Finite Group Databasebeta

← #14913342

Subgroups — #14913342

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
3C2×D11×#117C211yesmaximal, characteristic, complemented
4#13071658C211yesmaximal, characteristic, complemented
5#13071643C211yesmaximal, characteristic, complemented
6#13071641C211yesmaximal, characteristic, complemented
7#13071637C211yesmaximal, characteristic, complemented
8#13071628C211yesmaximal, characteristic, complemented
9#13071623C211yesmaximal, characteristic, complemented
10#13071620C211yesmaximal, characteristic, complemented
11#13071609C212yesmaximal, complemented
12#13071605C212yesmaximal, complemented
13#13071599C212yesmaximal, complemented
14#13071597C212yesmaximal, complemented
15#13071103C211yesmaximal, characteristic, complemented
16#13071097C211yesmaximal, characteristic, complemented
17#13071078C212yesmaximal, complemented
18#13071058C212yesmaximal, complemented
19#13071056C212yesmaximal, complemented
20C4×(C22⋊D11)⋊C4C212yesmaximal, complemented
21C4×#66945C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2363C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic, complemented
28C2×C11×#117C2211yescharacteristic
29C2×#66991C2211yescharacteristic
30C2×#66990C2212yes—
31C2×D4×Dic11C2212yes—
32C2×D4×Dic11C2211yescharacteristic, complemented
33C2×C4×C22⋊D11C2212yes—
34C2×C4×C22⋊D11C2212yes—
35C2×#66979C2211yescharacteristic
36C2×#66977C2211yescharacteristic
37C22×C4×Dic11C2212yescomplemented
38#10623137C4116yescomplemented
39C4×#4341—28no—
40D11×#117—28no—
41C2×#66950C2211yescharacteristic
42C2×#66945C2211yescharacteristic
43C2×#66945C2211yescharacteristic
44C2×#66945C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×#66940C2211yescharacteristic, complemented
48C2×#66936C2212yes—
49C2×(C22⋊D11)⋊C4C2212yes—
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×C22⋊C4×D11C2211yescharacteristic
54C2×C22⋊C4×D11C2212yes—
55C2×#66930C2212yes—
56C2×#66930C2212yescomplemented
57C2×#66925C2212yes—
58C2×C42×D11C2211yescharacteristic
59C2×C42×D11C2211yescharacteristic
60C2×C42×D11C2212yes—
61C2×C4×Dic22C2211yescharacteristic, complemented
62C11×#390C2212yes—
63C11×#390C2211yescharacteristic, complemented
64C11×#389C2211yescharacteristic, complemented
65C11×#388C2212yescomplemented
66C11×#386C2212yes—
67C4×C11×C4⋊C4C2211yescharacteristic, complemented
68C4×C11×C22⋊C4C2211yescharacteristic
69C4×C11×C22⋊C4C2212yescomplemented
70#10622834C2212yes—
71#10622834C2211yescharacteristic, complemented
72#10622833C2212yes—
73#10622823C2212yescomplemented
74C4×C22⋊Dic11C2211yescharacteristic
75#10622602C2212yes—
76#10622602C2212yes—
77#10622598C2211yescharacteristic, complemented
78C4⋊C4×Dic11C2211yescharacteristic, complemented
79C4⋊C4×Dic11C2211yescharacteristic, complemented
80C4⋊C4×Dic11C2212yescomplemented
81#10622587C2211yescharacteristic, complemented
82#10622586C2212yescomplemented
83#10622586C2211yescharacteristic, complemented
84#10622569C2212yes—
85#10622569C2212yes—
86#10622569C2212yes—
87#10622569C2212yes—
88#10622564C2212yescomplemented
89#10622559C2212yescomplemented
90#10622558C2212yes—
91#10622558C2212yes—
92#10622558C2212yescomplemented
93#10622557C2212yes—
94#10622557C2212yes—
95#10622557C2212yescomplemented
96C22⋊C4×Dic11C2211yescharacteristic
97C22⋊C4×Dic11C2211yescharacteristic
98C22⋊C4×Dic11C2212yescomplemented
99C22⋊C4×Dic11C2212yescomplemented
100C22⋊C4×Dic11C2212yescomplemented
101C4×(C2×D11)⋊C4C2211yescharacteristic
102C4×(C2×D11)⋊C4C2211yescharacteristic
103C4×(C2×D11)⋊C4C2212yes—
104C4×(C2×D11)⋊C4C2212yes—
105C4×C4⋊Dic11C2211yescharacteristic, complemented
106#10622546C2212yescomplemented
107C4×Dic11⋊C4C2212yescomplemented
108C42×Dic11C2212yescomplemented
109#10622542C2211yescharacteristic, complemented
110#10622541C2212yescomplemented
111#10622541C2211yescharacteristic, complemented
112#10622281C2212yes—
113#10622281C2212yes—
114#10622279C2212yes—
115#10622279C2211yescharacteristic
116#10622279C2211yescharacteristic
117#10622279C2212yes—
118D11×#95C2211yescharacteristic
119D11×#95C2211yescharacteristic
120#10622267C2212yescomplemented
121#10622266C2212yescomplemented
122#10622265C2212yescomplemented
123#10622262C2212yescomplemented
124#10622262C2212yescomplemented
125#10622261C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2312yes—
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2312yes—
136C2×#4341—24no—
137C2×#4341—24no—
138C2×#4341C2×C418yescomplemented
139C22×C4×D11—24no—
140C22×C4×D11—24no—
141C22×C4×D11C2×C418yescomplemented
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2312yes—
144C22×C4×D11C2312yes—
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—
155C11×#117—24no—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2312yes—
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179#66991C2×C418yescomplemented
180#66990C2×C4116yescomplemented
181D4×Dic11—24no—
182D4×Dic11C2×C4116yescomplemented
183C4×C22⋊D11—28no—
184C4×C22⋊D11—28no—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193#66979—24no—
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2312yes—
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199#66977C2×C418yescomplemented
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×C4×Dic11—28no—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
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—
223#66950C2×C418yescomplemented
224#66945—24no—
225#66945C2×C418yescomplemented
226#66945D418yescomplemented
227C4⋊C4×D11—24no—
228C4⋊C4×D11—24no—
229#66940—24no—
230#66936C2×C4116yescomplemented
231(C22⋊D11)⋊C4—28no—
232(C22⋊D11)⋊C4—28no—
233(C22⋊D11)⋊C4C2×C4116yescomplemented
234C22⋊C4×D11—28no—
235C22⋊C4×D11—24no—
236C22⋊C4×D11—24no—
237#66930—28no—
238#66930—28no—
239#66925—28no—
240C42×D11—24no—
241C42×D11—24no—
242C42×D11—28no—
243C4×Dic22—24no—
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11×#95C2312yes—
247C11×#95C2311yescharacteristic
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258C11⋊#95C2311yescharacteristic
259C11⋊#95C2311yescharacteristic
260C11⋊#95C2311yescharacteristic
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34136—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C24×C11C2412yes—
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—22no—
277C2×D4×C11—22no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C2×D4×C11C22×C414yes—
281C2×D4×C11C22×C418yes—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11—24no—
286C22×C4×C11—42no—
287C22×C4×C11C22×C414yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11C22×C418yes—
302C2×C22⋊D11C22×C418yes—
303C22×Dic11—22no—
304C22×Dic11—24no—
305C22×Dic11—22no—
306C22×Dic11—24no—
307C22×Dic11—24no—
308C22×Dic11—24no—
309C22×Dic11—42no—
310C22×Dic11C22×C418yes—
311C22×Dic11C22×C414yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322#4341—232no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—232no—
326C2×C4×D11—24no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—41no—
343C2×C4×D11—42no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—42no—
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—22no—
358C11×C4⋊C4—42no—
359C11×C4⋊C4C22×C414yes—
360C11×C4⋊C4C2×D414yes—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4C22×C418yes—
368C42×C11—22no—
369C42×C11—24no—
370C42×C11—22no—
371C42×C11—42no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376C22⋊Dic11—24no—
377C22⋊Dic11—42no—
378C22⋊Dic11C22×C418yes—
379C22⋊Dic11C22×C418yes—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4C22×C418yes—
384(C2×D11)⋊C4C22×C418yes—
385(C2×D11)⋊C4C2×D418yes—
386(C2×D11)⋊C4#4114yescomplemented
387(C2×D11)⋊C4#4114yescomplemented
388C4⋊Dic11—22no—
389C4⋊Dic11—42no—
390C4⋊Dic11C22×C418yes—
391C4⋊Dic11C22×C414yes—
392C4⋊Dic11C2×D414yes—
393Dic11⋊C4—24no—
394Dic11⋊C4—24no—
395Dic11⋊C4—24no—
396Dic11⋊C4—24no—
397Dic11⋊C4—24no—
398Dic11⋊C4—24no—
399Dic11⋊C4C22×C418yes—
400C4×Dic11—24no—
401C4×Dic11—24no—
402C4×Dic11—22no—
403C4×Dic11—24no—
404C4×Dic11—22no—
405C4×Dic11—22no—
406C4×Dic11—22no—
407C4×Dic11—24no—
408C4×Dic11—22no—
409C4×Dic11—24no—
410C4×Dic11—22no—
411C4×Dic11—24no—
412C4×Dic11—42no—
413C4×Dic11C22×C418yes—
414C4×Dic11C2×D418yes—
415C2×#525—111no—
416C2×C4×#41—111no—
417C22×#117—111no—
418#2363—111no—
419#2363D1111yescharacteristic, complemented
420#2362—111no—
421#2362—111no—
422#2361—111no—
423#2361—111no—
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—22no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—21no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11C23×C412yes—
451C23×C11C23×C414yes—
452C23×C11C2511yescharacteristic
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—28no—
462C22×D11—28no—
463C22×D11—44no—
464C22×D11—44no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11C23×C412yes—
469C22×D11C23×C412yes—
470C22×D11C22×D412yes—
471C22×D11C2×#4112yes—
472C22×D11C2×#4112yes—
473C22×D11C2×#4112yes—
474D4×C11—28no—
475D4×C11—48no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—28no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—21no—
496C2×C4×C11—48no—
497C2×C4×C11C23×C414yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11C23×C412yes—
500C2×C4×C11C22×D414yes—
501C2×C4×C11C22×D412yes—
502C2×C4×C11C2×#4112yes—
503C2×C4×C11C2×#4112yes—
504C2×C4×C11C2×#4112yes—
505C22⋊D11—216no—
506C22⋊D11—216no—
507C2×Dic11—21no—
508C2×Dic11—22no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—22no—
518C2×Dic11—21no—
519C2×Dic11—28no—
520C2×Dic11—216no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—21no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—21no—
530C2×Dic11—48no—
531C2×Dic11C23×C414yes—
532C2×Dic11C23×C414yes—
533C2×Dic11C23×C412yes—
534C2×Dic11C23×C412yes—
535C2×Dic11C22×D414yes—
536C2×Dic11C22×D412yes—
537C2×Dic11C2×#4112yes—
538C2×Dic11C2×#4112yes—
539C2×Dic11C2×#4112yes—
540C4×D11—28no—
541C4×D11—28no—
542C4×D11—28no—
543C4×D11—44no—
544C4×D11—48no—
545C4×D11—44no—
546C4×D11—44no—
547C4×D11—48no—
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—111no—
565C2×C4×D4—112no—
566C2×C4×D4—112no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—112no—
570C2×C4×D4C2×D1111yescharacteristic, complemented
571C2×#117—111no—
572C2×#117—111no—
573C2×#117—111no—
574C2×#117—111no—
575C2×#117—112no—
576C2×#117—112no—
577C2×#117—112no—
578C2×#117—228no—
579C2×#117C2×D1111yescharacteristic
580C22×C4⋊C4—111no—
581C22×C4⋊C4—111no—
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—112no—
592#390—111no—
593#390C2×D1112yes—
594#390C2×D1111yescharacteristic, complemented
595#389—112no—
596#389—111no—
597#389—111no—
598#389—112no—
599#389—111no—
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#385—112no—
625C4×C4⋊C4—111no—
626C4×C4⋊C4—111no—
627C4×C4⋊C4—112no—
628C4×C4⋊C4—112no—
629C4×C4⋊C4—111no—
630C4×C4⋊C4—112no—
631C4×C4⋊C4—112no—
632C4×C4⋊C4C2×D1111yescharacteristic, complemented
633C4×C22⋊C4—111no—
634C4×C22⋊C4—112no—
635C4×C22⋊C4—111no—
636C4×C22⋊C4—111no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—111no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4C2×D1111yescharacteristic
648C4×C22⋊C4C2×D1112yescomplemented
649#376—112no—
650C2×#95—111no—
651C2×#95—111no—
652C43—112no—
653C22×C11—22no—
654C22×C11—24no—
655C22×C11—22no—
656C22×C11—24no—
657C22×C11—22no—
658C22×C11—24no—
659C22×C11—42no—
660C22×C11—41no—
661C22×C11—41no—
662C22×C11—42no—
663C22×C11—41no—
664C22×C11—41no—
665C22×C11—42no—
666C22×C11—42no—
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—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—416no—
687C2×D11C2×C4×D414yes—
688C2×D11C4×#4114yescomplemented
689C4×C11—22no—
690C4×C11—24no—
691C4×C11—22no—
692C4×C11—24no—
693C4×C11—22no—
694C4×C11—41no—
695C4×C11—42no—
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×D1111yescharacteristic
716C22×D4C22×D1112yes—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—112no—
720C23×C4—118no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—112no—
725C23×C4—112no—
726C23×C4—112no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—224no—
732C23×C4—224no—
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—1116no—
745C4×D4—1116no—
746C4×D4—228no—
747C4×D4—228no—
748C4×D4—228no—
749C4×D4—228no—
750C4×D4—224no—
751#117—24no—
752#117—118no—
753#117—118no—
754#117—228no—
755#117—228no—
756#117—228no—
757#117—224no—
758#117—224no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—111no—
761C2×C4⋊C4—112no—
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⋊C4—224no—
773C2×C4⋊C4C22×D1111yescharacteristic
774C2×C4⋊C4C22×D1112yes—
775C2×C4⋊C4C22×D1111yescharacteristic
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—228no—
794C2×C22⋊C4—224no—
795C2×C22⋊C4—224no—
796C2×C22⋊C4C22×D1112yes—
797C2×C22⋊C4C22×D1111yescharacteristic
798C2×C22⋊C4C22×D1111yescharacteristic
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C22⋊C4C22×D1112yes—
803C2×C42—112no—
804C2×C42—112no—
805C2×C42—112no—
806C2×C42—111no—
807C2×C42—112no—
808C2×C42—111no—
809C2×C42—112no—
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—228no—
819C2×C42—224no—
820C2×C42—224no—
821C2×C42—228no—
822C2×C42C22×D1112yes—
823C2×C42C22×D1111yescharacteristic
824C2×C42C22×D1111yescharacteristic
825C2×C42C22×D1112yes—
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—42no—
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—24no—
857C24—111no—
858C24—111no—
859C24—114no—
860C24—222no—
861C24—222no—
862C24—222no—
863C24—222no—
864C24—441no—
865C24—441no—
866C24C23×D1111yescharacteristic
867C24C23×D1112yes—
868#41—2232no—
869C2×Q8—114no—
870C2×Q8—222no—
871C2×Q8—222no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—118no—
877C2×D4—118no—
878C2×D4—224no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—224no—
882C2×D4C2×C4×D1114yes—
883C2×D4C2×C4×D1118yes—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—42no—
889C22×C4—111no—
890C22×C4—114no—
891C22×C4—114no—
892C22×C4—114no—
893C22×C4—114no—
894C22×C4—118no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—112no—
898C22×C4—112no—
899C22×C4—111no—
900C22×C4—112no—
901C22×C4—114no—
902C22×C4—114no—
903C22×C4—114no—
904C22×C4—111no—
905C22×C4—111no—
906C22×C4—112no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—2232no—
910C22×C4—224no—
911C22×C4—222no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—222no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—224no—
930C22×C4—222no—
931C22×C4—222no—
932C22×C4—441no—
933C22×C4—442no—
934C22×C4—441no—
935C22×C4—441no—
936C22×C4—442no—
937C22×C4—441no—
938C22×C4—442no—
939C22×C4C2×C4×D1114yes—
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1112yes—
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1112yes—
945C22×C4C23×D1112yes—
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1111yescharacteristic
949C4⋊C4—22no—
950C4⋊C4—42no—
951C4⋊C4—114no—
952C4⋊C4—118no—
953C4⋊C4—118no—
954C4⋊C4—114no—
955C4⋊C4—224no—
956C4⋊C4—224no—
957C4⋊C4—224no—
958C4⋊C4—224no—
959C4⋊C4—222no—
960C4⋊C4—224no—
961C4⋊C4—224no—
962C4⋊C4—442no—
963C4⋊C4C2×C4×D1114yes—
964C4⋊C4D4×D1114yes—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—24no—
970C22⋊C4—42no—
971C22⋊C4—118no—
972C22⋊C4—118no—
973C22⋊C4—118no—
974C22⋊C4—118no—
975C22⋊C4—118no—
976C22⋊C4—114no—
977C22⋊C4—114no—
978C22⋊C4—224no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—224no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C22⋊C4—224no—
985C22⋊C4—224no—
986C22⋊C4—442no—
987C22⋊C4C2×C4×D1118yes—
988C42—24no—
989C42—22no—
990C42—22no—
991C42—42no—
992C42—118no—
993C42—118no—
994C42—222no—
995C42—224no—
996C42—222no—
997C42—224no—
998C42—224no—
999C42—222no—
1000C42—222no—
1001C42—224no—
1002C42—224no—
1003C42—222no—
1004C42—222no—
1005C42—224no—
1006C42—442no—
1007C11#3413611yescharacteristic, complemented, Sylow
1008C23—21no—
1009C23—22no—
1010C23—21no—
1011C23—21no—
1012C23—22no—
1013C23—22no—
1014C23—21no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—21no—
1019C23—21no—
1020C23—112no—
1021C23—112no—
1022C23—112no—
1023C23—112no—
1024C23—112no—
1025C23—112no—
1026C23—228no—
1027C23—228no—
1028C23—221no—
1029C23—221no—
1030C23—221no—
1031C23—221no—
1032C23—221no—
1033C23—221no—
1034C23—221no—
1035C23—221no—
1036C23—444no—
1037C23—444no—
1038C23—444no—
1039C23—444no—
1040C23—444no—
1041C23C22×C4×D1112yes—
1042C23C22×C4×D1114yes—
1043C23C24×D1111yescharacteristic
1044Q8—228no—
1045D4—28no—
1046D4—48no—
1047D4—2216no—
1048D4—2216no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—28no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—48no—
1070C2×C4—112no—
1071C2×C4—112no—
1072C2×C4—112no—
1073C2×C4—1116no—
1074C2×C4—114no—
1075C2×C4—112no—
1076C2×C4—114no—
1077C2×C4—114no—
1078C2×C4—112no—
1079C2×C4—112no—
1080C2×C4—228no—
1081C2×C4—228no—
1082C2×C4—228no—
1083C2×C4—2216no—
1084C2×C4—221no—
1085C2×C4—222no—
1086C2×C4—221no—
1087C2×C4—221no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—221no—
1092C2×C4—222no—
1093C2×C4—221no—
1094C2×C4—222no—
1095C2×C4—221no—
1096C2×C4—228no—
1097C2×C4—222no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—222no—
1103C2×C4—221no—
1104C2×C4—222no—
1105C2×C4—221no—
1106C2×C4—444no—
1107C2×C4—444no—
1108C2×C4—448no—
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×C4#41×D1112yes—
1119C2×C4#41×D1112yes—
1120C2×C4#41×D1112yes—
1121C22—22no—
1122C22—24no—
1123C22—24no—
1124C22—22no—
1125C22—22no—
1126C22—24no—
1127C22—41no—
1128C22—42no—
1129C22—41no—
1130C22—42no—
1131C22—42no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—114no—
1136C22—114no—
1137C22—222no—
1138C22—222no—
1139C22—222no—
1140C22—222no—
1141C22—222no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22—222no—
1146C22—222no—
1147C22—222no—
1148C22—222no—
1149C22—4416no—
1150C22C23×C4×D1111yescharacteristic
1151C22C22×D4×D1111yescharacteristic
1152C22C2×#41×D1111yescharacteristic
1153C22C2×#41×D1111yescharacteristic
1154C22C2×#41×D1111yescharacteristic
1155C22#1062345511yescharacteristic
1156C22#1062345511yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—24no—
1160C4—22no—
1161C4—24no—
1162C4—41no—
1163C4—41no—
1164C4—42no—
1165C4—114no—
1166C4—222no—
1167C4—222no—
1168C4—224no—
1169C4—224no—
1170C4—222no—
1171C4—224no—
1172C4—441no—
1173C4—441no—
1174C4—442no—
1175C4C4×D4×D1114yes—
1176C2—42no—
1177C2—44no—
1178C2—224no—
1179C2—224no—
1180C2C2×C4×D4×D1111yescharacteristic
1181C2C4×#41×D1111yescharacteristic
1182C2#1308181411yescharacteristic
1183C2#1308210011yescharacteristic
1184C2#1308210611yescharacteristic
1185C2#1308217311yescharacteristic
1186C2#1308217511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2363C2
socle, cosocleC23×C11C25
prime radicalC2×#10623137C2
hypercenter#2363D11
hypocenterC11#34136
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4341C2semidirect
3. C2×D11×#117C2semidirect
4. #13071658C2semidirect
5. #13071643C2semidirect
6. #13071641C2semidirect
7. #13071637C2semidirect
8. #13071628C2semidirect
9. #13071623C2semidirect
10. #13071620C2semidirect
11. #13071609C2semidirect
12. #13071605C2semidirect
13. #13071599C2semidirect
14. #13071597C2semidirect
15. #13071103C2semidirect
16. #13071097C2semidirect
17. #13071078C2semidirect
18. #13071058C2semidirect
19. #13071056C2semidirect
20. C4×(C22⋊D11)⋊C4C2semidirect
21. C4×#66945C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2363C2semidirect
27. C2×C4×D4×C11C22semidirect
32. C2×D4×Dic11C22semidirect
37. C22×C4×Dic11C22semidirect
38. #10623137C4semidirect
47. C2×#66940C22semidirect
56. C2×#66930C22semidirect
61. C2×C4×Dic22C22semidirect
63. C11×#390C22semidirect
64. C11×#389C22semidirect
65. C11×#388C22semidirect
67. C4×C11×C4⋊C4C22semidirect
69. C4×C11×C22⋊C4C22semidirect
71. #10622834C22semidirect
73. #10622823C22semidirect
77. #10622598C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. C4⋊C4×Dic11C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. #10622587C22semidirect
82. #10622586C22semidirect
83. #10622586C22semidirect
88. #10622564C22semidirect
89. #10622559C22semidirect
92. #10622558C22semidirect
95. #10622557C22semidirect
98. C22⋊C4×Dic11C22semidirect
99. C22⋊C4×Dic11C22semidirect
100. C22⋊C4×Dic11C22semidirect
105. C4×C4⋊Dic11C22semidirect
106. #10622546C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. C42×Dic11C22semidirect
109. #10622542C22semidirect
110. #10622541C22semidirect
111. #10622541C22semidirect
120. #10622267C22semidirect
121. #10622266C22semidirect
122. #10622265C22semidirect
123. #10622262C22semidirect
124. #10622262C22semidirect
125. #10622261C22semidirect
138. C2×#4341C2×C4semidirect
141. C22×C4×D11C2×C4semidirect
153. C11×#121C2×C4semidirect
179. #66991C2×C4semidirect
180. #66990C2×C4semidirect
182. D4×Dic11C2×C4semidirect
199. #66977C2×C4semidirect
223. #66950C2×C4semidirect
225. #66945C2×C4semidirect
226. #66945D4semidirect
230. #66936C2×C4semidirect
233. (C22⋊D11)⋊C4C2×C4semidirect
386. (C2×D11)⋊C4#41semidirect
387. (C2×D11)⋊C4#41semidirect
419. #2363D11semidirect
549. C4×D11C4×D4semidirect
570. C2×C4×D4C2×D11semidirect
594. #390C2×D11semidirect
600. #389C2×D11semidirect
608. #388C2×D11semidirect
632. C4×C4⋊C4C2×D11semidirect
648. C4×C22⋊C4C2×D11semidirect
688. C2×D11C4×#41semidirect
739. #121C4×D11semidirect
1007. C11#34136semidirect

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
C2×D11×#1172
#130716582
#130716432
#130716412
#130716372
#130716282
#130716232
#130716202
#130716092
#130716052
#130715992
#130715972
#130711032
#130710972
#130710782
#130710582
#130710562
C4×(C22⋊D11)⋊C42
C4×#669452
C4×C22⋊C4×D112
C11×#23632
#3413611