Finite Group Databasebeta

← #14920614

Subgroups — #14920614

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623069C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13074519C212yesmaximal, complemented
4#13074517C212yesmaximal, complemented
5#13074488C212yesmaximal, complemented
6#13074472C212yesmaximal, complemented
7#13074427C211yesmaximal, characteristic, complemented
8#13074425C211yesmaximal, characteristic, complemented
9#13074402C211yesmaximal, characteristic, complemented
10#13074400C211yesmaximal, characteristic, complemented
11#13074356C211yesmaximal, characteristic, complemented
12#13074354C211yesmaximal, characteristic, complemented
13#13074331C211yesmaximal, characteristic, complemented
14#13074330C211yesmaximal, characteristic, complemented
15#13071903C212yesmaximal, complemented
16#13071895C212yesmaximal, complemented
17#13071860C212yesmaximal, complemented
18#13071858C212yesmaximal, complemented
19C4×#66935C211yesmaximal, characteristic, complemented
20C4×#67006C211yesmaximal, characteristic, complemented
21C4×#66990C211yesmaximal, characteristic, complemented
22#13071010C211yesmaximal, characteristic, complemented
23C4×C11×#120C211yesmaximal, characteristic, complemented
24C24×C4×C11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C2×C11×#120C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yescomplemented
30C2×#67006C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66992C2211yescharacteristic
33C2×#66990C2211yescharacteristic
34C2×#66988C2211yescharacteristic
35C2×C4×C22⋊D11—28no—
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×C4×C22⋊D11C2212yes—
38C2×C4×C22⋊D11C2212yes—
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2211yescharacteristic, complemented
42C2×C4×C22⋊D11C2212yescomplemented
43C2×C4×C22⋊D11C2212yescomplemented
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C2×#66979C2211yescharacteristic, complemented
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48#10623069—28no—
49C2×#66951C2211yescharacteristic, complemented
50C2×#66942C2211yescharacteristic, complemented
51C2×#66939C2211yescharacteristic
52C2×#66938C2211yescharacteristic, complemented
53C2×#66935C2211yescharacteristic
54C2×#66932C2211yescharacteristic, complemented
55C2×#66931C2211yescharacteristic
56C2×C4×D44C2212yescomplemented
57C2×#66925C2211yescharacteristic, complemented
58C2×C4×Dic22C2211yescharacteristic, complemented
59C11×#386C2211yescharacteristic
60C11×#386C2212yescomplemented
61C11×#385C2211yescharacteristic
62C11×#385C2212yescomplemented
63C11×#379C2211yescharacteristic
64C4×C11×C22⋊C4C2211yescharacteristic
65C4×C11×C22⋊C4C2212yescomplemented
66#10622860C2211yescharacteristic
67#10622836C2212yes—
68#10622836C2212yes—
69#10622836C2212yescomplemented
70#10622835C2212yescomplemented
71#10622833C2211yescharacteristic
72#10622826C2211yescharacteristic
73#10622826C2212yescomplemented
74#10622823C2211yescharacteristic
75#10622823C2212yescomplemented
76C4×C22⋊Dic11C2211yescharacteristic
77C4×C22⋊Dic11C2212yescomplemented
78#10622607C2212yescomplemented
79#10622605C2212yescomplemented
80#10622605C2212yescomplemented
81#10622602C2212yescomplemented
82#10622597C2212yescomplemented
83#10622574C2212yes—
84#10622574C2212yes—
85#10622573C2212yes—
86#10622573C2212yes—
87#10622573C2212yescomplemented
88#10622572C2212yes—
89#10622572C2212yes—
90#10622572C2212yescomplemented
91#10622572C2212yescomplemented
92#10622571C2211yescharacteristic
93#10622569C2212yescomplemented
94#10622568C2211yescharacteristic
95#10622568C2211yescharacteristic
96#10622565C2212yescomplemented
97#10622565C2212yescomplemented
98#10622563C2211yescharacteristic
99#10622562C2212yescomplemented
100#10622562C2212yescomplemented
101#10622561C2212yescomplemented
102#10622561C2212yescomplemented
103#10622560C2212yescomplemented
104#10622559C2211yescharacteristic
105#10622556C2211yescharacteristic
106#10622556C2211yescharacteristic
107#10622555C2211yescharacteristic
108#10622555C2211yescharacteristic
109C4×(C2×D11)⋊C4C2212yescomplemented
110C4×(C2×D11)⋊C4C2212yescomplemented
111#10622545C2212yescomplemented
112C4×Dic11⋊C4C2212yescomplemented
113#10622289C2212yescomplemented
114#10622288C2212yescomplemented
115#10622288C2212yescomplemented
116#10622286C2212yescomplemented
117#10622285C2212yescomplemented
118#10622281C2212yescomplemented
119#10622278C2212yescomplemented
120#10622273C2212yescomplemented
121#10622271C2212yescomplemented
122#10622270C2212yescomplemented
123#10622264C2212yescomplemented
124#10622263C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11—24no—
130C23×C4×C11—44no—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2312yes—
136C22×C22⋊D11—24no—
137C22×C22⋊D11—24no—
138C22×C22⋊D11—24no—
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2312yes—
144C22×C22⋊D11C2312yes—
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2311yescharacteristic
148C22×D44C2312yes—
149C22×C4×D11—24no—
150C22×C4×D11—44no—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2312yes—
153C22×C4×D11C2312yes—
154C22×Dic22C2311yescharacteristic
155C11×#120—24no—
156C4×D4×C11—24no—
157C4×D4×C11—44no—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2312yes—
170#67006—24no—
171C2×C22⋊Dic11—24no—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184#66992—24no—
185#66990—24no—
186#66988—24no—
187C4×C22⋊D11—24no—
188C4×C22⋊D11—28no—
189C4×C22⋊D11—28no—
190C4×C22⋊D11—28no—
191C4×C22⋊D11—28no—
192C4×C22⋊D11—24no—
193C4×C22⋊D11—44no—
194C4×C22⋊D11—44no—
195C2×(C2×D11)⋊C4—24no—
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210#66979—24no—
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2312yes—
215C2×Dic11⋊C4—24no—
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×C4×Dic11D418yescomplemented
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2311yescharacteristic
234C2×C4×Dic11C2311yescharacteristic
235#66951—24no—
236#66942—24no—
237#66939—24no—
238#66938—24no—
239#66935—24no—
240#66932—24no—
241#66931—24no—
242C4×D44—44no—
243#66925—24no—
244C4×Dic22—24no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261#34593—111nomaximal, Sylow
262C24×C11—22no—
263C24×C11—22no—
264C24×C11—42no—
265C24×C11—42no—
266C24×C11#4114yes—
267C24×C11C2411yescharacteristic
268C24×C11C2412yes—
269C24×C11C2411yescharacteristic
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11#4114yes—
275C23×D11C2411yescharacteristic
276C23×D11C2412yes—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—24no—
280C2×D4×C11—22no—
281C2×D4×C11—42no—
282C2×D4×C11—42no—
283C22×C4×C11—24no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—24no—
288C22×C4×C11—24no—
289C22×C4×C11—24no—
290C22×C4×C11—24no—
291C22×C4×C11—42no—
292C22×C4×C11—42no—
293C22×C4×C11—42no—
294C22×C4×C11—416no—
295C22×C4×C11C2×D414yes—
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C2×C22⋊D11—232no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11—42no—
322C22×Dic11—22no—
323C22×Dic11—22no—
324C22×Dic11—22no—
325C22×Dic11—42no—
326C22×Dic11—42no—
327C22×Dic11C2×D414yes—
328C22×Dic11C2×D414yes—
329C22×Dic11C2412yes—
330C22×Dic11C2412yes—
331C22×Dic11C2411yescharacteristic
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2412yes—
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2411yescharacteristic
339C2×D44—24no—
340C2×D44—42no—
341C2×D44—42no—
342C2×C4×D11—22no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—416no—
351C2×Dic22—22no—
352C2×Dic22—42no—
353C11×C4⋊C4—22no—
354C11×C4⋊C4—42no—
355C11×C22⋊C4—22no—
356C11×C22⋊C4—22no—
357C11×C22⋊C4—24no—
358C11×C22⋊C4—22no—
359C11×C22⋊C4—22no—
360C11×C22⋊C4—42no—
361C11×C22⋊C4—42no—
362C11×C22⋊C4—42no—
363C42×C11—22no—
364C42×C11—24no—
365C22⋊Dic11—22no—
366C22⋊Dic11—22no—
367C22⋊Dic11—22no—
368C22⋊Dic11—24no—
369C22⋊Dic11—24no—
370C22⋊Dic11—22no—
371C22⋊Dic11—22no—
372C22⋊Dic11—24no—
373C22⋊Dic11—22no—
374C22⋊Dic11—42no—
375C22⋊Dic11—42no—
376C22⋊Dic11—42no—
377(C2×D11)⋊C4—22no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—22no—
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—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391C4⋊Dic11—22no—
392C4⋊Dic11—22no—
393C4⋊Dic11—22no—
394C4⋊Dic11—42no—
395Dic11⋊C4—22no—
396Dic11⋊C4—22no—
397Dic11⋊C4—22no—
398Dic11⋊C4—22no—
399Dic11⋊C4—22no—
400Dic11⋊C4—24no—
401Dic11⋊C4—24no—
402Dic11⋊C4—22no—
403Dic11⋊C4—42no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407C4×Dic11—22no—
408C4×Dic11—24no—
409C4×Dic11C2×D414yes—
410C4×Dic11C2×D414yes—
411C4×Dic11C2×D414yes—
412C4×Dic11C2×D414yes—
413C2×#529—111no—
414C22×C4×D4—111no—
415#2636—112no—
416#2636—112no—
417#2633—112no—
418#2631—112no—
419#2626—111no—
420#2626—111no—
421#2623—111no—
422#2623—111no—
423#2617—111no—
424#2617—111no—
425#2613—111no—
426#2613—111no—
427#2398—112no—
428#2397—112no—
429#2392—112no—
430#2392—112no—
431C4×#120—111no—
432C4×#120—111no—
433C4×#120—111no—
434C4×#120D1111yescharacteristic, complemented
435#2283—111no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—28no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—48no—
451C23×C11—44no—
452C23×C11—44no—
453C23×C11—48no—
454C23×C11C22×D412yes—
455C23×C11C2×#4114yes—
456C23×C11C2×#4112yes—
457C23×C11C2×#4112yes—
458C23×C11C2511yescharacteristic
459C22×D11—28no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—21no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—48no—
472C22×D11—44no—
473C22×D11—44no—
474C22×D11—48no—
475C22×D11C2×#4114yes—
476D4×C11—48no—
477D4×C11—44no—
478C2×C4×C11—22no—
479C2×C4×C11—28no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
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—48no—
497C2×C4×C11—44no—
498C2×C4×C11—44no—
499C2×C4×C11—48no—
500C2×C4×C11C22×D412yes—
501C2×C4×C11C22×D412yes—
502C2×C4×C11H(5,𝔽2)14yes—
503C22⋊D11—216no—
504C22⋊D11—216no—
505C22⋊D11—44no—
506C22⋊D11—48no—
507C22⋊D11—48no—
508C22⋊D11—44no—
509C2×Dic11—28no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—21no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—44no—
533C2×Dic11—44no—
534C2×Dic11C22×D412yes—
535C2×Dic11C22×D412yes—
536C2×Dic11C22×D412yes—
537C2×Dic11C22×D412yes—
538D44—48no—
539C4×D11—48no—
540C4×D11—44no—
541C4×D11—48no—
542Dic22—44no—
543C23×D4—111no—
544C24×C4—111no—
545C24×C4C2×D1111yescharacteristic
546#529—228no—
547C2×#126—111no—
548C2×#126—111no—
549C2×#125—111no—
550C2×#124—111no—
551C2×#123—111no—
552C2×#123—111no—
553C2×C22⋊Q8—111no—
554C2×#121—111no—
555C2×#120—111no—
556C2×#120—111no—
557C2×#120—111no—
558C2×#120C2×D1111yescharacteristic
559C2×C4×Q8—111no—
560C2×C4×D4—112no—
561C2×C4×D4—112no—
562C2×C4×D4—112no—
563C2×C4×D4—112no—
564C2×C4×D4—111no—
565C2×C4×D4—111no—
566C2×C4×D4—112no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—228no—
570C2×C4×D4C2×D1111yescharacteristic
571C2×C4×D4C2×D1112yescomplemented
572C2×#117—111no—
573C2×#117—111no—
574C22×C4⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C42—111no—
578#400—112no—
579#400—112no—
580#399—112no—
581#399—112no—
582#399—112no—
583#399—112no—
584#398—112no—
585#398—112no—
586#397—112no—
587#397—112no—
588#397—112no—
589#397—112no—
590#396—112no—
591#396—112no—
592#396—112no—
593#396—112no—
594#394—112no—
595#394—112no—
596#394—112no—
597#394—112no—
598#394—112no—
599#394—112no—
600#394—112no—
601#394—112no—
602#393—112no—
603#393—112no—
604#392—112no—
605#392—112no—
606#392—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#386—111no—
611#386—111no—
612#386—112no—
613#386—111no—
614#386—112no—
615#386—112no—
616#386C2×D1111yescharacteristic
617#386C2×D1112yescomplemented
618#385—111no—
619#385—112no—
620#385—112no—
621#385—111no—
622#385—111no—
623#385—112no—
624#385C2×D1111yescharacteristic
625#385C2×D1112yescomplemented
626#383—112no—
627#382—112no—
628#381—111no—
629#381—111no—
630#380—111no—
631#380—111no—
632#379—111no—
633#379—111no—
634#379—111no—
635#379C2×D1111yescharacteristic
636C4×C4⋊C4—112no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—111no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4C2×D1111yescharacteristic
642C4×C22⋊C4C2×D1112yescomplemented
643#376—112no—
644C22×C11—22no—
645C22×C11—22no—
646C22×C11—24no—
647C22×C11—24no—
648C22×C11—24no—
649C22×C11—24no—
650C22×C11—24no—
651C22×C11—416no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—41no—
657C22×C11—41no—
658C22×C11—41no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11#52514yes—
662C22×C11C23×D411yescharacteristic
663C22×C11C22×#4111yescharacteristic
664C22×C11C22×#4111yescharacteristic
665C22×C11C2×H(5,𝔽2)12yes—
666C22×C11#58512yes—
667C2×D11—24no—
668C2×D11—24no—
669C2×D11—24no—
670C2×D11—416no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—41no—
676C2×D11—41no—
677C2×D11—41no—
678C2×D11—42no—
679C2×D11—42no—
680C4×C11—22no—
681C4×C11—41no—
682C4×C11—41no—
683C4×C11—42no—
684C4×C11—41no—
685C4×C11—42no—
686C4×C11—42no—
687C4×C11#53514yes—
688Dic11—22no—
689Dic11—22no—
690Dic11—22no—
691Dic11—22no—
692Dic11—41no—
693Dic11—42no—
694Dic11—41no—
695Dic11—41no—
696Dic11—42no—
697Dic11—42no—
698C25—111no—
699C25C22×D1111yescharacteristic
700C22×Q8—111no—
701C22×D4—112no—
702C22×D4—112no—
703C22×D4—111no—
704C22×D4—112no—
705C22×D4—112no—
706C22×D4—111no—
707C22×D4—112no—
708C22×D4—224no—
709C22×D4—224no—
710C22×D4—224no—
711C22×D4C22×D1111yescharacteristic
712C22×D4C22×D1112yes—
713C23×C4—24no—
714C23×C4—44no—
715C23×C4—111no—
716C23×C4—111no—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—112no—
720C23×C4—112no—
721C23×C4—224no—
722C23×C4—444no—
723C23×C4C22×D1111yescharacteristic
724C23×C4C22×D1112yes—
725C23×C4C22×D1111yescharacteristic
726C23×C4C22×D1111yescharacteristic
727C23×C4C22×D1112yes—
728#126—224no—
729#126—224no—
730#125—224no—
731#124—224no—
732#123—224no—
733#123—224no—
734C22⋊Q8—224no—
735#121—224no—
736#120—24no—
737#120—224no—
738#120—224no—
739#120—224no—
740C4×Q8—224no—
741C4×D4—24no—
742C4×D4—44no—
743C4×D4—228no—
744C4×D4—228no—
745C4×D4—228no—
746C4×D4—228no—
747C4×D4—224no—
748C4×D4—224no—
749C4×D4—444no—
750C4×D4—444no—
751C4×D4—444no—
752#117—224no—
753#117—224no—
754C2×C4⋊C4—112no—
755C2×C4⋊C4—112no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—111no—
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—224no—
771C2×C4⋊C4C22×D1111yescharacteristic
772C2×C4⋊C4C22×D1112yes—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
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—224no—
800C2×C22⋊C4—224no—
801C2×C22⋊C4C22×D1111yescharacteristic
802C2×C22⋊C4C22×D1111yescharacteristic
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×C42—118no—
810C2×C42—111no—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—112no—
816C2×C42C22×D1111yescharacteristic
817C2×C42C22×D1112yes—
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—
834C2×C11—24no—
835C2×C11—44no—
836C2×C11—81no—
837C2×C11C2×#52511yescharacteristic
838C2×C11C2×#53511yescharacteristic
839C2×C11#344911yescharacteristic
840C2×C11#345912yes—
841C2×C11#345912yes—
842D11—44no—
843D11—81no—
844C24—22no—
845C24—22no—
846C24—42no—
847C24—42no—
848C24—112no—
849C24—114no—
850C24—111no—
851C24—222no—
852C24—222no—
853C24—442no—
854C24—442no—
855C24#433914yes—
856C24C23×D1111yescharacteristic
857C24C23×D1112yes—
858C24C23×D1111yescharacteristic
859C2×Q8—222no—
860C2×Q8—442no—
861C2×D4—24no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—224no—
868C2×D4—224no—
869C2×D4—224no—
870C2×D4—222no—
871C2×D4—224no—
872C2×D4—224no—
873C2×D4—2232no—
874C2×D4—224no—
875C2×D4—224no—
876C2×D4—224no—
877C2×D4—224no—
878C2×D4—222no—
879C2×D4—222no—
880C2×D4—222no—
881C2×D4—442no—
882C2×D4—442no—
883C2×D4—442no—
884C2×D4—442no—
885C2×D4—442no—
886C2×D4—442no—
887C2×D4—442no—
888C22×C4—24no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—416no—
900C22×C4—114no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—111no—
905C22×C4—114no—
906C22×C4—112no—
907C22×C4—112no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—112no—
911C22×C4—111no—
912C22×C4—222no—
913C22×C4—222no—
914C22×C4—222no—
915C22×C4—222no—
916C22×C4—224no—
917C22×C4—224no—
918C22×C4—224no—
919C22×C4—224no—
920C22×C4—224no—
921C22×C4—442no—
922C22×C4—442no—
923C22×C4—4416no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4D4×D1114yes—
927C22×C4C23×D1112yes—
928C22×C4C23×D1112yes—
929C22×C4C23×D1111yescharacteristic
930C22×C4C23×D1111yescharacteristic
931C22×C4C23×D1112yes—
932C22×C4C23×D1111yescharacteristic
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C4⋊C4—22no—
936C4⋊C4—42no—
937C4⋊C4—224no—
938C4⋊C4—224no—
939C4⋊C4—222no—
940C4⋊C4—222no—
941C4⋊C4—222no—
942C4⋊C4—222no—
943C4⋊C4—222no—
944C4⋊C4—222no—
945C4⋊C4—222no—
946C4⋊C4—222no—
947C4⋊C4—222no—
948C4⋊C4—442no—
949C4⋊C4—442no—
950C4⋊C4—442no—
951C4⋊C4—442no—
952C4⋊C4—442no—
953C22⋊C4—24no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—22no—
957C22⋊C4—22no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—224no—
962C22⋊C4—224no—
963C22⋊C4—222no—
964C22⋊C4—222no—
965C22⋊C4—222no—
966C22⋊C4—224no—
967C22⋊C4—224no—
968C22⋊C4—224no—
969C22⋊C4—224no—
970C22⋊C4—222no—
971C22⋊C4—222no—
972C22⋊C4—222no—
973C22⋊C4—224no—
974C22⋊C4—222no—
975C22⋊C4—222no—
976C22⋊C4—222no—
977C22⋊C4—222no—
978C22⋊C4—442no—
979C22⋊C4—442no—
980C22⋊C4—442no—
981C22⋊C4—442no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4—442no—
987C42—22no—
988C42—24no—
989C42—114no—
990C42—114no—
991C42—114no—
992C42—114no—
993C42—222no—
994C42—224no—
995C11#3459311yescharacteristic, complemented, Sylow
996C23—22no—
997C23—22no—
998C23—28no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—21no—
1009C23—22no—
1010C23—48no—
1011C23—44no—
1012C23—44no—
1013C23—48no—
1014C23—114no—
1015C23—228no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—222no—
1021C23—222no—
1022C23—221no—
1023C23—221no—
1024C23—222no—
1025C23—221no—
1026C23—222no—
1027C23—448no—
1028C23—444no—
1029C23—444no—
1030C23—448no—
1031C23C2×#433914yes—
1032C23C2×#433912yes—
1033C23C2×D4×D1112yes—
1034C23#41×D1112yes—
1035C23C24×D1111yescharacteristic
1036Q8—444no—
1037D4—48no—
1038D4—44no—
1039D4—2216no—
1040D4—2216no—
1041D4—448no—
1042D4—444no—
1043D4—448no—
1044D4—448no—
1045D4—444no—
1046C2×C4—22no—
1047C2×C4—28no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—48no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—48no—
1068C2×C4—112no—
1069C2×C4—112no—
1070C2×C4—112no—
1071C2×C4—112no—
1072C2×C4—228no—
1073C2×C4—221no—
1074C2×C4—221no—
1075C2×C4—221no—
1076C2×C4—221no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—221no—
1080C2×C4—222no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—221no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—448no—
1096C2×C4—444no—
1097C2×C4—444no—
1098C2×C4—448no—
1099C2×C4—444no—
1100C2×C4C2×D4×D1112yes—
1101C2×C4C2×D4×D1112yes—
1102C2×C4#6703714yes—
1103C22—22no—
1104C22—22no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—416no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—41no—
1116C22—41no—
1117C22—41no—
1118C22—42no—
1119C22—42no—
1120C22—224no—
1121C22—224no—
1122C22—224no—
1123C22—4416no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22—441no—
1129C22—441no—
1130C22—441no—
1131C22—442no—
1132C22—442no—
1133C22#1062307814yes—
1134C22C22×#433911yescharacteristic
1135C22C22×D4×D1111yescharacteristic
1136C22C2×#6703712yes—
1137C22C2×#41×D1111yescharacteristic
1138C22#1062345312yes—
1139C4—22no—
1140C4—41no—
1141C4—42no—
1142C4—41no—
1143C4—41no—
1144C4—42no—
1145C4—42no—
1146C4—222no—
1147C4—222no—
1148C4—222no—
1149C4—222no—
1150C4—441no—
1151C4—442no—
1152C4—441no—
1153C4—441no—
1154C4—442no—
1155C4—442no—
1156C4#1062312314yes—
1157C2—24no—
1158C2—44no—
1159C2—81no—
1160C2—444no—
1161C2—881no—
1162C2C2×#1062307811yescharacteristic
1163C2C2×#1062312311yescharacteristic
1164C2#1308194611yescharacteristic
1165C2#1308202312yes—
1166C2#1308202512yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#120C2
hypercenterC4×#120D11
hypocenterC11#34593
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10623069C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13074519C2semidirect
4. #13074517C2semidirect
5. #13074488C2semidirect
6. #13074472C2semidirect
7. #13074427C2semidirect
8. #13074425C2semidirect
9. #13074402C2semidirect
10. #13074400C2semidirect
11. #13074356C2semidirect
12. #13074354C2semidirect
13. #13074331C2semidirect
14. #13074330C2semidirect
15. #13071903C2semidirect
16. #13071895C2semidirect
17. #13071860C2semidirect
18. #13071858C2semidirect
19. C4×#66935C2semidirect
20. C4×#67006C2semidirect
21. C4×#66990C2semidirect
22. #13071010C2semidirect
23. C4×C11×#120C2semidirect
29. C2×C4×D4×C11C22semidirect
41. C2×C4×C22⋊D11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
43. C2×C4×C22⋊D11C22semidirect
45. C2×#66979C22semidirect
49. C2×#66951C22semidirect
50. C2×#66942C22semidirect
52. C2×#66938C22semidirect
54. C2×#66932C22semidirect
56. C2×C4×D44C22semidirect
57. C2×#66925C22semidirect
58. C2×C4×Dic22C22semidirect
60. C11×#386C22semidirect
62. C11×#385C22semidirect
65. C4×C11×C22⋊C4C22semidirect
69. #10622836C22semidirect
70. #10622835C22semidirect
73. #10622826C22semidirect
75. #10622823C22semidirect
77. C4×C22⋊Dic11C22semidirect
78. #10622607C22semidirect
79. #10622605C22semidirect
80. #10622605C22semidirect
81. #10622602C22semidirect
82. #10622597C22semidirect
87. #10622573C22semidirect
90. #10622572C22semidirect
91. #10622572C22semidirect
93. #10622569C22semidirect
96. #10622565C22semidirect
97. #10622565C22semidirect
99. #10622562C22semidirect
100. #10622562C22semidirect
101. #10622561C22semidirect
102. #10622561C22semidirect
103. #10622560C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. C4×(C2×D11)⋊C4C22semidirect
111. #10622545C22semidirect
112. C4×Dic11⋊C4C22semidirect
113. #10622289C22semidirect
114. #10622288C22semidirect
115. #10622288C22semidirect
116. #10622286C22semidirect
117. #10622285C22semidirect
118. #10622281C22semidirect
119. #10622278C22semidirect
120. #10622273C22semidirect
121. #10622271C22semidirect
122. #10622270C22semidirect
123. #10622264C22semidirect
124. #10622263C22semidirect
228. C2×C4×Dic11D4semidirect
434. C4×#120D11semidirect
571. C2×C4×D4C2×D11semidirect
617. #386C2×D11semidirect
625. #385C2×D11semidirect
642. C4×C22⋊C4C2×D11semidirect
995. C11#34593semidirect

Maximal subgroups

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

subgroupindex
C2×#106230692
C22×C4×C22⋊D112
#130745192
#130745172
#130744882
#130744722
#130744272
#130744252
#130744022
#130744002
#130743562
#130743542
#130743312
#130743302
#130719032
#130718952
#130718602
#130718582
C4×#669352
C4×#670062
C4×#669902
#130710102
C4×C11×#1202
#3459311