Finite Group Databasebeta

← #14914121

Subgroups — #14914121

Order 2816.

3642 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2C2×#10623076C212yesmaximal, complemented
3#13071665C212yesmaximal, complemented
4#13071662C212yesmaximal, complemented
5#13071635C212yesmaximal, complemented
6#13071629C212yesmaximal, complemented
7#13071482C212yesmaximal, complemented
8#13071463C212yesmaximal, complemented
9#13071460C212yesmaximal, complemented
10#13071434C212yesmaximal, complemented
11#13071321C211yesmaximal, characteristic, complemented
12#13071319C211yesmaximal, characteristic, complemented
13#13071316C211yesmaximal, characteristic, complemented
14#13071190C212yesmaximal, complemented
15#13071126C212yesmaximal, complemented
16C4×#66992C212yesmaximal, complemented
17D11×#380C211yesmaximal, characteristic, complemented
18C2×#10622279C211yesmaximal, characteristic, complemented
19C11×#2325C211yesmaximal, characteristic, complemented
20C22×D4×D11C2212yes—
21C22×D4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11C2212yescomplemented
25C2×#66992C2212yes—
26C2×#66991C2211yescharacteristic
27C2×D4×Dic11C2212yescomplemented
28C2×#66983C2211yescharacteristic
29C2×C4×C22⋊D11C2212yescomplemented
30C2×C4×C22⋊D11C2212yescomplemented
31C2×C4×C22⋊D11C2212yescomplemented
32C22×(C2×D11)⋊C4C2212yes—
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic, complemented
36C22×C4×Dic11C2211yescharacteristic, complemented
37D11×#121C4116yescomplemented
38#10623076—216no—
39C2×#66948C2211yescharacteristic
40C2×#66946C2212yescomplemented
41C2×#66945C2212yes—
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic, complemented
44C2×C4⋊C4×D11C2211yescharacteristic, complemented
45C2×#66937C2212yes—
46C2×(C22⋊D11)⋊C4C2212yescomplemented
47C2×(C22⋊D11)⋊C4C2212yescomplemented
48C2×(C22⋊D11)⋊C4C2212yescomplemented
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2212yes—
52C2×C4×D44C2212yescomplemented
53C2×#66925C2212yes—
54C11×#388C2212yescomplemented
55C11×#387C2212yescomplemented
56C11×#386C2212yescomplemented
57C11×#386C2212yescomplemented
58C11×#385C2212yescomplemented
59C11×#380C2211yescharacteristic, complemented
60C2×C11×#95C2211yescharacteristic, complemented
61#10622833C2212yescomplemented
62#10622833C2212yescomplemented
63#10622826C2212yescomplemented
64#10622825C2211yescharacteristic, complemented
65C4×C22⋊Dic11C2212yescomplemented
66C2×C11⋊#95C2211yescharacteristic, complemented
67#10622603C2212yescomplemented
68#10622603C2212yescomplemented
69#10622602C2212yescomplemented
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622594C2212yescomplemented
73#10622585C2212yescomplemented
74#10622571C2212yescomplemented
75#10622570C2212yescomplemented
76#10622570C2212yescomplemented
77#10622569C2212yescomplemented
78#10622569C2212yescomplemented
79#10622568C2212yes—
80#10622568C2212yes—
81#10622564C2212yescomplemented
82#10622563C2212yescomplemented
83#10622558C2212yescomplemented
84#10622557C2212yescomplemented
85#10622555C2212yescomplemented
86C22⋊C4×Dic11C2212yescomplemented
87C4×(C2×D11)⋊C4C2212yescomplemented
88C4×Dic11⋊C4C2212yescomplemented
89#10622283C2212yescomplemented
90#10622283C2212yescomplemented
91#10622281C2212yescomplemented
92#10622280C2212yes—
93#10622279C2212yes—
94#10622279C2212yes—
95#10622279C2212yescomplemented
96#10622279C2212yescomplemented
97#10622279C2212yescomplemented
98#10622278C2212yescomplemented
99#10622278C2212yescomplemented
100#10622278C2212yescomplemented
101#10622278C2212yescomplemented
102#10622277C2212yes—
103#10622277C2212yes—
104D11×#95C2212yescomplemented
105#10622267C2212yescomplemented
106#10622266C2212yescomplemented
107#10622262C2212yescomplemented
108#10622260C2212yescomplemented
109C24×D11C2312yes—
110C24×D11C2311yescharacteristic
111C22×D4×C11C2312yes—
112C22×D4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2312yes—
115C23×C4×C11C2311yescharacteristic
116C23×C4×C11C2311yescharacteristic
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C22×C22⋊D11C2312yes—
120C23×Dic11C2311yescharacteristic
121C23×Dic11C2312yes—
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2311yescharacteristic
124C2×D4×D11—28no—
125C2×D4×D11—28no—
126C2×D4×D11—42no—
127C2×D4×D11—42no—
128C2×D4×D11C2×C4116yescomplemented
129C2×D4×D11C2×C418yescomplemented
130C22×D44C2312yes—
131C22×D44C2311yescharacteristic
132C22×C4×D11—42no—
133C22×C4×D11—42no—
134C22×C4×D11C2×C418yescomplemented
135C22×C4×D11C2312yes—
136C22×C4×D11C2311yescharacteristic
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2312yes—
139C22×C4×D11C2312yes—
140C22×C4×D11C2312yes—
141C22×C4×D11C2312yes—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C11×#121C2×C418yescomplemented
145C4×D4×C11—28no—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C22⋊C4C2312yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C11×C22⋊C4C2312yes—
153C2×C11×C22⋊C4C2312yes—
154C2×C11×C22⋊C4C2312yes—
155C2×C42×C11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161#66992C2×C4116yescomplemented
162#66991C2×C418yescomplemented
163D4×Dic11—28no—
164#66983C2×C418yescomplemented
165C4×C22⋊D11—28no—
166C4×C22⋊D11—28no—
167C4×C22⋊D11—44no—
168C2×(C2×D11)⋊C4—24no—
169C2×(C2×D11)⋊C4—28no—
170C2×(C2×D11)⋊C4D418yescomplemented
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×C4⋊Dic11C2312yes—
186C2×C4⋊Dic11C2311yescharacteristic
187C2×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2311yescharacteristic
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×C4×Dic11—42no—
195C2×C4×Dic11—42no—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2312yes—
203#66948C2×C418yescomplemented
204#66946—28no—
205#66945—28no—
206C4⋊C4×D11—42no—
207C4⋊C4×D11—42no—
208C4⋊C4×D11C2×C418yescomplemented
209#66937C2×C4116yescomplemented
210(C22⋊D11)⋊C4—28no—
211(C22⋊D11)⋊C4—28no—
212(C22⋊D11)⋊C4—44no—
213C22⋊C4×D11—28no—
214C22⋊C4×D11—28no—
215C22⋊C4×D11C2×C4116yescomplemented
216C4×D44—28no—
217#66925—28no—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2312yes—
221C11×#95C2312yes—
222C11×#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234#34205—111nomaximal, Sylow
235C24×C11C2412yes—
236C24×C11C2411yescharacteristic
237C23×D11—24no—
238C23×D11—24no—
239C23×D11—41no—
240C23×D11—41no—
241C23×D11—41no—
242C23×D11—41no—
243C23×D11—42no—
244C23×D11—42no—
245C23×D11—42no—
246C23×D11—42no—
247C23×D11C22×C418yes—
248C23×D11C22×C414yes—
249C23×D11C2×D414yes—
250C23×D11#4114yes—
251C23×D11C2412yes—
252C23×D11C2411yescharacteristic
253C23×D11C2411yescharacteristic
254C2×D4×C11—24no—
255C2×D4×C11—24no—
256C2×D4×C11—41no—
257C2×D4×C11—41no—
258C2×D4×C11C22×C418yes—
259C2×D4×C11C22×C414yes—
260C22×C4×C11—22no—
261C22×C4×C11—24no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11—41no—
265C22×C4×C11—41no—
266C22×C4×C11—41no—
267C22×C4×C11—41no—
268C22×C4×C11—42no—
269C22×C4×C11—42no—
270C22×C4×C11C22×C414yes—
271C22×C4×C11C2×D414yescomplemented
272C22×C4×C11C2412yes—
273C22×C4×C11C2412yes—
274C22×C4×C11C2412yes—
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2412yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2412yes—
279C2×C22⋊D11—24no—
280C2×C22⋊D11—24no—
281C2×C22⋊D11—24no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—24no—
284C2×C22⋊D11—24no—
285C2×C22⋊D11C22×C418yes—
286C2×C22⋊D11C22×C418yes—
287C2×C22⋊D11C22×C418yes—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—24no—
291C22×Dic11—22no—
292C22×Dic11—41no—
293C22×Dic11—41no—
294C22×Dic11—41no—
295C22×Dic11—41no—
296C22×Dic11—42no—
297C22×Dic11—42no—
298C22×Dic11C22×C414yes—
299C22×Dic11C2×D414yescomplemented
300C22×Dic11C2412yes—
301C22×Dic11C2412yes—
302C22×Dic11C2412yes—
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2412yes—
305C22×Dic11C2412yes—
306C22×Dic11C2411yescharacteristic
307D4×D11—264no—
308D4×D11—416no—
309C2×D44—24no—
310C2×D44—24no—
311C2×D44—41no—
312C2×D44—41no—
313C2×D44C22×C418yes—
314C2×D44C22×C414yes—
315C2×C4×D11—22no—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—24no—
322C2×C4×D11—24no—
323C2×C4×D11—24no—
324C2×C4×D11—24no—
325C2×C4×D11—41no—
326C2×C4×D11—41no—
327C2×C4×D11—41no—
328C2×C4×D11—41no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—416no—
338C2×C4×D11C22×C418yes—
339C2×C4×D11C22×C414yes—
340C2×C4×D11C22×C414yes—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C11×C4⋊C4—24no—
344C11×C4⋊C4—41no—
345C11×C4⋊C4—41no—
346C11×C4⋊C4C22×C414yes—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—24no—
349C11×C22⋊C4—42no—
350C11×C22⋊C4—42no—
351C11×C22⋊C4C22×C418yes—
352C42×C11—24no—
353C22⋊Dic11—24no—
354C22⋊Dic11—24no—
355C22⋊Dic11—42no—
356C22⋊Dic11—42no—
357C22⋊Dic11C22×C418yes—
358(C2×D11)⋊C4—24no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—24no—
361(C2×D11)⋊C4—24no—
362(C2×D11)⋊C4—24no—
363(C2×D11)⋊C4—24no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4—42no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4C22×C418yes—
369(C2×D11)⋊C4C22×C418yes—
370(C2×D11)⋊C4C2×D418yes—
371(C2×D11)⋊C4C2×D418yescomplemented
372C4⋊Dic11—24no—
373C4⋊Dic11—41no—
374C4⋊Dic11—41no—
375C4⋊Dic11C22×C414yes—
376Dic11⋊C4—24no—
377Dic11⋊C4—24no—
378Dic11⋊C4—24no—
379Dic11⋊C4—24no—
380Dic11⋊C4C22×C418yes—
381C4×Dic11—24no—
382C4×Dic11—24no—
383C4×Dic11—24no—
384C4×Dic11—24no—
385C4×Dic11—24no—
386C4×Dic11—42no—
387C4×Dic11—42no—
388C22×#121—111no—
389C2×#518—112no—
390#2364—112no—
391#2364—112no—
392#2361—112no—
393#2361—112no—
394#2344—112no—
395#2342—112no—
396#2342—112no—
397D4×C22⋊C4—112no—
398#2325—111no—
399#2325—111no—
400#2325—111no—
401#2325D1111yescharacteristic, complemented
402#2308—112no—
403C4×#121—112no—
404C4×#121—112no—
405C2×#380—111no—
406C2×C4×C22⋊C4—111no—
407C23×C11—21no—
408C23×C11—21no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11C23×C414yes—
418C23×C11C23×C412yes—
419C23×C11C22×D412yes—
420C23×C11C2×#4112yes—
421C23×C11C2511yescharacteristic
422C22×D11—21no—
423C22×D11—21no—
424C22×D11—21no—
425C22×D11—21no—
426C22×D11—21no—
427C22×D11—21no—
428C22×D11—21no—
429C22×D11—21no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—216no—
437C22×D11—44no—
438C22×D11—44no—
439C22×D11—44no—
440C22×D11—44no—
441C22×D11—44no—
442C22×D11—44no—
443C22×D11—48no—
444C22×D11—48no—
445C22×D11—84no—
446C22×D11—84no—
447C22×D11—84no—
448C22×D11—84no—
449C22×D11C4×D4116yescomplemented
450C22×D11C23×C414yes—
451C22×D11C23×C412yes—
452C22×D11C23×C412yes—
453C22×D11C22×D412yes—
454C22×D11C22×D412yes—
455C22×D11C2×#4112yes—
456C22×D11C2×#4112yes—
457D4×C11—216no—
458D4×C11—44no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—44no—
477C2×C4×C11—44no—
478C2×C4×C11—44no—
479C2×C4×C11—84no—
480C2×C4×C11C23×C414yes—
481C2×C4×C11C23×C412yes—
482C2×C4×C11C23×C412yes—
483C2×C4×C11C22×D414yes—
484C22⋊D11—216no—
485C22⋊D11—216no—
486C22⋊D11—216no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—21no—
491C2×Dic11—21no—
492C2×Dic11—22no—
493C2×Dic11—28no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—44no—
504C2×Dic11—44no—
505C2×Dic11—84no—
506C2×Dic11C23×C414yes—
507C2×Dic11C23×C412yes—
508C2×Dic11C23×C412yes—
509C2×Dic11C22×D414yes—
510C2×Dic11H(5,𝔽2)12yes—
511C2×Dic11H(5,𝔽2)12yes—
512D44—216no—
513D44—44no—
514C4×D11—216no—
515C4×D11—28no—
516C4×D11—28no—
517C4×D11—44no—
518C4×D11—44no—
519C4×D11—84no—
520C4×D11—84no—
521C4×D11—84no—
522C4×D11—84no—
523C23×D4—112no—
524C23×D4—111no—
525C24×C4—111no—
526C2×#121—111no—
527C2×#121—112no—
528C2×#121—111no—
529C2×#121—1116no—
530C2×#121—111no—
531C2×#121—112no—
532C2×#121C2×D1111yescharacteristic
533#518—2216no—
534C2×C4×D4—112no—
535C2×C4×D4—112no—
536C2×C4×D4—112no—
537C2×C4×D4—112no—
538C2×C4×D4—112no—
539C2×C4×D4—112no—
540C2×C4×D4—112no—
541C2×C4×D4—112no—
542C2×C4×D4—112no—
543C2×C4×D4C2×D1112yescomplemented
544C2×#117—112no—
545C2×#117—112no—
546C22×C4⋊C4—111no—
547C22×C4⋊C4—111no—
548C22×C4⋊C4—111no—
549C22×C22⋊C4—111no—
550C22×C22⋊C4—112no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—112no—
553C22×C22⋊C4—112no—
554C22×C22⋊C4—112no—
555C22×C42—111no—
556C22×C42—111no—
557#390—112no—
558#390—112no—
559#389—112no—
560#389—112no—
561#388—112no—
562#388—112no—
563#388—112no—
564#388—112no—
565#388—112no—
566#388—112no—
567#388—112no—
568#388C2×D1112yescomplemented
569#387—112no—
570#387—112no—
571#387—112no—
572#387C2×D1112yescomplemented
573#386—112no—
574#386—112no—
575#386—112no—
576#386—112no—
577#386—112no—
578#386—112no—
579#386—112no—
580#386—112no—
581#386—112no—
582#386—112no—
583#386C2×D1112yescomplemented
584#386C2×D1112yescomplemented
585#385—112no—
586#385—112no—
587#385—112no—
588#385C2×D1112yescomplemented
589#381—112no—
590#381—112no—
591#380—111no—
592#380—111no—
593#380—111no—
594#380—112no—
595#380—112no—
596#380C2×D1111yescharacteristic, complemented
597#379—112no—
598#379—112no—
599C4×C4⋊C4—112no—
600C4×C4⋊C4—112no—
601C4×C22⋊C4—112no—
602C4×C22⋊C4—112no—
603C4×C22⋊C4—112no—
604C4×C22⋊C4—112no—
605C4×C22⋊C4—112no—
606C4×C22⋊C4—112no—
607C4×C22⋊C4—112no—
608C4×C22⋊C4—112no—
609C2×#95—111no—
610C2×#95—112no—
611C2×#95C2×D1111yescharacteristic, complemented
612C22×C11—22no—
613C22×C11—22no—
614C22×C11—22no—
615C22×C11—22no—
616C22×C11—22no—
617C22×C11—22no—
618C22×C11—24no—
619C22×C11—24no—
620C22×C11—24no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11C2×C4×D414yes—
626C22×C11C24×C411yescharacteristic
627C22×C11C23×D411yescharacteristic
628C22×C11C22×#4111yescharacteristic
629C22×C11C2×H(5,𝔽2)11yescharacteristic
630C22×C11C2×H(5,𝔽2)11yescharacteristic
631C22×C11#58511yescharacteristic
632C22×C11#58511yescharacteristic
633C2×D11—22no—
634C2×D11—22no—
635C2×D11—22no—
636C2×D11—22no—
637C2×D11—22no—
638C2×D11—22no—
639C2×D11—22no—
640C2×D11—22no—
641C2×D11—22no—
642C2×D11—22no—
643C2×D11—22no—
644C2×D11—22no—
645C2×D11—24no—
646C2×D11—24no—
647C2×D11—24no—
648C2×D11—416no—
649C2×D11—42no—
650C2×D11—42no—
651C2×D11—42no—
652C2×D11—42no—
653C2×D11—816no—
654C2×D11C2×C4×D414yes—
655C2×D11C2×C4×D414yes—
656C4×C11—24no—
657C4×C11—22no—
658C4×C11—22no—
659C4×C11—24no—
660C4×C11—42no—
661C4×C11—42no—
662C4×C11—42no—
663Dic11—24no—
664Dic11—22no—
665Dic11—24no—
666Dic11—42no—
667Dic11—42no—
668Dic11—42no—
669Dic11#51814yescomplemented
670C25—111no—
671C25—112no—
672C22×D4—112no—
673C22×D4—112no—
674C22×D4—112no—
675C22×D4—1116no—
676C22×D4—118no—
677C22×D4—112no—
678C22×D4—111no—
679C22×D4—228no—
680C22×D4—228no—
681C22×D4—442no—
682C22×D4—442no—
683C22×D4C22×D1112yes—
684C22×D4C22×D1111yescharacteristic
685C23×C4—111no—
686C23×C4—111no—
687C23×C4—112no—
688C23×C4—111no—
689C23×C4—111no—
690C23×C4—118no—
691C23×C4—111no—
692C23×C4—111no—
693C23×C4—112no—
694C23×C4—111no—
695C23×C4—112no—
696C23×C4—112no—
697C23×C4—112no—
698C23×C4—112no—
699C23×C4—442no—
700C23×C4—442no—
701C23×C4C22×D1112yes—
702C23×C4C22×D1111yescharacteristic
703C23×C4C22×D1111yescharacteristic
704C23×C4C22×D1111yescharacteristic
705#121—118no—
706#121—1116no—
707#121—118no—
708#121—118no—
709#121—1116no—
710#121C4×D1118yescomplemented
711C4×D4—28no—
712C4×D4—228no—
713C4×D4—228no—
714C4×D4—228no—
715C4×D4—228no—
716C4×D4—228no—
717C4×D4—228no—
718C4×D4—228no—
719C4×D4—444no—
720C4×D4—444no—
721#117—228no—
722#117—228no—
723C2×C4⋊C4—112no—
724C2×C4⋊C4—111no—
725C2×C4⋊C4—118no—
726C2×C4⋊C4—112no—
727C2×C4⋊C4—112no—
728C2×C4⋊C4—112no—
729C2×C4⋊C4—112no—
730C2×C4⋊C4—112no—
731C2×C4⋊C4—111no—
732C2×C4⋊C4—111no—
733C2×C4⋊C4—442no—
734C2×C4⋊C4—442no—
735C2×C4⋊C4C22×D1112yes—
736C2×C4⋊C4C22×D1111yescharacteristic
737C2×C4⋊C4C22×D1111yescharacteristic
738C2×C4⋊C4C22×D1111yescharacteristic
739C2×C22⋊C4—112no—
740C2×C22⋊C4—118no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—112no—
744C2×C22⋊C4—112no—
745C2×C22⋊C4—1116no—
746C2×C22⋊C4—112no—
747C2×C22⋊C4—112no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—228no—
761C2×C22⋊C4—228no—
762C2×C22⋊C4—228no—
763C2×C22⋊C4—224no—
764C2×C22⋊C4C22×D1112yes—
765C2×C22⋊C4C22×D1112yes—
766C2×C22⋊C4C22×D1112yes—
767C2×C22⋊C4C22×D1112yes—
768C2×C22⋊C4C22×D1112yes—
769C2×C42—112no—
770C2×C42—112no—
771C2×C42—112no—
772C2×C42—112no—
773C2×C42—112no—
774C2×C42—112no—
775C2×C42—112no—
776C2×C42—442no—
777C2×C42—442no—
778C2×C42C22×D1112yes—
779#95—112no—
780#95—112no—
781#95—112no—
782#95—112no—
783#95—112no—
784#95—112no—
785#95—112no—
786#95—112no—
787#95—112no—
788#95—112no—
789#95—112no—
790#95C22×D1112yes—
791#95C22×D1112yes—
792#95C22×D1112yes—
793#95C22×D1112yes—
794#95C22×D1112yes—
795C2×C11—24no—
796C2×C11—44no—
797C2×C11C22×C4×D411yescharacteristic
798C2×C11C2×#51811yescharacteristic
799C2×C11#342811yescharacteristic
800C2×C11#349611yescharacteristic
801C2×C11#349611yescharacteristic
802C2×C11#350511yescharacteristic
803C2×C11#350511yescharacteristic
804D11—24no—
805D11—24no—
806D11—44no—
807C24—111no—
808C24—111no—
809C24—114no—
810C24—114no—
811C24—114no—
812C24—112no—
813C24—118no—
814C24—224no—
815C24—224no—
816C24—441no—
817C24—441no—
818C24—441no—
819C24—441no—
820C24—442no—
821C24—442no—
822C24—442no—
823C24—442no—
824C24C23×D1112yes—
825C24C23×D1111yescharacteristic
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—118no—
831C2×D4—118no—
832C2×D4—118no—
833C2×D4—118no—
834C2×D4—114no—
835C2×D4—224no—
836C2×D4—224no—
837C2×D4—224no—
838C2×D4—224no—
839C2×D4—2264no—
840C2×D4—224no—
841C2×D4—224no—
842C2×D4—224no—
843C2×D4—224no—
844C2×D4—441no—
845C2×D4—441no—
846C2×D4—4416no—
847C2×D4C2×C4×D1118yes—
848C2×D4C2×C4×D1114yes—
849C22×C4—22no—
850C22×C4—24no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—41no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—111no—
860C22×C4—114no—
861C22×C4—111no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—114no—
865C22×C4—118no—
866C22×C4—114no—
867C22×C4—114no—
868C22×C4—114no—
869C22×C4—114no—
870C22×C4—112no—
871C22×C4—112no—
872C22×C4—112no—
873C22×C4—222no—
874C22×C4—222no—
875C22×C4—222no—
876C22×C4—222no—
877C22×C4—224no—
878C22×C4—224no—
879C22×C4—224no—
880C22×C4—224no—
881C22×C4—224no—
882C22×C4—222no—
883C22×C4—222no—
884C22×C4—224no—
885C22×C4—222no—
886C22×C4—224no—
887C22×C4—441no—
888C22×C4—441no—
889C22×C4—441no—
890C22×C4—441no—
891C22×C4—442no—
892C22×C4—442no—
893C22×C4—442no—
894C22×C4—442no—
895C22×C4—442no—
896C22×C4—442no—
897C22×C4—442no—
898C22×C4—442no—
899C22×C4—4416no—
900C22×C4—441no—
901C22×C4—441no—
902C22×C4—441no—
903C22×C4—441no—
904C22×C4—442no—
905C22×C4—442no—
906C22×C4C2×C4×D1114yes—
907C22×C4D4×D1114yescomplemented
908C22×C4C23×D1112yes—
909C22×C4C23×D1112yes—
910C22×C4C23×D1112yes—
911C22×C4C23×D1111yescharacteristic
912C22×C4C23×D1112yes—
913C22×C4C23×D1111yescharacteristic
914C22×C4C23×D1112yes—
915C4⋊C4—24no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—118no—
919C4⋊C4—114no—
920C4⋊C4—224no—
921C4⋊C4—224no—
922C4⋊C4—224no—
923C4⋊C4—224no—
924C4⋊C4—224no—
925C4⋊C4—441no—
926C4⋊C4—441no—
927C4⋊C4C2×C4×D1114yes—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—118no—
933C22⋊C4—118no—
934C22⋊C4—118no—
935C22⋊C4—118no—
936C22⋊C4—118no—
937C22⋊C4—224no—
938C22⋊C4—224no—
939C22⋊C4—224no—
940C22⋊C4—224no—
941C22⋊C4—224no—
942C22⋊C4—224no—
943C22⋊C4—224no—
944C22⋊C4—224no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4—442no—
948C22⋊C4—442no—
949C22⋊C4—442no—
950C22⋊C4—442no—
951C22⋊C4C2×C4×D1118yes—
952C42—24no—
953C42—224no—
954C42—224no—
955C42—224no—
956C42—224no—
957C42—224no—
958C42—442no—
959C42—442no—
960C11#3420511yescharacteristic, complemented, Sylow
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—112no—
972C23—112no—
973C23—112no—
974C23—112no—
975C23—112no—
976C23—112no—
977C23—1116no—
978C23—114no—
979C23—2216no—
980C23—221no—
981C23—221no—
982C23—221no—
983C23—221no—
984C23—221no—
985C23—221no—
986C23—221no—
987C23—221no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—444no—
995C23—444no—
996C23—444no—
997C23—444no—
998C23—444no—
999C23—444no—
1000C23—448no—
1001C23—448no—
1002C23—884no—
1003C23—884no—
1004C23—884no—
1005C23—884no—
1006C23C22×C4×D1114yes—
1007C23C22×C4×D1112yes—
1008C23C2×D4×D1112yes—
1009C23#41×D1112yes—
1010C23C24×D1111yescharacteristic
1011D4—216no—
1012D4—44no—
1013D4—2216no—
1014D4—2216no—
1015D4—2216no—
1016D4—2216no—
1017D4—444no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—44no—
1038C2×C4—84no—
1039C2×C4—112no—
1040C2×C4—112no—
1041C2×C4—112no—
1042C2×C4—112no—
1043C2×C4—114no—
1044C2×C4—114no—
1045C2×C4—228no—
1046C2×C4—228no—
1047C2×C4—2216no—
1048C2×C4—228no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—221no—
1053C2×C4—221no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—444no—
1065C2×C4—444no—
1066C2×C4—444no—
1067C2×C4—444no—
1068C2×C4—884no—
1069C2×C4—884no—
1070C2×C4—884no—
1071C2×C4—884no—
1072C2×C4—884no—
1073C2×C4C22×C4×D1112yes—
1074C2×C4C22×C4×D1114yes—
1075C2×C4C22×C4×D1112yes—
1076C2×C4C2×D4×D1114yes—
1077C22—22no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—24no—
1084C22—24no—
1085C22—24no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—114no—
1091C22—114no—
1092C22—222no—
1093C22—222no—
1094C22—222no—
1095C22—222no—
1096C22—222no—
1097C22—222no—
1098C22—222no—
1099C22—222no—
1100C22—222no—
1101C22—222no—
1102C22—222no—
1103C22—222no—
1104C22—224no—
1105C22—224no—
1106C22—224no—
1107C22—4416no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—8816no—
1113C22C4×D4×D1114yes—
1114C22C23×C4×D1111yescharacteristic
1115C22C22×D4×D1111yescharacteristic
1116C22C2×#41×D1111yescharacteristic
1117C22D11×H(5,𝔽2)11yescharacteristic
1118C22D11×H(5,𝔽2)11yescharacteristic
1119C22#1062345511yescharacteristic
1120C22#1062345711yescharacteristic
1121C4—24no—
1122C4—24no—
1123C4—22no—
1124C4—22no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—114no—
1129C4—224no—
1130C4—224no—
1131C4—222no—
1132C4—442no—
1133C4—442no—
1134C4—442no—
1135C2—24no—
1136C2—44no—
1137C2—224no—
1138C2—224no—
1139C2—444no—
1140C2C2×C4×D4×D1111yescharacteristic
1141C2D11×#51811yescharacteristic
1142C2#1308181611yescharacteristic
1143C2#1308237711yescharacteristic
1144C2#1308237911yescharacteristic
1145C2#1308244811yescharacteristic
1146C2#1308245411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2325C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#121C2
hypercenter#2325D11
hypocenterC11#34205
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2325

Complements

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

NH ≅ G/Ntype
2. C2×#10623076C2semidirect
3. #13071665C2semidirect
4. #13071662C2semidirect
5. #13071635C2semidirect
6. #13071629C2semidirect
7. #13071482C2semidirect
8. #13071463C2semidirect
9. #13071460C2semidirect
10. #13071434C2semidirect
11. #13071321C2semidirect
12. #13071319C2semidirect
13. #13071316C2semidirect
14. #13071190C2semidirect
15. #13071126C2semidirect
16. C4×#66992C2semidirect
17. D11×#380C2semidirect
18. C2×#10622279C2semidirect
19. C11×#2325C2semidirect
24. C2×C4×D4×C11C22semidirect
27. C2×D4×Dic11C22semidirect
29. C2×C4×C22⋊D11C22semidirect
30. C2×C4×C22⋊D11C22semidirect
31. C2×C4×C22⋊D11C22semidirect
35. C22×C4×Dic11C22semidirect
36. C22×C4×Dic11C22semidirect
37. D11×#121C4semidirect
40. C2×#66946C22semidirect
43. C2×C4⋊C4×D11C22semidirect
44. C2×C4⋊C4×D11C22semidirect
46. C2×(C22⋊D11)⋊C4C22semidirect
47. C2×(C22⋊D11)⋊C4C22semidirect
48. C2×(C22⋊D11)⋊C4C22semidirect
52. C2×C4×D44C22semidirect
54. C11×#388C22semidirect
55. C11×#387C22semidirect
56. C11×#386C22semidirect
57. C11×#386C22semidirect
58. C11×#385C22semidirect
59. C11×#380C22semidirect
60. C2×C11×#95C22semidirect
61. #10622833C22semidirect
62. #10622833C22semidirect
63. #10622826C22semidirect
64. #10622825C22semidirect
65. C4×C22⋊Dic11C22semidirect
66. C2×C11⋊#95C22semidirect
67. #10622603C22semidirect
68. #10622603C22semidirect
69. #10622602C22semidirect
72. #10622594C22semidirect
73. #10622585C22semidirect
74. #10622571C22semidirect
75. #10622570C22semidirect
76. #10622570C22semidirect
77. #10622569C22semidirect
78. #10622569C22semidirect
81. #10622564C22semidirect
82. #10622563C22semidirect
83. #10622558C22semidirect
84. #10622557C22semidirect
85. #10622555C22semidirect
86. C22⋊C4×Dic11C22semidirect
87. C4×(C2×D11)⋊C4C22semidirect
88. C4×Dic11⋊C4C22semidirect
89. #10622283C22semidirect
90. #10622283C22semidirect
91. #10622281C22semidirect
95. #10622279C22semidirect
96. #10622279C22semidirect
97. #10622279C22semidirect
98. #10622278C22semidirect
99. #10622278C22semidirect
100. #10622278C22semidirect
101. #10622278C22semidirect
104. D11×#95C22semidirect
105. #10622267C22semidirect
106. #10622266C22semidirect
107. #10622262C22semidirect
108. #10622260C22semidirect
128. C2×D4×D11C2×C4semidirect
129. C2×D4×D11C2×C4semidirect
134. C22×C4×D11C2×C4semidirect
144. C11×#121C2×C4semidirect
161. #66992C2×C4semidirect
162. #66991C2×C4semidirect
164. #66983C2×C4semidirect
170. C2×(C2×D11)⋊C4D4semidirect
203. #66948C2×C4semidirect
208. C4⋊C4×D11C2×C4semidirect
209. #66937C2×C4semidirect
215. C22⋊C4×D11C2×C4semidirect
271. C22×C4×C11C2×D4semidirect
299. C22×Dic11C2×D4semidirect
371. (C2×D11)⋊C4C2×D4semidirect
401. #2325D11semidirect
449. C22×D11C4×D4semidirect
543. C2×C4×D4C2×D11semidirect
568. #388C2×D11semidirect
572. #387C2×D11semidirect
583. #386C2×D11semidirect
584. #386C2×D11semidirect
588. #385C2×D11semidirect
596. #380C2×D11semidirect
611. C2×#95C2×D11semidirect
669. Dic11#518semidirect
710. #121C4×D11semidirect
907. C22×C4D4×D11semidirect
960. C11#34205semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
C2×#106230762
#130716652
#130716622
#130716352
#130716292
#130714822
#130714632
#130714602
#130714342
#130713212
#130713192
#130713162
#130711902
#130711262
C4×#669922
D11×#3802
C2×#106222792
C11×#23252
#3420511