Finite Group Databasebeta

← #14926721

Subgroups — #14926721

Order 2816.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623188C212yesmaximal, complemented
2#13076984C211yesmaximal, characteristic, complemented
3#13076970C211yesmaximal, characteristic, complemented
4#13076961C211yesmaximal, characteristic, complemented
5#13074759C212yesmaximal, complemented
6#13074744C212yesmaximal, complemented
7#13073688C212yesmaximal, complemented
8#13073683C212yesmaximal, complemented
9#13073204C211yesmaximal, characteristic, complemented
10#13072975C211yesmaximal, characteristic, complemented
11#13072740C212yesmaximal, complemented
12#13072383C211yesmaximal, characteristic, complemented
13#13072316C211yesmaximal, characteristic, complemented
14#13072252C211yesmaximal, characteristic, complemented
15#13072200C211yesmaximal, characteristic, complemented
16#13072151C212yesmaximal, complemented
17#13072058C211yesmaximal, characteristic, complemented
18#13071968C211yesmaximal, characteristic, complemented
19#13071269C212yesmaximal, complemented
20#13071124C211yesmaximal, characteristic, complemented
21D11×#390C211yesmaximal, characteristic, complemented
22C42×C22⋊D11C211yesmaximal, characteristic, complemented
23C11×#2854C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×#123C2212yescomplemented
26C2×C11×#121C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic, complemented
28C2×#66993C2211yescharacteristic
29C2×#66991C2212yescomplemented
30C2×#66990C2212yes—
31C2×#66983C2211yescharacteristic
32C2×#66983C2212yescomplemented
33C2×#66983C2212yescomplemented
34C2×#66983C2211yescharacteristic, complemented
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic
37C2×C4×C22⋊D11C2211yescharacteristic
38#10623188—216no—
39C2×#66951C2212yescomplemented
40C2×#66950C2212yes—
41C2×#66948C2211yescharacteristic
42C2×#66947C2212yescomplemented
43C2×#66946C2212yes—
44C2×#66946C2211yescharacteristic, complemented
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66941C2211yescharacteristic, complemented
47C2×#66938C2212yescomplemented
48C2×#66938C2212yescomplemented
49C2×#66938C2212yescomplemented
50C2×#66937C2212yes—
51C2×#66935C2212yes—
52C2×#66935C2212yes—
53C2×C22⋊C4×D11C2212yes—
54C2×C22⋊C4×D11C2212yes—
55C2×#66932C2212yescomplemented
56C2×#66927C2211yescharacteristic
57C2×C42×D11C2211yescharacteristic
58C11×#390C2211yescharacteristic
59C11×#390C2211yescharacteristic
60C11×#389C2211yescharacteristic, complemented
61C11×#389C2211yescharacteristic, complemented
62C11×#388C2212yescomplemented
63C11×#388C2212yescomplemented
64C11×#386C2212yescomplemented
65C11×#380C2211yescharacteristic, complemented
66#10622836C2212yes—
67#10622836C2212yescomplemented
68#10622834C2211yescharacteristic
69#10622834C2211yescharacteristic
70C4×C22⋊Dic11C2211yescharacteristic, complemented
71C4×C22⋊Dic11C2211yescharacteristic, complemented
72C4×C22⋊Dic11C2211yescharacteristic, complemented
73#10622604C2212yescomplemented
74#10622603C2212yescomplemented
75#10622603C2212yescomplemented
76#10622601C2211yescharacteristic
77#10622601C2211yescharacteristic
78#10622601C2211yescharacteristic
79#10622601C2211yescharacteristic, complemented
80#10622600C2211yescharacteristic
81#10622598C2211yescharacteristic, complemented
82#10622596C2212yescomplemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622586C2211yescharacteristic, complemented
85#10622574C2212yescomplemented
86#10622573C2212yes—
87#10622573C2212yes—
88#10622572C2212yes—
89#10622572C2212yescomplemented
90#10622572C2212yescomplemented
91#10622570C2212yes—
92#10622570C2212yes—
93#10622570C2212yescomplemented
94#10622570C2212yescomplemented
95#10622569C2212yescomplemented
96#10622568C2212yes—
97#10622566C2212yescomplemented
98#10622564C2212yescomplemented
99#10622561C2212yescomplemented
100#10622552C2211yescharacteristic
101#10622552C2212yescomplemented
102#10622552C2211yescharacteristic, complemented
103#10622552C2212yescomplemented
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2211yescharacteristic
107#10622548C2211yescharacteristic, complemented
108C4×Dic11⋊C4C2211yescharacteristic, complemented
109C4×Dic11⋊C4C2211yescharacteristic, complemented
110C4×Dic11⋊C4C2211yescharacteristic, complemented
111C42×Dic11C2211yescharacteristic, complemented
112#10622289C2212yescomplemented
113#10622286C2212yescomplemented
114#10622285C2212yescomplemented
115#10622283C2212yescomplemented
116#10622282C2212yescomplemented
117#10622282C2212yescomplemented
118#10622281C2212yes—
119#10622279C2212yescomplemented
120#10622278C2212yes—
121#10622278C2212yes—
122#10622278C2212yescomplemented
123#10622269C2212yescomplemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2312yes—
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C2×D4×D11—24no—
137C2×D4×D11—42no—
138C2×D4×D11—42no—
139C22×D44C2311yescharacteristic
140C22×D44C2311yescharacteristic
141C22×D44C2312yes—
142C22×D44C2312yes—
143C22×D44C2312yes—
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2312yes—
150C11×#123—28no—
151C11×#121—42no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11—42no—
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2311yescharacteristic
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175#66993—42no—
176#66991—28no—
177#66990—28no—
178#66983—28no—
179#66983—42no—
180#66983—42no—
181#66983—44no—
182C4×C22⋊D11—24no—
183C4×C22⋊D11—24no—
184C4×C22⋊D11D418yescomplemented
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226#66951—28no—
227#66950—28no—
228#66948—24no—
229#66947—28no—
230#66946—28no—
231#66946—42no—
232C4⋊C4×D11—42no—
233#66941—42no—
234#66938—28no—
235#66938—28no—
236#66938—44no—
237#66937—28no—
238#66935—28no—
239#66935—28no—
240C22⋊C4×D11—28no—
241C22⋊C4×D11—44no—
242#66932—28no—
243#66927—42no—
244C42×D11—42no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2311yescharacteristic
258#35007—111nomaximal, Sylow
259C24×C11C2412yes—
260C24×C11C2411yescharacteristic
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11C2412yes—
269C23×D11C2412yes—
270C23×D11C2411yescharacteristic
271C2×D4×C11—24no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—22no—
275C2×D4×C11—42no—
276C2×D4×C11—42no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—41no—
283C22×C4×C11—41no—
284C22×C4×C11—41no—
285C22×C4×C11C2×D414yescomplemented
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11—42no—
305C2×C22⋊D11—42no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11—42no—
309C2×C22⋊D11—42no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11C2×D414yes—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322D4×D11—416no—
323C2×D44—24no—
324C2×D44—24no—
325C2×D44—24no—
326C2×D44—24no—
327C2×D44—22no—
328C2×D44—22no—
329C2×D44—24no—
330C2×D44—22no—
331C2×D44—22no—
332C2×D44—22no—
333C2×D44—22no—
334C2×D44—42no—
335C2×D44—42no—
336C2×D44—42no—
337C2×D44—42no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—41no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11C2×D414yes—
352C2×C4×D11#4114yes—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—24no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—22no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—42no—
367C42×C11—22no—
368C42×C11—22no—
369C42×C11—41no—
370C42×C11—41no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—22no—
374C22⋊Dic11—22no—
375C22⋊Dic11—42no—
376C22⋊Dic11—42no—
377C22⋊Dic11C2×D414yescomplemented
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—24no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4C2×D414yes—
397(C2×D11)⋊C4#4114yes—
398C4⋊Dic11—24no—
399C4⋊Dic11—24no—
400C4⋊Dic11—22no—
401C4⋊Dic11—22no—
402C4⋊Dic11—42no—
403Dic11⋊C4—24no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408Dic11⋊C4C2×D414yescomplemented
409C4×Dic11—24no—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—41no—
416C4×Dic11—41no—
417C4×Dic11—41no—
418C4×Dic11C2×D414yescomplemented
419C2×#538—112no—
420#2860—111no—
421#2858—111no—
422#2856—111no—
423#2854D1111yescharacteristic, complemented
424#2662—112no—
425#2661—112no—
426#2555—112no—
427#2554—112no—
428#2512—111no—
429#2491—111no—
430#2472—112no—
431#2445—111no—
432#2440—111no—
433#2433—111no—
434#2428—111no—
435#2424—112no—
436#2416—111no—
437#2408—111no—
438#2321—112no—
439C4×#121—111no—
440C2×#390—111no—
441C42×D4—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11C22×D412yes—
456C23×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11—84no—
479C22×D11—84no—
480C22×D11—84no—
481C22×D11—84no—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4112yes—
485D4×C11—44no—
486D4×C11—84no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—22no—
507C2×C4×C11—44no—
508C2×C4×C11—44no—
509C2×C4×C11—44no—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C2×#4112yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11H(5,𝔽2)12yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C2×C4×C11H(5,𝔽2)12yes—
517C22⋊D11—28no—
518C22⋊D11—48no—
519C22⋊D11—84no—
520C22⋊D11—84no—
521C22⋊D11—84no—
522C22⋊D11—84no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—21no—
544C2×Dic11—21no—
545C2×Dic11C22×D412yes—
546C2×Dic11C22×D412yes—
547C2×Dic11C22×D412yes—
548C2×Dic11C2×#4112yes—
549C2×Dic11C2×#4112yes—
550D44—48no—
551D44—44no—
552D44—44no—
553D44—84no—
554D44—84no—
555C4×D11—28no—
556C4×D11—44no—
557C4×D11—44no—
558C4×D11—84no—
559C4×D11—84no—
560Dic22—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127—111no—
565C2×#127—111no—
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
571C2×#123—112no—
572C2×#123C2×D1112yescomplemented
573C2×C22⋊Q8—112no—
574C2×#121—112no—
575C2×#121—112no—
576C2×#121—111no—
577C2×#121—111no—
578C2×#121—112no—
579C2×#121—111no—
580C2×#121—112no—
581C2×#121C2×D1111yescharacteristic
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—111no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—112no—
589C2×C4×D4—111no—
590C22×C4⋊C4—111no—
591C22×C22⋊C4—112no—
592C22×C22⋊C4—112no—
593C22×C42—111no—
594C22×C42C2×D1111yescharacteristic, complemented
595#398—112no—
596#397—112no—
597#396—112no—
598#396—112no—
599#395—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#393—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—111no—
612#390—111no—
613#390—111no—
614#390—111no—
615#390—111no—
616#390—111no—
617#390—112no—
618#390—112no—
619#390—112no—
620#390—112no—
621#390—112no—
622#390—111no—
623#390—111no—
624#390—112no—
625#390C2×D1111yescharacteristic
626#390C2×D1111yescharacteristic
627#389—111no—
628#389—111no—
629#389C2×D1111yescharacteristic, complemented
630#389C2×D1111yescharacteristic, complemented
631#388—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388—112no—
637#388C2×D1112yescomplemented
638#388C2×D1112yescomplemented
639#386—112no—
640#386—112no—
641#386—112no—
642#386—112no—
643#386C2×D1112yescomplemented
644#385—112no—
645#384—111no—
646#380—111no—
647#380C2×D1111yescharacteristic, complemented
648#379—112no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—111no—
653C4×C22⋊C4—111no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4—112no—
660C43—111no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—41no—
667C22×C11—41no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11C23×D411yescharacteristic
676C22×C11C22×#4111yescharacteristic
677C22×C11C22×#4111yescharacteristic
678C22×C11C2×H(5,𝔽2)11yescharacteristic
679C22×C11C2×H(5,𝔽2)11yescharacteristic
680C22×C11C2×H(5,𝔽2)11yescharacteristic
681C22×C11#58511yescharacteristic
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—816no—
703C2×D11#53214yes—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—42no—
709C4×C11—41no—
710C4×C11—42no—
711C4×C11—42no—
712C4×C11#53814yescomplemented
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—41no—
719Dic11—42no—
720Dic11—42no—
721Dic11—41no—
722C25—112no—
723C22×Q8—112no—
724C22×D4—111no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—111no—
732C22×D4—111no—
733C22×D4—112no—
734C22×D4—112no—
735C22×D4—224no—
736C22×D4—442no—
737C22×D4—442no—
738C22×D4C22×D1111yescharacteristic
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—112no—
744C23×C4—112no—
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C4⋊Q8—442no—
749#127—442no—
750#127—442no—
751#126—228no—
752#126—228no—
753#124—228no—
754#124—228no—
755#124—444no—
756#123—28no—
757#123—228no—
758C22⋊Q8—228no—
759#121—42no—
760#121—228no—
761#121—228no—
762#121—224no—
763#121—228no—
764#121—444no—
765#121—442no—
766#121—442no—
767#120—228no—
768#120—228no—
769#120—228no—
770C4×D4—118no—
771C4×D4—224no—
772C4×D4—228no—
773C4×D4—224no—
774C4×D4—442no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—442no—
787C2×C4⋊C4C22×D1111yescharacteristic
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1112yes—
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1112yes—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—228no—
820C2×C22⋊C4—444no—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1112yes—
827C2×C42—42no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—111no—
835C2×C42—111no—
836C2×C42—111no—
837C2×C42—111no—
838C2×C42—442no—
839C2×C42C22×D1111yescharacteristic
840C2×C42C22×D1111yescharacteristic
841C2×C42C22×D1111yescharacteristic
842C2×C42C22×D1111yescharacteristic
843#95—111no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—111no—
848#95—111no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95C22×D1112yes—
854#95C22×D1112yes—
855#95C22×D1112yes—
856C2×C11—42no—
857C2×C11—82no—
858C2×C11C2×#53211yescharacteristic
859C2×C11C2×#53811yescharacteristic
860C2×C11#346011yescharacteristic
861C2×C11#349611yescharacteristic
862C2×C11#349811yescharacteristic
863C2×C11#351411yescharacteristic
864C2×C11#351911yescharacteristic
865D11—24no—
866D11—82no—
867D11—82no—
868C24—111no—
869C24—112no—
870C24—112no—
871C24—224no—
872C24—224no—
873C24—224no—
874C24—442no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24C23×D1112yes—
879C24C23×D1111yescharacteristic
880C2×Q8—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—24no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—114no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—222no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—224no—
906C2×D4—222no—
907C2×D4—222no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C2×D4—4416no—
913C2×D4—442no—
914C2×D4—442no—
915C2×D4—442no—
916C2×D4—442no—
917C2×D4—442no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4—442no—
921C2×D4—442no—
922C2×D4—442no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—111no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—114no—
937C22×C4—114no—
938C22×C4—111no—
939C22×C4—111no—
940C22×C4—112no—
941C22×C4—112no—
942C22×C4—224no—
943C22×C4—222no—
944C22×C4—224no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—441no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4D4×D1114yescomplemented
956C22×C4C23×D1112yes—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1112yes—
959C22×C4C23×D1112yes—
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—114no—
971C4⋊C4—222no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—224no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—42no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—222no—
998C22⋊C4—224no—
999C22⋊C4—222no—
1000C22⋊C4—222no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4—442no—
1012C22⋊C4—442no—
1013C22⋊C4—442no—
1014C42—22no—
1015C42—22no—
1016C42—41no—
1017C42—41no—
1018C42—114no—
1019C42—224no—
1020C42—222no—
1021C42—222no—
1022C42—222no—
1023C42—222no—
1024C42—222no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—112no—
1043C23—112no—
1044C23—112no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—448no—
1064C23—448no—
1065C23—448no—
1066C23—884no—
1067C23—884no—
1068C23—884no—
1069C23—884no—
1070C23C2×D4×D1112yes—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—44no—
1074D4—84no—
1075D4—228no—
1076D4—448no—
1077D4—448no—
1078D4—444no—
1079D4—444no—
1080D4—884no—
1081D4—884no—
1082D4—884no—
1083D4—884no—
1084D4—884no—
1085D4—884no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—44no—
1107C2×C4—44no—
1108C2×C4—44no—
1109C2×C4—112no—
1110C2×C4—112no—
1111C2×C4—112no—
1112C2×C4—112no—
1113C2×C4—112no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—221no—
1124C2×C4—228no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—221no—
1128C2×C4—221no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—884no—
1140C2×C4—884no—
1141C2×C4C2×D4×D1112yes—
1142C2×C4C2×D4×D1112yes—
1143C2×C4#6703712yes—
1144C2×C4#41×D1112yes—
1145C2×C4#41×D1112yes—
1146C2×C4#6704212yes—
1147C2×C4#6704212yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—114no—
1163C22—222no—
1164C22—222no—
1165C22—222no—
1166C22—222no—
1167C22—222no—
1168C22—222no—
1169C22—442no—
1170C22—442no—
1171C22—442no—
1172C22—442no—
1173C22—442no—
1174C22—442no—
1175C22—442no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—8816no—
1184C22C22×D4×D1111yescharacteristic
1185C22C2×#6703711yescharacteristic
1186C22C2×#41×D1111yescharacteristic
1187C22C2×#41×D1111yescharacteristic
1188C22C2×#6704211yescharacteristic
1189C22C2×#6704211yescharacteristic
1190C22#1062345311yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—41no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—441no—
1205C4—442no—
1206C4—442no—
1207C4—441no—
1208C4#1062318814yescomplemented
1209C2—42no—
1210C2—82no—
1211C2—224no—
1212C2—882no—
1213C2—882no—
1214C2D11×#53211yescharacteristic
1215C2C2×#1062318811yescharacteristic
1216C2#1308203711yescharacteristic
1217C2#1308237311yescharacteristic
1218C2#1308238911yescharacteristic
1219C2#1308257911yescharacteristic
1220C2#1308263611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2854C2
hypercenter#2854D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#10623188C2semidirect
2. #13076984C2semidirect
3. #13076970C2semidirect
4. #13076961C2semidirect
5. #13074759C2semidirect
6. #13074744C2semidirect
7. #13073688C2semidirect
8. #13073683C2semidirect
9. #13073204C2semidirect
10. #13072975C2semidirect
11. #13072740C2semidirect
12. #13072383C2semidirect
13. #13072316C2semidirect
14. #13072252C2semidirect
15. #13072200C2semidirect
16. #13072151C2semidirect
17. #13072058C2semidirect
18. #13071968C2semidirect
19. #13071269C2semidirect
20. #13071124C2semidirect
21. D11×#390C2semidirect
22. C42×C22⋊D11C2semidirect
23. C11×#2854C2semidirect
25. C2×C11×#123C22semidirect
27. C22×C42×C11C22semidirect
29. C2×#66991C22semidirect
32. C2×#66983C22semidirect
33. C2×#66983C22semidirect
34. C2×#66983C22semidirect
39. C2×#66951C22semidirect
42. C2×#66947C22semidirect
44. C2×#66946C22semidirect
46. C2×#66941C22semidirect
47. C2×#66938C22semidirect
48. C2×#66938C22semidirect
49. C2×#66938C22semidirect
55. C2×#66932C22semidirect
60. C11×#389C22semidirect
61. C11×#389C22semidirect
62. C11×#388C22semidirect
63. C11×#388C22semidirect
64. C11×#386C22semidirect
65. C11×#380C22semidirect
67. #10622836C22semidirect
70. C4×C22⋊Dic11C22semidirect
71. C4×C22⋊Dic11C22semidirect
72. C4×C22⋊Dic11C22semidirect
73. #10622604C22semidirect
74. #10622603C22semidirect
75. #10622603C22semidirect
79. #10622601C22semidirect
81. #10622598C22semidirect
82. #10622596C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622586C22semidirect
85. #10622574C22semidirect
89. #10622572C22semidirect
90. #10622572C22semidirect
93. #10622570C22semidirect
94. #10622570C22semidirect
95. #10622569C22semidirect
97. #10622566C22semidirect
98. #10622564C22semidirect
99. #10622561C22semidirect
101. #10622552C22semidirect
102. #10622552C22semidirect
103. #10622552C22semidirect
107. #10622548C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. C4×Dic11⋊C4C22semidirect
110. C4×Dic11⋊C4C22semidirect
111. C42×Dic11C22semidirect
112. #10622289C22semidirect
113. #10622286C22semidirect
114. #10622285C22semidirect
115. #10622283C22semidirect
116. #10622282C22semidirect
117. #10622282C22semidirect
119. #10622279C22semidirect
122. #10622278C22semidirect
123. #10622269C22semidirect
184. C4×C22⋊D11D4semidirect
285. C22×C4×C11C2×D4semidirect
377. C22⋊Dic11C2×D4semidirect
408. Dic11⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
423. #2854D11semidirect
572. C2×#123C2×D11semidirect
594. C22×C42C2×D11semidirect
629. #389C2×D11semidirect
630. #389C2×D11semidirect
637. #388C2×D11semidirect
638. #388C2×D11semidirect
643. #386C2×D11semidirect
647. #380C2×D11semidirect
712. C4×C11#538semidirect
955. C22×C4D4×D11semidirect
1028. C11#35007semidirect
1208. C4#10623188semidirect

Maximal subgroups

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

subgroupindex
C2×#106231882
#130769842
#130769702
#130769612
#130747592
#130747442
#130736882
#130736832
#130732042
#130729752
#130727402
#130723832
#130723162
#130722522
#130722002
#130721512
#130720582
#130719682
#130712692
#130711242
D11×#3902
C42×C22⋊D112
C11×#28542
#3500711