Finite Group Databasebeta

← #14916567

Subgroups — #14916567

Order 2816.

2586 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2#13071780C212yesmaximal, complemented
3#13071771C212yesmaximal, complemented
4#13071698C212yesmaximal, complemented
5#13071662C212yesmaximal, complemented
6#13071567C211yesmaximal, characteristic, complemented
7#13071563C211yesmaximal, characteristic, complemented
8#13071548C211yesmaximal, characteristic, complemented
9#13071548C211yesmaximal, characteristic, complemented
10#13071542C211yesmaximal, characteristic, complemented
11#13071542C211yesmaximal, characteristic, complemented
12C4⋊C4×D44C211yesmaximal, characteristic, complemented
13#13071516C211yesmaximal, characteristic, complemented
14#13071411C212yesmaximal, complemented
15#13071399C212yesmaximal, complemented
16#13071278C212yesmaximal, complemented
17#13071269C212yesmaximal, complemented
18#13071225C211yesmaximal, characteristic, complemented
19#13071205C211yesmaximal, characteristic, complemented
20#13071205C211yesmaximal, characteristic, complemented
21#13070998C211yesmaximal, characteristic, complemented
22D11×#380C211yesmaximal, characteristic, complemented
23C11×#2314C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27#10623055C4116yescomplemented
28C2×#66950C2211yescharacteristic
29C2×#66950C2211yescharacteristic
30C2×#66948C2211yescharacteristic
31C2×#66948C2211yescharacteristic
32C2×#66946C2212yes—
33C2×#66945C2211yescharacteristic
34C2×#66945C2211yescharacteristic
35C2×#66945C2211yescharacteristic, complemented
36C2×#66945C2211yescharacteristic, complemented
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic, complemented
40C2×C4⋊C4×D11C2211yescharacteristic, complemented
41C2×#66939C2211yescharacteristic
42C2×#66939C2211yescharacteristic
43C2×#66935C2211yescharacteristic
44C2×#66935C2211yescharacteristic
45C2×C22⋊C4×D11C2212yes—
46C2×C4×D44C2212yes—
47C2×C4×D44C2211yescharacteristic
48C2×C4×D44C2211yescharacteristic
49C2×C4×D44C2211yescharacteristic
50C2×C4×D44C2211yescharacteristic
51C11×#388C2212yes—
52C11×#388C2212yes—
53C11×#387C2212yescomplemented
54C11×#387C2212yescomplemented
55C11×#384C2211yescharacteristic, complemented
56C11×#382C2211yescharacteristic, complemented
57C11×#380C2211yescharacteristic
58C11×#380C2211yescharacteristic
59C4×C11×C4⋊C4C2211yescharacteristic, complemented
60C4×C11×C4⋊C4C2211yescharacteristic, complemented
61#10622825C2211yescharacteristic
62#10622825C2211yescharacteristic
63#10622603C2212yes—
64#10622603C2212yescomplemented
65#10622602C2212yes—
66#10622602C2212yescomplemented
67#10622601C2212yes—
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2211yescharacteristic
72#10622600C2211yescharacteristic, complemented
73#10622600C2211yescharacteristic, complemented
74#10622600C2211yescharacteristic, complemented
75#10622600C2211yescharacteristic, complemented
76#10622594C2212yescomplemented
77#10622594C2212yescomplemented
78C4⋊C4×Dic11C2212yescomplemented
79#10622586C2212yescomplemented
80#10622570C2212yes—
81#10622570C2212yes—
82#10622569C2212yes—
83#10622569C2212yes—
84#10622568C2212yes—
85#10622564C2212yes—
86#10622564C2212yes—
87#10622555C2212yes—
88C22⋊C4×Dic11C2212yes—
89#10622553C2212yes—
90#10622553C2212yescomplemented
91#10622552C2212yes—
92C4×(C2×D11)⋊C4C2212yes—
93C4×(C2×D11)⋊C4C2212yescomplemented
94#10622549C2211yescharacteristic, complemented
95#10622548C2211yescharacteristic, complemented
96C4×C4⋊Dic11C2212yescomplemented
97C4×C4⋊Dic11C2211yescharacteristic, complemented
98C4×C4⋊Dic11C2211yescharacteristic, complemented
99#10622541C2212yescomplemented
100#10622283C2212yes—
101#10622283C2212yescomplemented
102#10622282C2212yes—
103#10622282C2212yescomplemented
104#10622281C2212yes—
105#10622281C2212yescomplemented
106#10622280C2212yes—
107#10622279C2212yes—
108#10622279C2212yes—
109#10622279C2212yescomplemented
110#10622278C2212yes—
111#10622278C2212yes—
112#10622278C2212yes—
113#10622278C2212yes—
114#10622278C2212yescomplemented
115#10622278C2212yescomplemented
116#10622277C2212yes—
117D11×#95C2212yes—
118#10622267C2212yescomplemented
119#10622267C2212yescomplemented
120#10622266C2212yescomplemented
121#10622266C2212yescomplemented
122#10622259C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C22×C22⋊D11C2311yescharacteristic
127C22×C22⋊D11C2311yescharacteristic
128C23×Dic11C2311yescharacteristic
129C2×#4339—42no—
130C2×#4339—42no—
131C2×#4339C2×C418yescomplemented
132C22×D44C2311yescharacteristic
133C22×D44C2311yescharacteristic
134C22×D44C2311yescharacteristic
135C22×D44C2311yescharacteristic
136C22×D44C2311yescharacteristic
137C22×C4×D11—42no—
138C22×C4×D11—42no—
139C22×C4×D11C2×C418yescomplemented
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C22×Dic22C2311yescharacteristic
151C11×#117C2×C418yescomplemented
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C42×C11C2312yes—
165C2×C42×C11C2312yes—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2311yescharacteristic
183C2×(C2×D11)⋊C4C2311yescharacteristic
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×C4⋊Dic11C2311yescharacteristic
191C2×C4⋊Dic11C2311yescharacteristic
192C2×C4⋊Dic11C2311yescharacteristic
193C2×C4⋊Dic11C2311yescharacteristic
194C2×C4⋊Dic11C2312yes—
195C2×C4⋊Dic11C2312yes—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210#66950C2×C418yescomplemented
211#66950C2×C418yescomplemented
212#66948C2×C418yes—
213#66948C2×C418yescomplemented
214#66946—44no—
215#66945—42no—
216#66945—42no—
217#66945—42no—
218#66945—42no—
219C4⋊C4×D11—42no—
220C4⋊C4×D11—42no—
221C4⋊C4×D11—42no—
222C4⋊C4×D11—42no—
223#66939C2×C418yescomplemented
224#66939C2×C418yescomplemented
225#66935C2×C418yescomplemented
226#66935C2×C418yescomplemented
227C22⋊C4×D11—44no—
228C4×D44—44no—
229C4×D44C2×C418yescomplemented
230C4×D44C2×C418yescomplemented
231C4×D44C2×C418yescomplemented
232C4×D44C2×C418yescomplemented
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253#34362—111nomaximal, Sylow
254C24×C11C2411yescharacteristic
255C23×D11—22no—
256C23×D11—22no—
257C23×D11—41no—
258C23×D11—41no—
259C23×D11—41no—
260C23×D11—41no—
261C23×D11C22×C414yes—
262C23×D11C2411yescharacteristic
263C23×D11C2411yescharacteristic
264C23×D11C2411yescharacteristic
265C23×D11C2411yescharacteristic
266C22×C4×C11—22no—
267C22×C4×C11—22no—
268C22×C4×C11C22×C414yes—
269C22×C4×C11C2412yes—
270C22×C4×C11C2412yes—
271C22×C4×C11C2412yes—
272C22×C4×C11C2412yes—
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C2×C22⋊D11—41no—
280C2×C22⋊D11—41no—
281C2×C22⋊D11—41no—
282C2×C22⋊D11—41no—
283C2×C22⋊D11C22×C414yes—
284C2×C22⋊D11C22×C414yes—
285C22×Dic11—41no—
286C22×Dic11—41no—
287C22×Dic11C22×C414yes—
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C22×Dic11C2412yes—
291C22×Dic11C2412yes—
292C22×Dic11C2411yescharacteristic
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2411yescharacteristic
296#4339—416no—
297C2×D44—22no—
298C2×D44—22no—
299C2×D44—22no—
300C2×D44—22no—
301C2×D44—41no—
302C2×D44—41no—
303C2×D44—41no—
304C2×D44—41no—
305C2×D44—41no—
306C2×D44—41no—
307C2×D44C22×C414yes—
308C2×D44C22×C414yes—
309C2×D44C22×C414yes—
310C2×D44C22×C414yes—
311C2×D44C22×C414yes—
312C2×C4×D11—24no—
313C2×C4×D11—24no—
314C2×C4×D11—22no—
315C2×C4×D11—22no—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—41no—
323C2×C4×D11—41no—
324C2×C4×D11—41no—
325C2×C4×D11—41no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—416no—
337C2×C4×D11C22×C414yes—
338C2×C4×D11C22×C414yes—
339C2×C4×D11C22×C414yes—
340C2×C4×D11C22×C414yes—
341C2×C4×D11C22×C414yes—
342C2×C4×D11C22×C414yes—
343C2×Dic22—41no—
344C2×Dic22—41no—
345C2×Dic22C22×C414yes—
346C11×C4⋊C4—22no—
347C11×C4⋊C4—22no—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—42no—
351C11×C4⋊C4—42no—
352C11×C4⋊C4C22×C414yes—
353C11×C4⋊C4C22×C414yes—
354C11×C22⋊C4—42no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4C22×C414yes—
357C11×C22⋊C4C22×C414yes—
358C42×C11—42no—
359C42×C11—42no—
360C42×C11C22×C414yes—
361C42×C11C22×C414yes—
362C22⋊Dic11—42no—
363C22⋊Dic11—42no—
364(C2×D11)⋊C4—24no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—42no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4C22×C414yes—
377(C2×D11)⋊C4C22×C414yes—
378(C2×D11)⋊C4C22×C414yes—
379(C2×D11)⋊C4C22×C414yes—
380(C2×D11)⋊C4C22×C414yes—
381(C2×D11)⋊C4C22×C414yes—
382(C2×D11)⋊C4C22×C414yes—
383(C2×D11)⋊C4C22×C414yes—
384C4⋊Dic11—22no—
385C4⋊Dic11—22no—
386C4⋊Dic11—22no—
387C4⋊Dic11—22no—
388C4⋊Dic11—42no—
389C4⋊Dic11—42no—
390C4⋊Dic11C22×C414yes—
391C4⋊Dic11C22×C414yes—
392C4⋊Dic11C22×C414yes—
393C4⋊Dic11C22×C414yes—
394Dic11⋊C4—42no—
395Dic11⋊C4—42no—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398C4×Dic11—42no—
399C4×Dic11—42no—
400C4×Dic11—42no—
401C4×Dic11—42no—
402C4×Dic11—42no—
403C4×Dic11—42no—
404C2×#525—111no—
405#2378—112no—
406#2377—112no—
407#2368—112no—
408#2364—112no—
409#2354—111no—
410#2354—111no—
411#2352—111no—
412#2352—111no—
413#2352—111no—
414#2352—111no—
415D4×C4⋊C4—111no—
416D4×C4⋊C4—111no—
417#2335—112no—
418#2335—112no—
419#2321—112no—
420#2321—112no—
421#2314—111no—
422#2314D1111yescharacteristic, complemented
423#2311—111no—
424#2311—111no—
425#2280—111no—
426C2×#380—111no—
427C23×C11—21no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11C23×C412yes—
434C23×C11C2511yescharacteristic
435C22×D11—21no—
436C22×D11—21no—
437C22×D11—21no—
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—21no—
441C22×D11—21no—
442C22×D11—21no—
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—21no—
447C22×D11—21no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—28no—
458C22×D11—44no—
459C22×D11—44no—
460C22×D11—44no—
461C22×D11—44no—
462C22×D11—44no—
463C22×D11—44no—
464C22×D11C23×C412yes—
465C22×D11C23×C412yes—
466C22×D11C23×C412yes—
467C22×D11C23×C412yes—
468C22×D11H(5,𝔽2)12yes—
469C22×D112−1+412yes—
470C2×C4×C11—21no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—28no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11C23×C412yes—
494C2×C4×C11C23×C412yes—
495C2×C4×C11C23×C412yes—
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11H(5,𝔽2)12yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C22⋊D11—44no—
502C22⋊D11—44no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—44no—
524C2×Dic11C23×C412yes—
525C2×Dic11C23×C412yes—
526C2×Dic11C23×C412yes—
527C2×Dic11C23×C412yes—
528D44—28no—
529D44—28no—
530D44—44no—
531D44—44no—
532D44—44no—
533C4×D11—28no—
534C4×D11—28no—
535C4×D11—28no—
536C4×D11—28no—
537C4×D11—44no—
538C4×D11—44no—
539C4×D11—84no—
540C4×D11—84no—
541C4×D11—84no—
542C4×D11—84no—
543Dic22—44no—
544C22×#41—111no—
545C24×C4—111no—
546#525—1116no—
547C2×#123—111no—
548C2×#123—111no—
549C2×C22⋊Q8—111no—
550C2×C22⋊Q8—111no—
551C2×#121—111no—
552C2×#121—111no—
553C2×#120—111no—
554C2×#120—111no—
555C2×C4×D4—112no—
556C2×C4×D4—111no—
557C2×C4×D4—111no—
558C2×C4×D4—111no—
559C2×C4×D4—111no—
560C2×C4×D4—112no—
561C2×#117—111no—
562C2×#117—111no—
563C2×#117—111no—
564C2×#117—111no—
565C2×#117C2×D1111yescharacteristic
566C22×C4⋊C4—111no—
567C22×C4⋊C4—111no—
568C22×C4⋊C4—111no—
569C22×C4⋊C4—111no—
570C22×C22⋊C4—112no—
571#391—112no—
572#391—112no—
573#390—112no—
574#390—112no—
575#390—112no—
576#390—112no—
577#389—112no—
578#389—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#388—112no—
586#388—112no—
587#388—112no—
588#388—112no—
589#388C2×D1112yes—
590#388C2×D1112yes—
591#387—112no—
592#387—112no—
593#387—112no—
594#387—112no—
595#387—112no—
596#387—112no—
597#387C2×D1112yescomplemented
598#387C2×D1112yescomplemented
599#386—112no—
600#386—112no—
601#386—112no—
602#386—112no—
603#386—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#385—112no—
608#385—112no—
609#385—112no—
610#385—112no—
611#384—111no—
612#384C2×D1111yescharacteristic, complemented
613#382—111no—
614#382C2×D1111yescharacteristic, complemented
615#381—112no—
616#380—111no—
617#380—111no—
618#380—111no—
619#380—111no—
620#380—111no—
621#380—111no—
622#380—111no—
623#380—111no—
624#380—111no—
625#380—111no—
626#380—112no—
627#380—112no—
628#380C2×D1111yescharacteristic
629#380C2×D1111yescharacteristic
630#379—112no—
631C4×C4⋊C4—112no—
632C4×C4⋊C4—111no—
633C4×C4⋊C4—111no—
634C4×C4⋊C4—112no—
635C4×C4⋊C4C2×D1111yescharacteristic, complemented
636C4×C4⋊C4C2×D1111yescharacteristic, complemented
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C2×#95—112no—
644C22×C11—22no—
645C22×C11—22no—
646C22×C11—22no—
647C22×C11—41no—
648C22×C11—41no—
649C22×C11—41no—
650C22×C11—41no—
651C22×C11C24×C411yescharacteristic
652C22×C11C2×H(5,𝔽2)11yescharacteristic
653C22×C11C2×H(5,𝔽2)11yescharacteristic
654C22×C11C2×H(5,𝔽2)11yescharacteristic
655C22×C11C2×2−1+411yescharacteristic
656C22×C11#58511yescharacteristic
657C22×C11#58511yescharacteristic
658C2×D11—22no—
659C2×D11—22no—
660C2×D11—22no—
661C2×D11—22no—
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—416no—
674C2×D11—41no—
675C2×D11—41no—
676C2×D11—41no—
677C2×D11—41no—
678C2×D11—41no—
679C2×D11—41no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11#52014yes—
687C4×C11—22no—
688C4×C11—22no—
689C4×C11—22no—
690C4×C11—22no—
691C4×C11—22no—
692C4×C11—42no—
693C4×C11—42no—
694C4×C11—42no—
695C4×C11—42no—
696C4×C11#51814yes—
697Dic11—22no—
698Dic11—22no—
699Dic11—22no—
700Dic11—22no—
701Dic11—42no—
702Dic11—42no—
703Dic11—42no—
704Dic11—42no—
705C25—111no—
706C2×#41—118no—
707C2×#41—442no—
708C2×#41—442no—
709C22×Q8—111no—
710C22×D4—111no—
711C22×D4—111no—
712C22×D4—111no—
713C22×D4—111no—
714C22×D4—111no—
715C22×D4—111no—
716C22×D4—111no—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4—118no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—112no—
726C23×C4—112no—
727C23×C4—112no—
728C23×C4—112no—
729C23×C4—442no—
730C23×C4—442no—
731C23×C4C22×D1111yescharacteristic
732#123—118no—
733#123—118no—
734C22⋊Q8—118no—
735C22⋊Q8—118no—
736#121—118no—
737#121—118no—
738#120—118no—
739#120—118no—
740C4×D4—118no—
741C4×D4—118no—
742C4×D4—118no—
743C4×D4—118no—
744C4×D4—444no—
745C4×D4—444no—
746#117—442no—
747#117—442no—
748#117—442no—
749#117—442no—
750#117C4×D1118yescomplemented
751C2×C4⋊C4—111no—
752C2×C4⋊C4—111no—
753C2×C4⋊C4—111no—
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—111no—
757C2×C4⋊C4—111no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—112no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4—112no—
762C2×C4⋊C4—112no—
763C2×C4⋊C4—112no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—442no—
766C2×C4⋊C4—442no—
767C2×C4⋊C4—442no—
768C2×C4⋊C4—442no—
769C2×C4⋊C4C22×D1111yescharacteristic
770C2×C4⋊C4C22×D1111yescharacteristic
771C2×C4⋊C4C22×D1111yescharacteristic
772C2×C4⋊C4C22×D1111yescharacteristic
773C2×C4⋊C4C22×D1112yes—
774C2×C4⋊C4C22×D1112yes—
775C2×C4⋊C4C22×D1111yescharacteristic
776C2×C4⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—444no—
800C2×C22⋊C4C22×D1112yes—
801C2×C22⋊C4C22×D1112yes—
802C2×C22⋊C4C22×D1111yescharacteristic
803C2×C22⋊C4C22×D1111yescharacteristic
804C2×C42—112no—
805C2×C42—112no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42C22×D1112yes—
811C2×C42C22×D1112yes—
812C2×C42C22×D1111yescharacteristic
813C2×C42C22×D1111yescharacteristic
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95C22×D1112yes—
829#95C22×D1112yes—
830#95C22×D1112yes—
831#95C22×D1112yes—
832#95C22×D1112yes—
833#95C22×D1112yes—
834C2×C11—42no—
835C2×C11C2×#51811yescharacteristic
836C2×C11C2×#52011yescharacteristic
837C2×C11#342811yescharacteristic
838C2×C11#354111yescharacteristic
839C2×C11#354111yescharacteristic
840C2×C11#354211yescharacteristic
841C2×C11#354211yescharacteristic
842D11—24no—
843D11—42no—
844D11—42no—
845D11—42no—
846C24—111no—
847C24—111no—
848C24—111no—
849C24—111no—
850C24—114no—
851C24—222no—
852C24—222no—
853C24—441no—
854C24—441no—
855C24—441no—
856C24—441no—
857C24C23×D1111yescharacteristic
858#41—4416no—
859C2×Q8—114no—
860C2×Q8—441no—
861C2×Q8—441no—
862C2×D4—114no—
863C2×D4—114no—
864C2×D4—114no—
865C2×D4—114no—
866C2×D4—114no—
867C2×D4—114no—
868C2×D4—114no—
869C2×D4—222no—
870C2×D4—222no—
871C2×D4—222no—
872C2×D4—222no—
873C2×D4—441no—
874C2×D4—441no—
875C2×D4—441no—
876C2×D4—441no—
877C2×D4—441no—
878C2×D4—441no—
879C2×D4—441no—
880C2×D4—441no—
881C2×D4—441no—
882C2×D4—441no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—111no—
886C22×C4—111no—
887C22×C4—111no—
888C22×C4—111no—
889C22×C4—114no—
890C22×C4—114no—
891C22×C4—114no—
892C22×C4—114no—
893C22×C4—114no—
894C22×C4—114no—
895C22×C4—114no—
896C22×C4—112no—
897C22×C4—112no—
898C22×C4—112no—
899C22×C4—112no—
900C22×C4—224no—
901C22×C4—224no—
902C22×C4—222no—
903C22×C4—222no—
904C22×C4—222no—
905C22×C4—222no—
906C22×C4—222no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—4416no—
911C22×C4—441no—
912C22×C4—441no—
913C22×C4—441no—
914C22×C4—441no—
915C22×C4—442no—
916C22×C4—442no—
917C22×C4—442no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—442no—
921C22×C4—442no—
922C22×C4—442no—
923C22×C4—442no—
924C22×C4—442no—
925C22×C4—441no—
926C22×C4—441no—
927C22×C4C2×C4×D1114yes—
928C22×C4C23×D1112yes—
929C22×C4C23×D1112yes—
930C22×C4C23×D1112yes—
931C22×C4C23×D1112yes—
932C22×C4C23×D1111yescharacteristic
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1111yescharacteristic
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1111yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—114no—
945C4⋊C4—114no—
946C4⋊C4—114no—
947C4⋊C4—114no—
948C4⋊C4—222no—
949C4⋊C4—222no—
950C4⋊C4—222no—
951C4⋊C4—222no—
952C4⋊C4—442no—
953C4⋊C4—442no—
954C4⋊C4—442no—
955C4⋊C4—442no—
956C4⋊C4—442no—
957C4⋊C4—442no—
958C4⋊C4C2×C4×D1114yes—
959C4⋊C4C2×C4×D1114yes—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—114no—
963C22⋊C4—114no—
964C22⋊C4—114no—
965C22⋊C4—114no—
966C22⋊C4—114no—
967C22⋊C4—114no—
968C22⋊C4—114no—
969C22⋊C4—114no—
970C22⋊C4—224no—
971C22⋊C4—224no—
972C22⋊C4—442no—
973C22⋊C4—442no—
974C22⋊C4—442no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C22⋊C4—442no—
978C22⋊C4—442no—
979C22⋊C4—442no—
980C22⋊C4—442no—
981C22⋊C4—442no—
982C22⋊C4—442no—
983C22⋊C4—442no—
984C22⋊C4C2×C4×D1114yes—
985C22⋊C4C2×C4×D1114yes—
986C42—42no—
987C42—42no—
988C42—442no—
989C42—442no—
990C42—442no—
991C42—442no—
992C42—442no—
993C42—442no—
994C42C2×C4×D1114yes—
995C42C2×C4×D1114yes—
996C11#3436211yescharacteristic, complemented, Sylow
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—112no—
1004C23—112no—
1005C23—112no—
1006C23—112no—
1007C23—112no—
1008C23—112no—
1009C23—228no—
1010C23—221no—
1011C23—221no—
1012C23—221no—
1013C23—221no—
1014C23—221no—
1015C23—221no—
1016C23—221no—
1017C23—221no—
1018C23—221no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—221no—
1023C23—221no—
1024C23—221no—
1025C23—221no—
1026C23—221no—
1027C23—221no—
1028C23—221no—
1029C23—221no—
1030C23—221no—
1031C23—221no—
1032C23—444no—
1033C23—444no—
1034C23—444no—
1035C23—444no—
1036C23—444no—
1037C23—444no—
1038C23C22×C4×D1112yes—
1039C23C24×D1111yescharacteristic
1040Q8—444no—
1041D4—228no—
1042D4—228no—
1043D4—444no—
1044D4—444no—
1045D4—444no—
1046D4—444no—
1047D4—444no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—28no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—112no—
1072C2×C4—112no—
1073C2×C4—112no—
1074C2×C4—112no—
1075C2×C4—221no—
1076C2×C4—221no—
1077C2×C4—221no—
1078C2×C4—221no—
1079C2×C4—221no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—228no—
1084C2×C4—228no—
1085C2×C4—228no—
1086C2×C4—228no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—444no—
1100C2×C4—444no—
1101C2×C4—444no—
1102C2×C4—884no—
1103C2×C4—884no—
1104C2×C4—884no—
1105C2×C4—884no—
1106C2×C4C22×C4×D1112yes—
1107C2×C4C22×C4×D1112yes—
1108C2×C4C22×C4×D1112yes—
1109C2×C4C22×C4×D1112yes—
1110C2×C4C22×C4×D1112yes—
1111C2×C4C22×C4×D1112yes—
1112C2×C4#6704212yes—
1113C2×C4#6704212yes—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—41no—
1118C22—41no—
1119C22—41no—
1120C22—41no—
1121C22—114no—
1122C22—222no—
1123C22—222no—
1124C22—222no—
1125C22—222no—
1126C22—222no—
1127C22—222no—
1128C22—222no—
1129C22—222no—
1130C22—222no—
1131C22—222no—
1132C22—222no—
1133C22—222no—
1134C22—222no—
1135C22—222no—
1136C22—222no—
1137C22—4416no—
1138C22—441no—
1139C22—441no—
1140C22—441no—
1141C22—441no—
1142C22—441no—
1143C22—441no—
1144C22—441no—
1145C22—441no—
1146C22—441no—
1147C22—441no—
1148C22—441no—
1149C22—441no—
1150C22C23×C4×D1111yescharacteristic
1151C22C2×#6704211yescharacteristic
1152C22C2×#6704211yescharacteristic
1153C22D11×H(5,𝔽2)11yescharacteristic
1154C22#1062345511yescharacteristic
1155C22D11×2−1+411yescharacteristic
1156C22#1062345711yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—222no—
1167C4—222no—
1168C4—222no—
1169C4—222no—
1170C4—442no—
1171C4—442no—
1172C4—442no—
1173C4—442no—
1174C4#1062305214yes—
1175C2—42no—
1176C2—224no—
1177C2—442no—
1178C2—442no—
1179C2—442no—
1180C2C2×#1062305211yescharacteristic
1181C2D11×#52011yescharacteristic
1182C2#1308181611yescharacteristic
1183C2#1308290511yescharacteristic
1184C2#1308291511yescharacteristic
1185C2#1308292811yescharacteristic
1186C2#1308293811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2314C2
socle, cosocleC23×C11C25
prime radicalC2×#10623055C2
hypercenter#2314D11
hypocenterC11#34362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #13071780C2semidirect
3. #13071771C2semidirect
4. #13071698C2semidirect
5. #13071662C2semidirect
6. #13071567C2semidirect
7. #13071563C2semidirect
8. #13071548C2semidirect
9. #13071548C2semidirect
10. #13071542C2semidirect
11. #13071542C2semidirect
12. C4⋊C4×D44C2semidirect
13. #13071516C2semidirect
14. #13071411C2semidirect
15. #13071399C2semidirect
16. #13071278C2semidirect
17. #13071269C2semidirect
18. #13071225C2semidirect
19. #13071205C2semidirect
20. #13071205C2semidirect
21. #13070998C2semidirect
22. D11×#380C2semidirect
23. C11×#2314C2semidirect
27. #10623055C4semidirect
35. C2×#66945C22semidirect
36. C2×#66945C22semidirect
39. C2×C4⋊C4×D11C22semidirect
40. C2×C4⋊C4×D11C22semidirect
53. C11×#387C22semidirect
54. C11×#387C22semidirect
55. C11×#384C22semidirect
56. C11×#382C22semidirect
59. C4×C11×C4⋊C4C22semidirect
60. C4×C11×C4⋊C4C22semidirect
64. #10622603C22semidirect
66. #10622602C22semidirect
72. #10622600C22semidirect
73. #10622600C22semidirect
74. #10622600C22semidirect
75. #10622600C22semidirect
76. #10622594C22semidirect
77. #10622594C22semidirect
78. C4⋊C4×Dic11C22semidirect
79. #10622586C22semidirect
90. #10622553C22semidirect
93. C4×(C2×D11)⋊C4C22semidirect
94. #10622549C22semidirect
95. #10622548C22semidirect
96. C4×C4⋊Dic11C22semidirect
97. C4×C4⋊Dic11C22semidirect
98. C4×C4⋊Dic11C22semidirect
99. #10622541C22semidirect
101. #10622283C22semidirect
103. #10622282C22semidirect
105. #10622281C22semidirect
109. #10622279C22semidirect
114. #10622278C22semidirect
115. #10622278C22semidirect
118. #10622267C22semidirect
119. #10622267C22semidirect
120. #10622266C22semidirect
121. #10622266C22semidirect
122. #10622259C22semidirect
123. #10622259C22semidirect
131. C2×#4339C2×C4semidirect
139. C22×C4×D11C2×C4semidirect
151. C11×#117C2×C4semidirect
210. #66950C2×C4semidirect
211. #66950C2×C4semidirect
213. #66948C2×C4semidirect
223. #66939C2×C4semidirect
224. #66939C2×C4semidirect
225. #66935C2×C4semidirect
226. #66935C2×C4semidirect
229. C4×D44C2×C4semidirect
230. C4×D44C2×C4semidirect
231. C4×D44C2×C4semidirect
232. C4×D44C2×C4semidirect
422. #2314D11semidirect
597. #387C2×D11semidirect
598. #387C2×D11semidirect
612. #384C2×D11semidirect
614. #382C2×D11semidirect
635. C4×C4⋊C4C2×D11semidirect
636. C4×C4⋊C4C2×D11semidirect
750. #117C4×D11semidirect
996. C11#34362semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
#130717802
#130717712
#130716982
#130716622
#130715672
#130715632
#130715482
#130715422
C4⋊C4×D442
#130715162
#130714112
#130713992
#130712782
#130712692
#130712252
#130712052
#130709982
D11×#3802
C11×#23142
#3436211