C4—224no—
1169C4—224no—
1170C4—222no—
1171C4—224no—
1172C4—441no—
1173C4—441no—
1174C4—442no—
1175C4C4×D4×D1114yes—
1176C2—24no—
1177C2—44no—
1178C2—224no—
1179C2—442no—
1180C2C2×C4×D4×D1111yescharacteristic
1181C2C2×C4×#434111yescharacteristic
1182C2#1308181611yescharacteristic
1183C2D4×#434111yescharacteristic
1184C2#1308210511yescharacteristic
1185C2#1308217511yescharacteristic
1186C2#1308217911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2361C2
socle, cosocleC23×C11C25
prime radicalC2×#10623137C2
hypercenter#2361D11
hypocenterC11#34136
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4341C2semidirect
3. C22×#66945C2semidirect
4. #13071659C2semidirect
5. #13071650C2semidirect
6. #13071645C2semidirect
7. #13071642C2semidirect
8. #13071636C2semidirect
9. #13071621C2semidirect
10. #13071619C2semidirect
11. #13071611C2semidirect
12. #13071607C2semidirect
13. #13071596C2semidirect
14. #13071593C2semidirect
15. #13071103C2semidirect
16. #13071097C2semidirect
17. #13071076C2semidirect
18. #13071056C2semidirect
19. #13071052C2semidirect
20. C4×D4×Dic11C2semidirect
21. C4×#66945C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2361C2semidirect
28. C2×C4×D4×C11C22semidirect
34. C2×D4×Dic11C22semidirect
40. C22×C4×Dic11C22semidirect
41. #10623137C4semidirect
52. C2×#66940C22semidirect
58. C2×#66930C22semidirect
61. C2×C4×Dic22C22semidirect
62. C11×#390C22semidirect
63. C11×#389C22semidirect
64. C11×#388C22semidirect
66. C11×#385C22semidirect
67. C4×C11×C4⋊C4C22semidirect
69. #10622834C22semidirect
75. C4×C22⋊Dic11C22semidirect
78. #10622598C22semidirect
79. #10622591C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622587C22semidirect
85. #10622586C22semidirect
86. #10622585C22semidirect
92. #10622564C22semidirect
93. #10622563C22semidirect
95. #10622558C22semidirect
96. #10622557C22semidirect
100. C22⋊C4×Dic11C22semidirect
101. C22⋊C4×Dic11C22semidirect
102. C22⋊C4×Dic11C22semidirect
107. C4×C4⋊Dic11C22semidirect
108. C4×C4⋊Dic11C22semidirect
109. C42×Dic11C22semidirect
110. #10622542C22semidirect
111. #10622541C22semidirect
120. #10622268C22semidirect
121. #10622267C22semidirect
122. #10622266C22semidirect
123. #10622262C22semidirect
124. #10622261C22semidirect
125. #10622260C22semidirect
140. C2×#4341C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
153. C11×#121C2×C4semidirect
178. #66991C2×C4semidirect
179. #66990C2×C4semidirect
182. D4×Dic11C2×C4semidirect
202. #66977C2×C4semidirect
226. #66950C2×C4semidirect
232. #66945C2×C4semidirect
233. #66945D4semidirect
235. #66936C2×C4semidirect
237. (C22⋊D11)⋊C4C2×C4semidirect
367. C11×C22⋊C4#41semidirect
377. C22⋊Dic11#41semidirect
423. #2361D11semidirect
549. C4×D11C4×D4semidirect
570. C2×C4×D4C2×D11semidirect
594. #390C2×D11semidirect
600. #389C2×D11semidirect
608. #388C2×D11semidirect
624. #385C2×D11semidirect
632. C4×C4⋊C4C2×D11semidirect
666. C22×C11C4×#41semidirect
739. #121C4×D11semidirect
987. C22⋊C4#4341semidirect
1007. C11#34136semidirect
1149. C22C4×#4341semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
C2×C4×#43412
C22×#669452
#130716592
#130716502
#130716452
#130716422
#130716362
#130716212
#130716192
#130716112
#130716072
#130715962
#130715932
#130711032
#130710972
#130710762
#130710562
#130710522
C4×D4×Dic112
C4×#669452
C4×C22⋊C4×D112
C11×#23612
#3413611