Finite Group Databasebeta

← #14926331

Subgroups — #14926331

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×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13076941C211yesmaximal, characteristic, complemented
4#13076937C211yesmaximal, characteristic, complemented
5#13076910C211yesmaximal, characteristic, complemented
6#13076906C211yesmaximal, characteristic, complemented
7#13074402C211yesmaximal, characteristic, complemented
8#13074400C211yesmaximal, characteristic, complemented
9#13074389C211yesmaximal, characteristic, complemented
10#13072361C212yesmaximal, complemented
11#13072359C212yesmaximal, complemented
12#13072346C212yesmaximal, complemented
13#13072344C212yesmaximal, complemented
14#13072088C212yesmaximal, complemented
15#13072086C212yesmaximal, complemented
16#13072073C212yesmaximal, complemented
17#13072071C212yesmaximal, complemented
18#13071227C211yesmaximal, characteristic, complemented
19#13071192C211yesmaximal, characteristic, complemented
20#13071190C211yesmaximal, characteristic, complemented
21D11×#386C211yesmaximal, characteristic, complemented
22D11×#385C211yesmaximal, characteristic, complemented
23C11×#2622C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic, complemented
26C22×D4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic, complemented
30C2×#67006C2211yescharacteristic
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic
33C2×#66990C2211yescharacteristic
34C2×#66990C2211yescharacteristic
35C2×#66988C2211yescharacteristic
36C2×#66988C2212yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic, complemented
39C22×C4×Dic11C2211yescharacteristic, complemented
40#10623120—28no—
41C2×C4⋊C4×D11C2212yescomplemented
42C2×#66939C2211yescharacteristic
43C2×#66939C2212yescomplemented
44C2×#66937C2211yescharacteristic
45C2×#66937C2211yescharacteristic
46C2×#66936C2211yescharacteristic
47C2×#66936C2211yescharacteristic
48C2×(C22⋊D11)⋊C4—28no—
49C2×(C22⋊D11)⋊C4C2212yes—
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yescomplemented
52C2×(C22⋊D11)⋊C4C2212yescomplemented
53C2×C22⋊C4×D11C2211yescharacteristic
54C2×C22⋊C4×D11C2211yescharacteristic
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2212yescomplemented
57C11×#397C2212yescomplemented
58C11×#397C2212yescomplemented
59C11×#394C2212yescomplemented
60C11×#394C2212yescomplemented
61C11×#386C2211yescharacteristic
62C11×#386C2211yescharacteristic
63C11×#385C2211yescharacteristic, complemented
64C11×#385C2211yescharacteristic, complemented
65C11×#379C2211yescharacteristic, complemented
66#10622860C2211yescharacteristic, complemented
67#10622833C2211yescharacteristic
68#10622833C2211yescharacteristic
69#10622833C2212yescomplemented
70#10622826C2211yescharacteristic
71#10622826C2211yescharacteristic
72#10622823C2211yescharacteristic, complemented
73#10622823C2211yescharacteristic, complemented
74#10622605C2212yescomplemented
75#10622603C2212yescomplemented
76#10622602C2212yescomplemented
77#10622602C2212yescomplemented
78#10622600C2212yescomplemented
79#10622597C2212yescomplemented
80#10622594C2212yescomplemented
81#10622572C2212yescomplemented
82#10622572C2212yescomplemented
83#10622571C2211yescharacteristic
84#10622571C2211yescharacteristic
85#10622571C2212yescomplemented
86#10622569C2212yes—
87#10622569C2212yes—
88#10622569C2212yescomplemented
89#10622569C2212yescomplemented
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622568C2212yescomplemented
93#10622565C2212yescomplemented
94#10622565C2212yescomplemented
95#10622565C2212yescomplemented
96#10622564C2212yescomplemented
97#10622563C2211yescharacteristic, complemented
98#10622563C2211yescharacteristic, complemented
99#10622563C2212yescomplemented
100#10622562C2212yescomplemented
101#10622559C2211yescharacteristic, complemented
102#10622559C2211yescharacteristic, complemented
103#10622559C2212yescomplemented
104#10622558C2212yescomplemented
105#10622556C2211yescharacteristic, complemented
106#10622556C2211yescharacteristic, complemented
107#10622556C2212yescomplemented
108#10622556C2212yescomplemented
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×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C22×C22⋊D11—24no—
134C22×C22⋊D11—24no—
135C22×C22⋊D11D418yes—
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2311yescharacteristic
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2311yescharacteristic
144C23×Dic11—24no—
145C23×Dic11—44no—
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2312yes—
148C23×Dic11C2312yes—
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×#120—24no—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C22⋊C4—24no—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179#67006—24no—
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2311yescharacteristic
187C2×C22⋊Dic11C2311yescharacteristic
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2312yes—
191#66991—24no—
192#66991—24no—
193#66990—24no—
194#66990—24no—
195#66988—24no—
196#66988—44no—
197C2×(C2×D11)⋊C4—24no—
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2311yescharacteristic
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2312yes—
213C2×C4⋊Dic11C2312yes—
214C2×Dic11⋊C4—24no—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×C4×Dic11—24no—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226C4⋊C4×D11—44no—
227#66939—24no—
228#66939—44no—
229#66937—24no—
230#66937—24no—
231#66936—24no—
232#66936—24no—
233(C22⋊D11)⋊C4—28no—
234(C22⋊D11)⋊C4—28no—
235(C22⋊D11)⋊C4—28no—
236(C22⋊D11)⋊C4—28no—
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—22no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2411yescharacteristic
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—232no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11C2×D414yes—
322C2×C22⋊D11C2×D414yes—
323C2×C22⋊D11C2×D414yes—
324C2×C22⋊D11C2×D414yes—
325C22×Dic11—24no—
326C22×Dic11—24no—
327C22×Dic11—24no—
328C22×Dic11—22no—
329C22×Dic11—24no—
330C22×Dic11—24no—
331C22×Dic11—22no—
332C22×Dic11—22no—
333C22×Dic11—22no—
334C22×Dic11—42no—
335C22×Dic11—42no—
336C22×Dic11—42no—
337C22×Dic11—416no—
338C22×Dic11C2×D414yes—
339C22×Dic11C2411yescharacteristic
340C22×Dic11C2411yescharacteristic
341C22×Dic11C2412yes—
342C22×Dic11C2412yes—
343C22×Dic11C2412yes—
344C22×Dic11C2411yescharacteristic
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2411yescharacteristic
347C22×Dic11C2412yes—
348D4×D11—416no—
349C2×D44—22no—
350C2×D44—22no—
351C2×D44—22no—
352C2×C4×D11—24no—
353C2×C4×D11—24no—
354C2×C4×D11—24no—
355C2×C4×D11—24no—
356C2×C4×D11—22no—
357C2×C4×D11—22no—
358C2×C4×D11—22no—
359C2×C4×D11—24no—
360C2×C4×D11—22no—
361C2×C4×D11—22no—
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—42no—
373C11×C4⋊C4—42no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—24no—
377C11×C22⋊C4—22no—
378C11×C22⋊C4—22no—
379C11×C22⋊C4—22no—
380C11×C22⋊C4—22no—
381C11×C22⋊C4—42no—
382C11×C22⋊C4—42no—
383C11×C22⋊C4—42no—
384C11×C22⋊C4—42no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—24no—
388C22⋊Dic11—22no—
389C22⋊Dic11—22no—
390C22⋊Dic11—22no—
391C22⋊Dic11—22no—
392C22⋊Dic11—22no—
393C22⋊Dic11—42no—
394C22⋊Dic11—42no—
395C22⋊Dic11—42no—
396(C2×D11)⋊C4—22no—
397(C2×D11)⋊C4—22no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—22no—
400(C2×D11)⋊C4—22no—
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—24no—
411C4⋊Dic11—42no—
412Dic11⋊C4—24no—
413Dic11⋊C4—24no—
414Dic11⋊C4—22no—
415Dic11⋊C4—22no—
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#2849—111no—
428#2623—111no—
429#2623—111no—
430#2622—111no—
431#2622D1111yescharacteristic, complemented
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—22no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
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—44no—
519C2×C4×C11—44no—
520C22⋊D11—28no—
521C22⋊D11—28no—
522C22⋊D11—28no—
523C22⋊D11—28no—
524C22⋊D11—44no—
525C22⋊D11—44no—
526C22⋊D11—82no—
527C22⋊D11—82no—
528C2×Dic11—28no—
529C2×Dic11—28no—
530C2×Dic11—22no—
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—48no—
553C2×Dic11—48no—
554C2×Dic11—44no—
555C2×Dic11C22×D412yes—
556C2×Dic11C22×D412yes—
557C2×Dic11H(5,𝔽2)14yes—
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×C4—111no—
570#534—228no—
571C2×#123—111no—
572C2×#123—112no—
573C2×#123—111no—
574C2×#123—111no—
575C2×#123—111no—
576C2×#123—112no—
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—112no—
597C22×C22⋊C4C2×D1111yescharacteristic, complemented
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#397C2×D1112yescomplemented
610#397C2×D1112yescomplemented
611#394—112no—
612#394—112no—
613#394C2×D1112yescomplemented
614#394C2×D1112yescomplemented
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—112no—
626#386—111no—
627#386—111no—
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#386—112no—
639#386C2×D1111yescharacteristic
640#386C2×D1111yescharacteristic
641#385—111no—
642#385—111no—
643#385—112no—
644#385—112no—
645#385—111no—
646#385—111no—
647#385—111no—
648#385—111no—
649#385—112no—
650#385—112no—
651#385—112no—
652#385—112no—
653#385C2×D1111yescharacteristic, complemented
654#385C2×D1111yescharacteristic, complemented
655#381—111no—
656#381—111no—
657#381—112no—
658#381—112no—
659#381—112no—
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—41no—
711C4×C11—42no—
712C4×C11—42no—
713C4×C11—41no—
714C4×C11—42no—
715C4×C11—41no—
716C4×C11—42no—
717Dic11—22no—
718Dic11—22no—
719Dic11—24no—
720Dic11—41no—
721Dic11—42no—
722Dic11—41no—
723Dic11—42no—
724Dic11—41no—
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—111no—
748C23×C4—111no—
749C23×C4—112no—
750C23×C4—112no—
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—224no—
761C23×C4—444no—
762C23×C4—444no—
763C23×C4C22×D1111yescharacteristic
764C23×C4C22×D1111yescharacteristic
765#123—224no—
766#123—224no—
767#123—224no—
768#123—224no—
769#123—444no—
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—112no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—111no—
790C2×C4⋊C4—111no—
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—24no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—112no—
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—224no—
824C2×C22⋊C4—224no—
825C2×C22⋊C4—224no—
826C2×C22⋊C4—224no—
827C2×C22⋊C4—444no—
828C2×C22⋊C4C22×D1111yescharacteristic
829C2×C22⋊C4C22×D1111yescharacteristic
830C2×C22⋊C4C22×D1111yescharacteristic
831C2×C22⋊C4C22×D1112yes—
832C2×C22⋊C4C22×D1112yes—
833C2×C22⋊C4C22×D1111yescharacteristic
834C2×C22⋊C4C22×D1111yescharacteristic
835C2×C22⋊C4C22×D1112yes—
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—22no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—114no—
935C22×C4—111no—
936C22×C4—111no—
937C22×C4—112no—
938C22×C4—111no—
939C22×C4—112no—
940C22×C4—112no—
941C22×C4—111no—
942C22×C4—112no—
943C22×C4—111no—
944C22×C4—224no—
945C22×C4—224no—
946C22×C4—224no—
947C22×C4—224no—
948C22×C4—224no—
949C22×C4—222no—
950C22×C4—222no—
951C22×C4—222no—
952C22×C4—222no—
953C22×C4—222no—
954C22×C4—224no—
955C22×C4—224no—
956C22×C4—224no—
957C22×C4—224no—
958C22×C4—222no—
959C22×C4—222no—
960C22×C4—222no—
961C22×C4—222no—
962C22×C4—224no—
963C22×C4—224no—
964C22×C4—442no—
965C22×C4—442no—
966C22×C4—442no—
967C22×C4—442no—
968C22×C4—442no—
969C22×C4—442no—
970C22×C4—442no—
971C22×C4—442no—
972C22×C4—4416no—
973C22×C4—442no—
974C22×C4—442no—
975C22×C4—442no—
976C22×C4—4416no—
977C22×C4C23×D1111yescharacteristic
978C22×C4C23×D1112yes—
979C22×C4C23×D1112yes—
980C22×C4C23×D1111yescharacteristic
981C22×C4C23×D1112yes—
982C22×C4C23×D1112yes—
983C22×C4C23×D1111yescharacteristic
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—224no—
987C4⋊C4—224no—
988C4⋊C4—224no—
989C4⋊C4—224no—
990C4⋊C4—222no—
991C4⋊C4—222no—
992C4⋊C4—222no—
993C4⋊C4—222no—
994C4⋊C4—442no—
995C4⋊C4—442no—
996C4⋊C4—442no—
997C4⋊C4—442no—
998C22⋊C4—24no—
999C22⋊C4—24no—
1000C22⋊C4—22no—
1001C22⋊C4—22no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—224no—
1010C22⋊C4—222no—
1011C22⋊C4—222no—
1012C22⋊C4—224no—
1013C22⋊C4—224no—
1014C22⋊C4—222no—
1015C22⋊C4—222no—
1016C22⋊C4—224no—
1017C22⋊C4—224no—
1018C22⋊C4—224no—
1019C22⋊C4—222no—
1020C22⋊C4—222no—
1021C22⋊C4—222no—
1022C22⋊C4—222no—
1023C22⋊C4—222no—
1024C22⋊C4—222no—
1025C22⋊C4—222no—
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—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—22no—
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—221no—
1068C23—221no—
1069C23—222no—
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—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—44no—
1118C2×C4—44no—
1119C2×C4—112no—
1120C2×C4—112no—
1121C2×C4—114no—
1122C2×C4—228no—
1123C2×C4—228no—
1124C2×C4—222no—
1125C2×C4—221no—
1126C2×C4—221no—
1127C2×C4—221no—
1128C2×C4—221no—
1129C2×C4—222no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—222no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—221no—
1138C2×C4—222no—
1139C2×C4—222no—
1140C2×C4—222no—
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—448no—
1151C2×C4—448no—
1152C2×C4—444no—
1153C2×C4—884no—
1154C2×C4—882no—
1155C2×C4—882no—
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×#41×D1111yescharacteristic
1196C22C2×#41×D1111yescharacteristic
1197C22D11×H(5,𝔽2)12yes—
1198C22#1062345512yes—
1199C4—42no—
1200C4—42no—
1201C4—41no—
1202C4—42no—
1203C4—41no—
1204C4—42no—
1205C4—41no—
1206C4—224no—
1207C4—222no—
1208C4—222no—
1209C4—442no—
1210C4—442no—
1211C4—441no—
1212C4—441no—
1213C4—442no—
1214C4—441no—
1215C2—24no—
1216C2—42no—
1217C2—42no—
1218C2—81no—
1219C2—224no—
1220C2—224no—
1221C2—881no—
1222C2C2×D11×#12311yescharacteristic
1223C2#1308202712yes—
1224C2#1308224811yescharacteristic
1225C2#1308225711yescharacteristic
1226C2#1308245412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2622C2
prime radicalC2×#10623120C2
hypercenter#2622D11
hypocenterC11#34983
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2622

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13076941C2semidirect
4. #13076937C2semidirect
5. #13076910C2semidirect
6. #13076906C2semidirect
7. #13074402C2semidirect
8. #13074400C2semidirect
9. #13074389C2semidirect
10. #13072361C2semidirect
11. #13072359C2semidirect
12. #13072346C2semidirect
13. #13072344C2semidirect
14. #13072088C2semidirect
15. #13072086C2semidirect
16. #13072073C2semidirect
17. #13072071C2semidirect
18. #13071227C2semidirect
19. #13071192C2semidirect
20. #13071190C2semidirect
21. D11×#386C2semidirect
22. D11×#385C2semidirect
23. C11×#2622C2semidirect
25. C24×Dic11C22semidirect
29. C22×C11×C22⋊C4C22semidirect
36. C2×#66988C22semidirect
38. C22×Dic11⋊C4C22semidirect
39. C22×C4×Dic11C22semidirect
41. C2×C4⋊C4×D11C22semidirect
43. C2×#66939C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
52. C2×(C22⋊D11)⋊C4C22semidirect
56. C2×C22⋊C4×D11C22semidirect
57. C11×#397C22semidirect
58. C11×#397C22semidirect
59. C11×#394C22semidirect
60. C11×#394C22semidirect
63. C11×#385C22semidirect
64. C11×#385C22semidirect
65. C11×#379C22semidirect
66. #10622860C22semidirect
69. #10622833C22semidirect
72. #10622823C22semidirect
73. #10622823C22semidirect
74. #10622605C22semidirect
75. #10622603C22semidirect
76. #10622602C22semidirect
77. #10622602C22semidirect
78. #10622600C22semidirect
79. #10622597C22semidirect
80. #10622594C22semidirect
81. #10622572C22semidirect
82. #10622572C22semidirect
85. #10622571C22semidirect
88. #10622569C22semidirect
89. #10622569C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
92. #10622568C22semidirect
93. #10622565C22semidirect
94. #10622565C22semidirect
95. #10622565C22semidirect
96. #10622564C22semidirect
97. #10622563C22semidirect
98. #10622563C22semidirect
99. #10622563C22semidirect
100. #10622562C22semidirect
101. #10622559C22semidirect
102. #10622559C22semidirect
103. #10622559C22semidirect
104. #10622558C22semidirect
105. #10622556C22semidirect
106. #10622556C22semidirect
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
431. #2622D11semidirect
489. C22×D11#123semidirect
597. C22×C22⋊C4C2×D11semidirect
609. #397C2×D11semidirect
610. #397C2×D11semidirect
613. #394C2×D11semidirect
614. #394C2×D11semidirect
653. #385C2×D11semidirect
654. #385C2×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×(C22⋊D11)⋊C42
#130769412
#130769372
#130769102
#130769062
#130744022
#130744002
#130743892
#130723612
#130723592
#130723462
#130723442
#130720882
#130720862
#130720732
#130720712
#130712272
#130711922
#130711902
D11×#3862
D11×#3852
C11×#26222
#3498311