Finite Group Databasebeta

← #14914154

Subgroups — #14914154

Order 2816.

3054 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3C2×#10623054C211yesmaximal, characteristic, complemented
4#13071667C212yesmaximal, complemented
5#13071665C212yesmaximal, complemented
6#13071662C212yesmaximal, complemented
7#13071660C212yesmaximal, complemented
8#13071548C211yesmaximal, characteristic, complemented
9#13071547C211yesmaximal, characteristic, complemented
10#13071546C211yesmaximal, characteristic, complemented
11#13071545C211yesmaximal, characteristic, complemented
12#13071542C211yesmaximal, characteristic, complemented
13#13071541C211yesmaximal, characteristic, complemented
14#13071538C211yesmaximal, characteristic, complemented
15#13071337C212yesmaximal, complemented
16#13071331C212yesmaximal, complemented
17#13071205C211yesmaximal, characteristic, complemented
18#13071205C211yesmaximal, characteristic, complemented
19#13071157C212yesmaximal, complemented
20C4×#66938C212yesmaximal, complemented
21D11×#382C211yesmaximal, characteristic, complemented
22C4×#66945C211yesmaximal, characteristic, complemented
23C11×#2352C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×#66993C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2212yes—
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×#66979C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37#10623079C4116yescomplemented
38#10623054—28no—
39C2×#66948C2211yescharacteristic
40#10623035—28no—
41C2×#66946C2212yes—
42C2×#66945C2211yescharacteristic
43C2×#66945C2211yescharacteristic
44C2×#66945C2211yescharacteristic
45C2×#66945C2211yescharacteristic
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×C4⋊C4×D11C2211yescharacteristic
48C2×C4⋊C4×D11C2211yescharacteristic
49C2×C4⋊C4×D11C2211yescharacteristic
50C2×#66941C2211yescharacteristic
51C2×#66940C2212yes—
52C2×#66938C2211yescharacteristic
53C2×#66938C2211yescharacteristic
54C2×#66937C2211yescharacteristic
55C2×#66937C2211yescharacteristic
56C2×(C22⋊D11)⋊C4C2212yes—
57C2×(C22⋊D11)⋊C4C2212yes—
58C2×C4×D44C2212yes—
59C2×C4×D44C2211yescharacteristic
60C2×C42×D11C2211yescharacteristic
61C2×C4×Dic22C2212yes—
62C11×#388C2212yes—
63C11×#387C2212yes—
64C11×#386C2212yes—
65C11×#382C2211yescharacteristic
66C11×#380C2211yescharacteristic
67C11×#380C2211yescharacteristic
68C4×C11×C4⋊C4C2211yescharacteristic
69C4×C11×C22⋊C4C2212yes—
70#10622833C2212yes—
71#10622826C2212yes—
72#10622825C2211yescharacteristic
73#10622825C2211yescharacteristic
74C4×C22⋊Dic11C2212yes—
75#10622603C2212yes—
76#10622600C2211yescharacteristic
77#10622600C2211yescharacteristic
78#10622600C2211yescharacteristic
79#10622600C2211yescharacteristic
80#10622594C2212yes—
81#10622591C2212yes—
82#10622590C2211yescharacteristic
83#10622590C2211yescharacteristic
84C4⋊C4×Dic11C2211yescharacteristic
85C4⋊C4×Dic11C2211yescharacteristic
86#10622571C2212yes—
87#10622570C2212yes—
88#10622570C2212yes—
89#10622569C2212yes—
90#10622569C2212yes—
91#10622569C2212yes—
92#10622569C2212yes—
93#10622564C2212yes—
94#10622558C2212yes—
95#10622557C2212yes—
96C22⋊C4×Dic11C2212yes—
97C22⋊C4×Dic11C2212yes—
98#10622553C2212yes—
99C4×(C2×D11)⋊C4C2212yes—
100C4×(C2×D11)⋊C4C2212yes—
101C4×(C2×D11)⋊C4C2212yes—
102#10622549C2211yescharacteristic
103C4×C4⋊Dic11C2211yescharacteristic
104#10622546C2212yes—
105C42×Dic11C2212yes—
106#10622283C2212yes—
107#10622282C2212yes—
108#10622279C2212yes—
109#10622279C2212yes—
110#10622279C2212yes—
111#10622278C2212yes—
112#10622278C2212yes—
113#10622278C2212yes—
114#10622278C2212yes—
115D11×#95C2212yes—
116D11×#95C2212yes—
117#10622268C2212yes—
118#10622267C2212yes—
119#10622266C2212yes—
120#10622265C2212yes—
121#10622263C2212yes—
122#10622263C2212yes—
123#10622261C2212yes—
124#10622259C2212yes—
125#10622259C2212yes—
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2311yescharacteristic
136C23×Dic11C2312yes—
137C2×#4339—24no—
138C2×#4339—24no—
139C2×#4339—24no—
140C2×#4339—24no—
141C2×#4339C2×C418yescomplemented
142C2×#4339C2×C418yescomplemented
143C22×D44C2311yescharacteristic
144C22×D44C2311yescharacteristic
145C22×D44C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×Dic22C2311yescharacteristic
156C22×Dic22C2311yescharacteristic
157C4×D4×C11C2×C418yescomplemented
158C11×#117—24no—
159C2×C11×C4⋊C4—24no—
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C42×C11C2312yes—
172C2×C42×C11C2312yes—
173C2×C42×C11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179#66993C2×C418yescomplemented
180#66991C2×C418yescomplemented
181C4×C22⋊D11—28no—
182C4×C22⋊D11—28no—
183C4×C22⋊D11C2×C418yescomplemented
184C4×C22⋊D11C2×C418yescomplemented
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2312yes—
197#66979—24no—
198C2×C4⋊Dic11—24no—
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2312yes—
222#66948C2×C418yescomplemented
223#66946—28no—
224#66945—24no—
225#66945—24no—
226#66945—24no—
227#66945D418yescomplemented
228C4⋊C4×D11—24no—
229C4⋊C4×D11—24no—
230C4⋊C4×D11—24no—
231C4⋊C4×D11—24no—
232#66941C2×C418yescomplemented
233#66940—28no—
234#66938C2×C418yescomplemented
235#66938C2×C418yescomplemented
236#66937C2×C418yescomplemented
237#66937C2×C418yescomplemented
238(C22⋊D11)⋊C4—28no—
239(C22⋊D11)⋊C4—28no—
240C4×D44—28no—
241C4×D44C2×C418yescomplemented
242C42×D11C2×C418yescomplemented
243C4×Dic22—28no—
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#34208—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C24×C11C2411yescharacteristic
267C23×D11C2411yescharacteristic
268C23×D11C2411yescharacteristic
269C23×D11C2411yescharacteristic
270C2×D4×C11—41no—
271C2×D4×C11—41no—
272C2×D4×C11C22×C414yes—
273C22×C4×C11—22no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—22no—
277C22×C4×C11—24no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11C22×C414yes—
281C22×C4×C11C22×C414yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C2×C22⋊D11—22no—
292C2×C22⋊D11—22no—
293C2×C22⋊D11—22no—
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—41no—
300C2×C22⋊D11—41no—
301C2×C22⋊D11—41no—
302C2×C22⋊D11—41no—
303C2×C22⋊D11C22×C414yes—
304C2×C22⋊D11C22×C414yes—
305C2×C22⋊D11C22×C414yes—
306C2×C22⋊D11C22×C414yes—
307C2×C22⋊D11C22×C414yes—
308C2×C22⋊D11C22×C414yes—
309C22×Dic11—24no—
310C22×Dic11—42no—
311C22×Dic11—42no—
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2412yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2412yes—
320C22×Dic11C2411yescharacteristic
321#4339—232no—
322#4339—232no—
323C2×D44—22no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44—22no—
327C2×D44—41no—
328C2×D44—41no—
329C2×D44C22×C414yes—
330C2×D44C22×C414yes—
331C2×D44C22×C414yes—
332C2×C4×D11—24no—
333C2×C4×D11—24no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—41no—
341C2×C4×D11—41no—
342C2×C4×D11—41no—
343C2×C4×D11—41no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11C22×C414yes—
353C2×C4×D11C22×C414yes—
354C2×C4×D11C22×C414yes—
355C2×C4×D11C22×C414yes—
356C2×C4×D11C22×C414yes—
357C2×C4×D11C2×D414yes—
358C2×C4×D11#4114yes—
359C2×Dic22—22no—
360C2×Dic22—22no—
361C2×Dic22—22no—
362C2×Dic22—22no—
363C2×Dic22C22×C414yes—
364C2×Dic22C22×C414yes—
365C11×C4⋊C4—24no—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4C22×C414yes—
370C11×C4⋊C4C2×D414yes—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—42no—
373C11×C22⋊C4—42no—
374C11×C22⋊C4C22×C414yes—
375C11×C22⋊C4C22×C414yes—
376C42×C11—24no—
377C42×C11—42no—
378C42×C11C22×C414yes—
379C22⋊Dic11—24no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382C22⋊Dic11C22×C414yes—
383C22⋊Dic11C22×C414yes—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4C22×C414yes—
392(C2×D11)⋊C4C22×C414yes—
393(C2×D11)⋊C4C22×C414yes—
394(C2×D11)⋊C4C22×C414yes—
395(C2×D11)⋊C4C2×D418yes—
396C4⋊Dic11—24no—
397C4⋊Dic11—22no—
398C4⋊Dic11—22no—
399C4⋊Dic11—22no—
400C4⋊Dic11C22×C414yes—
401C4⋊Dic11C2×D414yes—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—24no—
406Dic11⋊C4C22×C414yes—
407Dic11⋊C4C22×C414yes—
408C4×Dic11—24no—
409C4×Dic11—24no—
410C4×Dic11—24no—
411C4×Dic11—24no—
412C4×Dic11—42no—
413C4×Dic11—42no—
414C4×Dic11—42no—
415C4×Dic11C22×C414yes—
416C4×Dic11C22×C414yes—
417C4×Dic11C22×C414yes—
418C4×Dic11C2×D418yes—
419C2×#532—111no—
420C2×#520—111no—
421C2×#520—111no—
422#2364—112no—
423#2364—112no—
424#2364—112no—
425#2364—112no—
426#2352—111no—
427#2352—111no—
428#2352—111no—
429#2352—111no—
430#2352—111no—
431#2352—111no—
432#2352—111no—
433#2352D1111yescharacteristic, complemented
434#2328—112no—
435#2327—112no—
436#2311—111no—
437#2311—111no—
438C4×#124—112no—
439C4×#124—112no—
440C2×#382—111no—
441C4×#117—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—21no—
452C23×C11—21no—
453C23×C11—21no—
454C23×C11C23×C412yes—
455C23×C11C23×C412yes—
456C23×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—21no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—21no—
473C22×D11C23×C412yes—
474C22×D11C23×C412yes—
475C22×D11C23×C412yes—
476C22×D11C22×D412yes—
477C22×D11C2×#4112yes—
478D4×C11—44no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—28no—
490C2×C4×C11—28no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—84no—
501C2×C4×C11C23×C412yes—
502C2×C4×C11C23×C412yes—
503C2×C4×C11C23×C412yes—
504C2×C4×C11C23×C412yes—
505C2×C4×C11C23×C412yes—
506C2×C4×C11C22×D414yes—
507C2×C4×C11C22×D412yes—
508C2×C4×C11C2×#4112yes—
509C22⋊D11—28no—
510C22⋊D11—28no—
511C22⋊D11—28no—
512C22⋊D11—28no—
513C22⋊D11—44no—
514C22⋊D11—44no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—84no—
535C2×Dic11C23×C412yes—
536C2×Dic11C23×C412yes—
537C2×Dic11C23×C412yes—
538C2×Dic11C23×C412yes—
539C2×Dic11C23×C412yes—
540C2×Dic11C22×D414yes—
541C2×Dic11C22×D412yes—
542C2×Dic11C2×#4112yes—
543D44—28no—
544D44—28no—
545D44—44no—
546C4×D11—28no—
547C4×D11—28no—
548C4×D11—44no—
549C4×D11—44no—
550C4×D11—84no—
551C4×D11—84no—
552C4×D11—84no—
553C4×D11—84no—
554C4×D11C4×D4116yes—
555Dic22—28no—
556Dic22—28no—
557C22×#41—111no—
558C22×#41—111no—
559#532—1116no—
560C2×C4⋊Q8—111no—
561C2×#127—111no—
562C2×#124—111no—
563C2×#124—111no—
564C2×#121—111no—
565C2×#121—111no—
566C2×#121—111no—
567C2×#121—111no—
568#520—228no—
569#520—228no—
570C2×C4×Q8—112no—
571C2×C4×Q8—112no—
572C2×C4×D4—111no—
573C2×C4×D4—111no—
574C2×C4×D4—112no—
575C2×C4×D4—112no—
576C2×C4×D4—112no—
577C2×C4×D4—112no—
578C2×C4×D4—112no—
579C2×C4×D4—111no—
580C2×C4×D4—112no—
581C2×C4×D4C2×D1111yescharacteristic
582C2×#117—111no—
583C2×#117—111no—
584C2×#117—111no—
585C2×#117—111no—
586C2×#117—111no—
587C2×#117C2×D1111yescharacteristic
588C22×C4⋊C4—111no—
589C22×C4⋊C4—111no—
590C22×C4⋊C4—111no—
591C22×C4⋊C4—111no—
592C22×C4⋊C4—111no—
593C22×C4⋊C4C2×D1111yescharacteristic
594C22×C42—111no—
595#391—112no—
596#391—112no—
597#390—112no—
598#390—112no—
599#388—112no—
600#388—112no—
601#388—112no—
602#388—112no—
603#388—112no—
604#388—112no—
605#388—112no—
606#388C2×D1112yes—
607#387—112no—
608#387—112no—
609#387—112no—
610#387—112no—
611#387—112no—
612#387—112no—
613#387—112no—
614#387C2×D1112yes—
615#386—112no—
616#386—112no—
617#386—112no—
618#386—112no—
619#386—112no—
620#386—112no—
621#386—112no—
622#386—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#386C2×D1112yes—
627#382—111no—
628#382—111no—
629#382—111no—
630#382—112no—
631#382—112no—
632#382C2×D1111yescharacteristic
633#380—111no—
634#380—111no—
635#380—111no—
636#380—111no—
637#380—111no—
638#380—111no—
639#380C2×D1111yescharacteristic
640#380C2×D1111yescharacteristic
641C4×C4⋊C4—111no—
642C4×C4⋊C4—111no—
643C4×C4⋊C4—111no—
644C4×C4⋊C4C2×D1111yescharacteristic
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4—112no—
651C4×C22⋊C4—112no—
652C4×C22⋊C4—112no—
653C4×C22⋊C4—112no—
654C4×C22⋊C4C2×D1112yes—
655#376—112no—
656C2×#95—112no—
657C2×#95—112no—
658C43—112no—
659C22×C11—22no—
660C22×C11—22no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—41no—
666C22×C11—41no—
667C22×C11—41no—
668C22×C11—41no—
669C22×C11—41no—
670C22×C11—41no—
671C22×C11—41no—
672C22×C11—41no—
673C22×C11C24×C411yescharacteristic
674C22×C11C23×D411yescharacteristic
675C22×C11C22×#4111yescharacteristic
676C22×C11#58511yescharacteristic
677C22×C11#58511yescharacteristic
678C22×C11#58511yescharacteristic
679C22×C11#58511yescharacteristic
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—41no—
693C2×D11—41no—
694C2×D11—41no—
695C2×D11—41no—
696C2×D11—41no—
697C2×D11—41no—
698C2×D11—41no—
699C2×D11—41no—
700C2×D11C2×C4×D414yes—
701C4×C11—22no—
702C4×C11—22no—
703C4×C11—22no—
704C4×C11—22no—
705C4×C11—24no—
706C4×C11—42no—
707C4×C11—42no—
708C4×C11—42no—
709C4×C11C2×C4×D414yes—
710Dic11—22no—
711Dic11—22no—
712Dic11—22no—
713Dic11—22no—
714Dic11—24no—
715Dic11—42no—
716Dic11—42no—
717Dic11—42no—
718Dic11C2×C4×D414yes—
719C2×#41—118no—
720C2×#41—118no—
721C2×#41—224no—
722C2×#41—224no—
723C2×#41—224no—
724C2×#41—224no—
725C22×Q8—111no—
726C22×Q8—111no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—111no—
730C22×D4—111no—
731C22×D4—111no—
732C22×D4—111no—
733C22×D4—111no—
734C22×D4—111no—
735C22×D4—111no—
736C22×D4C22×D1111yescharacteristic
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—112no—
743C23×C4—112no—
744C23×C4—112no—
745C23×C4—112no—
746C23×C4—112no—
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1112yes—
750C4⋊Q8—118no—
751#127—118no—
752#124—118no—
753#124—118no—
754#121—118no—
755#121—118no—
756#121—118no—
757#121—118no—
758C4×Q8—228no—
759C4×Q8—228no—
760C4×D4—118no—
761C4×D4—118no—
762C4×D4—118no—
763C4×D4—228no—
764C4×D4—228no—
765C4×D4—228no—
766C4×D4—228no—
767C4×D4—228no—
768C4×D4—228no—
769C4×D4C4×D1118yescomplemented
770#117—24no—
771#117—118no—
772#117—224no—
773#117—224no—
774#117—224no—
775#117—224no—
776C2×C4⋊C4—24no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—224no—
790C2×C4⋊C4—224no—
791C2×C4⋊C4—224no—
792C2×C4⋊C4—224no—
793C2×C4⋊C4—224no—
794C2×C4⋊C4C22×D1111yescharacteristic
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1112yes—
797C2×C4⋊C4C22×D1111yescharacteristic
798C2×C4⋊C4C22×D1111yescharacteristic
799C2×C4⋊C4C22×D1111yescharacteristic
800C2×C22⋊C4—111no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4C22×D1112yes—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1111yescharacteristic
821C2×C22⋊C4C22×D1111yescharacteristic
822C2×C42—112no—
823C2×C42—111no—
824C2×C42—111no—
825C2×C42—111no—
826C2×C42—118no—
827C2×C42—112no—
828C2×C42—112no—
829C2×C42—112no—
830C2×C42—112no—
831C2×C42—112no—
832C2×C42—112no—
833C2×C42—112no—
834C2×C42C22×D1112yes—
835C2×C42C22×D1112yes—
836C2×C42C22×D1111yescharacteristic
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95C22×D1112yes—
853#95C22×D1112yes—
854#95C22×D1112yes—
855#95C22×D1112yes—
856#95C22×D1112yes—
857C2×C11—42no—
858C2×C11—42no—
859C2×C11C22×C4×D411yescharacteristic
860C2×C11#342811yescharacteristic
861C2×C11#342811yescharacteristic
862C2×C11#350011yescharacteristic
863C2×C11#350011yescharacteristic
864C2×C11#351211yescharacteristic
865C2×C11#351211yescharacteristic
866D11—24no—
867D11—42no—
868D11—42no—
869C24—111no—
870C24—111no—
871C24—111no—
872C24C23×D1111yescharacteristic
873C24C23×D1111yescharacteristic
874#41—2232no—
875#41—2232no—
876C2×Q8—114no—
877C2×Q8—114no—
878C2×Q8—222no—
879C2×Q8—222no—
880C2×Q8—222no—
881C2×Q8—222no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—114no—
885C2×D4—114no—
886C2×D4—114no—
887C2×D4—114no—
888C2×D4—114no—
889C2×D4—114no—
890C2×D4—114no—
891C2×D4—114no—
892C2×D4—114no—
893C2×D4—222no—
894C2×D4—222no—
895C2×D4—222no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4—222no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—222no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—441no—
906C2×D4—441no—
907C2×D4—441no—
908C2×D4—441no—
909C2×D4—441no—
910C2×D4—441no—
911C2×D4C2×C4×D1114yes—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—24no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—111no—
920C22×C4—114no—
921C22×C4—114no—
922C22×C4—114no—
923C22×C4—111no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—112no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—114no—
931C22×C4—114no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—224no—
936C22×C4—224no—
937C22×C4—224no—
938C22×C4—224no—
939C22×C4—222no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—224no—
944C22×C4—441no—
945C22×C4—441no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4—442no—
957C22×C4—442no—
958C22×C4C2×C4×D1114yes—
959C22×C4C2×C4×D1114yes—
960C22×C4C23×D1112yes—
961C22×C4C23×D1112yes—
962C22×C4C23×D1112yes—
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C22×C4C23×D1111yescharacteristic
966C22×C4C23×D1111yescharacteristic
967C22×C4C23×D1112yes—
968C22×C4C23×D1111yescharacteristic
969C4⋊C4—22no—
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—114no—
974C4⋊C4—114no—
975C4⋊C4—114no—
976C4⋊C4—114no—
977C4⋊C4—224no—
978C4⋊C4—224no—
979C4⋊C4—224no—
980C4⋊C4—224no—
981C4⋊C4—222no—
982C4⋊C4—222no—
983C4⋊C4—224no—
984C4⋊C4—222no—
985C4⋊C4C2×C4×D1114yes—
986C4⋊C4D4×D1114yes—
987C22⋊C4—24no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—114no—
991C22⋊C4—114no—
992C22⋊C4—114no—
993C22⋊C4—114no—
994C22⋊C4—114no—
995C22⋊C4—114no—
996C22⋊C4—118no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—442no—
1002C22⋊C4—442no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4C2×C4×D1114yes—
1008C22⋊C4C2×C4×D1114yes—
1009C42—24no—
1010C42—42no—
1011C42—114no—
1012C42—114no—
1013C42—114no—
1014C42—118no—
1015C42—224no—
1016C42—224no—
1017C42—224no—
1018C42—224no—
1019C42—442no—
1020C42—442no—
1021C42—442no—
1022C42C2×C4×D1114yes—
1023C11#3420811yescharacteristic, complemented, Sylow
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—112no—
1037C23—112no—
1038C23—112no—
1039C23—112no—
1040C23—112no—
1041C23—221no—
1042C23—221no—
1043C23—221no—
1044C23—221no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—221no—
1050C23—221no—
1051C23—221no—
1052C23—221no—
1053C23—221no—
1054C23—221no—
1055C23—221no—
1056C23—221no—
1057C23C22×C4×D1112yes—
1058C23C22×C4×D1112yes—
1059C23C24×D1111yescharacteristic
1060Q8—228no—
1061Q8—228no—
1062D4—44no—
1063D4—228no—
1064D4—228no—
1065D4—228no—
1066D4—228no—
1067D4—228no—
1068D4—228no—
1069D4—444no—
1070D4—444no—
1071D4—444no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—28no—
1083C2×C4—28no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—84no—
1094C2×C4—112no—
1095C2×C4—112no—
1096C2×C4—112no—
1097C2×C4—1116no—
1098C2×C4—112no—
1099C2×C4—112no—
1100C2×C4—112no—
1101C2×C4—112no—
1102C2×C4—114no—
1103C2×C4—221no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—222no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—221no—
1113C2×C4—228no—
1114C2×C4—228no—
1115C2×C4—222no—
1116C2×C4—222no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—222no—
1124C2×C4—444no—
1125C2×C4—444no—
1126C2×C4—884no—
1127C2×C4—884no—
1128C2×C4—884no—
1129C2×C4—884no—
1130C2×C4—884no—
1131C2×C4C22×C4×D1112yes—
1132C2×C4C22×C4×D1112yes—
1133C2×C4C22×C4×D1112yes—
1134C2×C4C22×C4×D1112yes—
1135C2×C4C22×C4×D1112yes—
1136C2×C4C2×D4×D1114yes—
1137C2×C4C2×D4×D1112yes—
1138C2×C4#41×D1112yes—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—22no—
1145C22—41no—
1146C22—41no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—114no—
1154C22—222no—
1155C22—222no—
1156C22—222no—
1157C22—222no—
1158C22—222no—
1159C22—222no—
1160C22—222no—
1161C22—222no—
1162C22—222no—
1163C22—222no—
1164C22—222no—
1165C22—222no—
1166C22—441no—
1167C22—441no—
1168C22—441no—
1169C22—441no—
1170C22—441no—
1171C22—441no—
1172C22—441no—
1173C22—441no—
1174C22C23×C4×D1111yescharacteristic
1175C22C22×D4×D1111yescharacteristic
1176C22C2×#41×D1111yescharacteristic
1177C22#1062345311yescharacteristic
1178C22#1062345311yescharacteristic
1179C22#1062345511yescharacteristic
1180C22#1062345711yescharacteristic
1181C4—24no—
1182C4—22no—
1183C4—22no—
1184C4—22no—
1185C4—22no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—114no—
1190C4—224no—
1191C4—222no—
1192C4—222no—
1193C4—222no—
1194C4—222no—
1195C4—442no—
1196C4—442no—
1197C4—442no—
1198C4C4×D4×D1114yes—
1199C2—42no—
1200C2—42no—
1201C2—224no—
1202C2—442no—
1203C2—442no—
1204C2C2×C4×D4×D1111yescharacteristic
1205C2#1308181611yescharacteristic
1206C2#1308181711yescharacteristic
1207C2#1308240211yescharacteristic
1208C2#1308240711yescharacteristic
1209C2#1308253011yescharacteristic
1210C2#1308253411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2352C2
socle, cosocleC23×C11C25
prime radicalC2×#10623079C2
hypercenter#2352D11
hypocenterC11#34208
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. C2×#10623054C2semidirect
4. #13071667C2semidirect
5. #13071665C2semidirect
6. #13071662C2semidirect
7. #13071660C2semidirect
8. #13071548C2semidirect
9. #13071547C2semidirect
10. #13071546C2semidirect
11. #13071545C2semidirect
12. #13071542C2semidirect
13. #13071541C2semidirect
14. #13071538C2semidirect
15. #13071337C2semidirect
16. #13071331C2semidirect
17. #13071205C2semidirect
18. #13071205C2semidirect
19. #13071157C2semidirect
20. C4×#66938C2semidirect
21. D11×#382C2semidirect
22. C4×#66945C2semidirect
23. C11×#2352C2semidirect
37. #10623079C4semidirect
141. C2×#4339C2×C4semidirect
142. C2×#4339C2×C4semidirect
157. C4×D4×C11C2×C4semidirect
179. #66993C2×C4semidirect
180. #66991C2×C4semidirect
183. C4×C22⋊D11C2×C4semidirect
184. C4×C22⋊D11C2×C4semidirect
222. #66948C2×C4semidirect
227. #66945D4semidirect
232. #66941C2×C4semidirect
234. #66938C2×C4semidirect
235. #66938C2×C4semidirect
236. #66937C2×C4semidirect
237. #66937C2×C4semidirect
241. C4×D44C2×C4semidirect
242. C42×D11C2×C4semidirect
433. #2352D11semidirect
769. C4×D4C4×D11semidirect
1023. C11#34208semidirect

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×#106230352
C2×#106230542
#130716672
#130716652
#130716622
#130716602
#130715482
#130715472
#130715462
#130715452
#130715422
#130715412
#130715382
#130713372
#130713312
#130712052
#130711572
C4×#669382
D11×#3822
C4×#669452
C11×#23522
#3420811