Finite Group Databasebeta

← #14913346

Subgroups — #14913346

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic
2C2×C4×#4339C211yesmaximal, characteristic, complemented
3C2×D11×#117C211yesmaximal, characteristic, complemented
4#13071657C212yesmaximal, complemented
5#13071646C212yesmaximal, complemented
6#13071635C212yesmaximal, complemented
7#13071624C212yesmaximal, complemented
8#13071615C212yesmaximal, complemented
9#13071611C212yesmaximal, complemented
10#13071599C212yesmaximal, complemented
11#13071594C212yesmaximal, complemented
12#13071102C211yesmaximal, characteristic, complemented
13#13071096C211yesmaximal, characteristic, complemented
14#13071081C211yesmaximal, characteristic, complemented
15#13071075C211yesmaximal, characteristic, complemented
16#13071062C211yesmaximal, characteristic, complemented
17#13071062C211yesmaximal, characteristic, complemented
18#13071060C211yesmaximal, characteristic, complemented
19C42×C22⋊D11C211yesmaximal, characteristic, complemented
20C4×#66946C211yesmaximal, characteristic, complemented
21#13070955C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2290C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic, complemented
29C2×#66992C2211yescharacteristic
30C2×#66990C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2212yes—
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×C4×C22⋊D11C2212yescomplemented
36C2×#66979C2211yescharacteristic
37C2×#66979C2211yescharacteristic, complemented
38#10623078C4116yescomplemented
39D11×#117—28no—
40C2×#66949C2211yescharacteristic
41C2×#66947C2211yescharacteristic
42C2×#66946C2212yes—
43C2×#66945C2212yes—
44C2×C4⋊C4×D11C2212yes—
45C2×#66937C2211yescharacteristic
46C2×#66936C2211yescharacteristic
47C2×#66935C2211yescharacteristic
48C2×C22⋊C4×D11C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×#66931C2211yescharacteristic
51C2×#66930C2212yes—
52C4×#4339—28no—
53C2×C4×D44C2212yes—
54C2×C4×D44C2211yescharacteristic
55C2×#66925C2211yescharacteristic
56C2×#66925C2211yescharacteristic
57C2×#66925C2211yescharacteristic
58C2×#66925C2211yescharacteristic, complemented
59C2×C42×D11C2211yescharacteristic
60C2×C42×D11C2211yescharacteristic
61C2×C42×D11C2211yescharacteristic
62C2×C42×D11C2211yescharacteristic
63C2×C42×D11C2211yescharacteristic, complemented
64C2×C4×Dic22C2212yescomplemented
65C11×#388C2212yes—
66C11×#387C2212yescomplemented
67C11×#386C2212yes—
68C11×#385C2212yescomplemented
69C4×C11×C4⋊C4C2211yescharacteristic, complemented
70C4×C11×C22⋊C4C2211yescharacteristic
71C4×C11×C22⋊C4C2211yescharacteristic, complemented
72C11×#376C2211yescharacteristic, complemented
73#10622834C2212yes—
74C4×C22⋊Dic11C2211yescharacteristic
75C4×C22⋊Dic11C2212yescomplemented
76C4×C22⋊Dic11C2211yescharacteristic, complemented
77#10622603C2212yescomplemented
78#10622602C2212yes—
79#10622598C2212yescomplemented
80C4⋊C4×Dic11C2212yescomplemented
81#10622585C2212yescomplemented
82#10622585C2212yescomplemented
83#10622570C2212yes—
84#10622570C2212yescomplemented
85#10622569C2212yes—
86#10622569C2212yes—
87#10622569C2212yes—
88#10622564C2212yes—
89#10622564C2212yescomplemented
90#10622558C2212yes—
91#10622558C2212yes—
92#10622558C2212yescomplemented
93C22⋊C4×Dic11C2212yes—
94C4×(C2×D11)⋊C4C2212yes—
95C4×(C2×D11)⋊C4C2211yescharacteristic
96C4×(C2×D11)⋊C4C2211yescharacteristic
97C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
98C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
99C4×C4⋊Dic11C2211yescharacteristic, complemented
100#10622545C2211yescharacteristic, complemented
101C4×Dic11⋊C4C2212yescomplemented
102C4×Dic11⋊C4C2211yescharacteristic, complemented
103C4×Dic11⋊C4C2211yescharacteristic, complemented
104C42×Dic11C2211yescharacteristic, complemented
105C42×Dic11C2211yescharacteristic, complemented
106#10622283C2212yescomplemented
107#10622281C2212yes—
108#10622281C2212yes—
109#10622281C2212yes—
110#10622281C2212yescomplemented
111#10622279C2212yes—
112#10622279C2212yes—
113#10622279C2212yes—
114#10622279C2212yes—
115#10622279C2212yescomplemented
116#10622278C2212yes—
117#10622278C2212yes—
118D11×#95C2212yes—
119#10622268C2212yescomplemented
120#10622268C2212yescomplemented
121#10622266C2212yescomplemented
122#10622262C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2212yescomplemented
125#10622259C2212yescomplemented
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C2×#4339—24no—
137C2×#4339—24no—
138C2×#4339C2×C418yescomplemented
139C22×D44C2311yescharacteristic
140C22×D44C2311yescharacteristic
141C22×C4×D11—24no—
142C22×C4×D11—24no—
143C22×C4×D11C2×C418yescomplemented
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×Dic22C2311yescharacteristic
155C4×D4×C11C2×C418yescomplemented
156C11×#117—24no—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C42×C11—24no—
166C2×C42×C11C2312yes—
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178#66992C2×C418yescomplemented
179#66990C2×C418yescomplemented
180C4×C22⋊D11—28no—
181C4×C22⋊D11—28no—
182C4×C22⋊D11—28no—
183C4×C22⋊D11C2×C418yescomplemented
184C4×C22⋊D11C2×C418yescomplemented
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198#66979—24no—
199#66979—24no—
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2312yes—
203C2×C4⋊Dic11C2311yescharacteristic
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227#66949C2×C418yescomplemented
228#66947C2×C418yescomplemented
229#66946—28no—
230#66945—28no—
231C4⋊C4×D11—28no—
232#66937C2×C418yescomplemented
233#66936C2×C418yescomplemented
234#66935C2×C418yescomplemented
235C22⋊C4×D11—28no—
236C22⋊C4×D11—28no—
237#66931C2×C418yescomplemented
238#66930—28no—
239C4×D44—28no—
240C4×D44C2×C418yescomplemented
241#66925—24no—
242#66925—24no—
243#66925C2×C418yescomplemented
244#66925D418yescomplemented
245C42×D11—24no—
246C42×D11—24no—
247C42×D11—24no—
248C42×D11—24no—
249C42×D11—24no—
250C4×Dic22—28no—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11×#95C2312yes—
254C11×#95C2312yes—
255C11×#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267#34136—111nomaximal, Sylow
268C24×C11C2411yescharacteristic
269C24×C11C2411yescharacteristic
270C23×D11—22no—
271C23×D11—24no—
272C23×D11—22no—
273C23×D11—42no—
274C23×D11C22×C414yes—
275C23×D11C2411yescharacteristic
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C2×D4×C11—42no—
279C2×D4×C11C22×C414yes—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—22no—
284C22×C4×C11—24no—
285C22×C4×C11—24no—
286C22×C4×C11—42no—
287C22×C4×C11C22×C414yes—
288C22×C4×C11C22×C414yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11C22×C414yes—
305C2×C22⋊D11C22×C414yes—
306C2×C22⋊D11C22×C414yes—
307C2×C22⋊D11C22×C414yes—
308C22×Dic11—22no—
309C22×Dic11—22no—
310C22×Dic11C22×C414yes—
311C22×Dic11C2412yes—
312C22×Dic11C2412yes—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2412yes—
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320#4339—232no—
321C2×D44—22no—
322C2×D44—24no—
323C2×D44—22no—
324C2×D44C22×C414yes—
325C2×D44C22×C414yes—
326C2×C4×D11—22no—
327C2×C4×D11—22no—
328C2×C4×D11—232no—
329C2×C4×D11—24no—
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—22no—
333C2×C4×D11—24no—
334C2×C4×D11—22no—
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—24no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11C22×C414yes—
351C2×C4×D11C22×C414yes—
352C2×C4×D11C22×C414yes—
353C2×C4×D11C22×C414yes—
354C2×C4×D11C22×C414yes—
355C2×C4×D11C2×D414yes—
356C2×C4×D11#4114yes—
357C2×Dic22—22no—
358C2×Dic22—22no—
359C2×Dic22C22×C414yes—
360C11×C4⋊C4—24no—
361C11×C4⋊C4—24no—
362C11×C4⋊C4C22×C414yes—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4C22×C414yes—
367C11×C22⋊C4C22×C414yes—
368C42×C11—24no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—22no—
372C42×C11C22×C414yes—
373C42×C11C2×D414yes—
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11C22×C414yes—
379C22⋊Dic11C22×C414yes—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4C22×C414yes—
386(C2×D11)⋊C4C22×C414yes—
387(C2×D11)⋊C4C22×C414yes—
388(C2×D11)⋊C4C22×C414yes—
389(C2×D11)⋊C4C22×C414yes—
390(C2×D11)⋊C4C22×C414yes—
391(C2×D11)⋊C4C2×D418yes—
392(C2×D11)⋊C4#4118yescomplemented
393C4⋊Dic11—24no—
394C4⋊Dic11—24no—
395C4⋊Dic11—42no—
396C4⋊Dic11C22×C414yes—
397Dic11⋊C4—24no—
398Dic11⋊C4—24no—
399Dic11⋊C4—24no—
400Dic11⋊C4—42no—
401Dic11⋊C4C22×C414yes—
402Dic11⋊C4C22×C414yes—
403Dic11⋊C4C22×C414yes—
404Dic11⋊C4C22×C414yes—
405Dic11⋊C4C2×D418yes—
406C4×Dic11—24no—
407C4×Dic11—24no—
408C4×Dic11—24no—
409C4×Dic11—24no—
410C4×Dic11—24no—
411C4×Dic11—24no—
412C4×Dic11—22no—
413C4×Dic11—22no—
414C4×Dic11—24no—
415C4×Dic11—22no—
416C4×Dic11—42no—
417C4×Dic11—42no—
418C4×Dic11C22×C414yes—
419C4×Dic11C2×D414yes—
420C2×#525—111no—
421C2×C4×#41—111no—
422C22×#117—111no—
423#2363—112no—
424#2362—112no—
425#2361—112no—
426#2360—112no—
427#2359—112no—
428#2359—112no—
429#2358—112no—
430#2358—112no—
431#2297—111no—
432#2296—111no—
433#2293—111no—
434#2293—111no—
435#2290—111no—
436#2290—111no—
437#2290—111no—
438#2290D1111yescharacteristic, complemented
439C42×D4—111no—
440C42×D4—111no—
441C4×#117—111no—
442C2×C4×C22⋊C4—111no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11C23×C412yes—
452C23×C11C23×C412yes—
453C23×C11C2511yescharacteristic
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—21no—
460C22×D11—22no—
461C22×D11—21no—
462C22×D11—22no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—44no—
466C22×D11—48no—
467C22×D11—48no—
468C22×D11C23×C412yes—
469C22×D11C23×C412yes—
470C22×D11C23×C412yes—
471C22×D11C22×D412yes—
472C22×D11C2×#4112yes—
473C22×D11C2×#4114yes—
474D4×C11—44no—
475C2×C4×C11—22no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—28no—
486C2×C4×C11—28no—
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×C11—48no—
494C2×C4×C11C23×C412yes—
495C2×C4×C11C23×C412yes—
496C2×C4×C11C23×C412yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11C22×D414yes—
500C2×C4×C11C22×D412yes—
501C2×C4×C11C2×#4114yes—
502C2×C4×C11C2×#4112yes—
503C22⋊D11—28no—
504C22⋊D11—28no—
505C22⋊D11—28no—
506C22⋊D11—44no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—28no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11C23×C412yes—
525C2×Dic11C23×C412yes—
526C2×Dic11C23×C412yes—
527C2×Dic11C23×C412yes—
528C2×Dic11C23×C412yes—
529C2×Dic11C22×D414yes—
530C2×Dic11C22×D412yes—
531C2×Dic11C2×#4114yes—
532C2×Dic11C2×#4112yes—
533D44—28no—
534D44—28no—
535C4×D11—28no—
536C4×D11—28no—
537C4×D11—28no—
538C4×D11—28no—
539C4×D11—48no—
540C4×D11—48no—
541C4×D11—48no—
542C4×D11—48no—
543C4×D11—48no—
544C4×D11C4×D4116yescomplemented
545Dic22—28no—
546C22×#41—111no—
547C24×C4—111no—
548#525—1116no—
549C2×#123—111no—
550C2×#123—111no—
551C2×C22⋊Q8—111no—
552C2×C22⋊Q8—111no—
553C2×#121—111no—
554C2×#121—111no—
555C2×#120—111no—
556C2×#120—111no—
557C4×#41—228no—
558C2×C4×Q8—112no—
559C2×C4×D4—111no—
560C2×C4×D4—111no—
561C2×C4×D4—112no—
562C2×C4×D4—112no—
563C2×C4×D4—112no—
564C2×C4×D4—112no—
565C2×C4×D4—111no—
566C2×C4×D4—112no—
567C2×C4×D4C2×D1111yescharacteristic
568C2×#117—111no—
569C2×#117—111no—
570C2×#117—112no—
571C2×#117—112no—
572C2×#117—111no—
573C2×#117—111no—
574C2×#117—111no—
575C2×#117—111no—
576C2×#117—228no—
577C2×#117C2×D1111yescharacteristic
578C22×C4⋊C4—112no—
579C22×C22⋊C4—112no—
580C22×C22⋊C4—112no—
581C22×C42—111no—
582C22×C42—111no—
583C22×C42—111no—
584C22×C42—111no—
585C22×C42—111no—
586C22×C42C2×D1111yescharacteristic, complemented
587#391—112no—
588#390—112no—
589#390—112no—
590#390—112no—
591#389—112no—
592#389—112no—
593#389—112no—
594#389—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388—112no—
599#388—112no—
600#388—112no—
601#388—112no—
602#388C2×D1112yes—
603#387—112no—
604#387—112no—
605#387—112no—
606#387C2×D1112yescomplemented
607#386—112no—
608#386—112no—
609#386—112no—
610#386—112no—
611#386—112no—
612#386C2×D1112yes—
613#385—112no—
614#385—112no—
615#385—112no—
616#385—112no—
617#385—112no—
618#385C2×D1112yescomplemented
619C4×C4⋊C4—112no—
620C4×C4⋊C4—112no—
621C4×C4⋊C4—111no—
622C4×C4⋊C4—111no—
623C4×C4⋊C4—111no—
624C4×C4⋊C4—112no—
625C4×C4⋊C4—112no—
626C4×C4⋊C4C2×D1111yescharacteristic, complemented
627C4×C22⋊C4—112no—
628C4×C22⋊C4—111no—
629C4×C22⋊C4—111no—
630C4×C22⋊C4—112no—
631C4×C22⋊C4—112no—
632C4×C22⋊C4—111no—
633C4×C22⋊C4—111no—
634C4×C22⋊C4—111no—
635C4×C22⋊C4—111no—
636C4×C22⋊C4—112no—
637C4×C22⋊C4—112no—
638C4×C22⋊C4—112no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4C2×D1111yescharacteristic
642C4×C22⋊C4C2×D1111yescharacteristic, complemented
643#376—111no—
644#376C2×D1111yescharacteristic, complemented
645C2×#95—112no—
646C43—111no—
647C43—111no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—22no—
652C22×C11—22no—
653C22×C11—22no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11C24×C411yescharacteristic
659C22×C11C23×D411yescharacteristic
660C22×C11C22×#4111yescharacteristic
661C22×C11C22×#4112yes—
662C22×C11#58512yes—
663C2×D11—22no—
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—24no—
668C2×D11—24no—
669C2×D11—24no—
670C2×D11—24no—
671C2×D11—22no—
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—416no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11C2×C4×D414yes—
678C2×D11C4×#4114yescomplemented
679C4×C11—22no—
680C4×C11—22no—
681C4×C11—22no—
682C4×C11—22no—
683C4×C11—24no—
684C4×C11—24no—
685C4×C11—42no—
686C4×C11—42no—
687C4×C11C2×C4×D414yes—
688Dic11—22no—
689Dic11—22no—
690Dic11—22no—
691Dic11—22no—
692Dic11—24no—
693Dic11—24no—
694Dic11—42no—
695Dic11—42no—
696Dic11C2×C4×D414yes—
697C25—111no—
698C2×#41—118no—
699C2×#41—224no—
700C2×#41—224no—
701C22×Q8—111no—
702C22×D4—111no—
703C22×D4—111no—
704C22×D4—111no—
705C22×D4—111no—
706C22×D4—111no—
707C22×D4—111no—
708C22×D4C22×D1111yescharacteristic
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—118no—
712C23×C4—111no—
713C23×C4—111no—
714C23×C4—111no—
715C23×C4—111no—
716C23×C4—112no—
717C23×C4—112no—
718C23×C4—112no—
719C23×C4—112no—
720C23×C4—112no—
721C23×C4—224no—
722C23×C4—224no—
723C23×C4C22×D1112yes—
724C23×C4C22×D1111yescharacteristic
725C23×C4C22×D1111yescharacteristic
726#123—118no—
727#123—118no—
728C22⋊Q8—118no—
729C22⋊Q8—118no—
730#121—118no—
731#121—118no—
732#120—118no—
733#120—118no—
734C4×Q8—228no—
735C4×D4—118no—
736C4×D4—118no—
737C4×D4—118no—
738C4×D4—228no—
739C4×D4—228no—
740C4×D4—228no—
741C4×D4—228no—
742C4×D4—228no—
743C4×D4C4×D1118yescomplemented
744#117—24no—
745#117—118no—
746#117—118no—
747#117—224no—
748#117—224no—
749#117—224no—
750#117—228no—
751#117—228no—
752#117—224no—
753C2×C4⋊C4—112no—
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—112no—
766C2×C4⋊C4—228no—
767C2×C4⋊C4C22×D1112yes—
768C2×C4⋊C4C22×D1112yes—
769C2×C4⋊C4C22×D1111yescharacteristic
770C2×C22⋊C4—111no—
771C2×C22⋊C4—111no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—111no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—111no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—112no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—228no—
790C2×C22⋊C4—228no—
791C2×C22⋊C4C22×D1112yes—
792C2×C22⋊C4C22×D1112yes—
793C2×C22⋊C4C22×D1112yes—
794C2×C22⋊C4C22×D1111yescharacteristic
795C2×C22⋊C4C22×D1111yescharacteristic
796C2×C42—24no—
797C2×C42—111no—
798C2×C42—111no—
799C2×C42—112no—
800C2×C42—112no—
801C2×C42—112no—
802C2×C42—112no—
803C2×C42—112no—
804C2×C42—112no—
805C2×C42—112no—
806C2×C42—111no—
807C2×C42—111no—
808C2×C42—111no—
809C2×C42—112no—
810C2×C42—112no—
811C2×C42—224no—
812C2×C42—224no—
813C2×C42—224no—
814C2×C42—224no—
815C2×C42—224no—
816C2×C42C22×D1112yes—
817C2×C42C22×D1111yescharacteristic
818C2×C42C22×D1111yescharacteristic
819C2×C42C22×D1111yescharacteristic
820C2×C42C22×D1111yescharacteristic
821C2×C42C22×D1111yescharacteristic
822#95—112no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95C22×D1112yes—
834#95C22×D1112yes—
835#95C22×D1112yes—
836#95C22×D1112yes—
837#95C22×D1112yes—
838C2×C11—42no—
839C2×C11—42no—
840C2×C11C22×C4×D411yescharacteristic
841C2×C11C2×C4×#4111yescharacteristic
842C2×C11#342811yescharacteristic
843C2×C11D4×#4112yes—
844C2×C11#347512yes—
845D11—24no—
846D11—24no—
847D11—42no—
848C24—111no—
849C24—111no—
850C24—111no—
851C24—114no—
852C24—222no—
853C24—224no—
854C24—222no—
855C24—442no—
856C24C23×D1111yescharacteristic
857C24C23×D1111yescharacteristic
858#41—2232no—
859C2×Q8—114no—
860C2×Q8—222no—
861C2×Q8—222no—
862C2×D4—42no—
863C2×D4—114no—
864C2×D4—114no—
865C2×D4—114no—
866C2×D4—114no—
867C2×D4—114no—
868C2×D4—114no—
869C2×D4—222no—
870C2×D4—224no—
871C2×D4—222no—
872C2×D4—222no—
873C2×D4—222no—
874C2×D4—222no—
875C2×D4—224no—
876C2×D4—222no—
877C2×D4—442no—
878C2×D4C2×C4×D1114yes—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—42no—
886C22×C4—111no—
887C22×C4—114no—
888C22×C4—114no—
889C22×C4—114no—
890C22×C4—114no—
891C22×C4—112no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—112no—
897C22×C4—114no—
898C22×C4—114no—
899C22×C4—114no—
900C22×C4—114no—
901C22×C4—112no—
902C22×C4—112no—
903C22×C4—222no—
904C22×C4—222no—
905C22×C4—2232no—
906C22×C4—224no—
907C22×C4—224no—
908C22×C4—224no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—224no—
912C22×C4—224no—
913C22×C4—224no—
914C22×C4—224no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—224no—
922C22×C4—224no—
923C22×C4—224no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4—442no—
929C22×C4C2×C4×D1114yes—
930C22×C4C2×C4×D1114yes—
931C22×C4C23×D1112yes—
932C22×C4C23×D1112yes—
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1111yescharacteristic
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1112yes—
938C22×C4C23×D1112yes—
939C22×C4C23×D1111yescharacteristic
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—114no—
943C4⋊C4—114no—
944C4⋊C4—114no—
945C4⋊C4—114no—
946C4⋊C4—114no—
947C4⋊C4—118no—
948C4⋊C4—224no—
949C4⋊C4—224no—
950C4⋊C4—224no—
951C4⋊C4—224no—
952C4⋊C4—224no—
953C4⋊C4—442no—
954C4⋊C4—442no—
955C4⋊C4C2×C4×D1114yes—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—42no—
959C22⋊C4—114no—
960C22⋊C4—114no—
961C22⋊C4—114no—
962C22⋊C4—114no—
963C22⋊C4—114no—
964C22⋊C4—114no—
965C22⋊C4—114no—
966C22⋊C4—114no—
967C22⋊C4—118no—
968C22⋊C4—118no—
969C22⋊C4—224no—
970C22⋊C4—224no—
971C22⋊C4—224no—
972C22⋊C4—224no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—442no—
978C22⋊C4C2×C4×D1114yes—
979C22⋊C4C2×C4×D1114yes—
980C42—22no—
981C42—24no—
982C42—22no—
983C42—22no—
984C42—114no—
985C42—114no—
986C42—224no—
987C42—224no—
988C42—224no—
989C42—224no—
990C42—224no—
991C42—224no—
992C42—224no—
993C42—222no—
994C42—222no—
995C42—222no—
996C42—442no—
997C42—442no—
998C42C2×C4×D1114yes—
999C42D4×D1114yes—
1000C11#3413611yescharacteristic, complemented, Sylow
1001C23—21no—
1002C23—21no—
1003C23—22no—
1004C23—22no—
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23—22no—
1009C23—112no—
1010C23—112no—
1011C23—112no—
1012C23—114no—
1013C23—112no—
1014C23—112no—
1015C23—228no—
1016C23—228no—
1017C23—221no—
1018C23—222no—
1019C23—221no—
1020C23—222no—
1021C23—222no—
1022C23—221no—
1023C23—222no—
1024C23—221no—
1025C23—222no—
1026C23—444no—
1027C23—448no—
1028C23—448no—
1029C23C22×C4×D1112yes—
1030C23C22×C4×D1112yes—
1031C23C24×D1111yescharacteristic
1032Q8—228no—
1033D4—44no—
1034D4—228no—
1035D4—228no—
1036D4—228no—
1037D4—228no—
1038D4—228no—
1039D4—444no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—28no—
1051C2×C4—28no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—48no—
1059C2×C4—112no—
1060C2×C4—112no—
1061C2×C4—112no—
1062C2×C4—1116no—
1063C2×C4—112no—
1064C2×C4—112no—
1065C2×C4—112no—
1066C2×C4—112no—
1067C2×C4—114no—
1068C2×C4—114no—
1069C2×C4—228no—
1070C2×C4—228no—
1071C2×C4—228no—
1072C2×C4—221no—
1073C2×C4—221no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—221no—
1078C2×C4—221no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—228no—
1083C2×C4—228no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—448no—
1091C2×C4—448no—
1092C2×C4—448no—
1093C2×C4—448no—
1094C2×C4—448no—
1095C2×C4C22×C4×D1112yes—
1096C2×C4C22×C4×D1112yes—
1097C2×C4C22×C4×D1112yes—
1098C2×C4C22×C4×D1112yes—
1099C2×C4C22×C4×D1112yes—
1100C2×C4C2×D4×D1114yes—
1101C2×C4C2×D4×D1112yes—
1102C2×C4#41×D1114yes—
1103C2×C4#41×D1112yes—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—114no—
1115C22—114no—
1116C22—224no—
1117C22—224no—
1118C22—222no—
1119C22—222no—
1120C22—222no—
1121C22—222no—
1122C22—224no—
1123C22—224no—
1124C22—222no—
1125C22—222no—
1126C22—222no—
1127C22—4416no—
1128C22—442no—
1129C22—442no—
1130C22C23×C4×D1111yescharacteristic
1131C22C22×D4×D1111yescharacteristic
1132C22C2×#41×D1111yescharacteristic
1133C22C2×#41×D1112yes—
1134C22#1062345312yes—
1135C4—22no—
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—24no—
1140C4—24no—
1141C4—42no—
1142C4—42no—
1143C4—114no—
1144C4—224no—
1145C4—222no—
1146C4—222no—
1147C4—222no—
1148C4—222no—
1149C4—224no—
1150C4—442no—
1151C4—442no—
1152C4C4×D4×D1114yes—
1153C2—42no—
1154C2—42no—
1155C2—224no—
1156C2—224no—
1157C2—442no—
1158C2C2×C4×D4×D1111yescharacteristic
1159C2C4×#41×D1111yescharacteristic
1160C2#1308181711yescharacteristic
1161C2#1308209912yes—
1162C2#1308217212yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2290C2
socle, cosocleC23×C11C25
prime radicalC2×#10623078C2
hypercenter#2290D11
hypocenterC11#34136
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4339C2semidirect
3. C2×D11×#117C2semidirect
4. #13071657C2semidirect
5. #13071646C2semidirect
6. #13071635C2semidirect
7. #13071624C2semidirect
8. #13071615C2semidirect
9. #13071611C2semidirect
10. #13071599C2semidirect
11. #13071594C2semidirect
12. #13071102C2semidirect
13. #13071096C2semidirect
14. #13071081C2semidirect
15. #13071075C2semidirect
16. #13071062C2semidirect
17. #13071062C2semidirect
18. #13071060C2semidirect
19. C42×C22⋊D11C2semidirect
20. C4×#66946C2semidirect
21. #13070955C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C11×#2290C2semidirect
28. C22×C42×C11C22semidirect
35. C2×C4×C22⋊D11C22semidirect
37. C2×#66979C22semidirect
38. #10623078C4semidirect
58. C2×#66925C22semidirect
63. C2×C42×D11C22semidirect
64. C2×C4×Dic22C22semidirect
66. C11×#387C22semidirect
68. C11×#385C22semidirect
69. C4×C11×C4⋊C4C22semidirect
71. C4×C11×C22⋊C4C22semidirect
72. C11×#376C22semidirect
75. C4×C22⋊Dic11C22semidirect
76. C4×C22⋊Dic11C22semidirect
77. #10622603C22semidirect
79. #10622598C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. #10622585C22semidirect
82. #10622585C22semidirect
84. #10622570C22semidirect
89. #10622564C22semidirect
92. #10622558C22semidirect
97. C4×(C2×D11)⋊C4C22semidirect
98. C4×(C2×D11)⋊C4C22semidirect
99. C4×C4⋊Dic11C22semidirect
100. #10622545C22semidirect
101. C4×Dic11⋊C4C22semidirect
102. C4×Dic11⋊C4C22semidirect
103. C4×Dic11⋊C4C22semidirect
104. C42×Dic11C22semidirect
105. C42×Dic11C22semidirect
106. #10622283C22semidirect
110. #10622281C22semidirect
115. #10622279C22semidirect
119. #10622268C22semidirect
120. #10622268C22semidirect
121. #10622266C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
125. #10622259C22semidirect
138. C2×#4339C2×C4semidirect
143. C22×C4×D11C2×C4semidirect
155. C4×D4×C11C2×C4semidirect
178. #66992C2×C4semidirect
179. #66990C2×C4semidirect
183. C4×C22⋊D11C2×C4semidirect
184. C4×C22⋊D11C2×C4semidirect
227. #66949C2×C4semidirect
228. #66947C2×C4semidirect
232. #66937C2×C4semidirect
233. #66936C2×C4semidirect
234. #66935C2×C4semidirect
237. #66931C2×C4semidirect
240. C4×D44C2×C4semidirect
243. #66925C2×C4semidirect
244. #66925D4semidirect
392. (C2×D11)⋊C4#41semidirect
438. #2290D11semidirect
544. C4×D11C4×D4semidirect
586. C22×C42C2×D11semidirect
606. #387C2×D11semidirect
618. #385C2×D11semidirect
626. C4×C4⋊C4C2×D11semidirect
642. C4×C22⋊C4C2×D11semidirect
644. #376C2×D11semidirect
678. C2×D11C4×#41semidirect
743. C4×D4C4×D11semidirect
1000. C11#34136semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C2×C4×#43392
C2×D11×#1172
#130716572
#130716462
#130716352
#130716242
#130716152
#130716112
#130715992
#130715942
#130711022
#130710962
#130710812
#130710752
#130710622
#130710602
C42×C22⋊D112
C4×#669462
#130709552
C4×C22⋊C4×D112
C11×#22902
#3413611