Finite Group Databasebeta

← #14925898

Subgroups — #14925898

Order 2816.

3394 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074205C212yesmaximal, complemented
4#13074202C212yesmaximal, complemented
5#13073964C212yesmaximal, complemented
6#13073963C211yesmaximal, characteristic, complemented
7#13073508C211yesmaximal, characteristic, complemented
8#13073507C212yesmaximal, complemented
9#13073502C211yesmaximal, characteristic, complemented
10#13072896C211yesmaximal, characteristic, complemented
11#13071945C211yesmaximal, characteristic, complemented
12#13071942C211yesmaximal, characteristic, complemented
13#13071928C211yesmaximal, characteristic
14#13071861C212yesmaximal, complemented
15#13071857C212yesmaximal, complemented
16#13071141C211yesmaximal, characteristic, complemented
17#13071137C212yesmaximal, complemented
18#13071135C211yesmaximal, characteristic, complemented
19#13071121C211yesmaximal, characteristic, complemented
20#13071117C211yesmaximal, characteristic, complemented
21#13071117C212yesmaximal, complemented
22#13070998C211yesmaximal, characteristic, complemented
23C11×#2579C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic, complemented
28C23×C4×D11C2211yescharacteristic, complemented
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic, complemented
31C2×#66990C2211yescharacteristic
32C2×#66988C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×C4×C22⋊D11C2211yescharacteristic, complemented
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
38C22×C4×Dic11C2211yescharacteristic, complemented
39C4×D4×D11—28no—
40C2×#66947C2212yes—
41C2×#66946—28no—
42C2×#66946C2212yes—
43C2×#66946C2212yes—
44C2×#66946C2212yescomplemented
45C2×#66946C2211yescharacteristic, complemented
46C2×#66946C2212yescomplemented
47C2×#66946C2212yescomplemented
48C2×#66945C2212yescomplemented
49C2×C4⋊C4×D11C2211yescharacteristic, complemented
50C2×#66939C2211yescharacteristic
51C2×#66935C2212yes—
52C2×#66935C2211yescharacteristic
53C2×(C22⋊D11)⋊C4C2211yescharacteristic
54C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
55C2×(C22⋊D11)⋊C4C2212yescomplemented
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×C22⋊C4×D11C2211yescharacteristic, complemented
58C2×C4×D44C2211yescharacteristic, complemented
59C2×C42×D11C2211yescharacteristic, complemented
60C11×#398C2212yescomplemented
61C11×#396C2212yescomplemented
62C11×#387C2212yescomplemented
63C11×#386C2211yescharacteristic
64C11×#386C2211yescharacteristic
65C11×#385C2211yescharacteristic, complemented
66C11×#385C2212yescomplemented
67C11×#385C2211yescharacteristic, complemented
68C11×#380C2211yescharacteristic, complemented
69#10622826C2211yescharacteristic
70#10622826C2211yescharacteristic
71#10622826C2212yescomplemented
72#10622825C2211yescharacteristic, complemented
73#10622823C2211yescharacteristic, complemented
74#10622823C2211yescharacteristic, complemented
75#10622607C2212yescomplemented
76#10622607C2212yescomplemented
77#10622607C2212yescomplemented
78#10622606C2212yescomplemented
79#10622604C2212yescomplemented
80#10622604C2212yescomplemented
81#10622603C2212yescomplemented
82#10622602C2212yescomplemented
83#10622602C2212yescomplemented
84#10622602C2212yescomplemented
85#10622600C2212yescomplemented
86#10622597C2212yescomplemented
87#10622591C2212yescomplemented
88C4⋊C4×Dic11C2212yescomplemented
89#10622574C2212yescomplemented
90#10622574C2212yescomplemented
91#10622573C2212yes—
92#10622569C2212yescomplemented
93#10622568C2211yescharacteristic
94#10622568C2211yescharacteristic
95#10622568C2212yescomplemented
96#10622568C2211yescharacteristic, complemented
97#10622568C2211yescharacteristic, complemented
98#10622558C2212yescomplemented
99#10622556C2211yescharacteristic, complemented
100#10622556C2211yescharacteristic, complemented
101C22⋊C4×Dic11C2211yescharacteristic, complemented
102C22⋊C4×Dic11C2212yescomplemented
103C22⋊C4×Dic11C2211yescharacteristic, complemented
104#10622553C2212yescomplemented
105#10622288C2212yescomplemented
106#10622285C2212yescomplemented
107#10622285C2212yescomplemented
108#10622284C2212yes—
109#10622283C2212yescomplemented
110#10622281C2212yescomplemented
111#10622281C2212yescomplemented
112#10622279C2212yescomplemented
113#10622279C2212yescomplemented
114#10622279C2212yescomplemented
115#10622279C2212yescomplemented
116#10622278C2212yes—
117#10622278C2212yes—
118#10622278C2212yescomplemented
119#10622278C2212yescomplemented
120#10622277C2212yescomplemented
121#10622277C2212yescomplemented
122#10622268C2212yescomplemented
123#10622267C2212yescomplemented
124#10622262C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C2×D4×D11—24no—
142C22×D44—24no—
143C22×D44—28no—
144C22×D44C2311yescharacteristic
145C22×D44C2312yes—
146C22×D44C2312yes—
147C22×D44C2312yes—
148C22×C4×D11—24no—
149C22×C4×D11—24no—
150C22×C4×D11—44no—
151C22×C4×D11—44no—
152C22×C4×D11—44no—
153C22×C4×D11D418yescomplemented
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2312yes—
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2312yes—
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2311yescharacteristic
165C4×D4×C11—24no—
166C2×C11×C4⋊C4—24no—
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2312yes—
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C4⋊C4C2312yes—
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2311yescharacteristic
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2311yescharacteristic
178C2×C11×C22⋊C4C2312yes—
179C2×C42×C11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2311yescharacteristic
185#66990—24no—
186#66988—24no—
187D4×Dic11—24no—
188C4×C22⋊D11—24no—
189C4×C22⋊D11—24no—
190C2×(C2×D11)⋊C4—24no—
191C2×(C2×D11)⋊C4—24no—
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2312yes—
215C2×C4⋊Dic11C2312yes—
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×C4×Dic11—24no—
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2312yes—
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229#66947—28no—
230#66946—28no—
231#66946—28no—
232#66946—28no—
233#66946—28no—
234#66946—24no—
235#66946—44no—
236#66945—44no—
237C4⋊C4×D11—24no—
238#66939—24no—
239#66935—24no—
240#66935—28no—
241(C22⋊D11)⋊C4—24no—
242(C22⋊D11)⋊C4—24no—
243(C22⋊D11)⋊C4—44no—
244C22⋊C4×D11—24no—
245C22⋊C4×D11—24no—
246C4×D44—24no—
247C42×D11—24no—
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#34956—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C24×C11C2411yescharacteristic
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—24no—
273C23×D11—24no—
274C23×D11—22no—
275C23×D11—22no—
276C23×D11—22no—
277C23×D11—24no—
278C23×D11—42no—
279C23×D11—42no—
280C23×D11—42no—
281C23×D11C2×D414yes—
282C23×D11C2411yescharacteristic
283C23×D11C2412yes—
284C23×D11C2411yescharacteristic
285C23×D11C2411yescharacteristic
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11#4114yes—
289C22×C4×C11—22no—
290C22×C4×C11—24no—
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11—42no—
296C22×C4×C11C2×D414yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2412yes—
301C22×C4×C11C2412yes—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2412yes—
305C22×C4×C11C2411yescharacteristic
306C2×C22⋊D11—22no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11#4114yes—
315C22×Dic11—24no—
316C22×Dic11—22no—
317C22×Dic11—24no—
318C22×Dic11—22no—
319C22×Dic11—22no—
320C22×Dic11—22no—
321C22×Dic11C2×D414yes—
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2412yes—
325C22×Dic11C2412yes—
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330D4×D11—232no—
331C2×D44—232no—
332C2×D44—22no—
333C2×D44—24no—
334C2×D44—24no—
335C2×D44—24no—
336C2×D44—24no—
337C2×D44—22no—
338C2×D44—24no—
339C2×D44—24no—
340C2×D44—24no—
341C2×D44—22no—
342C2×D44—42no—
343C2×D44#4118yes—
344C2×C4×D11—22no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—22no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—22no—
356C2×C4×D11—24no—
357C2×C4×D11—22no—
358C2×C4×D11—22no—
359C2×C4×D11—42no—
360C2×C4×D11—42no—
361C2×C4×D11—42no—
362C2×C4×D11—42no—
363C2×C4×D11—42no—
364C2×C4×D11—42no—
365C2×C4×D11—416no—
366C2×C4×D11—416no—
367C2×C4×D11—416no—
368C2×C4×D11C2×D414yes—
369C2×C4×D11C2×D414yes—
370C2×C4×D11C2×D414yes—
371C2×C4×D11C2×D414yes—
372C11×C4⋊C4—22no—
373C11×C4⋊C4—24no—
374C11×C4⋊C4—24no—
375C11×C4⋊C4—24no—
376C11×C4⋊C4—42no—
377C11×C4⋊C4—42no—
378C11×C22⋊C4—22no—
379C11×C22⋊C4—22no—
380C11×C22⋊C4—22no—
381C11×C22⋊C4—22no—
382C11×C22⋊C4—24no—
383C11×C22⋊C4—42no—
384C42×C11—22no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—24no—
388C22⋊Dic11—22no—
389C22⋊Dic11—22no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—22no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—24no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—22no—
402(C2×D11)⋊C4—24no—
403(C2×D11)⋊C4—24no—
404(C2×D11)⋊C4—24no—
405(C2×D11)⋊C4—24no—
406(C2×D11)⋊C4—42no—
407(C2×D11)⋊C4—42no—
408(C2×D11)⋊C4—42no—
409(C2×D11)⋊C4—42no—
410(C2×D11)⋊C4—42no—
411C4⋊Dic11—22no—
412C4⋊Dic11—24no—
413C4⋊Dic11—42no—
414Dic11⋊C4—22no—
415Dic11⋊C4—22no—
416Dic11⋊C4—24no—
417Dic11⋊C4—24no—
418Dic11⋊C4—42no—
419C4×Dic11—22no—
420C4×Dic11—22no—
421C4×Dic11—24no—
422C4×Dic11—24no—
423C4×Dic11—24no—
424C4×Dic11—24no—
425C4×Dic11—22no—
426C22×C4×D4—111no—
427C22×C4×D4—111no—
428#2600—112no—
429#2600—112no—
430#2579—112no—
431#2579—111no—
432#2579D1111yescharacteristic, complemented
433#2534—112no—
434#2534—111no—
435#2534—111no—
436#2483—111no—
437#2405—111no—
438#2405—111no—
439#2403—111no—
440#2392—112no—
441#2392—112no—
442C4×#123—112no—
443C4×#123—111no—
444C4×#123—111no—
445C4×#120—111no—
446C4×#120—112no—
447C4×#120—111no—
448#2280—111no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—21no—
452C23×C11—22no—
453C23×C11—21no—
454C23×C11—22no—
455C23×C11C22×D412yes—
456C23×C11C2×#4112yes—
457C23×C11C2×#4112yes—
458C23×C11C2×#4112yes—
459C23×C11C2511yescharacteristic
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—22no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—28no—
466C22×D11—22no—
467C22×D11—21no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—21no—
474C22×D11—21no—
475C22×D11—21no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—28no—
481C22×D11—44no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11—48no—
485C22×D11—48no—
486C22×D11—48no—
487C22×D11—48no—
488C22×D11—44no—
489C22×D11—44no—
490C22×D11—44no—
491C22×D11—44no—
492C22×D11C22×D412yes—
493C22×D11C22×D412yes—
494C22×D11C2×#4112yes—
495C22×D11C2×#4114yes—
496C22×D11C2×#4114yes—
497D4×C11—28no—
498C2×C4×C11—28no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—44no—
519C2×C4×C11—44no—
520C2×C4×C11—44no—
521C2×C4×C11C22×D412yes—
522C2×C4×C11C22×D412yes—
523C2×C4×C11C2×#4112yes—
524C2×C4×C11C2×#4114yes—
525C22⋊D11—28no—
526C22⋊D11—28no—
527C22⋊D11—48no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—22no—
531C2×Dic11—28no—
532C2×Dic11—22no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—44no—
546C2×Dic11—44no—
547C2×Dic11C22×D412yes—
548C2×Dic11C22×D412yes—
549C2×Dic11C2×#4112yes—
550C2×Dic11H(5,𝔽2)14yes—
551D44—216no—
552D44—28no—
553D44—216no—
554D44—48no—
555C4×D11—28no—
556C4×D11—28no—
557C4×D11—28no—
558C4×D11—44no—
559C4×D11—44no—
560C4×D11—48no—
561C4×D11—44no—
562C4×D11—44no—
563C4×D11—44no—
564C4×D11—44no—
565C4×D11—48no—
566C23×D4—111no—
567C23×D4—111no—
568C24×C4—111no—
569C24×C4—111no—
570C24×C4—111no—
571C2×#123—111no—
572C2×#123—112no—
573C2×#123—111no—
574C2×#120—111no—
575C2×#120—112no—
576C2×#120—111no—
577C2×C4×D4—111no—
578C2×C4×D4—111no—
579C2×C4×D4—111no—
580C2×C4×D4—112no—
581C2×C4×D4—112no—
582C2×C4×D4—112no—
583C2×C4×D4—111no—
584C2×C4×D4—112no—
585C2×C4×D4—112no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—112no—
589C2×C4×D4—111no—
590C2×C4×D4—228no—
591C2×C4×D4—228no—
592C2×C4×D4C2×D1111yescharacteristic
593C2×#117—112no—
594C22×C4⋊C4—111no—
595C22×C4⋊C4C2×D1111yescharacteristic, complemented
596C22×C22⋊C4—111no—
597C22×C22⋊C4—111no—
598C22×C22⋊C4—111no—
599C22×C22⋊C4—111no—
600C22×C42—111no—
601C22×C42—111no—
602#398—112no—
603#398C2×D1112yescomplemented
604#397—112no—
605#397—112no—
606#396—112no—
607#396—112no—
608#396—112no—
609#396C2×D1112yescomplemented
610#394—112no—
611#394—112no—
612#394—112no—
613#394—112no—
614#394—112no—
615#394—112no—
616#392—112no—
617#392—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388—112no—
622#387—112no—
623#387—112no—
624#387—112no—
625#387C2×D1112yescomplemented
626#386—111no—
627#386—111no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386—112no—
634#386C2×D1111yescharacteristic
635#386C2×D1111yescharacteristic
636#385—111no—
637#385—111no—
638#385—112no—
639#385—112no—
640#385—112no—
641#385—112no—
642#385—112no—
643#385C2×D1112yescomplemented
644#385C2×D1111yescharacteristic, complemented
645#385C2×D1111yescharacteristic, complemented
646#381—111no—
647#381—111no—
648#381—112no—
649#381—112no—
650#380—111no—
651#380—112no—
652#380C2×D1111yescharacteristic, complemented
653#379—111no—
654#379—111no—
655#379—111no—
656#379—111no—
657#379—112no—
658C4×C4⋊C4—112no—
659C4×C4⋊C4—112no—
660C4×C22⋊C4—112no—
661C4×C22⋊C4—111no—
662C4×C22⋊C4—111no—
663C4×C22⋊C4—112no—
664C4×C22⋊C4—112no—
665C4×C22⋊C4—112no—
666C4×C22⋊C4—112no—
667C22×C11—22no—
668C22×C11—22no—
669C22×C11—24no—
670C22×C11—24no—
671C22×C11—22no—
672C22×C11—24no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11—42no—
676C22×C11#52514yes—
677C22×C11C23×D411yescharacteristic
678C22×C11C22×#4111yescharacteristic
679C22×C11C22×#4111yescharacteristic
680C22×C11C22×#4112yes—
681C22×C11C2×H(5,𝔽2)12yes—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—24no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—24no—
692C2×D11—24no—
693C2×D11—24no—
694C2×D11—416no—
695C2×D11—416no—
696C2×D11—416no—
697C2×D11—42no—
698C2×D11—41no—
699C2×D11—42no—
700C2×D11—41no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11#52514yes—
707C4×C11—24no—
708C4×C11—22no—
709C4×C11—22no—
710C4×C11—22no—
711C4×C11—41no—
712C4×C11—41no—
713C4×C11—42no—
714C4×C11—42no—
715C4×C11—42no—
716Dic11—22no—
717Dic11—22no—
718Dic11—41no—
719Dic11—42no—
720Dic11—41no—
721Dic11—42no—
722Dic11—42no—
723Dic11#53414yes—
724C25—111no—
725C25—111no—
726C25—111no—
727C22×D4—111no—
728C22×D4—111no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—111no—
732C22×D4—112no—
733C22×D4—112no—
734C22×D4—228no—
735C22×D4—224no—
736C22×D4—224no—
737C22×D4—224no—
738C22×D4—224no—
739C22×D4C22×D1111yescharacteristic
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—118no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—112no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—112no—
754C23×C4—111no—
755C23×C4—224no—
756C23×C4—224no—
757C23×C4—444no—
758C23×C4—444no—
759C23×C4—444no—
760C23×C4C22×D1111yescharacteristic
761C23×C4C22×D1111yescharacteristic
762C23×C4C22×D1111yescharacteristic
763C23×C4C22×D1111yescharacteristic
764#123—224no—
765#123—228no—
766#123—224no—
767#120—224no—
768#120—228no—
769#120—224no—
770C4×D4—24no—
771C4×D4—224no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—228no—
775C4×D4—228no—
776C4×D4—228no—
777C4×D4—228no—
778C4×D4—224no—
779C4×D4—224no—
780C4×D4—224no—
781C4×D4—224no—
782C4×D4—444no—
783C4×D4—444no—
784#117—444no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—111no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—112no—
790C2×C4⋊C4—112no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—112no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—224no—
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1112yes—
797C2×C4⋊C4C22×D1112yes—
798C2×C4⋊C4C22×D1112yes—
799C2×C4⋊C4C22×D1112yes—
800C2×C4⋊C4C22×D1112yes—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—111no—
813C2×C22⋊C4—111no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—112no—
823C2×C22⋊C4—112no—
824C2×C22⋊C4—112no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—112no—
827C2×C22⋊C4—224no—
828C2×C22⋊C4—224no—
829C2×C22⋊C4—224no—
830C2×C22⋊C4—224no—
831C2×C22⋊C4C22×D1111yescharacteristic
832C2×C22⋊C4C22×D1111yescharacteristic
833C2×C22⋊C4C22×D1111yescharacteristic
834C2×C22⋊C4C22×D1112yes—
835C2×C22⋊C4C22×D1111yescharacteristic
836C2×C22⋊C4C22×D1112yes—
837C2×C42—112no—
838C2×C42—112no—
839C2×C42—111no—
840C2×C42—111no—
841C2×C42—112no—
842C2×C42—112no—
843C2×C42—111no—
844C2×C42—224no—
845C2×C42—224no—
846C2×C42C22×D1111yescharacteristic
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95—112no—
855#95—112no—
856#95—112no—
857#95—112no—
858#95C22×D1112yes—
859#95C22×D1112yes—
860#95C22×D1112yes—
861#95C22×D1112yes—
862#95C22×D1112yes—
863C2×C11—24no—
864C2×C11—42no—
865C2×C11C2×#52511yescharacteristic
866C2×C11C2×#52511yescharacteristic
867C2×C11C2×#53411yescharacteristic
868C2×C11#348112yes—
869C2×C11#348112yes—
870D11—24no—
871D11—42no—
872D11—44no—
873D11—42no—
874C24—111no—
875C24—111no—
876C24—112no—
877C24—111no—
878C24—114no—
879C24—222no—
880C24—224no—
881C24—224no—
882C24—222no—
883C24—224no—
884C24—222no—
885C24—222no—
886C24—222no—
887C24—222no—
888C24—222no—
889C24—222no—
890C24—442no—
891C24—442no—
892C24—442no—
893C24C23×D1111yescharacteristic
894C24C23×D1111yescharacteristic
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—114no—
898C2×D4—118no—
899C2×D4—222no—
900C2×D4—224no—
901C2×D4—224no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—222no—
905C2×D4—2232no—
906C2×D4—224no—
907C2×D4—224no—
908C2×D4—222no—
909C2×D4—2232no—
910C2×D4—222no—
911C2×D4—222no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—224no—
915C2×D4—224no—
916C2×D4—222no—
917C2×D4—224no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4#434314yes—
921C22×C4—22no—
922C22×C4—24no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—111no—
929C22×C4—114no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—114no—
933C22×C4—114no—
934C22×C4—114no—
935C22×C4—114no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—111no—
939C22×C4—112no—
940C22×C4—111no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—224no—
946C22×C4—224no—
947C22×C4—224no—
948C22×C4—224no—
949C22×C4—224no—
950C22×C4—222no—
951C22×C4—222no—
952C22×C4—222no—
953C22×C4—224no—
954C22×C4—224no—
955C22×C4—222no—
956C22×C4—224no—
957C22×C4—222no—
958C22×C4—222no—
959C22×C4—222no—
960C22×C4—222no—
961C22×C4—222no—
962C22×C4—442no—
963C22×C4—442no—
964C22×C4—442no—
965C22×C4—442no—
966C22×C4—442no—
967C22×C4—442no—
968C22×C4—4416no—
969C22×C4—4416no—
970C22×C4—4416no—
971C22×C4D4×D1114yes—
972C22×C4C23×D1112yes—
973C22×C4C23×D1111yescharacteristic
974C22×C4C23×D1111yescharacteristic
975C22×C4C23×D1112yes—
976C22×C4C23×D1112yes—
977C22×C4C23×D1111yescharacteristic
978C22×C4C23×D1111yescharacteristic
979C22×C4C23×D1111yescharacteristic
980C22×C4C23×D1112yes—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—22no—
984C4⋊C4—24no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—222no—
988C4⋊C4—222no—
989C4⋊C4—224no—
990C4⋊C4—222no—
991C4⋊C4—224no—
992C4⋊C4—224no—
993C4⋊C4—442no—
994C4⋊C4—442no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—24no—
1000C22⋊C4—42no—
1001C22⋊C4—222no—
1002C22⋊C4—224no—
1003C22⋊C4—222no—
1004C22⋊C4—222no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—224no—
1008C22⋊C4—224no—
1009C22⋊C4—224no—
1010C22⋊C4—224no—
1011C22⋊C4—224no—
1012C22⋊C4—222no—
1013C22⋊C4—222no—
1014C22⋊C4—222no—
1015C22⋊C4—222no—
1016C22⋊C4—224no—
1017C22⋊C4—224no—
1018C22⋊C4—222no—
1019C22⋊C4—224no—
1020C22⋊C4—224no—
1021C22⋊C4—224no—
1022C22⋊C4—442no—
1023C22⋊C4—442no—
1024C22⋊C4—442no—
1025C22⋊C4—442no—
1026C22⋊C4—442no—
1027C42—22no—
1028C42—222no—
1029C42—224no—
1030C42—224no—
1031C42—222no—
1032C42—224no—
1033C42—224no—
1034C42—222no—
1035C11#3495611yescharacteristic, complemented, Sylow
1036C23—22no—
1037C23—22no—
1038C23—21no—
1039C23—22no—
1040C23—21no—
1041C23—22no—
1042C23—112no—
1043C23—114no—
1044C23—112no—
1045C23—112no—
1046C23—114no—
1047C23—228no—
1048C23—228no—
1049C23—228no—
1050C23—221no—
1051C23—221no—
1052C23—222no—
1053C23—228no—
1054C23—221no—
1055C23—222no—
1056C23—222no—
1057C23—221no—
1058C23—221no—
1059C23—222no—
1060C23—222no—
1061C23—221no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23—444no—
1069C23—448no—
1070C23—448no—
1071C23—448no—
1072C23—448no—
1073C23—448no—
1074C23—444no—
1075C23—444no—
1076C23—448no—
1077C23—444no—
1078C23—444no—
1079C23C2×D4×D1112yes—
1080C23C2×#434312yes—
1081C23C2×#434312yes—
1082C23#41×D1112yes—
1083C23C24×D1111yescharacteristic
1084D4—28no—
1085D4—2216no—
1086D4—228no—
1087D4—2216no—
1088D4—228no—
1089D4—228no—
1090D4—448no—
1091D4—448no—
1092C2×C4—28no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—112no—
1116C2×C4—114no—
1117C2×C4—112no—
1118C2×C4—112no—
1119C2×C4—228no—
1120C2×C4—228no—
1121C2×C4—228no—
1122C2×C4—228no—
1123C2×C4—221no—
1124C2×C4—221no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—221no—
1128C2×C4—221no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—222no—
1137C2×C4—222no—
1138C2×C4—222no—
1139C2×C4—444no—
1140C2×C4—444no—
1141C2×C4—444no—
1142C2×C4—444no—
1143C2×C4—448no—
1144C2×C4—448no—
1145C2×C4—444no—
1146C2×C4—444no—
1147C2×C4—444no—
1148C2×C4—444no—
1149C2×C4C2×D4×D1112yes—
1150C2×C4C2×D4×D1112yes—
1151C2×C4C2×#434312yes—
1152C2×C4#41×D1114yes—
1153C22—22no—
1154C22—24no—
1155C22—24no—
1156C22—22no—
1157C22—22no—
1158C22—24no—
1159C22—41no—
1160C22—42no—
1161C22—41no—
1162C22—114no—
1163C22—222no—
1164C22—222no—
1165C22—224no—
1166C22—224no—
1167C22—222no—
1168C22—222no—
1169C22—222no—
1170C22—224no—
1171C22—224no—
1172C22—224no—
1173C22—224no—
1174C22—222no—
1175C22—4416no—
1176C22—4416no—
1177C22—4416no—
1178C22—442no—
1179C22—441no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—442no—
1184C22—442no—
1185C22—442no—
1186C22—441no—
1187C22#1062315814yes—
1188C22C22×D4×D1111yescharacteristic
1189C22C22×#434311yescharacteristic
1190C22C2×#41×D1111yescharacteristic
1191C22C2×#41×D1112yes—
1192C22D11×H(5,𝔽2)12yes—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—24no—
1197C4—41no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—41no—
1202C4—114no—
1203C4—222no—
1204C4—222no—
1205C4—442no—
1206C4—441no—
1207C4—442no—
1208C4—442no—
1209C4—441no—
1210C2—24no—
1211C2—42no—
1212C2—224no—
1213C2—442no—
1214C2—442no—
1215C2—444no—
1216C2D11×#52511yescharacteristic
1217C2C2×#1062315811yescharacteristic
1218C2D11×#53411yescharacteristic
1219C2#1308222312yes—
1220C2#1308222712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2579C2
prime radical#13071928C2
hypercenter#2579D11
hypocenterC11#34956
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2579

Complements

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

NH ≅ G/Ntype
1. C22×#66946C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074205C2semidirect
4. #13074202C2semidirect
5. #13073964C2semidirect
6. #13073963C2semidirect
7. #13073508C2semidirect
8. #13073507C2semidirect
9. #13073502C2semidirect
10. #13072896C2semidirect
11. #13071945C2semidirect
12. #13071942C2semidirect
14. #13071861C2semidirect
15. #13071857C2semidirect
16. #13071141C2semidirect
17. #13071137C2semidirect
18. #13071135C2semidirect
19. #13071121C2semidirect
20. #13071117C2semidirect
21. #13071117C2semidirect
22. #13070998C2semidirect
23. C11×#2579C2semidirect
27. C23×C4×D11C22semidirect
28. C23×C4×D11C22semidirect
30. C22×C11×C4⋊C4C22semidirect
35. C2×C4×C22⋊D11C22semidirect
37. C22×(C2×D11)⋊C4C22semidirect
38. C22×C4×Dic11C22semidirect
44. C2×#66946C22semidirect
45. C2×#66946C22semidirect
46. C2×#66946C22semidirect
47. C2×#66946C22semidirect
48. C2×#66945C22semidirect
49. C2×C4⋊C4×D11C22semidirect
54. C2×(C22⋊D11)⋊C4C22semidirect
55. C2×(C22⋊D11)⋊C4C22semidirect
57. C2×C22⋊C4×D11C22semidirect
58. C2×C4×D44C22semidirect
59. C2×C42×D11C22semidirect
60. C11×#398C22semidirect
61. C11×#396C22semidirect
62. C11×#387C22semidirect
65. C11×#385C22semidirect
66. C11×#385C22semidirect
67. C11×#385C22semidirect
68. C11×#380C22semidirect
71. #10622826C22semidirect
72. #10622825C22semidirect
73. #10622823C22semidirect
74. #10622823C22semidirect
75. #10622607C22semidirect
76. #10622607C22semidirect
77. #10622607C22semidirect
78. #10622606C22semidirect
79. #10622604C22semidirect
80. #10622604C22semidirect
81. #10622603C22semidirect
82. #10622602C22semidirect
83. #10622602C22semidirect
84. #10622602C22semidirect
85. #10622600C22semidirect
86. #10622597C22semidirect
87. #10622591C22semidirect
88. C4⋊C4×Dic11C22semidirect
89. #10622574C22semidirect
90. #10622574C22semidirect
92. #10622569C22semidirect
95. #10622568C22semidirect
96. #10622568C22semidirect
97. #10622568C22semidirect
98. #10622558C22semidirect
99. #10622556C22semidirect
100. #10622556C22semidirect
101. C22⋊C4×Dic11C22semidirect
102. C22⋊C4×Dic11C22semidirect
103. C22⋊C4×Dic11C22semidirect
104. #10622553C22semidirect
105. #10622288C22semidirect
106. #10622285C22semidirect
107. #10622285C22semidirect
109. #10622283C22semidirect
110. #10622281C22semidirect
111. #10622281C22semidirect
112. #10622279C22semidirect
113. #10622279C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
118. #10622278C22semidirect
119. #10622278C22semidirect
120. #10622277C22semidirect
121. #10622277C22semidirect
122. #10622268C22semidirect
123. #10622267C22semidirect
124. #10622262C22semidirect
153. C22×C4×D11D4semidirect
432. #2579D11semidirect
595. C22×C4⋊C4C2×D11semidirect
603. #398C2×D11semidirect
609. #396C2×D11semidirect
625. #387C2×D11semidirect
643. #385C2×D11semidirect
644. #385C2×D11semidirect
645. #385C2×D11semidirect
652. #380C2×D11semidirect
1035. C11#34956semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×C4×D4×D112
#130742052
#130742022
#130739642
#130739632
#130735082
#130735072
#130735022
#130728962
#130719452
#130719422
#130719282
#130718612
#130718572
#130711412
#130711372
#130711352
#130711212
#130711172
#130709982
C11×#25792
#3495611