Finite Group Databasebeta

← #14926797

Subgroups — #14926797

Order 2816.

2930 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic
3#13076951C212yesmaximal, complemented
4#13076902C212yesmaximal, complemented
5#13074434C212yesmaximal, complemented
6#13074426C212yesmaximal, complemented
7#13073965C211yesmaximal, characteristic, complemented
8#13073963C211yesmaximal, characteristic, complemented
9#13073959C211yesmaximal, characteristic, complemented
10#13073801C212yesmaximal, complemented
11#13073795C212yesmaximal, complemented
12#13072932C211yesmaximal, characteristic, complemented
13#13072930C211yesmaximal, characteristic, complemented
14#13072062C212yesmaximal, complemented
15#13072060C212yesmaximal, complemented
16#13071980C211yesmaximal, characteristic, complemented
17#13071978C211yesmaximal, characteristic, complemented
18#13071227C211yesmaximal, characteristic, complemented
19#13071227C211yesmaximal, characteristic, complemented
20#13071190C211yesmaximal, characteristic
21#13071190C211yesmaximal, characteristic
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2579C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×Dic22C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic, complemented
30C2×D4×Dic11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic, complemented
36C22×Dic11⋊C4C2211yescharacteristic, complemented
37C4×D4×D11—28no—
38C2×#66949—28no—
39C2×#66949C2212yes—
40C2×#66949C2212yes—
41C2×#66949C2212yescomplemented
42C2×#66949C2212yescomplemented
43C2×#66949C2212yescomplemented
44C2×#66946C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×C4⋊C4×D11C2212yescomplemented
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×C22⋊C4×D11C2211yescharacteristic
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×#66931C2212yescomplemented
54C2×C4×D44C2211yescharacteristic
55C2×C42×D11C2211yescharacteristic
56C11×#398C2212yescomplemented
57C11×#396C2212yescomplemented
58C11×#387C2212yescomplemented
59C11×#386C2211yescharacteristic
60C11×#386C2211yescharacteristic
61C11×#385C2211yescharacteristic, complemented
62C11×#385C2211yescharacteristic, complemented
63C11×#385C2212yescomplemented
64C11×#380C2211yescharacteristic, complemented
65#10622833C2211yescharacteristic
66#10622833C2211yescharacteristic
67#10622826C2211yescharacteristic
68#10622826C2211yescharacteristic
69#10622825C2211yescharacteristic, complemented
70#10622823C2211yescharacteristic, complemented
71#10622823C2212yescomplemented
72#10622823C2211yescharacteristic, complemented
73#10622607C2212yescomplemented
74#10622607C2212yescomplemented
75#10622605C2212yescomplemented
76#10622602C2212yes—
77#10622602C2212yes—
78#10622602C2212yescomplemented
79#10622600C2212yes—
80#10622600C2212yescomplemented
81#10622600C2212yescomplemented
82#10622597C2212yescomplemented
83#10622597C2212yescomplemented
84#10622596C2212yescomplemented
85#10622592C2212yescomplemented
86#10622591C2212yescomplemented
87#10622585C2212yescomplemented
88#10622571C2211yescharacteristic
89#10622571C2211yescharacteristic
90#10622569C2212yes—
91#10622569C2212yes—
92#10622568C2212yes—
93#10622568C2212yes—
94#10622563C2211yescharacteristic, complemented
95#10622563C2211yescharacteristic, complemented
96#10622562C2212yescomplemented
97#10622561C2212yescomplemented
98#10622560C2212yescomplemented
99#10622559C2211yescharacteristic, complemented
100#10622559C2211yescharacteristic, complemented
101#10622555C2211yescharacteristic, complemented
102#10622555C2212yescomplemented
103#10622555C2211yescharacteristic, complemented
104#10622546C2212yescomplemented
105#10622286C2212yescomplemented
106#10622281C2212yes—
107#10622281C2212yes—
108#10622281C2212yescomplemented
109#10622280C2212yes—
110#10622280C2212yescomplemented
111#10622280C2212yescomplemented
112#10622280C2212yescomplemented
113#10622278C2212yes—
114#10622278C2212yes—
115#10622277C2212yes—
116#10622277C2212yes—
117D11×#95C2212yescomplemented
118#10622273C2212yescomplemented
119#10622271C2212yescomplemented
120#10622269C2212yescomplemented
121#10622266C2212yescomplemented
122#10622260C2212yescomplemented
123#10622259C2212yescomplemented
124#10622259C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C2×D4×D11—24no—
139C2×D4×D11—24no—
140C2×D4×D11Q818yescomplemented
141C22×D44C2311yescharacteristic
142C22×C4×D11—24no—
143C22×C4×D11—44no—
144C22×C4×D11—44no—
145C22×C4×D11D418yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×Dic22—24no—
158C22×Dic22—44no—
159C22×Dic22C2312yes—
160C22×Dic22C2312yes—
161C4×D4×C11—24no—
162C2×C11×C4⋊C4—24no—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C42×C11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182D4×Dic11—24no—
183C4×C22⋊D11—24no—
184C4×C22⋊D11—24no—
185C2×(C2×D11)⋊C4—24no—
186C2×(C2×D11)⋊C4—24no—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2312yes—
205C2×Dic11⋊C4—24no—
206C2×Dic11⋊C4—24no—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222#66949—28no—
223#66949—28no—
224#66949—28no—
225#66949—28no—
226#66949—44no—
227#66946—24no—
228C4⋊C4×D11—24no—
229C4⋊C4×D11—44no—
230(C22⋊D11)⋊C4—24no—
231(C22⋊D11)⋊C4—24no—
232C22⋊C4×D11—24no—
233C22⋊C4×D11—24no—
234C22⋊C4×D11—24no—
235C22⋊C4×D11—24no—
236#66931—44no—
237C4×D44—24no—
238C42×D11—24no—
239C11×#95C2312yes—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
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—
259#35010—111nomaximal, Sylow
260C24×C11C2411yescharacteristic
261C24×C11C2411yescharacteristic
262C23×D11—22no—
263C23×D11—22no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11C2×D414yes—
269C23×D11C2×Q814yes—
270C23×D11C2×Q814yescomplemented
271C23×D11#4114yes—
272C23×D11C2411yescharacteristic
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11C2×Q814yes—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11C2×D414yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2412yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11C2×Q814yes—
300C2×C22⋊D11C2×Q814yescomplemented
301C22×Dic11—24no—
302C22×Dic11—22no—
303C22×Dic11—24no—
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—42no—
307C22×Dic11—42no—
308C22×Dic11C2×D414yes—
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2412yes—
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318D4×D11—232no—
319C2×D44—22no—
320C2×D44—22no—
321C2×D44C2×Q814yescomplemented
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—22no—
325C2×C4×D11—24no—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—22no—
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—22no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—416no—
343C2×C4×D11—416no—
344C2×C4×D11C2×D414yes—
345C2×C4×D11C2×D414yes—
346C2×C4×D11C2×D414yes—
347C2×C4×D11C2×D414yes—
348C2×C4×D11C2×Q814yescomplemented
349C2×Dic22—24no—
350C2×Dic22—24no—
351C2×Dic22—24no—
352C2×Dic22—24no—
353C2×Dic22—42no—
354C2×Dic22—42no—
355C2×Dic22—416no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—24no—
358C11×C4⋊C4—24no—
359C11×C4⋊C4—42no—
360C11×C4⋊C4—42no—
361C11×C4⋊C4—42no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—22no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C42×C11—22no—
369C22⋊Dic11—22no—
370C22⋊Dic11—22no—
371C22⋊Dic11—22no—
372C22⋊Dic11—22no—
373C22⋊Dic11—42no—
374C22⋊Dic11—42no—
375(C2×D11)⋊C4—22no—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—22no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389C4⋊Dic11—22no—
390C4⋊Dic11—42no—
391C4⋊Dic11—42no—
392C4⋊Dic11—42no—
393Dic11⋊C4—22no—
394Dic11⋊C4—24no—
395Dic11⋊C4—24no—
396Dic11⋊C4—24no—
397Dic11⋊C4—24no—
398Dic11⋊C4—22no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—42no—
402Dic11⋊C4—42no—
403Dic11⋊C4—42no—
404Dic11⋊C4—42no—
405C4×Dic11—22no—
406C4×Dic11—22no—
407C4×Dic11—22no—
408C22×C22⋊Q8—111no—
409C22×C4×D4—111no—
410#2855—112no—
411#2848—112no—
412#2627—112no—
413#2626—112no—
414#2579—111no—
415#2579—111no—
416#2579—111no—
417#2579D1111yescharacteristic, complemented
418#2564—112no—
419#2564—112no—
420#2487—111no—
421#2487—111no—
422#2417—112no—
423#2417—112no—
424#2409—111no—
425#2409—111no—
426#2315—111no—
427#2315—111no—
428#2308—111no—
429#2308—111no—
430C2×#380—111no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—21no—
434C23×C11—21no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11C22×D412yes—
438C23×C11C22×Q812yes—
439C23×C11C22×Q812yes—
440C23×C11C2×#4112yes—
441C23×C11C2511yescharacteristic
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—28no—
451C22×D11—44no—
452C22×D11—44no—
453C22×D11—48no—
454C22×D11—48no—
455C22×D11—48no—
456C22×D11—44no—
457C22×D11—44no—
458C22×D11—48no—
459C22×D11C22⋊Q8116yescomplemented
460C22×D11C22×D412yes—
461C22×D11C22×D412yes—
462C22×D11C22×Q812yes—
463C22×D11C22×Q812yes—
464C22×D11C22×Q812yes—
465C22×D11C2×#4112yes—
466C22×D11C2×#4112yes—
467D4×C11—28no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—44no—
489C2×C4×C11—44no—
490C2×C4×C11—44no—
491C2×C4×C11—44no—
492C2×C4×C11C22×D412yes—
493C2×C4×C11C22×D412yes—
494C2×C4×C11C22×Q812yes—
495C22⋊D11—28no—
496C22⋊D11—28no—
497C2×Dic11—21no—
498C2×Dic11—21no—
499C2×Dic11—22no—
500C2×Dic11—28no—
501C2×Dic11—21no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—44no—
518C2×Dic11—44no—
519C2×Dic11—44no—
520C2×Dic11C22×D412yes—
521C2×Dic11C22×D412yes—
522C2×Dic11C22×Q812yes—
523C2×Dic11H(5,𝔽2)14yes—
524D44—28no—
525C4×D11—28no—
526C4×D11—28no—
527C4×D11—28no—
528C4×D11—44no—
529C4×D11—44no—
530C4×D11—44no—
531C4×D11—44no—
532C4×D11—44no—
533C4×D11—44no—
534C4×D11—84no—
535C4×D11—84no—
536Dic22—48no—
537Dic22—48no—
538C23×Q8—111no—
539C23×D4—111no—
540C24×C4—111no—
541C24×C4—111no—
542C2×C22⋊Q8—112no—
543C2×C22⋊Q8—112no—
544C2×C22⋊Q8—112no—
545C2×C22⋊Q8—112no—
546C2×C22⋊Q8—112no—
547C2×C22⋊Q8—112no—
548C2×C22⋊Q8—228no—
549C2×C4×D4—111no—
550C2×C4×D4—111no—
551C2×C4×D4—111no—
552C2×C4×D4—111no—
553C2×C4×D4—111no—
554C2×C4×D4—111no—
555C2×C4×D4—111no—
556C2×C4×D4—228no—
557C2×C4×D4C2×D1111yescharacteristic
558C22×C4⋊C4—111no—
559C22×C4⋊C4—111no—
560C22×C4⋊C4—111no—
561C22×C4⋊C4—112no—
562C22×C4⋊C4C2×D1111yescharacteristic, complemented
563C22×C22⋊C4—111no—
564C22×C22⋊C4—111no—
565C22×C22⋊C4—111no—
566C22×C22⋊C4—111no—
567C22×C22⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C42—111no—
570#400—112no—
571#400—112no—
572#399—112no—
573#399—112no—
574#398—112no—
575#398—112no—
576#398—112no—
577#398C2×D1112yescomplemented
578#396—112no—
579#396—112no—
580#396—112no—
581#396C2×D1112yescomplemented
582#395—112no—
583#395—112no—
584#393—112no—
585#393—112no—
586#391—112no—
587#391—112no—
588#389—112no—
589#389—112no—
590#387—112no—
591#387—112no—
592#387—112no—
593#387C2×D1112yescomplemented
594#386—111no—
595#386—111no—
596#386—111no—
597#386—111no—
598#386—112no—
599#386—112no—
600#386—111no—
601#386—111no—
602#386—112no—
603#386—112no—
604#386C2×D1111yescharacteristic
605#386C2×D1111yescharacteristic
606#385—112no—
607#385—111no—
608#385—111no—
609#385—112no—
610#385—112no—
611#385—112no—
612#385—111no—
613#385—111no—
614#385—111no—
615#385—111no—
616#385—112no—
617#385—112no—
618#385—112no—
619#385C2×D1112yescomplemented
620#385C2×D1111yescharacteristic, complemented
621#385C2×D1111yescharacteristic, complemented
622#381—112no—
623#381—112no—
624#380—111no—
625#380—112no—
626#380—112no—
627#380—112no—
628#380—112no—
629#380—111no—
630#380—111no—
631#380—112no—
632#380—112no—
633#380—112no—
634#380—112no—
635#380C2×D1111yescharacteristic, complemented
636#379—112no—
637#379—112no—
638C2×#95—112no—
639C22×C11—22no—
640C22×C11—22no—
641C22×C11—24no—
642C22×C11—24no—
643C22×C11—22no—
644C22×C11—24no—
645C22×C11—41no—
646C22×C11—41no—
647C22×C11—42no—
648C22×C11C2×C22⋊Q814yes—
649C22×C11C23×D411yescharacteristic
650C22×C11C23×Q811yescharacteristic
651C22×C11C22×#4111yescharacteristic
652C22×C11C2×H(5,𝔽2)12yes—
653C22×C11#58512yes—
654C2×D11—22no—
655C2×D11—22no—
656C2×D11—22no—
657C2×D11—22no—
658C2×D11—24no—
659C2×D11—24no—
660C2×D11—24no—
661C2×D11—24no—
662C2×D11—22no—
663C2×D11—24no—
664C2×D11—416no—
665C2×D11—416no—
666C2×D11—41no—
667C2×D11—41no—
668C2×D11—42no—
669C2×D11C2×C22⋊Q814yes—
670C2×D11C2×C22⋊Q814yes—
671C4×C11—22no—
672C4×C11—22no—
673C4×C11—22no—
674C4×C11—42no—
675C4×C11—41no—
676C4×C11—42no—
677C4×C11—41no—
678C4×C11—42no—
679C4×C11—42no—
680Dic11—22no—
681Dic11—22no—
682Dic11—42no—
683Dic11—41no—
684Dic11—41no—
685Dic11—42no—
686Dic11—42no—
687Dic11—42no—
688Dic11#53414yes—
689C25—111no—
690C25—111no—
691C22×Q8—112no—
692C22×Q8—112no—
693C22×Q8—224no—
694C22×Q8—444no—
695C22×D4—111no—
696C22×D4—111no—
697C22×D4—118no—
698C22×D4—111no—
699C22×D4—224no—
700C22×D4—224no—
701C22×D4C22×D1111yescharacteristic
702C23×C4—111no—
703C23×C4—111no—
704C23×C4—111no—
705C23×C4—111no—
706C23×C4—118no—
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—111no—
712C23×C4—111no—
713C23×C4—111no—
714C23×C4—111no—
715C23×C4—112no—
716C23×C4—112no—
717C23×C4—111no—
718C23×C4—224no—
719C23×C4—444no—
720C23×C4—444no—
721C23×C4C22×D1111yescharacteristic
722C23×C4C22×D1111yescharacteristic
723C23×C4C22×D1111yescharacteristic
724C23×C4C22×D1111yescharacteristic
725C22⋊Q8—228no—
726C22⋊Q8—228no—
727C22⋊Q8—228no—
728C22⋊Q8—228no—
729C22⋊Q8—444no—
730C22⋊Q8—444no—
731C4×D4—24no—
732C4×D4—224no—
733C4×D4—224no—
734C4×D4—224no—
735C4×D4—224no—
736C4×D4—224no—
737C4×D4—224no—
738C4×D4—224no—
739C2×C4⋊C4—24no—
740C2×C4⋊C4—111no—
741C2×C4⋊C4—111no—
742C2×C4⋊C4—111no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—112no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—112no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4—112no—
751C2×C4⋊C4—112no—
752C2×C4⋊C4—112no—
753C2×C4⋊C4—112no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—224no—
757C2×C4⋊C4—224no—
758C2×C4⋊C4—224no—
759C2×C4⋊C4—444no—
760C2×C4⋊C4C22×D1111yescharacteristic
761C2×C4⋊C4C22×D1112yes—
762C2×C4⋊C4C22×D1112yes—
763C2×C4⋊C4C22×D1112yes—
764C2×C4⋊C4C22×D1112yes—
765C2×C4⋊C4C22×D1112yes—
766C2×C22⋊C4—111no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—111no—
771C2×C22⋊C4—111no—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—111no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—224no—
787C2×C22⋊C4—224no—
788C2×C22⋊C4—224no—
789C2×C22⋊C4—224no—
790C2×C22⋊C4—224no—
791C2×C22⋊C4—224no—
792C2×C22⋊C4C22×D1111yescharacteristic
793C2×C22⋊C4C22×D1111yescharacteristic
794C2×C22⋊C4C22×D1111yescharacteristic
795C2×C22⋊C4C22×D1111yescharacteristic
796C2×C22⋊C4C22×D1112yes—
797C2×C22⋊C4C22×D1112yes—
798C2×C42—111no—
799C2×C42—111no—
800C2×C42—111no—
801C2×C42—224no—
802C2×C42C22×D1111yescharacteristic
803#95—112no—
804#95—112no—
805#95—112no—
806#95—112no—
807#95—112no—
808#95—112no—
809#95—112no—
810#95—112no—
811#95—112no—
812#95—112no—
813#95—112no—
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95C22×D1112yes—
819#95C22×D1112yes—
820#95C22×D1112yes—
821#95C22×D1112yes—
822#95C22×D1112yes—
823C2×C11—24no—
824C2×C11—42no—
825C2×C11C22×C22⋊Q811yescharacteristic
826C2×C11C2×#53411yescharacteristic
827C2×C11#344911yescharacteristic
828C2×C11#350112yes—
829C2×C11#350512yes—
830D11—24no—
831D11—24no—
832D11—42no—
833C24—111no—
834C24—111no—
835C24—114no—
836C24—114no—
837C24—114no—
838C24—111no—
839C24—114no—
840C24—222no—
841C24—222no—
842C24—442no—
843C24—442no—
844C24—442no—
845C24—442no—
846C24C23×D1111yescharacteristic
847C24C23×D1111yescharacteristic
848C2×Q8—224no—
849C2×Q8—224no—
850C2×Q8—224no—
851C2×Q8—224no—
852C2×Q8—442no—
853C2×Q8—442no—
854C2×Q8—4416no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—114no—
858C2×D4—114no—
859C2×D4—114no—
860C2×D4—222no—
861C2×D4—222no—
862C2×D4—2232no—
863C2×D4—222no—
864C2×D4—222no—
865C2×D4—222no—
866C2×D4—222no—
867C2×D4Q8×D1114yes—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—111no—
876C22×C4—114no—
877C22×C4—111no—
878C22×C4—111no—
879C22×C4—114no—
880C22×C4—114no—
881C22×C4—114no—
882C22×C4—114no—
883C22×C4—114no—
884C22×C4—112no—
885C22×C4—112no—
886C22×C4—111no—
887C22×C4—112no—
888C22×C4—112no—
889C22×C4—111no—
890C22×C4—224no—
891C22×C4—224no—
892C22×C4—222no—
893C22×C4—224no—
894C22×C4—222no—
895C22×C4—222no—
896C22×C4—222no—
897C22×C4—222no—
898C22×C4—224no—
899C22×C4—224no—
900C22×C4—224no—
901C22×C4—222no—
902C22×C4—224no—
903C22×C4—222no—
904C22×C4—222no—
905C22×C4—222no—
906C22×C4—442no—
907C22×C4—442no—
908C22×C4—442no—
909C22×C4—442no—
910C22×C4—442no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4—442no—
914C22×C4—442no—
915C22×C4—4416no—
916C22×C4—4416no—
917C22×C4—442no—
918C22×C4—442no—
919C22×C4D4×D1114yes—
920C22×C4C23×D1112yes—
921C22×C4C23×D1112yes—
922C22×C4C23×D1111yescharacteristic
923C22×C4C23×D1112yes—
924C22×C4C23×D1112yes—
925C22×C4C23×D1111yescharacteristic
926C22×C4C23×D1111yescharacteristic
927C22×C4C23×D1111yescharacteristic
928C22×C4C23×D1111yescharacteristic
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—22no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—222no—
936C4⋊C4—222no—
937C4⋊C4—224no—
938C4⋊C4—224no—
939C4⋊C4—224no—
940C4⋊C4—224no—
941C4⋊C4—222no—
942C4⋊C4—224no—
943C4⋊C4—224no—
944C4⋊C4—442no—
945C4⋊C4—442no—
946C4⋊C4—442no—
947C4⋊C4—442no—
948C4⋊C4—442no—
949C4⋊C4—442no—
950C4⋊C4—442no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—222no—
958C22⋊C4—222no—
959C22⋊C4—222no—
960C22⋊C4—224no—
961C22⋊C4—224no—
962C22⋊C4—224no—
963C22⋊C4—224no—
964C22⋊C4—224no—
965C22⋊C4—224no—
966C22⋊C4—222no—
967C22⋊C4—222no—
968C22⋊C4—222no—
969C22⋊C4—222no—
970C22⋊C4—222no—
971C22⋊C4—442no—
972C22⋊C4—442no—
973C22⋊C4—442no—
974C22⋊C4—442no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C42—22no—
978C42—222no—
979C42—222no—
980C42—222no—
981C11#3501011yescharacteristic, complemented, Sylow
982C23—22no—
983C23—22no—
984C23—21no—
985C23—21no—
986C23—22no—
987C23—22no—
988C23—112no—
989C23—112no—
990C23—112no—
991C23—112no—
992C23—112no—
993C23—112no—
994C23—1116no—
995C23—112no—
996C23—228no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—221no—
1002C23—221no—
1003C23—222no—
1004C23—222no—
1005C23—444no—
1006C23—448no—
1007C23—448no—
1008C23—444no—
1009C23—448no—
1010C23—444no—
1011C23—448no—
1012C23—444no—
1013C23C2×D4×D1112yes—
1014C23C2×Q8×D1112yes—
1015C23C2×Q8×D1112yes—
1016C23#41×D1112yes—
1017C23C24×D1111yescharacteristic
1018Q8—448no—
1019Q8—448no—
1020D4—28no—
1021D4—228no—
1022D4—228no—
1023D4—228no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—44no—
1048C2×C4—112no—
1049C2×C4—114no—
1050C2×C4—112no—
1051C2×C4—112no—
1052C2×C4—228no—
1053C2×C4—228no—
1054C2×C4—228no—
1055C2×C4—228no—
1056C2×C4—221no—
1057C2×C4—221no—
1058C2×C4—222no—
1059C2×C4—221no—
1060C2×C4—222no—
1061C2×C4—221no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—444no—
1076C2×C4—444no—
1077C2×C4—444no—
1078C2×C4—444no—
1079C2×C4—444no—
1080C2×C4—444no—
1081C2×C4—444no—
1082C2×C4—444no—
1083C2×C4—444no—
1084C2×C4—884no—
1085C2×C4—884no—
1086C2×C4C2×D4×D1112yes—
1087C2×C4C2×D4×D1112yes—
1088C2×C4C2×Q8×D1112yes—
1089C22—24no—
1090C22—22no—
1091C22—24no—
1092C22—22no—
1093C22—24no—
1094C22—22no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—114no—
1099C22—114no—
1100C22—224no—
1101C22—224no—
1102C22—222no—
1103C22—222no—
1104C22—224no—
1105C22—224no—
1106C22—222no—
1107C22—222no—
1108C22—224no—
1109C22—222no—
1110C22—4416no—
1111C22—4416no—
1112C22—441no—
1113C22—442no—
1114C22—441no—
1115C22D11×C22⋊Q814yes—
1116C22C22×D4×D1111yescharacteristic
1117C22C22×Q8×D1111yescharacteristic
1118C22C2×#41×D1111yescharacteristic
1119C22#1062345312yes—
1120C22D11×H(5,𝔽2)12yes—
1121C4—22no—
1122C4—22no—
1123C4—22no—
1124C4—41no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—41no—
1130C4—114no—
1131C4—222no—
1132C4—222no—
1133C4—441no—
1134C4—442no—
1135C4—442no—
1136C4—442no—
1137C4—441no—
1138C4—442no—
1139C2—24no—
1140C2—42no—
1141C2—224no—
1142C2—224no—
1143C2—442no—
1144C2C2×D11×C22⋊Q811yescharacteristic
1145C2D11×#53411yescharacteristic
1146C2#1308194611yescharacteristic
1147C2#1308241512yes—
1148C2#1308244912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2579C2
prime radicalC22×D4×D11C22
hypercenter#2579D11
hypocenterC11#35010
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2579

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
3. #13076951C2semidirect
4. #13076902C2semidirect
5. #13074434C2semidirect
6. #13074426C2semidirect
7. #13073965C2semidirect
8. #13073963C2semidirect
9. #13073959C2semidirect
10. #13073801C2semidirect
11. #13073795C2semidirect
12. #13072932C2semidirect
13. #13072930C2semidirect
14. #13072062C2semidirect
15. #13072060C2semidirect
16. #13071980C2semidirect
17. #13071978C2semidirect
18. #13071227C2semidirect
19. #13071227C2semidirect
22. D11×#380C2semidirect
23. C11×#2579C2semidirect
27. C23×Dic22C22semidirect
29. C22×C11×C4⋊C4C22semidirect
35. C22×Dic11⋊C4C22semidirect
36. C22×Dic11⋊C4C22semidirect
41. C2×#66949C22semidirect
42. C2×#66949C22semidirect
43. C2×#66949C22semidirect
46. C2×C4⋊C4×D11C22semidirect
53. C2×#66931C22semidirect
56. C11×#398C22semidirect
57. C11×#396C22semidirect
58. C11×#387C22semidirect
61. C11×#385C22semidirect
62. C11×#385C22semidirect
63. C11×#385C22semidirect
64. C11×#380C22semidirect
69. #10622825C22semidirect
70. #10622823C22semidirect
71. #10622823C22semidirect
72. #10622823C22semidirect
73. #10622607C22semidirect
74. #10622607C22semidirect
75. #10622605C22semidirect
78. #10622602C22semidirect
80. #10622600C22semidirect
81. #10622600C22semidirect
82. #10622597C22semidirect
83. #10622597C22semidirect
84. #10622596C22semidirect
85. #10622592C22semidirect
86. #10622591C22semidirect
87. #10622585C22semidirect
94. #10622563C22semidirect
95. #10622563C22semidirect
96. #10622562C22semidirect
97. #10622561C22semidirect
98. #10622560C22semidirect
99. #10622559C22semidirect
100. #10622559C22semidirect
101. #10622555C22semidirect
102. #10622555C22semidirect
103. #10622555C22semidirect
104. #10622546C22semidirect
105. #10622286C22semidirect
108. #10622281C22semidirect
110. #10622280C22semidirect
111. #10622280C22semidirect
112. #10622280C22semidirect
117. D11×#95C22semidirect
118. #10622273C22semidirect
119. #10622271C22semidirect
120. #10622269C22semidirect
121. #10622266C22semidirect
122. #10622260C22semidirect
123. #10622259C22semidirect
124. #10622259C22semidirect
140. C2×D4×D11Q8semidirect
270. C23×D11C2×Q8semidirect
300. C2×C22⋊D11C2×Q8semidirect
321. C2×D44C2×Q8semidirect
348. C2×C4×D11C2×Q8semidirect
417. #2579D11semidirect
459. C22×D11C22⋊Q8semidirect
562. C22×C4⋊C4C2×D11semidirect
577. #398C2×D11semidirect
581. #396C2×D11semidirect
593. #387C2×D11semidirect
619. #385C2×D11semidirect
620. #385C2×D11semidirect
621. #385C2×D11semidirect
635. #380C2×D11semidirect
981. C11#35010semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
C2×C4×D4×D112
#130769512
#130769022
#130744342
#130744262
#130739652
#130739632
#130739592
#130738012
#130737952
#130729322
#130729302
#130720622
#130720602
#130719802
#130719782
#130712272
#130711902
D11×#3802
C11×#25792
#3501011