Finite Group Databasebeta

← #14926334

Subgroups — #14926334

Order 2816.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623120C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13076941C211yesmaximal, characteristic, complemented
4#13076937C211yesmaximal, characteristic, complemented
5#13076908C211yesmaximal, characteristic, complemented
6#13074402C211yesmaximal, characteristic, complemented
7#13074400C211yesmaximal, characteristic, complemented
8#13074392C211yesmaximal, characteristic, complemented
9#13074391C211yesmaximal, characteristic, complemented
10#13072365C212yesmaximal, complemented
11#13072363C212yesmaximal, complemented
12#13072350C212yesmaximal, complemented
13#13072348C212yesmaximal, complemented
14#13072092C212yesmaximal, complemented
15#13072090C212yesmaximal, complemented
16#13072077C212yesmaximal, complemented
17#13072075C212yesmaximal, complemented
18#13071227C211yesmaximal, characteristic, complemented
19#13071192C211yesmaximal, characteristic, complemented
20#13071190C211yesmaximal, characteristic, complemented
21D11×#386C211yesmaximal, characteristic, complemented
22D11×#385C211yesmaximal, characteristic, complemented
23C11×#2849C211yesmaximal, characteristic, complemented
24C24×C4×C11C2211yescharacteristic, complemented
25C23×C22⋊D11C2211yescharacteristic
26C22×D4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#123C2212yescomplemented
29C2×C11×#120C2211yescharacteristic
30C2×#67006C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic, complemented
32C2×#66991C2211yescharacteristic
33C2×#66991C2211yescharacteristic
34C2×#66990C2211yescharacteristic
35C2×#66990C2211yescharacteristic
36C2×#66988C2211yescharacteristic
37C2×#66982C2212yescomplemented
38C2×C4×C22⋊D11—28no—
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2212yescomplemented
42C2×C4×C22⋊D11C2212yescomplemented
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic, complemented
45C22×C4×Dic11C2211yescharacteristic, complemented
46#10623120—28no—
47C2×C4⋊C4×D11C2212yescomplemented
48C2×#66939C2211yescharacteristic
49C2×#66937C2211yescharacteristic
50C2×#66937C2211yescharacteristic
51C2×#66936C2211yescharacteristic
52C2×#66936C2211yescharacteristic
53C2×C22⋊C4×D11C2211yescharacteristic
54C2×C22⋊C4×D11C2211yescharacteristic
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2212yescomplemented
57C11×#386C2211yescharacteristic
58C11×#386C2211yescharacteristic
59C11×#386C2212yescomplemented
60C11×#385C2211yescharacteristic, complemented
61C11×#385C2211yescharacteristic, complemented
62C11×#385C2212yescomplemented
63C11×#381C2212yescomplemented
64C11×#379C2211yescharacteristic, complemented
65#10622860C2211yescharacteristic, complemented
66#10622835C2212yescomplemented
67#10622835C2212yescomplemented
68#10622833C2211yescharacteristic
69#10622833C2211yescharacteristic
70#10622826C2211yescharacteristic
71#10622826C2211yescharacteristic
72#10622826C2212yescomplemented
73#10622824C2212yescomplemented
74#10622823C2211yescharacteristic, complemented
75#10622823C2211yescharacteristic, complemented
76#10622823C2212yescomplemented
77#10622605C2212yescomplemented
78#10622603C2212yescomplemented
79#10622602C2212yescomplemented
80#10622602C2212yescomplemented
81#10622600C2212yescomplemented
82#10622597C2212yescomplemented
83#10622594C2212yescomplemented
84#10622574C2212yescomplemented
85#10622574C2212yescomplemented
86#10622571C2211yescharacteristic
87#10622571C2211yescharacteristic
88#10622569C2212yes—
89#10622569C2212yes—
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622569C2212yescomplemented
93#10622569C2212yescomplemented
94#10622568C2212yescomplemented
95#10622566C2212yescomplemented
96#10622566C2212yescomplemented
97#10622565C2212yescomplemented
98#10622565C2212yescomplemented
99#10622565C2212yescomplemented
100#10622564C2212yescomplemented
101#10622563C2211yescharacteristic, complemented
102#10622563C2211yescharacteristic, complemented
103#10622562C2212yescomplemented
104#10622559C2211yescharacteristic, complemented
105#10622559C2211yescharacteristic, complemented
106#10622558C2212yescomplemented
107#10622556C2211yescharacteristic, complemented
108#10622556C2211yescharacteristic, complemented
109#10622288C2212yescomplemented
110#10622282C2212yescomplemented
111#10622281C2212yescomplemented
112#10622281C2212yescomplemented
113#10622280C2212yescomplemented
114#10622278C2212yescomplemented
115#10622278C2212yescomplemented
116#10622277C2212yescomplemented
117D11×#95C2212yescomplemented
118D11×#95C2212yescomplemented
119#10622273C2212yescomplemented
120#10622271C2212yescomplemented
121#10622270C2212yescomplemented
122#10622268C2212yescomplemented
123#10622267C2212yescomplemented
124#10622265C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C23×C4×C11—24no—
132C23×C4×C11—44no—
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C23×C4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C22×C22⋊D11—24no—
138C22×C22⋊D11—24no—
139C22×C22⋊D11D418yes—
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2311yescharacteristic
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2311yescharacteristic
144C22×C22⋊D11C2311yescharacteristic
145C22×C22⋊D11C2311yescharacteristic
146C22×C22⋊D11C2311yescharacteristic
147C22×C22⋊D11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C23×Dic11C2311yescharacteristic
150C23×Dic11C2311yescharacteristic
151C2×D4×D11—24no—
152C2×D4×D11—24no—
153C2×D4×D11—24no—
154C22×D44C2311yescharacteristic
155C22×C4×D11—24no—
156C22×C4×D11—44no—
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2312yes—
159C22×C4×D11C2312yes—
160C22×C4×D11C2312yes—
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2312yes—
164C11×#123—44no—
165C11×#120—24no—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177#67006—24no—
178C2×C22⋊Dic11—24no—
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2311yescharacteristic
187C2×C22⋊Dic11C2311yescharacteristic
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2312yes—
191C2×C22⋊Dic11C2312yes—
192#66991—24no—
193#66991—24no—
194#66990—24no—
195#66990—24no—
196#66988—24no—
197#66982—44no—
198C4×C22⋊D11—28no—
199C4×C22⋊D11—28no—
200C4×C22⋊D11—28no—
201C4×C22⋊D11—28no—
202C2×(C2×D11)⋊C4—24no—
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2311yescharacteristic
209C2×(C2×D11)⋊C4C2311yescharacteristic
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×C4⋊Dic11C2311yescharacteristic
216C2×C4⋊Dic11C2311yescharacteristic
217C2×C4⋊Dic11C2312yes—
218C2×C4⋊Dic11C2312yes—
219C2×Dic11⋊C4—24no—
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×Dic11—24no—
229C2×C4×Dic11C2312yes—
230C2×C4×Dic11C2312yes—
231C4⋊C4×D11—44no—
232#66939—24no—
233#66937—24no—
234#66937—24no—
235#66936—24no—
236#66936—24no—
237C22⋊C4×D11—24no—
238C22⋊C4×D11—24no—
239C22⋊C4×D11—24no—
240C22⋊C4×D11—44no—
241C11×#95C2312yes—
242C11×#95C2312yes—
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261#34983—111nomaximal, Sylow
262C24×C11—22no—
263C24×C11—22no—
264C24×C11—42no—
265C24×C11—42no—
266C24×C11C2×D414yes—
267C24×C11C2411yescharacteristic
268C24×C11C2411yescharacteristic
269C24×C11C2411yescharacteristic
270C24×C11C2411yescharacteristic
271C23×D11—22no—
272C23×D11—22no—
273C23×D11—22no—
274C23×D11—42no—
275C23×D11—42no—
276C23×D11—42no—
277C23×D11—42no—
278C23×D11C2×D414yes—
279C23×D11#4114yes—
280C23×D11#4114yes—
281C23×D11C2411yescharacteristic
282C23×D11C2411yescharacteristic
283C23×D11C2411yescharacteristic
284C2×D4×C11—22no—
285C2×D4×C11—22no—
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11—22no—
289C2×D4×C11—42no—
290C2×D4×C11—42no—
291C22×C4×C11—22no—
292C22×C4×C11—24no—
293C22×C4×C11—22no—
294C22×C4×C11—24no—
295C22×C4×C11—24no—
296C22×C4×C11—24no—
297C22×C4×C11—24no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11—42no—
301C22×C4×C11—416no—
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2412yes—
304C22×C4×C11C2412yes—
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2412yes—
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2412yes—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—232no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—22no—
320C2×C22⋊D11—22no—
321C2×C22⋊D11—22no—
322C2×C22⋊D11—22no—
323C2×C22⋊D11—22no—
324C2×C22⋊D11—22no—
325C2×C22⋊D11—22no—
326C2×C22⋊D11—42no—
327C2×C22⋊D11—42no—
328C2×C22⋊D11C2×D414yes—
329C2×C22⋊D11C2×D414yes—
330C2×C22⋊D11C2×D414yes—
331C2×C22⋊D11C2×D414yes—
332C22×Dic11—22no—
333C22×Dic11—22no—
334C22×Dic11—22no—
335C22×Dic11—22no—
336C22×Dic11—42no—
337C22×Dic11—42no—
338C22×Dic11C2×D414yes—
339C22×Dic11C2411yescharacteristic
340C22×Dic11C2412yes—
341C22×Dic11C2412yes—
342C22×Dic11C2411yescharacteristic
343C22×Dic11C2412yes—
344C22×Dic11C2412yes—
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2411yescharacteristic
347C22×Dic11C2411yescharacteristic
348D4×D11—416no—
349C2×D44—22no—
350C2×D44—22no—
351C2×D44—22no—
352C2×C4×D11—22no—
353C2×C4×D11—24no—
354C2×C4×D11—24no—
355C2×C4×D11—22no—
356C2×C4×D11—22no—
357C2×C4×D11—24no—
358C2×C4×D11—22no—
359C2×C4×D11—22no—
360C2×C4×D11—24no—
361C2×C4×D11—24no—
362C2×C4×D11—24no—
363C2×C4×D11—42no—
364C2×C4×D11—42no—
365C2×C4×D11—42no—
366C2×C4×D11—42no—
367C2×C4×D11—42no—
368C2×C4×D11—42no—
369C2×C4×D11—42no—
370C2×C4×D11—42no—
371C2×C4×D11—416no—
372C11×C4⋊C4—24no—
373C11×C4⋊C4—42no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—22no—
377C11×C22⋊C4—22no—
378C11×C22⋊C4—22no—
379C11×C22⋊C4—24no—
380C11×C22⋊C4—42no—
381C11×C22⋊C4—42no—
382C11×C22⋊C4—42no—
383C22⋊Dic11—22no—
384C22⋊Dic11—22no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—22no—
388C22⋊Dic11—24no—
389C22⋊Dic11—24no—
390C22⋊Dic11—22no—
391C22⋊Dic11—22no—
392C22⋊Dic11—42no—
393C22⋊Dic11—42no—
394C22⋊Dic11—42no—
395C22⋊Dic11—42no—
396(C2×D11)⋊C4—22no—
397(C2×D11)⋊C4—22no—
398(C2×D11)⋊C4—22no—
399(C2×D11)⋊C4—22no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—24no—
402(C2×D11)⋊C4—24no—
403(C2×D11)⋊C4—24no—
404(C2×D11)⋊C4—24no—
405(C2×D11)⋊C4—42no—
406(C2×D11)⋊C4—42no—
407(C2×D11)⋊C4—42no—
408C4⋊Dic11—22no—
409C4⋊Dic11—22no—
410C4⋊Dic11—42no—
411C4⋊Dic11—42no—
412Dic11⋊C4—22no—
413Dic11⋊C4—22no—
414Dic11⋊C4—24no—
415Dic11⋊C4—24no—
416Dic11⋊C4—24no—
417Dic11⋊C4—42no—
418Dic11⋊C4—42no—
419Dic11⋊C4—42no—
420C4×Dic11—24no—
421C4×Dic11—24no—
422C2×#534—111no—
423C22×C4×D4—111no—
424#2853—111no—
425#2853—111no—
426#2849—111no—
427#2849D1111yescharacteristic, complemented
428#2623—111no—
429#2623—111no—
430#2622—111no—
431#2622—111no—
432#2444—112no—
433#2444—112no—
434#2443—112no—
435#2443—112no—
436#2419—112no—
437#2419—112no—
438#2418—112no—
439#2418—112no—
440#2315—111no—
441#2308—111no—
442#2308—111no—
443C2×#386—111no—
444C2×#385—111no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—28no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—21no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—21no—
457C23×C11—21no—
458C23×C11—21no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11—44no—
462C23×C11—44no—
463C23×C11—48no—
464C23×C11—48no—
465C23×C11C22×D412yes—
466C23×C11C22×D412yes—
467C23×C11C22×D412yes—
468C23×C11C2×#4112yes—
469C23×C11C2×#4112yes—
470C23×C11C2511yescharacteristic
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—21no—
476C22×D11—21no—
477C22×D11—21no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—44no—
481C22×D11—44no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11—48no—
485C22×D11—44no—
486C22×D11—82no—
487C22×D11—82no—
488C22×D11—84no—
489C22×D11#123116yescomplemented
490C22×D11C22×D412yes—
491C22×D11C22×D412yes—
492C22×D11C2×#4112yes—
493C22×D11C2×#4112yes—
494C22×D11C2×#4112yes—
495C22×D11C2×#4112yes—
496D4×C11—44no—
497D4×C11—82no—
498D4×C11—82no—
499C2×C4×C11—28no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—21no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—48no—
519C2×C4×C11—48no—
520C2×C4×C11—44no—
521C2×C4×C11H(5,𝔽2)14yes—
522C22⋊D11—28no—
523C22⋊D11—28no—
524C22⋊D11—28no—
525C22⋊D11—28no—
526C22⋊D11—44no—
527C22⋊D11—44no—
528C22⋊D11—82no—
529C22⋊D11—82no—
530C2×Dic11—28no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—21no—
538C2×Dic11—21no—
539C2×Dic11—21no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—44no—
555C2×Dic11—44no—
556C2×Dic11C22×D412yes—
557C2×Dic11C22×D412yes—
558D44—44no—
559C4×D11—48no—
560C4×D11—48no—
561C4×D11—48no—
562C4×D11—44no—
563C4×D11—82no—
564C4×D11—82no—
565C4×D11—84no—
566C23×D4—111no—
567C23×D4—111no—
568C24×C4—111no—
569C24×C4C2×D1111yescharacteristic, complemented
570#534—228no—
571C2×#123—111no—
572C2×#123—112no—
573C2×#123—111no—
574C2×#123—111no—
575C2×#123—111no—
576C2×#123C2×D1112yescomplemented
577C2×#121—111no—
578C2×#121—111no—
579C2×#121—111no—
580C2×#121—111no—
581C2×#120—111no—
582C2×#120—111no—
583C2×#120—111no—
584C2×#120C2×D1111yescharacteristic
585C2×C4×D4—112no—
586C2×C4×D4—112no—
587C2×C4×D4—112no—
588C2×C4×D4—112no—
589C2×C4×D4—228no—
590C22×C4⋊C4—111no—
591C22×C4⋊C4—112no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C22⋊C4—111no—
597C22×C22⋊C4—112no—
598C22×C42—111no—
599#400—112no—
600#400—112no—
601#399—112no—
602#399—112no—
603#398—112no—
604#398—112no—
605#397—112no—
606#397—112no—
607#397—112no—
608#397—112no—
609#397—112no—
610#397—112no—
611#394—112no—
612#394—112no—
613#394—112no—
614#394—112no—
615#388—112no—
616#388—112no—
617#388—112no—
618#388—112no—
619#387—112no—
620#387—112no—
621#387—112no—
622#387—112no—
623#386—111no—
624#386—111no—
625#386—111no—
626#386—111no—
627#386—112no—
628#386—111no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386—112no—
634#386—111no—
635#386—112no—
636#386—112no—
637#386—112no—
638#386C2×D1111yescharacteristic
639#386C2×D1111yescharacteristic
640#386C2×D1112yescomplemented
641#385—111no—
642#385—111no—
643#385—112no—
644#385—112no—
645#385—112no—
646#385—111no—
647#385—111no—
648#385—111no—
649#385—111no—
650#385—112no—
651#385—112no—
652#385C2×D1111yescharacteristic, complemented
653#385C2×D1111yescharacteristic, complemented
654#385C2×D1112yescomplemented
655#381—112no—
656#381—111no—
657#381—111no—
658#381—112no—
659#381C2×D1112yescomplemented
660#380—112no—
661#380—112no—
662#379—111no—
663#379—112no—
664#379C2×D1111yescharacteristic, complemented
665C2×#95—112no—
666C2×#95—112no—
667C22×C11—24no—
668C22×C11—22no—
669C22×C11—22no—
670C22×C11—24no—
671C22×C11—22no—
672C22×C11—22no—
673C22×C11—22no—
674C22×C11—22no—
675C22×C11—22no—
676C22×C11—22no—
677C22×C11—416no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11—41no—
683C22×C11—42no—
684C22×C11—41no—
685C22×C11—41no—
686C22×C11—42no—
687C22×C11C2×#12314yes—
688C22×C11C23×D411yescharacteristic
689C22×C11C22×#4111yescharacteristic
690C22×C11C22×#4111yescharacteristic
691C22×C11C2×H(5,𝔽2)12yes—
692C22×C11#58512yes—
693C2×D11—24no—
694C2×D11—24no—
695C2×D11—22no—
696C2×D11—22no—
697C2×D11—22no—
698C2×D11—22no—
699C2×D11—24no—
700C2×D11—24no—
701C2×D11—416no—
702C2×D11—41no—
703C2×D11—42no—
704C2×D11—41no—
705C2×D11—41no—
706C2×D11—42no—
707C2×D11—88no—
708C2×D11C2×#12314yes—
709C2×D11C2×#12314yes—
710C4×C11—24no—
711C4×C11—41no—
712C4×C11—42no—
713C4×C11—42no—
714C4×C11—41no—
715C4×C11—41no—
716C4×C11—42no—
717Dic11—22no—
718Dic11—22no—
719Dic11—41no—
720Dic11—42no—
721Dic11—42no—
722Dic11—41no—
723Dic11—41no—
724Dic11—42no—
725Dic11—42no—
726C25—111no—
727C25—111no—
728C25C22×D1111yescharacteristic
729C22×D4—118no—
730C22×D4—111no—
731C22×D4—111no—
732C22×D4—111no—
733C22×D4—111no—
734C22×D4—111no—
735C22×D4—111no—
736C22×D4—111no—
737C22×D4—111no—
738C22×D4—111no—
739C22×D4—224no—
740C22×D4—224no—
741C22×D4—224no—
742C22×D4—224no—
743C22×D4—224no—
744C22×D4C22×D1111yescharacteristic
745C22×D4C22×D1111yescharacteristic
746C22×D4C22×D1111yescharacteristic
747C23×C4—24no—
748C23×C4—44no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4—112no—
754C23×C4—112no—
755C23×C4—112no—
756C23×C4—111no—
757C23×C4—112no—
758C23×C4—111no—
759C23×C4—224no—
760C23×C4—444no—
761C23×C4C22×D1111yescharacteristic
762C23×C4C22×D1112yes—
763C23×C4C22×D1112yes—
764C23×C4C22×D1111yescharacteristic
765#123—44no—
766#123—224no—
767#123—224no—
768#123—224no—
769#123—224no—
770#123—444no—
771#121—224no—
772#121—224no—
773#121—224no—
774#121—224no—
775#120—24no—
776#120—224no—
777#120—224no—
778#120—224no—
779C4×D4—228no—
780C4×D4—228no—
781C4×D4—228no—
782C4×D4—228no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—111no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—111no—
790C2×C4⋊C4—112no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—112no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—112no—
795C2×C4⋊C4—224no—
796C2×C4⋊C4—444no—
797C2×C4⋊C4C22×D1112yes—
798C2×C4⋊C4C22×D1112yes—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—111no—
811C2×C22⋊C4—111no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—111no—
816C2×C22⋊C4—111no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—112no—
823C2×C22⋊C4—112no—
824C2×C22⋊C4—224no—
825C2×C22⋊C4—224no—
826C2×C22⋊C4—224no—
827C2×C22⋊C4—224no—
828C2×C22⋊C4—224no—
829C2×C22⋊C4—444no—
830C2×C22⋊C4C22×D1111yescharacteristic
831C2×C22⋊C4C22×D1112yes—
832C2×C22⋊C4C22×D1111yescharacteristic
833C2×C22⋊C4C22×D1111yescharacteristic
834C2×C22⋊C4C22×D1111yescharacteristic
835C2×C22⋊C4C22×D1111yescharacteristic
836C2×C22⋊C4C22×D1112yes—
837C2×C22⋊C4C22×D1112yes—
838C2×C22⋊C4C22×D1112yes—
839C2×C42—112no—
840C2×C42—112no—
841C2×C42—224no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95—112no—
855#95—112no—
856#95—112no—
857#95—112no—
858#95C22×D1112yes—
859#95C22×D1112yes—
860#95C22×D1112yes—
861#95C22×D1112yes—
862C2×C11—24no—
863C2×C11—42no—
864C2×C11—42no—
865C2×C11—81no—
866C2×C11C22×#12311yescharacteristic
867C2×C11#345912yes—
868C2×C11#348411yescharacteristic
869C2×C11#348511yescharacteristic
870C2×C11#350512yes—
871D11—24no—
872D11—24no—
873D11—81no—
874C24—22no—
875C24—22no—
876C24—42no—
877C24—42no—
878C24—111no—
879C24—111no—
880C24—114no—
881C24—114no—
882C24—114no—
883C24—111no—
884C24—222no—
885C24—222no—
886C24—222no—
887C24—442no—
888C24—442no—
889C24—442no—
890C24—442no—
891C24D4×D1114yes—
892C24C23×D1111yescharacteristic
893C24C23×D1111yescharacteristic
894C24C23×D1111yescharacteristic
895C24C23×D1111yescharacteristic
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—114no—
904C2×D4—114no—
905C2×D4—114no—
906C2×D4—114no—
907C2×D4—222no—
908C2×D4—222no—
909C2×D4—222no—
910C2×D4—2232no—
911C2×D4—222no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—222no—
915C2×D4—222no—
916C2×D4—222no—
917C2×D4—222no—
918C2×D4—222no—
919C2×D4—222no—
920C2×D4—222no—
921C2×D4—222no—
922C2×D4—222no—
923C2×D4—222no—
924C2×D4—222no—
925C2×D4—222no—
926C2×D4—222no—
927C2×D4—442no—
928C2×D4—442no—
929C2×D4—4416no—
930C22×C4—22no—
931C22×C4—24no—
932C22×C4—22no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—416no—
941C22×C4—114no—
942C22×C4—111no—
943C22×C4—111no—
944C22×C4—111no—
945C22×C4—112no—
946C22×C4—112no—
947C22×C4—111no—
948C22×C4—112no—
949C22×C4—112no—
950C22×C4—111no—
951C22×C4—224no—
952C22×C4—224no—
953C22×C4—224no—
954C22×C4—222no—
955C22×C4—222no—
956C22×C4—222no—
957C22×C4—222no—
958C22×C4—222no—
959C22×C4—224no—
960C22×C4—222no—
961C22×C4—222no—
962C22×C4—222no—
963C22×C4—222no—
964C22×C4—224no—
965C22×C4—224no—
966C22×C4—442no—
967C22×C4—442no—
968C22×C4—442no—
969C22×C4—442no—
970C22×C4—442no—
971C22×C4—442no—
972C22×C4—442no—
973C22×C4—442no—
974C22×C4—4416no—
975C22×C4—442no—
976C22×C4—442no—
977C22×C4C23×D1111yescharacteristic
978C22×C4C23×D1112yes—
979C22×C4C23×D1112yes—
980C22×C4C23×D1111yescharacteristic
981C22×C4C23×D1112yes—
982C22×C4C23×D1111yescharacteristic
983C22×C4C23×D1112yes—
984C4⋊C4—24no—
985C4⋊C4—42no—
986C4⋊C4—224no—
987C4⋊C4—224no—
988C4⋊C4—222no—
989C4⋊C4—222no—
990C4⋊C4—222no—
991C4⋊C4—222no—
992C4⋊C4—224no—
993C4⋊C4—442no—
994C4⋊C4—442no—
995C4⋊C4—442no—
996C4⋊C4—442no—
997C4⋊C4—442no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—24no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—222no—
1008C22⋊C4—222no—
1009C22⋊C4—224no—
1010C22⋊C4—224no—
1011C22⋊C4—222no—
1012C22⋊C4—222no—
1013C22⋊C4—224no—
1014C22⋊C4—224no—
1015C22⋊C4—222no—
1016C22⋊C4—222no—
1017C22⋊C4—224no—
1018C22⋊C4—224no—
1019C22⋊C4—222no—
1020C22⋊C4—222no—
1021C22⋊C4—222no—
1022C22⋊C4—222no—
1023C22⋊C4—222no—
1024C22⋊C4—224no—
1025C22⋊C4—442no—
1026C22⋊C4—442no—
1027C22⋊C4—442no—
1028C22⋊C4—442no—
1029C22⋊C4—442no—
1030C22⋊C4—442no—
1031C22⋊C4—442no—
1032C42—224no—
1033C42—224no—
1034C11#3498311yescharacteristic, complemented, Sylow
1035C23—22no—
1036C23—22no—
1037C23—28no—
1038C23—22no—
1039C23—22no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—22no—
1045C23—22no—
1046C23—21no—
1047C23—22no—
1048C23—21no—
1049C23—21no—
1050C23—22no—
1051C23—44no—
1052C23—44no—
1053C23—48no—
1054C23—48no—
1055C23—112no—
1056C23—112no—
1057C23—112no—
1058C23—112no—
1059C23—112no—
1060C23—112no—
1061C23—1116no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—221no—
1067C23—222no—
1068C23—221no—
1069C23—221no—
1070C23—222no—
1071C23—444no—
1072C23—448no—
1073C23—444no—
1074C23—448no—
1075C23—444no—
1076C23—448no—
1077C23—884no—
1078C23—882no—
1079C23—882no—
1080C23C2×D4×D1112yes—
1081C23C2×D4×D1112yes—
1082C23C2×D4×D1112yes—
1083C23#41×D1112yes—
1084C23#41×D1112yes—
1085C23C24×D1111yescharacteristic
1086D4—44no—
1087D4—82no—
1088D4—82no—
1089D4—228no—
1090D4—228no—
1091D4—228no—
1092D4—228no—
1093D4—444no—
1094D4—444no—
1095D4—444no—
1096D4—882no—
1097D4—882no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—48no—
1118C2×C4—48no—
1119C2×C4—44no—
1120C2×C4—112no—
1121C2×C4—112no—
1122C2×C4—228no—
1123C2×C4—221no—
1124C2×C4—221no—
1125C2×C4—221no—
1126C2×C4—221no—
1127C2×C4—222no—
1128C2×C4—221no—
1129C2×C4—221no—
1130C2×C4—222no—
1131C2×C4—221no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—222no—
1137C2×C4—222no—
1138C2×C4—222no—
1139C2×C4—221no—
1140C2×C4—221no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—222no—
1146C2×C4—448no—
1147C2×C4—448no—
1148C2×C4—444no—
1149C2×C4—448no—
1150C2×C4—444no—
1151C2×C4—444no—
1152C2×C4—884no—
1153C2×C4—882no—
1154C2×C4—882no—
1155C2×C4#6703714yes—
1156C22—24no—
1157C22—22no—
1158C22—22no—
1159C22—24no—
1160C22—22no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—416no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—41no—
1173C22—41no—
1174C22—42no—
1175C22—41no—
1176C22—114no—
1177C22—114no—
1178C22—224no—
1179C22—224no—
1180C22—222no—
1181C22—222no—
1182C22—222no—
1183C22—222no—
1184C22—224no—
1185C22—224no—
1186C22—4416no—
1187C22—442no—
1188C22—441no—
1189C22—441no—
1190C22—442no—
1191C22—441no—
1192C22—888no—
1193C22D11×#12314yes—
1194C22C22×D4×D1111yescharacteristic
1195C22C2×#6703712yes—
1196C22C2×#41×D1111yescharacteristic
1197C22C2×#41×D1111yescharacteristic
1198C22#1062345312yes—
1199C4—24no—
1200C4—42no—
1201C4—42no—
1202C4—41no—
1203C4—41no—
1204C4—42no—
1205C4—41no—
1206C4—222no—
1207C4—222no—
1208C4—442no—
1209C4—442no—
1210C4—441no—
1211C4—442no—
1212C4—441no—
1213C4—442no—
1214C4—441no—
1215C2—24no—
1216C2—42no—
1217C2—42no—
1218C2—81no—
1219C2—224no—
1220C2—224no—
1221C2—881no—
1222C2C2×D11×#12311yescharacteristic
1223C2#1308202312yes—
1224C2#1308224511yescharacteristic
1225C2#1308225411yescharacteristic
1226C2#1308244412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2849C2
prime radicalC2×#10623120C2
hypercenter#2849D11
hypocenterC11#34983
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2849

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. #13076941C2semidirect
4. #13076937C2semidirect
5. #13076908C2semidirect
6. #13074402C2semidirect
7. #13074400C2semidirect
8. #13074392C2semidirect
9. #13074391C2semidirect
10. #13072365C2semidirect
11. #13072363C2semidirect
12. #13072350C2semidirect
13. #13072348C2semidirect
14. #13072092C2semidirect
15. #13072090C2semidirect
16. #13072077C2semidirect
17. #13072075C2semidirect
18. #13071227C2semidirect
19. #13071192C2semidirect
20. #13071190C2semidirect
21. D11×#386C2semidirect
22. D11×#385C2semidirect
23. C11×#2849C2semidirect
24. C24×C4×C11C22semidirect
28. C2×C11×#123C22semidirect
31. C22×C22⋊Dic11C22semidirect
37. C2×#66982C22semidirect
41. C2×C4×C22⋊D11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. C22×C4×Dic11C22semidirect
47. C2×C4⋊C4×D11C22semidirect
56. C2×C22⋊C4×D11C22semidirect
59. C11×#386C22semidirect
60. C11×#385C22semidirect
61. C11×#385C22semidirect
62. C11×#385C22semidirect
63. C11×#381C22semidirect
64. C11×#379C22semidirect
65. #10622860C22semidirect
66. #10622835C22semidirect
67. #10622835C22semidirect
72. #10622826C22semidirect
73. #10622824C22semidirect
74. #10622823C22semidirect
75. #10622823C22semidirect
76. #10622823C22semidirect
77. #10622605C22semidirect
78. #10622603C22semidirect
79. #10622602C22semidirect
80. #10622602C22semidirect
81. #10622600C22semidirect
82. #10622597C22semidirect
83. #10622594C22semidirect
84. #10622574C22semidirect
85. #10622574C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
92. #10622569C22semidirect
93. #10622569C22semidirect
94. #10622568C22semidirect
95. #10622566C22semidirect
96. #10622566C22semidirect
97. #10622565C22semidirect
98. #10622565C22semidirect
99. #10622565C22semidirect
100. #10622564C22semidirect
101. #10622563C22semidirect
102. #10622563C22semidirect
103. #10622562C22semidirect
104. #10622559C22semidirect
105. #10622559C22semidirect
106. #10622558C22semidirect
107. #10622556C22semidirect
108. #10622556C22semidirect
109. #10622288C22semidirect
110. #10622282C22semidirect
111. #10622281C22semidirect
112. #10622281C22semidirect
113. #10622280C22semidirect
114. #10622278C22semidirect
115. #10622278C22semidirect
116. #10622277C22semidirect
117. D11×#95C22semidirect
118. D11×#95C22semidirect
119. #10622273C22semidirect
120. #10622271C22semidirect
121. #10622270C22semidirect
122. #10622268C22semidirect
123. #10622267C22semidirect
124. #10622265C22semidirect
427. #2849D11semidirect
489. C22×D11#123semidirect
569. C24×C4C2×D11semidirect
576. C2×#123C2×D11semidirect
640. #386C2×D11semidirect
652. #385C2×D11semidirect
653. #385C2×D11semidirect
654. #385C2×D11semidirect
659. #381C2×D11semidirect
664. #379C2×D11semidirect
1034. C11#34983semidirect

Maximal subgroups

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

subgroupindex
C2×#106231202
C22×C4×C22⋊D112
#130769412
#130769372
#130769082
#130744022
#130744002
#130743922
#130743912
#130723652
#130723632
#130723502
#130723482
#130720922
#130720902
#130720772
#130720752
#130712272
#130711922
#130711902
D11×#3862
D11×#3852
C11×#28492
#3498311