Finite Group Databasebeta

← #14926336

Subgroups — #14926336

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×#10623184C211yesmaximal, characteristic
2C22×#66946C211yesmaximal, characteristic, complemented
3#13076939C211yesmaximal, characteristic, complemented
4#13076935C211yesmaximal, characteristic, complemented
5#13076911C211yesmaximal, characteristic, complemented
6#13076907C211yesmaximal, characteristic, complemented
7#13074396C211yesmaximal, characteristic, complemented
8#13074394C211yesmaximal, characteristic, complemented
9#13074393C211yesmaximal, characteristic, complemented
10#13072369C212yesmaximal, complemented
11#13072367C212yesmaximal, complemented
12#13072354C212yesmaximal, complemented
13#13072352C212yesmaximal, complemented
14#13072096C212yesmaximal, complemented
15#13072094C212yesmaximal, complemented
16#13072081C212yesmaximal, complemented
17#13072079C212yesmaximal, complemented
18#13071227C211yesmaximal, characteristic, complemented
19#13071193C211yesmaximal, characteristic, complemented
20#13071190C211yesmaximal, characteristic, complemented
21D11×#386C211yesmaximal, characteristic, complemented
22D11×#385C211yesmaximal, characteristic, complemented
23C11×#2623C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic, complemented
28C2×C11×#123C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic, complemented
30C2×#66990C2211yescharacteristic
31C2×#66982C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
34C22×C4×Dic11C2211yescharacteristic, complemented
35#10623184—28no—
36C2×#66948C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66947C2211yescharacteristic
39C2×#66947C2211yescharacteristic
40C2×#66947C2212yescomplemented
41C2×#66946—28no—
42C2×#66946C2212yes—
43C2×#66946C2212yes—
44C2×#66946C2212yescomplemented
45C2×#66946C2212yescomplemented
46C2×C4⋊C4×D11C2212yescomplemented
47C2×#66937C2211yescharacteristic
48C2×#66937C2211yescharacteristic
49C2×#66936C2212yescomplemented
50C2×#66935C2211yescharacteristic
51C2×#66935C2211yescharacteristic
52C2×#66935C2211yescharacteristic
53C2×C22⋊C4×D11C2211yescharacteristic
54C2×C22⋊C4×D11C2211yescharacteristic
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2212yescomplemented
57C11×#400C2212yescomplemented
58C11×#399C2212yescomplemented
59C11×#398C2212yescomplemented
60C11×#397C2212yescomplemented
61C11×#386C2211yescharacteristic
62C11×#386C2211yescharacteristic
63C11×#385C2211yescharacteristic, complemented
64C11×#385C2211yescharacteristic, complemented
65C11×#381C2211yescharacteristic, complemented
66#10622833C2211yescharacteristic
67#10622833C2211yescharacteristic
68#10622826C2211yescharacteristic
69#10622826C2211yescharacteristic
70#10622824C2211yescharacteristic, complemented
71#10622823C2211yescharacteristic, complemented
72#10622823C2211yescharacteristic, complemented
73#10622606C2212yescomplemented
74#10622606C2212yescomplemented
75#10622605C2212yescomplemented
76#10622604C2212yescomplemented
77#10622602C2212yescomplemented
78#10622602C2212yescomplemented
79#10622602C2212yescomplemented
80#10622600C2212yescomplemented
81#10622595C2212yescomplemented
82#10622593C2212yescomplemented
83#10622591C2212yescomplemented
84#10622591C2212yescomplemented
85#10622574C2212yescomplemented
86#10622572C2212yescomplemented
87#10622571C2211yescharacteristic
88#10622571C2211yescharacteristic
89#10622569C2212yescomplemented
90#10622569C2212yescomplemented
91#10622569C2212yescomplemented
92#10622568C2212yescomplemented
93#10622568C2211yescharacteristic, complemented
94#10622568C2211yescharacteristic, complemented
95#10622563C2211yescharacteristic, complemented
96#10622563C2211yescharacteristic, complemented
97#10622559C2211yescharacteristic, complemented
98#10622559C2211yescharacteristic, complemented
99#10622557C2212yescomplemented
100#10622557C2212yescomplemented
101#10622288C2212yescomplemented
102#10622288C2212yescomplemented
103#10622287C2212yescomplemented
104#10622285C2212yescomplemented
105#10622283C2212yescomplemented
106#10622283C2212yescomplemented
107#10622281C2212yescomplemented
108#10622281C2212yescomplemented
109#10622281C2212yescomplemented
110#10622280C2212yescomplemented
111#10622278C2212yes—
112#10622278C2212yes—
113#10622278C2212yescomplemented
114#10622278C2212yescomplemented
115#10622278C2212yescomplemented
116#10622278C2212yescomplemented
117#10622278C2212yescomplemented
118#10622277C2212yescomplemented
119#10622277C2212yescomplemented
120#10622277C2212yescomplemented
121D11×#95C2212yescomplemented
122D11×#95C2212yescomplemented
123#10622266C2212yescomplemented
124#10622266C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C2×D4×D11—24no—
139C2×D4×D11—24no—
140C2×D4×D11—24no—
141C22×D44—24no—
142C22×D44—24no—
143C22×D44D418yes—
144C22×D44C2311yescharacteristic
145C22×D44C2311yescharacteristic
146C22×D44C2311yescharacteristic
147C22×D44C2311yescharacteristic
148C22×D44C2311yescharacteristic
149C22×D44C2311yescharacteristic
150C22×D44C2311yescharacteristic
151C22×C4×D11—24no—
152C22×C4×D11—24no—
153C22×C4×D11—44no—
154C22×C4×D11—44no—
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2312yes—
157C22×C4×D11C2312yes—
158C22×C4×D11C2312yes—
159C22×C4×D11C2312yes—
160C22×C4×D11C2312yes—
161C22×C4×D11C2311yescharacteristic
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2312yes—
164C11×#123—24no—
165C2×C11×C4⋊C4—24no—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C4⋊C4C2311yescharacteristic
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C4⋊C4C2312yes—
171C2×C11×C4⋊C4C2312yes—
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2311yescharacteristic
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2311yescharacteristic
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184#66990—24no—
185#66982—24no—
186C2×(C2×D11)⋊C4—24no—
187C2×(C2×D11)⋊C4—24no—
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
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—
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2312yes—
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×C4×Dic11—24no—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221#66948—24no—
222#66948—24no—
223#66947—24no—
224#66947—24no—
225#66947—44no—
226#66946—28no—
227#66946—28no—
228#66946—28no—
229#66946—28no—
230C4⋊C4×D11—44no—
231#66937—24no—
232#66937—24no—
233#66936—44no—
234#66935—24no—
235#66935—24no—
236#66935—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×C11C2411yescharacteristic
263C24×C11C2411yescharacteristic
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—42no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11—42no—
275C23×D11C2×D414yes—
276C23×D11C2×D414yes—
277C23×D11#4114yes—
278C23×D11#4114yes—
279C23×D11C2411yescharacteristic
280C23×D11C2411yescharacteristic
281C23×D11C2411yescharacteristic
282C23×D11C2411yescharacteristic
283C23×D11C2411yescharacteristic
284C2×D4×C11—22no—
285C2×D4×C11—22no—
286C2×D4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—42no—
292C22×C4×C11—42no—
293C22×C4×C11C2×D414yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C22×Dic11—24no—
314C22×Dic11—22no—
315C22×Dic11—22no—
316C22×Dic11—42no—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2412yes—
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2412yes—
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2412yes—
324D4×D11—416no—
325C2×D44—232no—
326C2×D44—22no—
327C2×D44—22no—
328C2×D44—22no—
329C2×D44—22no—
330C2×D44—22no—
331C2×D44—22no—
332C2×D44—22no—
333C2×D44—22no—
334C2×D44—22no—
335C2×D44—22no—
336C2×D44—22no—
337C2×D44—22no—
338C2×D44—22no—
339C2×D44—42no—
340C2×D44—42no—
341C2×D44C2×D414yes—
342C2×D44C2×D414yes—
343C2×D44C2×D414yes—
344C2×D44C2×D414yes—
345C2×C4×D11—24no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—22no—
354C2×C4×D11—22no—
355C2×C4×D11—22no—
356C2×C4×D11—24no—
357C2×C4×D11—22no—
358C2×C4×D11—22no—
359C2×C4×D11—24no—
360C2×C4×D11—42no—
361C2×C4×D11—42no—
362C2×C4×D11—42no—
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—416no—
371C2×C4×D11—416no—
372C11×C4⋊C4—24no—
373C11×C4⋊C4—24no—
374C11×C4⋊C4—22no—
375C11×C4⋊C4—22no—
376C11×C4⋊C4—42no—
377C11×C4⋊C4—42no—
378C11×C22⋊C4—22no—
379C11×C22⋊C4—22no—
380C11×C22⋊C4—22no—
381C11×C22⋊C4—22no—
382C11×C22⋊C4—22no—
383C11×C22⋊C4—42no—
384C11×C22⋊C4—42no—
385C22⋊Dic11—24no—
386C22⋊Dic11—22no—
387C22⋊Dic11—22no—
388C22⋊Dic11—22no—
389C22⋊Dic11—42no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—22no—
394(C2×D11)⋊C4—22no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—24no—
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—22no—
404(C2×D11)⋊C4—22no—
405(C2×D11)⋊C4—42no—
406(C2×D11)⋊C4—42no—
407(C2×D11)⋊C4—42no—
408(C2×D11)⋊C4—42no—
409(C2×D11)⋊C4—42no—
410(C2×D11)⋊C4—42no—
411(C2×D11)⋊C4—42no—
412C4⋊Dic11—24no—
413C4⋊Dic11—42no—
414Dic11⋊C4—24no—
415Dic11⋊C4—22no—
416Dic11⋊C4—22no—
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#2623D1111yescharacteristic, complemented
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—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11C22×D412yes—
453C23×C11C2×#4112yes—
454C23×C11C2×#4112yes—
455C23×C11C2511yescharacteristic
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—28no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11—44no—
477C22×D11—44no—
478C22×D11—48no—
479C22×D11—48no—
480C22×D11—48no—
481C22×D11—48no—
482C22×D11—48no—
483C22×D11—44no—
484C22×D11—82no—
485C22×D11—82no—
486C22×D11—84no—
487C22×D11#123116yescomplemented
488C22×D11C22×D412yes—
489C22×D11C22×D412yes—
490C22×D11C22×D412yes—
491C22×D11C22×D412yes—
492C22×D11C2×#4112yes—
493C22×D11C2×#4112yes—
494C22×D11C2×#4112yes—
495C22×D11C2×#4112yes—
496D4×C11—44no—
497C2×C4×C11—28no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
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—22no—
508C2×C4×C11—22no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
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—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—44no—
522C2×C4×C11—44no—
523C2×C4×C11C22×D412yes—
524C2×C4×C11C22×D412yes—
525C22⋊D11—44no—
526C22⋊D11—44no—
527C22⋊D11—82no—
528C22⋊D11—82no—
529C2×Dic11—28no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—21no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—44no—
549C2×Dic11H(5,𝔽2)14yes—
550D44—28no—
551D44—28no—
552D44—28no—
553D44—28no—
554D44—44no—
555D44—82no—
556D44—82no—
557C4×D11—48no—
558C4×D11—48no—
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—111no—
573C2×#123—111no—
574C2×#123—112no—
575C2×#123—112no—
576C2×#123C2×D1111yescharacteristic
577C2×#121—111no—
578C2×#121—111no—
579C2×#121—111no—
580C2×#121—111no—
581C2×#120—111no—
582C2×#120—111no—
583C2×#120—111no—
584C2×#120—111no—
585C2×C4×D4—112no—
586C2×C4×D4—112no—
587C2×C4×D4—112no—
588C2×C4×D4—112no—
589C2×C4×D4—228no—
590C22×C4⋊C4—112no—
591C22×C4⋊C4C2×D1111yescharacteristic, complemented
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#400C2×D1112yescomplemented
601#399—112no—
602#399C2×D1112yescomplemented
603#398—112no—
604#398C2×D1112yescomplemented
605#397—112no—
606#397—112no—
607#397—112no—
608#397—112no—
609#397—112no—
610#397C2×D1112yescomplemented
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—111no—
628#386—112no—
629#386—111no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386—112no—
634#386—112no—
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—112no—
646#385—111no—
647#385—111no—
648#385—111no—
649#385—111no—
650#385—112no—
651#385—112no—
652#385—112no—
653#385C2×D1111yescharacteristic, complemented
654#385C2×D1111yescharacteristic, complemented
655#381—111no—
656#381—112no—
657#381—112no—
658#381—112no—
659#381C2×D1111yescharacteristic, complemented
660#380—112no—
661#380—112no—
662#379—111no—
663#379—111no—
664#379—112no—
665C2×#95—112no—
666C2×#95—112no—
667C22×C11—24no—
668C22×C11—22no—
669C22×C11—22no—
670C22×C11—24no—
671C22×C11—41no—
672C22×C11—42no—
673C22×C11—41no—
674C22×C11—41no—
675C22×C11—42no—
676C22×C11C2×#12314yes—
677C22×C11C23×D411yescharacteristic
678C22×C11C22×#4111yescharacteristic
679C22×C11C22×#4111yescharacteristic
680C22×C11C2×H(5,𝔽2)12yes—
681C22×C11#58512yes—
682C2×D11—24no—
683C2×D11—24no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—24no—
689C2×D11—24no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C2×D11—22no—
696C2×D11—416no—
697C2×D11—416no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
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—22no—
711C4×C11—22no—
712C4×C11—41no—
713C4×C11—42no—
714C4×C11—42no—
715C4×C11—42no—
716C4×C11—41no—
717C4×C11—41no—
718C4×C11—42no—
719Dic11—24no—
720Dic11—41no—
721Dic11—42no—
722Dic11—41no—
723Dic11—41no—
724Dic11—42no—
725Dic11—42no—
726C25—111no—
727C25—111no—
728C25—111no—
729C22×D4—111no—
730C22×D4—111no—
731C22×D4—111no—
732C22×D4—111no—
733C22×D4—118no—
734C22×D4—111no—
735C22×D4—111no—
736C22×D4—111no—
737C22×D4—111no—
738C22×D4—111no—
739C22×D4—111no—
740C22×D4—111no—
741C22×D4—224no—
742C22×D4—224no—
743C22×D4—224no—
744C22×D4—224no—
745C22×D4—224no—
746C22×D4C22×D1111yescharacteristic
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—112no—
751C23×C4—112no—
752C23×C4—112no—
753C23×C4—112no—
754C23×C4—112no—
755C23×C4—111no—
756C23×C4—112no—
757C23×C4—111no—
758C23×C4—224no—
759C23×C4—224no—
760C23×C4—444no—
761C23×C4—444no—
762C23×C4C22×D1111yescharacteristic
763C23×C4C22×D1111yescharacteristic
764C23×C4C22×D1111yescharacteristic
765#123—24no—
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—224no—
776#120—224no—
777#120—224no—
778#120—224no—
779C4×D4—228no—
780C4×D4—228no—
781C4×D4—228no—
782C4×D4—228no—
783C2×C4⋊C4—24no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—111no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—112no—
789C2×C4⋊C4—112no—
790C2×C4⋊C4—112no—
791C2×C4⋊C4—112no—
792C2×C4⋊C4—444no—
793C2×C4⋊C4C22×D1112yes—
794C2×C4⋊C4C22×D1112yes—
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C4⋊C4C22×D1112yes—
798C2×C4⋊C4C22×D1112yes—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—111no—
813C2×C22⋊C4—111no—
814C2×C22⋊C4—111no—
815C2×C22⋊C4—111no—
816C2×C22⋊C4—111no—
817C2×C22⋊C4—111no—
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—112no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—224no—
827C2×C22⋊C4—224no—
828C2×C22⋊C4—224no—
829C2×C22⋊C4—224no—
830C2×C22⋊C4—224no—
831C2×C22⋊C4—444no—
832C2×C22⋊C4C22×D1111yescharacteristic
833C2×C22⋊C4C22×D1111yescharacteristic
834C2×C22⋊C4C22×D1111yescharacteristic
835C2×C22⋊C4C22×D1111yescharacteristic
836C2×C22⋊C4C22×D1111yescharacteristic
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#95C22×D1112yes—
857#95C22×D1112yes—
858#95C22×D1112yes—
859#95C22×D1112yes—
860#95C22×D1112yes—
861#95C22×D1112yes—
862C2×C11—24no—
863C2×C11—81no—
864C2×C11C22×#12311yescharacteristic
865C2×C11#345912yes—
866C2×C11#348411yescharacteristic
867C2×C11#348511yescharacteristic
868C2×C11#350512yes—
869D11—24no—
870D11—24no—
871D11—42no—
872D11—42no—
873D11—81no—
874C24—111no—
875C24—111no—
876C24—114no—
877C24—114no—
878C24—114no—
879C24—111no—
880C24—111no—
881C24—114no—
882C24—111no—
883C24—222no—
884C24—222no—
885C24—222no—
886C24—222no—
887C24—222no—
888C24—442no—
889C24—442no—
890C24—442no—
891C24—442no—
892C24—442no—
893C24—442no—
894C24C23×D1111yescharacteristic
895C24C23×D1111yescharacteristic
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—114no—
900C2×D4—114no—
901C2×D4—114no—
902C2×D4—114no—
903C2×D4—2232no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—222no—
908C2×D4—222no—
909C2×D4—222no—
910C2×D4—222no—
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—442no—
926C2×D4—442no—
927C2×D4—442no—
928C2×D4—442no—
929C2×D4—4416no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—112no—
937C22×C4—111no—
938C22×C4—112no—
939C22×C4—112no—
940C22×C4—111no—
941C22×C4—112no—
942C22×C4—111no—
943C22×C4—224no—
944C22×C4—224no—
945C22×C4—224no—
946C22×C4—224no—
947C22×C4—224no—
948C22×C4—224no—
949C22×C4—224no—
950C22×C4—224no—
951C22×C4—224no—
952C22×C4—222no—
953C22×C4—222no—
954C22×C4—222no—
955C22×C4—222no—
956C22×C4—222no—
957C22×C4—224no—
958C22×C4—224no—
959C22×C4—222no—
960C22×C4—222no—
961C22×C4—442no—
962C22×C4—442no—
963C22×C4—442no—
964C22×C4—442no—
965C22×C4—442no—
966C22×C4—442no—
967C22×C4—442no—
968C22×C4—442no—
969C22×C4—442no—
970C22×C4—442no—
971C22×C4—4416no—
972C22×C4—4416no—
973C22×C4—442no—
974C22×C4D4×D1114yes—
975C22×C4C23×D1111yescharacteristic
976C22×C4C23×D1112yes—
977C22×C4C23×D1112yes—
978C22×C4C23×D1111yescharacteristic
979C22×C4C23×D1112yes—
980C22×C4C23×D1112yes—
981C22×C4C23×D1111yescharacteristic
982C22×C4C23×D1111yescharacteristic
983C22×C4C23×D1111yescharacteristic
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—224no—
991C4⋊C4—224no—
992C4⋊C4—222no—
993C4⋊C4—222no—
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—42no—
1004C22⋊C4—42no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—224no—
1008C22⋊C4—224no—
1009C22⋊C4—224no—
1010C22⋊C4—222no—
1011C22⋊C4—222no—
1012C22⋊C4—224no—
1013C22⋊C4—224no—
1014C22⋊C4—222no—
1015C22⋊C4—222no—
1016C22⋊C4—222no—
1017C22⋊C4—222no—
1018C22⋊C4—224no—
1019C22⋊C4—222no—
1020C22⋊C4—222no—
1021C22⋊C4—222no—
1022C22⋊C4—222no—
1023C22⋊C4—222no—
1024C22⋊C4—442no—
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—21no—
1038C23—21no—
1039C23—21no—
1040C23—22no—
1041C23—22no—
1042C23—112no—
1043C23—112no—
1044C23—112no—
1045C23—112no—
1046C23—112no—
1047C23—112no—
1048C23—1116no—
1049C23—112no—
1050C23—112no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—228no—
1056C23—221no—
1057C23—221no—
1058C23—221no—
1059C23—221no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—221no—
1065C23—221no—
1066C23—221no—
1067C23—222no—
1068C23—222no—
1069C23—444no—
1070C23—444no—
1071C23—448no—
1072C23—444no—
1073C23—444no—
1074C23—448no—
1075C23—448no—
1076C23—448no—
1077C23—444no—
1078C23—448no—
1079C23—884no—
1080C23—882no—
1081C23—882no—
1082C23C2×D4×D1112yes—
1083C23#41×D1112yes—
1084C23#41×D1112yes—
1085C23C24×D1111yescharacteristic
1086D4—44no—
1087D4—228no—
1088D4—228no—
1089D4—228no—
1090D4—228no—
1091D4—444no—
1092D4—444no—
1093D4—444no—
1094D4—882no—
1095D4—882no—
1096D4—882no—
1097D4—882no—
1098C2×C4—28no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—44no—
1123C2×C4—44no—
1124C2×C4—114no—
1125C2×C4—228no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—221no—
1135C2×C4—221no—
1136C2×C4—222no—
1137C2×C4—222no—
1138C2×C4—222no—
1139C2×C4—222no—
1140C2×C4—222no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—448no—
1145C2×C4—448no—
1146C2×C4—448no—
1147C2×C4—448no—
1148C2×C4—444no—
1149C2×C4—448no—
1150C2×C4—444no—
1151C2×C4—884no—
1152C2×C4—882no—
1153C2×C4—882no—
1154C2×C4C2×D4×D1112yes—
1155C2×C4C2×D4×D1112yes—
1156C22—24no—
1157C22—22no—
1158C22—22no—
1159C22—24no—
1160C22—42no—
1161C22—41no—
1162C22—41no—
1163C22—42no—
1164C22—41no—
1165C22—114no—
1166C22—114no—
1167C22—224no—
1168C22—224no—
1169C22—222no—
1170C22—222no—
1171C22—222no—
1172C22—222no—
1173C22—224no—
1174C22—224no—
1175C22—222no—
1176C22—222no—
1177C22—222no—
1178C22—222no—
1179C22—222no—
1180C22—222no—
1181C22—4416no—
1182C22—4416no—
1183C22—442no—
1184C22—442no—
1185C22—442no—
1186C22—442no—
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#1062345712yes—
1199C4—22no—
1200C4—22no—
1201C4—42no—
1202C4—42no—
1203C4—42no—
1204C4—41no—
1205C4—41no—
1206C4—42no—
1207C4—41no—
1208C4—224no—
1209C4—442no—
1210C4—441no—
1211C4—442no—
1212C4—441no—
1213C4—442no—
1214C4—441no—
1215C2—24no—
1216C2—81no—
1217C2—224no—
1218C2—224no—
1219C2—442no—
1220C2—442no—
1221C2—881no—
1222C2C2×D11×#12311yescharacteristic
1223C2#1308202412yes—
1224C2#1308225011yescharacteristic
1225C2#1308225911yescharacteristic
1226C2#1308244812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2623C2
prime radicalC2×#10623184C2
hypercenter#2623D11
hypocenterC11#34983
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2623

Complements

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

NH ≅ G/Ntype
2. C22×#66946C2semidirect
3. #13076939C2semidirect
4. #13076935C2semidirect
5. #13076911C2semidirect
6. #13076907C2semidirect
7. #13074396C2semidirect
8. #13074394C2semidirect
9. #13074393C2semidirect
10. #13072369C2semidirect
11. #13072367C2semidirect
12. #13072354C2semidirect
13. #13072352C2semidirect
14. #13072096C2semidirect
15. #13072094C2semidirect
16. #13072081C2semidirect
17. #13072079C2semidirect
18. #13071227C2semidirect
19. #13071193C2semidirect
20. #13071190C2semidirect
21. D11×#386C2semidirect
22. D11×#385C2semidirect
23. C11×#2623C2semidirect
27. C23×C4×D11C22semidirect
29. C22×C11×C4⋊C4C22semidirect
33. C22×(C2×D11)⋊C4C22semidirect
34. C22×C4×Dic11C22semidirect
40. C2×#66947C22semidirect
44. C2×#66946C22semidirect
45. C2×#66946C22semidirect
46. C2×C4⋊C4×D11C22semidirect
49. C2×#66936C22semidirect
56. C2×C22⋊C4×D11C22semidirect
57. C11×#400C22semidirect
58. C11×#399C22semidirect
59. C11×#398C22semidirect
60. C11×#397C22semidirect
63. C11×#385C22semidirect
64. C11×#385C22semidirect
65. C11×#381C22semidirect
70. #10622824C22semidirect
71. #10622823C22semidirect
72. #10622823C22semidirect
73. #10622606C22semidirect
74. #10622606C22semidirect
75. #10622605C22semidirect
76. #10622604C22semidirect
77. #10622602C22semidirect
78. #10622602C22semidirect
79. #10622602C22semidirect
80. #10622600C22semidirect
81. #10622595C22semidirect
82. #10622593C22semidirect
83. #10622591C22semidirect
84. #10622591C22semidirect
85. #10622574C22semidirect
86. #10622572C22semidirect
89. #10622569C22semidirect
90. #10622569C22semidirect
91. #10622569C22semidirect
92. #10622568C22semidirect
93. #10622568C22semidirect
94. #10622568C22semidirect
95. #10622563C22semidirect
96. #10622563C22semidirect
97. #10622559C22semidirect
98. #10622559C22semidirect
99. #10622557C22semidirect
100. #10622557C22semidirect
101. #10622288C22semidirect
102. #10622288C22semidirect
103. #10622287C22semidirect
104. #10622285C22semidirect
105. #10622283C22semidirect
106. #10622283C22semidirect
107. #10622281C22semidirect
108. #10622281C22semidirect
109. #10622281C22semidirect
110. #10622280C22semidirect
113. #10622278C22semidirect
114. #10622278C22semidirect
115. #10622278C22semidirect
116. #10622278C22semidirect
117. #10622278C22semidirect
118. #10622277C22semidirect
119. #10622277C22semidirect
120. #10622277C22semidirect
121. D11×#95C22semidirect
122. D11×#95C22semidirect
123. #10622266C22semidirect
124. #10622266C22semidirect
429. #2623D11semidirect
487. C22×D11#123semidirect
591. C22×C4⋊C4C2×D11semidirect
600. #400C2×D11semidirect
602. #399C2×D11semidirect
604. #398C2×D11semidirect
610. #397C2×D11semidirect
653. #385C2×D11semidirect
654. #385C2×D11semidirect
659. #381C2×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×#106231842
C22×#669462
#130769392
#130769352
#130769112
#130769072
#130743962
#130743942
#130743932
#130723692
#130723672
#130723542
#130723522
#130720962
#130720942
#130720812
#130720792
#130712272
#130711932
#130711902
D11×#3862
D11×#3852
C11×#26232
#3498311