Finite Group Databasebeta

← #14920196

Subgroups — #14920196

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074536C211yesmaximal, characteristic, complemented
4#13074533C211yesmaximal, characteristic, complemented
5#13074501C211yesmaximal, characteristic, complemented
6#13074463C212yesmaximal, complemented
7#13074459C212yesmaximal, complemented
8#13074430C211yesmaximal, characteristic, complemented
9#13074422C211yesmaximal, characteristic, complemented
10#13074388C212yesmaximal, complemented
11#13074357C211yesmaximal, characteristic, complemented
12#13074349C211yesmaximal, characteristic, complemented
13#13074327C212yesmaximal, complemented
14#13071882C211yesmaximal, characteristic, complemented
15#13071881C211yesmaximal, characteristic, complemented
16#13071859C212yesmaximal, complemented
17#13071851C212yesmaximal, complemented
18#13071830C211yesmaximal, characteristic, complemented
19#13071828C211yesmaximal, characteristic, complemented
20#13071143C212yesmaximal, complemented
21#13071121C212yesmaximal, complemented
22#13070996C211yesmaximal, characteristic, complemented
23C11×#2635C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic, complemented
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic, complemented
29C2×C4×D4×C11C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66990C2212yes—
32C2×#66990C2212yes—
33C2×D4×Dic11C2211yescharacteristic
34C2×D4×Dic11C2212yescomplemented
35C2×D4×Dic11C2212yescomplemented
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×C4×C22⋊D11C2211yescharacteristic
38C2×#66977C2211yescharacteristic, complemented
39#10623137—28no—
40C4×D4×D11—28no—
41C2×#66950C2211yescharacteristic
42C2×#66946C2211yescharacteristic
43C2×#66945C2211yescharacteristic, complemented
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×#66936C2212yes—
46C2×#66936C2212yescomplemented
47C2×(C22⋊D11)⋊C4C2212yes—
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2211yescharacteristic
50C2×(C22⋊D11)⋊C4C2212yescomplemented
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×#66930C2212yescomplemented
54C2×C4×D44C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56C11×#400C2211yescharacteristic, complemented
57C11×#399C2211yescharacteristic, complemented
58C11×#394C2211yescharacteristic, complemented
59C11×#394C2212yescomplemented
60C11×#392C2212yes—
61C11×#392C2211yescharacteristic, complemented
62C11×#388C2212yescomplemented
63C11×#386C2212yescomplemented
64C11×#381C2211yescharacteristic, complemented
65#10622836C2212yes—
66#10622836C2212yes—
67#10622836C2211yescharacteristic, complemented
68#10622835C2212yes—
69#10622835C2212yescomplemented
70#10622835C2211yescharacteristic, complemented
71#10622835C2212yescomplemented
72#10622824C2211yescharacteristic, complemented
73#10622823C2212yescomplemented
74#10622607C2212yescomplemented
75#10622606C2212yescomplemented
76#10622605C2211yescharacteristic, complemented
77#10622602C2212yes—
78#10622596C2211yescharacteristic, complemented
79#10622595C2211yescharacteristic, complemented
80#10622592C2211yescharacteristic, complemented
81C4⋊C4×Dic11C2212yescomplemented
82#10622574C2212yes—
83#10622574C2212yes—
84#10622574C2212yescomplemented
85#10622573C2212yes—
86#10622572C2212yescomplemented
87#10622572C2212yescomplemented
88#10622569C2212yes—
89#10622569C2212yes—
90#10622569C2212yescomplemented
91#10622568C2212yes—
92#10622568C2212yes—
93#10622566C2211yescharacteristic, complemented
94#10622566C2212yescomplemented
95#10622565C2212yescomplemented
96#10622561C2212yescomplemented
97#10622561C2212yescomplemented
98#10622561C2212yescomplemented
99#10622560C2211yescharacteristic, complemented
100#10622557C2212yescomplemented
101C22⋊C4×Dic11C2212yescomplemented
102C22⋊C4×Dic11C2212yescomplemented
103C22⋊C4×Dic11C2212yescomplemented
104#10622546C2212yescomplemented
105#10622288C2212yescomplemented
106#10622287C2211yescharacteristic, complemented
107#10622286C2211yescharacteristic, complemented
108#10622285C2212yes—
109#10622281C2212yes—
110#10622281C2212yescomplemented
111#10622280C2211yescharacteristic
112#10622280C2211yescharacteristic
113#10622280C2212yescomplemented
114#10622279C2212yes—
115#10622279C2211yescharacteristic, complemented
116#10622279C2212yescomplemented
117#10622279C2211yescharacteristic, complemented
118#10622277C2212yes—
119#10622274C2211yescharacteristic, complemented
120#10622274C2212yescomplemented
121#10622270C2212yescomplemented
122#10622269C2211yescharacteristic, complemented
123#10622266C2212yescomplemented
124#10622262C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C22×D4×C11C2312yes—
130C22×D4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C23×Dic11C2312yes—
139C23×Dic11C2311yescharacteristic
140C23×Dic11C2311yescharacteristic
141C2×#4341—24no—
142C2×#4341—44no—
143C2×D4×D11—24no—
144C2×D4×D11—24no—
145C2×D4×D11—24no—
146C22×D44C2311yescharacteristic
147C22×C4×D11—24no—
148C22×C4×D11—44no—
149C22×C4×D11—44no—
150C22×C4×D11D418yescomplemented
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×Dic22C2311yescharacteristic
161C11×#121—24no—
162C4×D4×C11—24no—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185#66991—24no—
186#66990—28no—
187#66990—28no—
188D4×Dic11—24no—
189D4×Dic11—28no—
190D4×Dic11—44no—
191C4×C22⋊D11—24no—
192C4×C22⋊D11—24no—
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
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×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2312yes—
211#66977—24no—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226#66950—24no—
227#66946—24no—
228#66945—24no—
229C4⋊C4×D11—24no—
230#66936—28no—
231#66936—28no—
232(C22⋊D11)⋊C4—24no—
233(C22⋊D11)⋊C4—24no—
234(C22⋊D11)⋊C4—28no—
235(C22⋊D11)⋊C4—44no—
236C22⋊C4×D11—24no—
237C22⋊C4×D11—24no—
238#66930—44no—
239C4×D44—24no—
240C42×D11—24no—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2311yescharacteristic
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259#34562—111nomaximal, Sylow
260C24×C11C2412yes—
261C24×C11C2411yescharacteristic
262C24×C11C2411yescharacteristic
263C23×D11—22no—
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11—42no—
270C23×D11—42no—
271C23×D11C2×D414yes—
272C23×D11#4114yescomplemented
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C23×D11C2411yescharacteristic
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—24no—
279C2×D4×C11—24no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C2×D4×C11—42no—
286C2×D4×C11—42no—
287C22×C4×C11—22no—
288C22×C4×C11—42no—
289C22×C4×C11—42no—
290C22×C4×C11C2×D414yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C22×Dic11—24no—
315C22×Dic11—22no—
316C22×Dic11—24no—
317C22×Dic11—24no—
318C22×Dic11—24no—
319C22×Dic11—24no—
320C22×Dic11C2×D414yes—
321C22×Dic11C2412yes—
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2412yes—
324C22×Dic11C2412yes—
325C22×Dic11C2412yes—
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330#4341—416no—
331D4×D11—232no—
332C2×D44—22no—
333C2×D44—22no—
334C2×D44—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—22no—
343C2×C4×D11—22no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—416no—
350C2×C4×D11—416no—
351C2×C4×D11C2×D414yes—
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11#4114yescomplemented
356C2×Dic22—22no—
357C2×Dic22—42no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—42no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4—42no—
369C42×C11—22no—
370C22⋊Dic11—22no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—22no—
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—42no—
377C22⋊Dic11—42no—
378C22⋊Dic11—42no—
379C22⋊Dic11—42no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393C4⋊Dic11—22no—
394C4⋊Dic11—24no—
395C4⋊Dic11—24no—
396C4⋊Dic11—22no—
397C4⋊Dic11—42no—
398Dic11⋊C4—22no—
399Dic11⋊C4—24no—
400Dic11⋊C4—22no—
401Dic11⋊C4—24no—
402Dic11⋊C4—42no—
403Dic11⋊C4—42no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406C4×Dic11—22no—
407C4×Dic11—22no—
408C4×Dic11—24no—
409C4×Dic11—24no—
410C4×Dic11—24no—
411C4×Dic11—22no—
412C2×#525—111no—
413C22×C4×D4—111no—
414#2638—111no—
415#2638—111no—
416#2635—111no—
417#2635D1111yescharacteristic, complemented
418#2630—112no—
419#2630—112no—
420#2627—111no—
421#2626—111no—
422#2622—112no—
423#2618—111no—
424#2617—111no—
425#2613—112no—
426#2395—111no—
427#2395—111no—
428#2392—112no—
429#2392—112no—
430#2388—111no—
431#2388—111no—
432C4×#123—112no—
433C4×#120—112no—
434#2280—111no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11C22×D412yes—
451C23×C11C2×#4112yes—
452C23×C11C2511yescharacteristic
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—48no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11C22×D412yes—
474C22×D11C22×D412yes—
475C22×D11C2×#4112yes—
476C22×D11C2×#4112yes—
477C22×D11C2×#4112yes—
478D4×C11—28no—
479D4×C11—44no—
480D4×C11—48no—
481D4×C11—48no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
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—44no—
500C2×C4×C11—44no—
501C2×C4×C11C22×D412yes—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C2×#4112yes—
504C22⋊D11—28no—
505C22⋊D11—28no—
506C22⋊D11—48no—
507C22⋊D11—48no—
508C22⋊D11—48no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—28no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—21no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—44no—
530C2×Dic11—48no—
531C2×Dic11C22×D412yes—
532C2×Dic11C22×D412yes—
533C2×Dic11C2×#4112yes—
534C2×Dic11H(5,𝔽2)14yes—
535D44—28no—
536C4×D11—28no—
537C4×D11—28no—
538C4×D11—28no—
539C4×D11—44no—
540C4×D11—44no—
541C4×D11—44no—
542C4×D11—44no—
543C4×D11—44no—
544C4×D11—44no—
545Dic22—44no—
546C22×#41—111no—
547C23×D4—111no—
548C24×C4—111no—
549C24×C4—111no—
550#525—228no—
551C2×#123—112no—
552C2×#123—112no—
553C2×C22⋊Q8—111no—
554C2×C22⋊Q8—111no—
555C2×#121—111no—
556C2×#121C2×D1111yescharacteristic, complemented
557C2×#120—112no—
558C2×#120—112no—
559C2×C4×D4—111no—
560C2×C4×D4—112no—
561C2×C4×D4—111no—
562C2×C4×D4—111no—
563C2×C4×D4—112no—
564C2×C4×D4—111no—
565C2×C4×D4—111no—
566C2×C4×D4—111no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—111no—
570C2×C4×D4—228no—
571C2×C4×D4C2×D1111yescharacteristic
572C2×#117—111no—
573C2×#117—112no—
574C22×C4⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C42—111no—
578#400—111no—
579#400C2×D1111yescharacteristic, complemented
580#399—111no—
581#399C2×D1111yescharacteristic, complemented
582#398—111no—
583#398—111no—
584#398—112no—
585#398—112no—
586#397—112no—
587#397—111no—
588#397—112no—
589#397—112no—
590#397—111no—
591#397—112no—
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#395—111no—
597#395—111no—
598#394—112no—
599#394—112no—
600#394—111no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#394—112no—
608#394C2×D1111yescharacteristic, complemented
609#394C2×D1112yescomplemented
610#393—111no—
611#393—111no—
612#392—112no—
613#392—112no—
614#392—111no—
615#392—112no—
616#392C2×D1112yes—
617#392C2×D1111yescharacteristic, complemented
618#388—112no—
619#388C2×D1112yescomplemented
620#387—112no—
621#387—112no—
622#386—112no—
623#386—112no—
624#386—112no—
625#386C2×D1112yescomplemented
626#385—112no—
627#385—112no—
628#385—112no—
629#385—112no—
630#381—111no—
631#381—112no—
632#381C2×D1111yescharacteristic, complemented
633#380—111no—
634#380—111no—
635#380—112no—
636#379—112no—
637#379—112no—
638C4×C4⋊C4—112no—
639C4×C4⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—112no—
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—41no—
653C22×C11—41no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11C23×D411yescharacteristic
665C22×C11C22×#4111yescharacteristic
666C22×C11C22×#4111yescharacteristic
667C22×C11C2×H(5,𝔽2)12yes—
668C22×C11#58512yes—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—24no—
672C2×D11—24no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—24no—
678C2×D11—416no—
679C2×D11—416no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11#52514yes—
686C4×C11—22no—
687C4×C11—22no—
688C4×C11—22no—
689C4×C11—41no—
690C4×C11—42no—
691C4×C11—41no—
692C4×C11—42no—
693C4×C11—42no—
694Dic11—22no—
695Dic11—22no—
696Dic11—42no—
697Dic11—42no—
698Dic11—41no—
699Dic11—41no—
700Dic11—42no—
701Dic11—42no—
702Dic11#53414yes—
703C25—111no—
704C25—111no—
705C2×#41—224no—
706C2×#41—444no—
707C22×Q8—111no—
708C22×D4—111no—
709C22×D4—111no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—112no—
713C22×D4—111no—
714C22×D4—224no—
715C22×D4—224no—
716C22×D4—224no—
717C22×D4C22×D1111yescharacteristic
718C22×D4C22×D1112yes—
719C22×D4C22×D1112yes—
720C22×D4C22×D1111yescharacteristic
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—118no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—112no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—224no—
735C23×C4—444no—
736C23×C4—444no—
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1111yescharacteristic
739#123—228no—
740#123—228no—
741C22⋊Q8—224no—
742C22⋊Q8—224no—
743#121—24no—
744#121—224no—
745#120—228no—
746#120—228no—
747C4×D4—24no—
748C4×D4—224no—
749C4×D4—224no—
750C4×D4—224no—
751C4×D4—228no—
752C4×D4—224no—
753C4×D4—224no—
754C4×D4—224no—
755C4×D4—228no—
756C4×D4—224no—
757C4×D4—444no—
758C4×D4—444no—
759#117—224no—
760#117—444no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—111no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—224no—
775C2×C4⋊C4C22×D1111yescharacteristic
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C4⋊C4C22×D1112yes—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—224no—
802C2×C22⋊C4—224no—
803C2×C22⋊C4C22×D1111yescharacteristic
804C2×C22⋊C4C22×D1111yescharacteristic
805C2×C22⋊C4C22×D1112yes—
806C2×C22⋊C4C22×D1112yes—
807C2×C22⋊C4C22×D1112yes—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C42—112no—
812C2×C42—112no—
813C2×C42—112no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—224no—
818C2×C42C22×D1111yescharacteristic
819#95—112no—
820#95—111no—
821#95—111no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95C22×D1112yes—
833#95C22×D1111yescharacteristic
834#95C22×D1111yescharacteristic
835#95C22×D1112yes—
836#95C22×D1112yes—
837C2×C11—42no—
838C2×C11—42no—
839C2×C11—82no—
840C2×C11C2×#52511yescharacteristic
841C2×C11C2×#53411yescharacteristic
842C2×C11#344911yescharacteristic
843C2×C11#345912yes—
844C2×C11#346012yes—
845D11—24no—
846D11—42no—
847D11—42no—
848C24—111no—
849C24—111no—
850C24—111no—
851C24—114no—
852C24—114no—
853C24—222no—
854C24—222no—
855C24—222no—
856C24—222no—
857C24—442no—
858C24—442no—
859C24—442no—
860C24—442no—
861C24C23×D1112yes—
862C24C23×D1111yescharacteristic
863C24C23×D1111yescharacteristic
864#41—4416no—
865C2×Q8—222no—
866C2×Q8—442no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—24no—
870C2×D4—24no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—222no—
879C2×D4—222no—
880C2×D4—222no—
881C2×D4—222no—
882C2×D4—2232no—
883C2×D4—222no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—222no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—222no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C22×C4—22no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—111no—
901C22×C4—114no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—114no—
909C22×C4—112no—
910C22×C4—111no—
911C22×C4—112no—
912C22×C4—112no—
913C22×C4—111no—
914C22×C4—112no—
915C22×C4—224no—
916C22×C4—224no—
917C22×C4—222no—
918C22×C4—224no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—224no—
924C22×C4—222no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—222no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—442no—
935C22×C4—4416no—
936C22×C4—4416no—
937C22×C4D4×D1114yes—
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1112yes—
940C22×C4C23×D1112yes—
941C22×C4C23×D1112yes—
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—42no—
949C4⋊C4—222no—
950C4⋊C4—222no—
951C4⋊C4—224no—
952C4⋊C4—224no—
953C4⋊C4—222no—
954C4⋊C4—222no—
955C4⋊C4—224no—
956C4⋊C4—224no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4—442no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—222no—
971C22⋊C4—222no—
972C22⋊C4—222no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—222no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—222no—
982C22⋊C4—224no—
983C22⋊C4—224no—
984C22⋊C4—222no—
985C22⋊C4—442no—
986C22⋊C4—442no—
987C22⋊C4—442no—
988C22⋊C4—442no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C42—22no—
994C42—222no—
995C42—222no—
996C42—224no—
997C42—224no—
998C42—224no—
999C42—222no—
1000C11#3456211yescharacteristic, complemented, Sylow
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—112no—
1017C23—112no—
1018C23—112no—
1019C23—112no—
1020C23—112no—
1021C23—228no—
1022C23—228no—
1023C23—222no—
1024C23—222no—
1025C23—221no—
1026C23—221no—
1027C23—221no—
1028C23—221no—
1029C23—222no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—444no—
1034C23—444no—
1035C23—448no—
1036C23—444no—
1037C23—444no—
1038C23—448no—
1039C23—448no—
1040C23—448no—
1041C23C2×D4×D1112yes—
1042C23#41×D1112yes—
1043C23C24×D1111yescharacteristic
1044Q8—444no—
1045D4—28no—
1046D4—44no—
1047D4—48no—
1048D4—48no—
1049D4—228no—
1050D4—228no—
1051D4—228no—
1052D4—448no—
1053D4—448no—
1054D4—448no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—112no—
1075C2×C4—114no—
1076C2×C4—112no—
1077C2×C4—112no—
1078C2×C4—228no—
1079C2×C4—228no—
1080C2×C4—228no—
1081C2×C4—228no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—222no—
1085C2×C4—221no—
1086C2×C4—222no—
1087C2×C4—221no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—444no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—444no—
1105C2×C4—444no—
1106C2×C4—444no—
1107C2×C4—444no—
1108C2×C4—448no—
1109C2×C4C2×D4×D1112yes—
1110C2×C4C2×D4×D1112yes—
1111C2×C4#41×D1112yes—
1112C22—22no—
1113C22—22no—
1114C22—24no—
1115C22—22no—
1116C22—22no—
1117C22—41no—
1118C22—41no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—114no—
1130C22—222no—
1131C22—222no—
1132C22—224no—
1133C22—224no—
1134C22—222no—
1135C22—222no—
1136C22—224no—
1137C22—222no—
1138C22—222no—
1139C22—4416no—
1140C22—4416no—
1141C22—441no—
1142C22—441no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22C22×D4×D1111yescharacteristic
1147C22C2×#41×D1111yescharacteristic
1148C22C2×#41×D1111yescharacteristic
1149C22D11×H(5,𝔽2)12yes—
1150C22#1062345512yes—
1151C4—22no—
1152C4—22no—
1153C4—22no—
1154C4—41no—
1155C4—41no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—114no—
1160C4—222no—
1161C4—222no—
1162C4—441no—
1163C4—442no—
1164C4—441no—
1165C4—442no—
1166C4—442no—
1167C4—442no—
1168C2—42no—
1169C2—42no—
1170C2—82no—
1171C2—224no—
1172C2—442no—
1173C2—442no—
1174C2D11×#52511yescharacteristic
1175C2D11×#53411yescharacteristic
1176C2#1308194711yescharacteristic
1177C2#1308202712yes—
1178C2#1308203112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2635C2
hypercenter#2635D11
hypocenterC11#34562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. C2×#10623137C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074536C2semidirect
4. #13074533C2semidirect
5. #13074501C2semidirect
6. #13074463C2semidirect
7. #13074459C2semidirect
8. #13074430C2semidirect
9. #13074422C2semidirect
10. #13074388C2semidirect
11. #13074357C2semidirect
12. #13074349C2semidirect
13. #13074327C2semidirect
14. #13071882C2semidirect
15. #13071881C2semidirect
16. #13071859C2semidirect
17. #13071851C2semidirect
18. #13071830C2semidirect
19. #13071828C2semidirect
20. #13071143C2semidirect
21. #13071121C2semidirect
22. #13070996C2semidirect
23. C11×#2635C2semidirect
24. C22×#4341C22semidirect
28. C2×C11×#121C22semidirect
34. C2×D4×Dic11C22semidirect
35. C2×D4×Dic11C22semidirect
38. C2×#66977C22semidirect
43. C2×#66945C22semidirect
46. C2×#66936C22semidirect
50. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×#66930C22semidirect
56. C11×#400C22semidirect
57. C11×#399C22semidirect
58. C11×#394C22semidirect
59. C11×#394C22semidirect
61. C11×#392C22semidirect
62. C11×#388C22semidirect
63. C11×#386C22semidirect
64. C11×#381C22semidirect
67. #10622836C22semidirect
69. #10622835C22semidirect
70. #10622835C22semidirect
71. #10622835C22semidirect
72. #10622824C22semidirect
73. #10622823C22semidirect
74. #10622607C22semidirect
75. #10622606C22semidirect
76. #10622605C22semidirect
78. #10622596C22semidirect
79. #10622595C22semidirect
80. #10622592C22semidirect
81. C4⋊C4×Dic11C22semidirect
84. #10622574C22semidirect
86. #10622572C22semidirect
87. #10622572C22semidirect
90. #10622569C22semidirect
93. #10622566C22semidirect
94. #10622566C22semidirect
95. #10622565C22semidirect
96. #10622561C22semidirect
97. #10622561C22semidirect
98. #10622561C22semidirect
99. #10622560C22semidirect
100. #10622557C22semidirect
101. C22⋊C4×Dic11C22semidirect
102. C22⋊C4×Dic11C22semidirect
103. C22⋊C4×Dic11C22semidirect
104. #10622546C22semidirect
105. #10622288C22semidirect
106. #10622287C22semidirect
107. #10622286C22semidirect
110. #10622281C22semidirect
113. #10622280C22semidirect
115. #10622279C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
119. #10622274C22semidirect
120. #10622274C22semidirect
121. #10622270C22semidirect
122. #10622269C22semidirect
123. #10622266C22semidirect
124. #10622262C22semidirect
150. C22×C4×D11D4semidirect
272. C23×D11#41semidirect
355. C2×C4×D11#41semidirect
417. #2635D11semidirect
556. C2×#121C2×D11semidirect
579. #400C2×D11semidirect
581. #399C2×D11semidirect
608. #394C2×D11semidirect
609. #394C2×D11semidirect
617. #392C2×D11semidirect
619. #388C2×D11semidirect
625. #386C2×D11semidirect
632. #381C2×D11semidirect
1000. C11#34562semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
C2×C4×D4×D112
#130745362
#130745332
#130745012
#130744632
#130744592
#130744302
#130744222
#130743882
#130743572
#130743492
#130743272
#130718822
#130718812
#130718592
#130718512
#130718302
#130718282
#130711432
#130711212
#130709962
C11×#26352
#3456211