Finite Group Databasebeta

← #14914327

Subgroups — #14914327

Order 2816.

2698 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic
2#13071750C212yesmaximal, complemented
3#13071744C212yesmaximal, complemented
4#13071659C211yesmaximal, characteristic, complemented
5#13071650C211yesmaximal, characteristic, complemented
6#13071645C211yesmaximal, characteristic, complemented
7#13071642C211yesmaximal, characteristic, complemented
8#13071586C212yesmaximal, complemented
9#13071550C212yesmaximal, complemented
10#13071508C211yesmaximal, characteristic, complemented
11#13071497C211yesmaximal, characteristic, complemented
12#13071455C211yesmaximal, characteristic, complemented
13#13071441C211yesmaximal, characteristic, complemented
14#13071279C212yesmaximal, complemented
15#13071270C212yesmaximal, complemented
16#13071242C212yesmaximal, complemented
17C4×#66977C211yesmaximal, characteristic, complemented
18#13071144C211yesmaximal, characteristic, complemented
19#121×Dic11C211yesmaximal, characteristic, complemented
20#13070998C211yesmaximal, characteristic, complemented
21#13070977C212yesmaximal, complemented
22C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
23C4×C11×#121C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2211yescharacteristic, complemented
29C22×C42×C11C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66990C2212yes—
32C2×D4×Dic11C2212yes—
33C2×D4×Dic11C2212yes—
34C2×D4×Dic11C2211yescharacteristic, complemented
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39#10623137C4116yescomplemented
40C2×#66950C2211yescharacteristic
41C2×#66945C2211yescharacteristic
42C2×#66945C2211yescharacteristic
43C2×#66945C2211yescharacteristic
44C2×#66940C2211yescharacteristic, complemented
45C2×#66936C2212yes—
46C2×(C22⋊D11)⋊C4C2212yes—
47C2×C4×Dic22C2211yescharacteristic, complemented
48C11×#390C2211yescharacteristic, complemented
49C11×#389C2211yescharacteristic, complemented
50C11×#388C2212yescomplemented
51C11×#386C2212yes—
52C11×#380C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic, complemented
54C4×C11×C22⋊C4C2212yescomplemented
55#10622834C2211yescharacteristic, complemented
56#10622833C2212yes—
57#10622826C2212yes—
58#10622826C2212yes—
59#10622825C2211yescharacteristic
60#10622823C2212yes—
61C4×C22⋊Dic11C2212yes—
62C4×C22⋊Dic11C2212yescomplemented
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65C2×C11⋊#95C2212yescomplemented
66#10622603C2212yes—
67#10622603C2212yes—
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622598C2211yescharacteristic, complemented
71C4⋊C4×Dic11C2211yescharacteristic, complemented
72C4⋊C4×Dic11C2212yescomplemented
73C4⋊C4×Dic11C2211yescharacteristic, complemented
74C4⋊C4×Dic11C2212yescomplemented
75#10622587C2211yescharacteristic, complemented
76#10622586C2211yescharacteristic, complemented
77#10622571C2212yes—
78#10622571C2212yes—
79#10622570C2212yes—
80#10622570C2212yes—
81#10622570C2212yes—
82#10622570C2212yes—
83#10622568C2212yes—
84#10622564C2212yescomplemented
85#10622559C2212yes—
86#10622558C2212yescomplemented
87#10622557C2212yescomplemented
88#10622556C2212yescomplemented
89#10622555C2212yescomplemented
90C22⋊C4×Dic11C2212yes—
91C22⋊C4×Dic11C2212yes—
92C22⋊C4×Dic11C2212yescomplemented
93C22⋊C4×Dic11C2212yescomplemented
94C22⋊C4×Dic11C2212yescomplemented
95#10622553C2212yes—
96#10622553C2212yes—
97C4×(C2×D11)⋊C4C2211yescharacteristic
98C4×(C2×D11)⋊C4C2211yescharacteristic
99C4×(C2×D11)⋊C4C2211yescharacteristic
100C4×(C2×D11)⋊C4C2211yescharacteristic
101C4×(C2×D11)⋊C4C2211yescharacteristic
102C4×(C2×D11)⋊C4C2211yescharacteristic
103C4×(C2×D11)⋊C4C2211yescharacteristic
104C4×(C2×D11)⋊C4C2211yescharacteristic
105C4×C4⋊Dic11C2212yescomplemented
106C4×C4⋊Dic11C2211yescharacteristic, complemented
107#10622546C2212yescomplemented
108#10622545C2212yescomplemented
109C4×Dic11⋊C4C2212yescomplemented
110#10622542C2211yescharacteristic, complemented
111#10622541C2211yescharacteristic, complemented
112#10622283C2212yes—
113#10622283C2212yes—
114#10622282C2212yes—
115#10622282C2212yes—
116#10622279C2212yes—
117#10622277C2212yes—
118#10622267C2212yescomplemented
119#10622266C2212yescomplemented
120#10622265C2212yescomplemented
121#10622264C2212yescomplemented
122#10622263C2212yescomplemented
123#10622262C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2312yes—
135C23×Dic11C2312yes—
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C2×#4341—42no—
139C2×#4341—42no—
140C2×#4341C2×C418yescomplemented
141C22×C4×D11—42no—
142C22×C4×D11—42no—
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×Dic22C2311yescharacteristic
149C11×#121C2×C418yes—
150C4×D4×C11—28no—
151C4×D4×C11—42no—
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C42×C11—42no—
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173#66991C2×C418yescomplemented
174#66990C2×C4116yescomplemented
175D4×Dic11—28no—
176D4×Dic11—42no—
177D4×Dic11C2×C4116yescomplemented
178C2×(C2×D11)⋊C4—24no—
179C2×(C2×D11)⋊C4—24no—
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2311yescharacteristic
199#66977C2×C418yescomplemented
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×C4×Dic11—42no—
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2312yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218#66950C2×C418yescomplemented
219#66945—42no—
220#66945—42no—
221#66945C2×C418yescomplemented
222#66940—42no—
223#66936C2×C4116yescomplemented
224(C22⋊D11)⋊C4C2×C4116yescomplemented
225C4×Dic22—42no—
226C11×#95C2312yes—
227C11×#95C2312yes—
228C11×#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2312yes—
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250#34223—111nomaximal, Sylow
251C24×C11C2412yes—
252C24×C11C2411yescharacteristic
253C23×D11—22no—
254C23×D11—22no—
255C23×D11—41no—
256C23×D11—41no—
257C23×D11—41no—
258C23×D11—41no—
259C23×D11C22×C414yes—
260C23×D11C2411yescharacteristic
261C23×D11C2411yescharacteristic
262C2×D4×C11—24no—
263C2×D4×C11—24no—
264C2×D4×C11—22no—
265C2×D4×C11—22no—
266C2×D4×C11C22×C418yes—
267C2×D4×C11C22×C414yes—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—24no—
272C22×C4×C11—41no—
273C22×C4×C11—41no—
274C22×C4×C11—41no—
275C22×C4×C11—41no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11C22×C414yes—
279C22×C4×C11#4114yescomplemented
280C22×C4×C11C2412yes—
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C2×C22⋊D11—42no—
290C2×C22⋊D11—42no—
291C2×C22⋊D11—42no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11C22×C418yes—
294C2×C22⋊D11C22×C418yes—
295C22×Dic11—24no—
296C22×Dic11—22no—
297C22×Dic11—41no—
298C22×Dic11—41no—
299C22×Dic11—41no—
300C22×Dic11—41no—
301C22×Dic11—42no—
302C22×Dic11—42no—
303C22×Dic11—41no—
304C22×Dic11—41no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11C22×C418yes—
308C22×Dic11C22×C414yes—
309C22×Dic11#4114yescomplemented
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2412yes—
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320#4341—416no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—41no—
326C2×C4×D11—41no—
327C2×C4×D11—41no—
328C2×C4×D11—41no—
329C2×C4×D11—416no—
330C2×C4×D11C22×C414yes—
331C2×C4×D11C22×C414yes—
332C2×C4×D11C22×C414yes—
333C2×C4×D11C22×C414yes—
334C2×Dic22—22no—
335C2×Dic22—22no—
336C2×Dic22C22×C414yes—
337C11×C4⋊C4—24no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4C22×C414yes—
341C11×C22⋊C4—24no—
342C11×C22⋊C4—24no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4C22×C418yes—
346C42×C11—24no—
347C42×C11—22no—
348C42×C11—22no—
349C42×C11—41no—
350C42×C11—41no—
351C22⋊Dic11—24no—
352C22⋊Dic11—24no—
353C22⋊Dic11—42no—
354C22⋊Dic11—42no—
355C22⋊Dic11C22×C418yes—
356C22⋊Dic11C22×C418yes—
357(C2×D11)⋊C4—22no—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—22no—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—22no—
363(C2×D11)⋊C4—22no—
364(C2×D11)⋊C4—22no—
365(C2×D11)⋊C4—42no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—42no—
369(C2×D11)⋊C4C22×C418yes—
370(C2×D11)⋊C4C22×C418yes—
371C4⋊Dic11—24no—
372C4⋊Dic11—22no—
373C4⋊Dic11—22no—
374C4⋊Dic11C22×C418yes—
375C4⋊Dic11C22×C414yes—
376Dic11⋊C4—42no—
377Dic11⋊C4—42no—
378Dic11⋊C4—42no—
379Dic11⋊C4—42no—
380Dic11⋊C4C22×C418yes—
381C4×Dic11—24no—
382C4×Dic11—22no—
383C4×Dic11—22no—
384C4×Dic11—42no—
385C4×Dic11—42no—
386C4×Dic11—42no—
387C4×Dic11—42no—
388C4×Dic11—41no—
389C4×Dic11—41no—
390C4×Dic11—42no—
391C4×Dic11—42no—
392C4×Dic11C22×C418yes—
393C2×#525—111no—
394#2374—112no—
395#2374—112no—
396#2363—111no—
397#2363—111no—
398#2362—111no—
399#2362—111no—
400#2357—112no—
401#2353—112no—
402#2347—111no—
403#2346—111no—
404#2341—111no—
405#2339—111no—
406#2321—112no—
407#2321—112no—
408#2318—112no—
409C4×C22⋊Q8—111no—
410C4×C22⋊Q8—111no—
411C4×#121—111no—
412C4×#121D1111yescharacteristic, complemented
413#2280—111no—
414#2275—112no—
415C2×C4×C22⋊C4—111no—
416C23×C11—21no—
417C23×C11—21no—
418C23×C11—21no—
419C23×C11—21no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11C23×C414yes—
427C23×C11C23×C412yes—
428C23×C11C2×#4112yes—
429C23×C11C2×#4112yes—
430C23×C11C2511yescharacteristic
431C22×D11—28no—
432C22×D11—21no—
433C22×D11—21no—
434C22×D11—21no—
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—44no—
445C22×D11—44no—
446C22×D11—44no—
447C22×D11—44no—
448C22×D11—44no—
449C22×D11—44no—
450C22×D11C23×C412yes—
451C22×D11C23×C412yes—
452D4×C11—216no—
453D4×C11—28no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—28no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—21no—
470C2×C4×C11—21no—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—44no—
476C2×C4×C11—44no—
477C2×C4×C11—84no—
478C2×C4×C11C23×C414yes—
479C2×C4×C11C23×C412yes—
480C2×C4×C11C23×C412yes—
481C2×C4×C11C2×#4112yes—
482C2×C4×C11C2×#4112yes—
483C2×C4×C11H(5,𝔽2)12yes—
484C2×C4×C11H(5,𝔽2)12yes—
485C22⋊D11—48no—
486C22⋊D11—48no—
487C2×Dic11—21no—
488C2×Dic11—21no—
489C2×Dic11—21no—
490C2×Dic11—21no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—21no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—21no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—21no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—21no—
511C2×Dic11—44no—
512C2×Dic11—48no—
513C2×Dic11—44no—
514C2×Dic11—44no—
515C2×Dic11—84no—
516C2×Dic11C23×C412yes—
517C2×Dic11C23×C414yes—
518C2×Dic11C23×C414yes—
519C2×Dic11C23×C412yes—
520C2×Dic11C2×#4112yes—
521C2×Dic11C2×#4112yes—
522C4×D11—28no—
523C4×D11—28no—
524C4×D11—44no—
525C4×D11—44no—
526Dic22—28no—
527C22×#41—111no—
528C24×C4—111no—
529#525—1116no—
530C2×#123—112no—
531C2×C22⋊Q8—111no—
532C2×C22⋊Q8—111no—
533C2×#121—111no—
534C2×#121C2×D1111yescharacteristic
535C2×#120—112no—
536C2×C4×Q8—111no—
537C2×C4×Q8—111no—
538C2×C4×D4—112no—
539C2×C4×D4—112no—
540C2×C4×D4—111no—
541C2×C4×D4—112no—
542C2×C4×D4C2×D1112yes—
543C2×C4×D4C2×D1111yescharacteristic, complemented
544C2×#117—111no—
545C2×#117—111no—
546C2×#117—111no—
547C22×C22⋊C4—111no—
548C22×C22⋊C4—111no—
549C22×C42—111no—
550C22×C42C2×D1111yescharacteristic
551#391—111no—
552#391—111no—
553#390—111no—
554#390—112no—
555#390—112no—
556#390—112no—
557#390—112no—
558#390C2×D1111yescharacteristic, complemented
559#389—111no—
560#389—111no—
561#389—111no—
562#389C2×D1111yescharacteristic, complemented
563#388—112no—
564#388—112no—
565#388—112no—
566#388—112no—
567#388—112no—
568#388—112no—
569#388—112no—
570#388—112no—
571#388—112no—
572#388—112no—
573#388—112no—
574#388C2×D1112yescomplemented
575#387—112no—
576#387—112no—
577#387—112no—
578#387—112no—
579#386—112no—
580#386—112no—
581#386—112no—
582#386—112no—
583#386—112no—
584#386C2×D1112yes—
585#385—112no—
586#385—112no—
587#383—112no—
588#382—112no—
589#381—112no—
590#381—112no—
591#380—111no—
592#380—111no—
593#380—111no—
594#380—112no—
595#380C2×D1111yescharacteristic
596#379—112no—
597C4×C4⋊C4—111no—
598C4×C4⋊C4—112no—
599C4×C4⋊C4—111no—
600C4×C4⋊C4—112no—
601C4×C4⋊C4—111no—
602C4×C4⋊C4—112no—
603C4×C4⋊C4—112no—
604C4×C4⋊C4—112no—
605C4×C4⋊C4C2×D1111yescharacteristic, complemented
606C4×C22⋊C4—112no—
607C4×C22⋊C4—112no—
608C4×C22⋊C4—112no—
609C4×C22⋊C4—112no—
610C4×C22⋊C4—112no—
611C4×C22⋊C4—112no—
612C4×C22⋊C4—112no—
613C4×C22⋊C4—111no—
614C4×C22⋊C4—111no—
615C4×C22⋊C4—111no—
616C4×C22⋊C4—111no—
617C4×C22⋊C4—111no—
618C4×C22⋊C4—111no—
619C4×C22⋊C4—111no—
620C4×C22⋊C4—111no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4C2×D1112yescomplemented
623#376—112no—
624C2×#95—111no—
625C2×#95—112no—
626C2×#95—111no—
627C22×C11—22no—
628C22×C11—22no—
629C22×C11—22no—
630C22×C11—22no—
631C22×C11—22no—
632C22×C11—22no—
633C22×C11—24no—
634C22×C11—24no—
635C22×C11—24no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11C4×#4114yes—
641C22×C11C24×C411yescharacteristic
642C22×C11C22×#4111yescharacteristic
643C22×C11C22×#4111yescharacteristic
644C22×C11C2×H(5,𝔽2)11yescharacteristic
645C22×C11C2×H(5,𝔽2)11yescharacteristic
646C22×C11#58511yescharacteristic
647C22×C11#58511yescharacteristic
648C2×D11—22no—
649C2×D11—22no—
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—416no—
655C2×D11—41no—
656C2×D11—41no—
657C2×D11—41no—
658C2×D11—41no—
659C2×D11—41no—
660C2×D11—41no—
661C2×D11—41no—
662C2×D11—41no—
663C4×C11—24no—
664C4×C11—22no—
665C4×C11—22no—
666C4×C11—22no—
667C4×C11—42no—
668C4×C11—42no—
669C4×C11—41no—
670C4×C11—41no—
671C4×C11#51814yes—
672Dic11—24no—
673Dic11—22no—
674Dic11—22no—
675Dic11—24no—
676Dic11—22no—
677Dic11—22no—
678Dic11—42no—
679Dic11—42no—
680Dic11—41no—
681Dic11—41no—
682C25—111no—
683C2×#41—118no—
684C2×#41—442no—
685C2×#41—442no—
686C22×Q8—111no—
687C22×D4—112no—
688C22×D4—112no—
689C22×D4C22×D1112yes—
690C22×D4C22×D1111yescharacteristic
691C23×C4—111no—
692C23×C4—111no—
693C23×C4—112no—
694C23×C4—111no—
695C23×C4—111no—
696C23×C4—118no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—112no—
701C23×C4—442no—
702C23×C4—442no—
703C23×C4C22×D1111yescharacteristic
704C23×C4C22×D1111yescharacteristic
705C23×C4C22×D1112yes—
706C23×C4C22×D1111yescharacteristic
707#123—1116no—
708C22⋊Q8—118no—
709C22⋊Q8—118no—
710#121—118no—
711#121C4×D1118yes—
712#120—1116no—
713C4×Q8—442no—
714C4×Q8—442no—
715C4×D4—28no—
716C4×D4—42no—
717C4×D4—1116no—
718C4×D4—1116no—
719C4×D4—228no—
720C4×D4—442no—
721#117—118no—
722#117—442no—
723#117—442no—
724C2×C4⋊C4—111no—
725C2×C4⋊C4—112no—
726C2×C4⋊C4—112no—
727C2×C4⋊C4—111no—
728C2×C4⋊C4—111no—
729C2×C4⋊C4—112no—
730C2×C4⋊C4—112no—
731C2×C4⋊C4—112no—
732C2×C4⋊C4—112no—
733C2×C4⋊C4—112no—
734C2×C4⋊C4C22×D1111yescharacteristic
735C2×C4⋊C4C22×D1111yescharacteristic
736C2×C4⋊C4C22×D1112yes—
737C2×C4⋊C4C22×D1111yescharacteristic
738C2×C22⋊C4—112no—
739C2×C22⋊C4—112no—
740C2×C22⋊C4—112no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—112no—
744C2×C22⋊C4—111no—
745C2×C22⋊C4—111no—
746C2×C22⋊C4—111no—
747C2×C22⋊C4—111no—
748C2×C22⋊C4—111no—
749C2×C22⋊C4—111no—
750C2×C22⋊C4—111no—
751C2×C22⋊C4—111no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—224no—
759C2×C22⋊C4—224no—
760C2×C22⋊C4C22×D1112yes—
761C2×C22⋊C4C22×D1112yes—
762C2×C22⋊C4C22×D1112yes—
763C2×C22⋊C4C22×D1112yes—
764C2×C22⋊C4C22×D1112yes—
765C2×C42—42no—
766C2×C42—112no—
767C2×C42—112no—
768C2×C42—111no—
769C2×C42—111no—
770C2×C42—112no—
771C2×C42—112no—
772C2×C42—112no—
773C2×C42—112no—
774C2×C42—111no—
775C2×C42—112no—
776C2×C42—112no—
777C2×C42—111no—
778C2×C42—442no—
779C2×C42C22×D1112yes—
780C2×C42C22×D1111yescharacteristic
781C2×C42C22×D1111yescharacteristic
782C2×C42C22×D1111yescharacteristic
783C2×C42C22×D1111yescharacteristic
784#95—111no—
785#95—111no—
786#95—111no—
787#95—111no—
788#95—111no—
789#95—111no—
790#95—111no—
791#95—111no—
792#95—112no—
793#95—112no—
794#95—112no—
795#95—112no—
796#95—112no—
797#95—112no—
798#95—112no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95—112no—
803#95—112no—
804#95—112no—
805#95C22×D1112yes—
806#95C22×D1112yes—
807#95C22×D1112yes—
808C2×C11—24no—
809C2×C11—44no—
810C2×C11C2×C4×#4111yescharacteristic
811C2×C11C2×#51811yescharacteristic
812C2×C11#342811yescharacteristic
813C2×C11#350511yescharacteristic
814C2×C11#350511yescharacteristic
815C2×C11#350611yescharacteristic
816C2×C11#350611yescharacteristic
817D11—42no—
818D11—42no—
819C24—111no—
820C24—111no—
821C24—114no—
822C24—222no—
823C24—222no—
824C24—441no—
825C24—441no—
826C24—441no—
827C24—441no—
828C24C23×D1112yes—
829C24C23×D1111yescharacteristic
830#41—4416no—
831C2×Q8—114no—
832C2×Q8—222no—
833C2×Q8—222no—
834C2×D4—24no—
835C2×D4—24no—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—118no—
839C2×D4—118no—
840C2×D4—442no—
841C2×D4—442no—
842C2×D4—442no—
843C2×D4—442no—
844C2×D4C2×C4×D1118yes—
845C2×D4C2×C4×D1114yes—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—24no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—111no—
857C22×C4—111no—
858C22×C4—111no—
859C22×C4—112no—
860C22×C4—112no—
861C22×C4—111no—
862C22×C4—114no—
863C22×C4—118no—
864C22×C4—114no—
865C22×C4—114no—
866C22×C4—114no—
867C22×C4—114no—
868C22×C4—114no—
869C22×C4—111no—
870C22×C4—111no—
871C22×C4—112no—
872C22×C4—112no—
873C22×C4—224no—
874C22×C4—222no—
875C22×C4—222no—
876C22×C4—222no—
877C22×C4—222no—
878C22×C4—222no—
879C22×C4—4416no—
880C22×C4—441no—
881C22×C4—441no—
882C22×C4—441no—
883C22×C4—441no—
884C22×C4—441no—
885C22×C4—441no—
886C22×C4—441no—
887C22×C4—441no—
888C22×C4—442no—
889C22×C4—442no—
890C22×C4—441no—
891C22×C4—441no—
892C22×C4—442no—
893C22×C4—442no—
894C22×C4C2×C4×D1114yes—
895C22×C4#434114yescomplemented
896C22×C4C23×D1112yes—
897C22×C4C23×D1111yescharacteristic
898C22×C4C23×D1111yescharacteristic
899C22×C4C23×D1112yes—
900C22×C4C23×D1111yescharacteristic
901C22×C4C23×D1112yes—
902C22×C4C23×D1111yescharacteristic
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—114no—
909C4⋊C4—118no—
910C4⋊C4—118no—
911C4⋊C4—224no—
912C4⋊C4—222no—
913C4⋊C4—222no—
914C4⋊C4—442no—
915C4⋊C4—442no—
916C4⋊C4—442no—
917C4⋊C4—442no—
918C4⋊C4C2×C4×D1114yes—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—118no—
924C22⋊C4—118no—
925C22⋊C4—118no—
926C22⋊C4—118no—
927C22⋊C4—222no—
928C22⋊C4—222no—
929C22⋊C4—222no—
930C22⋊C4—222no—
931C22⋊C4—224no—
932C22⋊C4—224no—
933C22⋊C4—222no—
934C22⋊C4—222no—
935C22⋊C4—222no—
936C22⋊C4—222no—
937C22⋊C4—442no—
938C22⋊C4—442no—
939C22⋊C4—442no—
940C22⋊C4—442no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4C2×C4×D1118yes—
944C42—24no—
945C42—22no—
946C42—22no—
947C42—41no—
948C42—41no—
949C42—118no—
950C42—224no—
951C42—222no—
952C42—222no—
953C42—441no—
954C42—441no—
955C42—442no—
956C42—442no—
957C42—442no—
958C42—442no—
959C42—442no—
960C42—442no—
961C11#3422311yescharacteristic, complemented, Sylow
962C23—21no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—112no—
973C23—112no—
974C23—228no—
975C23—221no—
976C23—221no—
977C23—221no—
978C23—221no—
979C23—221no—
980C23—221no—
981C23—221no—
982C23—221no—
983C23—221no—
984C23—221no—
985C23—221no—
986C23—221no—
987C23—444no—
988C23—444no—
989C23—444no—
990C23—444no—
991C23—444no—
992C23—444no—
993C23C22×C4×D1114yes—
994C23C22×C4×D1112yes—
995C23C2×#434112yes—
996C23#41×D1112yes—
997C23C24×D1111yescharacteristic
998Q8—228no—
999D4—216no—
1000D4—28no—
1001D4—448no—
1002D4—448no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—28no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—84no—
1027C2×C4—112no—
1028C2×C4—114no—
1029C2×C4—112no—
1030C2×C4—114no—
1031C2×C4—112no—
1032C2×C4—112no—
1033C2×C4—221no—
1034C2×C4—222no—
1035C2×C4—221no—
1036C2×C4—221no—
1037C2×C4—221no—
1038C2×C4—221no—
1039C2×C4—222no—
1040C2×C4—221no—
1041C2×C4—221no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—221no—
1045C2×C4—228no—
1046C2×C4—228no—
1047C2×C4—221no—
1048C2×C4—221no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—221no—
1053C2×C4—221no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—221no—
1058C2×C4—221no—
1059C2×C4—444no—
1060C2×C4—444no—
1061C2×C4—444no—
1062C2×C4—448no—
1063C2×C4—444no—
1064C2×C4—444no—
1065C2×C4—884no—
1066C2×C4C22×C4×D1114yes—
1067C2×C4C22×C4×D1112yes—
1068C2×C4C22×C4×D1112yes—
1069C2×C4C2×#434112yes—
1070C2×C4C2×#434112yes—
1071C2×C4#6703712yes—
1072C2×C4#6704212yes—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—24no—
1080C22—24no—
1081C22—24no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—222no—
1087C22—222no—
1088C22—222no—
1089C22—222no—
1090C22—222no—
1091C22—222no—
1092C22—4416no—
1093C22—441no—
1094C22—441no—
1095C22—441no—
1096C22—441no—
1097C22—441no—
1098C22—441no—
1099C22—441no—
1100C22—441no—
1101C22C4×#434114yes—
1102C22C23×C4×D1111yescharacteristic
1103C22C22×#434111yescharacteristic
1104C22C2×#6703711yescharacteristic
1105C22C2×#41×D1111yescharacteristic
1106C22C2×#6704211yescharacteristic
1107C22#1062345311yescharacteristic
1108C22#1062345311yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—24no—
1112C4—22no—
1113C4—42no—
1114C4—41no—
1115C4—41no—
1116C4—42no—
1117C4—222no—
1118C4—222no—
1119C4—222no—
1120C4—222no—
1121C4—224no—
1122C4—224no—
1123C4—442no—
1124C4—442no—
1125C4—441no—
1126C4—441no—
1127C4#1062307614yes—
1128C2—24no—
1129C2—44no—
1130C2—442no—
1131C2—442no—
1132C2C2×C4×#434111yescharacteristic
1133C2C2×#1062307611yescharacteristic
1134C2#1308181511yescharacteristic
1135C2#1308245011yescharacteristic
1136C2#1308245111yescharacteristic
1137C2#1308245911yescharacteristic
1138C2#1308246511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×#121C2
socle, cosocleC23×C11C25
prime radicalC2×#10623137C2
hypercenterC4×#121D11
hypocenterC11#34223
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #13071750C2semidirect
3. #13071744C2semidirect
4. #13071659C2semidirect
5. #13071650C2semidirect
6. #13071645C2semidirect
7. #13071642C2semidirect
8. #13071586C2semidirect
9. #13071550C2semidirect
10. #13071508C2semidirect
11. #13071497C2semidirect
12. #13071455C2semidirect
13. #13071441C2semidirect
14. #13071279C2semidirect
15. #13071270C2semidirect
16. #13071242C2semidirect
17. C4×#66977C2semidirect
18. #13071144C2semidirect
19. #121×Dic11C2semidirect
20. #13070998C2semidirect
21. #13070977C2semidirect
22. C2×C4×(C2×D11)⋊C4C2semidirect
23. C4×C11×#121C2semidirect
28. C2×C4×D4×C11C22semidirect
34. C2×D4×Dic11C22semidirect
39. #10623137C4semidirect
44. C2×#66940C22semidirect
47. C2×C4×Dic22C22semidirect
48. C11×#390C22semidirect
49. C11×#389C22semidirect
50. C11×#388C22semidirect
53. C4×C11×C4⋊C4C22semidirect
54. C4×C11×C22⋊C4C22semidirect
55. #10622834C22semidirect
62. C4×C22⋊Dic11C22semidirect
65. C2×C11⋊#95C22semidirect
70. #10622598C22semidirect
71. C4⋊C4×Dic11C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. C4⋊C4×Dic11C22semidirect
74. C4⋊C4×Dic11C22semidirect
75. #10622587C22semidirect
76. #10622586C22semidirect
84. #10622564C22semidirect
86. #10622558C22semidirect
87. #10622557C22semidirect
88. #10622556C22semidirect
89. #10622555C22semidirect
92. C22⋊C4×Dic11C22semidirect
93. C22⋊C4×Dic11C22semidirect
94. C22⋊C4×Dic11C22semidirect
105. C4×C4⋊Dic11C22semidirect
106. C4×C4⋊Dic11C22semidirect
107. #10622546C22semidirect
108. #10622545C22semidirect
109. C4×Dic11⋊C4C22semidirect
110. #10622542C22semidirect
111. #10622541C22semidirect
118. #10622267C22semidirect
119. #10622266C22semidirect
120. #10622265C22semidirect
121. #10622264C22semidirect
122. #10622263C22semidirect
123. #10622262C22semidirect
140. C2×#4341C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
173. #66991C2×C4semidirect
174. #66990C2×C4semidirect
177. D4×Dic11C2×C4semidirect
199. #66977C2×C4semidirect
218. #66950C2×C4semidirect
221. #66945C2×C4semidirect
223. #66936C2×C4semidirect
224. (C22⋊D11)⋊C4C2×C4semidirect
279. C22×C4×C11#41semidirect
309. C22×Dic11#41semidirect
412. C4×#121D11semidirect
543. C2×C4×D4C2×D11semidirect
558. #390C2×D11semidirect
562. #389C2×D11semidirect
574. #388C2×D11semidirect
605. C4×C4⋊C4C2×D11semidirect
622. C4×C22⋊C4C2×D11semidirect
895. C22×C4#4341semidirect
961. C11#34223semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
#130717502
#130717442
#130716592
#130716502
#130716452
#130716422
#130715862
#130715502
#130715082
#130714972
#130714552
#130714412
#130712792
#130712702
#130712422
C4×#669772
#130711442
#121×Dic112
#130709982
#130709772
C2×C4×(C2×D11)⋊C42
C4×C11×#1212
#3422311