Finite Group Databasebeta

← #14927208

Subgroups — #14927208

Order 2816.

2966 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13076952C211yesmaximal, characteristic, complemented
4#13076944C211yesmaximal, characteristic, complemented
5#13076901C211yesmaximal, characteristic, complemented
6#13076896C211yesmaximal, characteristic, complemented
7#13074394C211yesmaximal, characteristic, complemented
8#13074393C211yesmaximal, characteristic, complemented
9#13074331C211yesmaximal, characteristic, complemented
10#13074330C211yesmaximal, characteristic, complemented
11#13074233C212yesmaximal, complemented
12#13074225C212yesmaximal, complemented
13#13074201C212yesmaximal, complemented
14#13074200C212yesmaximal, complemented
15#13072910C212yesmaximal, complemented
16#13072042C212yesmaximal, complemented
17#13072031C212yesmaximal, complemented
18#13071958C212yesmaximal, complemented
19#13071287C211yesmaximal, characteristic, complemented
20#13071281C211yesmaximal, characteristic, complemented
21#13071274C211yesmaximal, characteristic, complemented
22#13070997C211yesmaximal, characteristic, complemented
23C11×#2321C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C22×#4339C2211yescharacteristic, complemented
27C23×C4×D11C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C2×#67006C2211yescharacteristic
32C2×#66992C2211yescharacteristic
33C2×#66992C2212yescomplemented
34C2×#66990C2211yescharacteristic
35C2×#66988C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×C4×C22⋊D11C2211yescharacteristic, complemented
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41#10623078—28no—
42C2×#66949C2211yescharacteristic, complemented
43C2×#66947C2211yescharacteristic, complemented
44C2×#66939C2211yescharacteristic
45C2×#66937C2211yescharacteristic, complemented
46C2×#66936C2211yescharacteristic, complemented
47C2×#66935C2211yescharacteristic
48C2×(C22⋊D11)⋊C4—28no—
49C2×(C22⋊D11)⋊C4C2212yes—
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×#66931C2211yescharacteristic
54C2×#66931C2212yescomplemented
55C2×C4×D44C2211yescharacteristic, complemented
56C2×#66925C2211yescharacteristic, complemented
57C2×#66925C2212yescomplemented
58C11×#390C2212yescomplemented
59C11×#388C2212yescomplemented
60C11×#388C2212yescomplemented
61C11×#386C2211yescharacteristic
62C11×#386C2212yescomplemented
63C11×#385C2211yescharacteristic
64C11×#379C2211yescharacteristic
65C4×C11×C22⋊C4C2211yescharacteristic
66#10622860C2211yescharacteristic
67#10622836C2212yes—
68#10622836C2212yes—
69#10622833C2211yescharacteristic
70#10622833C2212yescomplemented
71#10622826C2211yescharacteristic
72#10622823C2211yescharacteristic
73#10622823C2212yescomplemented
74C4×C22⋊Dic11C2211yescharacteristic
75#10622606C2212yescomplemented
76#10622604C2212yescomplemented
77#10622594C2212yescomplemented
78#10622585C2212yescomplemented
79#10622585C2212yescomplemented
80#10622574C2212yes—
81#10622574C2212yes—
82#10622574C2212yescomplemented
83#10622573C2212yes—
84#10622573C2212yes—
85#10622572C2212yes—
86#10622572C2212yes—
87#10622572C2212yescomplemented
88#10622571C2211yescharacteristic
89#10622571C2212yescomplemented
90#10622570C2212yescomplemented
91#10622570C2212yescomplemented
92#10622569C2212yescomplemented
93#10622568C2211yescharacteristic
94#10622568C2211yescharacteristic
95#10622564C2212yescomplemented
96#10622563C2211yescharacteristic
97#10622563C2212yescomplemented
98#10622559C2211yescharacteristic
99#10622559C2212yescomplemented
100#10622558C2212yescomplemented
101#10622558C2212yescomplemented
102#10622557C2212yescomplemented
103#10622556C2211yescharacteristic
104#10622556C2211yescharacteristic
105#10622555C2211yescharacteristic
106#10622555C2211yescharacteristic
107#10622555C2212yescomplemented
108#10622555C2212yescomplemented
109#10622553C2212yescomplemented
110C4×(C2×D11)⋊C4C2212yescomplemented
111#10622546C2212yescomplemented
112#10622541C2212yescomplemented
113#10622288C2212yescomplemented
114#10622288C2212yescomplemented
115#10622287C2212yescomplemented
116#10622285C2212yescomplemented
117#10622282C2212yescomplemented
118#10622281C2212yescomplemented
119#10622280C2212yescomplemented
120#10622277C2212yescomplemented
121#10622266C2212yescomplemented
122#10622265C2212yescomplemented
123#10622260C2212yescomplemented
124#10622259C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11—24no—
133C22×C22⋊D11—24no—
134C22×C22⋊D11—24no—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2312yes—
142C23×Dic11—24no—
143C23×Dic11—44no—
144C23×Dic11C2312yes—
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2312yes—
148C23×Dic11C2311yescharacteristic
149C2×#4339—24no—
150C2×#4339—44no—
151C22×D44C2311yescharacteristic
152C22×D44C2311yescharacteristic
153C22×C4×D11—44no—
154C22×C4×D11D418yescomplemented
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×Dic22C2311yescharacteristic
161C11×#120—24no—
162C4×D4×C11—24no—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C22⋊C4—24no—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C42×C11C2311yescharacteristic
177C2×C42×C11C2312yes—
178#67006—24no—
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188#66992—24no—
189#66992—44no—
190#66990—24no—
191#66988—24no—
192C4×C22⋊D11—24no—
193C4×C22⋊D11—24no—
194C2×(C2×D11)⋊C4—24no—
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
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×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2312yes—
213C2×Dic11⋊C4—24no—
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×C4×Dic11—24no—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229C2×C4×Dic11C2312yes—
230#66949—24no—
231#66947—24no—
232#66939—24no—
233#66937—24no—
234#66936—24no—
235#66935—24no—
236(C22⋊D11)⋊C4—28no—
237(C22⋊D11)⋊C4—28no—
238(C22⋊D11)⋊C4—28no—
239(C22⋊D11)⋊C4—28no—
240#66931—24no—
241#66931—44no—
242C4×D44—24no—
243#66925—24no—
244#66925—44no—
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—
261#35031—111nomaximal, Sylow
262C24×C11—22no—
263C24×C11—22no—
264C24×C11—42no—
265C24×C11—42no—
266C24×C11#4114yescomplemented
267C24×C11C2411yescharacteristic
268C24×C11C2412yes—
269C24×C11C2411yescharacteristic
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11C2×D414yes—
275C23×D11C2411yescharacteristic
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—24no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11C2×D414yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C2×C22⋊D11—232no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11—42no—
317C22×Dic11—24no—
318C22×Dic11—24no—
319C22×Dic11—24no—
320C22×Dic11—24no—
321C22×Dic11—24no—
322C22×Dic11—22no—
323C22×Dic11—22no—
324C22×Dic11—22no—
325C22×Dic11—42no—
326C22×Dic11—42no—
327C22×Dic11—42no—
328C22×Dic11—416no—
329C22×Dic11C2×D414yes—
330C22×Dic11#4114yescomplemented
331C22×Dic11C2412yes—
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2412yes—
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2412yes—
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2412yes—
339C22×Dic11C2411yescharacteristic
340#4339—416no—
341C2×D44—22no—
342C2×D44—22no—
343C2×D44—42no—
344C2×D44—42no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—22no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—416no—
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11C2×D414yes—
356C2×Dic22—22no—
357C2×Dic22—24no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—42no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—22no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4—42no—
370C42×C11—22no—
371C42×C11—42no—
372C22⋊Dic11—22no—
373C22⋊Dic11—24no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376C22⋊Dic11—24no—
377C22⋊Dic11—22no—
378C22⋊Dic11—42no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396C4⋊Dic11—22no—
397C4⋊Dic11—24no—
398C4⋊Dic11—42no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—24no—
406Dic11⋊C4—24no—
407Dic11⋊C4—22no—
408Dic11⋊C4—42no—
409Dic11⋊C4—42no—
410C4×Dic11—24no—
411C4×Dic11—24no—
412C4×Dic11—22no—
413C4×Dic11—42no—
414C2×#525—111no—
415C22×C4×D4—111no—
416#2855—111no—
417#2854—111no—
418#2848—111no—
419#2847—111no—
420#2622—111no—
421#2622—111no—
422#2613—111no—
423#2613—111no—
424#2602—112no—
425#2602—112no—
426#2600—112no—
427#2600—112no—
428#2485—112no—
429#2415—112no—
430#2414—112no—
431#2407—112no—
432#2322—111no—
433#2322—111no—
434#2321—111no—
435#2321D1111yescharacteristic, complemented
436#2280—111no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—28no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—48no—
452C23×C11—44no—
453C23×C11—44no—
454C23×C11—48no—
455C23×C11C22×D412yes—
456C23×C11C2×#4114yes—
457C23×C11C2×#4112yes—
458C23×C11C2×#4112yes—
459C23×C11C2511yescharacteristic
460C22×D11—28no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11C22×D412yes—
479C22×D11C22×D412yes—
480D4×C11—44no—
481D4×C11—84no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
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—44no—
501C2×C4×C11—44no—
502C2×C4×C11—44no—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C22×D412yes—
505C22⋊D11—216no—
506C22⋊D11—216no—
507C22⋊D11—44no—
508C22⋊D11—44no—
509C22⋊D11—44no—
510C22⋊D11—44no—
511C22⋊D11—84no—
512C2×Dic11—28no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—28no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—22no—
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—48no—
534C2×Dic11—44no—
535C2×Dic11—48no—
536C2×Dic11C22×D412yes—
537C2×Dic11C22×D412yes—
538C2×Dic11C2×#4114yes—
539C2×Dic11H(5,𝔽2)14yes—
540D44—44no—
541D44—44no—
542C4×D11—28no—
543C4×D11—28no—
544C4×D11—44no—
545C4×D11—44no—
546C4×D11—44no—
547Dic22—44no—
548C22×#41—111no—
549C23×D4—111no—
550C24×C4—111no—
551C24×C4—111no—
552#525—228no—
553C2×#123—111no—
554C2×#123—111no—
555C2×#123—111no—
556C2×#123—111no—
557C2×C22⋊Q8—111no—
558C2×C22⋊Q8—111no—
559C2×C22⋊Q8—112no—
560C2×#121—111no—
561C2×#121—112no—
562C2×#121—111no—
563C2×#120—111no—
564C2×#120—111no—
565C2×#120—111no—
566C2×#120C2×D1111yescharacteristic
567C2×C4×D4—111no—
568C2×C4×D4—111no—
569C2×C4×D4—112no—
570C2×C4×D4—112no—
571C2×C4×D4—112no—
572C2×C4×D4—112no—
573C2×C4×D4—111no—
574C2×C4×D4—228no—
575C2×C4×D4C2×D1111yescharacteristic
576C2×#117—111no—
577C2×#117—112no—
578C22×C4⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4C2×D1111yescharacteristic
581C22×C42—111no—
582#397—112no—
583#397—112no—
584#397—112no—
585#397—112no—
586#394—112no—
587#394—112no—
588#394—112no—
589#394—112no—
590#394—112no—
591#394—112no—
592#394—112no—
593#394—112no—
594#392—112no—
595#392—112no—
596#392—112no—
597#392—112no—
598#391—112no—
599#390—112no—
600#390—112no—
601#390C2×D1112yescomplemented
602#389—112no—
603#389—112no—
604#389—112no—
605#389—112no—
606#388—112no—
607#388—112no—
608#388—112no—
609#388—112no—
610#388—112no—
611#388—112no—
612#388C2×D1112yescomplemented
613#388C2×D1112yescomplemented
614#387—112no—
615#387—112no—
616#387—112no—
617#387—112no—
618#386—111no—
619#386—112no—
620#386—111no—
621#386—112no—
622#386—111no—
623#386—112no—
624#386C2×D1111yescharacteristic
625#386C2×D1112yescomplemented
626#385—111no—
627#385—112no—
628#385—111no—
629#385—111no—
630#385—112no—
631#385—112no—
632#385—112no—
633#385C2×D1111yescharacteristic
634#381—111no—
635#381—111no—
636#381—112no—
637#380—111no—
638#380—112no—
639#380—111no—
640#380—112no—
641#380—112no—
642#379—111no—
643#379—111no—
644#379—111no—
645#379C2×D1111yescharacteristic
646C4×C22⋊C4—111no—
647C4×C22⋊C4—112no—
648C4×C22⋊C4C2×D1111yescharacteristic
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—24no—
656C22×C11—416no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—41no—
662C22×C11—41no—
663C22×C11—41no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11#52514yes—
667C22×C11C23×D411yescharacteristic
668C22×C11C22×#4111yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C2×H(5,𝔽2)12yes—
671C22×C11#58512yes—
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—416no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—42no—
687C2×D11—42no—
688C4×C11—22no—
689C4×C11—22no—
690C4×C11—41no—
691C4×C11—41no—
692C4×C11—42no—
693C4×C11—41no—
694C4×C11—42no—
695C4×C11—42no—
696Dic11—24no—
697Dic11—22no—
698Dic11—41no—
699Dic11—41no—
700Dic11—42no—
701Dic11—41no—
702Dic11—42no—
703Dic11—42no—
704Dic11#53414yes—
705C25—111no—
706C25C22×D1111yescharacteristic
707C2×#41—224no—
708C2×#41—444no—
709C22×Q8—111no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—111no—
713C22×D4—111no—
714C22×D4—111no—
715C22×D4—112no—
716C22×D4—111no—
717C22×D4—111no—
718C22×D4—111no—
719C22×D4—224no—
720C22×D4—224no—
721C22×D4—224no—
722C22×D4C22×D1111yescharacteristic
723C22×D4C22×D1112yes—
724C23×C4—111no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—118no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—112no—
734C23×C4—111no—
735C23×C4—224no—
736C23×C4—444no—
737C23×C4—444no—
738C23×C4C22×D1111yescharacteristic
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1111yescharacteristic
741#123—224no—
742#123—224no—
743#123—224no—
744#123—224no—
745C22⋊Q8—224no—
746C22⋊Q8—224no—
747C22⋊Q8—444no—
748#121—224no—
749#121—224no—
750#121—444no—
751#120—24no—
752#120—224no—
753#120—224no—
754#120—224no—
755C4×D4—24no—
756C4×D4—224no—
757C4×D4—228no—
758C4×D4—228no—
759C4×D4—228no—
760C4×D4—228no—
761C4×D4—224no—
762C4×D4—224no—
763#117—224no—
764#117—444no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—111no—
772C2×C4⋊C4—111no—
773C2×C4⋊C4—111no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—224no—
780C2×C4⋊C4C22×D1111yescharacteristic
781C2×C4⋊C4C22×D1112yes—
782C2×C22⋊C4—24no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—224no—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1111yescharacteristic
811C2×C22⋊C4C22×D1111yescharacteristic
812C2×C22⋊C4C22×D1111yescharacteristic
813C2×C22⋊C4C22×D1112yes—
814C2×C22⋊C4C22×D1111yescharacteristic
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C42—111no—
819C2×C42—112no—
820C2×C42—112no—
821C2×C42—112no—
822C2×C42—224no—
823C2×C42C22×D1111yescharacteristic
824C2×C42C22×D1112yes—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95C22×D1112yes—
839#95C22×D1112yes—
840#95C22×D1112yes—
841C2×C11—24no—
842C2×C11—44no—
843C2×C11—81no—
844C2×C11C2×#52511yescharacteristic
845C2×C11C2×#53411yescharacteristic
846C2×C11#344911yescharacteristic
847C2×C11#350512yes—
848C2×C11#350612yes—
849D11—42no—
850D11—42no—
851D11—81no—
852C24—22no—
853C24—22no—
854C24—42no—
855C24—42no—
856C24—111no—
857C24—111no—
858C24—114no—
859C24—111no—
860C24—222no—
861C24—222no—
862C24—442no—
863C24—442no—
864C24#433914yescomplemented
865C24C23×D1111yescharacteristic
866C24C23×D1112yes—
867C24C23×D1111yescharacteristic
868#41—4416no—
869C2×Q8—222no—
870C2×Q8—224no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—24no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—222no—
878C2×D4—222no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—222no—
882C2×D4—224no—
883C2×D4—224no—
884C2×D4—224no—
885C2×D4—2232no—
886C2×D4—224no—
887C2×D4—224no—
888C2×D4—222no—
889C2×D4—222no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—222no—
893C2×D4—224no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C2×D4—442no—
899C2×D4—442no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—111no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—112no—
909C22×C4—111no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—114no—
914C22×C4—112no—
915C22×C4—112no—
916C22×C4—111no—
917C22×C4—111no—
918C22×C4—112no—
919C22×C4—111no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—224no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—222no—
930C22×C4—222no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—4416no—
935C22×C4—442no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—4416no—
939C22×C4D4×D1114yes—
940C22×C4C23×D1112yes—
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1112yes—
943C22×C4C23×D1112yes—
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C4⋊C4—22no—
949C4⋊C4—42no—
950C4⋊C4—222no—
951C4⋊C4—222no—
952C4⋊C4—224no—
953C4⋊C4—224no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—224no—
957C4⋊C4—224no—
958C4⋊C4—224no—
959C4⋊C4—224no—
960C4⋊C4—222no—
961C4⋊C4—442no—
962C4⋊C4—442no—
963C4⋊C4—442no—
964C22⋊C4—24no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—22no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—222no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—222no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—222no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C42—22no—
999C42—42no—
1000C42—224no—
1001C42—224no—
1002C42—222no—
1003C42—442no—
1004C11#3503111yescharacteristic, complemented, Sylow
1005C23—22no—
1006C23—22no—
1007C23—28no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—22no—
1018C23—22no—
1019C23—48no—
1020C23—44no—
1021C23—44no—
1022C23—48no—
1023C23—112no—
1024C23—112no—
1025C23—228no—
1026C23—221no—
1027C23—221no—
1028C23—221no—
1029C23—221no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—222no—
1034C23—221no—
1035C23—221no—
1036C23—221no—
1037C23—222no—
1038C23—222no—
1039C23—444no—
1040C23—444no—
1041C23—448no—
1042C23—448no—
1043C23C2×#433914yes—
1044C23C2×#433912yes—
1045C23C2×D4×D1112yes—
1046C23#41×D1112yes—
1047C23C24×D1111yescharacteristic
1048Q8—444no—
1049D4—44no—
1050D4—84no—
1051D4—2216no—
1052D4—2216no—
1053D4—444no—
1054D4—444no—
1055D4—444no—
1056D4—444no—
1057D4—444no—
1058D4—444no—
1059D4—884no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—44no—
1081C2×C4—112no—
1082C2×C4—114no—
1083C2×C4—112no—
1084C2×C4—114no—
1085C2×C4—228no—
1086C2×C4—228no—
1087C2×C4—228no—
1088C2×C4—228no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—221no—
1093C2×C4—222no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—222no—
1097C2×C4—221no—
1098C2×C4—222no—
1099C2×C4—221no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—444no—
1109C2×C4—444no—
1110C2×C4—444no—
1111C2×C4—448no—
1112C2×C4—448no—
1113C2×C4—444no—
1114C2×C4C2×D4×D1112yes—
1115C2×C4C2×D4×D1112yes—
1116C22—22no—
1117C22—24no—
1118C22—22no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—416no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—41no—
1129C22—41no—
1130C22—42no—
1131C22—41no—
1132C22—42no—
1133C22—222no—
1134C22—222no—
1135C22—222no—
1136C22—222no—
1137C22—222no—
1138C22—222no—
1139C22—4416no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—441no—
1145C22—441no—
1146C22—442no—
1147C22—441no—
1148C22—442no—
1149C22#1062307814yes—
1150C22C22×#433911yescharacteristic
1151C22C22×D4×D1111yescharacteristic
1152C22C2×#41×D1111yescharacteristic
1153C22D11×H(5,𝔽2)12yes—
1154C22#1062345512yes—
1155C4—22no—
1156C4—22no—
1157C4—41no—
1158C4—41no—
1159C4—42no—
1160C4—42no—
1161C4—41no—
1162C4—42no—
1163C4—114no—
1164C4—224no—
1165C4—222no—
1166C4—441no—
1167C4—442no—
1168C4—441no—
1169C4—442no—
1170C4—441no—
1171C4—442no—
1172C2—24no—
1173C2—44no—
1174C2—81no—
1175C2—442no—
1176C2—442no—
1177C2—881no—
1178C2C2×#1062307811yescharacteristic
1179C2D11×#53411yescharacteristic
1180C2#1308194711yescharacteristic
1181C2#1308244612yes—
1182C2#1308246312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2321C2
hypercenter#2321D11
hypocenterC11#35031
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2321

Complements

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

NH ≅ G/Ntype
1. C2×#10623078C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13076952C2semidirect
4. #13076944C2semidirect
5. #13076901C2semidirect
6. #13076896C2semidirect
7. #13074394C2semidirect
8. #13074393C2semidirect
9. #13074331C2semidirect
10. #13074330C2semidirect
11. #13074233C2semidirect
12. #13074225C2semidirect
13. #13074201C2semidirect
14. #13074200C2semidirect
15. #13072910C2semidirect
16. #13072042C2semidirect
17. #13072031C2semidirect
18. #13071958C2semidirect
19. #13071287C2semidirect
20. #13071281C2semidirect
21. #13071274C2semidirect
22. #13070997C2semidirect
23. C11×#2321C2semidirect
26. C22×#4339C22semidirect
33. C2×#66992C22semidirect
37. C2×C4×C22⋊D11C22semidirect
42. C2×#66949C22semidirect
43. C2×#66947C22semidirect
45. C2×#66937C22semidirect
46. C2×#66936C22semidirect
54. C2×#66931C22semidirect
55. C2×C4×D44C22semidirect
56. C2×#66925C22semidirect
57. C2×#66925C22semidirect
58. C11×#390C22semidirect
59. C11×#388C22semidirect
60. C11×#388C22semidirect
62. C11×#386C22semidirect
70. #10622833C22semidirect
73. #10622823C22semidirect
75. #10622606C22semidirect
76. #10622604C22semidirect
77. #10622594C22semidirect
78. #10622585C22semidirect
79. #10622585C22semidirect
82. #10622574C22semidirect
87. #10622572C22semidirect
89. #10622571C22semidirect
90. #10622570C22semidirect
91. #10622570C22semidirect
92. #10622569C22semidirect
95. #10622564C22semidirect
97. #10622563C22semidirect
99. #10622559C22semidirect
100. #10622558C22semidirect
101. #10622558C22semidirect
102. #10622557C22semidirect
107. #10622555C22semidirect
108. #10622555C22semidirect
109. #10622553C22semidirect
110. C4×(C2×D11)⋊C4C22semidirect
111. #10622546C22semidirect
112. #10622541C22semidirect
113. #10622288C22semidirect
114. #10622288C22semidirect
115. #10622287C22semidirect
116. #10622285C22semidirect
117. #10622282C22semidirect
118. #10622281C22semidirect
119. #10622280C22semidirect
120. #10622277C22semidirect
121. #10622266C22semidirect
122. #10622265C22semidirect
123. #10622260C22semidirect
124. #10622259C22semidirect
154. C22×C4×D11D4semidirect
266. C24×C11#41semidirect
330. C22×Dic11#41semidirect
435. #2321D11semidirect
601. #390C2×D11semidirect
612. #388C2×D11semidirect
613. #388C2×D11semidirect
625. #386C2×D11semidirect
864. C24#4339semidirect
1004. C11#35031semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C22×(C22⋊D11)⋊C42
#130769522
#130769442
#130769012
#130768962
#130743942
#130743932
#130743312
#130743302
#130742332
#130742252
#130742012
#130742002
#130729102
#130720422
#130720312
#130719582
#130712872
#130712812
#130712742
#130709972
C11×#23212
#3503111