Finite Group Databasebeta

← D11×#2579 #14923973

Subgroups — D11×#2579 #14923973

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3#13073968C211yesmaximal, characteristic, complemented
4#13073967C212yesmaximal, complemented
5#13073966C211yesmaximal, characteristic, complemented
6#13073965C211yesmaximal, characteristic, complemented
7#13073964C212yesmaximal, complemented
8#13073963C211yesmaximal, characteristic, complemented
9#13073962C211yesmaximal, characteristic, complemented
10#13073961C212yesmaximal, complemented
11#13073960C211yesmaximal, characteristic, complemented
12#13073959C211yesmaximal, characteristic, complemented
13#13073958C212yesmaximal, complemented
14D11×#398C212yesmaximal, complemented
15D11×#396C212yesmaximal, complemented
16D11×#387C212yesmaximal, complemented
17D11×#386C211yesmaximal, characteristic
18D11×#386C211yesmaximal, characteristic
19D11×#385C211yesmaximal, characteristic, complemented
20D11×#385C211yesmaximal, characteristic, complemented
21D11×#385C212yesmaximal, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2579C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic, complemented
31C2×D4×Dic11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic, complemented
35C22×Dic11⋊C4C2211yescharacteristic, complemented
36C22×Dic11⋊C4C2211yescharacteristic, complemented
37C4×D4×D11—28no—
38C2×#66946C2211yescharacteristic
39C2×C4⋊C4×D11—28no—
40C2×C4⋊C4×D11C2212yes—
41C2×C4⋊C4×D11C2212yes—
42C2×C4⋊C4×D11C2212yes—
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×C4⋊C4×D11C2212yes—
45C2×C4⋊C4×D11C2212yes—
46C2×C4⋊C4×D11C2212yescomplemented
47C2×C4⋊C4×D11C2212yescomplemented
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2211yescharacteristic
50C2×C22⋊C4×D11C2211yescharacteristic
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×C22⋊C4×D11C2212yes—
54C2×C22⋊C4×D11C2211yescharacteristic
55C2×C22⋊C4×D11C2212yes—
56C2×C4×D44C2211yescharacteristic
57C2×C42×D11C2211yescharacteristic
58C11×#398C2212yescomplemented
59C11×#396C2212yescomplemented
60C11×#387C2212yescomplemented
61C11×#386C2211yescharacteristic
62C11×#386C2211yescharacteristic
63C11×#385C2212yescomplemented
64C11×#385C2211yescharacteristic, complemented
65C11×#385C2211yescharacteristic, complemented
66C11×#380C2211yescharacteristic, complemented
67#10622833C2211yescharacteristic
68#10622833C2211yescharacteristic
69#10622826C2211yescharacteristic
70#10622826C2211yescharacteristic
71#10622825C2211yescharacteristic, complemented
72#10622823C2212yescomplemented
73#10622823C2211yescharacteristic, complemented
74#10622823C2211yescharacteristic, complemented
75#10622607C2212yescomplemented
76#10622607C2212yescomplemented
77#10622607C2212yescomplemented
78#10622602C2212yescomplemented
79#10622602C2212yescomplemented
80#10622602C2212yescomplemented
81#10622602C2212yescomplemented
82#10622600C2212yescomplemented
83#10622597C2212yescomplemented
84#10622597C2212yescomplemented
85#10622596C2212yescomplemented
86#10622594C2212yescomplemented
87#10622593C2212yescomplemented
88#10622591C2212yescomplemented
89#10622571C2211yescharacteristic
90#10622571C2211yescharacteristic
91#10622569C2212yes—
92#10622569C2212yes—
93#10622563C2212yescomplemented
94#10622563C2211yescharacteristic, complemented
95#10622563C2211yescharacteristic, complemented
96#10622561C2212yescomplemented
97#10622561C2212yescomplemented
98#10622561C2212yescomplemented
99#10622559C2212yescomplemented
100#10622559C2211yescharacteristic, complemented
101#10622559C2211yescharacteristic, complemented
102#10622555C2211yescharacteristic, complemented
103#10622555C2211yescharacteristic, complemented
104#10622546C2212yescomplemented
105#10622289C2212yescomplemented
106#10622281C2212yescomplemented
107#10622281C2212yescomplemented
108#10622281C2212yescomplemented
109#10622281C2212yescomplemented
110#10622280C2212yescomplemented
111#10622278C2212yes—
112#10622278C2212yes—
113D11×#95C2212yes—
114D11×#95C2212yes—
115D11×#95C2212yes—
116D11×#95C2212yes—
117D11×#95C2212yes—
118#10622274C2212yescomplemented
119#10622270C2212yescomplemented
120#10622270C2212yescomplemented
121#10622268C2212yescomplemented
122#10622267C2212yescomplemented
123#10622266C2212yescomplemented
124#10622265C2212yescomplemented
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×D11Q818yes—
141C22×D44C2311yescharacteristic
142C22×C4×D11—24no—
143C22×C4×D11—28no—
144C22×C4×D11—24no—
145C22×C4×D11—24no—
146C22×C4×D11—44no—
147C22×C4×D11—44no—
148C22×C4×D11—44no—
149C22×C4×D11D418yes—
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2312yes—
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2312yes—
155C22×C4×D11C2312yes—
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2312yes—
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⋊C4C2312yes—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179C2×C42×C11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186D4×Dic11—24no—
187C4×C22⋊D11—24no—
188C4×C22⋊D11—24no—
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
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×C4⋊Dic11—24no—
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2312yes—
205C2×C4⋊Dic11C2312yes—
206C2×Dic11⋊C4—24no—
207C2×Dic11⋊C4—24no—
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×Dic11⋊C4C2312yes—
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223#66946—24no—
224C4⋊C4×D11—28no—
225C4⋊C4×D11—28no—
226C4⋊C4×D11—28no—
227C4⋊C4×D11—28no—
228C4⋊C4×D11—24no—
229C4⋊C4×D11—28no—
230C4⋊C4×D11—44no—
231C4⋊C4×D11—44no—
232(C22⋊D11)⋊C4—24no—
233(C22⋊D11)⋊C4—24no—
234C22⋊C4×D11—24no—
235C22⋊C4×D11—24no—
236C22⋊C4×D11—24no—
237C22⋊C4×D11—24no—
238C22⋊C4×D11—28no—
239C22⋊C4×D11—44no—
240C4×D44—24no—
241C42×D11—24no—
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—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C2×#2579—111nomaximal, Sylow
263C24×C11C2411yescharacteristic
264C24×C11C2411yescharacteristic
265C23×D11—24no—
266C23×D11—24no—
267C23×D11—22no—
268C23×D11—24no—
269C23×D11—22no—
270C23×D11—24no—
271C23×D11C2×D414yes—
272C23×D11C2×Q814yes—
273C23×D11C2×Q814yes—
274C23×D11#4114yes—
275C23×D11C2411yescharacteristic
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11C2×Q814yes—
281C22×C4×C11—22no—
282C22×C4×C11—24no—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11C2×D414yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11C2×Q814yes—
303C2×C22⋊D11C2×Q814yes—
304C22×Dic11—24no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11—42no—
311C22×Dic11C2×D414yes—
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321D4×D11—232no—
322C2×D44—22no—
323C2×D44—22no—
324C2×D44C2×Q814yes—
325C2×C4×D11—232no—
326C2×C4×D11—24no—
327C2×C4×D11—22no—
328C2×C4×D11—22no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—22no—
332C2×C4×D11—22no—
333C2×C4×D11—24no—
334C2×C4×D11—24no—
335C2×C4×D11—24no—
336C2×C4×D11—22no—
337C2×C4×D11—24no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—24no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—22no—
350C2×C4×D11—24no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—416no—
358C2×C4×D11—416no—
359C2×C4×D11—416no—
360C2×C4×D11C2×D414yes—
361C2×C4×D11C2×D414yes—
362C2×C4×D11C2×D414yes—
363C2×C4×D11C2×D414yes—
364C2×C4×D11C2×Q814yes—
365C2×C4×D11#4118yes—
366C11×C4⋊C4—24no—
367C11×C4⋊C4—24no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—24no—
370C11×C4⋊C4—42no—
371C11×C4⋊C4—42no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—22no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—42no—
378C42×C11—22no—
379C22⋊Dic11—22no—
380C22⋊Dic11—24no—
381C22⋊Dic11—22no—
382C22⋊Dic11—22no—
383C22⋊Dic11—22no—
384C22⋊Dic11—42no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395C4⋊Dic11—22no—
396C4⋊Dic11—24no—
397C4⋊Dic11—24no—
398C4⋊Dic11—24no—
399C4⋊Dic11—42no—
400C4⋊Dic11—42no—
401Dic11⋊C4—22no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—22no—
406Dic11⋊C4—24no—
407Dic11⋊C4—24no—
408Dic11⋊C4—24no—
409Dic11⋊C4—42no—
410Dic11⋊C4—42no—
411Dic11⋊C4—42no—
412Dic11⋊C4—42no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—22no—
416C22×C4×D4—111no—
417C23×C4⋊C4—111no—
418#2579—112no—
419#2579—112no—
420#2579—112no—
421#2579—111no—
422#2579—111no—
423#2579—112no—
424#2579—111no—
425#2579—111no—
426#2579—111no—
427#2579—111no—
428#2579—111no—
429#2579D1111yescharacteristic, direct product factor
430C2×#398—112no—
431C2×#396—112no—
432C2×#387—112no—
433C2×#386—111no—
434C2×#386—111no—
435C2×#385—112no—
436C2×#385—111no—
437C2×#385—111no—
438C2×#380—111no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—21no—
442C23×C11—22no—
443C23×C11—21no—
444C23×C11—22no—
445C23×C11C22×D412yes—
446C23×C11C22×Q812yes—
447C23×C11C22×Q812yes—
448C23×C11C2×#4112yes—
449C23×C11C2511yescharacteristic
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—28no—
453C22×D11—28no—
454C22×D11—216no—
455C22×D11—216no—
456C22×D11—21no—
457C22×D11—22no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—28no—
461C22×D11—216no—
462C22×D11—44no—
463C22×D11—44no—
464C22×D11—48no—
465C22×D11C22⋊Q8116yes—
466C22×D11C22×D412yes—
467C22×D11C22×D412yes—
468C22×D11C22×Q812yes—
469C22×D11C22×Q812yes—
470C22×D11C22×Q812yes—
471C22×D11C2×#4112yes—
472C22×D11C2×#4112yes—
473C22×D11C2×#4114yes—
474C22×D11H(5,𝔽2)14yes—
475D4×C11—28no—
476C2×C4×C11—28no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
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—44no—
497C2×C4×C11—44no—
498C2×C4×C11—44no—
499C2×C4×C11C22×D412yes—
500C2×C4×C11C22×D412yes—
501C2×C4×C11C22×Q812yes—
502C2×C4×C11C2×#4114yes—
503C22⋊D11—28no—
504C22⋊D11—28no—
505C2×Dic11—28no—
506C2×Dic11—21no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—21no—
515C2×Dic11—22no—
516C2×Dic11—22no—
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—44no—
526C2×Dic11—44no—
527C2×Dic11—44no—
528C2×Dic11C22×D412yes—
529C2×Dic11C22×D412yes—
530C2×Dic11C22×Q812yes—
531C2×Dic11C2×#4114yes—
532D44—28no—
533C4×D11—216no—
534C4×D11—28no—
535C4×D11—216no—
536C4×D11—28no—
537C4×D11—28no—
538C4×D11—44no—
539C4×D11—44no—
540C4×D11—44no—
541C4×D11—44no—
542C4×D11—48no—
543C4×D11—44no—
544C4×D11—44no—
545C4×D11—48no—
546C4×D11—48no—
547C4×D11—48no—
548C23×D4—111no—
549C24×C4—111no—
550C24×C4—111no—
551C24×C4—111no—
552C24×C4—111no—
553C2×C4×D4—111no—
554C2×C4×D4—111no—
555C2×C4×D4—111no—
556C2×C4×D4—111no—
557C2×C4×D4—111no—
558C2×C4×D4—111no—
559C2×C4×D4—111no—
560C2×C4×D4—228no—
561C2×C4×D4C2×D1111yescharacteristic
562C22×C4⋊C4—111no—
563C22×C4⋊C4—111no—
564C22×C4⋊C4—111no—
565C22×C4⋊C4—112no—
566C22×C4⋊C4—112no—
567C22×C4⋊C4—112no—
568C22×C4⋊C4—112no—
569C22×C4⋊C4—111no—
570C22×C4⋊C4—112no—
571C22×C4⋊C4—112no—
572C22×C4⋊C4—112no—
573C22×C4⋊C4—228no—
574C22×C4⋊C4C2×D1111yescharacteristic, complemented
575C22×C22⋊C4—111no—
576C22×C22⋊C4—112no—
577C22×C22⋊C4—111no—
578C22×C22⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4—112no—
581C22×C42—111no—
582#398—112no—
583#398—112no—
584#398—112no—
585#398—112no—
586#398—112no—
587#398—112no—
588#398—112no—
589#398C2×D1112yescomplemented
590#396—112no—
591#396—112no—
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#396—112no—
597#396C2×D1112yescomplemented
598#387—112no—
599#387—112no—
600#387—112no—
601#387—112no—
602#387—112no—
603#387—112no—
604#387—112no—
605#387C2×D1112yescomplemented
606#386—111no—
607#386—111no—
608#386—111no—
609#386—111no—
610#386—112no—
611#386—112no—
612#386—111no—
613#386—111no—
614#386—112no—
615#386—112no—
616#386C2×D1111yescharacteristic
617#386C2×D1111yescharacteristic
618#385—112no—
619#385—111no—
620#385—111no—
621#385—112no—
622#385—112no—
623#385—112no—
624#385—112no—
625#385—112no—
626#385—111no—
627#385—111no—
628#385—112no—
629#385—111no—
630#385—111no—
631#385—112no—
632#385—112no—
633#385—112no—
634#385—112no—
635#385C2×D1112yescomplemented
636#385C2×D1111yescharacteristic, complemented
637#385C2×D1111yescharacteristic, complemented
638#380—111no—
639#380—112no—
640#380—111no—
641#380—111no—
642#380—112no—
643#380C2×D1111yescharacteristic, complemented
644C2×#95—112no—
645C2×#95—112no—
646C2×#95—112no—
647C2×#95—112no—
648C2×#95—112no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—22no—
654C22×C11—24no—
655C22×C11—41no—
656C22×C11—41no—
657C22×C11—42no—
658C22×C11C2×C22⋊Q814yes—
659C22×C11C23×D411yescharacteristic
660C22×C11C23×Q811yescharacteristic
661C22×C11C22×#4111yescharacteristic
662C22×C11C22×#4112yes—
663C22×C11C2×H(5,𝔽2)12yes—
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—24no—
667C2×D11—24no—
668C2×D11—232no—
669C2×D11—22no—
670C2×D11—24no—
671C2×D11—41no—
672C2×D11—41no—
673C2×D11—42no—
674C2×D11—416no—
675C2×D11C2×C22⋊Q814yes—
676C2×D11C2×C22⋊Q814yes—
677C2×D11#52514yes—
678C2×D11#53414yes—
679C2×D11#55318yes—
680C2×D11#55418yes—
681C4×C11—22no—
682C4×C11—24no—
683C4×C11—22no—
684C4×C11—22no—
685C4×C11—41no—
686C4×C11—42no—
687C4×C11—41no—
688C4×C11—42no—
689C4×C11—42no—
690Dic11—22no—
691Dic11—24no—
692Dic11—22no—
693Dic11—22no—
694Dic11—41no—
695Dic11—41no—
696Dic11—42no—
697Dic11—42no—
698Dic11—42no—
699C25—111no—
700C25—111no—
701C22×D4—111no—
702C22×D4—111no—
703C22×D4—118no—
704C22×D4—111no—
705C22×D4—224no—
706C22×D4—224no—
707C22×D4C22×D1111yescharacteristic
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—112no—
711C23×C4—111no—
712C23×C4—111no—
713C23×C4—118no—
714C23×C4—111no—
715C23×C4—111no—
716C23×C4—111no—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—112no—
720C23×C4—112no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—112no—
724C23×C4—112no—
725C23×C4—112no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—228no—
729C23×C4—224no—
730C23×C4—224no—
731C23×C4—224no—
732C23×C4—444no—
733C23×C4—444no—
734C23×C4—444no—
735C23×C4C22×D1111yescharacteristic
736C23×C4C22×D1111yescharacteristic
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1111yescharacteristic
739C4×D4—24no—
740C4×D4—224no—
741C4×D4—224no—
742C4×D4—224no—
743C4×D4—224no—
744C4×D4—224no—
745C4×D4—224no—
746C4×D4—224no—
747C2×C4⋊C4—24no—
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—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—112no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4—112no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—228no—
767C2×C4⋊C4—228no—
768C2×C4⋊C4—228no—
769C2×C4⋊C4—228no—
770C2×C4⋊C4—224no—
771C2×C4⋊C4—228no—
772C2×C4⋊C4—224no—
773C2×C4⋊C4—224no—
774C2×C4⋊C4—224no—
775C2×C4⋊C4—444no—
776C2×C4⋊C4—444no—
777C2×C4⋊C4C22×D1112yes—
778C2×C4⋊C4C22×D1112yes—
779C2×C4⋊C4C22×D1111yescharacteristic
780C2×C4⋊C4C22×D1112yes—
781C2×C4⋊C4C22×D1112yes—
782C2×C4⋊C4C22×D1112yes—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
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—224no—
800C2×C22⋊C4—228no—
801C2×C22⋊C4—224no—
802C2×C22⋊C4—224no—
803C2×C22⋊C4—224no—
804C2×C22⋊C4—444no—
805C2×C22⋊C4C22×D1111yescharacteristic
806C2×C22⋊C4C22×D1111yescharacteristic
807C2×C22⋊C4C22×D1111yescharacteristic
808C2×C22⋊C4C22×D1111yescharacteristic
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—224no—
815C2×C42C22×D1111yescharacteristic
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
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#95C22×D1112yes—
832#95C22×D1112yes—
833#95C22×D1112yes—
834#95C22×D1112yes—
835#95C22×D1112yes—
836C2×C11—24no—
837C2×C11—42no—
838C2×C11C22×C22⋊Q811yescharacteristic
839C2×C11C2×#52511yescharacteristic
840C2×C11C2×#53411yescharacteristic
841C2×C11C2×#55312yes—
842C2×C11C2×#55412yes—
843D11—24no—
844D11—42no—
845D11#257918yesdirect product factor
846C24—111no—
847C24—114no—
848C24—114no—
849C24—114no—
850C24—111no—
851C24—114no—
852C24—111no—
853C24—224no—
854C24—224no—
855C24—222no—
856C24—224no—
857C24—224no—
858C24—222no—
859C24C23×D1111yescharacteristic
860C24C23×D1111yescharacteristic
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—114no—
864C2×D4—114no—
865C2×D4—114no—
866C2×D4—222no—
867C2×D4—222no—
868C2×D4—2232no—
869C2×D4—222no—
870C2×D4—222no—
871C2×D4—222no—
872C2×D4—222no—
873C2×D4Q8×D1114yes—
874C22×C4—22no—
875C22×C4—24no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—111no—
882C22×C4—111no—
883C22×C4—112no—
884C22×C4—111no—
885C22×C4—114no—
886C22×C4—114no—
887C22×C4—114no—
888C22×C4—114no—
889C22×C4—118no—
890C22×C4—114no—
891C22×C4—114no—
892C22×C4—112no—
893C22×C4—112no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—112no—
897C22×C4—224no—
898C22×C4—222no—
899C22×C4—222no—
900C22×C4—224no—
901C22×C4—224no—
902C22×C4—224no—
903C22×C4—224no—
904C22×C4—224no—
905C22×C4—222no—
906C22×C4—2232no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—224no—
910C22×C4—224no—
911C22×C4—224no—
912C22×C4—224no—
913C22×C4—224no—
914C22×C4—224no—
915C22×C4—224no—
916C22×C4—224no—
917C22×C4—224no—
918C22×C4—224no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—224no—
925C22×C4—222no—
926C22×C4—222no—
927C22×C4—442no—
928C22×C4—442no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—4416no—
934C22×C4—4416no—
935C22×C4—4416no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—442no—
939C22×C4D4×D1114yes—
940C22×C4C23×D1112yes—
941C22×C4C23×D1112yes—
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1112yes—
945C22×C4C23×D1111yescharacteristic
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1112yes—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—22no—
952C4⋊C4—24no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—224no—
956C4⋊C4—224no—
957C4⋊C4—224no—
958C4⋊C4—224no—
959C4⋊C4—222no—
960C4⋊C4—222no—
961C4⋊C4—224no—
962C4⋊C4—224no—
963C4⋊C4—224no—
964C4⋊C4—224no—
965C4⋊C4—222no—
966C4⋊C4—224no—
967C4⋊C4—442no—
968C4⋊C4—442no—
969C4⋊C4—442no—
970C4⋊C4—442no—
971C4⋊C4—442no—
972C4⋊C4—442no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—24no—
978C22⋊C4—42no—
979C22⋊C4—222no—
980C22⋊C4—224no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—222no—
986C22⋊C4—224no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—222no—
990C22⋊C4—222no—
991C22⋊C4—224no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C42—22no—
996C42—222no—
997C42—222no—
998C42—222no—
999C11C2×#257911yescharacteristic, complemented, Sylow
1000C23—22no—
1001C23—22no—
1002C23—21no—
1003C23—22no—
1004C23—21no—
1005C23—22no—
1006C23—112no—
1007C23—112no—
1008C23—114no—
1009C23—112no—
1010C23—114no—
1011C23—1116no—
1012C23—112no—
1013C23—112no—
1014C23—112no—
1015C23—112no—
1016C23—228no—
1017C23—228no—
1018C23—2216no—
1019C23—2216no—
1020C23—228no—
1021C23—2216no—
1022C23—222no—
1023C23—222no—
1024C23—221no—
1025C23—222no—
1026C23—221no—
1027C23—222no—
1028C23—444no—
1029C23—448no—
1030C23—444no—
1031C23C2×D4×D1112yes—
1032C23C2×Q8×D1112yes—
1033C23C2×Q8×D1112yes—
1034C23#41×D1112yes—
1035C23C24×D1111yescharacteristic
1036D4—28no—
1037D4—228no—
1038D4—228no—
1039D4—228no—
1040C2×C4—28no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—44no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—112no—
1064C2×C4—112no—
1065C2×C4—112no—
1066C2×C4—114no—
1067C2×C4—2216no—
1068C2×C4—228no—
1069C2×C4—228no—
1070C2×C4—228no—
1071C2×C4—2216no—
1072C2×C4—228no—
1073C2×C4—221no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—221no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—221no—
1080C2×C4—221no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—444no—
1093C2×C4—444no—
1094C2×C4—444no—
1095C2×C4—444no—
1096C2×C4—444no—
1097C2×C4—448no—
1098C2×C4—448no—
1099C2×C4—448no—
1100C2×C4—444no—
1101C2×C4—448no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—444no—
1105C2×C4C2×D4×D1112yes—
1106C2×C4C2×D4×D1112yes—
1107C2×C4C2×Q8×D1112yes—
1108C2×C4#41×D1114yes—
1109C22—24no—
1110C22—24no—
1111C22—22no—
1112C22—22no—
1113C22—24no—
1114C22—22no—
1115C22—42no—
1116C22—41no—
1117C22—41no—
1118C22—118no—
1119C22—118no—
1120C22—114no—
1121C22—114no—
1122C22—114no—
1123C22—114no—
1124C22—2232no—
1125C22—224no—
1126C22—224no—
1127C22—222no—
1128C22—222no—
1129C22—224no—
1130C22—222no—
1131C22—4416no—
1132C22—442no—
1133C22—441no—
1134C22—441no—
1135C22D11×C22⋊Q814yes—
1136C22C22×D4×D1111yescharacteristic
1137C22C22×Q8×D1111yescharacteristic
1138C22C2×#41×D1111yescharacteristic
1139C22C2×#41×D1112yes—
1140C22D11×H(5,𝔽2)12yes—
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—41no—
1148C4—42no—
1149C4—41no—
1150C4—222no—
1151C4—222no—
1152C4—222no—
1153C4—224no—
1154C4—442no—
1155C4—442no—
1156C4—441no—
1157C4—442no—
1158C4—441no—
1159C2—24no—
1160C2—42no—
1161C2—118no—
1162C2—224no—
1163C2—442no—
1164C2C2×D11×C22⋊Q811yescharacteristic
1165C2D11×#52511yescharacteristic
1166C2D11×#53411yescharacteristic
1167C2D11×#55312yes—
1168C2D11×#55412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2579C2
prime radicalC22×D4×D11C22
hypercenter#2579D11
hypocenterC11C2×#2579
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2579

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
3. #13073968C2semidirect
4. #13073967C2semidirect
5. #13073966C2semidirect
6. #13073965C2semidirect
7. #13073964C2semidirect
8. #13073963C2semidirect
9. #13073962C2semidirect
10. #13073961C2semidirect
11. #13073960C2semidirect
12. #13073959C2semidirect
13. #13073958C2semidirect
14. D11×#398C2semidirect
15. D11×#396C2semidirect
16. D11×#387C2semidirect
19. D11×#385C2semidirect
20. D11×#385C2semidirect
21. D11×#385C2semidirect
22. D11×#380C2semidirect
23. C11×#2579C2semidirect
30. C22×C11×C4⋊C4C22semidirect
34. C22×C4⋊Dic11C22semidirect
35. C22×Dic11⋊C4C22semidirect
36. C22×Dic11⋊C4C22semidirect
46. C2×C4⋊C4×D11C22semidirect
47. C2×C4⋊C4×D11C22semidirect
58. C11×#398C22semidirect
59. C11×#396C22semidirect
60. C11×#387C22semidirect
63. C11×#385C22semidirect
64. C11×#385C22semidirect
65. C11×#385C22semidirect
66. C11×#380C22semidirect
71. #10622825C22semidirect
72. #10622823C22semidirect
73. #10622823C22semidirect
74. #10622823C22semidirect
75. #10622607C22semidirect
76. #10622607C22semidirect
77. #10622607C22semidirect
78. #10622602C22semidirect
79. #10622602C22semidirect
80. #10622602C22semidirect
81. #10622602C22semidirect
82. #10622600C22semidirect
83. #10622597C22semidirect
84. #10622597C22semidirect
85. #10622596C22semidirect
86. #10622594C22semidirect
87. #10622593C22semidirect
88. #10622591C22semidirect
93. #10622563C22semidirect
94. #10622563C22semidirect
95. #10622563C22semidirect
96. #10622561C22semidirect
97. #10622561C22semidirect
98. #10622561C22semidirect
99. #10622559C22semidirect
100. #10622559C22semidirect
101. #10622559C22semidirect
102. #10622555C22semidirect
103. #10622555C22semidirect
104. #10622546C22semidirect
105. #10622289C22semidirect
106. #10622281C22semidirect
107. #10622281C22semidirect
108. #10622281C22semidirect
109. #10622281C22semidirect
110. #10622280C22semidirect
118. #10622274C22semidirect
119. #10622270C22semidirect
120. #10622270C22semidirect
121. #10622268C22semidirect
122. #10622267C22semidirect
123. #10622266C22semidirect
124. #10622265C22semidirect
429. #2579D11direct (N × H)
574. C22×C4⋊C4C2×D11semidirect
589. #398C2×D11semidirect
597. #396C2×D11semidirect
605. #387C2×D11semidirect
635. #385C2×D11semidirect
636. #385C2×D11semidirect
637. #385C2×D11semidirect
643. #380C2×D11semidirect
845. D11#2579direct (N × H)
999. C11C2×#2579semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
C22×C4⋊C4×D112
#130739682
#130739672
#130739662
#130739652
#130739642
#130739632
#130739622
#130739612
#130739602
#130739592
#130739582
D11×#3982
D11×#3962
D11×#3872
D11×#3862
D11×#3852
D11×#3802
C11×#25792
C2×#257911